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The Harwell backscattering spectrometer
NUCLEAR
INSTRUMENTS
AND
METHODS
14o (I977)
241-250;
©
NORTH-HOLLAND
PUBLISHING
CO.
THE HARWELL BACKSCATTERING SPECTROMETER C . G . W I N D S O R , L . J . B U N C E , P . H . B O R C H E R D S * , I. C O L E t, M. F I T Z M A U R I C E , D. A. G. J O H N S O N a n d R . N . S I N C L A I R
Materials Physics Division, A.E.R.E., Harwell, Oxon, O X l l ORA, England Received 4 October 1976 N e u t r o n diffraction spectra in which b o t h high resolution (A Q/Q "" 0.003) a n d high intensity are m a i n t a i n e d up to scattering vectors as high as 30 A.-t (sin 0/2 = 2.5) have been obtained with the backscattering spectrometer (BSS) recently installed on the Harwell electron linac. T h e theory behind the spectrometer design is described, a n d it is s h o w n h o w the above resolution r e q u i r e m e n t leads to its basic features o f a 12 m incident flight path, a 2 m scattering flight p a t h a n d a scattering angle (20) acceptance f r o m 165 ° to 175 °. Examples o f the resolution, intensity a n d b a c k g r o u n d are given. It is s h o w n that the p r o b l e m o f frame overlap m a y be overcome by u s i n g an absorbing filter.
1. Introduction
The principle behind the back-scattering method in total neutron diffraction is illustrated by fig. 1. The time-of-flight method allows a range of scattering vectors to be recorded at a single scattering angle (20). As this angle is increased towards back scattering the cot OAO term in the resolution vanishes and a wide counter aperture AO may be employed. This method was proposed by Mayer-Leibnitz and Springer 1) and has been exploited with success using a reactor source and guide tube flight path by Steichele and Arnold 2' 3). Using the short duration neutron pulses produced by an electron or proton source, back scattering diffraction may be employed with comparatively short flight paths thus removing the need for guide tubes with their inherent transmission penalty at short wavelengths. Work at lower resolutions of order A Q / Q =0.01 at Harwell by Windsor 4) and Windsor and Sinclair s) and at Argonne by Carpenter et al. 6) has shown that a great advantage of such spectrometers when used with pulsed sources is their ability to maintain a resolution A Q/Q essentially independent of Q out to higher values of Q than are practicable to achieve with reactor spectrometers of comparable resolution. In the new backscattering spectrometer on the Harwell linac good diffraction intensities withA Q/Q ,,, ---0.003 are maintained to Q vectors as high as 30 ,~- 1. This enables neutron powder diffraction to enter a regime not previously accessible. Spectra at scattering vectors above about 20 ,~-1 are not easily measured * P e r m a n e n t address: D e p a r t m e n t o f Physics, B i r m i n g h a m University, England. t P e r m a n e n t address: T h e C a v e n d i s h Laboratory, Cambridge, England.
with X-rays because the X-rays scatter from the electron rather than the nuclear density and the electron form factor is becoming very small in this region. The extension of powder diffraction patterns to high scattering vectors is of great importance in structure refinement studies since the spatial resolution achieved depends largely on the maximum value of Q at which significant diffraction information is obtained. Profile refinement studies by Hewat 7) using reactor powder diffraction data, and by Windsor and Sinclair 5) using MODERATOR I
•
IA
L0
\C
/
COUNTER
BANK
I
I
B
I \
SAMPLE
2~
Fig. 1. T h e principle o f a backscattering spectrometer. T h e source o f the n e u t r o n pulse is a slab m o d e r a t o r o f dimensions .4 x A. T h e sample at distance Lo is also a slab o f dimensions a x a x c. Counters at a scattering angle 2 0 a n d distance L1 have a thickness c a n d cover a n area B x B.
242
c . G . WINDSOR et al.
linac data, suggest that precision in fitted structural and thermal parameters is largely determined by the higher Q region of the diffraction pattern. 2. General design considerations Applying the philosophy of Buras and Holas a) to a fast pulsed source (i.e. one whose pulse time is dominated by the neutron moderation time), we seek to optimise the diffraction line intensity at given resolution with respect to the main instrumental variables in the present case; the incident and scattered flight paths Lo and L1 and the scattering angle 20 (see fig. I). We assume as fixed instrumental parameters 1) a square moderator of side A ( ~ 100 mm), 2) a square sample of side a ( ~ 50 mm) (a < A) with thickness not greater than c ( ~ 2 5 mm), 3) a square detector array of area B 2 ( a < B ) (B ~ 300 mm), 4) counters of diameter c ( ~ 25 mm). Following Buras 9) we note that the total powder cross-section per unit cell may be written 2dSZtF 2 o"l = - sin E0,
(1)
Yo
where d~, Zt and F z are the d-spacing, multiplicity and structure factor of the lth order, and vo is the unit cell volume. The observed integrated intensity I t of the lth order depends further on the number of unit cells in the sample Ns, the incident neutron flux i(2), the wavelength spread A2 accepted by the counter bank and the fraction f of the Debye-Scherrer ring intercepted by the counter bank. I t = N~at" i(2). d2. f .
(2)
The incident neutron flux depends inversely as the incident flight path L o and on the time average flux at the moderator surface q~(2) A E 4(2) i(2)
-
-
-
(3)
4 nL2o The accepted wavelength spread A2 defends on the scattering angle spread accepted by the counter bank as a whole A2 = 2 cot0 AO = 2 cot0 (B/2L1).
(4)
The intercepted fraction / depends on the counter bank height B compared with the circumference of the Debye-Scherrer ring f -
B 2rcL 1 sin 20
(5)
Combining all factors we observe that the intensity of the lth order depends as sin 0, and inversely as the square of L o and L~ A2B 2 I, = 2d~ZtF2 Ns q~(2) sin 0. vo (4n) 2 L20L]
(6)
The resolution in d-spacing or Q vector (R = A Q/Q) depends on the root-mean-square errors in the total flight path ( L = Lo+L~), the total flight time T and the angular spread 60 accepted by a single counter in the counter bankS). R = [(--~)2 + ( ~ ) 2
+ cot2 06021'.
(7)
With counter and sample thickness c the r.m.s, spread in total flight path will be of order c so that 5L/L ~,, c/L.
(8)
The time spread of the neutron pulse we assume is determined by the neutron moderation time of order 72 /~s with 2 in A. This will correspond to a moderation distance C = 7h/m ~_28 mm so that the fractional error in the time spread may be written 6 T / T ~- C/L.
(9)
The ,50 of eq. (7) is much less than the angular spread from the complete bank of counters which we denoted by AO in eq. (4). This is because by placing the individual counters along the "time focussed" locus 1o-12), the contribution to the resolution from the complete bank can be made no worse than that of the counter at the least scattering angle. The angular spread 30 from such a single counter has three contributions in increasing order of importance 1) that arising from the spread in incident neutron directions caused by the finite moderator dimension, of order (~0mod = ½A/L o ; 2) that arising from the finite counter size assuming a point sample. With counter size c, this will be of order (~0. . . . t = ½c/L1 ; 3) that arising from the finite sample size a. This is clearly of order ½alL1 but is complicated because of the existence of focussing properties which can reduce this effective angular spread. This effect may be treated in the back scattering limit using the formula for the distance error given by eq. (13) of ref. 5. Converting this distance uncertainty into the equivalent angular uncertainty gives the result for backscattering a (Lo-3LI~ ~Osample ~-- ~ 1
~kL o - ~ . / / .
(10)
HARWELL BACKSCATTERING SPECTROMETER Thus the contribution has the intuitive value ½a/L~ in the limit of short scattered flight paths (L1 < Lo), but focussing effects cause the contribution to decrease as L 1 is increased and indeed to vanish when L~ = ½L o. The time-focussed sample geometry is then a plane perpendicular to the beam and parallel to the timefocussed counter geometry. Collecting all the contributions to the resolution together we have R =
[Ic2+2C x
+ cot20
+ a2
A[_~o+ ~ -1~ x
~)'/J
"
(11)
B
sin 20 "" - - , L1 i.e. B
2Ll
and
sin0"-" 1.
(12)
Thus the expression for the resolution [eq. (11)] becomes
/ c2 "t- C 2
B2 a I ~ 0
R = [i~o+L--~-2 + 4L-"--~l
×
+ a2 (Lo-3L')
It is now straightforward to maximise the intensity as given by eq. (6) for a given value of R by adjusting Lo and L1 numerically. We shall present such results for the present case later, however it is also possible to optimise the intensity analytically with certain reasonable approximations. In particular if L 1 < L o the angular uncertainty 30sample becomes simply ½a/L t and generally dominates over the counter and moderator contributions to 60. Eq. (13) then simplifies to [- C2 d- C 2 B 2 a21½ R = LiL--~L,) / 2 + - 16L~l --71,
The objective is now to maximise the order intensity It of eq. (6) with respect to the variables L o, L~ and 0, subject to the resolution constraint of eq. (11). It is immediately seen that the scattering angle should be as close as possible to back scattering (0 = ½n) since the intensity is then maximised (sin 0 ~ 1) and the resolution optimised (cot 0 ~ 0 ) . In practice a maximum scattering angle will be set by the requirement of shielding the counters from the incident beam. A practical design will have a shielding thickness about equal to the width of the counter bank (B). Thus the mean scattering angle will be given by assuming
cot0"--
243
1 + L--~l
l I'
( - L - o ~ )-JJ "
(13)
(14)
If L0 >>L1 it is then possible to eliminate L~ from eqs. (6) and (13) and maximise the intensity It with respect to the remaining variable L1 by differentiation. The result is
Li =/F'/qll("3Ba)l. YL 4R
(15)
J
The total flight path now determined from eq. (13) as L = ½~/6 ~/(c 2 +
cZ)/R.
(16)
The expressions may be used to calculate the optimised dimensions for given values of the other parameters. In the present case using the parameter values given above and assuming a resolution R = 0.003 we obtain the values for L, L1 and 20 given in the first column of table 1. A numerical optimisation using the full expression of eq. (13) for the resolution gives the values for L and L 1 quoted in the second column. The last column shows the actual dimensions of the spectrometer constructed. It is seen that its scattered flight path is somewhat larger than is calculated, showing that the spectrometer would be somewhat better matched with a larger incident flight path. Having found the optimum path lengths we may reconsider the design criterion of matching the three components of the resolution considered for example by Sinclair and Windsor (1976). In fact the distance, timing and angular contributions to R 2 given by the
TABLE1 Parameters of the spectrometer for resolution R = 0.003. Analytic optimisation Total flight path L (m) Scattered flight path LI (in) Scattering angle 20 (°)
15.32 1.47 173
Numericaloptimisation 14.52 1.52 (173)
Spectrometerconstructed 14.04 2.00 165-175
244
c . G . W I N D S O R et al.
terms in eq. (13) are 0.00177, 0.00199 and 0.00188 respectively and thus are quite closely matched although the timing error is giving the largest contribution to the resolution.
3. Constructional details Fig. 2 shows the general layout of the condensed matter cell and the backscattering spectrometer on the Harwell electron linac. The linac produces a pulse of electrons every 2600 ps. These pulses are normally multiplexed between nuclear physics experiments and the condensed-matter cell, so that one pulse 2 #s long is sent to the condensed-matter cell every 5200/~s. In the cell the electrons strike a natural uranium target producing a fast pulse of neutrons 13). Close to this target is a heterogeneously poisoned moderator, consisting of two slabs of polyethylene, 27 and 13 mm
ELECT-RO ' N BEAM 0 BOOSTER
I~L-ECTRON LINAC S W I T C ~ T N G ~ ........ MAGNET
M~ D ERATO ' 0
{:~ TAR GET
ARGET CELL
TO TSS.
TO
EVACUATED FLIGHT TUBE
FISSION CHAM BER
COUNTER OPENINGS
SAMPLE OPENING
EVACUATED SPECTROMETER BOX
TO B E A M
STOP
Fig. 2. General layout of backscattering spectrometer showing target and moderator and flight tubes to the three spectrometers (backscattering BSS; total-scattering TSS; and inelastic-rotor, IRS). The linac pulses once every 2600 ps, the switching magnet directs every second pulse to the condensed-matter-cell target.
thick, separated by a gadolinium foil, 0.025 m m thick. This foil prevents the build up of a Maxwellian distribution of thermal neutrons in the moderator, and so shortens the time-spread of the neutron pulse 14). Three evacuated flight tubes penetrate the concrete wall around the cell, and carry neutrons from the moderator to three spectrometers; the backscattering spectrometer, the total-scattering spectrometer x 3) and the inelastic-rotor spectrometer. The flight tube to the backscattering spectrometer is 300 mm in diameter, and is lined with collimating rings of borated resin converging to a 70 m m aperture in front of the spectrometer, as shown in figs. 3 and 4. At this point the neutron beam passes into the open for 50 m m before entering the spectrometer itself. Here there is a fission counter for monitoring the beam and there is provision for inserting absorbing filters. It is a defect of back (or forward) scattering geometries that air scattering must be avoided since the counter views the incident beam over a long length. The spectrometer is therefore capable of being evacuated and in practice a vacuum of order 10- 5 torr is achieved, sufficient to allow a liquid nitrogen temperature sample changer without added containment. The incident beam is carried to the sample by a 75 mm diameter pipe. The sample is in the centre of a 0.5 m diameter aperture passing through the spectrometer allowing ample space around the sample position. There are two counter banks each at a mean distance of 2 m from the sample and covering angles from back-scattering from 5 ° to 15° in the horizontal plane and from - 5 ° to + 5 ° in the vertical plane. Each bank is composed of 14 25 m m diameter, 300 mm long 3He counters at 5 atm pressure, The counters are positioned to lie on the time focussing curve given by eq. (12) of Windsor and SinclairS). In fact this curve is quite shallow with the chosen path lengths, having a maximum angle of ~ 10 ° from the plane perpendicular to the beam. Each bank has an area of order 0.1 m z and the total subtended solid angle is 0.056 rad 2. The counters lie in cadmium lined boxes outside the vacuum. The apertures in front of each bank are designed to allow visibility of a 50 mm wide by 50 m m high sample. All surfaces seen by the counters are clad with cadmium (shown by the heavy lines in figs. 3 and 4). The incident beam contains many unwanted fast neutrons. The beam is therefore collimated as far as possible before entering the spectrometer, then finally collimated at A in figs. 3 and 4. The straight through beam is contained without break in the vacuum by a 150 m m diameter cadmium lined pipe to a beam stop some 2 m away, outside the spectrometer room.
HARWELL
BACKSCATTERING
4. Data collection
245
SPECTROMETER
trum may be recorded if desired but in general spectra are normalised by recording the total monitor counts between selected flight times. Since the neutron pulse times are as low as 3 #s for a wavelength of 0.3 A a channel width of 2 #s is acceptable. Some 2600 storage locations are therefore required to store a complete spectrum of period 5200 ps. In practice for most diffraction experiments
Although the outputs from selected groups of counters may be counted separately if desired, the normal mode of operation is for all counters of both banks to be gated together and recorded as a single time-of-flight spectrum. Tests have shown that this mode produces no detectable shift or broadening of diffraction lines. The moderator time-of-flight spec-
\ /COU.TER /
"
\ '
\
SAMPLE
to BEAM STOP
Fig. 3. Plan view o f the backscattering spectrometer. T h e n e u t r o n s enter the evacuated b o x from left to right a n d are collimated by a slit at A. T h e counters lie o n the time-focussed curve. T h e dashed line s h o w s the outline o f the concrete b l o c k h o u s e enclosing the spectrometer.
INCIDENT NEUTRON F L I G H/~/T U B E
ROTARY S A M P L E E ~ L _ CHA R GE R -------------~
SAMPLE
\ t"
AREA
I
lm
Fig. 4. Elevation o f the backscattering spectrometer. Access to the sample area is t h r o u g h 0.5 m diameter m a n h o l e s above a n d below the sample. T h e sample changer rotates to p u t o n e o f five samples in the b e a m line. It can operate at liquid nitrogen temperatures.
246
c.G.
WINDSOR
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there is less interest in the first 1000/~s of the spectrum (scattering vectors above 44 A - l ) and so 2048 channels suffice covering the wave-vector range 8 . 5 / ~ - ~ to 44 A -x. The data is collected by an on-line computer, ( P D P l l / G T 4 4 system). This permits the collection of up to seven spectra, each of 2048 channels. The sample changer is moved under the control of the computer after a pre-set number of monitor counts have been recorded. The sample changer has up to five positions allowing simultaneous collection of data from five different specimens or more usually from a specimen, can, vanadium and background runs. This eliminates normalisation errors from incident flux variations with time constants long compared to the sample changer period of typically 20 rain. The system includes a visual display, on which the spectra may be viewed while the experiment is running. Between experiments the computer is available for data processing and a comprehensive set of programmes has been written for this purpose, so that the experimental data can be converted into cross-sections for display, using either the visual display unit, or a Versatek graph plotter, connected to the computer (e.g. fig. 5). The computer has sufficient power that it can calculate powder diffraction profiles for cubic structures. 5. Modes of operation
7o'~
(t~t] ~ .===:
The conventional way to analyse a time-of-flight spectrum is to convert it into an absolute cross-section by recording a set of four spectra corresponding to sample plus can (S), can alone (C), vanadium (V) and background (B). The vanadium is assumed to have a constant incoherent cross-section, a~ of 5.13 b. The cross-section is then given by
r;.~.
ZV9
dtr
--
001~ [£
dt~ <
• .
j,
f
iI ,oo.,
o-
i°
..e
il i
W~*? NI
$~.NnO0
? ;
ct al.
v,~.o
=
Nv I+/ms - Ic/m~ try --,
(17)
Ns Iv/mv - IB/mB 4 ~
vhere I is the spectral intensity, N the respective numbers of unit cells in the beam, and m the respective monitor counts. A more detailed treatment involving absorption and scattering corrections has been described by Clarke 15). However the above equation is only valid when all detected neutrons correspond to the same initial pulse or "frame". With the present linac period and spectrometer total flight path "frame overlap" occurs for wave-vectors less than 8.5 A - 1 and double frame overlap for wave vectors less than 4.3/~-1 and so on. There are two straightforward ways of overcoming the problem of frame overlap: by reducing the pulse
HARWELL
BACKSCATTERING
247
SPECTROMETER
and are largely eliminated in the spectrum with can subtraction and normalisation shown in the lower part of fig. 5. Using a gadolinium neutron filter 0.025 mm thick the neutrons collected in the primary frame suffer only moderate attenuation. However the attenuation of neutrons of wave-vector below 8/k-2 is increasingly large so that orders arriving during the second frame are almost completely eliminated. Similarly the contribution to the vanadium spectrum from overlapped frames is negligible so that the simple calibration formula of equation 17 may be used. Fig. 6 shows the calibrated spectrum from nickel powder at 77 K recorded in this way. This figure is on a highly expanded scale and covers only the marked area to the extreme left of fig. 5. There is no sign in the measured spectrum of overlapped peaks which would have been expected near the 777 peak at 2080 ps (222 peak from the second frame) and near the 955 peak at 2200 ps (200 peak from the third frame and clearly visible in fig. 5). The solid line in fig. 6 is the powder profile calculated using the methods described in refs. 4 and 5. The excellent fit shows that the problems of spectrum calibration and frame overlap can certainly be solved for high scattering vectors using the filter method. There are other more complicated ways of dealing with frame overlap: data taken with and without a filter may be simultaneously analysed to give the spectrum from both first and second phase. Alternatively the composite spectrum including frame overlapped peaks may be studied by profile analysis if
repetition frequency of the source, or by discarding reflections not corresponding to the primary frame by inserting a filter with high absorbtion at low wavevectors. A comparison of these two methods has been made and some results are shown in figs. 5 and 6. The first method giving an increased pulsed neutron period seems the obvious method but has the major disadvantage of decreasing the rate of data collection both for the spectrometer being used, and also for other spectrometers sharing the same moderator. To eliminate frame overlap completely requires a threefold increase in the period even for a material with as small a unit cell as nickel (3.5 A). A more common unit cell size such as that of alumina (5.5 A) requires a five fold period increase. It is an important advantage of pulsed sources operating near 50 Hz (such as the proposed spallation sources at the Rutherford Laboratory, U.K. and the Argonne National Laboratory, U.S.A.) that frame overlap is largely avoided for powder diffraction. In fig. 5 we show the time-of-flight spectrum from an ambient temperature nickel powder specimen of dimensions (50x 50x 2 mm 3) with the cell pulsed at intervals of 10 400 #s. The 4096 time channels span scattering vectors from 5 to 44 A-~. Only the first two orders, from 111 and 200 planes suffer frame overlap and these are dearly visible. The can scattering also shown is seen to be low and featureless except for the two small sharp peaks at 2600 and 7800 #s caused by fast neutrons from the adjacent nuclear physics booster. These peaks also occur in the sample spectrum
5
b~
~o
:9 t
o 2LO0
o
=
.
. I 2O
z
I
I
I
I
I
I
I
2200
2000 TIME
OF
FLIGHT
I
I
25
0 I X -1 ) I
I
1800
(pS)
Fig. 6. T h e high region o f a nickel powder s p e c t r u m t a k e n at 77 K o n a highly expanded scale. T h e scattering vector Q increases f r o m 19 to 26 A -1 f r o m left to right. Orders are denoted by the n o t a t i o n hk. l(m), where m is the n u m b e r o f simultaneously observed orders, except when these are written in full a n d separated by c o m m a s . A 0.04 m m gadolinium filter was inserted in the incident b e a m to eliminate frame-overlapped peaks a n d the normalised cross section calculated u s i n g eq. (17). T h e solid line is a profile analysis fit to the observed spectrum.
248
c.G. WINDSOR et al.
the incident neutron spectrum for all frames is known. These methods will be the subject of a forthcoming paper.
The resolution predicted by eq. (13) assumes the validity of a "moderation" time 72/~s/A. The correct form for the moderation time is
6. Resolution performance
T = [ ( 7 2 ) 2 + Z2] "} ,
The nickel powder spectrum of fig. 5 has been used to assess the resolution of the spectrometer. The full width at half height A T was measured for each resolved peak, and the resolution R calculated as A T/T. The results are shown in fig. 8. We also show the theoretical value of eq. (13), and compare the performance with that of other high-resolution spectrometers. The resolution is close to the theoretical value at low and at high scattering vectors, but is worse at intermediate values corresponding to neutrons whose pulse time has been broadened by the Maxwellian distribution. This effect can be moved to smaller scattering vectors, which are of less interest on th s spectrometer, by cooling the moderator. A liquid-nitrogen cooled moderator is being built.
where z is the electron pulse-length of 2 Ms. Thus we expect the resolution to deteriorate at a scattering vector of about 40 A - 1 , after which the resolution will be proportional to the scattering vector. 7. Intensity performance A standard cintered A120 3 (7.5 mm diameter by 13 mm long) was supplied by A. F. Andreson for the purpose of making a comparison of powder diffract•meters for the Neutron Diffraction Commission. The spectrum from this sample obtained in some 40 h is shown in fig. 7. No filter was used, but all the peaks arrowed belong to the primary frame. The spectrum covers scattering vectors above I0 A -1 beyond that
11
10
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Q
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.
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ee
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jt'~
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e
tt~
m It~ ~o
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I,
a•
,.IJ,
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TIME
J,, 4400
4200
OF FLIGHT
(~uS)
Fig. 7. The time-of-flight spectrum from the standard alumina specimen of volume 0.57 ml. No:filter was used. The lines show the calculated intensities of the various orders.
H A R W E L L B A C K S C A T T E R I N G SPECTROMETER
sinelX 0.5
1-0
I
I
(~,-I)
249
1.5 I
PANDAh =1'5/,o2e=90" o¢.=17'~, =13'
0.005
.
, . . °
• •
•
° •
•
°
0.003 ~
A
LCULTEDi0(1=1°~,2=2@ 10=~111° ,,....--
~ 0.0
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I
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o 11-1 ) Fig. 8. The points show the resolution of the spectrometer evaluated from the widths of the nickel powder spectrum shown in fig. 5, compared with its calculated resolution Ad/d = 0.0033. The two parabolas show the experimental resolution from a typical conventional spectrometer, PANDA, at Harwell and the calculated spectrum from a high-resolution spectrometer operating at short wavelengths. The dashed line shows the resolution of the Garching back-scattering spectrometer.
obtainable from conventional reactor high resolution powder diffractometers. The peak intensities shown by the lines were calculated from the structure given by |-Iewat and Bailey 17). The profile maintains a recognisable structure out to scattering vectors of order 25 A - ~. The time average intensity of incident neutrons at the sample position is calculated from vanadium spectral intensities to be given by an expresssion of order N(2) ~ 5000/2 neutrons/s cm 2 A . 8. Background performance
The instrumental background shown by the dashed line in fig. 5 is composed of several components. The background is largely time-independent, and although small when expressed per time channel 0.04cts/m (12#s gate) amounts to 105 cts/m when expressed as a time average background. Some experiments have been performed to investigate the origins of the background. Some 12 cts/m are present when the linac is switched ,aft and so represent the "electronic noise". For a bank of 28 counters this is a satisfactory level. A further 20cts/m are present when the electron beam is
switched only to the adjoining nuclear physics booster facility and so is quite external to the spectrometer operation. Switching on the spectrometer's electron beam but covering the inlet port of the spectrometer (marked A in fig. 3) with a 25 mm boron carbide slab adds a further 20 cts/m. The remaining 50 cts/m are added by allowing the full beam through the evacuated spectrometer. 9. Conclusions The spectrometer thus shows great promise for diffraction experiments at 0.3% resolution in the scattering vector range from 8.5 to 45 A-1. Its performance with liquid and amorphous samples at even higher scattering vectors has yet to be tested but the tests on instrumental background suggest that measurements beyond 100 A-1 should be possible. Single crystal samples might also be used to investigate weak magnetic and nuclear reflections of high order without the order contamination problems of conventional twoaxis diffractometers.
Many people besides the authors contributed to the design, construction and installation of the spectrom-
250
c . G . WINDSOR et al.
eter. It is a p l e a s u r e to t h a n k in p a r t i c u l a r the P r o j e c t Officer Dr. B. C. G. H a y w o o d , the P r o j e c t E n g i n e e r L. M a s o n a n d the m a i n c o n t r a c t o r s W e s t e r n Details Ltd. for d e l i v e r i n g the s p e c t r o m e t e r w i t h i n the agreed t i m e a n d w i t h i n the agreed cost. Dr. A. H e w a t k i n d l y c a l c u l a t e d the p e a k intensities for the a l u m i n a s a m p l e s u p p l i e d b y Dr. A n d r e s o n .
References
1) t-I. Maier-Leibnitz and T. Springer, Ann. Rev. Nucl. Sci. 16 (1966) 2O7. 2) E. Steichele and P. Arnold, Phys. Lett. 44A (1973) 165. 3) E. Steichele and P. Arnold, Proc. Neutron diffraction Conf., Petten (1975) p. 176. 4) C. G. Windsor, Proc. Neutron diffraction Conf., Petten (1975) p. 209. 5) C. G. Windsor and R. N. Sinclair, Acta. Cryst. A32 (1976) 395.
6) j . M . Carpenter, M.H. MueUer, R.A. Beyerlein, T . G . Worlton, J.D. Jorgensen, T.O. Brun, K. Skold, C.A. Pelizzari, S. W. Peterson, N. Watanabe, M. Kimura and J. E. Gunning, Proc. Neutron diffraction Conf., Petten (1975) p. 192. 7) A. W. Hewat, J. Phys. C 6 (1973) 2559. a) B. Buras and A. Holas, Report INR 745/II/PS, Institute of Nuclear Research, Warsaw (1966). 9) B. Buras, Nukleonika 8 (1963) 259. lo) j. M. Carpenter, Nucl. Instr. and Meth. 47 (1967) 179. 11) A. Holas, Nukleonika 13 (1968) 871. 12) A. Holas, J. Holas, E. Maliszewski and L. Sedlakova, Nucl. Instr. and Meth. 69 (1969) 173. 13) R.N. Sinclair, D. A. G. Johnson, J. C. Dore, J. H. Clarke and A. C. Wright, Nucl. Instr. and Meth. 117 (1974) 44.5. 14) D.H. Day and R.N. Sinclair, Nucl. Instr. and Meth. 72 (1969) 237. 15) D. A. G. Johnson, Harwell memorandum M2757 (1976). 16) j. H. Clarke, Harwell Report R8121 (1976). 17) A. W. Hewat and I. Bailey, Proc. Neutron diffraction Conf. Petten (1975) p. 250.
INSTRUMENTS
AND
METHODS
14o (I977)
241-250;
©
NORTH-HOLLAND
PUBLISHING
CO.
THE HARWELL BACKSCATTERING SPECTROMETER C . G . W I N D S O R , L . J . B U N C E , P . H . B O R C H E R D S * , I. C O L E t, M. F I T Z M A U R I C E , D. A. G. J O H N S O N a n d R . N . S I N C L A I R
Materials Physics Division, A.E.R.E., Harwell, Oxon, O X l l ORA, England Received 4 October 1976 N e u t r o n diffraction spectra in which b o t h high resolution (A Q/Q "" 0.003) a n d high intensity are m a i n t a i n e d up to scattering vectors as high as 30 A.-t (sin 0/2 = 2.5) have been obtained with the backscattering spectrometer (BSS) recently installed on the Harwell electron linac. T h e theory behind the spectrometer design is described, a n d it is s h o w n h o w the above resolution r e q u i r e m e n t leads to its basic features o f a 12 m incident flight path, a 2 m scattering flight p a t h a n d a scattering angle (20) acceptance f r o m 165 ° to 175 °. Examples o f the resolution, intensity a n d b a c k g r o u n d are given. It is s h o w n that the p r o b l e m o f frame overlap m a y be overcome by u s i n g an absorbing filter.
1. Introduction
The principle behind the back-scattering method in total neutron diffraction is illustrated by fig. 1. The time-of-flight method allows a range of scattering vectors to be recorded at a single scattering angle (20). As this angle is increased towards back scattering the cot OAO term in the resolution vanishes and a wide counter aperture AO may be employed. This method was proposed by Mayer-Leibnitz and Springer 1) and has been exploited with success using a reactor source and guide tube flight path by Steichele and Arnold 2' 3). Using the short duration neutron pulses produced by an electron or proton source, back scattering diffraction may be employed with comparatively short flight paths thus removing the need for guide tubes with their inherent transmission penalty at short wavelengths. Work at lower resolutions of order A Q / Q =0.01 at Harwell by Windsor 4) and Windsor and Sinclair s) and at Argonne by Carpenter et al. 6) has shown that a great advantage of such spectrometers when used with pulsed sources is their ability to maintain a resolution A Q/Q essentially independent of Q out to higher values of Q than are practicable to achieve with reactor spectrometers of comparable resolution. In the new backscattering spectrometer on the Harwell linac good diffraction intensities withA Q/Q ,,, ---0.003 are maintained to Q vectors as high as 30 ,~- 1. This enables neutron powder diffraction to enter a regime not previously accessible. Spectra at scattering vectors above about 20 ,~-1 are not easily measured * P e r m a n e n t address: D e p a r t m e n t o f Physics, B i r m i n g h a m University, England. t P e r m a n e n t address: T h e C a v e n d i s h Laboratory, Cambridge, England.
with X-rays because the X-rays scatter from the electron rather than the nuclear density and the electron form factor is becoming very small in this region. The extension of powder diffraction patterns to high scattering vectors is of great importance in structure refinement studies since the spatial resolution achieved depends largely on the maximum value of Q at which significant diffraction information is obtained. Profile refinement studies by Hewat 7) using reactor powder diffraction data, and by Windsor and Sinclair 5) using MODERATOR I
•
IA
L0
\C
/
COUNTER
BANK
I
I
B
I \
SAMPLE
2~
Fig. 1. T h e principle o f a backscattering spectrometer. T h e source o f the n e u t r o n pulse is a slab m o d e r a t o r o f dimensions .4 x A. T h e sample at distance Lo is also a slab o f dimensions a x a x c. Counters at a scattering angle 2 0 a n d distance L1 have a thickness c a n d cover a n area B x B.
242
c . G . WINDSOR et al.
linac data, suggest that precision in fitted structural and thermal parameters is largely determined by the higher Q region of the diffraction pattern. 2. General design considerations Applying the philosophy of Buras and Holas a) to a fast pulsed source (i.e. one whose pulse time is dominated by the neutron moderation time), we seek to optimise the diffraction line intensity at given resolution with respect to the main instrumental variables in the present case; the incident and scattered flight paths Lo and L1 and the scattering angle 20 (see fig. I). We assume as fixed instrumental parameters 1) a square moderator of side A ( ~ 100 mm), 2) a square sample of side a ( ~ 50 mm) (a < A) with thickness not greater than c ( ~ 2 5 mm), 3) a square detector array of area B 2 ( a < B ) (B ~ 300 mm), 4) counters of diameter c ( ~ 25 mm). Following Buras 9) we note that the total powder cross-section per unit cell may be written 2dSZtF 2 o"l = - sin E0,
(1)
Yo
where d~, Zt and F z are the d-spacing, multiplicity and structure factor of the lth order, and vo is the unit cell volume. The observed integrated intensity I t of the lth order depends further on the number of unit cells in the sample Ns, the incident neutron flux i(2), the wavelength spread A2 accepted by the counter bank and the fraction f of the Debye-Scherrer ring intercepted by the counter bank. I t = N~at" i(2). d2. f .
(2)
The incident neutron flux depends inversely as the incident flight path L o and on the time average flux at the moderator surface q~(2) A E 4(2) i(2)
-
-
-
(3)
4 nL2o The accepted wavelength spread A2 defends on the scattering angle spread accepted by the counter bank as a whole A2 = 2 cot0 AO = 2 cot0 (B/2L1).
(4)
The intercepted fraction / depends on the counter bank height B compared with the circumference of the Debye-Scherrer ring f -
B 2rcL 1 sin 20
(5)
Combining all factors we observe that the intensity of the lth order depends as sin 0, and inversely as the square of L o and L~ A2B 2 I, = 2d~ZtF2 Ns q~(2) sin 0. vo (4n) 2 L20L]
(6)
The resolution in d-spacing or Q vector (R = A Q/Q) depends on the root-mean-square errors in the total flight path ( L = Lo+L~), the total flight time T and the angular spread 60 accepted by a single counter in the counter bankS). R = [(--~)2 + ( ~ ) 2
+ cot2 06021'.
(7)
With counter and sample thickness c the r.m.s, spread in total flight path will be of order c so that 5L/L ~,, c/L.
(8)
The time spread of the neutron pulse we assume is determined by the neutron moderation time of order 72 /~s with 2 in A. This will correspond to a moderation distance C = 7h/m ~_28 mm so that the fractional error in the time spread may be written 6 T / T ~- C/L.
(9)
The ,50 of eq. (7) is much less than the angular spread from the complete bank of counters which we denoted by AO in eq. (4). This is because by placing the individual counters along the "time focussed" locus 1o-12), the contribution to the resolution from the complete bank can be made no worse than that of the counter at the least scattering angle. The angular spread 30 from such a single counter has three contributions in increasing order of importance 1) that arising from the spread in incident neutron directions caused by the finite moderator dimension, of order (~0mod = ½A/L o ; 2) that arising from the finite counter size assuming a point sample. With counter size c, this will be of order (~0. . . . t = ½c/L1 ; 3) that arising from the finite sample size a. This is clearly of order ½alL1 but is complicated because of the existence of focussing properties which can reduce this effective angular spread. This effect may be treated in the back scattering limit using the formula for the distance error given by eq. (13) of ref. 5. Converting this distance uncertainty into the equivalent angular uncertainty gives the result for backscattering a (Lo-3LI~ ~Osample ~-- ~ 1
~kL o - ~ . / / .
(10)
HARWELL BACKSCATTERING SPECTROMETER Thus the contribution has the intuitive value ½a/L~ in the limit of short scattered flight paths (L1 < Lo), but focussing effects cause the contribution to decrease as L 1 is increased and indeed to vanish when L~ = ½L o. The time-focussed sample geometry is then a plane perpendicular to the beam and parallel to the timefocussed counter geometry. Collecting all the contributions to the resolution together we have R =
[Ic2+2C x
+ cot20
+ a2
A[_~o+ ~ -1~ x
~)'/J
"
(11)
B
sin 20 "" - - , L1 i.e. B
2Ll
and
sin0"-" 1.
(12)
Thus the expression for the resolution [eq. (11)] becomes
/ c2 "t- C 2
B2 a I ~ 0
R = [i~o+L--~-2 + 4L-"--~l
×
+ a2 (Lo-3L')
It is now straightforward to maximise the intensity as given by eq. (6) for a given value of R by adjusting Lo and L1 numerically. We shall present such results for the present case later, however it is also possible to optimise the intensity analytically with certain reasonable approximations. In particular if L 1 < L o the angular uncertainty 30sample becomes simply ½a/L t and generally dominates over the counter and moderator contributions to 60. Eq. (13) then simplifies to [- C2 d- C 2 B 2 a21½ R = LiL--~L,) / 2 + - 16L~l --71,
The objective is now to maximise the order intensity It of eq. (6) with respect to the variables L o, L~ and 0, subject to the resolution constraint of eq. (11). It is immediately seen that the scattering angle should be as close as possible to back scattering (0 = ½n) since the intensity is then maximised (sin 0 ~ 1) and the resolution optimised (cot 0 ~ 0 ) . In practice a maximum scattering angle will be set by the requirement of shielding the counters from the incident beam. A practical design will have a shielding thickness about equal to the width of the counter bank (B). Thus the mean scattering angle will be given by assuming
cot0"--
243
1 + L--~l
l I'
( - L - o ~ )-JJ "
(13)
(14)
If L0 >>L1 it is then possible to eliminate L~ from eqs. (6) and (13) and maximise the intensity It with respect to the remaining variable L1 by differentiation. The result is
Li =/F'/qll("3Ba)l. YL 4R
(15)
J
The total flight path now determined from eq. (13) as L = ½~/6 ~/(c 2 +
cZ)/R.
(16)
The expressions may be used to calculate the optimised dimensions for given values of the other parameters. In the present case using the parameter values given above and assuming a resolution R = 0.003 we obtain the values for L, L1 and 20 given in the first column of table 1. A numerical optimisation using the full expression of eq. (13) for the resolution gives the values for L and L 1 quoted in the second column. The last column shows the actual dimensions of the spectrometer constructed. It is seen that its scattered flight path is somewhat larger than is calculated, showing that the spectrometer would be somewhat better matched with a larger incident flight path. Having found the optimum path lengths we may reconsider the design criterion of matching the three components of the resolution considered for example by Sinclair and Windsor (1976). In fact the distance, timing and angular contributions to R 2 given by the
TABLE1 Parameters of the spectrometer for resolution R = 0.003. Analytic optimisation Total flight path L (m) Scattered flight path LI (in) Scattering angle 20 (°)
15.32 1.47 173
Numericaloptimisation 14.52 1.52 (173)
Spectrometerconstructed 14.04 2.00 165-175
244
c . G . W I N D S O R et al.
terms in eq. (13) are 0.00177, 0.00199 and 0.00188 respectively and thus are quite closely matched although the timing error is giving the largest contribution to the resolution.
3. Constructional details Fig. 2 shows the general layout of the condensed matter cell and the backscattering spectrometer on the Harwell electron linac. The linac produces a pulse of electrons every 2600 ps. These pulses are normally multiplexed between nuclear physics experiments and the condensed-matter cell, so that one pulse 2 #s long is sent to the condensed-matter cell every 5200/~s. In the cell the electrons strike a natural uranium target producing a fast pulse of neutrons 13). Close to this target is a heterogeneously poisoned moderator, consisting of two slabs of polyethylene, 27 and 13 mm
ELECT-RO ' N BEAM 0 BOOSTER
I~L-ECTRON LINAC S W I T C ~ T N G ~ ........ MAGNET
M~ D ERATO ' 0
{:~ TAR GET
ARGET CELL
TO TSS.
TO
EVACUATED FLIGHT TUBE
FISSION CHAM BER
COUNTER OPENINGS
SAMPLE OPENING
EVACUATED SPECTROMETER BOX
TO B E A M
STOP
Fig. 2. General layout of backscattering spectrometer showing target and moderator and flight tubes to the three spectrometers (backscattering BSS; total-scattering TSS; and inelastic-rotor, IRS). The linac pulses once every 2600 ps, the switching magnet directs every second pulse to the condensed-matter-cell target.
thick, separated by a gadolinium foil, 0.025 m m thick. This foil prevents the build up of a Maxwellian distribution of thermal neutrons in the moderator, and so shortens the time-spread of the neutron pulse 14). Three evacuated flight tubes penetrate the concrete wall around the cell, and carry neutrons from the moderator to three spectrometers; the backscattering spectrometer, the total-scattering spectrometer x 3) and the inelastic-rotor spectrometer. The flight tube to the backscattering spectrometer is 300 mm in diameter, and is lined with collimating rings of borated resin converging to a 70 m m aperture in front of the spectrometer, as shown in figs. 3 and 4. At this point the neutron beam passes into the open for 50 m m before entering the spectrometer itself. Here there is a fission counter for monitoring the beam and there is provision for inserting absorbing filters. It is a defect of back (or forward) scattering geometries that air scattering must be avoided since the counter views the incident beam over a long length. The spectrometer is therefore capable of being evacuated and in practice a vacuum of order 10- 5 torr is achieved, sufficient to allow a liquid nitrogen temperature sample changer without added containment. The incident beam is carried to the sample by a 75 mm diameter pipe. The sample is in the centre of a 0.5 m diameter aperture passing through the spectrometer allowing ample space around the sample position. There are two counter banks each at a mean distance of 2 m from the sample and covering angles from back-scattering from 5 ° to 15° in the horizontal plane and from - 5 ° to + 5 ° in the vertical plane. Each bank is composed of 14 25 m m diameter, 300 mm long 3He counters at 5 atm pressure, The counters are positioned to lie on the time focussing curve given by eq. (12) of Windsor and SinclairS). In fact this curve is quite shallow with the chosen path lengths, having a maximum angle of ~ 10 ° from the plane perpendicular to the beam. Each bank has an area of order 0.1 m z and the total subtended solid angle is 0.056 rad 2. The counters lie in cadmium lined boxes outside the vacuum. The apertures in front of each bank are designed to allow visibility of a 50 mm wide by 50 m m high sample. All surfaces seen by the counters are clad with cadmium (shown by the heavy lines in figs. 3 and 4). The incident beam contains many unwanted fast neutrons. The beam is therefore collimated as far as possible before entering the spectrometer, then finally collimated at A in figs. 3 and 4. The straight through beam is contained without break in the vacuum by a 150 m m diameter cadmium lined pipe to a beam stop some 2 m away, outside the spectrometer room.
HARWELL
BACKSCATTERING
4. Data collection
245
SPECTROMETER
trum may be recorded if desired but in general spectra are normalised by recording the total monitor counts between selected flight times. Since the neutron pulse times are as low as 3 #s for a wavelength of 0.3 A a channel width of 2 #s is acceptable. Some 2600 storage locations are therefore required to store a complete spectrum of period 5200 ps. In practice for most diffraction experiments
Although the outputs from selected groups of counters may be counted separately if desired, the normal mode of operation is for all counters of both banks to be gated together and recorded as a single time-of-flight spectrum. Tests have shown that this mode produces no detectable shift or broadening of diffraction lines. The moderator time-of-flight spec-
\ /COU.TER /
"
\ '
\
SAMPLE
to BEAM STOP
Fig. 3. Plan view o f the backscattering spectrometer. T h e n e u t r o n s enter the evacuated b o x from left to right a n d are collimated by a slit at A. T h e counters lie o n the time-focussed curve. T h e dashed line s h o w s the outline o f the concrete b l o c k h o u s e enclosing the spectrometer.
INCIDENT NEUTRON F L I G H/~/T U B E
ROTARY S A M P L E E ~ L _ CHA R GE R -------------~
SAMPLE
\ t"
AREA
I
lm
Fig. 4. Elevation o f the backscattering spectrometer. Access to the sample area is t h r o u g h 0.5 m diameter m a n h o l e s above a n d below the sample. T h e sample changer rotates to p u t o n e o f five samples in the b e a m line. It can operate at liquid nitrogen temperatures.
246
c.G.
WINDSOR
)
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O
O
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o
ca
O
oo~'
leg
..
J
:)
,.(
o
+
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~:¢S
there is less interest in the first 1000/~s of the spectrum (scattering vectors above 44 A - l ) and so 2048 channels suffice covering the wave-vector range 8 . 5 / ~ - ~ to 44 A -x. The data is collected by an on-line computer, ( P D P l l / G T 4 4 system). This permits the collection of up to seven spectra, each of 2048 channels. The sample changer is moved under the control of the computer after a pre-set number of monitor counts have been recorded. The sample changer has up to five positions allowing simultaneous collection of data from five different specimens or more usually from a specimen, can, vanadium and background runs. This eliminates normalisation errors from incident flux variations with time constants long compared to the sample changer period of typically 20 rain. The system includes a visual display, on which the spectra may be viewed while the experiment is running. Between experiments the computer is available for data processing and a comprehensive set of programmes has been written for this purpose, so that the experimental data can be converted into cross-sections for display, using either the visual display unit, or a Versatek graph plotter, connected to the computer (e.g. fig. 5). The computer has sufficient power that it can calculate powder diffraction profiles for cubic structures. 5. Modes of operation
7o'~
(t~t] ~ .===:
The conventional way to analyse a time-of-flight spectrum is to convert it into an absolute cross-section by recording a set of four spectra corresponding to sample plus can (S), can alone (C), vanadium (V) and background (B). The vanadium is assumed to have a constant incoherent cross-section, a~ of 5.13 b. The cross-section is then given by
r;.~.
ZV9
dtr
--
001~ [£
dt~ <
• .
j,
f
iI ,oo.,
o-
i°
..e
il i
W~*? NI
$~.NnO0
? ;
ct al.
v,~.o
=
Nv I+/ms - Ic/m~ try --,
(17)
Ns Iv/mv - IB/mB 4 ~
vhere I is the spectral intensity, N the respective numbers of unit cells in the beam, and m the respective monitor counts. A more detailed treatment involving absorption and scattering corrections has been described by Clarke 15). However the above equation is only valid when all detected neutrons correspond to the same initial pulse or "frame". With the present linac period and spectrometer total flight path "frame overlap" occurs for wave-vectors less than 8.5 A - 1 and double frame overlap for wave vectors less than 4.3/~-1 and so on. There are two straightforward ways of overcoming the problem of frame overlap: by reducing the pulse
HARWELL
BACKSCATTERING
247
SPECTROMETER
and are largely eliminated in the spectrum with can subtraction and normalisation shown in the lower part of fig. 5. Using a gadolinium neutron filter 0.025 mm thick the neutrons collected in the primary frame suffer only moderate attenuation. However the attenuation of neutrons of wave-vector below 8/k-2 is increasingly large so that orders arriving during the second frame are almost completely eliminated. Similarly the contribution to the vanadium spectrum from overlapped frames is negligible so that the simple calibration formula of equation 17 may be used. Fig. 6 shows the calibrated spectrum from nickel powder at 77 K recorded in this way. This figure is on a highly expanded scale and covers only the marked area to the extreme left of fig. 5. There is no sign in the measured spectrum of overlapped peaks which would have been expected near the 777 peak at 2080 ps (222 peak from the second frame) and near the 955 peak at 2200 ps (200 peak from the third frame and clearly visible in fig. 5). The solid line in fig. 6 is the powder profile calculated using the methods described in refs. 4 and 5. The excellent fit shows that the problems of spectrum calibration and frame overlap can certainly be solved for high scattering vectors using the filter method. There are other more complicated ways of dealing with frame overlap: data taken with and without a filter may be simultaneously analysed to give the spectrum from both first and second phase. Alternatively the composite spectrum including frame overlapped peaks may be studied by profile analysis if
repetition frequency of the source, or by discarding reflections not corresponding to the primary frame by inserting a filter with high absorbtion at low wavevectors. A comparison of these two methods has been made and some results are shown in figs. 5 and 6. The first method giving an increased pulsed neutron period seems the obvious method but has the major disadvantage of decreasing the rate of data collection both for the spectrometer being used, and also for other spectrometers sharing the same moderator. To eliminate frame overlap completely requires a threefold increase in the period even for a material with as small a unit cell as nickel (3.5 A). A more common unit cell size such as that of alumina (5.5 A) requires a five fold period increase. It is an important advantage of pulsed sources operating near 50 Hz (such as the proposed spallation sources at the Rutherford Laboratory, U.K. and the Argonne National Laboratory, U.S.A.) that frame overlap is largely avoided for powder diffraction. In fig. 5 we show the time-of-flight spectrum from an ambient temperature nickel powder specimen of dimensions (50x 50x 2 mm 3) with the cell pulsed at intervals of 10 400 #s. The 4096 time channels span scattering vectors from 5 to 44 A-~. Only the first two orders, from 111 and 200 planes suffer frame overlap and these are dearly visible. The can scattering also shown is seen to be low and featureless except for the two small sharp peaks at 2600 and 7800 #s caused by fast neutrons from the adjacent nuclear physics booster. These peaks also occur in the sample spectrum
5
b~
~o
:9 t
o 2LO0
o
=
.
. I 2O
z
I
I
I
I
I
I
I
2200
2000 TIME
OF
FLIGHT
I
I
25
0 I X -1 ) I
I
1800
(pS)
Fig. 6. T h e high region o f a nickel powder s p e c t r u m t a k e n at 77 K o n a highly expanded scale. T h e scattering vector Q increases f r o m 19 to 26 A -1 f r o m left to right. Orders are denoted by the n o t a t i o n hk. l(m), where m is the n u m b e r o f simultaneously observed orders, except when these are written in full a n d separated by c o m m a s . A 0.04 m m gadolinium filter was inserted in the incident b e a m to eliminate frame-overlapped peaks a n d the normalised cross section calculated u s i n g eq. (17). T h e solid line is a profile analysis fit to the observed spectrum.
248
c.G. WINDSOR et al.
the incident neutron spectrum for all frames is known. These methods will be the subject of a forthcoming paper.
The resolution predicted by eq. (13) assumes the validity of a "moderation" time 72/~s/A. The correct form for the moderation time is
6. Resolution performance
T = [ ( 7 2 ) 2 + Z2] "} ,
The nickel powder spectrum of fig. 5 has been used to assess the resolution of the spectrometer. The full width at half height A T was measured for each resolved peak, and the resolution R calculated as A T/T. The results are shown in fig. 8. We also show the theoretical value of eq. (13), and compare the performance with that of other high-resolution spectrometers. The resolution is close to the theoretical value at low and at high scattering vectors, but is worse at intermediate values corresponding to neutrons whose pulse time has been broadened by the Maxwellian distribution. This effect can be moved to smaller scattering vectors, which are of less interest on th s spectrometer, by cooling the moderator. A liquid-nitrogen cooled moderator is being built.
where z is the electron pulse-length of 2 Ms. Thus we expect the resolution to deteriorate at a scattering vector of about 40 A - 1 , after which the resolution will be proportional to the scattering vector. 7. Intensity performance A standard cintered A120 3 (7.5 mm diameter by 13 mm long) was supplied by A. F. Andreson for the purpose of making a comparison of powder diffract•meters for the Neutron Diffraction Commission. The spectrum from this sample obtained in some 40 h is shown in fig. 7. No filter was used, but all the peaks arrowed belong to the primary frame. The spectrum covers scattering vectors above I0 A -1 beyond that
11
10
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Q
J
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e~ to
p.•
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50O
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.
-.
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•
ee
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•
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jt'~
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e
tt~
m It~ ~o
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I,
a•
,.IJ,
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TIME
J,, 4400
4200
OF FLIGHT
(~uS)
Fig. 7. The time-of-flight spectrum from the standard alumina specimen of volume 0.57 ml. No:filter was used. The lines show the calculated intensities of the various orders.
H A R W E L L B A C K S C A T T E R I N G SPECTROMETER
sinelX 0.5
1-0
I
I
(~,-I)
249
1.5 I
PANDAh =1'5/,o2e=90" o¢.=17'~, =13'
0.005
.
, . . °
• •
•
° •
•
°
0.003 ~
A
LCULTEDi0(1=1°~,2=2@ 10=~111° ,,....--
~ 0.0
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GARCHING
I
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10
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2o
o 11-1 ) Fig. 8. The points show the resolution of the spectrometer evaluated from the widths of the nickel powder spectrum shown in fig. 5, compared with its calculated resolution Ad/d = 0.0033. The two parabolas show the experimental resolution from a typical conventional spectrometer, PANDA, at Harwell and the calculated spectrum from a high-resolution spectrometer operating at short wavelengths. The dashed line shows the resolution of the Garching back-scattering spectrometer.
obtainable from conventional reactor high resolution powder diffractometers. The peak intensities shown by the lines were calculated from the structure given by |-Iewat and Bailey 17). The profile maintains a recognisable structure out to scattering vectors of order 25 A - ~. The time average intensity of incident neutrons at the sample position is calculated from vanadium spectral intensities to be given by an expresssion of order N(2) ~ 5000/2 neutrons/s cm 2 A . 8. Background performance
The instrumental background shown by the dashed line in fig. 5 is composed of several components. The background is largely time-independent, and although small when expressed per time channel 0.04cts/m (12#s gate) amounts to 105 cts/m when expressed as a time average background. Some experiments have been performed to investigate the origins of the background. Some 12 cts/m are present when the linac is switched ,aft and so represent the "electronic noise". For a bank of 28 counters this is a satisfactory level. A further 20cts/m are present when the electron beam is
switched only to the adjoining nuclear physics booster facility and so is quite external to the spectrometer operation. Switching on the spectrometer's electron beam but covering the inlet port of the spectrometer (marked A in fig. 3) with a 25 mm boron carbide slab adds a further 20 cts/m. The remaining 50 cts/m are added by allowing the full beam through the evacuated spectrometer. 9. Conclusions The spectrometer thus shows great promise for diffraction experiments at 0.3% resolution in the scattering vector range from 8.5 to 45 A-1. Its performance with liquid and amorphous samples at even higher scattering vectors has yet to be tested but the tests on instrumental background suggest that measurements beyond 100 A-1 should be possible. Single crystal samples might also be used to investigate weak magnetic and nuclear reflections of high order without the order contamination problems of conventional twoaxis diffractometers.
Many people besides the authors contributed to the design, construction and installation of the spectrom-
250
c . G . WINDSOR et al.
eter. It is a p l e a s u r e to t h a n k in p a r t i c u l a r the P r o j e c t Officer Dr. B. C. G. H a y w o o d , the P r o j e c t E n g i n e e r L. M a s o n a n d the m a i n c o n t r a c t o r s W e s t e r n Details Ltd. for d e l i v e r i n g the s p e c t r o m e t e r w i t h i n the agreed t i m e a n d w i t h i n the agreed cost. Dr. A. H e w a t k i n d l y c a l c u l a t e d the p e a k intensities for the a l u m i n a s a m p l e s u p p l i e d b y Dr. A n d r e s o n .
References
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