Proceedings of an 
 
 Ara.ericai.Ti Ceramic Society Symposium 
 
 Pittsburab, Pa,, April 27-28, 1963 
 
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 National Bureau of Standards 
 Miscellaneous Publication 25/ 
 
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UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary 
 NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director 
 
 Microstructure of Ceramic Materials 
 
 Proceedings of a Symposium 
 April 27-28, 1963 
 
 Held under the auspices of the Ceramic Educational Council of the American 
 Ceramic Society, with the cooperation of the National Bureau of Standards, and 
 under the sponsorship of the Edward Orton Junior Ceramic Foundation and the 
 Office of Naval Research. The Symposium took place at the 65th Annual Meeting 
 of the American Ceramic Society in Pittsburgh. 
 
 National Bureau of Standards Miscellaneous Publication 257 
 
 Issued April 6, 1964 
 
 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402 
 
 Price $\. 75 (Buckram) 
 
Library of Congress Catalog Card Number: 64-60020 
 
Contents 
 
 Page 
 
 IV 
 
 Introduction 
 
 1. Geometry of Microstructures 1 
 
 Lawrence H. Van Vlack 
 
 Department of Chemical and Metallurgical Engineering 
 
 University of Michigan 
 
 Ann Arbor, Michigan 
 
 2. Experimental Techniques for Microstructure Observation 15 
 
 Van Derek Frechette 
 Alfred University 
 Alfred, New York 
 
 3. The Effect of Heat Treatment on Microstructure 29 
 
 Joseph E. Burke 
 Research Laboratory 
 General Electric Company 
 Schenectady, New York 
 
 4. Correlation of Mechanical Properties with Microstructure 41 
 
 Robert J. Stokes 
 Research Center 
 
 Minneapolis-Honeywell Regulator Co. 
 Hopkins, Minnesota 
 
 5. Microstructure of Magnetic Ceramics 73 
 
 A. L. Stuijts 
 
 Philips Research Labs. 
 
 Eindhoven 
 
 Netherlands 
 
 6. Microstructure of Porcelain 93 
 
 Sten T. Lundin 
 
 Royal Institute of Technology 
 
 Stockholm 
 
 Sweden 
 
Introduction 
 In all materials, the physical and even the chemical properties of a polycrystal- 
 line body are not exactly the same as those of a single crystal of the same materials. 
 Many materials are anisotropic - their properties depend upon the orientation of the 
 measuring system with respect to the crystallographic axes - and the polycrystalline 
 properties are some form of an average over the crystal directions. Thus the di- 
 electric constant, elastic constants, index of refraction, magnetic susceptibility, 
 and many other "bulk" properties depend to some extent on the microstructure of the 
 specimen. 
 
 Beyond this, some properties depend on the motion of various entities through 
 the material-transport of atoms and ions in diffusion, transport of phonons in ther- 
 mal conduction and electrons and ions in electrical conduction, motion of dislocations 
 and other defects in plastic deformation and of domain walls in ferromagnetic and 
 ferroelectric switching, and even the propagation of cracks in fracture. In these 
 transport processes, the grain boundaries between the crystals in a polycrystalline 
 body behave differently from the bulk material, and their presence markedly affects 
 the resulting properties. Diffusion is usually faster at grain boundaries, especial- 
 ly at low temperatures, so that diffusion is enhanced in polycrystalline bodies. 
 Electrons and phonons are scattered by grain boundaries, so that electrical and ther- 
 mal conduction tends to be lower in the polycrystals . The movements of dislocations 
 across grain boundaries are impeded, so that plastic deformation is inhibited by 
 their presence, and polycrystalline bodies tend to be stiff er and less ductile than 
 the corresponding single crystals. 
 
 Finally the presence of grain boundaries not only modifies the behavior, but 
 sometimes even introduces new elements. Thus in brittle fracture the grain bounda- 
 ries provide sources of cracks, making polycrystals weaker in general than single 
 crystals The presence of strain and of impurities at grain boundaries raises the 
 local free energy, so that chemical effects, such as etching rates, are enhanced. 
 
 It is clear then, that a knowledge of the microstructure of a polycrystalline 
 body is essential in any attempt to study and control its properties. This is par- 
 ticularly important in the field of ceramics, where the overwhelmingly important 
 form is the polycrystalline body. In order to review the problems involved in 
 specifying and studying microstructure in ceramics and the factors involved in the 
 interaction between microstructure and physical properties of ceramics, this 
 Symposium on Microstructure of Ceramic Materials was held. The papers presented are 
 published in this volume. Primary responsibility for their technical content must 
 rest, of course, with the individual authors and their organizations. 
 
 In the first two Chapters, Prof. Van Vlack reviews the geometry of microstruc- 
 tures and how they can be specified and Prof. Frechette describes the principal 
 experimental techniques by which observations of microstructures are made. In 
 Chapter 3, Dr. Burke then describes the factors controlling the development of the 
 microstructure during heat treatment of the ceramic, and their relation to the 
 processing variables of time and temperature. 
 
 In the next two Chapters, Dr. Stokes discusses the influence of microstructure 
 on the mechanical behavior, and Dr. Stuijts describes the influence on the ferro- 
 magnetic properties of ferrites. In the last Chapter, Prof. Lundin examines in 
 detail the microstructure of one material, porcelain, and its ramifications. 
 
 Ivan B. Cutler, Chairman 
 University of Utah 
 
 Joseph E. Burke 
 
 General Electric Company 
 
 William D. Kingery 
 
 Massachusetts Institute of 
 Technology 
 
 Willis E. Moody, Co-Chairman 
 
 Georgia Institute of Technology 
 
 Alan D. Franklin, Editor 
 
 National Bureau of Standards 
 
Geometry of Micro structures 
 Lawrence H. Van Vlack 
 
 1. Introduction 
 
 The internal structure that a material possesses on a microscopic scale is gen- 
 erally called micro structure . This presentation is concerned with the geometry of 
 such micro structures as encountered in ceramic materials. 
 
 A study of micro structures does not involve the study of atomic coordination as 
 it exists in various crystalline and amorphous phases. However, it does involve the 
 phase and grain relationships at the lower end of the electron microscopic range, and 
 extends through the size spectrum up to and well into the "hand lens" range. Examples 
 at the lower end of the micro structural size range include the nuclei which start the 
 crystallization of glass and therefore introduce a heterogeneity of structure. Micro- 
 structures at the coarse end of the size range are found in ceramic products which can 
 be illustrated by abrasive grinding wheels. These products contain a distribution of 
 specific sizes and shapes of abrasive phases that are bonded with a silicate or similar 
 material and include closely controlled porosity. 
 
 The geometric variations which are encountered in micros true tures include 
 (1) size, (2) shape, and (3) the preferred orientation of constituent grains 1 (Fig. 1). 
 In addition, when more than one phase is present, there can be the added variables: 
 (4) amount of phases, and (5) the distribution of phases among each other (Fig. 2). 
 Item (ij.) above is most closely related to the chemistry of the ceramic product because 
 the amount of phases depends directly upon the composition. The other structural 
 variables are less closely related to the composition and depend more specifically 
 upon factors of processing and service history. Each of the preceding five micro- 
 structural variations involves grain boundaries and the consequent crystal structural 
 discontinuities. 
 
 Many ceramic materials possess porosity. From a microstruc tural point of view, 
 pores can be considered as an additional phase of zero composition. Of course this' 
 'phase" is a very important feature in the microstruc ture, because the pores markedly 
 affect the micro structural dependent properties. 
 
 As will be pointed out in later presentations, the microstruc tures -and therefore 
 the consequent properties of the ceramic are not static in behavior, for they may be 
 altered by external factors such as mechanical forces, thermal conditions, chemical 
 environments, and electric or magnetic fields. Therefore, a microstruc ture may be 
 varied by processing factors and servicing conditions. This presentation will first 
 consider the characteristics of internal boundaries, then single phase microstruc tures 
 and finally polyphase mic rostruc tures . 
 
 2. Internal Boundaries 
 
 The most general characteristic of a mic rostruc ture is the presence of its 
 internal boundaries which separate the grains and phases within the material. Whether 
 
 boundaries are thus an important feature in a ceramic and have significant effects on 
 the properties of the material. 
 
 It Is possible to characterize boundaries as grain boundaries, domain boundaries 
 phase boundaries, or surfaces. However, such characterization is usually unnecessary' 
 for a general discussion, because each of the above boundaries may be considered to be 
 a surface or zone of crystalline mismatch. Boundary discontinuities in a micro structure 
 
 1 The term, grain, as used in the discussion of microstructure denotes a single 
 crystalline volume. This is in contrast to grog grains which are usually 1-10 mm in 
 size and contain numerous small crystals. 
 
represent locations of higher atomic energies; therefore a "driving force" exists 
 which tends to reduce the boundary areas with consequential boundary movements. 
 
 2.1. Boundary Structure 
 
 The atomic structure of a grain or phase boundary must be inferred because it is 
 currently impossible to view the involved atoms directly. However, several conclusions 
 m^y be mlde about these boundaries as a result of indirect experimental evidence and 
 on the basis of appropriate models. In doing so, several types of boundaries can be 
 cited The first of these is the small-angle boundary which consists of aligned dis- 
 locations as illustrated in Fig. 3 . Experimental evidence strongly supports this 
 structure For example, since dislocations are revealed by etching it is a simple 
 oTete to determine the angle of this boundary from the spacing of the etch pits 
 and lattice dimensions. An independent and corroborative check of the angle can then 
 be made by diffraction measurements. Figure 1+ reveals such etching pits along small 
 a^Rle boundaries in LiF. Similar boundaries have been observed in other materials 
 Kch as AI0S3 and Ti0 2 and have received specific interest in view of their indication 
 of deformation and its consequences [1,2]. 
 
 Large-angle boundaries are most simply represented by Fig $. This can be consi- 
 dered to be typical of most of the boundaries which are found between grains and 
 chases within various materials. Again it is impossible to be specific about the 
 structures' along these boundaries except by inference. However, substantial evidence 
 does Sply that the boundaries represent a zone of mismatch in atom spacings with a 
 consequence that the atoms at the boundary are at a higher energy level than those 
 within the %rain proper. Furthermore, the mismatch produces relatively large inter- 
 stices beLfen the atoms for grain boundary diffusion and fo ^ ira P^"j 1 J^" P ^°J; ige 
 Because such boundaries possess atoms with higher energies, it comes without surprise 
 Shrtlfae boundar^ is frequently the site for nucleation and subsequent crystalline 
 growth. 
 
 Twins, a not uncommon feature of mineral phases , represent a special large angle 
 boundary situation, in which the adjacent grains are coherent with one another (Fig. 6). 
 The only mismatch involves second-neighbor and more distant atoms. 
 
 Coherent boundaries may arise between unlike phases as represented in Fig. 7. As 
 with twin boundaries, coherency between phases is favored by specific crystallo graphic 
 orientations in which the atoms along the boundary are part of the two adjacent phases. 
 ?he presence of these boundaries leads to Widmanstatten-type structiores as shown in 
 Fig. 8. 
 
 Domain boundaries are often categorized separately from the above boundary types. 
 However there is no specific reason for such separation because they also represent 
 surfaces or zones of mismatch between adjacent groups of coordinated atoms. This is 
 indicated in Pip! 9 where separate parts (domains) of a single crystal will have 
 opposing polarity as a result of inverted unit cell alignments. The boundary between 
 ?nese areas is shown schematically in Fig. 10 as a transition zone which possesses 
 higher energy because of the changing alignment. 
 
 2.2. Boundary Energies 
 
 The interatomic spacings within equilibrated phases are ^ch that the atoms 
 possess the lowest total energy. Higher energies exist when the interatomic spac In gs 
 are either increased or decrefsed. The major part of the \^^\^\f^\^ ^, v 
 the variation in the spacing of adjacent atoms at the boundary. Additional but smaller 
 energies are required for the mismatch of second-neighbor or more distant atoms. It 
 may be "eSSeS Son. the above that the large-angle boundaries have high energies while 
 small-angle boundaries, twin boundaries, and coherent phase boundaries have lower 
 energies! This conclusion may be verified by calculations and by experiments. 
 
 Since the small-angle boundary is a series of aligned dislocat j™ 8 * "" W^ may 
 be calculated as a summation of the energy .associated with each J^^ J%y ldual 
 dislocations. As such, it possesses energies ranging from to 100 ergs/cm . 
 
 The energies of several large-angle metallic boundaries are indicated in. 
 Table 1 [3]. The determination of these energies commonly involves the experimental 
 use of dihedral angle measurements which are illustrated m Fig. 11 as a sectoral 
 balance [l^. Since the boundary area requires extra energy, there is a natural 
 
 'Figures in brackets indicate the literature references at the end of this paper. 
 
tendency for this area to be reduced. Thus the angle along grain and phase edges 
 undergoes an adjustment which is mathematically equivalent to the result of a surface 
 tension in the following relationship: 
 
 Y 1/3 Y 1/2 Y 2/3 
 
 (1) 
 
 s; 
 
 sin 02 s * n 0o s ^ n $\ 
 
 When two of the boundaries are comparable, Eq. 1 reduces to: 
 
 a/a = 2 Y a/b 
 
 Y„/o = 2 Y /k cos — (2) 
 
 2 
 
 as shown in Fig. 11(b). The dihedral angle, 0, is a special case of the edge angle <f) . 
 The energy of the boundary or interface between two grains or phases is represented 
 by Y. It is necessary to use statistical methods to determine the two dihedral angles 
 accurately if the observed angles are on a random 2-dimensional plane through the 
 usual 3-dimensional micros true ture [5]. However, a reasonably accurate approximation 
 is obtainable from the median angle of a small number of observed angles [6], Thus, 
 comparative values may be made of the boundaries of several types. 
 
 The energy of boundaries between adjacent grains .of the same phase will vary with 
 the relative orientation of the two adjacent grains. The extreme case is that of two 
 grains with identical orientation in which the boundary disappears and the energy drops 
 to zero. As the adjacent grains are rotated out of alignment, the boundary energy is 
 increased until there is a maximum amount of mismatch between the structures of the two 
 grains [7]. The specific orientation with these higher energies will vary with the 
 structure of the grains and with the direction of rotation. However, for many materials 
 it can be concluded that most boundaries have energies close to the maximum and only a 
 few favored low angle and twin orientations diverge significantly from the maximum 
 energy values. 
 
 2.3. Boundary Movements 
 
 The average grain size of a single-phase ceramic will increase with time if the 
 temperature is such as to give significant atom movements. The driving force for such 
 grain growth is the free energy released as the atom moves across the boundary from 
 the convex surface to the concave surface where the atom becomes coordinated with the 
 larger number of neighbors at equilibrium atom spacings (Fig. 12). As a result, the 
 boundary moves toward the center of curvature (Fig. 13) , and the larger grains will 
 grow at the expense of the smaller grains. This is true in both single phase micro- 
 structures and polyphase mic restructures , as will be indicated later. The net effect 
 is less boundary area per unit volume. 
 
 Boundary movements are influenced by grain size, temperature, and the presence of 
 insoluble impurities. Smaller grain sizes provide a greater driving force for atom 
 movements across the boundary as indicated in the previous paragraph. Beck [8] has 
 provided the relationship: 
 
 dD/dt = k/D m , (3) 
 
 where D is the index to grain diameter, t is time and k and m are constants. Since 
 experimental data indicate the value of m is close to 1, this equation integrates to: 
 
 D 2 - D 2 = 2 kt . (k) 
 
 Therefore the change in cross-sectional area of the grain is nearly proportional to 
 time, or if the initial size may be assumed to be zero, the diameter increases with the 
 square root of time. The value of k in Eq. 3 and l\. is usually an exponential function 
 of temperature in which k reflects the activation energy for the atom movements shown 
 in Fig". 12. 
 
 The most obvious limitation to grain growth occurs as the grain size approaches 
 the dimensions of the ceramic product, and therefore grain growth is inhibited. A less 
 obvious, but equally important, limitation occurs in the presence of an inhibiting 
 second phase as shown in Fig. 14. In general, the boundary as seen in two-dimensions 
 must be increased and the curvature reversed locally before a boundary can move beyond 
 the dispersed particles, thus inhibiting grain growth. Zener [9] has presented the 
 following relationship for the limitation of boundary movements: 
 
 R/r M 1/f (5) 
 
R and r are the radii of curvature for the grain surface and the dispersed phase res- 
 pectively. The volume fraction of the dispersed phase is given as f. Such grain 
 growth inhibitors have been used in various ceramic materials such as Al 2 0o and MgO. 
 
 The movements of domain boundaries are accentuated by the introduction of an 
 externally applied field. This is achieved by the inverting of the polarity of the 
 cells within and adjacent to the boundary zone so as to expand the favorably aligned 
 domains and reduce the volume of the unfavorably aligned domains (Fig. If?). These 
 boundary movements are reversible as the external field is inverted. Domain boundary 
 movements, like grain boundary movements, are influenced by the presence of external 
 surfaces and by impurity particles. 
 
 3. Single Phase Micro structures 
 
 It was pointed out previously that a single phase micro structure may have 
 variations in grain size, grain shape, and preferred orientation of the grains. These 
 are not wholly independent because grain shape and grain size are both consequences of 
 grain growth. Likewise, the grain shape is commonly dependent on the crystalline 
 orientation of the grains during growth. In the simplest situation the grain may be 
 considered to be uniform in size, equiaxed in shape, and random in orientation. This 
 can be illustrated in Pig. 16 for periclase (MgO). 
 
 3.1. Grain Size and Boundary Area 
 
 The grain size as shown in Pig. 16 does not indicate the true grain size distri- 
 bution inasmuch as that figure reveals a random 2-dimensional section through a 3-dim- 
 ensional solid, and very few grains show a maximum cross-sectional area. A theoretical 
 distribution of grain size areas for uniform grain size would provide a median area of 
 about 0.8 of the maximum area. Since the various measurements in ceramics reveal that 
 the median area is less than the above figure, it is to be concluded that there is a 
 distribution of grain sizes. This is to be expected since the process of grain growth 
 requires that certain grains decrease in size and disappear (Pig. 13). Burke [10] has 
 shown that this does not proceed uniformly for any one grain because of the complex 
 boundary network around any disappearing grain. Smith [11] used a soap bubble as a 
 model for grain growth and boundary movement. Since the analogy is theoretically sound, 
 qualitative comparisons are justified. This procedure provides the suitable means of 
 studying changes in 3-dimensional solids. 
 
 Abnormal grain growth may occur in materials. Burke [10] explains such growth in 
 metals by noting that if an individual grain is favored to become significantly larger 
 than the balance of the grains, then it possesses an additional advantage for still 
 further grain growth bv virtue of sharper boundary curvatures (Figs. 17 and lo) . The 
 circumstances which produce the initial size advantages for specific grains can only be 
 surmised. However, factors such as impurities, the distribution of inhibiting par- 
 ticles, location of nucleants, and the oxidation of adjacent grains are undoubtedly 
 important . 
 
 Grain size has commonly been indicated as the grain diameter. Also, an ASTM 
 procedure assigns a number, n, to a grain size where, 
 
 N = 2 n_1 (6) 
 
 and N is the number of grains observed in 0.0001 sq. in. of a 2-dimensional section 
 (i.eT, 1 in. 2 at a magnification of X100). These are appropriate for those ^micro- 
 structures in which it may be assumed that all grains are spheres with identical 
 diameters. Since micro structures seldom if ever meet these conditions, diameters and 
 grain numbers are at best only an index of size. 
 
 Statistical procedures are available which take into account a distribution of 
 actual sizes, as well as a distribution of observed sizes in a micros tructure which 
 arises because the grains are not cut through their greatest diameter [12,13]. Such pro 
 cedures require a knowledge of shape and size distributions before they are meaninfgul. 
 An alternate index of grain size is that of determining the gram boundary area in a 
 micro structure without regard to shape or size distribution. This area is often more 
 important than the grain size per se , because the amount of area influences the 
 properties which arise out of the micro structures. Several workers [12, Ik] arrived 
 independently at the following extremely simple relationship: 
 
 B V = 2 \ 
 In this equation, B is the boundary area (mm") per unit volume (im J ), and N L is the 
 
 4 
 
number of grain boundaries traversed per millimeter by a random line. The several 
 derivations of this equation are cited by Underwood [13] and Saltykov [12]. The signi- 
 ficant feature about Equation 7 is the fact that the boundary area is measurable with- 
 out determining the grain size and may be determined for materials with non-uniform 
 grain sizes. The only requirement is that the sample lacks grain size gradients or 
 grain shape heterogeneities. 
 
 The use of the random line technique is illustrated in Pig. 19 for the MgO of 
 Fig. 16. Several lines give a figure of about Q$ grains/mm, thus indicating a 
 boundary area of 170 mm2/mm3. 
 
 It is possible in a single phase material to relate the number of grains per unit 
 volume, N v , to the boundary area, B v , in that volume, if some assumptions are made 
 concerning the grain shapes. 
 
 % = (B v /F)3 (8) 
 
 where F is a shape factor equal to 3.0, 2.86, 2.67, and 2.66, respectively for cubes 
 hexagonal prisms, rhombic dodecahedrons, and truncated octahedrons, i.e. cube-octa- 
 hedrons [15]. Underwood [15] concludes that the latter are most appropriate in 
 equiaxed micro structures. Thus Equation 8 reduces to 
 
 % = bJ/19 (8a) 
 
 N v = 0.1+2 N3 (8b) 
 
 As a result, the MgO ceramic of Fig. 16 would contain about 260 000 grains per mm^. 
 Although this number could be converted to an equivalent grain "diameter," it is not 
 recommended because assumptions would have to be made concerning grain shapes. 
 
 3 . 2 Grain Shape 
 
 Although it is common to speak of grain size in terms of diameter, it is obvious 
 that grains of single-phase, nonporous ceramics are not spherical. Rather, they must 
 
 completely fill space and also maintain a minimum in total boundary energy. Thus 
 
 they have an irregular shape at best. The term, equiaxed, is used for those grains 
 that have approximately equal dimensions in the three coordinate directions. This is 
 
 the case for the periclase (MgO) of Fig. 16. In other cases there can be an elon- 
 gation in one direction as indicated for UOo in Fig. 20. 
 
 The grain shape in a single phase material may be described by a length/width 
 ratio. Thus both the schematic microstructure of Fig. 1(c) and the actual micro- 
 structure of Fig. 20 would possess an L/W ratio between 3/1 and I4/I, depending on 
 whether maximum or typical widths are used. Here, as with grain size, we also 
 encounter the question of 3-dimensional sizes vs. 2-dimensional observations. As a 
 result it may be desirable to utilize a statistical calculation of shape when there is 
 an elongation to the structure. However, instead of using the random lines of 
 Equation 7, lines are intentionally aligned in the two principal coordinate directions. 
 An elongation, E, may be calculated. 
 
 E = 
 
 ( Vj_ " < H L>|I 
 
 (9) 
 
 (Nr) I + (TT/2-1) (Nt) 
 
 '_L 
 
 As before, N L is the number of grain boundaries traversed per mm; Hand J_indicate 
 the two principal coordinate directions; and E is the degree of elongation [13] The 
 degree of elongation for Fig. 1(c) is about 0.55. This is in contrast to zero elon- 
 gation for the other three sketches of Fig. 1, and 1.0 for perfect elongation. 
 
 Microstructures may possess patterns of elongation of the grain shaoes other than 
 those shown in Fig. 1(c) where it is implied that the elongation in one direction is 
 greater than the other two, i.e., (Nr) a < (Nr) b = (N L ) C . Other possibilities include 
 ! N LU = ( N L'b < (%) c ,and (N L ) a < (N L ) b < (N L ) C . Because of these oossibilities, 
 it is not safe to draw conclusions about the grain shape and microstructural elon- 
 gation on the basis of one section only. As the minimum, it is necessary to examine 
 two perpendicular sections. 
 
 At this point it should be noted that there is a major contrast between metals and 
 ceramics. Because the grain shapes in single-phase metals normally tend to be equiaxed, 
 
have consi- 
 
 and as a rule, deformation and recrystallization are not important tactors. 
 
 3.3. Preferred Orientation of Grains 
 
 The crystalline orientation of the various grains in single-phase ceramic products 
 is typically quite random. Unlike metals, these ceramic products are not subject to 
 mechanical deformation, which favors an alignment of the individual grams both before 
 and after recrystallization. However, ceramic products with a preferred orientation 
 are possible and will undoubtedly have increased significance in the future. Grains 
 in a ceramic which are nucleated at an external surface to produce columnar recrystal- 
 lization commonly will have a preferred orientation with the fastest growth direction 
 aliened with the grain length (Fig. 20). Those grains which were nucleated so they 
 grew in other orientations were soon overtaken by the more favorably oriented grains. 
 Other factors, such as electrical or magnetic fields, become important in grain orien- 
 tation if they are present at the time when the product is made. This subject will 
 undoubtedly be covered in subsequent lectures. 
 
 Preferred orientation (Pig. Id) may be indicated geometrically as the direction 
 favored for the normals to specific crystal planes. Thus the preferred orientation of 
 U0? in Fig 20 is <100> , which was the direction of the thermal gradient during 
 solidification. This orientation is obviously not perfect, because if it were there 
 would be t^o remaining boundaries of mismatch, and only a large single crystal would 
 result. Quantitative measures of the amount of preferred orientation are difficult. 
 However, pole figures do provide an indication of the amount [16] . 
 
 14. Polyphase Mic restructures 
 
 I4.I. Introduction 
 
 The microstructural variations of polyphase (and porous) materials involve not 
 only the oreviously cited (1) grain size, (2) grain shape, and (3) preferred orien- 
 tation but also the geometric relationships of the phases. Included are: (ZjJ the 
 relative amounts of the phases, and (5) the mutual distribution of the two or more 
 phases which are present. 
 
 An analysis of the first three geometric factors for polyphase mic restructures 
 may be" approached much as they were for single-phase micros true tures. Equation 7 may 
 be used to describe the amount of any type of interface per unit volume. Thus, Fig. 
 can be shown to have 900 mm 2 /mm3 of coherent UC-UC 2 interface. Likewise, the domain 
 boundary area of Fig. 9 is about 700 mm 2 /mm3. Since the latter microstruc ture 
 contains dispersed domains within continuous matrix (also a domain), it is possible to 
 determine the average size of the dispersed areas from their numbers [15] . A ^o 
 relatively simple micro graphic procedures permit a determination of the distribution Ox 
 true plate thicknesses and spacings of the UC-TJC 2 microstruc ture shown in Jig. 0. Ihe 
 reader is referred to Cahn and Fullman [17] for further elaboration. 
 
 The energy of a phase boundary, like the energy of a grain boundary, is a driving 
 force which promotes grain growth in polyphase ceramics. Figure 21 illustrates the 
 changes which occur with added time and elevated temperatures [19]. The relative^ 
 amounts of the two phases are identical in the two examples, thus indicating chemical 
 or phase equilibrium. However, geometric equilibrium has not been fully attained, and 
 in fact will not be as long as there is an opportunity for further gram growth In 
 effect the growth process which is shown in Fig. 21 requires steps of solution (ot 
 erains'with small radii of curvature), diffusion, and precipitation (onto grams with 
 larger radii of curvature). Thus, unless the atomic mobilities and surface energies 
 are high the growth process is slower in polyphase materials than in single phase 
 microstructures where the atoms simply move across the grain boundary (Fig. 12). 
 
 The grain shape analysis of single phase microstructures (Equation 9) may be used 
 only if there is an alignment of the grain shapes. Even so, it is possible to obtain 
 information concerning the shapes of dispersed grains which are not equi dimensional. 
 For example, the mull it e grains which are present in a siliceous glass in Big. dd are 
 acicular or needle-like prisms with an euhedral outline of a«b<c. Hence we gen- 
 erally observe only the small cross-section. Occasionally, a grain lies in such a 
 manner that its major elongation is revealed. Likewise, the corundum of Fig. 23 (also 
 present in a siliceous glass) develops a plate-like grain which commonly reveals an 
 elongated trace on the 2-dimensional microsection. This arises because a«b>c. in 
 this example however, the third dimension is not as markedly different from the two 
 
as it was in Pig. 22, so the plate-like characteristics are less commonly revealed. 
 
 I4..2. Amounts of Phases 
 
 It is assumed that the reader is familiar with the relationships between relative 
 amounts of two or more phases and the compositions of ceramic materials as indicated 
 by a phase diagram. Therefore, that subject will be passed with only a mention of 
 references [18,20]. 
 
 There are several procedures for determining the quantity of a selected phase 
 within a micro structure. They all provide volumetric answers; s'o, of course, sub- 
 sequent calculations are required if weight percentages' are desired. Point analyses 
 and linear analyses are the most widely recommended procedures (Pig. 2l\) . 
 
 Point analyses utilize the following relationship:- a random point in a micro- 
 structure has a probability of lying within each phase which is equal to the volume 
 percent of that phase within the micro structure. The linear analysis is based on a 
 similar probability, viz., a random line will be within any phase in proportion to the 
 amount of that phase. It can be shown that a point analysis can be slightly more 
 accurate than the linear analysis for a given amount of effort on the part of the 
 micrographer. In each case, special efforts must be maintained to avoid any-nonsta- 
 tistical selection of points or lines, and care should be taken so that one phase is 
 not preferentially lost during sample preparation. On the other hand, if the micro- 
 section is representative, microporosity can be determined by either of these two 
 methods simply by determining the volume of the pore space as a fraction of the total 
 volume. 
 
 Assuming that the microscopic section is representative of the whole structure, 
 and statistical randomness has been maintained, the binomial accuracy standard 
 j deviation of the data is given by the following relationship: 
 
 c v =yF(1.0 - P)/N , (10) 
 
 or the fraction may be estimated from: ■ 
 
 F = (lWl - 4Nov)/2 . (10a) 
 
 Within these equations, c v is the standard deviation of analyzed volume fractions from 
 successive samplings, F is the estimated true fraction, and N is the number of randomly 
 selected observation points. 
 
 4.3. Distribution of Phases 
 
 The mutual distribution of two or more phases within a microstructure can be a 
 result of (1) changes in chemical equilibrium which modify the relative amounts of 
 phases, and (2) geometric equilibrium which arises from boundary energy relationships. 
 
 Changes in chemical equilibrium introduce solution and precipitation. This can be 
 illustrated by Fig. 2$ where tridymite is present in a silica-saturated iron oxide 
 liquid. During the active growth of the tridymite crystals, there was an euhedral 
 development of the crystal faces so that the boundaries are regular between the two 
 phases. 
 
 Geometric equilibrium often develops more slowly than chemical- equilibrium. This 
 is demonstrated when Pig. 26 is contrasted with Pig.' 25. The two have the same compo- 
 sition and the same volumetric phase ratios. However, with time at temperature, there 
 has been a partial anhedralization which reduces the total interface area (and energy). 
 The degree of anhedralization varies with the material. The microstructures of Fig. 21 
 do not show euhedral growth of wustite (PeO) in the times indicated. However, some 
 crystal faces are developed on the grains when saturation is exceeded during a quench. 
 
 The distributional variations of phases become most noticeable when one of the 
 phases is a liquid. .The schematic presentation of Fig. 2 is illustrated in actual 
 microstructures in Figs. 27 and 28. In the simplest case, it is possible to have a 
 liquid phase penetrate along the grain boundaries (Fig. 27). Under such a condition 
 there is negligible solid -to-solid contact at the elevated temperatures with consequent 
 effects upon properties [21]. Also, subsequent effects may be realized at lower 
 temperatures as indicated in Fig. 29 where the fracture path follows the silicate phase 
 which was originally distributed as a high temperature liquid. 
 
 A contrast to the foregoing conditions is shown in Pig. 28 where solid-to-solid 
 contact was maintained between cristobalite grains by a finite dihedral angle [22]. 
 
Thus, although there are channels of liquid distributed through the microstructure, 
 there remains a solid skeleton which maintains significant strength at high liquid 
 contents. 
 
 27 and 28 must be accounted for 
 ated in Equation 2. In general, it 
 least when the compositions of the 
 equal). In Fig. 28, there is a 
 between the cristobalite (SiC^) and 
 and liquid in Pig. 27. Furthermore, 
 es between two cristobalite grains 
 o the energy between two wustite 
 factor and therefore has additional 
 which accompanies the boundary. 
 
 The micro structural differences between Figs, 
 through the relative interfacial energies as indie 
 may be concluded that the phase boundary energy is 
 two adjacent phases are most similar (other things 
 markedly greater dissimilarity in the compositions 
 the liquid than there is between the wustite (FeO) 
 all evidence would suggest that the grain boundari 
 would have a relatively low energy as contrasted t 
 grains because the cristobalite has a low packing 
 degrees of freedom to compensate for the mismatch 
 
 5. Conclusions 
 
 The internal structure of a material may be analyzed on a basis of geometry^ with 
 factors such as grain size, grain shape, grain orientations being important in single- 
 phase micro structures . Polyphase micros true tures will include these variables plus 
 the variation in the quantities of the individual phases and their juxtaposition or 
 distribution. 
 
 While there are both qualitative and quantitative data on the factors which affect 
 geometric equilibrium and microstructure s, it has been impossible in this presentation 
 to present comparable information on the kinetics, or rate of obtaining geometric 
 equilibrium within the micro structures . This is a more complex consideration with 
 only a smattering of analytical information. At the same time it may be a^major consi- 
 deration because relatively few micro structures within ceramic materials will have^ 
 gained full geometric equilibrium at the time of their us e in engineering applications. 
 
 6. References 
 
 [1] R. Scheuplein and P. Gibbs, Surface 
 
 Structure in Corundum: I. Etching of 
 Dislocations, J. Am. Ceram. Soc. 
 1£, 458 (I960). 
 
 [2] W. M. Hirthe and J. 0. Britton, Dislo- 
 cations in Rutile as Revealed by the 
 Etch Pit Technique, J. Am. Ceram. 
 Soc. kS, 51+6 (1962). 
 
 [3] D. McLean, Grain Boundaries in Metals , 
 p. 77, Clarendon Press (Oxford, 1957) . 
 
 [if] C. S. Smith, Grains, Phases and Inter- 
 faces: An Interpretation of Micro- 
 structure, Trans. AIME, 175 , 15 
 (191+8). 
 
 [5] D. Harker and E. Parker, Grain Shape 
 and Grain Growth, Trans. ASM _3j£, 
 156 (191+5). 
 
 [6] 0. K. Riegger and L. H. Van Vlack, 
 
 Dihedral Angle Measurement, Trans. 
 AIME 218, 933 (I960) . 
 
 [7] C. G. Dunn and F. Lionetti, The Effect 
 of Orientation Difference on Grain 
 Boundary Energies, Trans. AIME 185, 
 125 (191+9). 
 
 [8] P. A. Beck, Effect of Recrystalliz ed 
 
 Grain Size in Grain Growth, J. Appl. 
 Physics 19, 507 (191+8). 
 
 [9] C. Zener, Grains, Phases and Inter- 
 faces: An Interpretation of Micro- 
 structure, Trans. AIME 175 , 1+8 
 (191+8). 
 
 [10] J. E. Burke, Recrystallization and 
 Grain Growth, Grain Control in 
 Industrial Metallurgy , p. 1, Am. 
 Soc. Metals (Metals Park, 0., 191+8). 
 
 [11] C. S. Smith, Grain Shapes and Other 
 Metallurgical Applications of Top- 
 ology, Metal Interfaces , p. 65, 
 Am, Soc. Metals (Metals Park, 0., 
 195D. 
 
 [12] S. A. Saltykov, Stereometricheskaya 
 
 Metallog'rafiya , Literatury Po Chernoy 
 i Tsvetnoy Metallurgii (Moskva, 1958). 
 
 [13] Ervin E. Underwood, Surface Area and 
 Length in Volume, Quantitative 
 Metallography , New York, McGraw-Hill, 
 to be published. 
 
 [11+] C. S. Smith and L. Guttman, Measurement 
 of Internal Boundaries in Three- 
 Dimensional Structures by Random 
 Sectioning, Trans. AIME 197, 81 
 (1953). 
 
 [15] Ervin E. Underwood, Quantitative Metal- 
 lography, Metals Engineering Quar- 
 terly, 1, [3] 70 (Aug., 1961). Also 
 see 1, [1+] 62 (Nov., 1961) for 
 Part 2 of the article. 
 
 [16] B. D. Cullity, Elements of X-ray 
 
 Diffraction , p. 2/2, Addison-wesley 
 Pub. Co. [Reading, Mass., 1956). 
 
[17] J. W. Cahn and R. L. Fullman, On 
 the Use of Lineal Analysis for 
 Obtaining Particle Size Distrib- 
 ution Functions in Opaque Samples, 
 Trans. AIME 206 , 610 (1956). 
 
 [18] E. M. Levin, H. F. McMurdie, and 
 F. P. Hall, Phase Diagrams for 
 Ceramists , Am. Ceram. Soc. 
 (Columbus, Ohio, 1956) . 
 
 [19] L. H. Van Vlack and O. K. Riegger, 
 Microstructures of Magnesio- 
 wustite [(Mg,Fe)0] in the Presence 
 of SiO s , Trans. AIME 224 , 957 
 (1962) . 
 
 [20] L. H. Van Vlack, Physical Ceramics , 
 Addison-Wesley Pub. Co. 
 (Reading, Mass., 1964). 
 
 [21] O. K. Riegger, G. I. Madden, and 
 
 L. H. Van Vlack, The Microstruc- 
 tures of Periclase When Subject- 
 ed to Steel-Making Variables, 
 Trans. AIME (1963), in press. 
 
 [22] L. H. Van Vlack, The Microstruc- 
 ture of Silica in the Presence 
 of Iron Oxide, J. Am. Ceram. 
 Soc. 43, 140 (1960) . 
 
 Table 1. Energies of Metallic Boundaries ' 
 
 Boundary 
 
 Energy 
 
 Copper 
 Iron (y) 
 Silver 
 
 Copper twin 
 Iron twin (11?) 
 Aluminum twin 
 
 6l\.6 ergs/cm 
 
 8$0 
 
 I4AO 
 
 19 
 187 
 120 
 
 Adapted from D. Mclean, Grain Boundaries in 
 Metals, p. 77, Clarendon Press (Oxford, 1957). 
 
 FIGURE 1. Microstructural variables 
 (single-phase materials). (a vs. b) 
 Grain size. (a vs. c) Grain shape, 
 (b vs. d) Preferred crystal orienta- 
 tion. (Schematic.) 
 
 FIGURE 2. Microstructural variables 
 (polyphase materials) . These are in 
 addition to those of fig. 1. (a vs. b) 
 and (c vs. d) Amounts of phases, 
 (a vs. c) and (b vs. d) Distribution 
 of phases. (Schematic). 
 
FIGURE 3. Small-angle boundary 
 
 (schematic) . This discontinuity in 
 the microstructures consists of a 
 series of aligned edge dislocations. 
 
 i 
 
 t 
 
 FIGURE 4. Small-angle boundary. 
 Example: Etch pits in LiF (X225). 
 Each etch pit is the site of an edge 
 dislocation. The angle of the bound- 
 ary can be calculated from the spacing 
 of the dislocations. 
 
 (courtesy A. S. Keh.) 
 
 FIGURE 5. Large-angle grain boundary. 
 Although this schematic representation 
 probably oversimplifies the grain 
 boundary structure, it does indicate 
 the major mismatch of structure which 
 results. 
 
 FIGURE 7. Coherent boundary (schematic) 
 The adjacent phases have a closely 
 matching repetition in structure. 
 
 FIGURE 6. Twin boundary (schematic) . 
 The mismatch does not involve first- 
 neighbor atoms. 
 
 FIGURE 8. Widmanstatten structures. 
 Example: UCg (bright) in UC (X281). 
 [Chang, R. , and C. G. Rhodes, "High- 
 Pressure Hot-Pressing of Uranium Car- 
 bide Powders and Mechanism of 
 Sintering of Refractory Bodies," J. 
 Am. Ceram. Soc. 45, 379 (1962]. 
 
 FIGURE 9. Domains. Example: BaTi0 3 
 aligned with the c-axes perpendicular 
 to the figure (X5625). Etched by 
 H a P0 4 . The positive ends etched more 
 rapidly than the negative ends. 
 [Belitz, R. K., "Differential Etching 
 of BaTi0 3 by H 3 P0 4 , " J. Am. Ceram. Soc. 
 45, 617 (1962)] . 
 
 
 
 
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 FIGURE 10. Domain boundaries (schematic) 
 The realignment across the boundary 
 requires energy. Therefore, there is 
 a driving force to reduce the boundary 
 area. 
 
 10 
 
FIGURE 11. Energy balances. (a) Three 
 unlike boundaries eq (1) . (b) Dihed- 
 ral angle between two like grains 
 eq (2) . 
 
 © O 
 
 000 ©000O0 
 G ° G © oo o q 
 
 FIGURE 12. Boundary movements. Less 
 energy is required to move an atom or 
 ion from the surface of the grain with 
 a convex surface to a grain with a con- 
 cave surface than in the opposite 
 direction. Therefore the boundary 
 moves toward the center of curvature. 
 
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 FIGURE 13. Grain growth. The movement 
 of boundaries toward their centers of 
 curvature produces grain growth and a 
 disappearance of the smaller, more 
 spherical grains. 
 
 FIGURE 14. Growth inhibition. Second 
 phases generally retard boundary move- 
 ments because they introduce reversals 
 in boundary curvature. 
 
 
 
 
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 FIGURE 15. Domain boundary movements. 
 The partially aligned dipoles along 
 the boundary (fig. 10) are pulled into 
 orientation with the external field, 
 thus shifting the boundary zone. 
 
 FIGURE 16. Equiaxed grains. Example: 
 periclase (MgO) . (approx. X140). This 
 microstructure corresponds to that in 
 fig. 1(a). [R. F. Gardner and G. W. 
 Robinson, Jr., "Improved Method of 
 Polishing Ultra-High Density MgO, " 
 Am. Ceram. Soc. 45, 46 (1962)]. 
 
 11 
 
FIGURE 17. Abnormal grain growth 
 
 (schematic) . Abnormally large grains 
 (A) have faster growth rates than nor- 
 mal grains (N) because the radii of 
 curvature of their boundaries are 
 smaller. 
 
 FIGURE 19. Boundary measurement. 
 Example: random line technique. 
 Eq (7) applies. (See fig. 16 for 
 references) . (approx. X140). 
 
 FIGURE 21. Grain Growth in poly- 
 phase microstructures. Example: 
 Wustite (FeO) growth in an iron 
 oxide saturated silicate liquid 
 (approx. X84). (a) Four hours 
 at 1200°C (2190°F) . (b) 64 hours 
 at 1200°C [19] . W - wustite; 
 S - silicate liquid. 
 
 FIGURE 18. Abnormal grain growth. 
 
 Example: corundum (Al 3 3 ) heated to 
 1900 °C (X281). 
 
 (courtesy R. L. Coble.) 
 
 FIGURE 20. Grain elongation. Example: 
 Uranium dioxide grains (approx. X42). 
 The UO e had been melted and then 
 solidified within a temperature gra- 
 dient. [J. R. MacEwan and V. B. 
 Lawson, "Grain Growth in Sintered 
 Uranium Dioxide: II, Columnar Grain 
 Growth," J. Am. Ceram. Soc. 4_5, 42 
 (1962)] . 
 
 FIGURE 22. Grain shape (acicular) . 
 Example: mullite (A^SisO^) in 
 an alumino-silicate glass (X281). 
 Most crystals of mullite are seen 
 in cross-section only, in this 
 reflected light microsection. 
 The elongation is observed in 
 the few which are aligned paral- 
 lel to the surface. M - mullite; 
 S - silicate glass. 
 
 12 
 
FIGURE 23. Grain shape (plates). Example: 
 corundum (Al s 3 ) in an alumina-saturated 
 silicate glass (X281). The elongated shapes 
 are cross-sections of the plate. Those 
 plates which lie parallel to the surface are 
 nearly equidimensional in the microsection. 
 C - corundum; S - silicate glass. 
 
 FIGURE 24. Volume analyses. (A) Point 
 analysis. (B) Linear analysis. The 
 probability that a point or a line 
 falls within a phase in a microsection 
 is equal to the volume fraction which 
 is present. 
 
 FIGURE 25. Euhedral growth. Example: 
 tridymite (SiGg ) in a silica- 
 saturated iron oxide liquid (XI 69). 
 In many situations the rate of growth 
 is sensitive to crystal direction. 
 T - tridymite; S - silicate glass. 
 
 FIGURE 26. Anhedralization. Example: 
 tridymite (Si0 2 ) in a silica-saturated 
 iron oxide liquid (XI 69). With time 
 at the equilibrating temperature, the 
 surface area is minimized. (Cf. 
 fig. 25.) T - tridymite; S - silicate 
 glass. 
 
 13 
 
" - ■ r 
 
 ^ 
 
 ^ 
 
 \ 
 
 <s 
 
 
 FIGURE 27. Grain separation. Example: peri- 
 clase (MgO) and an MgO-saturated calcium 
 silicate liquid (approx. X140).; Although 
 less than 10 percent liquid is present, it 
 allows only a negligible quantity of solid- 
 to-solid contact (Cf. fig. 28, fig. 2c, and 
 fig. lib.) [21] P - periclase; S - silicate 
 liquid. 
 
 FIGURE 28. Solid contact. Example: cristoba- 
 lite (SiO a ) and a silica-saturated iron oxide 
 liquid (XI 69). Although more than 25 percent 
 liquid is present, a large dihedral angle 
 (fig. lib) provides solid- to-solid contact and 
 structural rigidity at high temperatures. 
 (Cf. fig. 27 and fig. 2b.) C - cristobalite; 
 L - silicate glass. 
 
 FIGURE 29. Microstructural-controlled 
 behavior. Example: wustite (FeO) and 
 a silicate matrix. This, matrix was 
 liquid at the equilibrating temperature 
 and subsequently has crystallized to 
 fayalite (FesSi0 4 ) and more wustite 
 (approx. X84). The crack is in the 
 silicate matrix, but is closely associ- 
 ated with the silicate-wiistite boundary. 
 W - wustite; S - silicate liquid; 
 Arrow - crack. 
 
 14 
 
Experimental Techniques for Microstructure Investigation 
 
 V. D. Frechette 
 
 1. Introduction 
 
 The study of microstructures is concerned essentially with the ability to 
 distinguish between materials having different chemical composition, structure or 
 orientation and to distinguish between details separated by only small distances. 
 Techniques for revealing microstructural features are almost all based either on the 
 action of their details on incident radiation or on the quality and intensity of the 
 radiation emitted by them when appropriately excited. Working treatments of the 
 principles governing the resolution of microscopic details are available in standard 
 works [1-^1 and only the briefest review will be given here in order to identify the 
 effects involved. 
 
 When a homogeneous object is viewed in transmission, i.e. by means of radiation 
 transmitted through it, details corresponding to greater thickness may be revealed by 
 their greater absorption as dark regions in the image. At constant thickness, details 
 having greater absorption coefficients also yield darker images and, if the 
 absorptions differ sufficiently for different light wavelengths, they may yield image 
 color differences also. 
 
 Refraction effects at a boundary between grains may change the light path, 
 thereby darkening the corresponding region of the image and brightening adjacent 
 regions. The effect is intensified when the object is slightly out of focus and when 
 the illuminating aperture is restricted. Boundaries may also be revealed by the 
 scattering of light which takes place there to an extent which depends on the ratio 
 of the refractive indices of the bordering phases. With illumination of the bright 
 field type, i.e., when the light in the absence of any object in Its path illuminates 
 the entire field of view, the boundary layer shows up in the image as a darkening 
 because the light is scattered by it and is lost to the true image. Under dark field 
 conditions, in which illumination is arranged to just miss the field of view in the 
 absence of an object in its path, scattering provides a mechanism by which details 
 are rendered luminous and they form a bright image in a dark field. 
 
 Polarization-interference effects, which occur when an object is examined 
 between crossed nicols or other polarizing elements with or without the aid of 
 accessories, may be extremely valuable and the subject has been treated in numerous 
 works [5~7]- Crystalline solids, except those of the cubic system, and stressed 
 solids of any structure split plane-polarized light into two rays vibrating 
 perpendicular to one another which travel along essentially the same path but with 
 different velocities. During passage through a mineral grain one of these is 
 retarded behind the other owing to its slower velocity; when the two rays emerge from 
 the mineral and pass through the analysing nicol prism they interfere to an extent 
 determined by that retardation and by the wave length of the light. Under crossed 
 nicols, therefore, a mineral grain displays colors, corresponding to retardation, 
 which are determined by the thickness of the grain and by its effective birefringence 
 (birefringence is the difference between the refractive indices of the two rays) for 
 the orientation in which it lies. Not only may grains be distinguished from one 
 another by this process but their identity and their orientation may be inferred, 
 particularly with the aid of interference figures formed in the back opening of the 
 objective lens under strongly converging transmitted light. 
 
 In reflected light, details may be distinguished through operation of all of 
 the above effects [8]. In addition differences in reflecting power characterize 
 those materials whose refractive indices differ sufficiently as indicated by Fresnel's 
 formula, stated for normal incidence: 
 
 LN+lJ 
 
 15 
 
where R is the fractional amount of light reflected and N is the refractive index. 
 
 Under both transmission and reflection conditions, the light beam passing 
 through the grain or being reflected from its surface is retarded somewhat behind 
 those light rays which pass around it, or encounter materials of other refractive 
 index. In the phase contrast microscope [9] an annular diaphragm is inserted in the 
 condenser, while a second annular plate is set at the conjugate plane of the 
 condenser ring, to introduce an additional small phase shift. Interference between 
 these two in the image plane provides sharp contrast between details which vary only 
 very slightly from their surroundings. The phenomenon of interference is applied 
 also in the so called interference microscope [10-19] for the determination of 
 surface contours. In the simplest arrangement of this type the light rays reflected 
 downward by a semi-silvered mirror are partly reflected by an optically flat plate, 
 while those which are transmitted through the plate are reflected from the surface 
 of the specimen. These two are tipped slightly with respect to one another so that 
 there is seen in the field of view, for a perfectly flat specimen, a series of 
 parallel bright lines, or interference fringes. Each bright line is the locus 
 of those points on the specimen surface which are at a constant distance from the 
 optical flat, this distance being precisely an odd number of half wave lengths of the 
 light employed. Consequently any excursion of the specimen contour from the plane 
 of its surroundings results in a displacement of the fringes. The test is an 
 extremely sensitive one and make possible surface contouring of a specimen to within 
 a small fraction of the wavelength of light, i.e., to about a hundredth of a micron, 
 although lateral resolution is still confined to the usual limit of the lens system 
 or about 0.2 microns for visible light. 
 
 2. Optical Microscopy 
 
 A tremendous increase in the use of the optical microscope on ceramics [20-2^] 
 and other materials in recent years has acted as a spur to and has itself been 
 accelerated by the development of instruments and accessories [3,25] . Most 
 notable are the new microscopes of the universal type featuring permanently aligned 
 illuminators of high intensity and stable operation, conveniently mounted apparatus 
 for photography including automated cameras for films, plates and Polaroid, and 
 rapidly-interchangeable accessories for bright- and dark-field examination in 
 transmitted and reflected light with the option of phase contrast and interf erometric 
 optics. A growing list of polarizing accessories extends the range of optical_ 
 measurements that can be made and new mechanical devices facilitate particle size 
 measurement and quantitative analysis. Inclined binocular eyepieces reduce operator 
 fatigue to negligible proportions and high eyepoint eyepieces permit spectacles to 
 be worn without sacrificing breadth of visible field, an advantage to observers 
 having pronounced astigmatism. At lower magnifications zoom-type optics contribute 
 significantly to speed and convenience. 
 
 The limit of resolution of the microscope is approximately 0.6X /N.A. where 
 is the wavelength of the light used and N.A. is numerical aperture of the \ 
 illumination and objective lenses. For visible light this is approximately 0.2 
 microns. Ultraviolet light microscopy using photographic registration of the 
 (invisible) image extends the resolution by a factor of two but at great loss of 
 convenience . 
 
 3.' Electron Microscopy 
 
 Very much shorter wavelengths (about .015 millimicrons) are associated with a 
 beam of electrons. The electron microscope [26-37] uses an incandescent filament as 
 a source of electrons, accelerates them to high velocity by means of an electric 
 field, and focuses them with magnetic or electrostatic lenses in much the same way 
 as an optical microscope focuses light beams. In practice it is particularly 
 distinguished from the optical microscope by the very poor penetrating power of the 
 electron beam, which limits the object to extremely thin sections unless a reflect- 
 ing technique is to be employed. It is significant that the effectiveness of the 
 electron microscope has grown directly in proportion to the development of methods 
 of specimen preparation and particularly the replica techniques. Useful 
 magnifications up to about 2 x 10? are routinely employed, (although most work is under 
 2 x 10^") and under special conditions dislocations themselves may be directly 
 observed by it through diffraction effects [38,391- While the optical crystallography 
 of materials, based on refractive indices and polarization effects, does not apply in 
 the electron microscope, many instruments are provided with means for obtaining 
 electron diffraction uatterns of individual grains located in its field and thus 
 phase identification and orientation may be studied. 
 
 16 
 
The poor quality of reflected electron images has been overcome in an ingenious 
 way in the scanning electron microscope [31] . In this instrument the electron beam 
 is brought to a fine focus on a very small region of the sample and the scattered 
 electrons are picked up in a fixed detector whose signal is fed to a cathode ray- 
 oscilloscope. The beam is swept across the surface of the sample in synchronization 
 with the sweep of the oscilloscope which accordingly traces an image of the specimen 
 whose brightness corresponds to the atomic number and density of atoms in the 
 specimen components. Useful magnification by this method is not great and does not 
 exceed that of the optical microscope. The depth of focus, however, is very much 
 greater than that of the optical microscope at corresponding magnification, and 
 excellent photographs of fracture surfaces of aluminum oxide have been obtained with 
 it [VO]. 
 
 3. Electron Probe X-Ray Analysis 
 
 The high speed electrons of the electron microscope impinging on the sample 
 excite the atoms to emit X-rays. These X-rays may be analyzed with respect to 
 wavelength and intensity to yield spectra from which the constituent elements may be 
 identified both qualitively and quantitatively. If the electron beam is confined to 
 a very small area of the sample, a few square microns, complete chemical analysis 
 of the small area may be obtained, excepting only those elements under atomic number 
 eleven, whose emitted X-rays are so long in wavelength that they are easily lost. 
 If the electron beam is swept across the surface while the X-ray detector is set to 
 record a wavelength characteristic of a particular element, a plot may be obtained 
 on an oscilloscope sweeping in syncronization with the electron beam; brightness 
 in the oscilloscope image corresponds to points in the specimen where the element is 
 to be found in abundance. Instruments of this kind are termed electron probes or 
 electron micro-probe X-ray analyzers [hi]'. While few of these have seen application 
 on ceramic materials up to the present, a few studies show the method to be effective 
 and highly promising [^2,^31 • Indeed the application of the electron probe to 
 problems of ion species segregation in polycrystalline materials is one of the most 
 exciting on the present scene. 
 
 h. Emission Microscopes 
 
 Professor Castaing has suggested another way of imaging the specimen surface. 
 If it is bombarded with a beam of ions of appropriate energy, it may be excited to 
 give off secondary ions which may be focused with electro-magnetic lenses, passed 
 through a mass spectrometer set to select a particular ion species, and brought to 
 focus on an image converter which releases electrons to be focused in turn on a 
 photographic plate. 
 
 Other emission type microscopes have been developed [29, 3^] and have been 
 extremely successful with certain metals, -but their use with ceramic materials has 
 been limited I¥f] . 
 
 5. Microradiography and X-ray Microscopy 
 
 Specimens containing radioactive elements may be photographed by simply pressing 
 them against the photographic emulsion for an extended period of time. The resulting 
 autoradiograph is not usually sharp enough to permit much magnification but it is a 
 valuable technique for indicating concentration gradients as in the case of experiments 
 on diffusion and especially self-diffusion. Cyclotron activation techniques extend 
 the method to include a wide variety of elements and it should prove useful in 
 specialized structural studies. 
 
 The use of X-rays to disclose structural features is well known. When the 
 X-ray source is very small the radiograph attains high resolution [hj] ; in theory it 
 is that of the electron microscope but practical difficulties are formidable and it 
 is limited in the present state of development ■ to the limit of the optical 
 microscope Inland little work is done beyond 100X. Except in particularly favorable 
 cases good contrast in the image is difficult to obtain [hj]. Neutron microradio- 
 graphy [MJ-50.] seems to be a promising alternative, since the light elements which 
 are so frequently of interest in ceramic problems are extremely opaque to thermal 
 neutrons. 
 
 Two principal techniques are in use. Contact microradiography consists in 
 obtaining the image by radiography in which the specimen is in contact with a 
 photographic plate and enlarging it photographically. In point projection X-ray 
 microscopy the specimen is some distance away from the plate so that it casts an 
 enlarged shadow upon it. 
 
 17 
 
6. Specimen Preparation 
 
 The above are by no means the only methods for obtaining highly resolved images 
 of a specimen, but they represent those whose present state of development seems to 
 offer most promise for use on ceramic materials. It is especially significant that 
 the vastly increased knowledge of the microstructure of ceramics which has come' 
 during the past decade has been accompanied and has been largely the result of 
 greatly improved techniques in the preparation of specimens for examination. 
 
 Thin sections of specimens, fine-ground to flatness, cemented on a glass slide, 
 and ground down to a thickness of 30 microns, more or less, [20,21] are suitable for 
 the examination of course-grained materials, using the transmission optical micro- 
 scope. With the aid of polarized light accessories these are capable of yielding 
 structural information including grain orientation by the petrographic methods 
 (petrofabric analysis) originated in connection with petrological problems [51]. 
 For fine grained materials the thickness of these sections implies the overlapping 
 of a number of grains in the image so that information concerning both detail and 
 orientation are lost. Recently a method for making very much thinner sections has 
 been suggested [52,53] . A shallow well is etched with hydrofluoric acid in the 
 surface of the microscope slide. The specimen cemented in the bottom of this well 
 is protected by the glass down to the last stages of finish grinding, so that sections 
 6 microns in thickness can be produced with care. The technique restores' the thin 
 section to an extremely useful place in the microscopy of ceramic materials. At the 
 same time the ultra-microtome [5^-57] employing a diamond knife, has been used 
 successfully to get sections thin enough for direct electron microscopy although 
 they are small in area. 
 
 Splinters and chips of materials can be produced easily by simply crushing 
 materials under proper conditions and these have given results in optical and 
 electron microscopy [58] . In the case of porcelain enamels this may involve only 
 bending the specimen in the direction of the enameled surface. Thin scales may be 
 pulled from surfaces by applying a concentrated gelatine solution or certain glues 
 and drying in an oven. 
 
 Specimens for direct transmission electron microscopy may be prepared by special 
 fabrication and heat treatment. Glasses and enamels have been prepared by blowing 
 very thin bubbles followed by etching [591- Sinterable materials may be prepared 
 by sintering a little of the very fine powdered material on a metal grid [60]. 
 
 Polished sections, while yielding meager optical information, offer strong 
 advantages in quantitative studies, since they represent a single plane through 
 the specimen and so yield textural information with less quantitative ambiguity. 
 Distinction between the phases rests less on the optical properties of the phases 
 themselves, and more on particular treatments to which some of the constituents of 
 the specimen are more susceptible than others. On the one hand, this involves 
 attack by chemical or physical agents, while on the other hand, it may involve the 
 receptivity of certain details to decoration. The problem of preparing an initially 
 flat polished surface has largely been solved with the advent of impregnation 
 techniques to fill pores and diamond dust as the polishing medium, either fixed in 
 rotating laps or used as a paste on an appropriate surface [21] . In every case, 
 however, there is a certain art in the choice of the backing surface, the lubricant, 
 polishing speed, pressure, and time [61-651. 
 
 In order to enhance the contrast between grains in a specimen, to distinguish 
 phases from one another, and to reveal internal structure in the grains themselves, 
 such as dislocations, an etch is usually helpful A variety of procedures are in use 
 as the partial list in Table 1 indicates. The superb results obtained with portland 
 cement clinkers and basic refractories [21] and with metallurgical slags [103] m 
 differentiating between constituents of complex mixtures is a spur to more persistent 
 efforts. An almost complete lack of discussion of the reasons for the selection of 
 procedures lead to the suspicion that very much is still to be learned on this subject. 
 It would be surprising if there are not far more effective etching proceedures still 
 to be found. In the face of the difficulty of choosing an appropriate specific 
 chemical etch, there is of course a hope for a universal etchant. Three are claimed 
 in the field of ceramics. Thermal etching, i.e., raising the temperature of the 
 polished specimen in a furnace with an oxy-acetlyne torch or in an arc image, has 
 been found successful in bringing out grain boundaries in many cases. Examples are 
 given in Table 2, which includes also examples of the relief polish and ion 
 bombardment techniques. 
 
 18 
 
Table 1. 
 
 Material and Reagent 
 
 Aluminum Oxide 
 '% H PO, 
 
 3 •+ 
 
 H PO. cone. 
 3 h 
 
 KHSO 
 
 k 
 
 K S 
 2 2 7 
 
 H SO. 
 2 h 
 
 K 3 A1F 6 
 
 Dry H 2 
 
 Barium Ferrite 
 5% HC1 
 
 HC1 
 
 Barium Titanate 
 
 Few drops HF in 5 ml. 
 
 HC1, 95 ml. H 2 
 
 HF-HNO -H 
 
 0.5$HF in HNO 
 
 Some Chemical Etchants for Ceramics 
 Conditions Comments 
 
 Boiling 5-10 min. 
 
 Boiling h min. 
 
 210°C. 11-16 min. 
 
 h25°C. 120-180 sec. Polish (0001) 
 
 Melt 3 - l? sec. 
 
 675°C. 15-20 sec. Etch (0001) 
 
 675°C. 135 sec. ' Etch (1120) 
 
 300°C. 3 min. 
 
 200°C. 20 min. to 270°C. 5 min. 
 
 1000°C. 30-60 sec. Polish (1120) 
 1700°C. 1-2 min. 
 
 20 sec. 
 
 Reference 
 
 Houle 
 
 Gardner 
 
 Warshaw ' 
 
 Alford 
 
 Houle 
 
 Alford 
 
 Alford 
 
 Warshaw 
 
 McVickers 
 
 Alford 
 
 Houle 
 
 1% HF 
 
 3 
 
 1-7 min 
 
 During polishing 
 
 1-g- min. 
 
 H 3 P0^ 
 
 100°C, 
 
 1 hr. 
 
 Ba Fe 0^-BaBe 0^ Goto 
 BaFe 2 1+ -BaFe 12 19 Goto 
 
 Kulcsar 
 DeVries 
 Tennery 
 
 DeVries 
 
 Etched pos.,neg. Belitz 
 ends differentially 
 
 Beryllium Oxide 
 
 hFTWT 
 
 Calcium Fluoride 
 
 10 sec. - 5 min. 
 
 Houle 
 
 [62] 
 
 [63] 
 [66] 
 [67] 
 [62] 
 
 [67] 
 [67] 
 [66] 
 
 [6M 
 
 [67] 
 [62] 
 
 [68] 
 [68] 
 
 [69] 
 [70] 
 [71] 
 [72] 
 [73] 
 
 [62] 
 
 20$ HC1 
 
 
 near 
 
 boiling 5-10 
 
 sec . 
 
 Burn 
 
 [7*1 
 
 50% HC1 
 
 
 boiling 5 min. 
 
 to polish 
 
 Burn 
 
 [7^] 
 
 2% sulfamic acid in water 
 
 
 
 ^0-50 min 
 
 
 Phillips 
 
 175] 
 
 Calcium Fluoride - Sodium 
 
 Fluo 
 
 ride 
 
 
 
 
 
 H 2 S0i + . 
 
 
 
 
 
 Kingery 
 
 [76] 
 
 Calcium Oxide 
 
 
 
 
 
 
 
 h% picric acid in methyl alcohol 
 
 
 
 Daniels 
 
 [77] 
 
 Cadmium Manganese Ferrite 
 
 
 
 
 
 
 
 HF C+8J6) 
 
 
 
 10 sec. - 
 
 2 min. 
 
 Eichbaum 
 
 [78] 
 
 Cadmium Niobate 
 
 
 
 
 
 
 
 HF 
 
 
 
 
 
 de Brettevi 
 
 lle[7 
 
 Carbon( Diamond) 
 
 
 
 
 
 Frank 
 
 [80] 
 
 °2 
 
 
 Hot 
 
 
 
 Gualtieri 
 
 [81] 
 
 Chromium Sesquioxide 
 
 
 
 
 
 
 
 KHSOl^. 
 
 
 melt 
 
 3-15 sec. 
 
 
 Houle 
 
 [62] 
 
 Glasses 
 
 
 
 
 
 
 
 0.05$ HF 
 
 
 
 2 min. 
 
 Titama -opacified 
 enamel 
 
 Yee 
 
 [59] 
 
 Acetic Acid 
 
 
 
 
 Na 2 0.2Si0 2 
 
 Parikh 
 
 [82] 
 
 HF (dilute) 
 
 
 
 
 To bring out 
 cracks from 
 microindenter 
 
 Argon 
 
 [83] 
 
 NH^F (sat'd sol'n) 
 
 
 
 
 
 
 
 + NH I+ HF 2 
 
 
 Several hours 
 
 Lithia glass 
 
 Jaccodini 
 
 [8W] 
 
 2h% HF 
 
 
 15 sec. 
 
 Lithium silicate 
 
 Rindone 
 
 [85] 
 
 Lead Titanate Zirconate 
 
 
 
 
 
 
 
 Few drops HF in 100 ml. 
 
 
 
 
 
 Kulcsar 
 
 [69] 
 
 5% HC1 
 
 
 
 
 
 
 
 19 
 
Table 1. Some Chemical Etchants for Ceramics 
 
 Material and Reagent 
 
 Lithium Fluoride 
 
 2 x 10- 4 mol % FeF in H 2° 
 
 Magnesium Ferrite 
 SnCl 2 -HCl 
 
 Magnesium Oxide 
 30% HC1, 10% sat'd sol'n 
 of NHkCl, 60% water 
 HNO. in H 2 1:1 
 
 R^SO^ (dilute) 
 
 Conditions 
 
 1 min. 
 
 5-20 min. 
 1-5 min 
 
 C omments 
 
 H-.PO^ (Dilute) 
 
 Magnesium - Manganese Ferrites 
 
 (Thermal etch) 
 Mullite - Glass 
 10% HF 
 Porcelain 
 HF 
 
 Plutonium-Carbon System 
 Acetic acid-HN0 3 -H 2 0, 
 
 equal parts 
 Plutonium Monocarbide 
 H 2 
 
 Strontium Titanate 
 
 5 parts HF, 10 parts HNO^ , 
 
 10 parts H 2 
 
 Titanium Carbide-Molybdenum 
 
 Alkaline Ferricyanide 
 
 Titanium Carbide-Nickel 
 
 Alkaline Ferricyanide 
 
 Titanium Dioxide (Rutile) 
 
 KOH 
 
 85% H 3 P0 V 
 
 Tungsten Carbide-Cobalt 
 Alkaline Ferricyanide 
 Tungsten Carbide-Copper 
 Alkaline Ferricyanide 
 Uranium - Uranium Nitride 
 
 (Electrolytic) 
 Uranium Carbide-Plutonium Carbide 
 HNO3 
 
 Uranium Dioxide 
 HNO : Water 1:1 1-5 min. 
 
 3 sec, 
 
 80 ma. /cm 30 sec. 
 (electrolytic etch) 
 
 LfOO°C 20 min. 
 Boiling 2-£-3 min. 
 
 hot 10-30 min. (preferred) 
 
 H 2°2 
 
 9 Parts 
 
 H^O^ - 1 Part 
 Uranium Dioxide 
 
 H 3 P0 V 
 
 Lanthanum Oxide 
 ' Boiling 
 
 Uranium Sulfide 
 10% H 2 S0^ 
 
 Yttrium Iron Garnet 
 
 HC1 
 
 HC1 
 
 20% HC1 
 
 Zirconium Dioxide 
 
 HF CW) 
 
 Boiling 1 hr. 
 H hr. 
 2i hr. 
 
 1-5 min. 
 
 (Cont'd) 
 
 
 Reference 
 
 
 Gilman 
 
 [86] 
 
 Carter 
 
 [87] 
 
 Gorum 
 Houle 
 
 [88] 
 [62] 
 
 Daniels 
 
 177] 
 
 Daniels 
 
 177} 
 
 Palmer 
 
 [89] 
 
 Studt 
 
 [90] 
 
 Lundin 
 
 [91] 
 
 Kruger 
 
 [92] 
 
 Lied 
 
 [931 
 
 Waugh 
 
 [9M 
 
 Parikh 
 
 [83] 
 
 Parikh 
 
 [83] 
 
 Hirthe 
 Hirthe 
 
 [96] 
 [96] 
 
 Hirthe 
 
 Parikh 
 
 Parikh 
 
 Accary 
 
 Lied 
 
 Houle 
 
 Fuhrman 
 Hill 
 
 Shalek 
 
 Rudness 
 Lefever 
 Lefever 
 
 Houle 
 
 [96] 
 
 [82,95] 
 
 [82,95] 
 
 [97] 
 
 [93] 
 
 [62] 
 
 [98] 
 [99] 
 
 [100] 
 
 [101] 
 [102] 
 [102] 
 
 [62] 
 
 20 
 
Table 2. Universal Etch Techniques 
 
 Material and Technique Conditions 
 
 RELIEF P01ISH 
 Aluminum Oxide 
 
 Glass-metal Seals 
 
 THERMAL ETCH 
 Aluminum Oxide 
 
 Comments 
 
 0.1 micron AI2O3 on Microcloth 
 0.2 micron A1 2 0t 
 
 1700°C. in dry H 2 1-2 min. 
 
 1900 C. oxyacetylene torch 
 2-5 sec. 
 
 Uranium Dioxide-Lanthanum Oxide 
 
 Incipient fusion in arc 
 image furnace 
 
 ION BOMBARDMENT 
 
 Aluminum Oxide 
 
 Porcelain 
 
 Uranium oxide 
 
 Aluminum - aluminum oxide 
 
 Titanium carbide - nickel 
 
 Cobalt silicide - titanium carbide 
 
 Titanium diboride 
 
 PU0 2 - uo 2 
 
 Pyrolytic graphite 
 
 Reference 
 
 Angelides 
 Cole 
 
 Evans 
 
 Coy 
 
 [10M 
 
 [1051 
 
 Beauchamp [106] 
 
 [1071 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Bierlein 
 
 [108] 
 
 Keig 
 
 [1091 
 
 [110] 
 
 Thermal etching may develop surface detail by at least three processes [111] . 
 It may involve transfer of material by surface diffusion from high surface energy 
 to low surface energy regions and , therefore, away from grain boundaries. It may 
 involve loss of material by sublimation, and it may involve evaporation-condensation, 
 developing growth figures. 
 
 Relief polishing, involving a polishing step with a softer abrasive, .develops 
 a surface relief indicative of the abrasion resistance of the constituents at the 
 surface. Like the chemical etch, this is sensitive to grain orientation as well as 
 to the differences in hardness among phases and at grain boundaries. 
 
 Ion bombardment of the polished specimen surface is also promising as a 
 universal etch [108] . The specimen is placed in a chamber evacuated to 30-50 
 microns krypton pressure and is made the cathode with respect to a potential drop 
 of about *+000 volts across the chamber. Exceptionally fine etches have been 
 obtained on a variety of materials by this method, but experimentation is necessary 
 in every case to find the appropriate gas pressure, voltage, and time for best 
 results. 
 
 The decorating of surfaces before or after an etching treatment has not been 
 sufficiently explored. Important results with decoration by sodium vapor to reveal 
 cracks in glasses [112, 113] , decoration of sodium chloride with gold particles [11^-] 
 resulting from the decomposition of gold chloride, decoration of magnetic materials 
 with Fe 2 0:>and the use of small charged particles in crack location and polarity 
 
 determinations [115, 116] all suggest that decoration is well worth exploring 
 further. 
 
 The study of fracture-exposed surfaces [117-120] to disclose fracture origins, 
 grain orientation through cleavage traces and negative crystals and the path of 
 fracture, whether through grain boundaries or through the grains themselves, has 
 proved rewarding and shows great usefulness in connection with materials testing, 
 trouble shooting of fabrication problems and service failures, as well as micro- 
 structural details on which recent revisions of glass atomic arrangement have been 
 partly based [127-132] . 
 
 21 
 
7. Replication 
 
 Tn order to preserve the advantages of the polished section or fracture 
 surface Shouf the difficulty of ref lecting type ins rumen t. he sur a » ,_ 
 
 IS'SS.S'.S I? s" S if as rnf tecnni q ue C of P p esS a plastltpe softened 
 Sh n Ppropiate solvent against the h ^ S ^£^. « ^^boS.. 
 l^t%tp. fKL ;S h a h s heen JalSahle ^n-ning^urfaoe^a^e^e^el^ 
 
 with the optical microscope [13^1 • l£e ^P 1 ^!^/, The hlgh resolution 
 usually involves several stages [21 26 28 135 1J0 • | Formvar is first 
 technique of Bradley [1361 will ™ in chloroform. This is backed with a 
 coated on the specimen as a 1 or 2% solution in cnioroici replica is then stripped 
 
 microscope gives the impression of illumination at a glancing «m& 
 details into strong relief. 
 
 8. Conclusion 
 Of the many instruments and techniques discussed none ^uld be considered 
 "best" but each has its own particular aPP^f^ 3 ' c fhas i?s "blind spots" and 
 the temptation to rely on one _ te f^^tt 5 ca n lead to error. Most problems profit 
 areas of confusion where s P uriou %^ f ^^ s n ^ or e a me tSods and in almost every case 
 
 ^caTSc— at 10WSr «***«"°". 
 
 should be one of these. 
 
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 25 
 
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 I 
 
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 26 
 
117 W. L. Phillips, Jr., "Effect of 
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 119 Robert Scheuplein and Peter Gibbs, 
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 II Dislocation Structure and 
 
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 120 W. Schatt and D. Schulze, "Einige 
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 129 
 
 130 
 
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 Li 2 0-Si02-Ti02", J. Am. Ceram. Soc. 
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 Silicate Liquid Immiscibility 
 
 to Development of Opaoue Glazes", 
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 125 T. Y. Tien and F. A. Hummel, 
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 126 M. Krishna Murthy, "Influence of 
 Platinum Nucleation on Constitu- 
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 Sodium Phosphate Glasses", J. Am. 
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 127 T. F. Bates and M. V. Black, 
 "Electron Microscope Investigation 
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 487-92, 516, 518 (1948). 
 
 128 Muneo Watanabe, Haruo Noake and 
 Takeshi Aiba, "Electron Micro- 
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 Glasses and Their Internal 
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 131 
 
 132 
 
 133 
 
 13^ 
 
 135 
 
 136 
 
 137 
 
 138 
 
 139 
 
 140 
 
 Stanley M. Ohlberg, Helen R. Golob, 
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 Colloidal Immiscibility", J. Am. 
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 Fracture Surface of Silicate 
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 102-103 (1963). 
 
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 "Application of Replica Techniques 
 to the Study of Ceramic Surfaces 
 with the Optical Microscope", 
 J. Am. Ceram. Soc. 31, 83-88 
 (1948). ^ 
 
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 "Use of Plastic Replicas in 
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 its Application to the Study of 
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 Ceram. Soc. 4l, 397-406 (1958). 
 
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 Elektronenmikroskopische 
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 Keramischen Werkstoffen", 
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 V. J. Tennery and F. F. Anderson, 
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 29_,755-758 (1958). 
 
 27 
 
3.1*1 H. E. Simpson, "Study of Surface 
 Structure of Glass as Related to 
 Its Durability", J. Am. Ceram. 
 Soc. 1+1, h$-ko (1958). 
 
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 dasKristallgeftlge von Mn-Zn 
 Ferrites", Ber. deut. keram. Ges. 
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 (I960). 
 
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 R. G. Wells, "Electron Micro- 
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 150 T.Y. Tien and W. G. Carlson, 
 
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 28 
 
The Effect of Heat Treatment on Micros tructure 
 J. E. Burke 
 
 1. Introduction 
 
 At some stage during processing, most ceramics are heated to an elevated tempera- 
 ture, held for a time and then cooled. During this heat treatment, many profound 
 changes in structure may occur and the final micros tructure is established. For 
 example, the identity, amount, composition, perfection, size, geometrical arrangement 
 or crystallographic orientation of the phases initially present may change. The com- 
 position of the whole body may change if volatile species evaporate or are picked up 
 from the heat treating atmosphere. Our goal in this paper is to set down some simple 
 general principles governing the effect of heat treatment on micros tructure. Some of 
 the principles are concerned with establishing, from phase stability studies, what 
 phases are stable at the heat-treating temperatures. Some are concerned with the in- 
 fluence of forces such as surface tension upon the geometry of phases. These aspects 
 have been well covered by other speakers in this series, and I should like to concern 
 myself with the problem of relating temperature to the rate at which the approach to 
 equilibrium is made. This is not a new branch of science, although it has developed 
 rapidly over the past 20 years. Furthermore, this is not intended as an elegant treat- 
 ment, but rather as a practical one, to provide a way of thinking about reactions in 
 solids, with enough information so that semiquantitative calculations can be made. For 
 more quantitative treatment, the reader is referred to the standard texts. 
 
 2. Diffusion 
 
 Undoubtedly the most important single reaction which may occur during heat treat- 
 ment is the diffusional transport of individual atoms through the solid from their 
 initial positions to new positions of greater thermodynamic stability. It is by such 
 transport that concentration gradients are smoothed out, that phases form and disappear, 
 and that shrinkage and pore elimination during sintering is accomplished. 
 
 The elementary mathematics of the diffusion process was first formulated over 100 
 years ago, and during the ensuing period many measurements of diffusion rates of certain 
 atomic species in various solids have been made, and quite detailed knowledge of the 
 mechanisms by which diffusion occurs now exists. There are many review papers on the 
 subject, particularly in metals, and many textbooks of metallurgy and ceramics have 
 extensive treatments of the subject [IK In spite of all this work, it should be 
 mentioned that a complete understanding of diffusion does not yet exist, particularly 
 in ceramic materials, and it is an active field of research at the present time. In 
 this section an attempt is made to establish only the most elementary concepts so they 
 can be used in later discussions. 
 
 1 Figures in brackets indicate the literature references at the end of thi 
 
 s paper., 
 
 29 
 
Let us consider a system in which there is a sudden change in composition with 
 distance, such as might exist if a piece of pure aluminum oxide were to be welded to a 
 ruby which contains a small amount of dissolved Cr 2 3 replacing some of the Al-O^. It 
 has been established that in Al^O., the oxygen ions form a relatively rigid framework, 
 so that upon heating, some of the Cr ions will diffuse into the sapphire and this 
 diffusion will be compensated by a counter -diffusion of Al ions into the ruby. The 
 situation is presented schematically in Fig. 1, where the solid line shows the concen- 
 tration gradient assumed to exist initially and the two dotted lines show the concentra- 
 tion gradients after two successive times of heat treatment. 
 
 The general law governing this process, and the law from which the shape of these 
 penetration curves can be explained, at least in principle, was formulated by Fick in 
 1855. In its simplest form it states: 
 
 J - -D |f (1) 
 
 the quantity J of diffusion substance which passes per unit time through a unit area 
 of a plane at right angles to the direction of diffusion is proportional to the con- 
 centration gradient of the diffusing substance aC/aX. The negative sign appears to 
 compensate for the fact that the slope of concentration versus distance curve which 
 favors diffusion is negative. The proportionality constant, D, is called the diffusion 
 coefficient, and its absolute value serves to characterize the diffusion rate of the 
 diffusing species in that substance. Commonly it is stated in units of cm per second. 
 The larger is the value, the shorter will be the heat-treating times necessary to 
 accomplish a given amount of diffusion. The value of D can be measured in many ways, 
 typically from measurements of concentration - distance curves of the type presented 
 in Fig. 1. 
 
 It will be immediately evident from an examination of the literature that the 
 above description is greatly over-simplified. In particular, the value of D is not 
 independent of composition, and if a phase boundary is involved, it is possible for 
 diffusion of an atomic species to occur from one phase where its concentration is low 
 (but its thermodynamic activity is high) to another phase where its absolute concentra- 
 tion is higher (but its thermodynamic activity is lower). In spite of this, we shall 
 consider here that the diffusion constant has a single value for a given diffusing 
 species in a given material, at constant temperature. 
 
 Darken [11 has pointed out a simple relationship which can be very roughly used to 
 compute minimum heat treating times, and which permits a feeling to be obtained for the 
 absolute values of diffusion coefficients. 
 
 Diffusion is substantially complete when 
 
 t = -e 2 /D (2) 
 
 where t is the diffusion time in seconds and i is the radius (or minimum dimension of 
 the particle concerned) in centimeters. Thus, if one were concerned with determining 
 the minimum heat-treating time necessary to cause homogenization in an aggregate of 2|a. 
 radius particles at a temperature where the diffusion coefficient for the diffusing 
 species is 1 X 10" cm sec he would find 
 
 t = ( 2 x 10 ) = 4 x 10 2 seconds 
 1 X 10 
 
 If the particle size were doubled, the time would be increased by a factor of 4. In 
 practice, the actual times might be very much longer than those computed in this way 
 because pores and imperfect contacts between particles reduce the effective inter- 
 
 30 
 
diffusion area and increase the diffusion distance. On the other hand, if the 
 necessary time for one particle size is known, the increase in time for an increase 
 in particle size should be given reasonably well by this relationship, assuming that 
 the two systems are geometrically similar. 
 
 3. Factors Influence the Diffusion Rate 
 
 There are many factors which may influence the diffusion rate in ceramics. Un- 
 doubtedly the most important one is temperature, and this is discussed in some detail 
 in a following section. 
 
 Most theories of diffusion assume that the atoms move by utilizing crystallographic 
 defects, particularly unoccupied lattice sites, to accomplish the rearrangement. A 
 major effect of increasing the temperature is to increase this number of defects, so 
 that diffusion is speeded up. The addition of impurity atoms, particularly those of a 
 different valeijige, may also cause the formation of unoccupied lattice sites. For 
 example, if Ca ions are substituted for Zr ions in ZrO„, one unoccupied oxygen 
 site is formed for each such substitution. With large substitutions many such sites 
 are formed and the diffusion coefficient for oxygen ions is tremendously increased. 
 
 Many impurity additions may operate in a similar way to increase diffusion 
 coefficients and thus to increase the rate of heat-treating reactions, but it is not 
 assured that increasing the diffusion rate of one ionic species in a compound will 
 necessarily increase the reaction -rate. 
 
 Two categories of diffusion reactions may be considered - 
 
 1) In the example cited above, the oxygen framework remains fixed, and the 
 chromium and aluminum ions interchange. Any factors influencing the diffusivity of 
 these ions will influence the velocity of the homogenization of the two crystals. 
 
 2) In reactions such as sintering, both atomic species must move. If the 
 objective of the heat -treatment were to cause sintering of aluminum oxide particles, 
 the diffusion rate of the oxygen ion would be all -important since it is blower moving 
 and rate controlling. Any factor, such as an impurity, that would modify the oxygen ion 
 mobility, would greatly speed up the sintering rate. If the rate of aluminum ion 
 diffusion alone were affected, the sintering rate would be unchanged. 
 
 It is commonly observed also that diffusion at grain boundaries in polycrystalline 
 solids is greatly enhanced. There is presently some obscurity in determining whether 
 or not this is universally true, or whether only the slower moving species are 
 speeded up. More work needs to be done, but at the present time there are strong 
 indications that the behavior of ceramics does not parallel that of metals. 
 
 4. Effect of Temperature on Reaction Rates 
 
 Most chemical reactions are observed to increase rapidly in rate as the temperature 
 is increased. The so-called Arrhenius relationship is that: 
 
 Rate = K e^ 1 (3) 
 
 or In Rate = InK - Q/RT 
 or log Rate = log K - 2 .l\? 
 31 
 
where the pre -exponential proportionality constant and the exponent Q (the activation 
 energy) are characteristic of the reaction concerned. R is the gas laws' constant, and 
 T the absolute temperature. 
 
 In chemical usage, quantities are expressed in moles, or gram formula weights of 
 the reacting substances, R, the gas laws' constant, is expressed in calories per 
 degree (1.986 « 2.0), and Q has the dimensions of calories per gram formula weight. 
 Frequently, the computation is done on a per atom basis. Then the Boltzman gas con- 
 stant k is used in place of R, and it is commonly expressed in electron volts per 
 degree C (8.6 X 10~ 4 ) . Q has the dimension of electron volts per atom. Approximately, 
 1 ev per atom = 23,000 cal per gram atom. 
 
 The diffusion coefficient D is a measure of the rate of the diffusion reaction. 
 Its temperature dependence is commonly determined, and presented in the form 
 
 D = D c e 
 
 -Q/RT 
 
 (4) 
 
 If the value of D and Q are given, the value of the diffusion coefficient at any 
 temperature may be computed. A typical value of D e is unity and reported values range 
 at least from 10 -4 to 10 4 cm 8 per second. Occasionally very much larger or smaller 
 values for D c are published, but these should be viewed with caution. Values for Q 
 are not so variable. They range typically from 10,000 calories per mole for rapid 
 reactions which will occur at an appreciable rate at room temperature to 150,000 or 
 even 200,000 calories per mole for reactions in refractory materials that are observ- 
 able only at temperatures above 1000°C. A few typical values are listed in Table 1. 
 
 TABLE 1. Typical values for some diffusion coefficients 
 
 Matrix D 
 
 if fusing 
 
 
 D 
 
 Q 
 
 
 
 Substance 
 
 Ion 
 
 cm 8 /sec 
 
 KCal/Mole 
 
 Remarks 
 
 Reference 
 
 A1 S 3 
 
 = 
 
 1.9 
 
 X 10 3 
 
 152 
 
 Single Crystal 
 
 [3] 
 
 A1 S 3 
 
 = 
 
 2 X 
 
 10° 
 
 110 
 
 Polycrystal 
 
 [3] 
 
 A1 2 3 
 
 Al +3 
 
 2.8 
 
 X 10 1 
 
 114 
 
 Polycrystal 
 
 [4] 
 
 uo s 
 
 U+ 4 
 
 4.3 
 
 x io- 4 
 
 88 
 
 Stoichiometric U0 S 
 
 [5] 
 
 U0 S 
 
 = 
 
 1.2 
 
 X 10 3 
 
 65 
 
 Stoichiometric U0 E 
 
 [5] 
 
 UO 
 s 
 
 = 
 
 2.7 
 
 x io- 3 
 
 29.7 
 
 Non-Stoichiometric U0 s-06 
 
 [5] 
 
 CaO- 
 
 Stabilized < 
 ZrO s 
 
 "Ca + + 
 Zr +4 
 
 4.1 
 2.1 
 1 X 
 
 x io- 1 
 x io- 1 
 io- 2 
 
 100 
 100 
 
 28.1 
 
 12 and 16 mol % CaO 
 12 and 16 mol % CaO 
 15 mol % CaO 
 
 [6] 
 [6] 
 [7] ! 
 
 4a. Isothermal Reaction Rates 
 
 We have just seen that the use of the Arrhenius relationship relating reaction 
 rate to temperature provides a compact means of describing the diffusion rate of one 
 substance in another. The same approach may also be used to predict the effect of a 
 change of temperature upon the time necessary for a given amount of reaction if the 
 value of the activation energy, Q, is known or can be determined. This approach works 
 well only in those cases where the driving force for the reaction is not strongly in- 
 fluenced by temperature, as is commonly the case in sintering, viscous flow, homogeni- 
 zation by diffusion or grain growth. If a phase change is involved in the reaction the 
 situation may be more complicated, as is discussed below. 
 
 32 
 
It is common, for development purposes, to determine a proper firing temperature 
 for a ceramic by conducting a series of ISOCHRONAL observations , firing for a given 
 time at a series of temperatures, and presenting the results, for example, as a plot 
 of density, or grain size versus firing temperature. Fig. 2 presents such a plot, in 
 which for purposes of illustration, an arbitrary parameter V, having the dimensions of 
 length and representing a phenomenon such as a length change, has been plotted against 
 firing temperature. 
 
 Such an approach assumes that temperature is of primary importance in characteriz- 
 ing the heat -treatment, and that changing the time of heat -treatment has little effect. 
 It is apparently justified if one plots, on ordinary graph paper, the results of 
 measurements of the property concerned as a function of time. As is shown in Fig. 3, 
 the properties appear to reach more or less stable values at each temperature. 
 
 In Fig. 4, log V has been plotted versus log time, and it can be seen that the 
 reaction is continuing at each temperature in the same way. Only the time scale has 
 been shifted. Figure 3 incorrectly implies that the amount of reaction is controlled 
 by the temperature. It is controlled by temperature only if the same annealing time 
 is used at each temperature. 
 
 If one is concerned with commercial processing, and is limited to a period such 
 as an hour for heat treating, then such conclusions are correct. In those cases, heat- 
 ing a specimen to an elevated temperature will effectively stabilize it against change 
 with respect to short time heat -treatments at lower temperatures. On the other hand, 
 if one is concerned with long term stability, as in creep, then comprehension of the 
 fact that reaction may continue indefinitely even at low temperatures is of great 
 importance. 
 
 The curves in Figures 2-4 were computed from the relationship 
 
 V = kt 1/2 
 and k was assumed to vary with temperature. as 
 
 k = k e exp (^000) 
 
 This equation is reasonably representative of many of the structure-controlling re- 
 actions in ceramics. 
 
 In diffusion- controlled reactions, the thickness of a diffusion layer or the 
 thickness of an oxide film or reaction product formed by diffusion will be given, at 
 least approximately, by the relationship 
 
 1/2 
 Thickness = kt ' (5) 
 
 which gives rise to the so-called parabolic rate law for most tarnishing reactions. 
 The rate constant k is characteristic of that of a thermally activated process, and 
 increases exponentially with increasing temperature. 
 
 The rate of grain growth in most materials is found roughly to be inversely 
 proportional to the grain size S, thus: 
 
 dS k 
 dt S 
 
 33 
 
 (6) 
 
2 2 
 and S -So = kt 
 
 where S is the grain size at t ■ 0. Assuming it to be much smaller than S, one can 
 deduce the commonly used grain growth equation 
 
 S = kt 1/2 (7) 
 
 where k varies with temperature according to the Arrhenius relationship. 
 
 Sintering in many systems is observed to obey a similar law. The fractional 
 shrinkage in the initial stages -can commonly be approximated by 
 
 A = kt 2 / 5 (8) 
 
 where again the rate constant k varies exponentially with temperature. 
 
 Many of the reactions tend to be self -limiting in this way. If the concern is 
 with having a reaction go to completion for processing reasons, times at low tempera- 
 tures may become excessively long, and the only practical way to attain more complete 
 reaction is to use higher processing temperatures. On the other hand, if the concern 
 is with long term stability, say resistance to plastic deformation by creep, lowering 
 the temperature will lower the rate, but deformation will continue. 
 
 4b. The Effect of Heating Rate 
 
 It is obvious that many different reactions may go on simultaneously during heat 
 treatment. The question sometimes arises: can one of these be favored over the other 
 by changing the heating rate or the heat-treating temperature? For example, can 
 shrinkage be accomplished with less grain growth by raising the temperature to speed 
 up sintering and keeping the time short so that not much grain growth occurs? The 
 answer in general must be "no". The precise answer is shown by the relative values 
 of the activation energy, Q in equation 3 for the two competitive processes concerned. 
 If the Q for each process is about the same, (as it usually is) than raising the 
 reaction temperature or changing the heating rate will affect each of the processes 
 equally, and the only effect will be to change the time necessary for reaction. If, 
 however, for example, the activation energy for grain growth were to be higher than 
 the activation energy for sintering, then indeed, raising the temperature would 
 increase the rate of grain growth faster than it would increase the rate of sintering. 
 A fine grained body would be obtained in that case by firing at the lowest temperature 
 consistent with the available heat treatment time. 
 
 Usually, the activation energies for the independent processes are not known, and 
 the effect of temperature on the relative rates of two identifiable competing reactions 
 is best determined by examining micros tructures of specimens heated at two different 
 temperatures for times which are adjusted to cause comparable amounts of reaction at 
 each temperature. 
 
 5. Determination of Activation Energies 
 
 It is conventional to determine activation energies by evaluating some specific 
 rate constant in the reaction law, such as the diffusion coefficient D in equation 1, 
 at several temperatures. Then, a plot of the logarithm of the rate constant versus 
 the reciprocal of the absolute temperature should give a straight line whose slope is 
 Q/2.3R. 
 
 34 
 
This is readily seen from the rearrangement 
 
 D = D e"Q /RT (9) 
 
 In D = 2.3 log D = =& (|-) + In D 
 
 Rigorously speaking, this method is valid only if it can be independently demonstrated 
 that the sole effect of changing the temperature has been to change atomic mobility. 
 In practice, the existence of a straight line relationship on such a plot is usually 
 taken as evidence that the procedure is valid. 
 
 In Fig. 5, the data from Fig. 4 have been replotted to permit a determination of 
 the value of Q. A measure of the reaction rate, the reciprocal of the time necessary 
 to produce a given amount of reaction, has been plotted against the reciprocal of the 
 absolute temperature. The activation energy can be determined from the slope as 
 indicated 
 
 slope = ^= - = =i = -^ 
 
 5.64 X 10 ~* - 5.18 X 10 4.6 X 10 ~ 5 * 3 
 
 Q = 100,000 cal/gram formula weight. 
 
 It will be noticed that the value of the activation energy does not depend upon 
 the stage in the reaction at which the temperature dependence of the rate is determined 
 
 When the law governing the process at hand is complex, it is sometimes difficult 
 to evaluate a rate constant with precision. Under these conditions the following 
 relationship will be found useful: 
 
 2.3 log (^) = a ( i_ _ L_) (10) 
 
 where t, and t~ are the times at Kelvin temperatures T.. and T_. If the reaction 
 occurring at different temperatures is essentially the same one, all of the curves on 
 a plot of the type shown in Fig. 4 should be parallel (although they may not be 
 straight lines) and it should be possible to superimpose them by the use of an appro- 
 priate multiplying factor computed with the aid of equation 10. Such techniques 
 provide an approach to the selection of heat-treating times which should produce 
 comparable amounts of reaction if the temperature is changed. 
 
 In determining activation energies, proper selectivity must be exercised in 
 determining the value of the rate. It is not permissible to state a shrinkage rate 
 as a certain percentage shrinkage per unit time, because the value of this rate will 
 depend upon the time period considered, and upon the shrinkage which has previously 
 been accomplished. On the other hand, it is permissible to measure the time necessary 
 for a reaction to cause a property to change from a given initial value to a given 
 final value as a function of temperature, as was done for Fig. 5, and to plot the 
 reciprocal of this time versus 1/T to obtain a value for the activation energy. For 
 example, one might measure the time necessary to produce 5% shrinkage and plot its 
 reciprocal versus l/T. 
 
 6. Phase Transformation 
 
 The discussions presented above assumed that the driving force for the reaction 
 was not profoundly altered by temperature, so the rate would depend almost entirely 
 
 35 
 
upon atomic mobility. When a phase transformation occurs, there are problems in forming 
 nuclei of the new phase, and the driving force for the reaction increases with supercool- 
 ing while atomic mobility decreases. It is therefore sometimes difficult to predict 
 whether a change in temperature will increase or decrease the rate of the reaction „ 
 
 6a. Nucleation 
 
 The problem of nucleation of a new phase is well understood, and the kinetics of 
 the process have been studied in great detail. Discussions of the phenomenon may be 
 found in several reviews [2]. 
 
 In these theories, the driving force for the transformation is the free energy 
 decrease associated with the transformation of a volume of the phase 4/3ttt 3 to the more 
 stable modification. When this new phase forms, an interface of area 4-rr 2 is formed. 
 Thus the total energy change associated with the process is 
 
 aF = - prr 3 AF v + 4 T rr 2 r (11) 
 
 where aF v is the decrease in free energy per unit volume associated with the transform- 
 ation and r is the surface free energy of the interface per unit area. 
 
 The important geometrical parameters are set forth in Fig. 6 and a plot of this 
 behavior is shown in Fig. 7. 
 
 Most of the theoretical studies of nucleation and phase transformation have dealt 
 with the problem of describing the factors influencing the rate of nucleation. We shall 
 not attempt to reproduce these here, but shall merely qualitatively describe the con- 
 clusions. The stable nucleus must grow by the addition of atoms in the stable configura- 
 tion. In a pure system this is an energetically unfavorable process at temperatures 
 close to the transformation temperature, so considerable undercooling may be required, 
 and the rate of nucleation increases with increasing undercooling. 
 
 The need to supply an interface of energy 4nr 2 y , eq. (11), when a new phase forms 
 constitutes a nucleation barrier which can be greatly modified by impurities. If 
 impurities are in solid solution they may adsorb at the new interface, decrease the 
 interfacial energy y, and thus facilitate nucleation. If they are present as second 
 phase inclusions, they may serve as nucleation catalysts since the interfacial energy 
 between the inclusion and the new phase may be less than between the new phase and the 
 original matrix. 
 
 6b. Rate of Phase Transformations 
 
 Once nucleation is established, the rate of the phase transformation will be con- 
 trolled by two parameters, the driving force, which increases with the supercooling 
 below the transformation temperature, and the atomic mobility, measured for example by 
 the diffusion coefficient. Thus 
 
 Rate = Const, f (g) • Doe"^* 1 (12) 
 
 At the transformation temperature, Te, AT = and the reaction rate is low. As AT 
 increases the reaction rate will increase until it begins to be limited by the decreas- 
 ing atomic mobility at lower temperatures, when the rate will again fall. A schematic 
 presentation of such behavior is given in Fig. 8. 
 
 36 
 
Reactions of this type are well known in the heat treatment of metals, where their 
 understanding provides the basis for the control of the heat -treatment of steel. Prob- 
 ably the most striking example in ceramics is the devitrification or controlled crystalli' 
 zation of glass. At both high and low temperatures the transformation rate is low, and 
 at intermediate temperatures it is high. It is self-evident that although reactions of 
 this type are indeed thermally activated, one cannot compute activation energies in the 
 conventional way, nor can he without additional information predict the effect of 
 temperature on reaction rate. 
 
 7. Applications 
 
 Examples of the applications of these principles might be given almost without end. 
 In practically no case can they be applied without thought, however. This will be 
 illustrated by reference to the factors controlling the rate of sintering in an essential- 
 ly pure single phase oxide. 
 
 It is reasonably well demonstrated that sintering is accomplished by the diffusional 
 transport of atoms from grain boundaries to pores. The pores are filled, and the space 
 left at the grain boundaries is closed by moving the grains closer together and thus 
 accomplishing shrinkage. What factors may influence the sintering rate? 
 
 1) The sintering temperature, because with other conditions constant it will 
 control the rate at which the atoms move. 
 
 2) The initial particle size, because it will control the distance atoms must 
 move to accomplish shrinkage, and thus the time required for movement. 
 
 3) The possible occurrence of grain growth during sintering. This can be detected 
 only by microscopic examination, but it will alter the necessary diffusion distance just 
 as certainly as changing the particle size. In either case, doubling the particle size 
 will quadruple the sintering time. 
 
 4) The presence of an impurity in the starting material - it may do at least 
 three different things: 
 
 a) Modify the diffusion rate of the slower moving species, and thus modify 
 the sintering rate. 
 
 b) Inhibit grain growth, and thus control the diffusion distance and hence 
 the sintering time. 
 
 c) Cause the appearance of a liquid phase which can completely modify the 
 shrinkage mechanism. 
 
 5) Reaction with the atmosphere. This may modify the stoichiometry of the 
 sintering material, and thus diffusion coefficients and reaction rates. Or the 
 atmosphere may become entrapped in pores and mechanically prevent shrinkage. 
 
 There is no simple road to understanding the effect of heat -treatment on micro - 
 structure. To understand what is going on, and to be able to predict what effect changes 
 in processing conditions will have on structure and properties, the experimentalist will 
 however find it helpful to follow the process by measuring the changes in some sensitive 
 parameter in a series of isothermal heat treatments made at a sequence of times at a 
 variety of temperatures and at the same time, follow the changes in micros tructure which 
 occur as a consequence of these heat treatments. In this way, he should be able to at 
 least describe the process in quantitative terms, and under favorable conditions he 
 should be able to understand what is going on in a fundamental way. 
 
 37 
 
References 
 
 [1] See for example: 
 
 L. S. Darken and others, in Atom Move- 
 ments, A.S.M. (Cleveland, Ohio, 
 1951). [3] 
 
 W. D. Kingery, Introduction to Ceramics, 
 p. 217, John Wiley & Sons, Inc. (New 
 York, 1960). [4] 
 
 Ling Yang, and M. T. Simnad, in Physico- 
 chemical Measurements at High Temper- [5] 
 atures, edited by J. O'M. Bockris, 
 J. L. White, and J. D. Mackenzie, 
 Butterworths Scientific Publications, 
 p. 295 (London, 1951). 
 
 [2] S. D. Stookey and R. D. Maurer, Progr. 
 
 Ceram. Sci. 2, 77 (1961). [6] 
 
 J. E. Burke and D. Turnbull, Progr. in 
 
 Metal Phys. 3, 254 (1952). [? -| 
 
 J. H. Hollomon and D. Turnbull, Progr. 
 in Metal Phys. 4, 336 (1953). 
 
 W. D. Kingery, Introduction to Ceramics, 
 p. 296, John Wiley & Sons, Inc. (New 
 York, 1960). 
 
 Y. Oishi and W. D. Kingery, J. Chem. 
 Phys. 33, 480 (I960). 
 
 A. E. Paladino and W. D. Kingery, J. 
 Chem. Phys. 37, 957 (1962). 
 
 A. B. Auskern and J. Belle, in Uranium 
 Dioxide: Properties and Nuclear 
 Applications, edited by J. Belle, 
 USAEC, p. 309, Uo S. Government 
 Printing Office, Washington, D. C. 
 (1961). 
 
 W. H. Rhodes and R. E. Carter, Bull. 
 Am. Ceram. Soc. 41, 283 (1962). 
 
 W.'D. Kingery, J. Pappis , M. E. Doty, 
 and D. C. Hill, J. Am. Ceram. Soc. 
 42, 393 (1959). 
 
 Cr +3 
 Al +3 
 
 SAPPHIRE 
 
 RUBY 
 
 U- 
 
 
 > 
 
 o + 
 
 en 
 
 t— 
 
 (J> 
 
 o 
 o 
 
 
 // '2 
 
 t 2 >t, >t 
 
 FIGURE 1. Schematic representation 
 of diffusion. Upper diagram rep- 
 resents exchange of Cr 3 and Al 
 ions between ruby and sapphire. 
 Lower diagram shows Cr 3 concen- 
 tration gradient at various 
 times . 
 
 700 
 
 600 
 
 500 
 
 400 
 
 300 
 
 200 
 
 100 
 
 EFFECT AT TEMPERATURE 
 ON V - I HR. ANNEAL 
 
 1500 
 
 1700 1900 
 TEMPERATURE °K 
 
 2100 
 
 FIGURE 2. Isochronal reaction curve 
 showing variation of extent of re- 
 action, V, with temperature at con- 
 stant annealing time. 
 
 38 
 
10 
 
 20 
 
 30 
 
 40 50 60 
 
 TIME- MINUTES 
 
 70 
 
 80 
 
 90 
 
 100 
 
 FIGURE 3. Arithmetic plot of isothermal reaction data. Apparent cessation 
 of reaction at each temperature is misleading, and consequence of reaction 
 law. 
 
 20 40 70 100 
 
 TIME, MINUTES 
 
 400 700 1000 
 
 FIGURE 4. Logarithmic plot of 
 
 isothermal reaction data. Paral- 
 lel curves indicate that reaction 
 law is the same at all tempera- 
 tures. 
 
 a 50 
 
 0.54 
 
 1700 
 
 ]\ 
 
 i 
 
 1 
 
 1 1 
 
 \ 
 
 
 , V= 100 
 
 \ V=40 
 
 _ 
 
 \y=2oo 
 
 
 \ s 
 
 - 
 
 
 
 
 r 
 
 L 
 
 
 
 - 
 
 i 1 
 
 1 1 
 
 ill , 1 
 
 0.58 
 
 IOOO/t 
 
 FIGURE 5. Method of computing 
 activation energy, 
 
 log rate log 1/t = -^- (-) 
 y ' 2.3R T 
 
 so slope is -Q/2.3R. 
 
 39 
 
PHASE I 
 
 SURFACE AREA 
 = 4Ttr 2 
 
 INTERFACE FREE ENERGY 
 = y ergs/cm 2 
 
 FIGURE 6. Geometrical parameters 
 in nucleation, see eq. (11) . 
 
 FIGURE 7. Plot of conditions for 
 formation of stable nucleus of 
 radius r*. 
 
 RADIUS OF NUCLEUS - 
 
 TRANSFORMATION TEMPERATURE 
 
 FIGURE 8. Rate of transforma- 
 tion versus undercooling, 
 see eq. (12) . 
 
 RATE OF TRANSFORMATION ■ 
 
 40 
 
Correlation of Mechanical Properties with Microstructure 
 Robert J. Stokes 
 
 1. Introduction 
 
 The last review article on this subject was prepared by Coble in 1956 and was sub- 
 sequently published in 195$ D-] 1 • Since that time, a number of conferences on allied 
 topics have been held and the proceedings published but no review specifically on the 
 effects of microstructure has appeared. The period 1956 to the present has been par- 
 ticularly productive since it corresponded at the start with the beautiful etching ex- 
 periments on dislocations in lithium fluoride by Gilman and Johnston [2] and the de- 
 monstration by Gorum et alj3] that single crystals of magnesium oxide could be deformed 
 plastically at room temperature. The implication from this latter work that certain 
 ceramic materials might possess ductility led to increased research activity in the 
 field of the mechanical behavior of ceramics. Most of the early effort concentrated 
 on the behavior of dislocations in single crystals of a relatively few substances, 
 particularly those having the cubic rock salt structure. More recently the field has 
 broadened considerably to include a wider range of single crystal ceramic materials and 
 the earlier work on the rock salt structure has been extended to include the effects of 
 microstructure. 
 
 In this paper the influence of microstructure on the following aspects of mechani- 
 cal behavior will be considered in turn, (1) elastic deformation, (2) anelastic behavior, 
 (3) plastic deformation, (4) brittle fracture, (5) high temperature deformation and 
 creep. In addition to the familiar variables such as grain size and the presence and 
 distribution of porosity or a second phase, the term microstructure will be considered 
 broadly enough to allow discussion of the role that fundamental variables such as crystal 
 structure, bond character and crystalline defects such as impurities, vacancies and dis- 
 locations play in determining mechanical behavior. By necessity the paper is concerned 
 almost exclusively with the simple oxide ceramics since these materials have been the 
 most extensively studied. 
 
 2. Elastic Deformation 
 
 Purely elastic deformation of a single crystal corresponds to the variation in 
 spacing between atoms under stress. Thus, elastic extension is directly related to the 
 forces between atoms and the binding energy of the structure. Similarly the elastic 
 modulus, the ratio of stress to the extension it produces, is related to bond strength 
 and character. A simple way in which this correlation may be appreciated is to consider 
 the elastic moduli of a number of materials as a function of their melting temperature. 
 The points all fall within a fairly narrow band for which the elastic modulus increases 
 as the melting point increases [4] . Materials of similar type and structure fall in a 
 much narrower band. 
 
 Figures in brackets indicate the literature references at the end of this paper. 
 
 41 
 
The principal effects of microstructure on elastic modulus arise through the pre- 
 sence of a second phase. There are a considerable number of theoretical analyses re- 
 lating the elastic modulus of heterogeneous systems to the amount of second phase. 
 Each calculation leads to a slightly different relationship enjoying a different degree 
 of success in describing the experimental results. In the simplest case, where the 
 bond between the matrix (the continuous phase) and the inclusions remains continuous 
 and the two phases have the same value for Poisson's ratio, the resultant modulus (EJ 
 is given by the simple relationship: 
 
 or 
 
 E (l-c) + E]_c, 
 
 E = E - c (Eq-Eil) 
 
 (1) 
 
 where E is the modulus for the matrix, Ei is the modulus for the included second phase, 
 and c is the volume fraction of the second phase. This gives a _ linear relationship 
 between the modulus of the two end components as indicated in figure 1. 
 
 In general the elastic modulus of a two-phase solid does not vary linearly and the 
 value is always less than that predicted by the linear relationship. Probably the most 
 
 ratio of the two phases are not the same and examine the influence of particle shape. 
 Both Paul [5] and Hashin [6] used the system tungsten carbide-cobalt investigated by 
 Nishimatsui and Gurland [&] and others for verification of their equations, obtaining 
 good agreement with experiment. In later work, Hasselman and Shaffer [7] and 
 Hasselman[9j applied these equations to their measurements on the variation of elastic 
 modulus for zirconium carbide containing graphite. These results are reproduced in 
 figure 1, where it appears that Hashin' s equation, in particular the lower boundary, 
 shows the best agreement. The equations for shear or bulk modulus derived by Hashin |6J 
 can be written in the general form: 
 
 A E, 
 
 E - E - C(E - El , _____*_ ^--^ 
 
 (2) 
 
 where A = B + 1 is a numerical constant. 
 
 For the case where the second phase is porosity, i.e., E± = 0, equation (2) 
 reduces to 
 
 fl - -^-1 
 
 L i+bpJ 
 
 E - E | 1 - j^gj 
 
 (3) 
 
 where P is the porosity. Other simplified theoretical relationships for the dependence 
 of modulus on porosity are 
 
 E = E [l - 1.9P + 0.9P 2 ] 
 
 (4) 
 
 when y (Poisson's ratio) = 0.3 derived by MacKenzie[ 10] for an elastic solid containing 
 spherical holes and 
 
 E 
 
 ~ E o [_ l + P - P^73J 
 
 (5) 
 
 derived by Paul [5] for a solid containing holes of cubic shape. Pores of both shapes 
 can be seen in a ceramic body depending upon their location and the crystal structure. 
 The equation due to MacKenzie has been applied by Coble and Kingery[llJ to their 
 measurements on sintered alumina with excellent agreement. 
 
 42 
 
In addition, the relationship: 
 
 E = E e" k P (6) 
 
 where k is a numerical constant, has been devised on a purely empirical basis by- 
 Murray et al.[l2] , to describe experimental results on the effect of porosity on the 
 modulus of beryllium oxide. A similar relationship for alumina was suggested by 
 Spriggs [13] , and investigated by Knudsen [14] who accumulated all the available data on 
 this material and showed that the exponential relationship gave a very adequate re- 
 presentation out to 40% porosity with k = 4. Spriggs et al.|15] have also used it for 
 magnesia containing up to 25% porosity; their results are reproduced in figure 2. Use 
 of the empirical exponential relationship in equation (6) has been criticized by 
 Hasselmann [16] on the grounds that it does not have any fundamental basis and does not 
 satisfy the boundary condition E = when P = 1, he suggests that equation (3) due to 
 Hashin[6] can be used with equal success and is more flexible. 
 
 In fact the exponential function when expanded takes on a form similar to 
 equation (4) apart from the numerical factor which depends on k. All of the equations 
 (3) through (6; give a fairly adequate representation of the modulus dependence on 
 porosity and it is difficult to make a critical choice among them. Obviously the 
 microstructural variables from specimen to specimen make it virtually impossible to 
 define a practical ceramic in terms of a mathematical model. It is highly probable 
 that the size, shape and location of the pores as well as the total porosity governs 
 the success of any particular equation. 
 
 Other microstructural parameters such as grain size or texture have little or no 
 effect on the elastic modulus. In their studies on alumina and magnesia, Spriggs and 
 Vasilos[l7] found the dynamic modulus to be relatively insensitive to variations in 
 grain size for specimens having the same porosity. Although no specific studies have 
 been made, the major effects of texture (alignment of the grains in an extruded body 
 for example) are to be expected in those materials of non-cubic crystal structure 
 possessing strongly anisotropic elastic constants. 
 
 In conclusion, it may be stated that for purposes of mechanical strength and 
 rigidity the maximum elastic modulus is generally desirable and this is obtained in 
 material of the highest density, in structures where the solid phase is continuous 
 and the pores are closed and spherical. 
 
 3. Anelastic Behavior 
 
 When a stress is applied to a body in the elastic region it does not necessarily 
 come to equilibrium immediately but approaches the total strain value as3' r mptotically 
 with time. This so-called "anelastic" effect [18] becomes particularly important when 
 a periodic stress is applied since the resulting hysteresis loop causes energy to be 
 dissipated by the solid. 
 
 The magnitude of the energy dissipated at a particular temperature, generally 
 referred to as the inter nal friction, depends on the strain amplitude and frequency of 
 the imposed vibrations. With the amplitude constant, the internal friction goes through 
 a maximum when the frequency is varied, as shown in figure 3. The time interval at 
 this critical frequency corresponds to the relaxation time for the particular process 
 responsible for the peak. At the same frequency, the dynamic elastic modulus changes 
 discontinuously, increasing as the frequency is raised through the critical range be- 
 cause the relaxation process then has insufficient time to contribute to the "elastic" 
 strain. This is also illustrated in figure 3. For experimental purposes it is 
 generally more convenient to use the natural frequency of a specimen and to vary its 
 temperature. In this case the internal friction goes through a peak at a characteristic 
 temperature and there is usually an accompanying inflexion in the dynamic modulus versus 
 temperature curve. By studying the displacement of the peak along the temperature scale 
 for different specimen frequencies it is possible to estimate the activation energy for 
 the relaxation process. 
 
 43 
 
Studies of the internal friction spectrum as a function of temperature, strain 
 amplitude and microstructure have provided powerful research tools for understanding 
 internal structure and atomic movements in solids. But internal friction is also 
 important from a practical viewpoint in that it constitutes the damping capacity of a 
 freely vibrating solid; depending on the particular application, one may desire either 
 a very high or a very low rate of damping. In the remainder of this section we will 
 review briefly the effect of microstructure on the internal friction, or damping 
 capacity, -of ceramics. 
 
 The most important microstructural effect is that associated with the presence of 
 grain boundaries. Figure 4 due to Chang [19] shows the difference in internal friction 
 between monocrystalline and polycrystalline alumina as a function of temperature. The 
 internal friction peak at 1100°C is observed only in the polycrystalline material and 
 has been attributed to grain boundary sliding by Wachtman and Maxwell [20] and Chang [19] . 
 Correspondingly Wachtman and Maxwell [20] have shown that the dynamic elastic modulus 
 drops off in value very rapidly at this temperature due also to intergranular relaxa- 
 tion. By measuring the shift in the peak for different frequencies, Chang [19] was able 
 to measure the activation energy for this relaxation process. The value, 200 K cals/mole, 
 agreed fairly well with other measurements obtained from creep studies (see later) and 
 the activation energy for self-diffusion of aluminum or oxygen ions in alumina. The 
 implication was that the internal friction peak corresponded to diffusion controlled 
 grain boundary sliding. 
 
 The grain boundary relaxation peak in alumina has been the subject of extensive 
 investigation, particularly into the effect of purity. Conventional alumina shows the 
 peak around 1100°C, but for high purity alumina it has been reported as high as 
 140U°C[21]. The deliberate addition of impurity lowers the temperature of the internal 
 friction peak at a given frequency considerably. Figure 5, taken from the work of 
 Crandall et al.[22] , shows how the addition of just 1% Si0 2 introduces a new peak around 
 700°C. Similarly, the addition of small amounts of C^Oo or La20o result in the 
 appearance of internal friction peaks at lower temperatures [19,23/ . Also, the addition 
 of 1% MgO has been shown to increase the damping capacity of beryllium oxide at low 
 temperatures [23] . The general interpretation is that impurities tend to enhance 
 grain boundary sliding in ceramic materials, a phenomenon the opposite to that normally 
 observed in metals. The reason for the lower viscosity is not fully understood, it may 
 be associated with the precipitation of a complex or glassy phase in the grain 
 boundaries or it may be associated with the introduction of a non-equilibrium concen- 
 tration of vacancies necessary to maintain electrical neutrality when impurity ions of 
 a different valence are added. Obviously, the damping capacity of ceramics at low 
 temperature is exceedingly sensitive to purity. 
 
 Other microstructural features are known to be responsible for internal friction 
 peaks in solids. These include, stress induced phase tranformations, stress induced 
 ordering, and relaxation phenomena associated with the presence of incoherent inter- 
 faces (inclusions) and the motion of twin interfaces [24J . While these processes have 
 been studied extensively in metallic solids there has been little research in this 
 area on ceramic systems. Chang [23] has suggested that an internal friction peak 
 observed in zirconium hydride around 100°C may be due to twin interface motion. 
 
 Another microstructural effect on internal friction at low temperatures is that 
 associated with defects introduced by plastic deformation. Again this is a field which 
 has been investigated primarily in metals [24] and internal friction peaks due to dis- 
 location motion (the so-called Bordoni peak) have been identified. Of the ceramic 
 materials, sodium chloride has been studied in most detail [25, 26j , although a limited 
 amount of work has been done on lithium fluoride [27] , maenesia [28,29] and alumina [29] . 
 In general the damping increases with the amount of plastic deformation and is observed 
 so long as the dislocations are mobile. Thus procedures to lock dislocations by heat 
 treatment or X-irradiation [25] result in a decrease in the damping capacity. The 
 effect of plastic deformation on the internal friction spectrum of magnesium oxide is 
 illustrated in figure 6. In this material plastic deformation enhances the damping 
 capacity around room temperature. The equivalent dislocation damping peak is not ob- 
 served in alumina until around 1500°C and, as Chang [29] has pointed out, this difference 
 in behavior is a reflection of the relative dislocation mobility in these two solids 
 (see later). In this respect the damping capacity of a single crystal at a certain 
 temperature is influenced by its crystal structure, and similarly the damping capacity 
 may be regarded as a useful indicator as to whether dislocations are mobile in a 
 particular solid at a given temperature or not. 
 
 44 
 
4. Plastic Deformation 
 
 Plastic deformation in crystalline solids at low temperatures (ie.<^0.5Tm) is due 
 to the generation, motion, and multiplication of dislocations. The previous seminar 
 in this series [30j has dealt with some of the more sophisticated aspects of dislocation 
 theory and dislocation interactions in crystalline solids. However, it is important 
 to emphasize here that the properties of dislocations in ceramics are quite different 
 from those in metals. The reasons for this are the short range nature of the bonding 
 forces, the presence of two or more ion species of different size and a more complicated 
 crystal structure. Furthermore, the behavior of dislocations differs from one ceramic 
 material to another and it is dangerous to generalize between them. In this section 
 we shall be concerned with the influence of structural and microstructural elements on 
 the availability and mobility of dislocations and thus on the plastic properties of 
 ceramic materials. 
 
 4.1. Single Crystals 
 
 4.1.1. Crystal Structure and Bond Character 
 
 A dislocation line represents the boundary line between slipped and unslipped 
 portions of a crystal plane. The direction in which slip occurs and the plane selected 
 depend on crystallographic factors, the primary factor being that the slip (or Burgers) 
 vector should correspond to the shortest displacement resulting in crystalline identity. 
 The slip plane is generally the closest packed plane. However, in purely ionic solids 
 there is the additional restriction that displacement should occur in a direction or 
 over a plane which does not cause like ions to be forced into juxtaposition at any 
 stage of the displacement. It is for this reason that magnesium oxide slips in the 
 [110] direction over {110} planes rather than the more densely packed {001} planes [3lJ. 
 For similar reasons the slip direction of caesium chloride type crystals changes from 
 [ill] to [lOO] as the bonding changes from metallic to ionic in nature [32] . Thus bond 
 character is important in determining the slip elements. 
 
 Crystal structure also plays a very important role in determining the dislocation 
 configuration, in general the more complex the crystal structure, the more complex the 
 dislocation configuration. Consider alumina for example; the shortest direction of 
 crystalline identity is a [1120] , but as Kronberg [33] has shown, it is energetically 
 favorable for this displacement to be achieved in a series of four shorter displace- 
 ments where the ions ride through the saddle points in the structure. The passage of 
 one of these shorter displacements, or partial dislocations, results in the formation 
 of a planar stacking fault. Thus dislocations in alumina should consist of four 
 partial dislocations linked by three stacking fault layers. Dislocations in the 
 basal plane of the layer silicates similarly dissociate into four partials and this has 
 been observed directly in talc by the electron transmission technique [34 f 35] • Stacking 
 faults linking partial dislocations have been observed directly in a number of other 
 layer structures[34,35] , and in rutile [36] . In magnesium oxide the structure is rela- 
 tively simple and the dislocations can be thought of as being made by the insertion of 
 two supplementary (110) surfaces of positive and negative ions. The two surfaces are 
 necessary to maintain charge balance and they must remain adjacent to maintain 
 continuity. Any tendency for them to dissociate would force like ions into juxta- 
 position and consequently form a very high energy stacking fault. 
 
 The combined influences of bond character and crystal structure have their great- 
 est effect on the relative mobility of dislocations in various ceramic materials. 
 When a dislocation moves, bonds, ionic and covalent, must be broken and remade and in 
 the case of dissociated dislocations the partials must also be moved along together. 
 While the breaking of bonds due to the movement of dislocations is a relatively low 
 energy process in metals, in covalent solids it can be very high. The situation is 
 further complicated in alumina, for example, by the fact that when the dislocation 
 moves the aluminum ions and oxygen ions in the dislocation core must move in different 
 directions, referred to by Kronberg [33] as "synchro-shear". Only at high temperatures 
 where ion mobility is high and the motions easy to synchronize can dislocations move 
 easily in alumina. It is for this reason that it is necessary to go to extremely high 
 stresses or high temperatures [37,3^,39] (greater than 1000°C) to observe plastic de- 
 formation in single crystals of this material. It also explains the strong temperature 
 dependence of the yield strength of alumina [39] . In the case of rutile the movement 
 of dislocations requires the rupture of predominantly covalent bonds and this probably 
 explains the inability of this material to deform plastically below 600°C [36] . By 
 contrast the predominantly ionic nature of the bond and the relative simplicity of the 
 dislocation configuration in marnesium oxide makes it possible to deform this material 
 even at liquid nitrogen temperature. 
 
 45 
 
As mentioned earlier, the difference in dislocation mobility between alumina and 
 magnesia is reflected by their relative damping capacity [29] , it is also responsible 
 for many of the other contrasting features of their mechanical behavior as we shall 
 discuss in the following sections. Similarly, the effects of microstructure on the 
 mechanical properties of other ceramic materials at a given temperature are conditioned 
 by the relative ease with which dislocations can move. 
 
 It is important to realize that the conventional yield strength of a solid 
 corresponds to a stress level at which large numbers of dislocations are moving with 
 quite a high velocity. The plastic strain rate of a crystal may be written as: 
 
 k - n b v (7) 
 
 where n is the number of mobile dislocations per unit area, a factor which increases 
 rapidly due to dislocation multiplication [40J ; b is the Burgers vector; v is the 
 average velocity of the dislocations, a factor which is very sensitive to the local 
 stress. Direct measurements of the velocity-stress dependence by Johnston and 
 Gilman [41] have shown that the velocity of dislocations in lithium fluoride increases 
 approximately as the twenty-fifth power of the stress. Macroscopic yielding occurs 
 when £ , equation (7) , is approximately equal to the imposed strain rate of the testing 
 machine. With sensitive techniques however, it is possible to detect plastic deforma- 
 tion well below the conventional yield strength in the so-called microstrain region. 
 In particular etch pit techniques [42] can be used to measure the stress required to 
 get dislocations moving. This stress is defined as the microscopic yield stress. 
 
 Thus, to summarize, the plastic properties of a solid depend critically upon the 
 number of dislocation sources (n) and the mobility of dislocations (v). Dislocation 
 mobility is influenced fundamentally by bond character and crystal structure. All of 
 these parameters must be borne in mind when considering the extra effects due to 
 microstructure. 
 
 4.1.2. Solid Solution and Precipitation Hardening 
 
 First, we discuss the effects due to impurities. Impurities can be present either 
 in solid solution or in the form of precipitate particles and can act in two main ways 
 to change the plastic properties of a crystal. First, they can lock dislocations in 
 place, preventing them from participating in plastic flow and thus reducing the initial 
 value of n in equation (7); and second, they can impede the motion of dislocations 
 through the crystal lattice and thus reduce v in equation (7). Either way the crystal 
 increases in strength. 
 
 The most direct example of dislocation locking by impurity is that demonstrated 
 by Stokes [43] on magnesium oxide single crystals. He showed that crystals specially 
 treated to contain only "aged" or "grown in" dislocations supported stresses as high 
 as 140,000 psi in a purely elastic manner without yielding. In this case all of the 
 dislocations were immobilized and n in equation (7) was zero at all stress levels. 
 On the other hand, crystals containing "fresh" dislocations (ie. dislocations generated 
 at the surface at room temperature and therefore free from any contamination by 
 impurity) deformed plastically at a yield stress of approximately 10,000 psi. The 
 "fresh" dislocations could move and multiply fast enough at this stress level for the 
 plastic strain rate (£ ) to keep up with the testing machine. Similar differences in 
 mechanical behavior between crystals containing "fresh" and "aged" dislocations, 
 although on a less spectacular scale, have been noted in lithium fluoride by Gilman 
 and Johnston [2] . 
 
 "Grown in" dislocations in magnesium oxide have been observed directly by the 
 electron transmission technique and are found to have precipitate particles strung all 
 along their length [44] as illustrated in figure 7. The particles have been identified 
 as zirconium dioxide [45] , although considering the purity of the crystals there are 
 likely to be other oxides precipitated on the dislocations too. The mechanism by 
 which these particles lock the dislocations is not entirely understood, but it 
 probably involves an elastic interaction between the impurity ions and the stress 
 field of the dislocations. 
 
 46 
 
One of the characteristic features of impurity locking is that it represents a 
 metastable condition. As soon as a single dislocation escapes from its impurity- 
 environment it can move and multiply rapidly and the stress level needed to sustain the 
 imposed strain rate falls. Such catastrophic drops in strength at the onset of yielding 
 have been observed in magnesium oxide [43J • 
 
 The great difference in mechanical behavior between these two conditions in 
 magnesium oxide has proved to be extremely useful in understanding the origin of brittle 
 fracture in polycrystalline material. We shall return to this point later in connection 
 with table 2. 
 
 It is now generally agreed that the permanent strengthening associated with 
 impurities must arise from an increased resistance to dislocation motion through the 
 lattice, ie., by decreasing the velocity v for a given stress [46]. Local fluctuations 
 in the internal stress field due to the presence of impurity ions impede the dislocations 
 and cause the strengthening. Although the exact differences between solid solution and 
 precipitation hardening are by no means well understood, the stresses due to a coherent 
 precipitate are generally regarded as a much more effective impediment than those due 
 to impurities in solid solution. However, the situation is further complicated in ionic 
 solids by the requirement that electrical neutrality must be maintained at all times and 
 the valency of impurity ions going into solid solution must be taken into consideration. 
 There are, therefore, at least three conditions to be considered, (i) simple solid 
 solution with ions of the same valency, (ii) simple solid solution with ions of different 
 valency, (iii) precipitation. 
 
 When the valency of the added impurity ion is the same as that of the ion it is 
 replacing, simple solid solution strengthening is observed. This has been observed in 
 silver chloride, for example, hardened by the addition of silver bromide [47] and in 
 potassium chloride hardened by the addition of potassium bromide [48] . The stress 
 strai^ characteristics of silver chloride-sodium chloride alloys |_49J are compared 
 with the phase diagram in figure 8 and simple solid solution strengthening is observed 
 at the two extreme ends (ie., up to 10 mole percent and above 85 mole percent sodium 
 chloride) of the composition scale. 
 
 When the valency of the added impurity ion going into solution is different from 
 the ion it is replacing, then an equivalent number of vacancies must be introduced into 
 the host lattice to maintain electrical neutrality. This condition has a remarkable 
 strengthening effect. The influence of divalent alloying elements on the mechanical 
 properties of sodium chloride was studied extensively in Germany in the early 1930' s 
 and this work is reviewed in the book by Schmid and Boas [50] . While the solubility 
 of divalent cations is very restricted, marked hardening is observed for additions in 
 the range 10 -6 to 10 -4 mole fractions. Thus, 0.02% calcium chloride in" sodium chloride 
 raises the strength fivefold. Similarly, the addition of minute quantities of magnesium 
 fluoride to lithium fluoride result in a tenfold increase in strength [51] . Eshelby 
 et al [52] have proposed a mechanism to account for this strengthening in which they 
 take into consideration the electrostatic attraction between charged dislocations and 
 the charged vacancies, so that the dislocation lines become surrounded by a vacancy 
 cloud which restricts their motion. Other evidence concerning the role of vacancies 
 and point defects in the strengthening of ionic solids is reviewed in the paper by 
 Pratt [53] . 
 
 There are very few clear cut examples of precipitation hardening in ceramic systems. 
 The best example to date is that observed in the middle composition range of the sodium 
 chloride-silver chloride system illustrated in figure 8. Sodium chloride-silver chloride 
 alloys show a miscibility gap between 10% and 60% sodium chloride at room temperature 
 and in this same range the strength increases by 50 to 100-fold over that of the end 
 components [49]. However, even in this system rules of precipitation hardening are 
 not strictly followed in that solution heat-treated crystals are equally as strong as 
 fully precipitated crystals, and it is not certain whether internal stresses due to 
 co-precipitation of the two equilibrium phases are the true source of hardening or not. 
 
 47 
 
As a result of their studies on the effect of heat treatment and temperature on 
 the strength of commercial magnesium oxide crystals, Gorum et al. [54], May and 
 Kronberg L55] and Stokes [56] concluded that a precipitation hardening type of mechanism 
 was occurring. Crystals in the as-received (fully precipitated) condition containing 
 many "fresh" dislocation sources were approximately twice as strong as those annealed 
 above 1200°C, as shown in fip-ure 9 curve A; however, the higher strength could be re- 
 stored by a subsequent anneal around 800°C, figure 9 curve B. Presumably the anneal 
 above 1200°C dissolved the precipitate particles initially present into solid solution 
 making it easier for the dislocations to move at room temperature. The subsequent 
 anneal at 800°C forced them to reprecipitate again. Unfortunately, this work is 
 currently lacking direct experimental evidence concerning the nature and distribution 
 of the second phase. 
 
 Deliberate alloying of magnesium oxide single crystals with small quantities of 
 impurity can lead to remarkable changes in strength, although the strengthening 
 mechanism, i.e., whether due to solid solution, precipitation or point defect hardening, 
 has not yet been identified. Satkiewicz [57] showed that single crystals doped with 
 0.5% Cr20o raised the compressive strength fivefold to 80,000 psi, a value which 
 dropped by one-half on subsequent vacuum annealing. Liu et al [58] have found a 
 similar strength (80,000 psi) for magnesia containing a few mole percent of MnO, and 
 a strength of 40,000 psi for alloys containing only five mole percent NiO. In the 
 latter case microscopic studies indicate that the nickel ions are in solid solution. 
 There is a need for further work in this area with emphasis on the control of 
 stoichiometry, and the manipulation of microstructure through heat treatment based on 
 complete phase diagrams. 
 
 4.2. Polycrystals 
 
 Next, we consider the effect of grain boundaries on the plastic deformation of 
 ceramic materials. As was pointed out many years ago by von Mises [59] and by 
 Taylor [60] , for a fine grained polycrystalline solid to undergo plastic deformation 
 each of the individual grains must be capable of a perfectly general change in shape. 
 To satisfy this condition, each of the crystalline grains must possess five independent 
 slip systems. If not, then voids are likely to develop within the solid where the 
 individual grains cannot conform to the change in shape of their neighbors. Groves 
 and Kelly [61] have recently examined the observed crystallographic slip systems for 
 a number of common ceramic materials to determine whether they allow the- required 
 general change in shape or not. Their results, reproduced in Table 1, are most inter- 
 esting. They "find that none of the common ceramic materials is capable of a great 
 amount of plastic deformation at low temperatures (we shall discuss the high tempera- 
 ture case later). 
 
 TABLE 1. The number of independent slip systems for 
 s ome common ceramic crystal struc tures 
 
 Structure 
 
 NaCl (Low Temperatures) 
 (eg. MgO) 
 
 NaCl (High Temperatures) 
 (eg. MgO) 
 
 Hexagonal 
 
 (eg. Graphite, AI2O3 ) 
 
 CsCl 
 
 CaF2 (Low Temperatures) 
 tag. U0 2 ) 
 
 CaF2 (High Temperatures) 
 
 Ti0 2 
 
 Crystallographic 
 Slip Systems 
 
 {110} <110> 
 
 {110} <110> and 
 {001} <110> 
 
 {0001} <1120> 
 
 {100} <010> 
 {001} <110> 
 
 {001} <110> and 
 
 {110} <110> 
 
 {101} <10T> and 
 
 {110} <001> 
 
 Number of 
 Independent Systems 
 
 48 
 
One of the consequences of this failure to satisfy the von Mises criterion is 
 demonstrated by the marked effect of grain size on the plastic properties of ionic 
 solids at low temperatures. Figure 10 reproduces stress strain curves obtained on 
 polycrystalline sodium chloride at room temperature [62] . As can be seen, decreasing 
 the grain size has a comparatively small effect on the proportional limit, but a very 
 large effect on the rate of work hardening. By the time there are three to five grains 
 in the cross- section, the rate of work hardening has increased tenfold over that of 
 the cubic orientation single crystal and for the finest grain size tested (.035 mm) it 
 has increased thirtyfold over the Single crystal. Similar effects have been found in 
 polycrystalline silver chloride [63] and lithium fluoride [64] at low temperatures. 
 
 These observations may be interpreted as follows: 
 
 (i) Since "grown in" sources are not completely immobilized in these ionic solids 
 there are plenty of sources for slip over {.llOj planes. The stress to start these dis- 
 locations moving is relatively insensitive to grain size. In fact the slight dependence 
 noted in figure 10 would probably disappear with the use of higher sensitivity micro- 
 strain techniques. 
 
 (ii) As slip propagates and the whole polycrystalline matrix attempts to deform 
 plastically, constraints develop at the grain boundaries due to the fact that there are 
 only two independent slip systems (table 1). Consequently the material as a whole can- 
 not deform plastically and hardens at a rate almost determined by the elastic constants. 
 
 (iii) As the stress increases the constraints can be_relaxed somewhat by local 
 slip on additional systems. In particular slip on -{j001}<110> has been observed in the 
 vicinity of grain boundaries in polycrystallire lithium fluoride at room temperature as 
 shown in figure 11. This additional slip permits the small amount of plastic deformation 
 observed in the stress strain curves of figure 10. Unfortunately the applied stress 
 required to promote general slip throughout a grain on this -COO])- <110> system is far 
 too high, for example in sodium chloride it is four times [65] and in lithium fluoride 
 at least eight times [66] the stress to promote slip on the -(110} <110> system at room 
 temperature. Consequently the material as a whole cannot deform plastically by any 
 great amount at least until the applied stress reaches this level. 
 
 (iv) The actual rate at which the stress increases, ie. the rate of work hardening, 
 is dependent on the grain size since the smaller the grain size the greater the grain 
 boundary surface area and the greater the volume of constrained material wherein shear 
 cannot take place. The exact relationship between grain size and the rate of work 
 hardening under these conditions has neither been considered theoretically nor deter- 
 mined experimentally. 
 
 The situation in magnesium oxide is even worse than in the simple halides. The 
 stress to promote slip on the {001} <110> system at room temperature is approximately 
 one hundred times higher than that to cause slip on the £110} <110> system [67] so that 
 even local deformation of the kind illustrated in figure 11 cannot be expected until 
 extremely high stresses are reached. Thus, polycrystalline magnesium oxide shows 
 virtually no plastic deformation at room temperature even though dislocations are quite 
 mobile and the equivalent single crystals ductile. At higher temperatures the difference 
 in stress level for slip on the two systems is reduced and at 1000°C is down to a 
 factor of ten, equivalent to the situation in lithium fluoride at room temperature. A 
 slight amount of plastic deformation has been observed in compression in this tempera- 
 ture range [67J . 
 
 Again it must be emphasized that this discussion does not really apply to the low 
 temperature mechanical behavior of ceramic materials in which dislocations are immobile 
 (eg. Al 2 0o, TiOj, TiC, etc. at room temperature). In these materials the lattice 
 resistance to dislocation motion is so high that the cohesive strength of the crystal- 
 line planes is exceeded before any plastic deformation is possible. The extent to 
 which it may apply at high temperatures when these materials become plastic will be 
 considered later in section 6. 
 
 49 
 
5. Brittle Fracture 
 
 In most of the preceding sections attention has been drawn to the plastic 
 properties of ceramic materials, yet the fact remains that the most notorious mechanical 
 property of a ceramic, particularly at low temperatures, is its brittleness. Ine 
 strength of a ceramic is always limited by brittle fracture. In this section we shall 
 examine some of the aspects of brittle fracture in ceramics and shall show that in 
 many instances the fracture strength can be related to the plastic properties described 
 so far. 
 
 It is well known that the fracture strength of a brittle material falls far short 
 of the theoretical strength (E/10) expected from simple estimates of interatomic forces. 
 Equally familiar is the work of Griffith [68] who showed that the critical tensile 
 stress (cr) to propagate a crack of length c is given by; 
 
 (8) 
 
 where E is Young's modulus and X the surface energy of the fractured faces. It is 
 important to realize that equation (8) applies specifically to propagation in a purely 
 elastic medium and assumes the pre-existance of cracks. It was for these reasons that 
 Griffith was so successful in applying equation (8) to the strength of glass fibers, 
 since, in glass, surface flaws are nucleated spontaneously by chemical reaction with the 
 environment. 
 
 The nucleation, growth, and propagation of brittle fracture in crystalline solids 
 is a vastly more complicated phenomenon. In the absence of pre-existing surface or 
 internal defects a crack nucleus must be generated in some way and it has now been 
 clearly demonstrated in a number of ceramic materials that crack nucleation can occur 
 as a direct consequence of the limited amount of plastic deformation which precedes 
 fracture [30,69]. However, the cracks nucleated by these various mechanisms are often 
 too small to propagate catastrophically under the existing applied tensile stress and 
 either the stress must increase or the cracks must grow to reach the critical dimension, 
 Again it has been found that crack growth is assisted by local plastic deformation 
 [70,71]. When finally the crack reaches the critical dimension the condition for 
 propagation is dictated by a modified form of the Griffith equation due to Orowan L72J ; 
 
 cr = /e (X+X p ) (9) 
 
 where X represents the energy consumed by plastic deformation in the highly stressed 
 region ihead of the propagating crack. This term Xp is particularly important since 
 its magnitude determines whether the solid is ultimately brittle or not. When Xp is 
 large a crack may be stalled for an indefinite period but when 6 p is small propagation 
 may proceed without resistance. The value of Xp is strongly dependent on the plastic 
 properties of the solid. For most ceramic materials Xp is inherently small and they 
 are naturally brittle materials. Since much cannot be done to remedy this latter 
 situation most of the attention in ceramics has been focussed on the early stages ol 
 fracture. In particular fracture nucleation has been studied intensively and is 
 probably the stage where improvements in the fracture characteristics are most likely 
 to be implemented. Next, we shall discuss the role of structure and microstructure 
 in the nucleation of brittle fracture in ceramics. 
 
 50 
 
5.1. Crack Nucleation Due to Slip at Grain Boundaries 
 
 Crack nucleation has been studied most extensively in magnesium oxide. The 
 essential feature is that cracks nucleate wherever groups of dislocations are obstructed 
 either by other slip bands [73,74] or by grain boundaries [75,76,77,78]. The primary 
 reason why these observations can be made so readily in magnesium oxide is that shear 
 occurs at room temperature over flat {llO} planar surfaces in discreet slip bands. 
 Thus the deformation is distributed very inhomogeneously and when a slip band is 
 blocked by a microstructural barrier, such as a grain boundary, the stress concentration 
 due to the dislocation pile up [79, #6] cannot be dissipated by secondary slip in the 
 surrounding material. Instead a crack forms. Figure 12 shows a cleavage crack 
 generated where a slip band intercepts the grain boundary in a magnesium oxide bi- 
 crystal under compression. Under tension such a cleavage crack switches into the inter- 
 granular surface and propagates immediately for fracture [78] • 
 
 There are two possible ways to prevent the crack nucleation event recorded in 
 figure 12. Either slip within the grains should be made more homogeneous to relax the 
 local stress concentration at the tip of the dislocation pile up or slip should be 
 avoided altogether. 
 
 Efforts to make shear homogeneous have indeed resulted in a considerable improve- 
 ment in the ductility of magnesium oxide single crystals [74] but similar attempts 
 with bi-crystals and polycrystalline material have not been successful [78] . There 
 are a number of reasons for this but the most general and important one for the 
 present discussion arises from the fact that there are only two independent slip 
 systems as indicated in table 1 [6l] . Even when homogeneous slip does occur the high 
 stresses developed in the boundary regions due to the incompatability of the grains 
 eventually exceeds the intergranular strength at certain points causing cracks to 
 open up and the specimens to fracture. It is significant that the source of fracture 
 under these conditions is always intergranular [62] . Thus in polycrystalline sodium 
 chloride and lithium fluoride at room temperature, where slip is homogeneous and there 
 is some measurable plastic deformation (see figure 10) brittle fracture always 
 originates from an intergranular source. 
 
 On the basis of these observations Stokes and Li t62,78] have concluded that the 
 ability of magnesium oxide, or any other ceramic material for that matter, to slip at 
 low temperatures is in fact an undesirable feature, and they have shown how the 
 fracture strength of fully dense magnesia may be improved when steps are taken to 
 eliminate slip. 
 
 Table 2 summarizes recent results comparing the strength of polycrystalline 
 magnesia in the presence and absence of active slip sources [78] . The tensile fracture 
 strengths quoted in the right hand column represent the strength when "fresh" dis- 
 location sources (introduced by the simple expedient of sprinkling the surface with 
 fine silicon carbide powder [42] ) are known to be present; the left hand column 
 represents the strength when all possible precautions have been taken to remove 
 surface dislocations by a chemical polish. It is instructive first to compare the 
 fracture strength of bi-crystals with the yield strength of single crystals under the 
 two extreme conditions discussed earlier in connection with dislocation locking 
 (section 4.1). The extremely high fracture strength of the bi-crystal obtained in 
 the absence of slip (compare results 1 and 3) and the close agreement between the 
 fracture strength and yield strength when slip sources are present (compare results 
 2 and 4) indicate that it is not the presence of the grain boundary per se but the 
 interaction of slip with it which is responsible for the low fracture strength of the 
 bi-crystal in result 4. 
 
 51 
 
TABLE 2. Tensile strength of magnesium oxide in the absence and 
 presence of "fresh" surface dislocations 
 
 Result 
 
 10 
 
 11 
 
 12 
 
 Material 
 
 Single Crystal 
 
 Bi-Crystal 
 
 Fully Dense (100$), As-received 
 Hot Pressed Polycrystalline 
 (Grain size 20yu ) 
 
 Fully Dense (100%), Annealed, 
 Hot Pressed Polycrystalline 
 (Grain size 75 /t ) 
 
 99.7% Dense, As-received, 
 Hot Pressed Polycrystalline 
 (Grain size 30/u, ) 
 
 99.7% Dense, Annealed, 
 
 Hot Pressed Polycrystalline 
 
 (Grain size 50 u,) 
 
 Tensile Strength 
 
 "Fresh" 
 Dislocations 
 ABSENT 
 
 HO, 000 psi 
 
 110,000 psi 
 
 28,000 psi 
 
 19,500 psi 
 
 12,000 psi 
 
 11,500 psi 
 
 "Fresh" 
 Dislocations 
 
 PRESENT 
 
 10,000 psi 
 
 8,000 psi 
 
 18,500 psi 
 
 15,000 psi 
 
 9,000 psi 
 
 12,500 psi 
 
 52 
 
When similar care is taken to eliminate "fresh" dislocations from the surface of 
 fully dense (100$) fine grained polycrystalline magnesia the tensile strength can be 
 increased markedly, exceeding 30,000 psi in some cases. Again the average value 
 (26,000 psi, result 5) for such specimens drops down to 18,500 psi when dislocations 
 are reintroduced into the surface. It is believed that this remarkable surface 
 sensitivity is due to the fact that fracture originates in these fully dense poly- 
 crystalline magnesia specimens by the slip dislocation mechanism of figure 12. 
 
 Obviously this discussion of slip interaction with grain boundaries applies only 
 to those solids in which dislocations can move easily at low temperatures. The extreme 
 sensitivity to surface condition described in the previous paragraph is not likely to 
 be found in materials such as alumina or rutile. The effect of surface damage on 
 these materials will be discussed later. 
 
 5.2. Effect of Porosity and Grain Size 
 
 When just a slight amount of porosity is present the magnitude of the difference 
 in strength in Table 2 due to the presence or absence of surface dislocation sources 
 is much less. For example, annealing the fully dense hot pressed material at 2000°C 
 causes grain growth and the appearance of slight residual porosity in the grain 
 boundary interface. The strength of polished material is then reduced to 19,500 psi 
 (result 7) and drops further only by one quarter (to 15,000 psi, result 8) when surface 
 dislocations are introduced [78], In more conventional material of lower density 
 (99.7$) the tensile fracture strength is much lower (12,000 psi) and the value is then 
 apparently independent of surface treatment (results 9 through 12). These observations 
 have been interpreted by assuming that the pores themselves provide stress concen- 
 trations which either initiate slip or nucleate intergranular failure directly. Thus, 
 porosity in excess of 0.1 to 0.2$ tends to override any effects due to surface dis- 
 locations and the brittle fracture strength is more dependent on the amount and dis- 
 tribution of porosity. 
 
 • 
 
 It has long been realized that the strength of ceramics is sensitive to porosity 
 and that the greatest changes occur following small departures from theoretical 
 density. Ryshkewitch [81] and Duckworth [82J first demonstrated that the transverse 
 bend strength (S) of alumina, zirconia, and silicate porcelain decreased exponentially 
 with porosity as in equation (10); 
 
 S = S e _b P (10) 
 
 The form of this equation should be compared with equation (6). It is found 
 experimentally that the value of k is generally one half the value found for b. A 
 similar dependence has been established for thoria [83] , uranium dioxide [84] , and 
 magnesia t85] • While the empirical relationship holds quite well when the porosity 
 exceeds 0.3$, for values less than this the strength is determined by other variables. 
 In particular equation (10) makes no allowance for the distribution and location of 
 pores. It is to be expected that the stress concentration effect will depend critically 
 upon whether the pores are interconnected (open) or isolated (closed) in any particular 
 intergranular region at low porosity. 
 
 Similarly it is well known that decreasing the grain size increases the strength 
 of a ceramic material. Knudsen [83] has suggested that the combined effects of grain 
 size (d) and porosity (p) can be represented by equation (11); 
 
 S = S d- a e" b P (11) 
 
 The value of a varies from 1/2 to 1/3 for a variety of materials and the equation has 
 been found adequate to describe results of thoria [83] , uranium dioxide [84J , 
 magnesia [85] and alumina [22,85,86] and for beryllium oxide [87] with a =■ 1. 
 
 53 
 
Unfortunately most of this data on the transverse bend strength of ceramics as a 
 function of grain size and porosity has been obtained on specimens of variable surface 
 perfection. By surface perfection here we do not necessarily mean the presence or 
 absence of surface dislocations considered earlier with respect to magnesia, but gross 
 imperfections in the form of intergranular or cleavage ruptures generated by mechanical 
 preparation techniques. Surface perfection is extremely important, for the presence 
 or absence of flaws determines to a great extent the subsequent mechanical behavior and 
 certainly contributes to the statistical nature of the strength of ceramics L»«J« 
 Harrison [89] has emphasized how surface flaws and damage introduced during grinding 
 and lapping operations can lower the strength of polycrystalline magnesia. It follows 
 that the empirical relationship of equation (11) may well represent the stress required 
 to propagate existing surface defects through the microstructure rather than the stress 
 to initiate cracks. In this case when a - 1/2, equation (11) corresponds to the 
 Griffith equation (8) with the condition that c is related to the grain size d in some 
 simple manner. In order to determine the effects of porosity and grain size system- 
 atically much more attention should be paid in the future to surface condition. 
 
 It is not easy to anticipate what the fracture strength dependence on grain size 
 will be in the absence of surface flaws. Certainly it will depend on whether dis- 
 locations are mobile or not. When dislocations are mobile then the grain boundary 
 interactions discussed in the previous , section are important and the fracture strength 
 dependence on grain size may follow a d s relationship of the type developed by Petch 
 and Cottrell [.90] for brittle metals. When dislocations cannot move the fracture 
 strength will be limited by internal stresses developed during firing and heat treatment. 
 The internal stresses may be added to the applied stress and will be particularly severe 
 in the boundary regions of anisotropic materials. All in all it seems reasonable to 
 anticipate that the greatest low temperature fracture strengths will be obtained in 
 materials of high density, fine grain size, perfect surface condition, in which dis- 
 locations cannot move. It is encouraging to note that transverse strengths in alumina 
 in excess of 100,000 psi can be obtained under these conditions. 
 
 6. High Temperature Deformation and Creep 
 
 At elevated temperatures, two factors become important to change the dependence of 
 mechanical properties on microstructure. First, dislocations become more mobile on 
 existing slip systems and new slip systems become possible, and second, the diffusion 
 of point defects is enhanced to the point where they begin to contribute to the 
 deformation. 
 
 6.1. Plastic Deformation and Ductile Fracture 
 
 The increased mobility of dislocations at high temperatures is reflected by a 
 further drop in strength of single crystals of materials such as magnesium oxide [67J 
 which are already plastic at low temperatures. It is also responsible for the onset 
 of plasticity at reasonable stress levels in single crystals of materials like alumina 
 [37,38,39], rutile [36,91], and titanium carbide [92] which are not plastic at low 
 temperatures. For the most part these newly plastic ceramic materials slip on simple 
 systems and the restrictions on polycrystalline ductility discussed earlier still 
 apply. 
 
 The possibility of slip on multiple systems has more interesting consequences 
 particularly for materials having the rock salt structure. As indicated in Table 1, 
 slip becomes possible over -{100} planes in addition to the £110$; planes at high 
 temperatures. The occurrence of {100} slip contributes an additional three independent 
 slip systems, making a total of five, thereby satisfying the condition for polycrystalline 
 ductility. Stokes and Li [62] have shown that polycrystalline sodium chloride undergoes 
 appreciable extension above 150°C, the temperature at which "wavy" or multiple slip is 
 first observed. Under these conditions constraints do not develop in the grain boundary 
 region and brittle fracture does not occur, instead the specimens extend continuously 
 and neck right down to a point, giving a type of ductile fracture. The influence of 
 grain size and porosity on ductile fracture has not been studied in sufficient detail 
 yet to allow any conclusions to be drawn from the behavior of sodium chloride. However, 
 similar work on silver chloride [63] in the temperature range where it exhibits wavy 
 slip has shown that grain size has little or no effect on the rate of work hardening, 
 again consistent with the fact that grain boundary constraints have been completely 
 relaxed. 
 
 54 
 
6.2. Creep and High Temperature Fracture 
 
 Unfortunately, the temperature range where a multiplicity of slip systems becomes 
 available in most oxide ceramics is so high that additional complications come into 
 play and the occurrence of plastic deformation by the simple movement of dislocations 
 is never observed. Deformation at elevated temperatures is always enhanced by the 
 diffusion of point defects and by the onset of viscous sliding at grain boundaries. 
 The diffusion of vacancies or interstitial ions contributes to each of the three basic 
 processes considered responsible for creep; dislocation climb, vacancy migration under 
 stress, and grain boundary sliding. These will be described briefly in turn. 
 
 Dislocation climb occurs when vacant lattice sites condense on or escape from edge 
 dislocations causing them to be displaced vertically in a direction perpendicular to 
 the slip plane. The climb process permits unlike dislocations to move together and 
 annihilate and it also permits dislocations to detour around obstacles in the slip 
 plane. Thus, dislocations trapped in a pile-up against obstacles such as sub-grain 
 or grain boundaries can escape by climb and rearrange themselves, the relaxation of the 
 back stress enables the dislocation source to resume operation and deformation continues. 
 When the rate of dispersion of the dislocations is approximately equal to the rate at 
 which they are pumped into the pile-up a steady state creep rate is established. The 
 rate controlling step in this process is vacancy diffusion, a fact which has been well- 
 established for all metals for which accurate data is available [93] . In a derailed 
 analysis of the climb mechanism, Weertman [94] has shown that the creep rate ( £ ) 
 varies with the applied stress (o~) and temperature (T) according to the following 
 relationship; 
 
 where U is generally the activation energy for self diffusion. In ceramics the pre- 
 sence of two ion species having different activation energies for self diffusion and 
 the possibility that diffusion may occur in pairs makes the interpretation of U more 
 difficult. 
 
 The remaining creep processes do not involve the motion of dislocations and apply 
 specifically to polycrystalline material. In vacancy migration under stress , deforma- 
 tion results from diffusional flow within each crystal away from those boundaries 
 where there is a high local compressive stress towards those boundaries having a high 
 local tensile stress. This is generally referred to as Nabarro-Herring type creep and 
 it has been estimated by these authors [95,96] that the creep rate is related to the 
 stress, temperature and grain size (d) by; 
 
 where D is the diffusion coefficient and 
 
 D = D e- U / KT (14) 
 
 It should be noted that the relationship for t in (13) differs from that in (12) by the 
 power of the stress dependence and by the appearance of a grain size term. The linear 
 relationship of e and <r in equation (13) gives rise to a viscous type of flow, at a 
 rate determined by vacancy diffusion. 
 
 55 
 
The exact mechanism of the third contributor to high temperature creep, grain 
 boundary sliding, is not known. It has been shown that the shear strength of grain 
 boundaries in ionic materials can fall off catastrophically at high temperatures L97.98J 
 Whether this increased viscosity in the grain boundary region is due to the presence of 
 an impure glassy phase or whether it is controlled by vacancy diffusion or dislocation 
 motion through the disordered boundary region has not been determined. It is important 
 to note that the creep rate due to this process is also roughly proportional to the 
 applied stress but since it is dependent on the grain boundary surface area per unit 
 volume it varies inversely as the grain size, Le. 
 
 £oC 
 
 d 
 
 (15) 
 
 Obviously, all three of these mechanisms occur together, to a certain extent, during 
 high temperature creep. It is possible to distinguish which is the controlling 
 mechanism by measuring the dependence of the creep rate on temperature, stress and 
 grain size as may be appreciated by comparing equations (12) (13) and (15). inis 
 procedure is generally followed by workers in the field. There is comparatively little 
 systematic work on the effect of structure and microstructure on the creep of ceramics. 
 Probably the earliest work on this subject is that by Wygant L99J who compared the 
 creep rates of different ceramic materials. Data for materials of similar grain size 
 or porosity at the same temperature and stress level are almost impossible to obtain, 
 but Table 3, compiled by Kingery [4] gives some indication of the effect of crystal 
 structure when most of these other variables have been fixed. 
 
 TABLE 3 
 Comparison of torsional creep rate 
 for different polycrystalline ceramic materials 
 
 Material 
 
 Creep Rate at 1300°C 
 1800 psi (in/in/hr.) 
 
 A1 2 3 
 
 0.13 
 
 x 10" 5 
 
 Zr0 2 
 
 3.0 
 
 x 10"5 
 
 MgO (hydrostatic pressed, 
 2% Porosity) 
 
 3.3 
 
 x 10-5 
 
 MgO (slip cast, 12$ porosity) 
 
 33.0 
 
 x 10"5 
 
 BeO 
 
 30.0 
 
 x 10" 5 
 
 Th0 2 
 
 100.0 
 
 x 10~5 
 
 The most detailed studies of the effect of microstructure have been conducted on 
 alumina, although even here the agreement amongst workers is varied. Tests have been 
 performed on materials of different purity, porosity and grain size with different 
 methods of loading. However, an attempt to interpret the results in a logical manner 
 will be made with the help of Table 4. First, we compare the work of Rogers et al JIOOJ 
 and Kronberg [39] on single crystals in the temperature range 900-1700°C, (results 1 
 and 2 in Table 4). Although these tests were performed under different loading con- 
 ditions, the activation energy for flow in both cases is approximately the same, 
 85 Kcal/mole. Since in Kronberg' s tests the specimens were known to be deforming by 
 simple slip on the basal plane, this may be regarded as the activation energy to 
 initiate dislocation motion, i.e., to operate the synchro-shear mechanism [33] in 
 single crystals. 
 
 56 
 
At higher temperatures (above 1800°C) Chang LlOl] found single crystals to exhibit 
 steady state creep at a rate dependent upon stress to the power 4.5 as in equation (12), 
 indicating that it was controlled by the dislocation climb mechanism (result 3). The 
 activation energy, 180 Kcal/mole, for dislocation climb, compares fairly well with the 
 activation energy for diffusion of either the aluminum or oxygen ion determined by other 
 means. The steady state creep rate of the alumina crystals was reduced by four orders 
 of magnitude with the addition of 2% Cr20o as shown in figure 13, but the activation 
 energy for the process remained unchanged. The interpretation here is that the impurity 
 is restricting motion of the dislocations over the slip plane, but does not change the 
 rate at which they can climb. 
 
 With the introduction of grain boundaries there is an increase in the creep rate 
 and a change in the creep mechanism from one controlled by dislocation climb to vacancy 
 migration under stress. Studies on high density, fine grained alumina (Lucalox) by 
 Warshaw and Norton [102] and Folweiler [103] illustrate this point. Both find the 
 creep rate to vary linearly with the stress between 1500°C and 1800°C and the activa- 
 tion energy has been measured to be 130 Kcal/mole (results 4 and 5). Similarly 
 Chang [19] has also found a viscous behavior although with a higher activation energy 
 (result 8) in this temperature range. Paladino and Coble [105] have taken these 
 results and estimated the diffusion coefficients (D in equation (13)) using the exact 
 form of the Nabarro-Herring [96] equation. They have then compared them with the self- 
 diffusion coefficient for the aluminum ion determined by independent means. The 
 excellent agreement illustrated in figure 14 confirms that the Nabarro-Herring mechanism 
 is operating and indicates that the diffusion of aluminum ions is the rate controlling 
 process. A similar correlation has now been established between the beryllium ion 
 diffusion coefficient and the creep diffusion coefficient for beryllia [10$, 106], and 
 between the magnesium ion diffusion coefficient and the creep diffusion coefficient 
 for magnesia at low stresses [107] . 
 
 Folweiler [103] studied the effect of grain size on the creep rate of Lucalox 
 alumina and found a dependence inversely proportional to the square of the grain 
 diameter, again consistent with the Nabarro-Herring theory as can be seen from 
 equation (13). Thus, large grained material has a higher creep resistance than fine 
 grained material. 
 
 At higher temperatures (1800°C-1900°C ) and larger grain sizes the creep rate of 
 alumina was found to increase at a rate more rapid than predicted by the vacancy 
 migration theory (results 6 and 7). Warshaw and Norton [102] studied the stress 
 dependence and found it to vary as the fourth power and on this basis suggested that 
 a dislocation climb mechanism was rate controlling; however, in a more recent examina- 
 tion of this accelerated creep, Coble and Guerard [104] have suggested that grain 
 boundary sliding has taken over. Their reasoning is based on the fact that an 
 addition of CrpO^ increases the creep rate even further; an observation also reported 
 by Chang [19] for polycrystalline material (result 8). If dislocation climb is the 
 controlling mechanism, then an addition of ^203 should lower the creep rate as 
 observed on alumina single crystals [101] and reproduced in figure 13. If grain 
 boundary sliding is the controlling mechanism then, as is known from anelasticity 
 studies [19,22] (figure 6), the viscosity is lowered by the addition of impurities, 
 and the creep rate should increase consistent with the experimental observations. 
 
 These observations on alumina may be summarized briefly as follows; single crystals 
 creep by the dislocation climb mechanism and impurities lower the creep rate; poly- 
 crystals creep in the range 1200-1800°C by the migration of vacancies under a stress 
 gradient and above 1800°C by grain boundary sliding, in both cases impurities raise the 
 creep rate. There is a need for further experiments on bi-crystals to determine the 
 stress dependence of grain boundary sliding and the effect of impurities on grain 
 boundary viscosity. 
 
 57 
 
TABLE 4. High temperature deformation and creep 
 of single and polycrystalline alumina 
 
 Result 
 
 No. 
 
 3(a) 
 3(b) 
 
 7(a] 
 
 7(b) 
 
 8(a) 
 
 8(b) 
 
 8(c) 
 
 Material 
 
 Single Crystal 
 
 Single Crystal 1200-1700°C 
 
 Temperature 
 Range 
 
 900-1300°C 
 
 Single Crystal 
 
 Single Crystal 
 plus 2% Cr20 3 
 
 Polycrystalline 
 Lucalox, High 
 Density, 5-15k 
 grain size 
 
 Polycrystalline 
 Lucalox, High 
 Density, 5-35m 
 grain size 
 
 1800°C 
 1800 °C 
 
 Rate Controlling 
 
 Deformation 
 
 Mechanism 
 
 Basal Slip 
 
 Basal Slip 
 
 Activation 
 
 Energy 
 
 Kcal/mole 
 
 Polycrystalline 
 91% Density, 
 50-100^ 
 grain size 
 
 Polycrystalline 
 High Density, 
 lOOyU. grain 
 size 
 
 Same as 7(a), 
 plus C^O^ 
 
 Polycrystalline 
 
 Same as 8(a), 
 plus 1% Cr 2 3 
 
 Same as 8(a), 
 plus 0.25$ 
 
 ^ a 2^3 
 
 1600-1800°C 
 
 1600-1800°C 
 
 1600-1800 °C 
 
 1750-1900°C 
 
 1750-1900°C 
 
 Dislocation Climb 
 
 Dislocation Climb 
 
 Vacancy Migration 
 
 Vacancy Migration 
 
 1400-1700 °C 
 
 1400-1700 °C 
 
 1400-1700°C 
 
 Grain Boundary 
 Sliding 
 
 Grain Boundary 
 Sliding 
 
 Grain Boundary 
 Sliding 
 
 85 
 
 85 
 
 Vacancy Migration 
 and Grain Boundary 
 Sliding 
 
 Vacancy Migration 
 and Grain Boundary 
 
 Sliding 
 
 Vacancy Migration 
 and Grain Boundary 
 Sliding 
 
 180 
 
 180 
 
 130 
 
 130 
 
 185 
 
 280 
 
 280 
 
 200 
 
 200 
 
 200 
 
 Author 
 
 Rogers et al« 
 [100] 
 
 Kronberg [39] 
 
 Chang [101] 
 Chang [101] 
 
 Warshaw and 
 Norton [102] 
 
 Folweiler [103] 
 
 Warshaw and 
 Norton [102] 
 
 Coble and 
 Guerard [104] 
 
 Coble and 
 Guerard [104] 
 
 Chang [19] 
 Chang . [19] 
 Chang [19] 
 
 58 
 
Probably the reason why polycrystalline alumina creeps by the diffusion controlled 
 mechanism rather than by dislocation climb is a consequence of the number of independent 
 slip systems available. There are only two independent slip systems in alumina so long 
 as basal slip predominates (Table 1) and, even taking into account the additional flex- 
 ibility afforded by climb, polycrystalline material cannot deform by slip without the 
 generation of intergranular constraints. The constraints can be relieved somewhat at 
 high temperatures by the migration of vacancies but will eventually result in the 
 appearance of intergranular voids in the regions of locally high tensile stress. 
 Figure 15 shows the occurrence of grain boundary voids and sliding in polycrystalline 
 alumina deformed at 1600°C. In magnesia, on the other hand, at a sufficiently high 
 temperature and a high enough stress level, wavy slip occurs and recent tests in our 
 laboratory [108] have shown that high density polycrystalline magnesia can be deformed 
 substantially at 2000°C without the formation of intergranular voids. Under these 
 conditions the creep rate might be determined by dislocation climb although this 
 remains to be confirmed. At lower stress levels or slightly lower temperatures, slip 
 in magnesia remains confined to {110} planes and the two independent slip systems are 
 not then sufficient for creep to proceed by slip alone. Coble [107] has recently 
 shown that under these conditions creep is controlled by vacancy migration under 
 stress, although whether intergranular voids then open up remains to be determined. 
 Certainly the high temperature behavior of magnesia as a function of stress, tempera- 
 ture and microstructural variables is a subject for more systematic and detailed 
 investigation. The fact that fully dense material deforms without intergranular 
 separation may make it superior to alumina for certain high temperature applications. 
 
 An increase in creep rate with porosity has long been recognized. Wygant [99] showed 
 that the creep rate of a 2% porosity hydrostatically pressed magnesia was approximately 
 one-tenth the creep rate of a 12$ porosity slip cast material as shown in Table 3. 
 Coble and Kingery [109] studied the effect of porosity on the creep rate of sintered 
 alumina up to almost 50$ porosity; their results are reproduced in figure 16. 
 
 At temperatures where the deformation process is controlled by the migration of 
 point defects, it is to be expected that stoichiometry will play an important role. 
 Scott et al [110] showed that stoichiometric uranium dioxide (UO2) could not be deformed 
 until the temperature reached 1600°C, whereas a deviation in stoichiometry to 
 uo 2.06 allowed plastic deformation around 800°C. The non- equilibrium cation 
 vacancies are considered to contribute to creep at the lower temperatures. Similarly, 
 Hirthe and Brittain [111] have shown that the activation energy for steady state creep in 
 rutile changes gradually from 63 Kcal/mole at stoichiometric composition to 33 Kcal/mole 
 for reduced material. 
 
 7. Conclusions 
 
 This paper has attempted to correlate the mechanical properties of ceramics with 
 fundamental microstructural variables. By necessity the discussion is limited to the 
 simple alkali halide and pure oxide ceramics, but from this fundamental background it 
 is to be hoped that a better appreciation of the mechanical behavior of more conventional 
 ceramics can ultimately be attained. The salient points may be summarized as follows. 
 
 1) The maximum elastic modulus is obtained in material of highest density, in 
 structures where the solid phase is continuous and the pores closed and spherical. 
 The addition of a second phase of higher modulus causes the resultant modulus of the 
 heterogeneous mixture to be increased. 
 
 2) The damping capacity of a ceramic single crystal at a particular temperature 
 depends on the density and mobility of dislocations. The introduction of grain 
 boundaries raises the damping capacity in a certain characteristic temperature range, 
 this range can be broadened and extended to lower temperatures by the addition of 
 
 impurity. 
 
 59 
 
* ) Ceramic materials deform plastically at the stress level and temperature at 
 ^JLIZZLTIZ sufficientlymobile The mobility of a die -at.on can ^re- 
 duced by impurities in a number of W s J n ^ e ^™n,uIc interaction of the moving die- 
 
 to an increase in strength. 
 
 i ) p la ,tir deformation of polycrystalline ceramics at low temperatures is pro- 
 hibited bv ?he lack of Sufficient independent slip systems. At high temperatures some 
 ceramic materials {£ 5g6) slip on additional systems and macroscopic polycrystalline 
 ductility then becomes possible. 
 
 5) The tensile fracture strength at low temperatures is a maximum in fully dense. 
 SttL'fr^SSrf occu%rL" ho ^"amiceVwhil^dfalocatLne can move (a* MgO) by 
 
 single crystals. 
 
 miSratlo/uMre^^ 
 
 ^eSofmoSontnd 1 ^ 
 
 slip systems even at high temperatures. 
 
 Even with simple ceramic materials the above interpretations of mechanical behavior 
 arp sti n au ite flexible and there remains a great need for critical theoretical ana 
 experimental work! Current developments of fully dense polycrystalline ceramics by 
 SKliSiMSS techniques are P-vidin ? the experimentalist with a good opportunity 
 to nerform quantitative experiments on well defined systems. ihe next lew years snuuxu 
 be plrt?cular?y pr?ductive P with respect to understanding the mechanical properties of 
 polycrystalline material. 
 
 Acknowledgments 
 
 It is a pleasure to acknowledge the Office of Naval Research and Aeronautical 
 Svstems Division U. S. Air Force for their sustained support of this work. The 
 auSor has benefited from discussions with colleagues at Honeywell Research Center, 
 S particular ?he criticism of Dr. C. H. Li has been very helpful in arranging the 
 material for presentation. I am grateful to Drs. G. W. Groves and A. Kelly and 
 Professor l. I. C^ble for making their manuscripts available before publication. 
 
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 [74] R. J. Stokes, T. L. Johnston, and 
 C. H. Li, Phil. Mag. 6, 9 (1961). 
 
 [75] A. R. C. Westwood, Phil. Mag. 6, 
 195 (1961). B -' 
 
 [76] T. L. Johnston, R. J. Stokes, and 
 
 C H. Li, Phil. Mag. 7, 23 (1962). 
 
 [89] W. B. Harrison, Paper presented at 
 64th Annual Meeting, Am. Ceram. 
 Soc, see Am. Ceram. Soc Bull. 
 4J,, 311 (1962), to be published. 
 
 [90] Fracture . John Wiley and Sons, Inc., 
 New York (1959). 
 
 [91] W. M. Hirthe, N. R. Adsitt, and 
 
 J. 0. Brittain, Direct Observations 
 of Imperfections in Crystals . p. 135, 
 Interscience, New York (1962). 
 
 63 
 
92 W. S. Williams and R. D. Schaal, 
 J. Appl. Phys. 22. 955 (1962). 
 
 93 J. E. Dorn, Creep and Recovery , 
 
 p. 255, American Society for Metals, 
 Cleveland, Ohio (1957). 
 
 94 J. Weertman, J. Appl. Phys. 26, 
 1213 (1955): 28. 362 (1957). 
 
 95 F. R. N. Nabarro, Conference on 
 Strength of Solids , p. 75, The 
 Physical Society, London (1948). 
 
 96 C Herring, J. Appl. Phys. 21, 437 
 (1950). 
 
 97 M. A. Adams and G. T. Murray, J. 
 Appl. Phys. 22, 2126 (1962). 
 
 98 G. T. Murray, J. Silgailis, A. J. 
 Mountvala, Report on Air Force 
 Contract AF33(6l6)-796l. Report 
 No. ASD-TDR-62-225. 
 
 101 R. Chang, J. Appl. Phys. }!, 
 484 (I960). 
 
 102 S. I. Warshaw and F. H. Norton, 
 
 J. Am. Ceranu Soc. ££, 479 (1962). 
 
 103 R. C Folweiler, J. Appl. Phys. 
 22, 773 (1961). 
 
 104 R. L. Coble and Y. H. Guerard, 
 J. Am. Ceram. Soc, to be 
 published. 
 
 105 A. E. Paladino and R. L. Coble, 
 
 J. Am. Ceram. Soc. 4j5, 133 (1963). 
 
 106 R. R. Vandervoort and W. L. Barmore, 
 J. Am. Ceram. Soc. 4.6, 180 (1963). 
 
 107 R. L. Coble, private communication. 
 
 108 R. B. Day and R. J. Stokes, to be 
 published. 
 
 99 J. F. Wygant, J. Am. Ceram. Soc. 
 2k. 374 (1951). 
 
 100 W. A. Rogers, G. S. Baker, and 
 
 P. Gibbs, Mechanical Properties of 
 Engineering , Ceramics , p. 303, 
 Inter science, New York (1962). 
 
 109 R. L. Coble and W. D. Kingery, 
 
 J. Am. Ceram. Soc. 21, 377 (1956) 
 
 110 R. Scott, A. R.Hall, and J. Williams, 
 J. Nuclear Materials 1, 39 (1959). 
 
 111 W. M. Hirthe and J. 0. Brittain, 
 paper presented at 64th Annual 
 Meeting, Am. Ceram. Soc, see Am. 
 Ceram. Soc. Bulletin 4.1, 311 (1962). 
 
 64 
 
70r 
 
 Figure 1. 
 
 LINEAR 
 'PAUL 
 
 -HASHIN (UPPER BOUND) 
 
 HASHIN (APPROXIMATE) 
 
 100 
 
 VOLUME CONTENT GRAPHITE (PERCENT) 
 
 The variation in elastic modulus of a two phase solid. Comparison of 
 theoretical and experimental relationships for the system zirconium carbide 
 plus carbon. (After Hasselman and Shaffer [7] ). 
 
 
 60.0 
 
 
 50.0 
 
 <J> 
 
 
 <c 
 
 40.0 
 
 O 
 
 
 K 
 
 30.0 
 
 _l 
 
 
 3 
 
 
 Q 
 
 
 O 
 
 
 2 
 
 20.0 
 
 ^, 
 
 
 O 
 
 
 ^^ 
 
 
 cc 
 
 
 < 
 
 
 uJ 
 
 
 X 
 
 
 CO 
 
 
 Q 
 
 7 
 
 10.0 
 
 < 
 
 9.0 
 
 Mi 
 
 8.0 
 
 o 
 
 7.0 
 
 
 6.0 
 
 < 
 
 
 50 
 
 10 
 
 
 | 
 
 1 1 
 
 
 1 1 1 
 
 — 
 
 
 
 
 — 
 
 
 
 
 — 
 
 — 
 
 
 •""^wO 
 
 ♦' 
 
 — E=46,080,000e' (psi) 
 
 **"**« 
 
 
 
 
 ^^ — 
 
 © 
 
 
 
 ♦ 
 
 ^^^^^ 
 
 
 
 
 
 
 — G-20,240,000e~ 4 - 90P (psi) 
 
 . 
 
 SPRIGGS HP. 
 
 
 * 
 
 LANG C.P. 
 
 
 
 
 o 
 
 SCHWARTZ S.C. 
 
 
 
 — 
 
 a 
 
 WACHTMANC.P. 
 
 
 ^***>^^ — 
 
 — 
 
 o 
 
 © 
 
 TINKLEPAUGHH.P. 
 WYGANTS.C 
 
 
 1 1 1 
 
 1 
 
 1 1 
 
 8 12 16 20 
 
 POROSITY VOLUME, PERCENT 
 
 24 
 
 28 
 
 Figure 2, Effect of porosity on elastic (E) and shear (S) moduli of polycrystalline 
 magnesia at room temperature. Letters after author names are fabrication 
 codes, H.P. - hot pressed, C.P. - cold pressed and sintered, and S. C. - 
 slip cast and sintered. (After Spriggs et al, [15] )• 
 
 65 
 
0.001 
 
 0.01 
 
 Elastic modulus — 
 
 0.1 1 10 
 
 Frequency, tu> 
 
 1000 
 
 Figure 3 Change in damping capacity (internal friction) and dynamic elastic modulus 
 with frequency. Amplitude and temperature constant. 
 
 0.04 
 
 O 
 
 0.03 
 
 SINGLE CRYSTAL AL 2 3 
 (O SOLID LINE) 
 
 POLYCRYSTALLINE AL 2 3 
 (a DOTTED LINE) 
 
 200 400 600 800 IOOO 1200 1400 
 TEMPERATURE (°C) 
 
 Figure 4 The internal friction spectrum for single crystal and polycrystalline alumina. 
 (After Chang [19] )• 
 
 66 
 
z 
 o 
 I- 
 o 
 
 a. 
 u. 
 
 _i 
 < 
 
 a. 
 
 Mi 
 
 \- 
 
 17.5 
 
 _ I l l l I „ 1 
 
 P 
 
 15.0 
 
 -o — o — o- ALUMINA, ~ 5000 cps \ 
 
 
 -o— o--o-- ALUMINA- |% SILICA,- 15,000 cps ' 
 
 12.5 
 
 i _ 
 
 10.0 
 
 /I - 
 
 7.5 
 
 / \ - 
 
 5.0 
 2.5 
 
 9 : \ \ 
 
 — IK 
 
 
 o- o— i ro * 1 0— — T I I 
 
 200 400 600 800 
 
 TEMPERATURE. °C 
 
 1 000 
 
 I200 
 
 Figure 5. Effect of impurity on the internal friction spectrum of polycrystalline 
 
 alumina. The addition of 1% SiC>2 introduces a new low temperature internal 
 friction peak. (After Crandall et al. [22] ). 
 
 1.0 
 
 0.9 
 
 0.8 
 
 ■o 0.7 
 c 
 o 
 u 
 
 01 
 
 ■? 0.6 
 
 J3 
 
 ■o 
 
 0.5 
 
 < 0.4 
 
 Z 
 Ul 
 
 i 0i 
 
 0.2 
 
 0.1 
 
 
 
 
 
 
 
 
 
 2A LOWER CURVE: AS HEAT TREATED 
 28 MIDDLE CURVE: COLD WORKED BY 
 
 COMPRESSION ~0.4% AT 130° C 
 2C UPPER CURVE: COLD WORKED BY 
 
 COMPRESSIONS l.7%ATI30° C 
 FREQUENCY: 27 Megacycles/second 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^PT 
 
 
 -80 
 
 -60 
 
 -40 -20 20 
 
 TEMPERATURE (°C) 
 
 40 
 
 60 
 
 Figure 6, Effect of plastic deformation on the internal friction spectrum of magnesium 
 oxide single crystals. (After Chang [29] ). 
 
 67 
 
Ficure 7 "Grown in" dislocations in magnesium oxide. Note the impurity precipitate 
 particles spaced at fairly regular intervals. (Electron transmission 
 micrograph courtesy G. W. Groves). 
 
 900 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 LIQ 
 
 UID 
 
 
 
 
 
 
 
 O 600 
 bl 
 
 
 
 
 LIQUID + 
 SOLID 
 
 
 
 
 
 
 9j 500 
 
 
 
 
 
 
 
 
 
 
 
 K 
 
 U 
 
 
 
 
 s 
 
 UJ 
 
 1- 
 
 
 
 
 
 
 
 
 
 
 
 300 
 200 
 
 
 
 
 
 
 
 
 
 
 
 a, 
 
 
 
 
 
 
 
 
 a z 
 
 
 
 ; 
 
 
 
 
 
 100 
 
 : / 
 
 >' 
 
 
 a, + a 2 
 
 1 
 
 
 
 
 
 
 in 
 
 q.20 
 
 ( 
 
 </) 
 <n 
 
 Sl5 
 
 tfi 
 
 > 10 
 
 %~MOLECULAR 
 
 PER CENT NoCI 
 
 85% 
 /" 90% 
 
 STRAIN 
 
 (b) 
 
 10 
 
 A«CI 
 
 20 30 40 50 60 70 80 90 100 
 
 MOLECULAR PERCENT NaCI 
 
 (a) 
 
 Figure 8 Solid solution and precipitation hardening in the silver chloride-sodium 
 chloride alloy system. 
 
 (a) The AgCl-NaCl phase diagram 
 
 (b) Compression stress strain curves for AgCl-NaCl alloy single crystals. 
 
 68 
 
1.3 — 
 1.2- 
 l.l- 
 1.0 
 .9 
 
 
 .8 
 
 b~ 
 I 
 
 .7 
 
 o 
 
 < 
 
 .6 
 .5 
 
 
 .4 
 
 
 .3 
 
 
 .2 
 
 
 1 
 
 "1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 
 
 o o 
 
 J L 
 
 o o 
 
 CURVE A - AS RECEIVED 
 
 CURVE B - PRE-ANNEALED 2000°C 
 
 J I I I I l I i 
 
 J_ 
 
 J I I L 
 
 200 400 600 800 1000 1200 1400 
 
 ANNEALING TEMPERATURE °C 
 
 1600 
 
 J L 
 
 Tft 
 
 1800 2000 
 
 Figure 9- Effect of heat treatment on the room temperature yield strength of commercial 
 purity magnesium oxide single crystals. 
 
 a 1 - room temperature yield strength in as-received (fully precipitated) 
 condition. 
 
 a s - room temperature yield strength after annealing. 
 
 3000 
 
 .035 mm GRAIN DIAMETER 
 .07 mm 
 .10mm 
 
 TENSILE STRESS -STRAIN CURVES 
 FOR POLYCRYSTALLINE SODIUM 
 CHLORIDE AT ROOM TEMPERATURE 
 
 SINGLE 
 CRYSTAL 
 
 ELONGATION 
 
 Figure 10, Tensile stress strain curves for polycrystalline sodium chloride at room 
 temperature illustrating the effect of decreasing the grain size on the 
 proportional limit and rate of work hardening. 
 
 69 
 
Figure 11, 
 
 Slip distribution in the vicinity of grain bouiidarxesxnlxthxum fluoride 
 deformed at room temperature. Note very local slip on {001} planes near- 
 triple point. Slip revealed by etch pit technique, (courtesy W. D. Scott 
 and J. A. Pask) . 
 
 Figure 12 
 
 pit technique. 
 
 70 
 
Figure 13. Effect of purity on the steady state creep rate of alumina. The addition 
 of 2% Cr 2 C>3 lowers the creep rate by 1C*. (After Chang [lOl] ). 
 
 ...» 1900 
 10 9 I | — 
 
 Temperature (°C) 
 1800 1700 
 
 1600 
 
 -lO' 10 
 
 CM 
 
 6 
 o 
 
 10" 
 
 I0" ,s 
 
 Creep diffusion 
 coefficients in 
 
 AI 3+ diffusion 
 coefficients in Al 2 3 
 
 ± 
 
 1 
 
 I 
 
 0.46 0.48 0.50 0.52 
 
 1000 /T(°K-) 
 
 0.54 
 
 Figure 14. Comparison of the diffusion coefficient measured for self diffusion of the 
 aluminum ion with the diffusion coefficient calculated from creep data of 
 alumina using the Nabarro-Herring equation. (After Paladino and Coble [105] ) 
 
 71 
 

 
 
 
 Figure 15. Generation of intergranular voids during torsional creep of high density 
 alumina. (courtesy R. L. Coble). 
 
 40,000 
 
 1 1 1 
 
 # STRESS AT CREEP RATE 
 2.5x I0" 5 IN/IN. HR. 
 
 6 CREEP RATE 600 P.S.I. 
 
 0.1 0.2 0.3 0.4 0.5 
 VOLUME FRACTION PORES 
 
 Figure 16. Effect of porosity on the torsional creep of sintered alumina at 1275°C 
 
 The stress to promote a constant creep rate and the creep rate gt a wnatant 
 stress are both plotted as a function of the porosity. (After Coble ana 
 Kingery [109] )• 
 
 72 
 
Microstructure of Magnetic Ceramics 
 A.L. Stuijts 
 
 1. Introduction 
 
 Electrical engineering has made enormous strides since the beginning of this 
 century. Advances in the field of telecommunication and high-frequency tech- 
 niques have stimulated the development of the required high-frequency insulating, 
 dielectric and magnetic materials. 
 
 Important developments in the field of magnetic oxides were started in our la- 
 boratories in the late thirties by J.L. Snoek [1] *. Although other investigators had 
 realized the potential importance of ferrites for high-frequency applications, it 
 was Snoek and his collaborators who took the fundamental step to obtain control of 
 these materials so as to make their properties useful to the electrical engineer. 
 They were also able to explain a number of fundamental aspects of the high-frequen- 
 cy behaviour of ferrites. 
 
 Simultaneously pioneering work was done to gain further knowledge of the ionic 
 structure of these ferrites [2] . These studies made it possible to explain the semi- 
 conducting properties, and the basis was laid for a further interpretation of the 
 magnetic behaviour. 
 
 The French scientist L. Ne*el succeeded in predicting the magnitude of the magne- 
 tic moment as well as its curious temperature dependence [3], He introduced the 
 name "uncompensated anti-f erromagnetism" or "ferrimagnetism" , since, as opposed to 
 the case in ordinary ferromagnetic alloys, the exchange forces orient the magneti- 
 zation vectors of neighbouring spins antiparallel . The predictions of Ne"el have 
 been confirmed by the experimental work of Guillaud and Gorter [4], 
 
 After 1950 a new period in the development of magnetic oxides set in. New sys- 
 tems of magnetic oxides were discovered and developed, such as the hexagonal per- 
 manent-magnet material BaFe. „().„, the ferroxplana materials and the garnets. On the 
 
 other hand new developments in electronics occurred, thanks to the application of 
 such specific properties of magnetic oxides as their gyromagnetic effects and their 
 ability to store information. 
 
 An essential feature of the magnetic ceramics is the combination of moderate 
 magnetic permeability with high volume resistivity (from 10 up to 10 10 ohm. cm). 
 Thus eddy-current losses in an alternating field of high frequency can be very low. 
 
 The development of magnetic oxidic materials has many different aspects in- 
 volving physicists, chemists and engineers. Most of the properties are very sensi- 
 tive to variations in chemical composition, ionic distribution over different lat- 
 tice sites, ionic ordering phenomena, etc. Furthermore the shape of the product is 
 of importance for the application. Although magnetic oxides can be formed in any 
 shape by ceramic techniques, there are considerable problems in combining an exact 
 control of the chemistry with control of the microstructure of the shaped ceramic 
 product. It is with these problems that the present paper is concerned. 
 
 Although considerable progress has been made in the last decade with respect to 
 fundamental aspects of chemical reactions and sintering, we are still far from 
 being able to control the microstructure even in simple oxides. There is, however, 
 an overwhelming amount of information on the importance of such control. The main 
 part of this paper will deal with a number of obvious examples of the importance of 
 microstructure in the development of "tailor-made" magnetic ceramics. 
 
 Figures in brackets indicate the literature references at the end of this paper 
 
 73 
 
2. Crystal Structure and Intrinsic Magnetic Properties 
 
 The mineral magnetite, Fe 2+ Fe 3+ 4 , was already used in antiquity for its mag- 
 netic properties. The magnetic ceramic materials now used in electronics are found 
 in a limited range of crystal structures. The cubic ferrites have the spinel struc- 
 ture with the general formula MeFe 2 4 , in which Me is Mn, Ni, Co, Fe^, Mg, Zn, or 
 a combination as for instance Li 1+ +Fe 3+ . Moreover Fe 3+ can be substituted by e.g. 
 Al- or Cr-ions. Thus a great variety is possible in the chemical composition of fer- 
 rites with spinel structure [5] . The large oxygen ions form a close-packed structure, 
 in which two kinds of interstitial sites are occupied, viz. tetragonal sites and 
 twice as many octahedral sites. Some metal ions, like Zn and Cd. have a strong pre- 
 ference for the tetrahedrally-surrounded sites; others, like Fe^+ and Ni, for the 
 octahedrally- surrounded ones. The spins of neighbouring ions in these oxides are 
 oriented anti-parallel by the exchange forces. These forces, however, are strongest 
 for the interaction between the magnetic ions in tetrahedral and octahedral sitea 
 mutually. When the sum of the magnetic moments at tetrahedral sites differs from 
 that at octahedral sites, a net magnetic moment can result. In the case of ferrous 
 ferrite, for example, in which Fe 2 + contributes four Bohr magnetons and Fe^+ five: 
 
 Fe 3+ Fe 2+ Fe 3+ „ 
 
 5 4 5 ^4 . 
 there is a net magnetic moment of four Bohr magnetons per formula unit. 
 
 The study of the distribution of the constituent metal ions over the different 
 types of lattice sites is very important. The intrinsic magnetic properties, and 
 to a large extent also the technologically important properties, are intimately re- 
 lated to detailed aspects of the crystal chemistry of these compounds. 
 
 The same holds for the ferrites based on the structure of the mineral garnet, 
 for which the prototype is Y 3 Fe 5 12 . In this case the ionic distribution over the 
 tetrahedral and octahedral lattice sites has also been studied, but garnets are 
 very often used unsubstituted. 
 
 Next there is a group of ferrites with closely related hexagonal crystal struc- 
 tures. These compounds are found in the diagram of figure 1, the corners of which 
 represent the oxides BaO, MeO and Fe 2 0g. In the same way as in the spinel structure, 
 a great number of ions can be introduced. One of the compounds, BaFe g ±9 or barium 
 hexaferrite, has become a technically important permanent-magnetic material. Some of 
 the other hexagonal compounds, e .g. BagCOgFe^O^Co^) or Ba 2 Zn 2 Fe 12 22 (Zn 2 Y>, 
 
 have interesting high-frequency magnetic properties. 
 
 As for the chemistry of magnetic oxides, we will limit the description of the 
 intrinsic magnetic properties to the most essential points. For further study re- 
 ference may be made to the original literature in this field, which la readily ac- 
 cessible (see e.g. [ 6]). 
 
 A ferromagnetic material is characterized by its spontaneous magnetization, 
 originating from the magnetic moments of the magnetic ions. The exchange interac- 
 tion which aligns the magnetic moments of the electron spins parallel or antiparal- 
 lel is opposed by thermal agitation. Thus the spontaneous magnetization has a cha- 
 racteristic temperature dependence, which disappears at the Curie point. 
 
 There are several factors binding the magnetization vectors to certain direc- 
 tions : ,, j. . 
 1 The crystalline anisotropy. The spin of the electron which causes the magnetic 
 moment is coupled with the orbit of that electron; the electron orbit is in its 
 turn fixed by the symmetry of the crystal lattice. As a result of this spin-orbit 
 and orbit-lattice coupling, the magnetic moment has a preference to be directed 
 along certain crystallographic directions. These- directions are called directions 
 of easy magnetization and are related to the symmetry of the crystal lattice. Work 
 has to be supplied to rotate the magnetization into a difficult or hard direction, 
 the energy being the crystalline anisotropy energy E c . 
 
 In most spinels the easy direction is the cube diagonal. By the substitution 
 of a sufficient amount of Co-ions it changes into a cube edge. Most of the hexago- 
 nal compounds have large crystalline anisotropy energies, with the preferential di- 
 rection of magnetization either parallel to the c-direction, within the basal plane 
 perpendicular to the c-axis, or on a cone lying in between the c-axis and the basal 
 
 plane. 
 
 74 
 
2. When a body of a ferromagnetic material is magnetized its length changes. 
 The origin of this linear magnetostriction X = — is closely related to that of the 
 crystalline anisotropy. Conversely, external stresses act on the direction of mag- 
 netization by virtue of the presence of magnetostriction, and this strain aniso- 
 tropy energy is proportional to the linear magnetostriction \ St and the external 
 stress o : 
 
 E « \ o . 
 s s 
 
 For the further considerations in our paper we shall assume the crystalline 
 anisotropy to be predominant, since a similar treatment applies for both aniso- 
 tropics. In many cases it is convenient to express the binding force to a certain 
 direction as an anisotropy field H , proportional to K/M , where K is the absolute 
 value of the anisotropy constant. 
 
 3. Permeability and Hysteresis Loop 
 
 An externally applied magnetic field will cause the magnetization to turn toward 
 the field direction (see figure 2). The change in magnetic induction, A B, for an 
 applied field, AH, is the permeability of the material: 
 
 A B 
 
 M =-AH 
 
 The magnetic induction B is simply the sum of the magnetization 4 n M and the ex- 
 ternal magnetizing field H: 
 
 B = 4 n M+H 
 
 If there were no opposing forces, the permeability would be infinite. The forces . 
 which bind the magnetization vector to certain directions (the anisotropy field IT; 
 cause the external field necessary to obtain a given value of A B to have a defi- 
 nite value and thus the permeability to be finite. 
 
 The initial permeability, for a small value of AB, is proportional to the . 
 saturation magnetization M and inversely proportional to the anisotropy field H: 
 
 s M M 2 
 
 t* a "4 or H.«-|- 
 
 The presence of anisotropy, and thus a finite permeability gives rise to a 
 hysteresis loop when the magnetic induction B is measured as a function of a mag- 
 netic field H, the field being varied from a large negative to a large positive 
 value and back. The value of B for H = is the remanence or retentivity B . A 
 magnetic material has thus two equally large, but oppositely directed remanence 
 values (see figure 3). 
 
 When a specimen is cycled around the hysteresis loop, energy is expended which 
 is liberated as heat - the hysteresis losses. Ferromagnetic materials generally are 
 divided into "hard" and "soft" magnetic materials. The basis of this division is 
 the magnitude of the coercivity or coercive force H . This is the field necessary 
 to bring the induction, in the direction of the field, to zero. One would expect 
 the value of the coercive force to be closely related to the anisotropy field H A . 
 This is indeed the case in permanent or "hard" magnetic materials, where high 
 coercivities are an essential property. For "soft" magnetic materials, with low 
 coercive forces and narrow hysteresis loops, the magnetization changes direction in 
 an external field which is generally much smaller than the anisotropy field H A „ Al- 
 so the permeabilities found are several orders of magnitude higher than calculated 
 with the formula given above. This has to be explained by a different magnetization 
 process. 
 
 4. Domain Theory 
 
 Pierre Weiss introduced his domain theory at the beginning of this century [7] 
 to explain e.g. the non-magnetic state of a ferromagnetic material. He postulated 
 the existence of local regions in which the magnetization vectors are parallel. The 
 different regions are magnetized in different directions, as shown in an oversim- 
 plified way in figure 4. The uniformly magnetized regions are called Weiss domains. 
 
 The basic reason for the formation of domains is the reduction of the magneto- 
 static energy which arises from the external surface of the specimen. See Figure 5a. • 
 Such a uniformly magnetized domain possesses induced magnetic poles at the surface. 
 
 75 
 
The stray fields arising from these poles cause a high value of magnetic energy of 
 this system. By division of this hody into two domains, as shown in figure 5h, the 
 magnitude of the magnetostatic energy arising from the poles is reduced to one half. 
 It is even possible to eliminate the magnetostatic energy completely by the formation 
 of closure domains, as shown in figures 5c and 5d. In these cases no magnetic flux 
 leaves the structure. 
 
 The geometric configuration of the Weiss domain structure which actually is 
 formed is determined by the requirement that the total energy must be minimum. A 
 number of energies have to be taken into account, the most important of these being 
 the energy of the boundary between the domains, the domain wall energy. Bloch 8 
 showed that the magnetization does not abruptly shift direction at the boundary, 
 but changes direction gradually from atom to atom, as shown in figure 6. As a result 
 of a competition between exchange energy and crystal anisotropy there is a given mi- 
 nimum thickness of the domain wall, the energy of which is the sum of both energies. 
 
 The energy associated with the total domain wall area competes with the gain 
 in demagnetizing energy, thus giving rise to a specific width of the domains. Also 
 the magnetoelastic energy comes into play. Given a finite magnetostriction, strains 
 are set up in a configuration. Work has to be done to fit the domains together, 
 causing the configuration of figure 5d.with more closure domains to be energetical- 
 ly more favourable. 
 
 There are several methods of making the Weiss domain structure visible under 
 the microscope. With a colloidal solution of magnetic F e 3 4 the so-called powder 
 pattern or Bitter pattern can be made visible. Figure 7 gives an example of this. 
 Owing to stray fields at the surface of the crystal the powder coagulates at the 
 position of the Bloch walls. For optically transparent crystals the Weiss domains 
 can be seen by making use of the optical Faraday-effect [9], A third method is based 
 on the magneto-optical Kerr-ef f ect [ 10] . 
 
 In an external applied field H, and starting from the unmagnetized state, the 
 energy can be lowered in two ways (see figure 8): 
 
 i. Rotation processes, in which the magnetization is turned into the direction 
 of the applied field. 
 
 2. Domain wall movement, by which the domain having the magnetization vector 
 nearest to the field EL grows at the expense of its neighbour. 
 
 In the same way as indicated in a preceding paragraph a permeability caused 
 by wall movement would be infinite, if there were no opposing forces. However, the 
 permeability caused by domain wall movement is limited by the fact that the domain 
 wall configuration gives a minimum value for the magnetic energy of the system which 
 is measured [11]. Further it is at this point that the microstructure comes into 
 discussion. Any imperfections in the material - nonmagnetic inclusions or voids, dis- 
 locations, concentration fluctuations, internal stresses - will hinder wall move- 
 ment. If we limit our discussion to non-magnetic inclusions and holes it can be 
 stated that domain walls prefer to contain the inclusion. In figure 9 such a situa- 
 tion is shown. The effect is a decrease in magnetostatic energy, for the same reason 
 as discussed above in regard to the external surface of the specimen. The wall area 
 too, and thus the total wall energy, is reduced. The microstructural characteristics 
 therefore cause the walls to be bound with a certain stiffness to their positions of 
 equilibrium, limiting the wall mobility. 
 
 The magnetization curve can be discussed in terms of these two magnetization 
 processes (see figure 10). The initial slope of the curve, starting from the un- 
 magnetized state, is completely reversible. The domain walls are fixed at the im- 
 perfections in the material and reversible wall displacements predominate. At larger 
 field strengths the slope increases, the walls then being pulled loose from the im- 
 perfections. The walls can travel relatively large distances, but irreversibly, un- 
 til all domain walls have disappeared. A further increase in induction occurs by 
 rotation of the magnetization vector into the field direction until complete satura- 
 tion is reached. 
 
 Generally the magnetic field necessary.to obtain irreversible wall movements 
 is small compared to the anisotropy field H . Consequently the coercive force nor- 
 mally measured in any magnetic material is small. 
 
 as shown in figure 5c. In this configuration 
 
 76 
 
5. Single-domain particles. Permanent magnets. 
 
 The most straightforward relation between microstructure and magnetic proper- 
 ties is found in the permanent magnet materials based on single-domain behaviour of 
 their constituent particles. 
 
 We have seen that the basic reason for the formation of domains is the reduc- 
 tion in magnetostatic energy. When the diameter of a magnetized particle decreases 
 (see figure ll), the magnetostatic energy drops of f as the cube of the diameter D of 
 the particle. The domain wall energy, however, drops off only as the square of the 
 diameter. The effect will be that below some critical diameter, D » no magnetic 
 energy is gained by dividing the particle into Weiss domains. Below D cr single domain 
 particles exist in which no stable Bloch walls can be formed. 
 
 In the absence of domain walls demagnetization can only occur by rotation of 
 the magnetization vectors of the particles against the anisotropy forces. Thus, for 
 high anisotropy fields high coercive forces can result, with H c of the same order of 
 magnitude as H A , a necessary condition for permanent magnetic properties. 
 
 The critical size, D , can be calculated for simple geometrical configurations, 
 giving approximate values cr [12] . for soft magnetic materials, with low magnitude of 
 the wall energy and thus a relatively large wall thickness, D is small. For nickel 
 ferrite a value of 0.08 u can be calculated [13]. In hard magnetic materials, with a 
 large anisotropy, the wall energy is high and thus the value of D relatively large. 
 For the hexagonal compound BaFe. 2 0.„ a D of about i micron is calculated [14]. 
 
 The origin of the permanent magnetic properties of BaFe 12 1Q (or Ba0.6Fe 2 0g) is 
 
 the pronounced uniaxial magnetic anisotropy, with the preferred direction of the mag- 
 netization parallel to the c-axis. A large single crystal of this compound has low 
 coercivity, owing to the formation of Bloch walls. For permanent magnetic properties 
 the constituent crystallites must be made smaller than the critical diameter. In 
 figure 12 the coercive force H is plotted as a function of grain size for some ma- 
 terials, showing the increase ?n coercive force when the mean grain size decreases. 
 
 For a permanent magnet the demagnetization curve, which is the part of the hys- 
 teresis loop where B and H are opposite, is of importance. The quality of a perma- 
 nent magnet is described by its energy product B«H, which reaches a maximum some- 
 where on the demagnetization curve. It is clear that a high energy product also 
 calls for a high induction. But the induction is roughly proportional to the apparent 
 density of a material, and thus a sintering process is applied in order to increase 
 the density, in which growth of the constituent particles above D has to be avoided 
 [15]. This requirement can only be partly fulfilled, as heat treatment is generally 
 associated with grain growth. In figure 13 two hysteresis curves are drawn, one for 
 an optimally fired specimen (curve i), the other for a specimen with low coercive 
 force resulting from grain growth during sintering (curve 2). 
 
 Much work has been done on studies of grain growth phenomena during sintering, 
 and the effects on magnetic properties. As the value of D (about 1 micron) is just 
 within the range where the magnetic ceramics normally have their mean particle dia- 
 meter before sintering, fabrication is consequently critical. Much attention has 
 been given to the development of additions to aid in a better control of the manu- 
 facturing procedure, e.g. by retarding grain growth during sintering. Most of these 
 additions are only of value for the specific procedure used by the manufacturer 
 (raw materials, furnace, etc.). 
 
 The most disastrous effect on the magnetic properties arises from discontinuous 
 grain growth during sintering. Owing to the magnetic interaction of the domains in 
 adjacent grains, flux reversal in one grain will directly influence its surroundings 
 and finally introduce an avalanche-like effect, lowering the coercive force con- 
 siderably. Discontinuous grain growth in this material is characterized by the high 
 growth velocity. In the hexagonal material under discussion the g rowth velocity in 
 the different crystallographic directions is of especial importance. The growth ve- 
 locity is largest in the basal plane, causing the crystals to be thin plates, with 
 the c-axis perpendicular to the plate. This is shown in figure 14. The ratio of 
 diameter to thickness is about 2 for crystallites of about 1 micron diameter, and 
 appears to increase linearly to about 15 for discontinuously grown crystals of 500 
 microns diameter (figure 15). Magnetically this plate shape has significant conse- 
 quences, as the effective demagnetizing field is very large for these thin plates. 
 
 Another aspect of microstructure is that the constituent particles can have 
 
 77 
 
an orientation texture. In remanence the magnetization vectors of a uniaxial ma- 
 terial like barium hexaferrite will lie in the easy direction nearest to the sa- 
 turating field under the influence of the anisotropy forces, (gee figure 16.)This 
 decrease in induction, and thus in energy product;, will not occur when the con- 
 stituent particles are aligned with their c-axis parallel to the magnetizing field. 
 By a special procedure, in which use is made of the magnetic anisotropy field of 
 the material, this can actually be achieved and thus the maximum energy product in- 
 creased considerably [ 16] . In figure 17 hysteresis curves are given for barium hexa- 
 ferrite, relating to an isotropic and a crystal-oriented sample. Figure 18 shows a 
 photomicrograph of the crystal-oriented sample. 
 
 Other interesting aspects of microstructural events during sintering, e.g. in- 
 crease of texture during sintering and anisotropic shrinkage, are not discussed in 
 this paper. 
 
 6. Single Crystals vs Polycrystalline Materials 
 
 In the preceding section an example was given where a polycrystalline material 
 was essential for the hard magnetic properties. A single crystal can be considered 
 as the other extreme. Domain wall processes are favoured over rotations, which is 
 essential for soft magnetic materials. Apart from economic considerations, many dif- 
 ficulties arise in preparing single crystals with a controlled chemical constitution. 
 Moreover, no satisfactory techniques have yet been developed in which single crystals 
 of cubic materials can be grown from fluxes, as they generally contain inclusions. 
 
 Owing to the lack of a reference, e.g. a single crystal , the definite influence 
 of small v ariations in the material, unknown interactions between domains and a num- 
 ber of other factors, it is often difficult to decide whether the microstructure ac- 
 tually found is essential for the physical properties measured. Therefore we will 
 show in the following paragraphs only examples where gross effects in the physical 
 properties are related to microstructural variations. 
 
 7. Initial Permeability and Coercive Force 
 
 The initial permeability and coercive force of a material are closely related, 
 as both are determined by the two basic processes for magnetization. Thus they are 
 very sensitive to porosity, size and distribution of the pores, the average size 
 of the grains, and whether a s econd phase is present. 
 
 The initial permeability is determined by rotation processes or by reversible 
 bulging of the domain walls, without changing the Weiss domain pattern as a whole. 
 The coercive force is a mean critical field, governed by irreversible rotation pro- 
 cesses or by irreversible domain-wall displacements. As rotation processes are de- 
 termined predominantly by intrinsic properties of the material, they are fairly in- 
 dependent of microstructural variations and can be calculated with good approxima- 
 tion. It is found that the initial permeabilities of sintered specimens are much 
 higher and the coercive forces much lower than one can expect from rotation proces- 
 ses alone. Thus wall displacements do contribute appreciably. 
 
 In figure 19 the initial permeability is given as a function of the porosity p 
 of a series of nickel ferrites and of nickel-zinc ferrites [17] . The value for p=0 
 in this figure is the result measured on a nickel ferrite single-crystal. The value 
 of the permeability which has been calculated for p=0 when only rotation processes 
 occur, is about 8. It appears that the increase in permeability with decreasing po- 
 rosity of the material must be attributed to an increase in the contribution of wall 
 displacements. Also the coercive force becomes smaller with decreasing porosity, as 
 shown in figure 20. The linear dependence found is as expected for domain-wall dis- 
 placements. Presumably the sharp increase at the highest values of p is caused by 
 the fact that single-domain behaviour is approached. 
 
 The samples with varying porosities were obtained by sintering at different 
 temperatures. Sintering is accompanied as a rule by grain growth, which also affects 
 permeability. In figure 21 the measurements of Guillaud [18] have been given for the 
 initial permeability [i as a function of grain size for manganese zinc ferrites 
 with constant chemical 8omposition. There are two inflections in the curve. The 
 lower inflection, at about 5-6 microns, is attributed to a change from rotational 
 permeability in small grains to a permeability due to wall displacements for larger 
 grains. However, from recent results published by Paulus [19] on this system, it 
 appears that also an appreciable increase in density occurs in the same region of 
 grain sizes (see figure 22). Thus one cannot unambiguously attribute the increase 
 
 78 
 
in permeability to either the decrease in number of pores or the increase in grain 
 size. Owing to the fact that the chemical composition is very sensitive to changes 
 in the oxygen content of the atmosphere and to evaporation of zinc oxide, ceramic 
 technology has so far failed in this respect, as measurements should be made in a 
 range of porosities for a given constant grain size. Also the mean pore size has to 
 be taken into account, as the blocking of domain walls at pores is determined by the 
 ratio of pore size to wall thickness. In the manganese-zinc ferrites an appreciable 
 increase in the mean pore size occurs during the heat treatment. 
 
 The same considerations presumably hold for the measurements on nickel-zinc 
 ferrites, made by the same authors. However, no measurements on one and the same 
 chemical composition have been published. 
 
 The effects of discontinuous grain growth have not been investigated thoroughly. 
 Guillaud [18] attributes the upper limit of the permeability in figure 21 to the ap- 
 pearance of pores in the crystals. According to [19] discontinuous grain growth 
 starts in this system at about 10 microns. This can just as well be the reason for 
 densif ication to stop, as is known from theories on sintering [20] . We have studied 
 this phenomenon in a nickel-zinc ferrite, Ni„ „ g Zn 64 Fe 2^4> us i n S a material which 
 was known to give discontinuous grain growth during* sintering. In figure 23 results 
 are given of measurements on samples made from prefired powder. The samples were 
 heated at a constant heating rate of 250 C per hour up to the temperature given, 
 and next rapidly cooled to 900 0. From 900 C to room temperature the samples were 
 slowly cooled. Up to a temperature of 1200 C grain growth was very small, all grains 
 being smaller than one micron. Sintering was appreciable, as a density of about 
 97.5% of the X-ray density was obtainel. After 1200°C grain growth could be seen under 
 the microscope, up to 1 or 2 microns, and above this temperature discontinuous grain 
 growth started. A very sharp break in the density-temperature curve is seen at this 
 temperature. In figure 24 photomicrographs are given of the etched samples after 
 
 a) the temperature of 1200 C, where grain growth is clearly visible, 
 
 b) the temperature of 1210 C, where discontinuous grain growth has started; and 
 
 c) at a much higher temperature where the new equilibrium grain size is formed. 
 
 There is no break in the permeability curve. We believe that the main effect on the 
 initial permeability u is the decrease in porosity. A further increase in permea- 
 bility, when the density is constant, is obtained by the gradual disappearance of 
 the very small grains. Apparently the domain-wall mobility which favours a high per- 
 meability is more hindered when the pores are located on the grain boundaries of 
 the grains than when the pores are trapped within larger grains. 
 
 A second phase or inclusion should have the same influence on u and H as a 
 pore or void. However, because of the difference in thermal expansion of the 5 two pha- 
 ses, stresses are set up in the ferrite matrix. When the material has a certain 
 value for the magnetostriction, a stress anisotropy energy can be formed which can 
 be relatively high with respect to the other anisotropics. This effect has been 
 studied by Carter in magnesium ferrite [21] . The second phase was formed by partly 
 reducing the ferrite, as the solubility of the metal oxide phase MeO in the spinel 
 phase is generally very low. At a high content of the reduced oxide phase, stresses 
 were high enough to crack the ferrite crystals around the inclusion. 
 
 The decrease in initial permeability and the increase in coercive force found 
 by us in the nickel-zinc ferrites (Ni Q 33 Zn 67 0). ( Fe o°3)i_ for x >0, as shown 
 in figure 25, has to be attributed to the same effect. In these ferrites the crys- 
 talline anisotropy is very low, whereas the magnetostriction has a value still high 
 enough to cause a sufficiently large stress anisotropy to affect the permeability 
 and coercive force. In the range measured the volume fraction of the second phase, 
 a divalent metal oxide, is far too low to account for the decrease in M and the 
 increase in H . All these specimens have a density differing from the X-ray density 
 
 by less than 0.25%. Both n and H show a perfect inverse behaviour in this case. 
 
 o c 
 
 By a special method the internal demagnetization caused by pores can be de- 
 termined experimentally. In figure 26 the internal demagnetization coefficient N. 
 has been plotted as a function of the porosity p. Curve a was measured for a cu- 1 
 bic spinel (ferroxcube ) . The value of N. goes to zero for p=0. 
 
 A typical effect of microstructure occurs in the hexagonal ferroxplana ma- 
 terials, in which the basal plane is a preferential plane for the magnetization 
 
 79 
 
 
[22] In a polycrystalline sample, with random orientation of the crystallites, a 
 large demagnetizing effect arises from the strong forces which bind the magnetization 
 vectors to the preferential plane. In figure 27 the lines of force have been drawn 
 for a schematic situation in which the preferential planes lie within the plane of 
 the figure, except for one crystal. The lines of force bend around this crystal, 
 which therefore acts as an air gap. From measurements of N. it appears that in iso- 
 tropic ferroxplana materials an appreciable value ^or N ± remains when p=0 (curve b. Fig, 
 26.) Thus, even in a fully dense hexagonal ferrite a virtual porosity is present, cor- 
 responding to a cubic ferrite of 30$ porosity. 
 
 It is possible to give the crystallites a preferred orientation by utilising 
 the magnetic anisotropy forces. This can result either in a "fan" texture, in which 
 the c-axes of the crystallites lie at random in a plane (see figure 28), or in a 
 texture as shown for barium hexaferrite (see figure 18), in which the c-axes are 
 oriented more or less parallel. Measurements on specimens with an increased degree 
 of orientation f , in which f = for random and f = 1 for parallel orientation of 
 the c-axes, show the expected decrease of N., as shown by curve c in figure 26. The 
 technically important effect is a large increase of the permeability, mainly resulting 
 from this decrease of N ± , as shown in figure 29. 
 
 8. High-Frequency Behaviour 
 
 Dp till now we have only discussed the static magnetic properties of magnetic 
 ceramics. Except for the permanent magnets, their practical usefulness is at high 
 frequencies and we shall discuss some of the microstructural aspects of the high- 
 frequency behaviour. We shall limit our discussion to the properties up to radio 
 frequencies. 
 
 A sinusoidal field gives an induction that lags behind the field in time. This 
 time lag gives rise to losses, expressed as the loss angle tan 6. In low-induction 
 applications one is primarily interested in the quality factor = 1/tan 6. The los- 
 ses can be divided into hysteresis, eddy-current and residual losses. Because of the 
 complexity of the physical relation between these losses and the microstructural 
 characteristics of the ferrite, only some view-points will be brought forward. 
 
 For low hysteresis losses a homogeneous structure seems to be necessary. With 
 less uniform grain size distribution and with grains having pores enclosed, the 
 
 hysteresis losses are greatly increased [18], [23] . 
 
 The eddy-current losses in most ferrites are negligible, unless the ferrous 
 content is high. Ferrous ions lower the resistivity of ferrites considerably. In 
 manganese-zinc-ferrous ferrites, which have the most useful properties for many ap- 
 plications (especially for telecommunications) up to frequencies of about IMc/s, the 
 ferrous content is essential for the specific magnetic properties desired. The low 
 resistivity, about 10-100 fl-on, caused by this ferrous content results in eddy- 
 current losses which are relatively high, compared to the other magnetic losses. A 
 peculiar effect is the decrease in the eddy-current losses when Ca-ions are added in 
 a quantity of about 0.1 mole-* [18,24] . The preference for the Ca-ions to be located 
 at grain boundaries was concluded from several experiments. It was also shown that 
 the resistivity measured within the individual grains is lower than the resistivity 
 measured across the grain boundaries; when Ca-ions are present the difference is 
 much larger (Fig. 30). During cooling of these ferrites a reoxidation occurs. The 
 addition of Ca-ions apparently brings about the appearence of an open porosity, so 
 that quick reoxidation can also occur at the core of the specimen. Although the re- 
 oxidation of the bulk of the crystals is increased as compared with specimens in 
 which no Ca-ions are present, the main effect is the high state of oxidation at the 
 grain boundaries if Ca-ions are present. 
 
 Little effective work has been done on the influence of microstructure on re- 
 sidual losses. Among many other factors, domain-wall relaxation processes definite- 
 ly seem to have an influence, especially when inhomogeneities are present. The same 
 holds for the losses in those applications where high inductions are used (trans- 
 former cores) and thus irreversible wall movements play a preponderant role. 
 
 It appears that every group of materials has its optimum frequency range where 
 it can be used. The upper frequency limit is given by the so-called natural reso- 
 nance frequency, where the losses increase sharply. In fig. 31 the relative -loss 
 factor tan 6-/p is given for different classes of ferrites, as a function of fre- 
 quency. 
 
 80 
 
The very soft manganese-zine-f errous ferrite show excellent magnetic properties 
 in the lower frequency range. The high permeability in these materials is caused by 
 a large contribution from wall movements [18]. In this lower frequency range, wall 
 mobility is apparently high enough to cause no losses. 
 
 In the higher frequency ranges, however, wall mobility is generally not suf- 
 ficiently high. To obtain reasonably low losses at these high frequencies only mo- 
 derate permeabilities can be used, in which no large contribution from domain wall 
 movements is present. Although both small grain size and a finely divided porosity 
 within the grains are effective to make low-loss materials for these high frequen- 
 cies, the most effective way to obtain low losses is by completely freezing the do- 
 main walls by the substitution of a few percent of cobalt ions. 
 
 9. Conclusion 
 
 about 
 discu 
 crost 
 ceram 
 prope 
 dynam 
 creas 
 estab 
 
 The world pr 
 12,000 tons 
 ssion has be 
 ructure had 
 ic permanent 
 rties of the 
 ic condition 
 es. As many 
 lish a clear 
 
 oduction of magneti 
 
 a year with a valu 
 
 en limited to sever 
 
 a clear influence. 
 
 magnetic materials 
 
 static hysteresis 
 
 s, the number of ot 
 
 of them are physica 
 
 relationship betwe 
 
 c ceramics is rapidly increasing. It is now 
 e of about $30,000,000. In the foregoing the 
 al groups of magnetic ceramics, in which the mi- 
 This relationship is most straightforward in the 
 . A clear relationship is also found with the 
 loop. For the magnetic properties measured under 
 her factors influencing these properties in— 
 lly not well understood, it is more difficult to 
 en these phenomena and the microstructure . 
 
 Ceramic technology can supply the methods and tools necessary for achieving 
 certain required microstructures , also for fundamental studies of the physical phe- 
 nomena. Hot-pressing undoubtedly is one of these methods [25] . 
 
 There are several other applications in which specific properties of ferrites 
 form a keypoint. Ferrites for radar and microwave communication components require 
 a very low porosity [26] . The same holds for ferrites used in magnetostrictive trans- 
 ducers. In recent times the study of ferrites with square hysteresis loops, as used 
 in memory cores, has been directed to the microstructure with more success than be- 
 fore [27J . Further studies of the fundamental aspects in those fields of the techno- 
 logy of magnetic ceramics, which determine the microstructure, will certainly help 
 both to provide a better understanding of the physical properties and a better con- 
 trol of their fabrication. 
 
 The author thanks his collegues Dr. G.H. Jonker, Dr. E.W. Gorter, A. Broese 
 van Groenou and C. Kooy for critically reviewing the manuscript. 
 
 References 
 
 [i] J.L. Snoek, New Developments in Ferro- 
 magnetic Materials, Elsevier Publishing 
 Comp. New York-Amsterdam (1947). 
 
 [2] E.J.W. Verwey and E.L. Heilmann, Physical 
 Properties and Cation Arrangement of 
 Oxides with Spinel Structures, J.Chem. 
 Phys. 15, 174-180 (1947). 
 E.J.W. Verwey, P.W. Haaijman and F.C. 
 Romeyn, Physical Properties and Cation 
 Arrangement of Oxides with Spinel Struc- 
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 [3] L. Ne"el, Proprie'te's niagne'tiques des fer- 
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 magne'tisme, Ann. de Phys. 3^, 137-198 
 (1948). 
 
 [4] C. Guillaud and H. Creveaux, Prepara- 
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 Compt. Rend. Ac. Sc. Paris, 230 , 1256- 
 1258 (1950). 
 
 C. Guil 
 des f 
 239-2 
 
 C. Guil 
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 Rend. 
 (1950 
 
 C. Guil 
 Magne* 
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 Ac.Sc 
 
 E.W. Go 
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 (3), 
 
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 ) 
 
 laud and M. Sa 
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 1 of Spontaneo 
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 4s niagne'tiques 
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 44-946 (1951) 
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 us Magnetiza- 
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 Phys. Rev. ,90 
 
 [5] E.W. Gorter, Some Properties of Fer- 
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 Chemistry, Proc. I.R.E. 43, 1945- 
 -1973 (1955). 
 
 81 
 
[6] J. Smit and H.P.J. Wijn, Ferrites, 
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 [7] P. Weiss, L'Hypothese du Champ Mole*- 
 culaire et la Proprie*te" Ferromagne"- 
 tique. Journ. de Phys. 6, 661-690 
 , (1907) 
 
 [8] F. Bloch, Zur Theorie des Austausch- 
 
 problems und der Remanenzerscheinung [21] 
 der Ferromagnetika, Zeit . f .Physik, 74 
 295-335 (1932). 
 
 [91 C. Kooy and U. Enz , Domain Configura- 
 tion in Layers of BaFe 12 ig , Philips [ 2 % 
 
 Res.Repts. 15 (l), 7-29 (I960). 
 
 [10] I 
 
 [11] 
 
 [12] 
 
 [13] S 
 
 . Hanke und W. Metzdorf, Abbildung 
 magnetischer Bereichs-strukturen von [23] 
 Ferriten mit Hilfe des magnetooptischen 
 Kerr-Effekts, Z. angew. Phys. 15 (2), 
 191-192 (1963). 
 
 [24] 
 
 . Broese van Groenou, private communi- 
 cation. 
 
 Kittel, Phys. Theory of Ferromagnetic 
 Domains, Rev. Mod. Phys. 2_1 (4), 
 541-583 (1949). 
 
 .L. Blum, Microstructure and Properties 
 of Ferrites, J .Am.Ceram. Soc. 4_1 (11), 
 489-493 (1958). 
 
 [26 
 
 [14 1 J.J. Went, G.W. Rathenau, E.W. Gorter 
 and G.W. van Oosterhout, Ferroxdure, 
 a Class of New Permanent Magnet Ma- 
 terials, Philips Techn. Rev. 13, 
 194-208 (1951/52). 
 
 [15] A.L. Stuijts, Sintering of Ceramic Per- 
 manent Magnetic Material, Trans. Brit. 
 Ceram.Soc. 55, 57-74 (1956) 
 
 [16] A.L. Stuijts, G.W. Rathenau and G.H. 
 
 Weber, Ferroxdure II and III, Ani- [ 2 7 
 sotropic Permanent Magnet Materials, 
 Philips Techn. Rev. 16, 141-147 (1954). 
 
 [17] Reference [6] page 245. 
 
 [18] C. Guillaud, The Properties of Manganese- 
 Zinc Ferrites and the Physical Proces- 
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 Engrs.l04B, 165-173 (1957). 
 
 [19] M„ Paulus, Influence des pores et des 
 inclusions sur la croissance des 
 cristaux de ferrite, Phys . Stat .Sol . 
 2, 1325-1341 (1962) 
 
 [20] J.E. Burke, Role of Grain Boundaries in 
 Sintering, J .Am.Ceram. Soc . , 40, 80- 
 -85 (1957). 
 
 R.E. Carter, Effect of Oxygen Pressure 
 on Microstructure and Coercive Force 
 of Magnesium Ferrite, J. Am.Ceram. Soc , 
 41 (12), 545-550 (1958). 
 
 A.L. Stuijts and H.P.J. Wijn, Crys- 
 tal-Oriented Ferroxplana, Philips 
 Techn. Rev. 1_9, 209-217 (1957/58). 
 
 W. Heister, Magnetic Properties and 
 Grain Structure of Mn-Zn Ferrites, 
 J.Appl.Phys. 30 (4), 22S-24S (1959) 
 
 M. Paulus et Ch. Gaullaud, Structure 
 Granulaire et Proprie'te's des Fer- 
 rites, J. Phys. Soc. Japan, 1_7, 
 Suppl. B-I, 632-640 (1962). Proc. 
 Int.Conf. Magnetism and Crystallo- 
 graphy, 1961, Kyoto. 
 
 [25] W.W. Malinofsky and R.W. Babbitt, 
 Fine-Grained Ferrites. I. Nickel 
 Ferrite, J.Appl.Phys. 32 (3), 
 237S-238S (1961). 
 
 W.W. Malinofsky, R.W. Babbitt and 
 G.C. Sands, Fine-grained Ferrites, 
 
 11 ' Ni i-x Zn x Fe 2°4° Jo A-PP 1 - 1 ^^- 
 33 (3), 1206-1207 (1962). 
 
 ] A.L. Stuijts, J. Verweel and H.P. 
 Peloschek, Dense Ferrites and 
 Their Applications, Proc. Intern. 
 Conf. on Nonlinear Magnetics, 
 Washington, April 17-19, 1963; 
 I.E.E.E. Spec. Publ. T-149. 
 
 ] J.E. Knowles, Philips Techn. Rev., 
 24, 242-251 (1962/63). 
 P.D. Baba, E.M. Gyorgy, and F.J. 
 Schnettler, Two-Phase Ferrites 
 for High-Speed Switching. J.Appl. 
 Phys., 34 (4), 1125-1126 (1963). 
 E.A. Schwabe and D.A. Campbell, 
 Influence of Grain Size on Square- 
 Loop Properties of Lithium Fer- 
 rites, J.Appl.Phys., 34 (4), 
 1251-1253 (1963). 
 
 82 
 
Fe 2 03 
 100*0 
 
 M=BaFe )2 0,, 
 
 8a 
 
 W =Ba Me 2 Fe 16 2 7 
 
 Y =Ba 2 Me 2 Fe 12 22 
 
 20 z =Ba 3 Me 2 Fe 2A 41 
 
 Ba0 2Fe 2 3 
 60 ' 
 
 BaFe 2 Q4 
 
 H 
 
 FIGURE 1. Composition diagram for the 
 ferromagnetic ferrites. Me is a di- 
 valent ion or a combination of diva- 
 lent ions. 
 
 FIGURE 2. Change of the direction of 
 the magnetization vector M in an ap- 
 plied field H. 
 
 INDUCTION 1 
 B 
 
 EXTERNAL FIELD H 
 
 FIGURE 3. Hysteresis loop of a magnetic 
 material. 
 
 FIGURE 4. Weiss domains in a ferromag- 
 netic material. Unmagnetized state. 
 
 83 
 
FIGURE 5. Examples of Weiss 
 domain configurations. 
 
 'f' 
 
 ^ * 
 
 It 
 
 ll 
 1 1 
 w 
 
 NNNN 
 
 t 
 
 SSSS 
 
 3-7 <" 
 
 \ \ 
 
 ^'r»iV > - 
 
 SS 
 
 I 
 
 NN 
 
 •I' 
 
 3 
 
 ?C*fj->**> 
 
 Y Y Y 
 I 
 
 Ijl, 
 
 11 II J^ 
 
 1 
 
 WALL 
 
 -> 
 
 
 4- 
 
 t 
 
 DOMAIN 
 
 1 
 
 1 
 
 DOMAIN 
 
 J 
 
 
 V 
 
 FIGURE 6. Spin configuration 
 inside a Bloch wall. 
 
 FIGURE 7. "Bitter" powder 
 pattern on crystals of 
 
 BaF< 
 
 i Ox. 
 
 embedded in a 
 
 giassy phase (courtesy of 
 G. H. Jonker) . 
 
 84 
 
UNMA6NETIZED 
 
 MAGNETIZED 
 BY DOMAIN 
 ROTATION 
 
 MAGNETIZED 
 BY DOMAIN 
 GROWTH 
 
 FIGURE 8. Magnetization Processes: 
 
 (a) unmagnetized states (b) magnetized 
 by domain rotation; (c) magnetized by- 
 domain growth. 
 
 -O 
 
 f -r?+-^- 
 
 
 
 ■■■■■ '■'/// A 
 
 TZZ&ZZZZZZZ 
 
 INDUCTION 
 B 
 
 FIGURE 9. Decrease of demagnetization 
 energy when a domain wall intersects 
 a pore or inclusion. 
 
 ROTATION 
 PROCESSES 
 
 IRREVERSIBLE 
 WALL MOVEMENTS 
 
 REVERSIBLE 
 WALL MOVEMENTS 
 
 HELD STRENGTH H 
 
 FIGURE 10. Different magnetization pro- 
 cesses along the magnetization curve. 
 
 FIGURE 11. Magnetization in a small par- 
 ticle without and with a Bloch wall. 
 
 85 
 
 
FIGURE 12. Coercive force H 
 as a function of particle 
 diameter for iron, 
 BaFe 13 ia and manganese 
 bismuth. 
 
 PARTICLE DIAMETER (MICRONSj 
 
 1: FIRED 5 MIN AT1250°C 
 2: „ ,, „ „ 1350°C 
 
 FIGURE 13. Upper half of the 
 hysteresis loop for 
 BaO*6Fe with random 
 crystal orientations. 
 
 -4000 -2000 2000 4000 6000 
 »- H (OERSTED) 
 
 FIGURE 14. Photomicrographs 
 of sintered specimens of 
 polycrystalline BaO*6Fea0 3 
 showing a) grain size for 
 optimum magnetic properties 
 and b) discontinuous grain 
 growth. 
 
 86 
 
oh 
 
 20 
 16 
 '12 
 
 o 
 % 8 
 
 
 
 
 
 
 
 
 
 C-AXIS 
 f | 
 
 
 
 
 
 
 r-Md 
 U D J T 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 FIGURE 15 . Ratio of diameter to thickness 
 of discontinuous grown grains in sin- 
 tered Ba0.6Fe„0 as a function of grain 
 diameter D. 3 
 
 100 200 300 400 500 600 
 — GRAIN DIAMETER D (MICRONS) 
 
 H=0,4tTI=0 
 
 H=0,4lTl=B r 
 
 H=0,4rtl=0 
 a 
 
 H=o,4rrl=B r =4TtIs 
 c 
 
 FIGURE 16. A sintered mass of barium hexa- 
 ferrite a) unmagnetized, b) magnetized 
 in a field H and c) converted into a 
 permanent magnet. 
 
 Upper row: crystallites in random orien- 
 tation; bottom row: parallel-oriented 
 crystallites. 
 
 FIGURE 17. Demagnetization curves of barium 
 hexaferrite for a) isotropic and b) crys- 
 tal-oriented sample. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 AN ISOTR 
 
 DPIC 
 
 
 
 
 ISOTR 
 
 OPIC^-- 
 
 
 
 
 
 / 
 
 
 
 
 
 
 4000 
 (GAUSS) 
 4TTI 
 t 
 3000 
 
 2000 
 
 1000 
 
 -5000 -4000 -3000 
 
 -2000 -1000 
 *■ H (OERSTED) 
 
 87 
 
FIGURE 18. Photomicrograph of a crystal- 
 oriented barium hexaferrite sample, 
 thermally etched. 
 
 t 1 
 
 U 
 
 
 
 1350 °C 
 
 
 
 
 
 I 
 
 i 
 
 1300^\^ 
 
 '0.5^0 
 
 .5 Fe 2° 
 
 4 
 
 
 
 1250^^ 
 
 
 
 
 
 
 
 \o1200 
 
 10 2 
 
 
 
 
 
 
 
 
 
 
 
 (SINGLE . 
 CRYSTAL) ' 
 
 \ 
 
 ( 1450°C 
 
 
 1 
 
 1150 
 
 ioo\ 
 
 10 
 
 Frot- 
 (CALCULATED) 
 
 
 1327 
 
 
 
 
 N 
 
 iFe^Oz, 
 
 X > 
 
 \x 
 
 
 
 
 
 
 X 
 
 \960 
 
 
 1 
 
 
 
 
 
 
 
 10 
 H c (Oe) 
 
 t 
 
 8 
 
 Ni .< 
 
 , Zn 0.5 Fe 
 
 2°4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 0.1 
 
 0.2 
 
 0.3 0-4 0.5 
 
 0.1 
 
 0.2 0.3 0-4 0-5 
 
 FIGURE 20. Variation of the coercive 
 force H with the porosity p of a se- 
 ries of c nickel-zinc ferrites. (After 
 Smit and Wijn [6] ) . 
 
 FIGURE 19. Variation of the initial per- 
 meability m with the porosity p for 
 NiFe 2 4 and 8i 05 Zn 05 Fe o /1 . (After 
 
 Smit en Wijn [17] ) . 
 
 '2"4' 
 
 88 
 
UJ 
 
 JUUU 
 
 4000 
 3000 
 2000 
 
 1000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 10 15 20 
 
 ►CRYSTAL DIAMETER IN MICRONS 
 
 FIGURE 21. Variation of the initial per- 
 meability H- with grain diameter in 
 manganese-zinc ferrites. (After 
 Guillaud [18] ). 
 
 10 _ 15 
 
 -*-d 3 IN MICRONS 
 
 MGURE 22. Density of manganese-zinc fer- 
 rite, with the same chamical composition 
 as; those in fig. 21, as a function of 
 the mean diameter of the grains, (.Af- 
 ter Paulus [19] ) . 
 
 1240 1280 
 
 ►TEMPERATURE (°C) 
 
 FIGURE 23. Initial permeability and den- 
 sity as a function of the temperature 
 to which the samples have been heated. 
 Heating-rate 250 C/hr. 
 
 89 
 

 T = I200°C 
 
 i^ 
 
 T = I2I0°C 
 
 25/x J 
 
 
 
 *.v '^ 
 
 T = 1270 °C 
 
 FIGURE 24. Photomicrographs of samples from fig. 23 at a) 1200 °C, 
 b) 1210°C and c)~1270°C. 
 
 FIGURE 25. Initial permeability H- , 
 coercive force H and density for a 
 range of nickel-zinc ferrites with 
 excess metal oxide. All the specimens 
 are very near to X-ray density. 
 
 0-2B 
 
 ,'0.5 
 
 ;o.4 
 
 0.3 
 
 S0.2 
 
 0.1 
 
 0.4 
 
 (_> 
 o 
 
 K 
 
 33^067^ 
 
 1 J \ 
 
 ^5-3 
 tn 
 
 3 
 
 S5.2 
 
 > 
 
 ^5.1 
 
 ! 
 
 5.0 
 
 
 DENSITY-'' ~7\ 1 ' 
 
 
 
 
 / \ 
 
 / 1^ 
 
 A ' 
 
 
 
 
 ^INITIAL 1 
 
 PERMEABILITY 
 
 i 
 
 l 
 
 1 
 
 
 
 
 1 
 
 COERCIVE FORCE 
 
 1 
 
 X ' 
 
 
 
 
 1 
 1 
 
 1 
 
 0-04 
 x- 
 
 0JD2 
 
 2500 
 
 2000 1 
 
 1500 
 
 1000! 
 
 500 
 
 FIGURE 26. Internal demagnetization co- 
 efficient N. as a function of the po- 
 rosity p: a) for ferroxcube; b) for 
 isotropic ferroxplana; c) for crystal- 
 oriented Co„Z with different degree 
 of orientation f. 
 
 0.10 0-20 0.30 0.40 0-50 
 ^P 
 
 90 
 
FIGURE 27 „ Demagnetizing effect of a 
 crystal whose basal plane (hatched) 
 is at right angles to the magnetic 
 flux. 
 
 FIGURE 28. Photomicrograph of a ferroxplana material with "fan" texture. The c-axes 
 of the crystallites lie at random in the plane of the figure (thermally etched) . 
 
 91 
 
30 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 
 
 
 °s 
 
 
 10" 
 
 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 0.2 
 
 0-4 
 
 0-6 
 
 0.8 
 
 1.0 
 
 OHMS 
 10000 
 
 1000 
 
 100 
 
 *■*•* 
 
 N 
 
 X \ 
 \\ \ \ 
 
 A0GRE6A 
 WITH Cc 
 
 \ 
 
 \ 
 \ 
 
 TE 
 
 
 
 \ \ \ 
 \ \ 
 
 I 
 
 
 
 
 \ 
 
 \ 
 
 \ \ 
 
 
 
 
 
 
 - 
 
 1 — _ _ 
 
 10 
 
 * 
 
 
 
 \ AGGREGATE 
 i V"WITHOUT Ca 
 
 
 INSIDE THE 
 CRYSTALS : 
 WITH Ca-"" 
 
 
 
 
 
 WITHOUT Cs 
 
 
 ■T*"' 
 
 . ^— -— 
 
 0.1 
 
 
 
 
 
 
 47 
 
 49 
 
 51 
 
 53 
 
 55 
 
 57 
 
 7° Fe 2 : 
 
 FIGURE 29. Initial permeability H- of 
 Co„Z (Ba 3 Co 2 Fe 24°4l) with different 
 degree of orientation f. 
 
 FIGURE 30, Resistivity of manganese- zinc 
 ferrites, with and without Ca-addition, 
 as a function of the Fe 2 0„-content „ 
 (After Paulus and Guillaud [24] ) . 
 
 -7 
 10 
 
 10 
 
 10 
 
 10 
 
 10 6 10 7 10* 10 9 10 10 
 -FREQUENCY IN CYCLES PER SECOND 
 
 FIGURE 31. The relative loss factor 
 
 tan 8//i for different groups of fer- 
 rites as a function of frequency. 
 
 92 
 
Microstructure of Porcelain 
 Sten T. Lund in 
 
 1 . Introduction 
 
 The principal raw materials in the manufacture of porcelain are kaolin clay, feld- 
 spar and quartz. The primary purpose of these three components may be described rather 
 roughly in the following way. The clay gives the body the necessary plasticity during 
 forming and cohesion during drying. The feldspar acts as a flux and glass former in the 
 firing, and the quartz is a filler material ensuring less shrinkage and more stability 
 to the body during firing. 
 
 The bodies pass through several processes on their way to the final product, the 
 most important being forming, drying and firing. The composition of a body is not 
 determined only by the desired properties of the material in the finished product, but 
 also by the properties required of the body during the different phases of manufacture. 
 The composition of the body may vary considerably according to the purpose of the 
 product [_8j 1 . However, we will not discuss the differences between various types of 
 triaxial whiteware bodies here, but will deal with the common characteristic features 
 of their microstructure. 
 
 We are interested in the microstructure of the porcelain as it determines the 
 material properties. The things we want to know about the microstructure are the nature, 
 quantity and distribution of phases and pores. We also want to know the degree of in- 
 homogeneity in the glass phase, and the structural stresses present in the different 
 phases . 
 
 I will here give a review of our present knowledge and at the same time also try 
 to explain why the microstructure looks the way it does. 
 
 2. Composition of Porcelain 
 
 In table 1 the normal composition range of the raw body is given together with the 
 chemical composition of the fired bodies. If the raw materials in the bodies are pure 
 kaolinite , potash feldspar and quartz, the total system after dehydration can be 
 represented in the ternary system K 2 0-Al 2 0o-Si0 2 , for which Schairer and Bowen have 
 given the equilibrium diagram [l4, 15] • But technical bodies always have more than 
 these three components, and these minor constituents are important, for they have a 
 great influence on the changes during firing. In the absence of data on the multi- 
 component systems, Shelton has suggested converting the extra components to equivalent 
 contents of the main components similar in character Pi 7~] • 
 
 4 
 
 The phases occurring in triaxial whiteware bodies are normally mullite 
 3Al 2 03'2SiC>2, quartz and a glass phase. In addition cristobalite may sometimes be 
 present as a fourth phase in bodies with a high percentage of quartz. The nature and 
 percentages of the crystalline phases can be determined by X-ray diffraction analysis. 
 As a rule technical porcelain contains about 10 - 25 per cent mullite, 5-25 per cent 
 quartz, and 65 - 80 per cent glass. The glass phase is thus the major part of the 
 porcelain. In addition, there are always pores in whiteware bodies. Even when the bodies 
 are fired to impermeability, a porosity of 4 - 8 per cent remains as closed pores. 
 
 Figures in brackets indicate the literature references at the end of this paper, 
 
 93 
 
per 
 
 cent 
 
 70 
 
 - 801 
 
 
 < 11 
 
 15 
 
 - 25 
 
 2 
 
 " 5 I 
 
 1 
 
 " 2 
 
 
 < 1 
 
 
 < 1 
 
 
 < 1 
 
 R 2 
 
 TABLE 1 Composition Range of Porcelain 
 
 Components in the raw body 
 
 per cent 
 China clay ^0 - 60 
 
 Ball clay 
 
 Feldspar 25 - 35 
 
 Quartz 10 - h0 
 
 Chemical composition of the fired body 
 
 Shelton's grouping 
 Si0 2 70 - 80^ 
 
 Ti0 2 
 
 A1 2 3 15-25 Al2°3 
 
 K 2 
 Na 2 
 CaO 
 MgO 
 
 Fe 2°3 
 
 C. Phase composition of the fired body 
 
 per cent 
 Mullite 10 - 25 
 
 Quartz 5-25 
 
 Cristobalite 0-10 
 
 Glass 65 - 80 
 
 3. Appearance of the Micros true ture in the Optical Microscope 
 
 The microstructure of porcelain may be studied by different methods, but the 
 replica technique on polished and etched specimens is the simplest one and gives the 
 best results. A photomicrograph of an electrical insulator porcelain is shown in figure 
 1. This is a general picture with a magnification of about *400x taken on a collodion 
 replica with transmitted light. The micrograph shows that porcelain is a very hetero- 
 geneous material with the crystalline phases rather unevenly dispersed in a continuous 
 glass matrix. 
 
 Reminiscences of the original boundaries of the quartz and feldspar grains in the 
 raw body can be distinguished in the micrograph. In this porcelain an extensive dis- 
 solution of the quartz grains has occurred as shown by the wide solution rims. Of the 
 mullite phase, only the larger of the crystals which have grown in the feldspar relicts 
 can be seen. No formation of cristobalite is found in this sample. The pores of the 
 porcelain are indicated by black areas in the micrograph. 
 
 The occurrence of cracks around and even within the quartz grains can easily be 
 seen. Most or nearly all of these cracks do not exist in the untreated porcelain 
 material but are formed during the preparation of the specimen in the grinding and 
 polishing operations by the release of microstresses within the quartz grain and the 
 surrounding glass phase. These stresses are due to the great difference in the thermal 
 expansion coefficient between the crystalline quartz and the glass phase. 
 
 The information obtained from this type of micrograph is mainly concerned with the 
 grain size distribution of the quartz and feldspar components and their blending in the 
 raw body, the degree of dissolution of the quartz, and the orientation effects present. 
 
 Figure 2 shows the microstructure of another electrical insulator porcelain with 
 a higher quartz percentage and less quartz solution, and figure 3 the structure in a 
 vitreous sanitary ware at higher magnification. The firing temperatures have here been 
 too low to give an appearence of the individual mullite crystals. 
 
 In figure k, showing the structure of a porcelain fired at higher temperature, 
 mullite crystals can be seen in the feldspar relicts but not in the clay matrix. Some 
 of the quartz grains have started transformation into cristobalite. 
 
 k. Appearance of the Microstructure in the Electron Microscope 
 
 Only a small part of the mullite phase can be observed by the optical microscope, 
 owing to the extremely small size of the mullite crystals. In order to determine the 
 quantity and distribution of the mullite phase the replica method has to be used in 
 connection with the electron microscope. 
 
 94 
 
Figures 5a and 5h show electron micrographs of an electrical porcelain at a 
 magnification of about 2500. We see here still more strikingly that the original 
 composition of the raw body with respect to quartz, feldspar and clay determines the 
 distribution of the crystalline . phases in the fired product. The appearance of the 
 mullite phase in the feldspar relicts is as distinct as can be desired, for the mullite 
 crystals isolated by the etching have stuck to the replica. The mullite phase in the 
 original clay fields has a different appearance. The mullite crystals are here present 
 in more compact aggregates, and the isolated crystal layer in the surface does not 
 stick to the stripped replica, which, therefore, has an uneven surface at these places. 
 
 The mullite crystals in the original feldspar and clay fields are different in 
 size , shape and degree of aggregation. This is due to the different formation conditions 
 of the mullite phase in these two types of fields. In order to understand this, we must 
 study the reactions during the firing of the body. 
 
 5. Changes during Firing 
 
 First a short survey will be given of the different processes that occur in the 
 structure during the firing of the body. Then the high temperature changes resulting in 
 the mullite phase distribution, the quartz grain dissolution, and cristobalite formation 
 will be discussed in connection with the ternary diagram, K20-Al203-Si02« 
 
 In the raw body, relatively large quartz and feldspar grains are surrounded by 
 clay crystal plates and stacks. Thus the contact surfaces consist of quartz-kaolin and 
 feldspar-kaolin, but only exceptionally of quartz-feldspar. Then the potash feldspar 
 always contains some albite or soda feldspar. 
 
 When the body is heated, the chemically bound water in the kaolin clay is expelled 
 at 500-600°C giving a metakaolin phase Al203»2Si02 £lj . The next change occurs at 
 700-1 000°C in the feldspar, where the mixed alkali feldspars are transformed into the 
 homogeneous high temperature form sanidine [12J. 
 
 Brindley and Nakahira [2] showed in their excellent work (1959) that the meta- 
 kaolin phase at 925-950°C condenses to a spinel type phase 2Al s 3 • 3SiO s and amorphous 
 silica. 
 
 A melt phase begins to form in the same temperature interval by boundary reaction 
 between sanidine and the amorphous silica in the clay relicts. For a potash feldspar 
 with 20 per cent albite this occurs already 60° below the eutectic temperature of 985 C 
 in the ternary system K^O-A^Oo-SiOp [til* B u * at these low temperatures the diffusion 
 rates are very low, and thus the melt formation proceeds very slowly in the beginning. 
 The alkali liberated in the feldspar reaction starts diffusing into the clay relicts. 
 The sintering of the body also starts with the melt formation, very slowly at first, 
 but accelerating as the proportion of melt increases and its viscosity is lowered. 
 
 At about 1000-1050 C the mullite phase begins to develop in the clay phase relicts 
 from the spinel type phase with further discarding of silica. At a somewhat higher 
 temperature the mullite phase also begins to develop in the feldspar relicts by crystals 
 growing from the boundaries. 
 
 At about 1200 C the mullite phase is completely developed in the clay relicts and 
 
 normally also in most of the feldspar relicts. During the continued firing at higher 
 
 temperatures, recrystallization of the mullite phase continues resulting in larger 
 crystals . 
 
 The quartz phase has a very low reactivity and the grains are not noticeably 
 affected by the other components below 1200°C. But about this temperature the dissolu- 
 tion of the quartz grains begins developing solution rims of crystal-free glass. If 
 enough quartz is present to saturate the melt, the quartz dissolution stops and the 
 quartz begins to transform into cristobalite. 
 
 When the temperature is decreased during the last part of the firing, there is a 
 small increase in the mullite content due to crystallization from the melt. No other 
 crystallization occurs, and the melt now forms the glass phase in the porcelain. 
 
 6. The Use of the Phase Diagram K 0-Al„0_-SiO 
 
 Several attempts have been made to describe the changes occurring during firing 
 and also to explain the microstruc ture , starting from the equilibrium diagram of 
 K 2 0-Al 2 0--Si0 2 , and using Shelton's grouping [3, 5, 11, 1 7] . 
 
 95 
 
Equilibrium concerning the total system in a triaxial whiteware body is never 
 attained at any point in the current firing schedules. Not even the polymorphic forms 
 of the silica corresponding to equilibrium are present at high temperatures. Nor does 
 the melt crystallize to tridymite and potash feldspar during the cooling of the body. 
 However, the proportions of mullite phase and melt can be estimated satisfactorily from 
 the diagrams. This fact, combined with a consideration of the relative rates of the 
 different process elements, makes the diagram very useful for describing some of the 
 reaction changes at high temperatures. 
 
 But trying to predict from the ternary diagram the quantity of melt in the body 
 at temperatures below 1100 - 1200°C gives great divergence from experimental data. 
 There are two reasons for this. First the active phases do not correspond to the 
 equilibrium phases (the presence of the spinel phase and the absence of a leucite phase) 
 and second the presence of Na 2 lowers the liquidus surfaces appreciably. At these 
 temperatures the melt formation is not an equilibrium state problem but instead a rate 
 problem. 
 
 It is not until the feldspar phase has disappeared and the mullite phase formed 
 that the changes in the phase composition of the body can be represented advantageously 
 in the ternary" diagram. Here the use of the diagram will be demonstrated for two cases, 
 (a) an explanation and estimation of the mullite content in different fields and (b) 
 for describing the change in melt composition during the quartz grain dissolution [1 1j . 
 
 7. Formation and Distribution of the Mullite Phase 
 
 The diffusion processes within the reaction layer between the feldspar and the 
 clay relict will be determined by the concentration gradients and the diffusion rates 
 of the components . 
 
 The formation of the mullite phase and its distribution between the clay relicts 
 and the feldspar relicts will thus be determined by the relative magnitude of the 
 diffusion rates of K 2 and Al 2 3 components, and by the contact surface and diffusion 
 distances, i.e. the grain size and grain distribution of the feldspar phase. 
 
 The alkali, which diffuses over to the clay phase relicts, there accelerates the 
 formation of the mullite phase. The mullite phase is formed first within the clay phase 
 relicts beginning at about 1050°C by discard of silica from the cubic spinel phase. 
 When the alkali content in the melt of the feldspar relicts is reduced sufficiently and 
 the melt becomes supersaturated with mullite, the mullite phase in the feldspar relxcts 
 begins to form from nuclei and already existing mullite crystals at the original grain 
 boundary feldspar-kaolinite . The growth is determined here by the type and direction of 
 the crystal surfaces. The growth is most rapid on [001] surfaces directed toward the 
 inner part of the feldspar relicts, and the mullite phase within the feldspar fields 
 thus acquires its characteristic appearance of a great number of crystal needles running 
 outwards from the original grain boundary toward the inner parts of the feldspar relicts 
 (figure 6a) . 
 
 On the basis of the simplifying approximation that the mass transfer of A1 2 3 may 
 be ignored compared with the mass transfer of alkali over the grain boundaries, the 
 distribution of the mullite phase between the clay and the feldspar relicts after 
 completed reaction can be estimated from the equilibrium diagram. 
 
 Let us study the conditions in a particular body, consisting of 50 per cent 
 kaolinite, 25 per cent potash feldspar and 25 per cent quartz, corresponding to 
 traditional European hard porcelain. After dehydration of the clay the composition of 
 the total system is represented in the ternary phase diagram by the point P1 (, figure 1). 
 The total system now consists of the three reactants , potash feldspar, dehydrated clay 
 and quartz, with the corresponding composition points ¥ (K 2 • A1 2 3 • 6Si0 2 ) , P3 
 (Al o 0o.2Si0 ? ) and Si0 2 . The solution of the quartz grains below 1200°C can be neglected, 
 and the quartz phase be regarded as an isolated system, which does not affect the 
 remaining sub-system feldspar-clay relicts. 
 
 When the alkali content of the feldspar relicts is decreased, their composition 
 point moves from W toward the point Al 2 3 .6Si0 2 . At the same time the alkali content of 
 the clay relicts is increased, which causes their composition point to move toward 
 K 2 0.Al 2 3 «2Si0 2 . 
 
 When the firing temperature increases from 1100° to 1200°C the reaction rate of 
 the mullite formation increases very rapidly. At 1200°C the mullite formation may be 
 regarded as completed in both the clay and feldspar relicts, if the feldspar grains are 
 not too large. At this temperature the sub-system contains only mullite and melt in 
 
 96 
 
equilibrium. The melt will have the composition marked by a square point in the diagram 
 and the compositions of the feldspar and clay relicts are given by the points P4 and P5 
 respectively. This corresponds to a mullite content of 12 per cent in the feldspar 
 relicts and of 52 per cent in the clay relicts. The mullite content within the clay 
 relicts should thus be about four times as great as within the feldspar relicts. This 
 agrees well with the picture of the mullite phase distribution obtained from electron 
 micrographs of etched surfaces and of grains where the glass phase has been dissolved 
 with* hydrofluoric acid. 
 
 8. Size and Shape of the Mullite Crystals 
 
 It is very difficult to describe quantitatively, and simply, the mullite phase of 
 a body as to size, shape and distribution of the crystals. The electron micrographs of 
 etched surfaces give some idea, but local variations are so great that it is difficult 
 to obtain a reliable evaluation of the entire mullite phase (figures 6b and c). The 
 best way is to grind the sample and then isolate the mullite phase by treating with 
 hydrofluoric acid. From the large aggregates of mullite crystals obtained the individual 
 needles can be loosened without any extensive damage and dispersed in water by the action 
 of a colloid mill (figure 8). 
 
 In this way the mullite phase from different kinds of porcelain may be investigated 
 and compared, giving the result that mullite phase in technical porcelains fired at 
 different temperatures or with different feldspars may differ considerably as to mean 
 size and size distribution. But we still know very little about the effect of these 
 variations on the properties of the porcelain. 
 
 The mullite crystals have throughout the characteristic prismatic needle shape. 
 The length of the needles may be very great in the feldspar relicts. The present author 
 has observed mullite needles 0.05 p wide and 10 p. long, that is to say, with a propor- 
 tion of about 200 times between length and width. 
 
 As a result of the growth conditions, the crystals may, within small zones, 
 occasionally lie parallel to each other. The mullite aggregate in figure 9 illustrates 
 part of such a feldspar relict. The sample is taken from a ground electrical porcelain 
 and the glass phase in the grain dissolved in hydrofluoric acid. In stereo this picture 
 gives a good idea of the mutual positions of the mullite crystals in the glass. One is 
 inclined to make a comparision with the reinforcing bars used in a concrete structure. 
 We also notice how non-uniform the width of the crystals is, even within this small 
 section. In the same picture can also be seen some smaller crystal aggregates which 
 come from the original clay fields. These aggregates are much more compact, and are 
 made up of small and shorter mullite needles. 
 
 Comer has shown the orientation of mullite crystals in three preferred directions 
 120° to each other in kaolinite flakes fired at low temperatures [4J . In the clay 
 relicts in porcelain these orientation effects cannot be distinguished with certainty. 
 The explanation must be that the kaolinite relicts become deformed by viscous flow, 
 and this hexagonal outline destroyed or disordered. 
 
 9. The Dissolution of the Quartz Phase and the Formation of Cristobalite 
 
 When discussing the appearance of the quartz grains in the microstructure it is 
 best first to analyze the limiting equilibrium conditions. 
 
 It follows from the ternary diagrams, that if a homogeneous melt with the compo- 
 sition point P1 should crystallize under equilibrium conditions, mullite is the primary 
 phase starting crystallization at about 1800°C. When the temperature has decreased to 
 1230°C, the melt also becomes saturated with tridymite. The melt composition point then 
 follows the boundary line with simultaneous crystallization of mullite and tridymite down 
 to the eutectic at 985°C, where also feldspar starts crystallizing. In solid state 
 there follow two transitions in the silica phase, first to high temperature quartz at 
 870°C and then to low temperature quartz at 573°C. 
 
 There are two important deviations from this equilibrium schedule; (a) the only 
 silica forms that have been observed in technical porcelains are quartz and cristoba- 
 lite , (b) no crystallization from the melt of either silica or feldspar occurs during 
 the cooling, but a glass phase is formed instead. 
 
 When the body is fired, the reactions between clay and feldspar are relatively 
 rapid compared with the dissolution of the quartz grains in the melt. The formation 
 of the mullite phase is mainly completed before the dissolution of the quartz grains 
 becomes noticeable. At the beginning of the dissolution, therefore, the quartz particles 
 
 97 
 
are in a matrix of mullite and melt, where the melt has, on the whole, the same 
 composition. 
 
 The composition of the melt phase in a porcelain is determined by the presence of 
 mullite, the temperature, and the amount of quartz dissolved. Starting from the 
 proportion 2:1 of kaolinite and potash feldspar, and assuming that the melt is always 
 saturated with mullite, the composition point of the melt will move during an isothermal 
 quartz dissolution at 1300°C along the corresponding isotherm within the mullite field 
 (figure 10). Experimental data where the quartz and mullite percentages have been 
 determined by X-ray diffraction analyses and then the mean composition of the melt 
 calculated confirm this [l 1J . 
 
 The total mullite content is changed only slightly during the dissolution of the 
 quartz. If there is so much quartz in the system that the phase boundary line to the 
 tridymite field is reached just when the quartz has been completely dissolved, the 
 mullite content of the total system will be changed from 23.7 per cent at the beginning 
 of the quartz dissolution to 22.7 per cent at the completion of the dissolution. The 
 dissolution of the quartz is thus attended by a slight decrease in the total mullite 
 content. 
 
 If enough quartz is present, the melt will become saturated and the dissolution 
 stops. Then the transformation of the remaining quartz into cristobalite begins. More 
 precisely, the cristobalite phase begins to form when the rate of transition to 
 cristobalite at the phase boundary is greater than the rate of quartz dissolution. The 
 cristobalite phase forms an outer zone round the quartz, and the transformation is 
 apparently a solid state reaction starting from the surface of the quartz grain 
 (figure 11). 
 
 The quartz content at the start of the cristobalite formation may be estimated in 
 the following way. At this point, the phase boundary composition of the melt, and after 
 a certain time also the total composition of the melt, correspond to the saturation 
 point of cristobalite. This value is unknown, but may be approximated by the saturation 
 value of the tridymite according to the phase diagram, which gives a somewhat too high 
 result. The difference in temperature between the stable tridymite liquidus surface and 
 the metastable cristobalite surface is only small according to Schairer and Bowen [15] . 
 
 The dissolution of quartz is a transfer process where alumina and alkali diffuse 
 in the direction towards the quartz surface and there is a mass flow in the melt in the 
 opposite direction. Further, the rate-determining step in the dissolution process is 
 probably the alumina transfer through the crystal-free dissolution zones around the 
 quartz grains. The absence of mullite crystals in the solution rims is due to the fact 
 that the mullite phase in the matrix was already fully developed before the solution of 
 the quartz grains started, and then the solution of the quartz also involves a con- 
 sumption of alumina resulting in a dissolution of the mullite crystals nearest the 
 quartz grains. 
 
 10. Pores and Fracture Surfaces 
 
 Sometimes it is of interest to study the appearance of the pores in the fired and 
 sintered body. This is almost impossible with the optical microscope, but the electron 
 microscope, with its greath depth of field, is an excellent tool, and the stereoscopic 
 technique can be used with great advantage in the interpretation of the micrographs 
 [10, 16, 18]. These circumstances will be illustrated by a few pictures. 
 
 The first, figure 12, shows closed pores in an unetched fracture surface of a 
 normal insulator porcelain. Information about the size, shape and other characteristics 
 of the pores can be obtained from such micrographs. In this case, for example, a faint 
 image of mullite crystals can be seen on the inside surface of the pores. This reveals 
 a beginning bloating effect in the porcelain. If the porcelain is over fired, an in- 
 crease in porosity is obtained, due to the release of gases solved in the melt. In the 
 resulting bloating pores, the melt has been forced back and the mullite crystals are 
 left bare, as shown in figure 13. 
 
 In the same way, studies of the microstruc ture of fracture surfaces of whiteware 
 bodies are possible only with the aid of the electron microscope. My own investigations 
 confirm what can be expected from an ocular inspection of the shard. A smooth, high- 
 sheen fracture surface shows that the fracture runs practically independently of the 
 crystal structure, and a grainy surface shows that the fracture runs principally along 
 the old grain boundaries. 
 
 98 
 
In this connection only one especially interesting i] lustration will be given, fig- 
 ure 14. It is a picture of an unetched fracture surface from a test loaded rod and 
 shows a pore in more unusual surroundings. In one direction the pore merges into a zone 
 with a structure markedly different from both the appearance of the pore and the rest 
 of the fracture stir face. This zone was first assumed to be a drying crack, i.e. a local 
 crack formed during drying, and which later was not completely cured in firing. This 
 zone, however, has exactly the same structure as is found on delayed fracture surfaces 
 in porcelain (figure 15) » that is, cracks which, under constant or slightly varying 
 stress grow from an outer surface at a very low speed so that the total fracture time 
 might be a matter of years. This may imply that figure 14 illustrates the first stage 
 in the progress of a fracture, beginning at a pore in the material. 
 
 11. Degree of Inhomogeneity in the Glass Phase 
 
 The porcelain in its entirety is a very heterogeneous material with crystalline 
 phases and pores dispersed in a glass matrix. The distribution of the mullite phase is 
 very uneven between the clay and the feldspar relicts, which emphasizes the hetero- 
 geneity by giving the different regions different properties. 
 
 However, the most important phase is the continuous glass phase, which gives 
 porcelain its fundamental properties. What we want to know about the glass phase is its 
 local composition or degree of inhomogeneity. The direct experimental study of this in 
 the glass phase is subject to great difficulties. 
 
 A common mistake made earlier was to draw conclusions regarding the homogeneity of 
 the glass phase from values of the diffraction index measured on thin sections observed 
 in the optical microscope. As a matter of fact these observations have not been made on 
 a glass phase, but on a two phase system, glass and mullite, with varying mullite 
 content. This has given rise to the opinion that the glass phase in fired porcelain is 
 most inhomogeneous , having different compositions in different regions. The high 
 viscosity of the system has also contributed to this opinion, but on this point it must 
 be remembered that the high apparent viscosity can only partly be traced back to the 
 melt phase, for the dispersed mullite phase increases it most efficiently. 
 
 Instead conclusions regarding the homogeneity of the glass phase must be drawn 
 indirectly from a combination of (a) quantitative phase determinations, (b) rate 
 measurements, and (c) electron microscopic observations of the phase distribution. 
 Such studies have indicated that the melt phase is not at all so inhomogeneous as 
 previously believed, but instead has its composition regulated by the presence of the 
 mullite phase. The kinetic data provide evidence that at temperatures above 1200°C, 
 equilibrium conditions between melt and mullite phase are approximately reached. This 
 is also true of the feldspar regions once the mullite phase is formed there. The high 
 transfer rates are due to the high specific surface of the mullite phase, giving short 
 diffusion distances in the melt phase. 
 
 The greatest degree of inhomogeneity in the glass phase is caused by the dissolu- 
 tion of the quartz grains. The rate determining step is here assumed to be the alumina 
 diffusion from the adjacent mullite crystals, causing the essential part of the concen- 
 tration gradient to fall within the crystal-free solution rims around the quartz grains. 
 
 Within the types of porcelain in which a cristobalite phase is formed, this 
 concentration gradient has disappeared, too. The highest degree of homogeneity in the 
 glass phase will thus be reached in porcelain bodies with no quartz phase or with such 
 high quartz content that the melt has become saturated and cristobalite formed. 
 
 12. Internal Microstresses 
 
 Due to the great difference in the thermal expansion coefficient between the 
 crystalline quartz and the glass phase, high internal microstresses arise in the 
 porcelain during the cooling of the body. 
 
 A knowledge of the kind and magnitude of these stresses is very important when 
 studying and explaining the influence of microstructure on such properties as thermal 
 expansion and mechanical strength. This knowledge has to be gained by theoretical 
 analyses combined with experimental measurements on thermal expansion behavior and on 
 the induced strain in the lattice of the crystalline phases. 
 
 The quartz grains strive to contract more than the glass matrix during the cooling 
 of the body. As a result tensile stresses arise in the quartz grain. In the surrounding 
 glass phase radial tensile stresses and tangential compression stresses are formed, 
 both having their largest value at the boundary to the glass phase and then rapidly 
 
 99 
 
lOWS 
 
 tz 
 
 decreasing with incereasing distance from the quartz grain. The analysis also shcn 
 that the tensile stresses within the quartz grains decrease with increasing quart! 
 content, and that they are independent of the grain size at constant quartz percentage 
 [11]. 
 
 For example, experimental strain measurements on a particular porcelain body with 
 6 oer cent quartz gave a mean tensile stress in the quartz phase of about 4200 kg/cm . 
 This value may be compared with the normal range for the modulus of rupture of porcelain, 
 500-1000 kg/cm 2 , and the estimated flow point of silicate glasses 20,000 kg/cm . 
 
 The question now arises whether these internal stresses are of such a size that 
 thev may cause local fractures, with microfissures within or around the quartz grains 
 as indicated in the micrographs (figure 16). The modulus of rupture for porcelain is 
 much lower but refers to much larger volumes and gives, therefore no information in 
 this case, owing to the statistical nature of strength. Measurements of the strain in 
 the quartz phase, and of the temperature dependence of the thermal expansion, indicate 
 that the stress state is the normal and dominant one, but they do not exclude the 
 existence of microcracks [1 1 j . 
 
 Microfissures of this kind are believed to exist in porcelain bodies g , 7 , 9] , 
 but no reliable data on their frequency have yet been forthcoming. If they do exist, 
 they must be weak points in the material and presumptive starting points for growing 
 cracks when the body is mechanically loaded. A decrease in the grain size of the quartz 
 is Sown to give an increase in both mechanical strength and thermal expansion coeffi- 
 cien^Tand these effects could then be explained by the decrease in size and frequency 
 of the microfissures. 
 
 If .microfissures do not exist, but only the microstresses , what does that mean to 
 the mechanical strength? The existence of high tensile stresses in the quartz grains 
 and of high radial tfns-ile stresses in the surrounding glass phase must be a weakness 
 especially regarding the crack nucleation during loading. The existence of the tangential 
 compression sfressef must, on the other hand, make the crack nucleation in these direc- 
 tions and crack propagation in the glass phase more difficult. Which of these two 
 effectHs the most important is very much disputed [l 3 , 19}. An increase of the quartz 
 content in the porcelain usually means an increase in mechanical strength, and this 
 effect might be explained by the decreased proportion of the weaker glass phase combined 
 with higher mean tangential compression stresses in the glass phase. 
 
 13. The Microstructure of Porcelain - an Exhausted Field of Research? 
 
 There is always a need for improving the limiting properties of a material, and 
 porcelain is no exception. In technical porcelains, for instance, mechanical strength 
 ?S frequently ?he limiting property. In order to improve it in an efficient way , we must 
 aquire a much better understanding of the influence of the microstructure than we have 
 at present. 
 
 The electron microscope and the X-ray diffraction technique have given us a clear 
 pictur^ of the microstructure as far as the percentages and phase di str i uticna are 
 concerned. But we have to go further and investigate structural details in the con- 
 SJnuous glass phase, such as concentration gradients, pores, microfissures and solved 
 gases? In order to elucidate the effects of these different factors. The main interest 
 will be centered around the glass phase, and around the crystal phases mostly as 
 modifiers of the glass phase properties. 
 
 As to mechanical strength, special attention must also be paid to the ^ r [ a " 
 
 structure and the chemical conditions there. We do not yet know the nature of the weak 
 
 Joints in the porcelain, nor the nucleation mechanism of the cracks in the fracture, or 
 
 if Sere is a poss^oilily of stopping a crack once it has started. We have only some 
 empirical rules to follow but no real understanding. 
 
 The microstructure of porcelain and its influence on the material Properties is 
 thus far from being an exhausted field of research, and there is still scope for 
 significant future developments and improvements in this ancient and highly appreciated 
 material . 
 
 100 
 
[1] 
 
 [2] 
 
 [3] 
 W 
 
 G. W. Brindley and M. Nakahira , J 
 Ceram. Soc . 40, 346 (1957). 
 
 References 
 Am. [ll] 
 
 G. W. Brindley and M. Nakahira, J. Am, 
 Ceram. Soc. 42, 311 (1959). 
 
 G. W. Brindley and D. M. Maroney , J. 
 Am. Ceram. Soc. 4^» 511 (i960). 
 
 J. J. Comer, J. Am. Ceram. Soc. 43 , 
 378 (1960). 
 
 [5] A. Dietzel and N. N. Padurow, Ber. 
 deut. kerarn. Ges. 21 1 7 ( 1 95*0 • 
 
 [6] W. H. Earhart, Ohio State Univ. Eng . 
 Sta. News _12, 25 (1940); Ceram. 
 Abstr. 12, 206 (19*10). 
 
 [7] R. F. Geller, D. N. Evans and A. S. 
 
 Creamer, Bur. Standards J. Research 
 11, 327 (1933). 
 
 [8] W. D. Kingery , Introduction to Cera- 
 mics . p. 148, John Wiley & Sons 
 (New York, i960). 
 
 [9] I. M. Lachman and J. 0. Everhart , J. 
 Am. Ceram. Soc. 22* 30 (1956). 
 
 [10] S. T. Lundin, Trans. 4th Intern. Ce- 
 ram. Congr. Florence, p. 383 (195*0. 
 
 [12] 
 
 S. T. Lundin, Studies on Triaxial 
 Whiteware Bodies , Almqvist & Wik- 
 sell (Stockholm, Sweden, 1959). 
 
 V. S. MacKenzie and J. V. Smith, Am. 
 Mineralogist 40 , 707 ( 1955) i ibid 
 hi, 405 (1956). 
 
 [13] R. Masson, Trans. 8th Intern. Ceram. 
 Congr. Copenhagen, p. 393 (1962). 
 
 [l 4J J. F. Schairer and N. L. Bowen, Am. 
 J. Sci. 24J5, 193 (1947). 
 
 [l 5j J. F. Schairer and N. L. Bowen, Am. 
 J. Sci. 222, 68 1 (1955). 
 
 [16] K. Schuller, Ber. deut. keram. Ges, 
 38 , pp. 150, 208 and 241 (1961). 
 
 [17J G. R. Sheltoh, J. Am. Ceram. Soc. 
 21, 39 (1948). 
 
 [18] H. Stager and H, Studer, Tech. Mitt. 
 12. 170 (1956). 
 
 [19] A. Winterling, Ber. deut. keram. 
 Ges. J38, 9 (1961). 
 
 
 
 
 
 FIGURE 1. Electrical insulator porcelain 
 with extensive quartz grain dissolution 
 (etched 10 sec, °C, 40% HF, collodion 
 replica). 
 
 FIGURE 2. Electrical insulator porcelain 
 with low quartz grain dissolution 
 (etched 10 sec, °C, 40% HF, collodion 
 replica). 
 
 101 
 
FIGURE 3. Vitreous sanitary ware (etched 
 10 sec, °C, 40% HF, collodion replica). 
 
 
 
 
 50 /x 
 
 - a 
 
 HBBg^l 
 
 FIGURE 4. Vitreous triaxial whiteware 
 body fired at 1300 °C (etched 20 min, 
 50% NaOH, 100 °C, collodion replica). 
 
 FIGURE 5. Two examples (a and b) of electron micrographs of electrical 
 insulator porcelain (etched 10 sec, C, 40/ o HF, silica repiica/. 
 
 102 
 
FIGURE 6. Mullite needles 
 
 growing into feldspar relicts 
 (insulator porcelain, etched 
 10 sec, °C, 40% HF) ; (a) 
 silica replica, (b) aluminum 
 replica, (c) silica replica. 
 
 103 
 
K 1585t10°C 
 L U70±10°C 
 M 985±20°C 
 N 1140±20°C 
 
 W80 
 ^Al^Oj-SSiO, 
 
 o melt 
 
 K,0-Al,0,-2Si 
 
 FIGURE 7. Portion of the phase 
 diagram for the system 
 KeO-AlsOa-SiQs after Schairer 
 & Bowen [14,15]. The composi- 
 tion points correspond to, Pi- 
 total system. P2 = sub-system 
 clay and feldspar, P3 = meta- 
 kaolin, P4 = feldspar relicts, 
 and P5 = clay relicts. 
 
 FIGURE 8. Isolated and dispersed 
 mullite phase of an insulator 
 porcelain . 
 
 FTrURE 9 Stereoscopic views of a part (the large aggregate) of the 
 FI mullite phase from P a feldspar relict region sh owing the magn itude 
 and relative position of the mullxte crystals. To the left some 
 Smaller? mo?e P compact aggregates from clay relicts can be seen. 
 
 104 
 
/ ' 
 
 Sif^ 
 
 K 
 
 1585H0*C 
 
 
 Ak 
 
 L 
 
 1470110 "C 
 
 ?&— -. 
 
 fl^K 90 
 
 M 
 
 985* 20 *C 
 
 10- - 
 
 iW 
 
 N 
 
 1140± 20 *C 
 
 1252- s 
 
 
 
 
 Dli 
 
 V 
 
 start matrix 
 
 9\ 
 
 H 1 * \ 
 
 
 
 N 
 
 D 
 
 melt 
 
 A 
 
 Vjo 
 
 
 KiO-AlASS) 
 
 nVki Mullite 
 
 
 
 
 \\^\ x v 
 
 \ \ 
 
 
 & 
 
 
 \ 
 
 \60 
 
 K^-Al^Si 
 
 °A\ X s - 
 
 -^ \ 
 
 v \ 
 
 
 k50 
 
 FIGURE 10. The change in melt 
 composition during the quartz 
 dissolution, when the melt is 
 saturated with mullite. 
 
 :M% i 1 
 
 FIGURE 11. Quartz grain partly 
 transformed into cristobalite 
 (etched 20 min, 50% NaOH, 
 100 °C, silica replica). 
 
 FIGURE 12. Stereoscopic views of closed pores in an unetched fracture 
 surface (aluminium replica). 
 
 105 
 
FIGURE 13. Closed pore with mullite 
 crystals in an overfired body 
 (unetched fracture surface, 
 aluminium replica). 
 
 FIGURE 14 o Pore with crack in an 
 unetched fracture surface (alu- 
 minium replica ) 
 
 FIGURE 15. Surface structure of a 
 delayed fracture in an electrical 
 porcelain insulator (aluminium 
 replica)^ 
 
 FIGURE 16. Partly dissolved quartz 
 grains with microstress cracks 
 (fracture surface, silica replica). 
 
 106 
 
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