A quasielastic spectrometer using a linear accelerator cold neutron source

Nuclear Instruments and Methods 178 (1980) @North-Holland Publishing Company

A QUASIELASTIC

SPECTROMETER

K. INOUE, Y. KIYANAGI, Department Received

459-568

USING A LINEAR ACCELERATOR

COLD NEUTRON SOURCE

H. IWASA and Y. SAKAMOTO

of Nuclear Engineering,

Hokkaido University, Sapporo, 060 Hokkaido, Japan

22 July 1980

Herein we describe the design and performance capabilities of a neutron quasielastic scattering spectrometer with conventional resolution. The spectrometer is equipped with an accelerator pulsed cold neutron source (a 20 K methane moderator), and is installed in a 35 MeV electron linear accelerator. Using inverted geometry, the instrument analyses scattered neutrons by focused analyser mirrors. High efficiency is achieved by adopting the large area of the cold moderator and the analyser mirrors. The spectrometer has demonstrated considerable usefulness in experimental spectral profile analysis studies.

1. Introduction

source are its nearly flat distribution of the time-offlight spectra in the cold neutrons, and its ability to achieve a very low background level. These features are particularly advantageous in quasielastic experiments using a conventional energy resolution in which analyses of the quasielastic peak shape, and not only the peak width, are required [lo]. In this paper we describe the design and performance capabilities of a quasielastic spectrometer which is attached to an electron linac and employs a cold neutron source.

It has been widely recognized that as a source for neutron scattering research the electron linear accelerator is a very efficient and economical pulsed source [l-8]. We have developed a cold neutron source facility for installation in a modest capacity electron linac which reduces significantly the technical problems normally encountered in reactor equipment [9]. The important features of the pulsed cold neutron

ANALVSER

Fig. 1. General layout of the quasielastic spectrometer methane slab moderator at 20 K. The neutrons which filter, and then detected by a counter as monochromated

using an accelerator are scattered from neutrons.

459

cold neutron the specimen

source. Cold neutrons are produced by a are analysed by a mirror and a beryllium

460

K. lnoue et al. / Quasielastic spectrometer

Since the electron linac installed at Hokkaido University is a modest capacity facility (35 MeV at 2 kW mean power) in which the efficient use of neutrons is of utmost importance, we have adopted a cold moderator with a large emanating surface and a wide range o f angles for detecting the scattered neutrons. As illustrated in fig. 1, the spectrometer consists of the cold source at distance 11 from the specimen and a set of four assemblies of large area, crystal analyser mirrors, beryllium filters, and counters. The spectrometer operates as follows: neutrons are scattered through the second flight distance 12, they are reflected by the analyser mirrors, impinge on the beryllium falters, and subsequently are detected by the counters as monochromated neutrons. The so-called inverted geometry configuration of the time-of-flight spectrometer is free from the cumbersome distortion in spectral shape due to the t -a weighting factor in the time-of-flight which inevitably appears in ordinary direct geometry facilities.

2. Design considerations Using the pulsed neutron source, we have designed the spectrometer with respect to the instrumental set-up and parameters adopted in quasielastic experiments of conventional resolutions.

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Fig. 2. Measured neutron time-of-flight spectra from a 20 K methane moderator and an ambient temperature water moderator. ness of 5 cm, is approximately constant, and the spatial distribution of the neutron flux reveals an almost cosine curve-like distribution. Consequently, if the largest possible neutron emanating surface is used, a large beam intensity at the position of the specimen can be achieved. In addition, a large increase in source strength can be obtained by using a fast neutron reflector [2,13].

2.1. N e u t r o n s o u r c e

Emanating from a methane moderator at 20 K, the pulsed cold neutron source has a unique time-of-flight spectra. As shown in fig. 2, a large enhancement of the time-of-flight spectra takes place in the cold neutrons, and the spectral distribution, which is shown as a function of time, is almost fiat over an energy range of from 9 to 3 meV [ 11 ]. Fig. 3 demonstrates the time-energy spectra of the cold neutrons from the 20 K moderator surface, along with three representative time constants of the time distribution: the rise-time of the pulse, Tr; the half-width of the pulse, Tw; and the decay time, Td [12]. The risetime is about 20 /as for the cold neutrons, which corresponds to an energy spread of about 30/aeV in the time-of-flight measurement of a 6 m path length. The half width is about 55/as, which corresponds to an energy spread of about 80/aeV. The neutron flux intensity emanating from the center of the square surfaced moderator, which ranges from 10 × 10 cm 2 to 25 X25 cm 2 with a thick-

0t

Fig. 3. Time dependent neutron flux emanating from a 20 K methane moderator. The results of using a thermica monochrometer and the time-of-flight technique are shown by the dots, and the synthesized curves are indicated by the smooth calves.

K. lnoue et al. / Quasielastic spectrometer 2.2. Expression o f scattered intensity The measured intensity distribution y(t) of the scattered neutrons at scattering angle 0 is related to the neutron cross section and various instrumental conditions

y(t) = constlf ... r e ( E , , to,X)

face, specimen volume, mirror surface and counter window geometries. Consequently, eq. (2) is desirable as an alternative equation,

y(t) = cost.

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12/~/(2E2/m)]

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(2)

where

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(3)

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(1)

where ~)(EI, to, x) is the neutron flux of energy E1 emanating from position x on the moderator surface at time to, e(E1 -+E2, 0) is the differential scattering cross section of the specimen, E~ and E2 are the incident and scattered neutron energies respectively, and m is the neutron mass. More precisely, the scattering angle 0 is a function of x, r and E , but a relatively large tolerance for the scattering angle may be allowed for quasielastic scattering experiments. 0 is assumed to be an appropriate representative value. The incident and scattered flight path lengths are Ll(x,r) and L2(r, 12,S), with average values o f l l and 12 respectively, and p(x, r) and q(r, 12, S) are some of the correction factors representing efficiency and projection. The operation is as follows: the neutrons are scattered from the specimen at point r and reflected by the mirror surface 12. The monochromated neutrons then impinge upon the beryllium filter, and subsequently, upon window position S. Here the first 5-function with argument to expresses that only the neutrons with energy E l , whose flight time tl - to through the incident path is equal to L l(X, r)/x/(2E1/ m), can contribute to y(t). The second d-function with argument t is necessary because the flight time t - t~ of the scattered neutrons from r to the counter with energy E2 is equal to L2(r,Z, S)/x/(2E2/m). The third 6-function with argument /~2(r, 12 ,S) assures that the neutrons of Le2(r, 12, S), whose energy corresponds to the Bragg angle determined by the positions r, 12 and S, can be detected by the counter. For the purpose of data analyses, eq. (1) is intractable due to the multiple integrals of the source sur-

X q(r,~,,S) L~(r, ~,, S)

dr d~ ~ d S .

(4)

Here O(Eb t') represents the incident neutron flux on the specimen with energy E1 at time t', Fis a representative value of r, and R(E2) is the energy resolution function of the analyser mirrors.

2.3. Design parameters The following two conditions should be satisfied so that eq. (2) can become a sufficiently good approximation of eq. (1). First, the effect of the variance in L l(x, r) and p(x, r) is negligible in the integration with respect to r, which means that the incident neutron fluxes are the same for any positions of the specimen. Second, the effect of the variance in Ll(r, E,S) included in the f-function is also small, and 12 can replace L2(r,E ,S), which is included in the 6-function. More clearly, the variance in the second flight path between the specimen and the counter is negligibly small compared to the total flight path length. Our other design parameters are: (1) a square moderator, size A, (2) a cylindrical specimen of height a, diameter b, and thickness c, (3) a counter window of height a and width b, (4) a mirror of vertical dimension h and lateral dimension k. For increased efficiency, a cylindrical shaped specimen is connected to four analyser mirrors which can

K. Inoue et al. / Quasielastic spectrometer

462

measure simultaneously from different scattering angles. From eq. (1) we can express the efficiency approximately by using the design parameters as follows,

y o:

A 2 a2b2c

hk.

(5)

Our design parameters have been selected to satisfy the above-mentioned conditions, as well as to optimize the efficiency and resolution of the spectrometer. Adapting the considerations mentioned previously, we assign a large value for A, 25 cm, which is restricted by the refrigeration technique. The value of 11 is determined by the allowed incident neutron energy uncertainty, 6E1, which should be several times smaller than the scattered neutron energy uncertainty, 6Ez. Thus, the overall energy resolution of the spectrometer is effectively adjusted by varying the resolution of the analyser mirrors, which mainly determine 6E2. Assuming 6E~ ~ 80 ~eV for the case of 6E2 ~ 200 ~eV, we obtain the value of 11 ~ 6 m. The ratios of all2 and b/12 are restricted within certain values at the given energy resolution of the analyser mirrors. The other ratios of h/k and l J k have optimum values, which can be determined by numerical calculations using eq. (4). We obtain h/k and 12 ~ 120 cm at the given lateral dimension, k 20 cm, of the mirror. The distance spread 6L1 in the incident flight path originates mainly from the radial spread of the cylindrical specimen, which may be the order of 6L ~ ~ ½b. The contributions to 6L~ from the spread of the moderator and the axial spread of the specimen are minor. Converting this distance spread into the time uncertainty of tl results in

6tl ~ btl/(2ll).

dent neutron pulse, and also much less than the time spread, which originates from the spread o f E2(x,~2 ,S). Thus, we can assume L 2 ( r , ~ , S ) in the g-function in eq. (1) to be constant with respect to the integrations r, r , and S, and substitute 12, instead ofL2(r, 22, S), in the g-function in eq. (1).

2.4. Purely elastic scattering spectrum In a case of purely elastic scattering, i.e., o(Et -+ El, O)o:6(E~- E2), we can assume the incident neutron flux with the simple equation

do(E, t) = ~(E) Z[t - ll/~/(2E/m)] .

(8)

Here ~/(E) is the energy distribution of the neutron beam impinging on the specimen, and Z[t ll/ x/(2E/m)] is the time-dependent distribution of the neutrons ofenergyE. Substituting eq. (8) into eq. (2), E2 integration is performed directly, thus changing the variable Ea to the flight time t', Y (t) = const. F(t) f z ( t

t') R*(t') dt'

(9)

Here R*(t) is the time resolution function of the analyser mirrors. We also assume that the time-offlight spectrum F(t') is a slowly varying function which can be replaced by F(t). Fig. 4 shows the typical curves of R*(t'), Z(t - t') and y(t) in a case where the analyser mirror has an energy resolution of about 200 #eV. The rising side o f y ( t ) shows nearly

R*(t') z (t-t') z (t-t')/~

,

(a)

(6)

Using the parameters given above and assuming b 1 cm and t~ ~ 7 ms, we obtain 6t~ ~ 6/~s, which is much less than the rise time or pulse width in the incident neutron flux. Thus, we can assume that Ll(x,r) and p(x,r) are constant with respect to r dependence. The gL 2 spread in the second flight path L 1(r,12, S) results in the time uncertainty in total time t, which is expressed as

t; y (t)= const.F(t)~Z (t- t') R*(t')d t' (b)

t

6t2 ~ t(gL2)/(1, + 12)

(7)

Assuming 6L2 ~ 1 cm and t ~ 8 ms, we have 8t2 12 gs, which is less than the rise or width of the inci-

Fig. 4. Illustration showing the typical curve shapes in a case of pure elastic scattering: (a) the n e u t r o n pulse time distribution, Z ( t - t'), and the mirror resolution function, R * ( t ' ) ; (b) the intensity distribution, y(t).

K. lnoue et al. / Quasielastic spectrometer the same shape as R*(t), and thus the effective resolution can be determined mainly by R*(t). 2.5. Spectral distortion Until now, many quasielastic investigations have been dominated by measurements of energy-gain scattering, and the scattered neutron spectra observed by time-of-flight spectrometers have been considerably distorted by the time factor t -a. In the case of the energy-gain scattering spectrometer (direct geometry), y ( t ) is written approximately as follows y ( t ) = const, t-3o[El ~ E2 = lm(l/t)2, 0] .

(10)

As shown in fig. 5c, the spectral shape reveals a considerably large distortion at the wings of the quasielastic peak. Ideally, the scattered neutron spectra should be free of such large spectral distortion. By using appropriate approximations, i.e., the ideal resolution and a separate expression for the incident neutron time-energy spectrum as in eq. (8), we can simplify eq. (2) to y (t) = const. F(t) o [El = ~m (l/t) 2 -+ E2, 0 ] .

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463

Here F(t) is the neutron time spectrum observed by the time-of-flight method, which is of a nearly flat distribution in the cold neutron energy region, as shown in fig. 2. When inverted geometry is employed, this large spectral distortion is eliminated because of the nearly flat distribution ofF(t), as seen in fig. 5b.

3. Description of the spectrometer Fig. 6 shows the flow of the cold source and a view of the entire instrumental set-up. The accelerator is operated at 35 MeV with a repetition rate of 60 Hz and a pulse width of 3/Is, and the average beam power is about 1 kW. The fast neutron source utilizes a water-cooled tungsten target. Fast neutrons are moderated and thermalized by a 2 0 K methane moderator cooled by circulating helium gas. The moderator methane is contained in a 2 5 × 2 5 ×5 cm a aluminum chamber, and is surrounded by an approximately 15 cm thick graphite reflector. With the exception of the neutron emanating surface, the moderator is covered with decoupler cadmium sheets. Hydrogen production due to decomposition of the methane takes place as a result of irradiation, and the production rate of the hydrogen is about 3.5% of the methane during 1000h of irradiation. The irradiated methane must be exchanged for fresh gas within the decided operational period. The spectrometer has four sets of assemblies consisting of analyser mirrors made of pyrolitic graphite crystals, beryllium filters, and 3He counters. The 144 pyrolitic graphite crystals used in each analyser mirror are arranged on an optimally curved array. In order to minimize the spread of energy in the mirrors, the shapes and the dimensions of the specimen and the counter window have been fixed so that the various neutron •ght paths have nearly the same Bragg angle and the same length. The energy resolution and the detecting efficiency are adjusted by varying the shapes and the dimensions of the specimen and the counter window. The specimen and the four analyser assemblies are shielded by borated resin blocks laminated by cadmium sheets. Each set of the analyser assembly is additionally shielded by an inner-shield to repel the stray neutrons which are scattered from other analyser assemblies. The detected neutron pulses are analysed by a 4096-channel time-analyser which permits the simul-

K. lnoue et al. / Quasielastic spectrometer

464

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taneous collection of four spectra, each composed of 1024 channels. The collected data are transferred to a small computer (8-bit, 64kB) equipped with data processing and graph plotting functions via a hardwired interface. Both the raw and the processed data are stored in magnetic disks according to instructions.

4. Performance

4.1. Resolution We were able to estimate the resolution of the spectrometer in an experiment on the scattered inensity of ice (fig. 7). The rise time of the peak for the pure elastically scattered neutrons was short, and its shape, which appeared on the rising side, was nearly the same as that of the resolution function of the analyser mirrors described in the previous chapter. The decay time was relatively long, owing to the properties of the incident neutrons. We were able to obtain useful data by analysing the whole peak shape in which the full width at half-

maximum was relatively large. For further information on the areas showing composite peaks consisting of sharp and broad peaks, we analysed the spectra shape on the rising side. The peak shapes in figs. 4 and 7 exhibited a sharp rise, which allowed for the improvement of the energy resolution. As described previously, we were able to adjust the resolution of the analyser mirrors, to some extent, by varying the shapes and the dimensions of the specimen and the counter windows. Fig. 8 demonstrates /~(~b), the Bragg angle resolution function of the analyser mirrors versus Bragg angle ~b for typical cases. The figure also shows the results of surveying the shape and the arm length optimization under a given area of the analyser mirrors.

4.2. Intensity The measurements for water in cement paste shown in fig. 9 enabled us to evaluate the intensity performance of the spectrometer. The time-of-flight spectra from a sample of cement paste measuring 5 mm diameter by 35 mm long were measured at

K. Inoue et al. / Quasielastic spectrometer [

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relevant time intervals after preparations [14]. The bound water content was determined as a function o f the time b y analysing these data. We obtained sufficient statistics during the two hour observation periods. The measured peak cold neutron flux intensity on the emanating surface was 4 . 5 X 1 0 1 ° n/cm 2 . s , which corresponded to the thermal flux of 2.1 X 10 ~1 n/cm 2 • s at 1 kW average beam power. Since the flux intensity was insufficient, we employed the large

emanating area o f the moderator with the result that the neutron beam intensity at the specimen position was so large that we were able to measure the quasielastic spectra accurately. 4.3. Background We were able to estimate the background performance of the spectrometer b y the measurements o f the scattered intensity of ice (fig. 7). The observed

K. Inoue et al. / Quasielastic spectrometer

466

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intensity of the elastic peak wings was very small compared to the elastic peak. The spectra of the peak wings were composed of background neutrons, inelastically scattered neutrons, and electronic noise, which indicated that the instrumental background of the instrument was minimal. The neutrons reflected by the analyser mirror included higher order reflected neutrons which contributed to the background appreciably. We used the beryllium falters in order to remove the higher order reflections. Fig. 10 shows the scattered intensities with and without the filter. The filter length was 6 cm, which was sufficiently long to remove the higher order reflected neutrons.

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Fig. 9. The scattered intensities from cement paste which were measured at sequential time intervals after preparation of the specimen.

467

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quently, the relation between the scattered intensity and the unknown parameters which appear in the scattering function is not linear, and in these cases, successive minimization o f the specific objective functions must be made using data analysis computer programs. Fig. 11 illustrates some examples o f the measurements which can be made effectively with our apparatus. In one experiment we investigated the bound and free water contents in cement paste during the hardening process. Adopting the two-component hypothesis, we applied the statistical data analysis method to the curve fitting in the scattered intensities. Fig. l l a shows one result of the curve fitting, and fig. 1 l b shows the variation o f the bound water

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content as a function of the time which elapsed after the preparation of the paste. The two-component hypothesis, which assumes that water is in the bound or the free state, has not been rejected by the 9(2test for curve fitting nor the Student's test [15] for the simple time-independent hypothesis.

6. Conclusion The pulsed cold neutron source quasielastic spectrometer described herein has performed effectively under the experimental conditions we have imposed, and it has shown much promise as a reliable instrument for application in quasielastic studies where conventional energy resolution is involved. The signal-

468

K. Inoue et al. / Quasielastie spectrometer

to-background ratio is extremely good due to the pulsed source, and the spectral distortion is very small due to the inverted geometry and the cold source spectra . The energy resolution o f about 200 #eV is attainable with reasonable count rates. This spectrometer may also be of value in the performance of peak profile analyses in quasielastic studies. We are very much indebted to the many persons who have contributed to the design, construction, and installation of the spectrometer. It is a pleasure to thank, in particular, Mr. M. Mori for excellent technical assistance in the construction of the essential parts of the apparatus. We would also like to acknowledge Messrs. N. Nashimoto, K. Jinguji, and Y. Tanaka for their painstaking efforts in the installation o f the instrument.

References [1] D.H. Day and R.N. Sinclair, J. Chem. Phys. 55 (1971) 2807. [2] O.K. Harling, Nucl.Instr. and Meth. 119 (1974) 217.

[3] P.A. Egelstaff, W.G. Graham, L. Hahn, K. Suzuki and D.J. Winfield, Can. J. Phys. 52 (1974) 2093. [4] N. Watanabe, Y. Ishikawa and K. Tsuzuki, Nucl. Instr. and Meth. 120 (1974) 293. [5] C.G. Windsor, L.J. Bunce, P.H. Borcherds, I. Cole, M. Fitzmaurice, D.A.G. Johnson and R.N. Sinclair, Nucl. Instr. and Meth. 140 (1977) 241. [6] J.M. Carpenter, Nucl. Instr. and Meth. 145 (1977) 91. [7] K. Sk~51d, K. Crawford and S.H. Chen, Nucl. Instr. and Meth. 145 (1977) 115. [8] C.G. Windsor, R.K. Heeman, B.C. Boland and D.F.R. Mildner, Nucl. Instr. and Meth. 151 (1978) 477. [9] K. Inoue, H. Iwasa and Y. Kiyanagi, J. At. En. Soc. Japan 21 (1979) 865. [10] T. Springer, Springer tracts in modern physics, Vol. 64 (1972). [11] K. Inoue, N. Ohtomo, H. Iwasa and Y. Kiyanagi, J. Nucl. Sci. Tech. 11 (1974) 228. [ 12] K. Inoue, Y. Kiyanagi and H. Konno, J. Nucl. Sci. Tech. 14 (1977) 195. [13] J.M. Carpenter and G.J. Marmer, Informal Argonne National Laboratory Report, ANL-SSS-72-1 (1972). [14] K. Inoue, Y. Kiyanagi and Y. Sakamoto, J. At. En. Soc. Japan 22 (1980) 189. [15] S. Brandt, Statistical and computational methods in data analysis, 2nd ed. (North-Holland, Amsterdam, 1976).