REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 71, NUMBER 1
JANUARY 2000
Sapphire filter thickness optimization in neutron scattering instruments
I. E. Stamatelatosa) and S. Messoloras
Institute of Nuclear Technology and Radiation Protection, NCSR ‘‘Demokritos,’’
GR 15310, Aghia Paraskevi, Greece
!Received 9 July 1999; accepted for publication 15 September 1999"
The present work is concerned with the optimization of the sapphire fast neutron filter thickness
used in neutron diffraction instruments. The optimization is based on maximization of the slow
neutron transmission, minimization of the fast neutron transmission, and also taking into
consideration the neutron background at the vicinity of an instrument. Scattering properties of the
sapphire in the fast and slow neutron regions are discussed. © 2000 American Institute of Physics.
#S0034-6748!90"00301-X$
scopic linear attenuation, %!&", for sapphire in the wavelength region 0.04–1.2 nm and found it to fit well a function
given by Cassels.6 The different parameters of this function
were determined by a least squares fit to the experimental
data. Figure 1 presents the linear attenuation as a function of
wavelength as given by Cassels equation and the parameters
determined by the least squares fit to the experimental data.
Consequently, thermal neutron transmission of sapphire of
different thickness versus the wavelength can be calculated
!Fig. 2". It is observed that the transmission in the wavelength range of interest for a neutron instrument !0.12–0.25
nm" is almost constant and very close to unity depending on
the thickness. The fast decrease of the transmission for neutron wavelengths less than 0.1 nm makes also the sapphire an
effective filter for second and third order harmonics of the
monochromator. Cooling the sapphire to liquid nitrogen the
transmission of 0.12 nm neutrons through 101 mm sapphire
increases only by 18%,7 gain which does not justify the expense and complication of cooling the filter.
The above properties of the sapphire in the thermal region !high and almost constant transmission" makes it an
attractive candidate for a filter of the fast neutrons and thus
to a reduction of the background of a neutron instrument.
The effectiveness of such a filter will depend on its transmission in the fast neutron region and on the overall reduction of
the background in a neutron instrument. Such a determination requires detailed calculations using the MCNP code and
taking into account the energy spectrum of the neutrons
emerging from the reactor. For the purpose of using the sapphire as a filter the transmission has to be integrated over the
different neutron energies and the calculation has to be performed for different sapphire thickness. The results of such
calculations are presented in Fig. 3. It is of interest to notice
that the transmission in the fast neutron region # ' T(L) (
! ) * (E)T(E,L)dE, where * (E) the reactor spectrum$
shows an exponential attenuation. The calculated points can
be fitted well to the empirical equation
I. INTRODUCTION
Perfect single crystals can be used as filters to produce a
thermal-neutron beam almost free of fast neutron background. The filter material must have a wavelength dependent cross-section in such a way that is low for thermal but
strongly increasing at epithermal and high energies. The
choice of filter material and its dimensions are critical parameters affecting the performance of a neutron scattering
instrument. Several filter materials such as silicon, quartz
and sapphire have been used.1,2 Single crystal of Al2O3 !sapphire" has been proved an effective fast neutron filter and has
been incorporated in neutron instruments. However, there is
no detailed calculation concerning the optimization of the
parameters of such a filter and its overall performance in
reducing the neutron background of an instrument. The
present work addresses these questions and is related to the
design of a new powder diffractometer at GRR-1 ‘‘Demokritos’’ research reactor !Greece".
3
MCNP-4B continuous energy, generalized geometry,
coupled neutron, photon, electron Monte Carlo transport
code system was utilized to calculate fast neutron transmission through the sapphire assembly and moreover to investigate the effect of the sapphire filter on the instrument neutron
background. Neutron cross-section data from ENDL and
ENDF libraries were used. Both code and cross-section libraries were obtained from NEA data bank.
II. FILTER NEUTRON PARAMETERS
Sapphire filter is composed of a number of super optical
quality crystals with the #001$ axis parallel to the incoming
beam. The parameters necessary for the description of the
sapphire filter are its thermal and fast neutron transmission.4
In the thermal region the transmission has been measured
and the main features are summarized below. We have calculated the fast neutron properties of the sapphire by the
MCNP code.
The transmission data from sapphire single crystals do
not show any dips corresponding to Bragg reflections. Midner et al.5 measured by transmission experiments the macro-
T!
!1"
where L is the thickness of the crystal and ' L ( !31.3 mm
obtained from a least squares fit to the MCNP calculated
a"
Electronic mail: ion@ipta.demokritos.gr
0034-6748/2000/71(1)/70/4/$17.00
I
!exp! "L/ ' L ( " ,
I0
70
© 2000 American Institute of Physics
Downloaded 01 Oct 2011 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions
Rev. Sci. Instrum., Vol. 71, No. 1, January 2000
Sapphire fast neutron filter
71
FIG. 1. Macroscopic linear attenuation factor for sapphire as a function of
wavelength #line according to an equation given by Cassels !Ref. 6"$.
points. Moreover, the energy averaged free mean path of the
fast neutrons was calculated by MCNP code to be 33 mm,
which is in good agreement with that obtained by the fit.
Summarizing the filter properties of the sapphire can be
described in the thermal neutron region by Cassels equation
!Figs. 1 and 2" whereas in the fast neutron region by Eq. !1"
!Fig. 3". These equations will be used below for determining
the optimum parameters for a sapphire filter to be used in a
neutron instrument.
III. CRITERION OF OPTIMALITY
The optimum filter thickness will be a function of both
the fast and thermal neutron transmission. Thermal-neutron
transmission varies as a function of wavelength and thickness of the filter, whereas the fast neutron transmission varies
only as a function of the sapphire thickness. Since the useful
thermal-neutron wavelength range is from 0.1 to 0.25 nm we
need to examine the performance of the filter for these two
limiting wavelengths.
One might suggest that the optimum filter thickness is
that which maximizes the slow neutron transmission and
minimizes the fast one, provided that there is no severe reduction of the thermal neutron flux. Thus, we can define the
filter quality factor as:
Q 1 ! &,L " !
T thermal! &,L "
.
T fast! L "
!2"
FIG. 2. Sapphire transmission as a function of wavelength for 50-, 100-, and
150-mm-thick crystals !calculated using linear attenuation factor shown in
Fig. 1".
FIG. 3. Fast neutron transmission as a function of sapphire crystal thickness
for fission neutrons.
The quality factor Q 1 given by Eq. !2" was derived using
Eqs. !1" and !2" and is presented in Fig. 4. From Fig. 4 it
may be observed that the optimum filter thickness is around
150 mm. Sapphire of this thickness gives 62% transmission
of neutrons with 0.11 nm wavelength and 76% transmission
for 0.25 nm neutrons. The transmission of fast neutrons is
3%. Thus a sapphire filter of this thickness is an efficient fast
neutron remover but also reduces considerably the thermalneutron flux.
In an experiment one wishes to have a signal much
higher than the background, i.e., it is required to maximize
the function (I signal"I background). Both the signal and the
background are connected with a proportionality constant
with the transmission through the filter of the thermal and
fast neutrons, respectively. Thus, the quality factor for the
sapphire filter can be defined as
Q 2 ! &,L " !N thermalc 1 T thermal"N fastc 2 T fast
!A # T thermal! &,L " " + T fast! L "$ ,
!3"
where N thermal , N fast denote the flux and T thermal , T fast the
transmission of thermal and fast neutrons, respectively. The
parameters c 1 and c 2 connect the neutrons emerging from
the sapphire and those measured from the detectors in a neutron experiment. In particular, c 1 depends on the efficiency
of the thermal neutron components !collimator, monochro-
FIG. 4. Sapphire quality factor index Q 1 as a function of crystal thickness.
Downloaded 01 Oct 2011 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions
72
Rev. Sci. Instrum., Vol. 71, No. 1, January 2000
I. E. Stamatelatos and S. Messoloras
FIG. 7. Simulated shielding geometry of a generic neutron instrument.
FIG. 5. Sapphire quality factor index Q 2 as a function of crystal thickness,
for +!1.
mator, sample cross section, detection efficiency" and c 2 on
the effectiveness of the shielding and the detector response.
One should try to minimize the parameter + through better
shielding and in the worse case + would be around 1 assuming that the thermal and fast flux emerging from the reactor
are almost equal.
Figures 5 and 6 show the filter quality factor Q 2 as a
function of thickness for +!1 and 0.5, respectively. For
+!1 the optimum sapphire filter thickness is 75 mm, which
give 79% transmission for 0.11 nm and 88% for 0.25 nm.
The fast neutron transmission is around 10%. We note that
for +!0.5 the optimum thickness of 75 mm is more apparent.
Quality factor Q 2 is the one which determines the optimum performance of the sapphire filter, i.e., signal improvement. Sapphire filter thickness of 75 mm reduces considerably the fast neutron transmission and very little that of the
thermal neutrons. Increase of the thickness reduces further
the fast neutrons but the simultaneous decrease of the thermal neutrons results in a smaller signal. Further, the effectiveness of such a filter in reducing the overall background of
a scattering instrument has to be considered.
IV. NEUTRON BACKGROUND CONSIDERATIONS
Once the optimum thickness of the sapphire filter has
been determined its effectiveness on reducing the fast neutron background of a neutron instrument has to be consid-
FIG. 6. Sapphire quality factor index Q 2 as a function of crystal thickness,
for +!0.5.
ered. A generic outlay of a neutron instrument is presented in
Fig. 7. This schematic representation is adequate in calculating the performance of a neutron instrument with or without
a sapphire filter and quantifying the benefits of such a filter.
MCNP computations were carried out starting with a
Maxwellian fission neutron spectrum as a parallel cylindrical
beam of 3.5 cm radius incident on the sapphire filter. Sapphire filter was simulated as a L#40#40 mm3 parallelepiped block of Al2O3 with a density of 2 g/cm3, where the
thickness L was varied from 0 to 250 mm. The filter was
positioned within the ‘‘primary’’ shield wall. A Cu scatterer
in the form of a cylinder of 4 cm radius with its main axis
perpendicular to the beam was assumed, thus representing
the monochromator. We note that the Cu scatterer dimensions are larger than the dimensions of a usual monochromator. Nevertheless, it may be considered as providing the
same neutron scattering mass. The shielding material employed is a common commercial boron-lead-doped polyethylene !Reactor Experiments, RX-202™" with a density of
4.2 g cm"3. This material was assumed to contain 4.3
#1022, 2.4#1022, and 1.0#1021 atoms/cm3 of H, B, and Pb,
respectively.
Figure 8 shows the total neutron flux !n/cm2" per neutron
incident on the filter at several detector positions, as a function of filter thickness. Spherical cell tallies (r!20 cm" were
simulated with their centers at 60 cm from the shielding
outer surface and at angles 0°, 22.5°, 45°, and 90° with respect to the incident beam, thus representing ‘‘typical’’ neutron scattering instrument detector positions. From this figure
it may be observed that the background is higher at small
angles with respect to the incident beam and it decreases
FIG. 8. Neutron background as a function of filter thickness for the shielding geometry shown in Fig. 7.
Downloaded 01 Oct 2011 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions
Rev. Sci. Instrum., Vol. 71, No. 1, January 2000
with increasing angle. In addition the logarithm of the background reduction versus thickness for the different angles
has the same slope. This combined with the factor that different angles give different neutron paths and different
shielding thickness leads to the conclusion that the results of
Fig. 5 can be applied to any instrument arrangement, i.e., the
background reduction is independent of the exact shielding
arrangement. Between 0° and 90° a three orders of magnitude reduction in the neutron background is observed. This is
important in the design of an instrument or in the performance of experiments where low background is required.
V. DISCUSSION
In principle, the optimum sapphire filter thickness is that
which maximizes the slow neutron transmission and minimizes the fast one, provided that there is no severe reduction
of the thermal neutron flux. Based on this reasoning a quality
factor (Q 1 ) can be derived resulting in an optimum sapphire
filter thickness of around 150 mm. It was shown that sapphire of this thickness gives 62% transmission of neutrons
with 0.11 nm wavelength and 76% transmission for 0.25 nm
neutrons. The transmission of fast neutrons is 3%. Thus, a
sapphire filter of this thickness is an efficient fast neutron
remover but also reduces considerably the thermal-neutron
flux. However, in a neutron scattering instrument one wishes
also to have the higher signal to background ratio that can be
achieved, thus in addition to thermal and fast neutron transmission the neutron background at the detectors has also to
be taken under consideration. In the present study Monte
Sapphire fast neutron filter
73
Carlo calculations using MCNP-4B code system were performed in order to estimate the neutron background at the
vicinity of the neutron instrument and at the detectors’ position. Consequently, an attempt was made to derive an improved quality factor (Q 2 ) taking into consideration not only
thermal and fast neutron transmission through the filter but
also the neutron background at the detector. The results of
this study suggested that the sapphire filter with the best
neutronics properties would be of 75 mm instead of 150 mm,
which was deduced with the simpler reasoning of quality
factor Q1. The advantages of utilizing such a thinner sapphire filter are: a higher thermal neutron transmission, a
lower neutron background at the vicinity of the instrument,
and a lower cost. It is stressed that this approach is especially
useful at light water reactors and, in particular, at reactors
with beam tubes pointing directly to the core center, such as
Demokritos research reactor, where a lower neutron fluence
is encountered which also has a high fast neutron contamination.
1
H. F. Nieman, D. C. Tennant, and G. Dolling, Rev. Sci. Instrum. 51, 1299
!1980".
A. K. Freund, R. Pynn, W. G. Stirling, and C. M. E. Zeyen, Phys. Status
Solidi B 120, 86 !1983".
3
J. F. Briestmeister !Ed.", LA-12625-M, Los Alamos National Laboratory
!1993".
4
R. Born, D. Hohlwein, J. R. Schneider, and K. Kakurai, Nucl. Instrum.
Methods Phys. Res. A 262, 359 !1987".
5
D. F. R. Midner, M. Arif, and C. A. Stone, J. Appl. Crystallogr. 26, 438
!1993".
6
J. M. Cassels, Prog. Nucl. Phys. 1, 185 !1950".
7
D. C. Tennant, Rev. Sci. Instrum. 59, 380 !1988".
2
Downloaded 01 Oct 2011 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions