AE-24
Transmission of Thermal Neutrons
<
through Boral
F. Åkerhielm
AKTIEBOLAGET ATOMENERGI
STOCKHOLM • SWEDEN . I960
AE-24
Transmission of Thermal Neutrons through Boral
F. Åkerhielm
Summary;
Transmission measurements have been performed using Maxwellian
distributed neutrons from the Rl reactor perpendicularly incident upon
a boral absorption plate. American, English, German, Swedish and Swiss
samples have been investigated and the results are compared to calculated values. The influence of the absorber grain size is discussed.
Completion of manuscript in Aug. 1959
Printed and distributed in June 1960
LIST OF CONTENTS
Page
Experiments
3
Corrections
4
Sources of Errors
5
Theory
6
The Influence of the Grain Size
8
Results and Discussion
9
References
11
Transmission oi Thermal Neutrons through Boral
Experiments
The transmission of thermal neutrons through boral plates was
measured using neutrons from the Rl reactor. The plates consisted
of boron carbide grains embedded in aluminium and the plates were
in general clad with aluminium on both sides.
Integral measurements *)'were performed using neutrons from a
graphite scatterer placed in the inner part of a channel in the thermal
column. The neutrons passed through a collimator (30 mm in diameter,
1 m long), the plate to be investigated and a B
F« counter (BA type)
surrounded by a cover. Both the cover and the collimator were made
of boron paraffin clad in aluminium. The cover had a through hole
(diameter 50 mm) in line with the collimator. The vertical position
of the counter could be adjusted so that it could be placed in maximum
intensity.
Spectral neutron transmission measurements have been made with
the fast chopper at Rl. After having been chopped the neutrons from a
heavy water scatterer in the central channel of the reactor passed through
the plate. They were then counted by a set of B
F~ detectors connected
to a 100 channel time analyzer.
Both at integral and spectral measurements the transmission was
determined as the ratio of the counting rate with absorption plate to
that without absorption plate.
'The integral transmission measurements on most of the plates have
been made by J. Christensen and Stig Johansson, and they have kindly
permitted that their results are published in this report. They also
constructed the measuring apparatus.
•v* 1
American, English, German, Swedish, and Swiss samples
' have
been investigated. Measured transmission values in various regions on
these samples are found in Tables la and lb and in Fig. 2. Average
values of the transmission through different samples and information about
their origin and composition are found in Table 2. The Swedish samples
have been denoted by three numbers separated by points according to the
following. The first number gives the sheet from which the sample plate
is cut, the second number the location of this sample plate in the sheet and
the third number the position of the studied region on the sample plate.
For the foreign samples the number before the point indicates the sample
investigated and the number after the point the location of the studied
region on the sample plate.
Corrections
1.
Correction for the dead-time of the measuring apparatus has been
made. This dead-time has been determined by measuring the countingrates with (I) and without (II) a boral sample in front of the counter at
two reactor power levels (a and b). Ia/lb (—2) gave the ratio of the neutron
fluxes at the two power levels, and the dead-time could then be calculated
from Ila/llb. The transmission measurements were made at a power
level of 1 kW, at which a counting-rate of about 2500 cps for the unattenuated flux and a dead-time of 15 - 5 |isec were obtained.
2.
In order to eliminate the contribution to the counting-rate from the
non-Maxwellian flux and the background, the transmission has first been
calculated from
A- B
where A = counting- rate without absorber
B -
"
C=
,"
D=
"
with Cd only
with boral only
with boral and Cd
*) Suppliers:
Alcoa: Alcoa International Inc., 230 Park Avenue, New York 17, N. Y. USA
HDA: High Duty Alloys, Ltd. , Slough, Bucks, England
VDM: Vereinigte Deutsche Metallwerke, Frankfurt (Main)-Hedderheim,
Germany (Representative: Svensk-Tyska Handels AB, Stockholm 80)
Örne: Tekn. lic. Nils Örne, Banérgatan 81, Stockholm Ö, Sweden
AIAG: Aluminium-Industrie-A-G, Neuhausen am Rheinfall, Switzerland.
1)
IT
According to Westcott ' M-?p— = 4* 7- '
v
o
Cd
for a parallel flux and 1 mm Cd.
As T = T and R~ , = 320, r is equal to 0. 0062. A correction of t has later
o
Od
been made, which, however, due to the low r-value never exceeded the
experimental errors at the measurements.
3.
A correction for scattering in the plate has been made.
Sources of Errors
1.
For certain samples the transmission values are very small
(»*10~ ), resulting in lov
low counting rates and correspondingly large
statistical errors (< 30 %)
2.
The Maxwell spectrum incident on the absorption plate has a
characteristic temperature higher than 293 K. Due to the fact that
the measurements were made using a neutron beam from the thermal
column, it is reasonable to assume that this increase is negligible.
A t-curve for T = 343 K has, however, been drawn in diagram 1, in
order to indicate the temperature influence.
3.
Variations exist in the transmission along the surface of the boral
plate due to non-uniform distribution of boron carbide grains. For each
plate t has been measured at several places and the results (Table 1)
show that for all foreign samples and for about half of the Swedish ones
t
- t
r
.
< 5 % unless the low transmission limits the measuring
accuracy.
4.
Deviation from parallelism of the flux incident on the plate will
cause a decrease in the measured value for t. The boron paraffin collimator inserted in the channel should, however, reduce this deviation
to a minimum.
5.
Analyses of the boron content per unit area have been performed
at the KFAB section. The aluminium in the plates was dissolved byhydrochloric acid and the insoluble part was weighted. The boron content of the grains was then determined and the result was 72. 5 % by
weight B and consequently less boron than the formula B,C implies.
The weight per unit area is difficult to determine accurately, and the
error has been estimated to ^ 5 %. Using the fast chopper at Rl,
the dependence of the transmission on neutron energy has been measured.
The values for In t are plotted in Fig. 3 as a function of l/v. A straight
line has been fitted to these values, and the boron weight per unit area
was determined from its slope. The results obtained, agree well with
the above mentioned analyses with the exception of the Swiss samples,
all of which had a transmission corresponding to a boron weight per unit
area of 70 % of that measured by chemical analysis. This is probably due
to the fact that the grains during manufacturing were crushed with quartz
cylinders. Quartz powder mixed with the boron carbide grains and the
boron concentration of the insoluble part was less than that of the boron
carbide. Transmission calculations based on these lower boron contents
agree well with results from integral transmission measurements.
6.
The cross section used for boron is 755 b [ BNL 325 (1958)] .
Since the B
-content can vary somewhat, especially in boron compounds,
there is some uncertainty in the cross section, but this probably does
not exceed 1 %.
Theory
Nomenclature
N = total number of neutrons per cm
v = neutron velocity in cm/s
v T = most probable velocity at temperature T K
and 2—^ = absorbtion cross sections of absorber and
detector respectively in cm /g at velocity vr
9
d. and d_ = weight per unit area in g/cm
detector respectively
of absorber and
If Maxwellian distributed neutrons are incident normally on a homogeneous l/v-absorber
the number of transmitted neutrons per cm
and
second is
3
-
o
Introducing
X-L/N
\
F
\ s
(x) =
n
-s
e
2
- x/s ,
-
/o
' d s
the transmission may be written as
4NvT
As the spectrum hardens when passing through a l/v absorber,
the effective
ifective macroscopic
macros
cross section decreases with increasing
4, 5)
amount of absorber.
If a l/v-detector is placed behind the absorber, its counting rate
will be proportional to
F
33 <SAT dA> " F 3 <SAT ddA
+
and the follow^ing transmission is measured
d
(o) -
\
(2)
A'
d n has been calculated to 0. 19 for the BA detector used.
8
For a "black" detector one gets
t (E
A T
d
A
F , (S
(
d )
3
AA
3
^^
F 3 (o)
•) =
(4)
and for a thin detector
F
t (2
d
A T
0) =
A
22 ^AT
A>
A T A
(5)
F , (o)
and
t (x, o) <; t (x, s D T dD) < t (x, <»)
(6)
The "blacker" the detector is, the larger is the measured ratio of transmitted to incident flux for a given absorber.
In Fig. 1 t equals the calculated transmission for a homogeneous
layer plotted according to Eq. (3) as a function of d . Curves are drawn
A
for various detector thioknesses and various characteristic temperatures
of the Maxwell spectrum.
In Fig. 2 the measured transmissions are compared to those calculated for a BA-counter and T = 293 K.
The Influence of the Grain Size
If the absorbing material in a sample consists of grains with dimensions -
the mean free path in the absorbing material, the trans-
mission becomes larger than if the material is distributed homogeneously. '
*) dF
'
n
—
dx
'
'
="Fn-l
If the a b s o r b e r grains a r e a s s u m e d to be s p h e r i c a l with a d i a m e t e r
of 2R and stochastically distributed, this is equivalent to multiplying the
2)
boron content by an efficiency factor e
e =
a
,
r,
3 a ,
3a / ,
~aYI - 1
o ~
In L 1 - —T— + —T— ( 1 - ae
- e )J
c
a
1
a. a
V
where a =
S
T
,
volume of a b s o r b e r grains
and a =
total volume
V
T
€ is drawn as a function of ^Am * — * 2R in F i g . 4 . If in Eq. (7)
a—> O an equation is obtained which is in complete a g r e e m e n t with
3)
4)
those given in
and ' .
F r o m (3) and (7) we get
t = t[« ( S A T • I l - . 2R, a) • S A T • d A , S D T . d D ]
Results and Discussion
The computed value for t from (8) is plotted in F i g . 2 with 2R
a s a p a r a m e t e r . A comparison between this function and the values
obtained experimentally shows that for 2R in (7) a value < 0. 1 m m
should be i n s e r t e d for the foreign samples except one. The t r a n s m i s s i o n
m e a s u r e m e n t s with the fast chopper (Fig. 3) show that the deviation
from a l / v - c r o s s section is negligible even at low v e l o c i t i e s . The
chopper m e a s u r e m e n t s also indicate that 2R < 0. 1 m m . At section
RMM the boron carbide g r a i n size was d e t e r m i n e d using an eyepiece
m i c r o m e t e r . However, the analysis (Table 3) indicates that in s e v e r a l
c a s e s the grain size is l a r g e r than 0. 1 m m . F o r 2R in E q . (8) an
average value for the grain size should not be used, but a considerably
s m a l l e r value ( - l / 3 thereof). Eq. (8) is therefore qualitatively c o r r e c t
but quantitatively it has c e r t a i n d i s c r e p a n c i e s , which probably depends
on the fact that it only considers one grain size and does not include the
(8)
10
effect of small grains assembled between the large ones.
On comparison between calculated and measured values in 4), one
obtains similar results regarding the calculation of e . Information about
the boral samples is, however, incomplete which makes comparison
more difficult. The measurements described in this report refer to a
parallel flux while those in 4)' refer to neutrons emitted from an infinite
uniformally emitting surface. According to Fermi the angular distribution in the latter case is (1 + *J°3 cos 9) d (cos 9) and a t-curve (accor7)
ding to ') is drawn for this case in Fig. 1.
The foreign manufacturers have evidently succeeded in making
the boral sufficiently homogeneous. The effectivity (i.e. the ratio of
the boron content, calculated from (3) and the measured transmission,
to the measured boron content) of the foreign samples indicated in Fig. 2
is higher than 0. 9 for all samples except the German ones, for which it
is 0. 83. This is due to the very large grains (see Table 3). The homogeneity of the Swedish plates is not as good. Micrographs of Swedish
8 9^
and American boral ' ' show that the American plates are much more
homogeneous than the Swedish ones. For about half of the Swedish plates
the transmission and boron content vary along the surface of the plate
and the grain size is large. The relatively large transmission through
the Swedish samples is due to the decrease in effectivity caused by the
reasons mentioned above.
11
References.
1. WESTCOTT C. H. et al.
Effective Cross Sections and Cadmium Ratios for the Neutron Spectra
of Thermal Reactors
Gen. Conf. 1958 P/202
2. PERSSON R. and ÅKERHIELM F .
Transmission of thermal neutrons through boral
AEF-76 (1956) (internal report)
3. LAFORE P. and MILLOT J. P.
Determination de la reduction d'efficacite du bore ou d'un autre
absorbeur employe sous forme de poudre disséminé dans une
produit non absorbant, en fonction de la grosseur des grains.
CEA 675 (1957)
4. BURRUS W. B.
How Channeling between Chunks Raises Neutron Transmission
through Boral.
Nucleonics Jan. 1958
5. BEAUGE R.
Determination de 1'efficacité d'un écran de boral et mesure de la
quantité de bore contenue dans cet écran.
Service de la Pile de Chatillon (1957)
6. ZAHN C. T. and LAPORTE OTTO
Absorption Coefficients for Thermal Neutrons.
Phys. Rev. 52_67-74 (1937)
7. von DARDEL G.
The Interaction of Neutrons with Matter Studied with a Pulsed
Neutron Source.
Trans. Roy. Inst. Technol., Sweden,75 (1954)
8. HRU UR No. 21:57
(internal communication)
9. HRU UR No. 36:57
(Internal communication)
12
Table 1 a.
Measured Transmission of Swedish Samples
No.
Transmission
%
Table 1 b.
Measured Transmission of Foreign Samples
Sample
Country-
Transmission
%
Designation
England
Switzerland
USA
GermanyTable 2.
Sample
Country and
,,
r 4.
Manufacturer
,, ,
Mark
Boron Content
mg B/cm 2
a)
c)
Total
Thickness
mm
t
exp
Tiomogeneous
%
%
' Obtained by proportioning to the plate thickness
a) computed from, data given by the manufacturer
b) according to chemical analysis
c) according to chopper measurements
t,nom is calculated from Eq.
to the
i (3)
v / with T = 293 °K and d.A equal
^
value underlined in the table.
13
Table 3.
Measurements of the Boron Carbide Grain Size
(Performed at RMM)
Sample
Designation
Average Grain
Size in u
Max. Grain
Size in |i
Min. Grain
Size in |x
Remarks
1) approximately equal amounts of 2 grain sizes 25 J|L and 75 - 125
2) small amount of 25 \x grain size
3) plus a very small portion of sizes between 10 - 25 J|L
4) very uniform grain size
5) a very small portion of 5 \i size
6) rather uniform grain size
When not stated otherwise, the major portion of the powder is of average
grain size.
* * * * *
parallel flux
Flux having a distribution
100
Fig. I. Calculated transmission through boron
(Maxwell distributed flux)
300
mgB/cm
Legend
Alcoa
HDA
•
AIA6
s Örne
V VDM
X
•
-1
10
Grain diameters
A
B
C
D
0 mm
0.1
0.2
0.3
-2
10
10
10
100
200
mg B/cm
Fig. 2. Measured transmission values compared to calculated
values, assuming that the incident flux is Maxwell distributed
T = 293 °K and S D T dD = 0. 19 (BA detector). Parameter =
grain size
8
00
9
msec
10 T ravel-time
2100 Vel.
Fig. 3. Transmission measurements on samples H2, A and Wl using
the fast chopper at Rl (for absorber H2 calculations have been
made on the influence of the grain size)
1.0
0,5
0.2
0,5
10
Fig. 4. The efficiency (e) for the absorbing material versus the product
of macroscopic cross section and grain size (2
for different volume ratios (a).
. —
• 2R.)
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