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Submitted on 1 Jan 1980
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STATIC STRUCTURE FACTORS AT SMALL
MOMENTUM TRANSFERS FOR SOME LIQUID
METALS BY NEUTRON DIFFRACTION
U. Dahlborg, L. Olsson
To cite this version:
JOURNAL DE PHYSIQUE CoZZoque C8, s u p p l h e n t au n o 8 , Tome 41, a & t 1980, page
C8-214
S T A T I C STRUCTURE FACTORS A T SMALL MOMENTUM TRANSFERS FOR SOME L I Q U I D METALS
BY NEUTRON D I F F R A C T I O N
U. Dahlborg and L.G. Olsson
Department o f R e a c t o r p h y s i c s , Royal I n s t i t u t e o f TechnoZogy, 5-10044 StockhoZm, Sweden
I n r e c e n t y e a r s t h e r e has been a renewed i n t e r e s t in t h e d e t e r m i n a t i o n of t h e s t a - t i c s t r u c t u r e f a c t o r S(Q1 f o r liquids. A detailed k n o w l e d g e o f t h i s quantity i s n e - c e s s a r y in o r d e r t o o b t a i n an effective i n t e r - p a r t i c l e p o t e n t i a l $(r). S e v e r a l dif- ferent s c h e m e s e x i s t i n o r d e r to e x t r a c t t h e potential f r o m the measured data. O f p a r t i c u l a r i n t e r e s t today i s the inversion o f t h e WCA t h e o r y 1 and the u s e o f a m o d i -
2
f i e d h y p e r n e t t e d - c h a i n equation
.
T h e s m a l l Q r e g i o n is of p a r t i c u l a r i m p o r - t a n c e in the d e t e r m i n a t i o n o f a $(r) f r o m S(Q). T h e r e f o r e a c c u r a t e measurements on liquid lead, bismuth and aluminium f o r 0.2<4<1.5
A-'
w e r e undertaken. I n t h i s r e - port s o m e r e s u l t s on lead and aluminium a r e briefly discussed.Experimental d e t a i l s
T h e neutron diffraction measurements w e r e performed a t t h e R 2 r e a c t o r in S t u d s v i k , Sweden. T h e wavelength o f t h e i n c i d e n t n e w t r o n s w a s 1.21 8 . T h e s m a l l e s t
Q
v a l u e (Q= m o m e n t u m t r a n s f e r in the s c a t t e r i n g p r o - cess) a t w h i c h r e l i a b l e corrected d a t a could be obtained w a s 0.19 A-'. T h e Q r e - s o l u t i o n w a s 0.15 A-'. I t i s e x t r e m e l y important t o keep t h e c o n - tribution f r o m multiple s c a t t e r i n g e v e n t s in t h e s a m p l e a s s m a l l a s possible. T h e r e - f o r e s p e c i a l s a m p l e a r r a n g e m e n t s w e r e made. F o r lead a s a m p l e c o n t a i n e r m a d e up o f ho- r i z o n t a l aluminium t u b e s with i n n e r d i a - m e t e r
4
m m and w a l l t h i c k n e s s 0.5 m m w a s used. Gadolinium f o i l s w e r e inserted b e t - w e e n t h e t u b e s t h u s preventing m u l t i p l es c a t t e r i n g from o n e t u b e to another. T h e normal of t h e plane o f the tubes m a d e 60' a n g l e t o w a r d s t h e neutron beam direction. F o r the measurements on aluminium tantalum c y l i n d e r s with i n n e r d i a m e t e r 19.8 m m and w a l l thickness 0.9 m m w e r e used. T h e n e u - tron irradiated height of a c y l i n d e r w a s 7.0 m m and t h e s a m p l e a r r a n g e m e n t c o n s i s - ted o f f o u r cyli'nders placed a b o v e each other. I n o r d e r t o d e c r e a s e the s c a t t e r i n g from t h e bottom o f each c y l i n d e r and a l s o m u l t i p l e scattering between c y l i n d e r s s p a - c e r s of Lormn nitride w p r e inserted in between.
Both s a m p l e a r r a n g e m e n t s w e r e heated in a furnace w h i c h had no p a r t s in t h e neutron beam. T h e temperature w a s controlled to an accuracy of
*
.2'D a t a treatment
T h e procedure o f correcting measured d i f - fraction patterns f o r e x p e r i m e n t a l effects
3 has been described in d e t a i l e l s e w h e r e
.
H e r e w e only discuss the s p e c i a l c a r e w h i c h has to be taken w h e n looking a t S(Q) a t s m a l l 0 .1 ) Correction f o r multiple scattering.
Usually t h e i n t ~ n s i t y o f multiply s c a t t e - red neutrons is assumed isotropic. T h e a s - s u m p t i o n w a s checked by a calculation using t h e Monte C a r l o simulation program d e v e l o - ped by copley4. T h e m o d e l o f Ailawadi et a1.5 w a s used f o r the scattering function S(Q,El. T h e calculated multiple s c a t t e r i n g w a s compared t o the o n e obtained by using
6
r e c e n t experimental r e s u l t s on S(Q,E)
