LIQUID DIFFRACTION ON THE SNS

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LIQUID DIFFRACTION ON THE SNS

W. Howells

To cite this version:

W. Howells. LIQUID DIFFRACTION ON THE SNS. Journal de Physique Colloques, 1984, 45 (C7),

pp.C7-81-C7-84. �10.1051/jphyscol:1984708�. �jpa-00224269�

Colloque

C7,

supplément au n09, Tome 45, septembre 1984 page C7-81

LIQUID DIFFRACTION ON THE SNS

W.S. Howells

Neutron Division, Rutherford Appleton Laboratory, Chilton, Didcot, Ozfordshire 0x11 OQX,

U.K.

Résumé

-

L'avantage principal d'une source pulsée sur un réacteur, dans le cas de la diffraction par des liquides, est le flux plus important à courtes longueurs d'onde (1 Q l x ) . Ainsi la gamme de Q utilisable peut aller jusqu'à 100

A-'

ou plus, et la grande énergie des neutrons utilisés diminue les cor- rections d'inélasticité (corrections de Placzek). L'utilisation des neutrons de grande énergie sera ainsi utile pour des expériences sur des systèmes hydrogénés ou très absorbants. Ces avantages seront exploités sur le Diffrac- tomètre Liquides et Amorphes (LAD) situé auprès de la source à spallation (SNS) du Laboratoire Rutherford Appleton.

Abstract

-

The main advantages of a pulsed neutron source over a steady state reactor for liquid diffraction is the increased flux available for short wavelengths ( A 6 18). Thus the available Q range can be increased to 1008-1 or more and the high energy neutrons reduce the corrections necessary to account for inelastic scattering (Placzek corrections).

This use of high energy neutrons will therefore be useful for experiments on hydrogenous or highly absorbing materials. These advantages will be exploited by the Liquids and Amorphous Diffractometer (LAD) on the Spallation Neutron Source (SNS) at the Rutherford Appleton Laboratory.

1

-

INTRODUCTION

Neutron diffraction as a technique for structural studies of liquid and amorphous materials is now well established on pulsed neutron sources and total scattering spectrometers are in operation in several countries

-

UK (Harwell), Japan (KENS), USA (Argonne and Los Alamos). The energy regions of particular interest to pulsed sources are the epithermal region E

>

900 meV (A 6 0.3A) and the ambient region 900 meV

>

E

>

200 meV (0.3

<

A 6 28). The epithermal region is not readily accessible on steady state reactors whilst in the ambient region the pulsed source has a substantial gain in neutron flux. These higher fluxes can then be exploited to enable conventional experiments to be carried out with a much higher statistical accuracy, at a higher rate of data collection or with much smaller samples (either in physical dimensions or scattering power). The main advantage of a pulsed source is that the moderators have a characteristic undermoderated spectrum, which in the epithermal region decays as 1/E. Such a moderator will enable a new range of experiments to be performed. In particular:

( i) at higher energies the absorption of most materials is lower and hence experiments with highly absorbing samples are possible.

( ii) to extract structural information from total scattering experiments, inelastic scattering corrections have to be made. These Placzek corrections are easier to make at higher neutron energies.

(iii) the new region opened up by the intense epithermal spectrum enables

higher spatial resolution to be achieved. Q-values greater than 1 0 0 ~ ~ ~ can be obtained, so interatomic distances can be measured to better that

0.018.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984708

C7-82 JOURNAL

DE

PHYSIQUE

2

-

INELASTIC OR PLACZEK CORRECTIONS

On pulsed sources, where the time-of-flight technique is used, the Placzek corrections are more complicated than the steady state reactor case and are dependent on the neutron wavelength spectrum and thus the type of moderator used.

The wavelength distribution of the neutron flux is given by a superposition of a Maxwellian distribution with a characteristic temperature T (or its equivalent wavelength AT) and a slowing down spectrum with lethargy exponent a which cuts off sharply at an energy around 5 kT.

A

joining function A(A) is often required which is unity for E

>

10 kT and effectively zero for E < 3 kT. The wavelength distribution is given by

where $x, and

gepi

are constants.

The Placzek corrections for time-of-flight diffraction have been discussed by several authors /1,2/ and the expression for the self scattering correction /1/

is

1 la kgT

+---

^{{cos 9}

+

4D sin2 912) 2 M Ee

where m = neutron mass, M = nuclear mass of sample, T = temperature of sample, 8

= scattering angle. Ee is the energy of a neutron with wavelength Xe, which corresponds to elastic scattering, and R the flight path ratio L ~ / ( L ~

+

^L~),

where L1 and L2 are the incident and scattered flight paths respectively.

The terms FI and 2F are related to the detector law F(K) and F(A) by 3 (in F(k))

kz

a.?F

FI =

,

2F =

--

a

(in k) F ak2

The terms fl and 2f are related to the neutron spectrcm $ ( A ) by

3 (ln $(A)) k2

a2+

f l =

,

2f =--

a

(in A)

+ ^ax2

The calculations of P elf for M=14 are shown in figure 1 for two types of moderator (300K and 77~3. The first point to note is that the corrections become smaller for lower angles, a$ expected from the sin28/2 variation of equation 3 . Secondly, the correction for the high Q region is approximately constant and this Q region corresponds to the epithermal part of the flux spectrum. The constant

measurements on hydrogeneous materials such as D20. This has been demonstrated by Soper and Silver /3/ who carried out measurements on D20/H20 mixtures.

Figure 1 Placzek corrections for atomic mass 14 (300K moderator,

---

77K moderator) 3

-

INSTRUMENTATION

The Liquids and Amorphous Diffractometer (LAD) /4/ on the Spallation Neutron Source (SNS) consists of detectors at 7 fixed angles between 5' and 150°, with flight paths LI = 10m and L2 = lm. For a wavelength range of 0.1 to 2A, the available Q range is 0.05 to 120~-l. The lowest

Q

is obtained at 5 O with a resolution

-

IO%, whereas the highest Q region is at 150° with resolution

-

^0.4%.

For the future, instruments are likely to change in layout as a result of experience gained so far. In particular :

( i) instruments using a LAD type layout are inefficient at small scattering angles due to Q resolution and geometric criteria. Optimum measurements for this Q-range are therefore obtained by the close packing of small detector elements into a forward scattering array.

( ii) as shown above, use of short wavelength neutrons and low scattering angles improves the inelastic corrections.

C7-84 JOURNAL

DE

PHYSIQUE

The s o l u t i o n i s t o c o n c e n t r a t e t h e d e t e c t o r s i n t o forward s c a t t e r i n g and extend t h e Q range a t a p a r t i c u l a r a n g l e by u s i n g h i g h e r e n e r g y n e u t r o n s (up t o 100 eV, s a y ) . T h i s method i s now f e a s i b l e due t o developments a t RAL of s c i n t i l l a t i o n d e t e c t o r s . The proposed SANDALS i n s t r u m e n t f o r SNS w i l l employ s u c h d e t e c t o r s and have a maximum s c a t t e r i n g a n g l e of 50".

REFERENCES

[ l ] POWLES, J. G., Molec Phys,

26

(1973) 1325

[ 2 ] SINCLAIR, R. N. and WRIGHT, A. C., Nucl I n s t r and Meth,

114

(1974) 451

[ 3 ] ^{SOPER, A.} K. and SILVER, R. N., Phys Rev L e t t ,

2

(1982) 471

[ 4 ] ^{HOWELLS, W.} S., R u t h e r f o r d L a b o r a t o r y Report, RL-80-017 (1980)