AN X-RAY ANOMALOUS SCATTERING STUDY OF LIQUID GeBr4

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AN X-RAY ANOMALOUS SCATTERING STUDY OF

LIQUID GeBr4

K. Ludwig, Jr., L. Wilson, W. Warburton, A. Bienenstock

To cite this version:

J O U R N A L DE PHYSIQUE

Colloque C8, supplbment au n012, Tome 46, d6cembre 1985 page C8-193

AN X-RAY ANOMALOUS SCATTERING STUDY OF LIQUID

G e B r 4

*+

K.F. Ludwig, ~r

.*,

L . wilson*, W.K. warburton** and A . Bienenstock

* ~ e ~ a r t m e n t o f A p p l i e d P h y s i c s , S t a n f o r d U n i v e r s i t y , S t a n f o r d U n i v e r s i t y , CA 94305, U . S .

_**

A.

I n s t i t u t e o f P h y s i c s , USC School o f Medicine, 4676 A d m i r a l t y Way, S u i t e 932, Marina d e l Rey, CA 90292, U.S.A.

' S t a n f o r d S y n c h r o t r o n R a d i a t i o n L a b o r a t o r y , SLAC B i n 69, Menlo Park, CA 94305, U.S.A.

Rksurnk - Des mesures de d i s p e r s i o n anomale des r a y o n s X o n t 6 t 6 r k a l i s k e s SUP

l e l i q u i d e m o l 6 c u l a i r e Ge B r 4 pour t e s t e r l e s l i m i t e s de l a t e c h n i q u e e t pour k t u d i e r l a s t r u c t u r e i n t e r m o l k c u l a i r e du li u i d e . Les nombres de c o o r d i n a t i o n e t l e s d i s t a n c e s s o n t o b t e n u s 2 5% e t 0,02

2

p r s s r e s p e c t i v e m e n t . La f o n c t i o n de d i s t r i b u t i o n p a r t i e l l e Br - B r (PDF), q u i prkdomine dans l a d i f f u s i o n t o t a l e , a k t 6 dkterminge mais l e s c o r r k l a t i o n s Ge - Br e t Ge

-

Ge n ' o n t pu B t r e skpa- r k e s c o r r e c t e m e n t . Les r 6 s u l t a t s s o n t c o m p a t i b l e s a v e c l ' i d k e d'un changement dans l'empilement m o l 6 c u l a i r e a u moment de l a f u s i o n .

A b s t r a c t

-

X-ray anomalous s c a t t e r i n g d a t a from t h e molecular l i q u i d GeBr were c o l l e c t e d and analyzed i n o r d e r t o i n v e s t i g a t e t h e a c c u r a c y of t h e 4 anomalous s c a t t e r i n g t e c h n i q u e and s t u d y t h e i n t e r m o l e c u l a r s t r u c t u r e o f t h e l i q u i d . The d i f f e r e n t i a l anomalous s c a t t e r i n g t e c h n i q u e gave c o o r d i n a t i o n d i s t a n c e s and numbers a c c u r a t e t o 0.02 A and 5% r e s p e c t i v e l y a s compared w i t h t h e known i n t r a m o l e c u l a r s t r u c t u r e . The Br-Br p a r t i a l d i s t r i b u t i o n f u n c t i o n (PDF), which dominates t h e t o t a l s c a t t e r i n g , was determined b u t t h e Ge-Br and Ge-Ge c o r r e l a t i o n s could n o t be w e l l s e p a r a t e d . The modeling

r e s u l t s a r e c o n s i s t e n t with a c h a n g e i n molecular packing Upon rueltlng-

I n t r o d u c t i o n :

With t h e advent of s y n c h r o t r o n r a d i a t i o n , x-ray anomalous s c a t t e r i n g (AS) h a s become an i n c r e a s i n g l y popular t o o l f o r t h e s t r u c t u r a l s t u d y of multicomponent amorphous m a t e r i a l s . Due t o t h e r e l a t i v e l y modest s i z e of t h e AS e f f e c t , t h e i n d i v i d u a l p a r t i a l d i s t r i b u t i o n f u n c t i o n s (PDFfs) d e r i v e d have been s u b j e c t t o l a r g e e r r o r s . However, e x p e r i m e n t e r s have e n a b l e t o o b t a i n a p p a r e n t l y r e l i a b l e " d i f f e r e n t i a l d i s t r i b u t i o n functionsff1' (DDFfs) which show t h e environment around e a c h i n d i v i d u a l s p e c i e s . These a r e based on t h e change i n s c a t t e r i n g with photon e n e r g y n e a r a s i n g l e a b s o r p t i o n edge. We t h e r e f o r e f e l t it would be u s e f u l t o perform a t e s t o f t h e t e c h n i q u e by s t u d y i n g a d i s o r d e r e d m a t e r i a l with a p a r t i a l l y known s t r u c t u r e . L i q u i d GeBr,, was an obvious c h o i c e : i t c o n s i s t s of simple GeBr

4

t e t r a h e d r a of known s i z e , m e l t s a t a low t e m p e r a t u r e ( 2 6 ' ~ ) and both t h e Ge and Br edge e n e r g i e s a r e a c c e s s i b l e a t a s y n c h r o t r o n s o u r c e .

Experimental Method:

I n o r d e r t o i n t e r p r e t AS d a t a q u a n t i t a t i v e l y , t h e AS f a c t o r s must be determined a c c u r a t e l y . Near a b s o r p t i o n e d g e s , chemical e f f e c t s s i g n i f i c a n t l q change f f

(E)

and f f t ( E ) from t h e free-atom v a l u e s c a l c u l a t e d by Cromer and Liberman

.

T h e r e f o r e , we measured t h e x-ray a b s o r p t i o n c o e f f i c i e n t o v e r a n e x t e n s i v e energy range n e a r t h e K-absorption edges of l i q u i d GeBr,, t o determine f"(E). We t h e used t h e Kramers-Kronig d i s p e r s i o n r e l a t i o n w i t h a r e l a t i v i s t i c c o r r e c t i o n ' t o c a l c u l a t e f V ( E ) . S i n c e t h e Ce and Br 1 s wavefunctions a r e much s m a l l e r t h a n t h e photon

C8- 194 JOURNAL DE PHYSIQUE

wavelength i n t h e energy range of i n t e r e s t , we assumed t h a t t h e a n g u l a r dependence o f t h e AS f a c t o r s was n e g l i g i b l e . The same a b s o r p t i o n scan t h a t was used f o r t h e energy c a l i b r a t i o n of t h e s c a t t e r i n g experiments was a l s o used f o r t h e Kramers-Kronig t r a n s f o r m a t i o n s o t h a t t h e d e r i v e d s e t of f 1 v a l u e s had t h e proper energy c a l i b r a t i o n . I n a d d i t i o n , s i n c e t h e same monochromater and slits were used f o r both t h e s c a t t e r i n g and a b s o r p t i o n measurements, t h e energy r e s o l u t i o n of t h e c a l c u l a t e d f l ( E ) w a s t h e same a s t h e energy r e s o l u t i o n of t h e s c a t t e r i n g experiment.

S c a t t e r i n g d a t a were c o l l e c t e d on beam l i n e IV-3 a t t h e S t a n f o r d Synchrotron R a d i a t i o n Laboratory during d e d i c a t e d beamtime. A h i g h p u r i t y Ge d e t e c t o r from ORTEC was used t o d e t e c t t h e s c a t t e r e d photons. It had s u f f i c i e n t energy r e s o l u t i o n

(approximately 320 eV) t o d i s c r i m i n a t e a g a i n s t t h e K-alpha f l u o r e s c e n c e e x c i t e d by t h e i n c i d e n t photons. We measured t h e s c a t t e r i n g a t f o u r e n e r g i e s below each edge t o check t h e c o n s i s t e n c y of t h e d a t a . The sample was held a t a temperature of 3351 OC.

Data Analysis:

The s c a t t e r i n g d a t a a t eachgenergy was c o r r e c t e d and normalized t o a per-atom v a l u e u s i n g t h e method of Fuoss

.

Each d a t a s e t was t h e n F o u r i e r transformed t o y i e l d a r a d i a l d i s t r i b u t i o n f u n c t i o n (RDF). A l l RDF1s were of good q u a l i t y a s judged by agreement with known i n t r a m o l e c u l a r s t r u c t u r e . A t y p i c a l curve is p r e s e n t e d i n f i g . 1. The two peaks a t 2.30 A and 3.79 A c o n t a i n Ge-Br and Br-Br c o n t r i b u t i o n s r e s p e c t i v e l y . The f i r s t peak corresponds t o t h e f o u r i n t r a m o l e c u l a r bromine atoms about each germanium and a l l RDF's gave experimental c o o r d i n a t i o n numbers of 3.92-4.01. The known v a l u e of t h e Ge-Br c o o r d i n a t i o n d i s t a n c e i s 2.29 A

, i n e x c e l l e n t agreement with t h e observed bond l e n g t h . The second peak c o n t a i n s both i n t r a - and i n t e r m o l e c u l a r Br-Br c o r r e l a t i o n s and a g r e e s with t h e known molecular s t r u c t u r e .

A h i g h e r l e v e l o f complexity and e r r o r s e n s i t i v i t y was involved i n e v a l u a t i n g t h e DDF's. A DDF i s t h e transform of t h e normalized d i f f e r e n c e i n s c a t t e r i n g a t two d i f f e r e n t photon e n e r g i e s below an atom's a b s o r p t i o n edge. It is s e n s i t i v e only t o t h e environment of t h a t p a r t i c u l a r atom. A t each edge, s e v e r a l DDFfs were c a l c u l a t e d using t h e d a t a a t d i f f e r e n t e n e r g i e s t o a s s u r e c o n s i s t e n c y . A t y p i c a l Ge-edge DDF i s d i s p l a y e d i n f i g . 1. The Br-Br peak observed i n t h e RDF i s no l o n g e r p r e s e n t . A l l Ge-edge DDF1s gave Ge-Br c o o r d i n a t i o n numbers of 3.96-4.00 and a c o s r d i n a t i o n d i s t a n c e of 2.30 A , i n good agreement with t h e known values. A t y p i c a l Br-edge DDF i s a l s o shown i n f i g . 1. The Br-edge DDFts a l l had i n t r a m o l e c u l a r peak p o s i t i o n s and c o o r d i n a t i o n numbers a c c u r a t e t o t 0 . 0 2 A and 5% r e s p e c t i v e l y .

Fig.1: RDF, Ge-edge DDF and Br-edge DDF. Fig. 2: Ge-Ge, Ge-Br and Br-Br PDF's. (The d i s t r i b u t i o n s a r e weighted by

For a b i n a r y m a t e r i a l l i k e GeBr4, only t h r e e d a t a s e t s a t d i f f e r e n t e n e r g i e s a r e needed t o determine t h e t h r e e s p e c i e s - s p e c i f i c P D F ' S ~ s o t h a t s e v e r a l

combinations were p o s s i b l e with t h e d a t a s e t s we measured. I d e a l l y t h e d e r i v e d PDF's should be independent of t h e p a r t i c u l a r combination of e n e r g i e s used, but i n p r a c t i c e t h e poor c o n d i t i o n i n g of t h e weighting m a t r i x and s m a l l e r r o r s i n t h e d a t a s e t s can l e a d t o s i g n i f i c a n t d i f f e r e n c e s between r e s u l t s o b t a i n e d with d i f f e r e n t combinations. We found t h a t t h e d e r i v e d Br-Br PDF ( s e e f i g . 2) i s f a i r l y independent of t h e p a r t i c u l a r s e t of e n e r g i e s used and appears q u i t e reasonable. The low-r r e g i o n of t h e Br-Br PDF i s e s s e n t i a l l y f l a t up t o t h e Br-Br peak a t 3.79 A

and t h e Ge-Br peak has completely disappeared. The Ge-Ge and Ge-Br PDFfs, though, vary s i g n i f i c a n t l y w i t h t h e energy d a t a s e t s used, e x h i b i t unphysical s t r u c t u r e a t low-r and show n e g a t i v e c o o r d i n a t i o n peaks. The accuracy of t h e PDF's is q u a l i t a t i v e l y understandable given t h e i r r e l a t i v e importance i n t h e t o t a l s c a t t e r i n g from t h e m a t e r i a l (roughly Br-Br: 578, Ge-Br: 29% and Ge-Ge 14%).

I n s p e c t i o n of t h e Ge-Br and Ge-Ge PDFfs i n f i g . 2 r e v e a l s an i n t e r e s t i n g behavior. The two PDFrs have many f e a t u r e s which m i r r o r each o t h e r . T h i s i s a common r e s u l t when s e p a r a t i n g PDF's using an i l l - c o n d i t i o n e d matrix. The "mirrortt behavior a s w e l l a s t h e r e l a t i v e accuracy of t h e PDF7s can be q u a n t i t a t i v e l y understood using s i n g u l a r value d e c o m p o s i t i o ~ f g V D ) , a s t a n d a r d mathematical method of analyzing i l l - c o n d i t i o n e d l i n e a r problems

'

.

The mathematical problem i s t o f i n d t h e v e c t o r of p a r t i a l s t r u c t u r e f a c t o r s (PSF's) s g i v e n t h e s c a t t e r i n g weighting m a t r i x W and t h e d a t a v e c t o r y:

I n g e n e r a l t h e m a t r i x W can be d i a g o n a l i z e d using a Householder transformation: ( s i g m a ( 1 ) 0 0

1

U W V = ( 0 sigma ( 2 ) 0 ) ( 0 0 s i w a ( 3 ) )

where U and V a r e orthogonal m a t r i c e s and t h e s i g m a ( i ) a r e known a s t h e s i n g u l a r v a l u e s of t h e m a t r i x W. The s o l u t i o n of t h e o r i g i n a l problem can t h e r e f o r e be w r i t t e n a s :

where t h e ui and vi a r e t h e orthonormal column v e c t o r s o f U and V. Thus t h e + v e c t o r of PSF's a t a given k-space p o i n t can be expressed a s a sum of t h r e e orthonormal v e c t o r s which span t h e space. For an experimental e r r o r dy, t h e e r r o r i n t h e r e s u l t i n g v e c t o r s w i l l be:

I n p r a c t i c e one of t h e s i g m a ( i ) w i l l o f t e n be much s m a l l e r t h a n t h e o t h e r s f o r an i l l - c o n d i t i o n e d problem. For t h e weighting m a t r i c e s i n t h i s work sigma( 1 )=2000, sigma(2)=200 and sigma(3)=4. Thus t h e experimental r e s u l t s a r e much more s e n s i t i v e t o d a t a e r r o r s i n t h e d i r e c t i o n o f

u

t h a n any o t h e r and, on a v e r a g e , most of t h e e r r o r i n t h e r e s u l t i n g s v e c t o r w i l l

8e

o f t h e form eg. For t h i s experiment:

JOURNAL

DE

PHYSIQUE

S t r u c t u r a l Models:

U n f o r t u n a t e l y AS e x p e r i m e n t s y i e l d only t h e r a d i a l l y averaged PDF's; they do n o t show t h e a c t u a l three-dimensional s t r u c t u r e of t h e l i q u i d . We t h e r e f o r e t u r n e d t o modeling t o l e a r n more about t h e packing of t h e molecules i n t h e l i q u i d . The i n t r a m o l e c u l a r Br-Br s e p a r a t i o n (3.76 A ) i s c l o s e t o t h e bromine van d e r Waals diameter ( 3 . 8 A ) . T h e r e f o r e a simple model would c o n s i s t o f c l o s e packed bromine atoms with germanium atoms occupying one e i g h t h of t h e t e t r a h e d r a l v o i d s t o form molecules. The two c r y s t a l s t r u c t u r e s common t o t h e group I V t e t r a h a l i d e s do indeed c o n s i s t of d i s t o r t e d c l o s e packings of h a l i d e s . There i s a cubic l a t t i c e i n which t h e h a l i d e s form a d i s t o r t e d face-centered cubic s t r u c t u r e (e.g. Ge14) and a monoclinic l a t t i c e i n which t h e h a l i d e s a r e e s s e n t i a l l y hexagonal c l o s e packed (e.g. SnBr4). We found no p r e v i o u s l y r e p o r t e d c r y s t a l s t r u c t u r e of GeBry, but performed powder d i f f r a c t i o n and confirmed t h a t GeBr4 c r y s t a l l i z e s i n t h e cubic s t r u c t u r e ,

The two models w e t e s t e d were o b t a i n e d by expanding each c r y s t a l s t r u c t u r e t o t h e known d e n s i t y of l i q u i d GeBr4, r e l a x i n g t h e bromine atoms back toward t h e c e n t r a l germanium t o t h e known i n t r a m o l e c u l a r d i s t a n c e , and adding a g a u s s i a n r a d i a l d i s o r d e r which i n c r e a s e s l i n e a r l y w i t h i n c r e a s i n g d i s t a n c e . The r a t e of i n c r e a s e of d i s o r d e r w i t h d i s t a n c e was t h e only a d j u s t a b l e parameter. The model based upon t h e a c t u a l c u b i c c r y s t a l s t r u c t u r e of s o l i d GeBr4 d i s a g r e e d s i g n i f i c a n t l y with t h e d a t a . However, t h e monoclinic model i s promising. Fig. 4 c o n t a i n s a comparison of t h e model Br-Br PDF w i t h t h e experimental Br-Br PDF

.

The b a s i c s i n u s o i d a l shape of t h e model PDF a g r e e s w i t h t h e experimental Br-Br PDF

.

The d i s c r e p a n c i e s might be due t o a more complicated i n c r e a s e of d i s o r d e r with d i s t a n c e t h a n t h e simple l i n e a r one assumed i n t h e model. A comparison between t h e experimental

Ge-edge DDF and t h e model's p r e d i c t i o n a p p e a r s i n f i g . 3. The agreement i s good. Thus GeBr4 a p p e a r s t o undergo a s i g n i f i c a n t change i n l o c a l s t r u c t u r e upon m e l t i n g , with t h e l i q u i d more c l o s e l y resembling t h e d i s t o r t e d hexagonal c l o s e packing s t r u c t u r e of c r y s t a l l i n e SnBr4 r a t h e r than t h e d i s t o r t e d FCC s t r u c t u r e of s o l i d GeBr

.

4 ~ n c o n c l u s i o n , we have found t h e d i f f e r e n t i a l s c a t t e r i n g technique t o be q u i t e a c c u r a t e ( 0 . 0 2 A and 5% c o o r d i n a t i o n number) a s t e s t e d by t h e known molecular s t r u c t u r e of GeBr4. We obtained a r e l i a b l e Br-Br PDF b u t t h e Ge-Ge and Ge-Br PDFfs could n o t be uniquely s e p a r a t e d . We've found t h a t t h e SVD a n a l y s i s can be used t o understand t h e way i n which experimental e r r o r s a f f e c t t h e r e s u l t i n g PDFVs.

T h e o r e t i c a l d i s t r i b u t i o n f u n c t i o n s from were compared with t h e experimental r e s u l t s and i n d i c a t e a p o s s i b l e change i n t h e molecular packing of GeBrll upon melting. We w i l l d i s c u s s t h e s e p o i n t s more f u l l y i n a f u t u r e p u b l i c a t i o n . _----

----

_-

0 0 100 0 F 0 075 0 050 0 025 0 000 -0 025 -0 050 -0 075 -0 lGO 0 125 ----A -.-----A U 0 2 5 7 0 I 5 I0 (1 1 2 1 15 3 r ( A )

_

__-l-.-l-...-.._

_

___

p 0. 150 . o experiment \ F 0. 125 . 0.100 .

1

0. 075 . 0.050 . model 0. 025 . 0.000 - -0.025 . -0. 050 - -1 _ _ 1 I L _ _ - 0. 0 2. 5 5. 0 7 . 5 10. 0 12.5 ... . -. - - r ( A )

Fig. 4: Br-Br PDF's from experiment and monoclinic model.

This work was performed at and supported by the Stanford Synchrotron Radiation Laboratory (SSRL) which is supported by the Department of Energy, Office of Basic Energy Sciences and the National Institutes of Health, Biotechnology Resource Program.

References:

/I/ Fuoss, P.H., Eisenberger, P., Warburton, W.K. and Bienenstock, A., Phys. Rev. Lett. 46, (1981) 1537.

/2/ Shevchik, N.J., Phil. Mag. 35, (1977) 805,1289.

/3/ Lowden, L.J. and Chandler, D.,

J.

Chem. Phys.

59,

(1974) 6587. /4/ Cromer, D.T. and Liberman, D., J. Chem. Phys.

53,

(1970) 1891. /5/ Jensen, M.S., Phys. Lett. 74A, (1979) 41.

/6/ Fuoss, P.H., Ph.D. Thesis (Stanford University), Stanford Synchrotron Radiation Laboratory Report 80/06.

/7/ Keating, D.T., J. Appl. Phys. 34, (1963) 923.

/8/

Forsythe, Malcolm and Moler, Computer Methods for Mathematical Computation, Prentice-Hall Inc. (1977).