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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963

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LEGAL NOTICE
This report was prepared as an account of
Government sponsored work. Neither the
United States, nor the Commission, nor any
person acting on behalf of the Commission:
A. Makes any warranty or representa-
tion, expressed or implied, with respect to
the accuracy, completeness, or usefulness
of the information contained in this report,
or that the use of any information, appa-
ratus, method, or process disclosed in this
report may not infringe privately owned
rights; or
B. Assumes any liabilities with respect
to the use of, or for damages resulting from
the use of any information, apparatus,
method, or process disclosed in this report.
As used in the above, “person acting on
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that such employee or contractor of the
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prepares, disseminates, or provides access
to, any information pursuant to his employ-
ment or contract with the Commission, or
his employment with such contractor.
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PULSED-NEUTRON MEASUREMENT OF THE DIFFUSION PARAMETERS IN
ORDINARY ICE AS A FUNCTION OF TEMPERATURE
Ernest Gerard Silver
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U.S.A.
7.
1. Introduction
The method of time-dependent neutron diffusion measurements as a means
to determine the diffusion parameters in moderators is by now well established
through the work of numerous investigators (1-8] who have worked with a number
of materials including H20, D20, Be, graphite, and others. In particular,
light water has been investigated by VON DARDEL and SJÖSTRAND (9), A. V. ::
ANTONOV et al. (10,11), DIO and SCHOPPER (12), BRACCI and COCEVA [13], LOPEZ
and BEYSTER [14), and KÜCHLE (15). In VON DARDEL's first paper on the method
[l] a crude measurement of the temperature effect in ice is given, and ANTONOV
(11) reports a measurement at -80°C and at the temperature of liquid nitrogen
(-196°C).
....
In the investigations of DE SAUSSURE and SILVER on beryllium at low
temperatures (16,17) it was found that long-persisting changes in the effec-
tive mean neutron velocity made measurement of the asymptotic spectrum impos-
sible at times when the neutron density in the assembly was still sufficiently
high to be accessible to measurement. The "trapping effect" which was
proposed to explain the observations depends on the existence of narrow energy
domains in which the ratio of the transport cross section to the inelastic
scattering cross section, Otr/oinel, 18 very high. In particular, in the
1. Research sponsored by the U.S. Atomic Energy Commission wder contract
with the Union Carbide Corporation.'
ORX-A8C - OFFICIAL.
TENANCE OBTAINED: MELATO
THE PUBLIC IS APPROVED. 25PUNTES
ARE ON FIECA S in wbwi N.
ORX1 - AEC - OFFICIAL
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first Bragg peak the ratio approches w 36. Neutrons inelastically scattered
to this energy will diffuse slowly, and have low probabilities of scattering
out of the energy trap. 'A quasi-independent subpopulation is thus formed,
whose relative density, as compared to that of the main population, continues
to increase with time. The very large rise in the diffusion cooling con-
stant which has been predicted by SINGWI (18) but has not been observed
experimentally would be due to an asymptotic spectrum of "trapped" neutrons.
If this mechanism is the correct one to explain the observed effects
in beryllium, then ir 120 ice, where the inelastic scattering 18 relatively
much larger, this trapp:ing effect should be substantially absent, and
asymptotic spectra, evidenced by en mchanging decay period, should be ob-
served at low temperatures. The present work was therefore wdertaken to
determine (1) whether the spectrum doer, indeed, become asymptotic in rela-
tively short times at low temperatures and (2) what the temperature effects
on the diffusion coefficient and the diffusion cooling coefficients are.
.
ects
2.
Experimentel Arrangements
.
..
-
All the test bodies were cylinders of ice made from distilled water.
Initial experiments showed that density reductions of up to 7.8% occurred
in the last-freezing top-central portion of the cylinder as compared to the
lower and outer regions which froze first. This was due to entrapment of gas
that evolved from the solution during freezing. Further problems were
encoimtered due to stress cracking and irregularities in the shapes of the
ice surface as frozen.
For the large cylinders (with radii > 10 cm) these problems were
solved by development and use of a "plug" shown in Fig. 1. The water in
each cylinder was boiled for about 1 hr wder a surface layer of melted
paraffin about 5 cm. thick. Then the plug was set into the container and
lowered by means of the leveling screws wtil the 0.3-cm-thick space between
the cylinder wall and plug was filled with paraffin as seal. A tube extended
about 2.0 on into the water to allow expansion into the volume above, which
was covered with a ~ 3-cm-thick layer of viscous mineral oil to prevent
2.
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ORNL - AEC - OFFICIAL
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VICLASH
2-01-034
719
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LEVELING
SCREW (JUSCO)
- WATER INLET AND OUTLET (1 EACH)
UUUUUUU
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MACKET
(Mo
MINERAL OIL LAYER
EXPANSION =
VOLUME
WATER COILS,
ALUMINUM
CYLINDER
MULAITTAVI777
-VIIIIIIIIIII/17/prinn
III
II/
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PARAFFIN
t!!! 12:11:15:17:11
WATER (ICE)
**
*
***
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**1111111
Fig. 1. Diagram of the Plug Used to produce large
Ice Cylinders. The plug is shown in place in the aluminum
water container.
reabsorption of air. Room-temperature water was circulated through a spiral
coil soldered to the plug plate to prevent freezing of the water from the
top, and consequently cracking due to expansion of trapped water. A thick
layer of paraffin between the coil-warmed plate and the water was required
for freezing to occur. Without this layer the water would not freeze even
in a refrigerator at -50°C due to convective circulation and heat exchange
with the top plate. After freezing was complete the plug and paraffin were
removed, the remaining small irregularities were filled with water, and the
cylinder was refrozen.
!
The small cylinders were made by a different technique, indicated in
Fig. 2. For each ice cylinder to be formed an aluminum cylinder with ac-
curately machined thin walls (approximately 0.1 cm thick) and accurately
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ANA

TRANSFER POSITION
FLEXIBLE
TUBING -
THREE - WAY
VALVE
PRESSURE
GAGE
VAPOR TRAP
BRASS
FLANGE PLATE
GROUND-GLASS
JOINT
DRY ICE-
GASKET
(NEOPRENE)
- THIN-WALL
Hgo ALUMINUM
CYLINDER
SAPIEZON "Q"
VACUUM
PUMP
GLASS BASE PLATE
.
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.
Fig. 2. Diagram of System Used to Produce Small Ice Cylinders.
Both flasks can be shifted to transfer position. The aluminum cylinder:
is shown filled and ready to be removed from the vacuum.
flat, parallel end planes, was placed on a glass plate and sealed to it with
a vacuum sealing compound (Apiezon Q) around the outside. In each case the
aluminum cylinder was about 12 cm longer than the ice cylinder to be pro-
duced. A flange connected to the vacuum system was placed on top of the
cylinder with a neoprene gasket seal. Water and mineral oil flasks were then
connected to the system as shown in the figure and the system was prmped for
several hours. The water and oil were then transferred into the cylinder
to a water height of about om above the desired level, with the oil layer
nos 5 com thick. The cylinder was then removed from the flange and placed in i
ORNL - AEC - OFFICIAL
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a refrigerator at about -5°C. Once freezing was complete, the cylinder was
cooled further to -80°C. At this temperature the vacuum sealing material
was brittle and the base plate could be removed by a sharp blow, leaving
the bottom surface accurately flat and smooth. The entire cylinder was then
sawed off at just above the desired height, removing the solidified oil and
the uppermost portion of the ice with its nonuniform surface and any residual
alr inclusions. The cylinder was then placed in a lathe and the upper plana
faced of? to produce the final accurately shaped body. The outer aluminum
remained in place, and the ends were sealed with aluminum foil to prevent
sublimation of the ice. The presence of the aluminum, amounting to a reflec-
tor savings of 0.005 cm, had only negligible effect on the bucklings.
All cylinders were completely covered with cadmium, except for a cir-
cular hole at the center of one plane face, just large enough to permit a
detector to be placed in contact with the ice.
The measurements were performed in a refrigerated test chamber which
had inside dimensions of about 60 cm x 60 cm x 50 cm and was lined with Boral
(a dispersion of boron in aluminum) about 0.63 cm thick. Deuterono from a
300-kV accelerator entered the chamber through a beam tube and struck a
water-cooled deuterium target positioned within 0.5 cm of the curved surface
of the ice cylinder on the plane of symmetry. The detector was a 4.45-cm-
diam by 0.3-cm-thick BLI(Eu) crystal attached to a photomultiplier.
The accelerator beam was pulsed both by a pre-acceleration beam deflec-
tor in the ion source and a post-acceleration deflector operated in synchronism
with it. With this arrangement, beam on-off ratios of 5 x 104 to 5 x 105 were
attained. The pulse width and repetition rates were controlled by a circuit
which also served to gate the detector pulses into the 28 channels of the
time analyzer. The time from the end of the neutron pulse to the beginning
of counting in the first channel and the widths of both the pulse and count-
:ing channels were all adjustable within wide limits. For the work under
discussion the detector channel widths ranged from 18.18 to 10 used. The
waiting times, to allow for establishment of the asymptotic spectrum and for
a higher spatial'mode decay, ranged from 440 MBec for the largest cylinder
to 140 hsec for the smallest.
-50
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.
Table I lists the cylinders investigated and their bucklings. The .
latter are temperature dependent (see below) and are given for -45°C. The ..
neutron time decay was measured for cylinder temperatures of -j, -25, 245,
-65, and -85°C. At each temperature 2 to 5 x 108 counts were recorded in
the analyzer.
TABLE I. DIMENSIONS AND BUCKLINGS OF THE CYLINDERS
USED IN THE EXPERIMENT
.
Cylinder
No.
I
Height
(cm)
Ranius
(cm)
B2 (at_-45°c)
* Cam2).
-
gantno
ima
E E Boonoinf win
24.95 + 0.31
18.54 + 0.20
25.30 + 0.22
21.27 + 0.18
16.51 + 0.13
16.05 * 0.12
10.44 + 0.06
9.069 + 0.05
6.400 + 0.040
4.196 + 0.040
7.520 + 0.040
7.188 + 0.027
15.13 + 0.17
.55 + 0.12
10.035 + 0.10
10.035 + 0.10
10.035 + 0.10
7.325 + 0.04
5.575 + 0.025
.4.190 + 0.02
4.001 + 0.015
5.550 + 0.032
3.073 + 0.012
2.858 + 0.012
0.0394 + 0.0010
0.0620 + 0.0008
0.0689 + 0.0011
0.0748 + 0.0011
0.0880 + 0.0013
0.1352 + 0.0012
0.2489 + 0.0017
0.3933 + 0.0028
0.5161 + 0.0032
0.6058 4 0.0076
0.6606 + 0.0039
0.7460 + 0.0046
.
.
www.am
.
Data Analysis
The decay deta were analyzed by use of a nonlinear least-squares fit
computer program, using the model
.
.
i
c(t) = P2- + P2 exp(-P3t) + P4, exp(-P5t),
.. (1)
.
that
where c(t) 18 the count rate t seconds after the pulse and P2 ... Ps are
parameters to be fitted.
* Direct attempts to fit the data to such a model usually failed to con-
verge even after many iterations, so an alternative process was adopted
'n leer esterna
.
ORNI - AEC - 087ICIAL
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1
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.
Whereby a number of fits were performed with a range of fixed values for Ps,
the exponent of the second decay component. The "best" fit, that 18, the
one giving the smallest sum of weighted residuals, was found and the corre- :::
sponding value of Pa was taken to be the decay constant 1. In all cases
Pa/Pal, the ratio of the amplitudes of the two components at t= 0 (the
end of the neutron pulse), was less than 4% for the best fit. In the largest
cylinders the second component appears to be mostly due to small dead-time
counting losses as evidenced by negative values of P4. The source in the
smallest cylinders is uncertain, but is most likely due either to imperfect
beam cutoff or to room return. Either would be consistent with the observed
buckling and temperature independence of the values of Ps. Figure 3 is a
typical example of the effect of varying Ps in a series of fixed-Ps least-
squares Calculations. For each of the decay measurements analyses were
carried out using all 18 channels and overlapping sections consisting of the
data in channels 1-15, 2-16, 3-17, and 4-18, respectively. The latter series
were used as a check for time trends in the measured decay constants. Where
no such trends were found, it was concluded that asymptotic spectra had been
obtained. Some cylinders at various temperatures were pulsed with extended
waiting times, as well as with the waiting times used for the main work. The
results of these extended-waiting-time tests are shown in Table II. In all ..
.
.
TABLE II. EFFECT OF EXTENDED WAITING TIME
ON MEASURED DECAY CONSTANT
Cylinder
No.
Waiting Time From:
End of Pulse
Termperature (°C) (usec)
Decay
Constant, a
(103 sec 2)
1
6
-65
280
400
175
T
250
7.891 + 0.064
7.864 + 0.078
13.290 + 0.100
13.199 + 0.180
16.085 1 0.129
16.217 4 0.220
19.412 1 0.321
19.561 + 0.570
220
.
.
140
220
ORNL - AEC - OFFICIAL
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Orni - AEC - OFFICIAL
namna ne odnosi na drama-kelamaananition hat underveridunia
d
ORNL-DWB 68-1930

-----
P
6.2
6
16,1
a
CYLINDER I
-5°C CHANNELS 1-15
.
I
n
ak
PaPz %)
MINIMUM Σε
Pa (kc)
a n menunai
"BEST"
5.356 kc
...
5.
kan satunnar samantalanaminia
2, 3-1.
:
,
,
i suhakemine
n
-5
0
5
15
20
10
Ps (kc)
::::
*
Fig. 3. The Weighted Sum of Residuals Squared, 22, the
Parameter P3, and the Ratio 1P4/Pal, as a Function of Ps for
a Iypical Example of the Results of a Series of Nonlinear
Least-Squares Fits of the Neutron Decay Data to the Equation
c(t) = Pa + Pa e-Pgt + PA e Pst. P5 is fixed, and te o at
the end of the neutron pulse.
ilmankaikan makanan
makan
cases the effect of a longer waiting time was less than the wcertainties in
the decay constant. The final values of Ps, the dominant decay constant, were
taken from the results of analyses of channels 1-18 and from analyses using
only the odd- or even-numbered channels. The latter procedure yielded two
independent values from which the wcertainties due to counting errors could
be Laferred.
dan tanaman
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ORNL - AEC - OFFICIAL
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Figure 4 shows the measured decay constants obtaineå for each buckling
and temperature.
ORHi AEC - OFFICIAL
The diffusion parameters were then calculated from the measured cylinder
dimensions and decay periods by an iterative procedure to obtain consistency
between the transport mean free path entering the extrapolation distance calcu-
lations and the diffusion coefficient obtained. First the buckling for tho
1th cylinder at a given texnperature T was found by the equation
.
(B2)!).
72
__
(VD)(0) K Qi., 23:.
[
+
2(vn))
where
3 x 0.7103/T..
= 6.9024 x 10–5 sec (ⓇK)7cm-1,'.
(3)
Hi and Ry are the height and radius of the ith cylinder, P4 and Q1 are extrapo-
lation distance correction factors discussed below, L. 1s the temperature in
OK, and (VD) (°) is a first estimate of the diffusion coefficient. ::
the equation
1-
; [(32(0)ye
(4)
j=0
using n = 1, 2, 3. The coefficient of the linear term, &, was then used as
an improved estimate, (VD) (+) in Eq. 2, and the process was repeated until the
values of VD from successive trials differed by less than a preassigned value.
The errors associated with the coefficients ay are obtained directly .
from the least-squares fitting proceciure, which allows explicit specification
of values of both 6(BO) and 814 (19). The former are given by
ORNL – AEC - OFFICIAL
.-25.
.-65
-85.
A, DECAY.CONSTANT (kc/sec)
--OT
0.1
0.2
0.3
0.6
0.7
0.8
0.4 0.5
B2 (cm2)
ORNL - AEC
na
Fig. 4. Measured Values of the Decay Constants, n, as a Friction of B2 for All Cylinders
orioną. Temperatures. Note the change in buckling with temperature due to the change in extragalas arc - OSSICIAL
t ion stance with temperature.

-
-
ORNI - ALC - OFTICIA
6(B) =
(8H.)2 +
4V
- (OR4J277
2(VD) KP1_78
(VD). K Qy98
[R: + -
7-
?
-
T
.
.
:
!
and the latter are obtained from the results of the decay curve analyses. In
all cases the attempt to find terms of order B® (the coefficient ag) resulted
in much larger errors in all the coefficients and in errors in ag several
times as large as as. Therefore the present results were all based on a
three-parameter fit to the 1(B2) data, of the explicit form:
T
+
1
1 = VE + (VD) B+ C B*
.
The familiar extrapolation distance factor 0.71031 tr is obtained from
one-velocity transport theory for flat surfaces and large media. In the case
oz dimensions of only a few diffusion lengths and large surface curvature,
corrections are needed to improve the calculation of the extrapolation dis-
tance. GELEARD and DAVIS [20] have made careful investigation of this effect
for water and have obtained extrapolation distances as a function of buckling
for infinite slabs and cylinders. The ratio of the GET.BARD-DAVIS extrapola-
tion distance to the one-velocity transport-theory extrapolation distance in
water was computed for each geometry and applied to the buckling calculation.
The resulting correction factors are shown in Fig. 5, where P and Q refer to
the slab and cylinder geometries and are applied to the axial and radial
buckling calculations, respectively.
Results and Discussion
-
.
.
.
1. Asymptotic Decay. As is seen from Table II, one result of the experi-
ment is that no noticeable trapping effect appears in ice. At all bucklings
and temperatures an equilibrium spectrum was attained at times of the order of
140 usec or less. This is in accord with the expectation based on the ratio
Oinea/otr in water.
...
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-12.
ORNL - AEC - OFFICIAL
...
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.
.
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--
ORNI - AIC OFFICIAL
ORNL-OWO 45-1926

:
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O(R)
Fig. 5. The Correction Factors
P and Q Used to Correct Axial and
Radial Extrapolation Distances, 1,
Respectively, in Ice Cylinders. The
values are obtained from the work of
GELBARD and DAVIS (20].
::
me
Pihi fontian
5
20
10
15
H OR R (cm)
2. Inverse Absorption Lifetime via. Since the absorptioa cross section
oi oxygen, Calo), is negligibly small and since the absorption cross section
for hydrogen is inversely proportional to the velocity, the value of via would
be expected to be independent of temperature and was found to be so within the
limits of accuracy, as shown in Fig. 6. Care was taken in the experiment to
preserve water purity and to extend the data to small bucklings to obtain an ..
independent measurement of the proton-tieutron absorption cross section. The : :
result is oa(H) = (331.5 325) mb. The uncertainty is divided into +1.6 mb .
Que to measurement errors and +1.5 mb due to uncertainty in the ice density.
This value is in excellent agreement with the value 332 + 2 mb given by STEHN
et al. [21] who quoted numerous other workers.
3. Diffusion coefficient vd. The diffusion coefficient has been meas-
ured by several workers in liquid water and by ANTONOV in ice at 0°C, -80°C,
and -196°C. Several measurements of the temperature dependence of vD above
the freezing point are also in the literature. However, below the freezing
point there is only ANTONOV'S report [11] which gives ratios for the values
in ice to those in water at 0°C. This, combined with oºC values of ANTONOV
(10), was used to inter absolute values. The errors therefore appear large.
ORNI - AEC - OFFICIAL
3.
ouni - AEC - OFFICIAL
7
.
4.6 m
ORNL-OWO 48-1987
340

.
:
,
:
'-
“
..
(v Egl (mol.wt)
*
."
* 10? (v2)
[ -0.917)
!.
. (kc/sec)
(milibarns)
v
328
veo (sec-1) OM (mb)
-5° (4.48510.064) x103 332.216.3
-25* 14.44530.062)* 108 329.26:6
-450 (4.48430.056) x103 332.175.0
-650 (4.46730.056) x103 330.8+5.6
-85* (4.5000.050) *103 333.3+)?
MEAN VALUE: (4.476+0.022) x103 331.5.3.1
320
.
4.3
-85
-65
-45
TEMPERATURE (°C)
-
--
tosti
Fig. 6. Measured Values of as a function of Temperature.
The corresponding microscopic hydrogen absorption cross section is
indicated on the right-hand ordinate scale (based on pe = 0.917
g/cm).
.
:
:
Figure 7 shows the results of the present experiment, and, for compari-
son, the data of other workers. All data in water were adjusted to the densiy
oł ice by the relation DwAwli) - pi/ow, where w,'i, and w(1) refer,
respectively, to water, ice, and water of the artificial density of ice.
. The data from the present work are consistent with a linear fit, yield-
ing the coefficients
(vn) (Tºx) = (o.047 + 0.202) x 1ơ + (1.225 + 0.087) x 1.(TK).
mis fit is shown in the figure.
-136
.ORNL - AEC - OFFICIAL
171213.
.
.
AB
ORM: -O
; 65-1020
O
..........
UD (104cm2/sec)
KÜCHLE (16]
DIO AND SCHOPPER (12)
VON DARDEL AND :
SJÖSTRAND [9]
ANTONOV (10,11]
WATERT
-ANTONOV (1.05 + 0.04) x 10°
AT -196°C
2.0
-100 -75 :-50 -25 0
25 50 75
. TEMPERATURE (°C)
Mg. 7. Measured Values of the Diffusion coefficient VD. Results obtained by other workers
Officiata ice and water and also shown. All values in water are modified by (pi/ow)? to comportats Sorornici
the density difference. ..
.
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T
ANTONOV found a discontinuity in vD at the freezing point of (VD) i/(vb)
= 1.04 + 0.02; correcting this for the difference in density gives at 0°C
(VD)/(VD)x(i) = 0.95 + 0.02, where 1, w, and w(1) are as defined above.
Using (VD) w(1) = (3.58 + 0.14) x 104 cm/sec as a best value obtained from
the results of ANTONOV and the extrapolated data of VON DARDELL, KUCHLE, and
DIO and SCHOPPER, the present data lead to a value (VD)1/(VD) wl 1:) - 0.95 + 0.15.
This is in agreement with ANTONOV'S results.
Extrapolation of the data for D to -196°C yields a value of D(-196°c)
= (0.99 + 0.11) x 104 cm2/sec, which 18, within the limits of error, in agree-
ment with ANTONOV'S value. ANTONOV'S value at -80°C is also been to agree,
within the limits of error, with the results of the measurements reported
here.
.
:
.
::..
.
4. Diffusion Cooling Coefficient C. Figure 8 shows the values of C.
obtained in the present work, as well as data of other workers. The same":
sources as were quoted for vD above are available here. ANTONOV finds a
ratio (C) /(C)w = 2.5 + 0.4 at 0°C and also gives ratio values at +80°C and
-196°C. In comparing the diffusion cooling coefficient in water with that
in ice it is necessary to correct for the density difference. Since C has
dizensions of cm* /sec = cm x (velocity), the value of C is proportional to
the inverse cube of the density. Hence the water data have been multiplied
by (1.0905) to correspond to the density of ice. This correction makes the
0°C ratio of AVIONOV (C) 1/(C) w(1) = 1.9 + 0.3.
Due to the large scatter of the points, the extrapolation of the data
cKÜCHLE and DIO to 0°C has large associated uncertainties. However,
surely fortuitously, the results of both investigators (based on four and
three points, respectively) agree almost exactly on a value of -3.8 x 103
cza /sec, with a combined uncertainty of about 1.15 x 10 cm* /sec. ANTONOV
found, for water at 0.5ºC, a value -(5.2 + 1.3) x 108 cm* /sec, whereas a
linear fit to all his C-data up to 200°C yields a 0°C value of -4.7 x 109
cals/sec.
The present data were fitted to a linear model which yielded the
relacion
..
ORHL - AEC - OFFICIAL
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.
.
.
".
.
+
.
.
I.
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...
...
.
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.
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.
A
-
-
-
-
-
ORNL-DWG 65-1931
--
Q=0.5
C, DIFFUSION COOLING COEFFICIENT (109 cm/sec)
-16-
a=0.4
Q=0.5
La=0.4
----O PRESENT WORK
-- ANTONOV. [10, 11]
O DIO [23]
-----A KÜCHILE (15)
.. VON DARDEL, SJÖSTRAND [9]
ERACCI AD COCEVA [13]
----- CALCULATION SY NELKIN MODEL
.
.
-200
-75
-50
-25
25
:
50
.
75
100
:
www www.com ante
TEIGERATURE (°C)
8. 8. Measured Valves of the Diffusion Cooling Coefficient, C. Values obtained hy other
woxons ice and water are also shown. All. values in vatci have been scaled by (pilot) 3 co.
.9 for the density girrerence.
0 :::!-::
C
.
O CUL


I
.
F
;
III.)
ii.
I
.
.
:,
.
.
.
.
.
4
-
.
A
-
-
.
-
.
CT°C) = - [(4.55 + 0.62) x 108 + (0.025 + 0.011) (TC) ] cm/sec.
.
.
1.
-
is gives
LI
(0°C) = • (4.55 + 0.63) x 208 cm* /sec,
L.
ALCAOV on the other. However, since the present data disagree considerably
with the AIONOV values at lower temperatures, the ANTONOV water values are
probably also of low relative significance. Restricting consideration to the
other results, we arrive at a ratio of (C) /(c), = (1.2 + 0.4) from which
it cannot be concluded unequivocally that there is a discontinuity in C.
zowever, the discontinuity of a factor of (1.9 4.0.3) found by ANTONOV appears
inconsistent with the present results. The present absolute data for C in
ice can be compared only with those of ANTONOV and are seen to disagree
seriously outside the large error limits.
For comparison, the figure includes computed values of C obtained by
tåe iollowing equation due to NELKIN [22]:
(a +
) V (VD)
.
Me v
where 2 is a parameter obtained from my (E) « , and Ma has the dimensions
como a macroscopic cross section, i.e., Me = N o. The calculations were made
for C-values of 0.4 and 0.5, using a constant value of Me corresponding to
E medicroscopic cross section of 31.2 barn per hydrogen aton. These values
correspond to those found by KUCHLE over a temperature range from 22 to 80°C.
I is to be noted that for a = 0.4 a good fit to the present ice data is ob-
taidea. me calculation is based on the linear fit to the present data for
VD in ice, and on a linear fit to the published data in water. However, the
caicuated values exhibit a discontinuity at the phase transition of the
02posite äirection as that found in the experiment.
-17-
7
oani - AEC - OFFICIAL
REFERENCES
L
8.
. VON DARDEL, G. F., Kungl. Tekniska Hogskolans Handlingar N.75 (1954).
2. SCOIT, F. R., THOMSON, D. B., and WRIGHT, W., Phys. Rev. 95 (1954) 582.
3. CAMPBELL, E. C., and STEISON, P. H., Oak Ridge National laboratory Report
ORNL-2076 (1956) 32.
4. BECKURTS, K. H., Nucl. Sai. Eng. 2 (1957) 516/522.
5. KONOTO, T. T., and KLOVERSTROM, F., Trans. Am. Nuc. Soc. (1958).94.
6. DE SAUSSURE, G., and SILVER, E. G., Nucl. Sci. Eng. 6 (1959). 159.
7. ANDREWS, W. M., University of California Radiation Laboratory Report
UCRL-6083 (1960) 193...
BECKURIS, K. H., Nucl. Sci. Eng. 2 (1957) 516/522.
9. VON DARDEL, G., and SJÖSTRAND, N. G., Phys. Rev. 26 (1954) 1245.
10. ANTONOV, A. V., et al., IAEA Report: Inelastic Scattering of Neutrons.!
... in Solids and Liquids (IS-1960) IS/54, 377/394.
11. ANTONOV, A. V., et al. At. Energ. 13 (1962) 373/374.
12. DIO, W. H., and SCHOPPER, E., Nucl. Phys. 6 (1958) 175/176.
· 13. BRACCI, A., and COCEVA, C., Nuovo Cimento IV (1956) 59.
14. LOPEZ, W. M., and BEYSTER, J. R., Nucl. Sci. Enig. 12 (1962) 190/202.
15. KÜCHLE, M., Nukleonik 2 (1958); No. IV (1960) 131.
16. DE SAUSSURE, G., Proc. of Brookhaven Conf. on Neutron Termalization,
BNL 719 IV (1962) 1158/1174.
17. SILVER, E. G., op cit., III (1962) 981/996.
*28. SIGWI, K. S. Arkiv Fysik 16 (1960) 385/411.
19. JARRARD, J. D., and CHAPMAN, G. T., Oak Ridge National Laboratory Report
ORNU-M-659 (see DEMING, W. E., "Statistical Adjustment of Data," 1944,
Wiley, P. 50/55).
20. GEIBARD, E. Mo, and DAVIS, J. A., Nucl. Sci. Eng. 13 (1962) 237/244.
-18-
.
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References Conta.)
.
.
THEIR
-
-
.
:
:
.-
.
:
.
.
.
or
21. STV, J. R., GOLDBERG, M. D., MAGURNO, B. A., and WIENER-CHASMAN, R.;
"Neutron Cross Sections, " BNL-325, 2nd ed., Suppl. 2 (1964) 1-0-1/1-0-2.
22. NEIKIN, M., J. Nucl. Energy g (1958) 48.
23. DIO, W. H., Nukleonik 1 (1958) 13.
.
.
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