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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
ORNLP-1727
Conf.651106-3
be
NOV 1 8 1865
65-98 LAOREET
NOTE:
This is a draft of a paper which is being submitted for
publication Contents of this paper should noither be
quoted nor referred to without permission of the authors.

RNDASIAD NOR ANNOUNCTADEST
IN MICILAR SCIENCE ABSTRACTS
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The Magnetic Form Factor of Chromium
R. M. Moon, W. C. Koehler and A. L. Trego
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SOLID STATE DIVISION
OAK RIDGE NATIONAL LABORATORY
Operated by
UNION CARBIDE CORPORATION
for the
U. S. Atomic Energy Commission
. Oak Ridge, Tennessee, V.8.A.
October, 1965
LEGAL NOTICE
w
The report mo preparod u an account of Government sponsored work. Noithor the Unicod
Statı, por the Commission, nor any poraua acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or wrofulness of the information coutalund bi tbls report, or that the use:
of way Informatica, apparatus, method, or proces disclosed in this report may not infringe :
privately owned riccato; or
B. Asrunas any liabilten mith respect to the use of, or for damago. resulting from the
un of any information, appuntuc, betbod, or procon disolond in this report
Ao unod in the abovo, "person acting on behall of the compuselon" includes any on-
ploys or contractor of the Commission, or employs of such contractor, to the extent that !.
such employs or contractor of the Commission, or employee of such coatractor prepares,
denominator, or provides access to, any information pur munnt to his employment or contract
with the Commission, or bis oraployment with such contractor.
ith
Mie Magnetic Form Factor of Chromium"
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R. M. Moon and W. C. Koehlor
Solid State Division, Oak Ridge National Laboratory
Oak Ridge, Tennessee
and
A. L. Trego
Iowa State University
Ames, Iowa
ABSTRACT
Neutron diffraction measurements of the magnetic Bragg peaks from
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single crystals of chromium with small additions of manganese have been
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11851.11
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PIITTIM!!!:
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used to determine the magnetic form factor of chromium. The addition
of manganese simplifies the experimental problem by stabilizing the
simple antiferromagnetic structure. A single magnetic peak is observed
at reciprocal lattice positions, rather than a group of six satellite
peaks as in pure chromium. Also, manganese increases the Néel point 80
that the measurements were performed at room temperature. The results
are in good agreement with free atom Hartree–Fock calculations for the
chromium 3d electrons. A definite indication of nonspherical symmetry
was obtained by comparing the (221) and (300) reflections. These reflec-
tions come at the same scattering angle, yet the (221) intensity is
larger by about a factor of six. This indicates a to population of 79%,
compared to 60% for a spherical spin distribution. The results are in-
dependent of manganese concentration over a range from 1.7 to 4.1 atomic
percent.
Research sponsored by the U. 8. Atomic Energy Commission under contr
... with the Union Carbide Corporation.
! Evin iipliidii
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INTRODUCTION
The spatial distribution of the spin density in chromium 18 of parti-
cular interest because this material exhibits many of the properties
Associated with Overhauser cpin density waves." The neutron dil'fraction
investigations of Corliss, Hastings and Weiss 2) and of Shirane and Takei (3)
indicated that the magnetic form factor of chromiun 18 in agreement with
the experimental Mm** form factor. The present investigation was under
taken to define the shape of the form factor more succurately and to extend
the data to higher values of the scattering vector.
EXPERIMENTAL
Single crystals of chromium with small additions of manganese were
used as samples and a conventional neutron diffractometer was used to measure
the antiferromagnetic reflections out to the (311). The addition of manganese
stabilizes the simple antiferromagnetic structure, thus greatly reducing the
experimental problem, A single magnetic peak is observed at reciprocal
lattice positions, instead of a group of six satellite peaks as in pure chromium.
This results in the dual advantage of higher peak intensities and an easy re-
solution problem. Both of these factors are important in measuring peaks
at large scattering angles. In addition, the average moment per atom is in-
creased from about 0.5 wo to about.0.8 Mg, and the Néel temperature is raised
so that measurements may be made at room temperature without suffering a
large loss of intensity.
Because it was planned to measure intensities differing by three orders
of magnitude, it was apparent that a crystal large enough to give a measur-
able intensity for the weakest reflection would have a serious extinction
erfect for the strongest reflection. Accordingly, crystals of various sizes
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Gibellicul
DL:112111
were prepared with masses varying from 0.174 8 to 2,272 8. The samples were
in the shape of disks with various diameters and with thicknesses ranging!
from 0.46 mm to 4.8 mm.
These crystals have the body-centered cubic structure with the spin at
the body-center position opposite in direction and equal in magnitude to
those at the corner positions. The direction of the spin 18 along one of
the three (100) directions, thus there are three magnetic domains possible.
These domains were not equally populated and so it was necessary to determine
the populations for each crystal by measuring three reflections with permuted VIGHT
Indices. Absorption factors were calculated using the computer program of Miller
Wehe, Busing and Lavy,"") approximating the circular cross section of the Millen
sample by a sixteen-sided polygon of equal area. After correcting for absorp-
tion and domain population, the intensities for each crystal were normalized
to the (111) intensity and these ratios compared for crystals of different
sizes to identify and eliminate any extinction effects. Comparisons between
crystals of different Mn concentration but of comparable size showed no varia-
tion in intensity ratios. Three different concentrations were used of 1.7,
2.0 and 4.1 atomic percent manganese. These intensity ratios, when further
corrected by geometric and temperature factors gave a series of numbers prom
portional to pé. The temperature factor was calculated using B = 0.35 +0.06.
This range of values is consistent with measurements made on high order
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nuclear peaks for the thinnest crystal and with accepted values.'
A weak magnetic reflection at (hke) can be strongly affected by the half-
wavelength contaminant from the nuclear (2h, 2k, 26). This 1/2 cortaminant:
was removed from the inclúent beam by means of a Pu filter. The 1/3 con i
taminant would involve a magnetic (3h, 3k, 3l) reflection and was entirely
negligible.
One major source of experimental error not yet considered was the
possible presence of simultaneous reflections. For the weak outer reflec-
tions, the double reflection process could produce a large increase in the
observed intensity. This process would necessarily involve a magnetic re-
flection followed by a nuclear reflection, or the reverse, and its magnitude
would involve the product of the squares of the magnetic and nuclear etructure
factors. '07 The rapid decrease of the magnetic form factor leads to the con-
clusion that only those simultaneous reflections involving the (100), or
possibly the (111), magnetic reflections are important. As far as possible,
crystal orientations were selected which avoided the possibility of any
simultaneous reflections involving the (100) or (111).
RESULTS
Insteas comparing the results with the Mn ** experimental form factor,
we have chosen to make the comparison with the restricted Hartree–Fock cal-
culation by Freeman and Watson for atomic chromium with a 30*48? configura-
tion. This calculation is very close to the experimental Mn** form factor
given by Corliss, Elliott and Hastings.'° As already described, the present
experiments gave the set of form factor ratios fnkelfun: These data were
renormalized so that the experimental and calculated form factors were in :
agreement for the (100) reflection and the results are shown in Fig. 1.
of particular interest is the difference in the experimental points for:
the (221) and (300) reflections. These reflections come at the same value
of sino/A and their difference indicates a departure from spherical symmetry
in the spin distribution around each lattice point. The observed (221) 1n-
tensity was larger than the (300) by about a factor of six. Special efforts
were made to assure that the (221) reflection was not affected by simultaneous
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reflections. Using the observed difference in the (221) and (300) form
factors and the work cá W6i88 and Freeman with the tabulated <3,> values
of Watson and Freeman, (10) the 3& unpaired spin population was determined
to be 0.79 1 0.02 tag and 0.21 + 0.02 @ Spherical symmetry would corres-
pond to a population of 0.6 tz Using this population, the form factor
for each reflection was calculated on the basis of the Watson-Freeman 3d
form factors and these values are shown in Fig. 1 as the solid points.
The normalization to the calculated curve at the (100) reflection was
done to test how closely the spin distribution approximates that calculated
for the free atom. The good agreement between the remainder of the calcu-
lated and experimental points indicates that the spin distribution may be
described to a good approximation by a model consisting of free atom 3d
electron density functions centered at each site. Because of the overlap
of chromium electron density functions, there is a partial cancellation of
the spin density in this model. Integration of the periodic spin density
of the model over the spiere inscribed within the Wigner-Seitz cell indicates
that about 7% of the atomic spin 18 lost by this cancellation. Thus it is
concluded that the total spin enclosed within the Wigner-Seitz cell for
chromium is 7% lower than the reported values, which were based on-sitting
observed scattering amplitudes to a form factor equivalent to the one con-
sidered hore.
ACKNOWLEDGMENT
It is a pleasure for the authors to express their gratitude to F. A.
Schmidt and A. R. Mackintosh of Iowa State University for supplying the
single
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REFERENCES
1o) A. W. Overhauser, Pays, Rev. 128, 1437 (1962).
(2) L. M. Corliss, J. M. Hastings and R. J. Weiss, Phys. Rev. Letters 3,
211 (1959).
G. Shirane and W, J. Takei, Proceedings of the International Con-
ference on Magnetisk and Crystallography, Kyoto, 1961. (J. Phys. Soc.
Japan 17, Suppl. BIII, 35 (1962)).
(4) D. J. Wehe, W. R. Busing and H. A. Levy', Oak Ridge National Laboratory
TM-229.
(5) International Tabies for X-Ray Crystallography, Vol. III, 235.
(6) R. M. Moon and C. G. Shull, Acta Cryst. 17, 805 (1964).
(7) A. J. Freeman and Fl. E. Watson, Acta Cryst. 14, 231 (1961).
(8) L. M. Corliss, N. Elliott and J. M. Hastings, Phys. Rev. 104, 924
(1956).
(9) R. J. Weiss and A. J. Freeman, J. Phys. Chem. Solids 10, 147 (1959).
(10) R. E. Watson and A. J. Freeman, Acta Cryst. 14, 27 (1961).
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FIGURE CAPTION
Fig. 1. The magnetic form factor or chromium.
The size of the circles
indicates the magnitude of experimental error.
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ORNL-DWG 65-10813

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CHROMIUM
ATOMIC HARTREE-FOCK, SPHERICAL 30
MAGNETIC FONIA FACTOR
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CALCULATED: 0.79 420
0.21ea
iesinia
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END
DATE FILMED
12/ 18 /65
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