RADIAL DISTRIBUTION FUNCTION STUDIES OF GLASSY GERMANIUM-SILVER-CHALCOGEN ALLOYS

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RADIAL DISTRIBUTION FUNCTION STUDIES OF GLASSY GERMANIUM-SILVER-CHALCOGEN

ALLOYS

L. Bourne, S. Rowland, A. Bienenstock

To cite this version:

L. Bourne, S. Rowland, A. Bienenstock. RADIAL DISTRIBUTION FUNCTION STUDIES OF

GLASSY GERMANIUM-SILVER-CHALCOGEN ALLOYS. Journal de Physique Colloques, 1981, 42

(C4), pp.C4-951-C4-954. �10.1051/jphyscol:19814208�. �jpa-00220836�

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Colloque suppl6ment nu n070, Tome octobre 7981 page C4-951

R A D I A L DISTRIBUTION FUNCTION S T U D I E S OF G L A S S Y GERMANIUM-SILVER- CHALCOGEN A L L O Y S

a L.C. B o u r n e , S.C. Rowland and A . B i e n e n s t o c k

Ccpartnent o f Physics, Andrews University, Berrien Springs Michigan 49104, b.S.A.

*

Pepartment o f 1.lateriaZs Science, Stunford U n i v e r s i t y , S t a n f ~ r d , California S4.305, 1l.S.A.

A b s t r a c t . - X - r a y d i f f r a c t i o n 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 ( r d f ) s t u d i e s h a v e b e e n p e r f o r m e d o n 1 5 d i f f e r e n t a l l o y s i n t h e g l a s s y Ge Ag ,X s y s t e m s , w h e r e X i s S o r S e . A s s u m p t i o n o f f o u r f o l d

~ e ~ c o g r a i n a x i o n and no S-S b o n d s i n t h e s u l f u r a l l o y s l e a d s t o d i r e c t d e t e r m i n a t i o n o f Ag c o o r d i n a t i o n numbers i n t h e r a n g e 3 t o 4 . The f u r t h e r a s s u m p t i o n t h a t t h e S and Se m a t e r i a l s h a v e t h e same n e a r n e i g h b o r c o o r d i n a t i o n numbers l e a d s t o t h e d e t e r m i n a t i o n o f c h a l c o g e n c o o r d i n a t i o n numbers w h i c h i n c r e a s e w i t h y t o a p p r o x i m a t e l y 4 . The r e s u l t i n g c o o r d i n a t i o n numbers a r e , o n t h e a v c r a g e , c o n s i s t e n t w i t h t h e 8-6 r u l e . The Ag-X d i s t a n c e s a r e c l o s e r t o t h e c o v a l e n t

t h a n t o t h e i o n i c d i s t a n c e s a n d a r e c o n s i s t e n t w i t h t h o s e i n t h e c r y s t a l l i n e compound Ag GeX

8 6 '

I n t r o d u c t i o n . - 'Je r e p o r t h e r e t h e r e s u l t s o f x - r a y d i f f r a c t i o n 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 ( r d f ) s t u d i e s o f 15 a l l o y s i n t h e g l a s s y Ge Ag,X,-x- s y s t e m s , w h e r e X i s S o r S e . To o u r k n o w l e d g e , t h i s work c o n s t i t u t e s t h g f i r 5 t r Z p u r t o f g l a s s e s i n t h e s y s t e m c o n s t a i n i n g S e . T h e s e s y s t e m s were c h o s e n f o r s t r u c t u r a l s t u d i e s f o r a number o f r e a s o n s . The f i r s t f o l l o w s from t h e work o f L i a n g e t a l . ( 1 ) and H u n t e r e t a l . ( 2 ) on t h e Cu-As,Se s y s t e m i n w h i c h i t was f o u n d t h a t m o n o v a l e n t Cu i s a f o u r f o l d c o o r d i n a t e d n s t w o r k f o r m e r , r a t h e r t h a n b e i n g a n e t w o r k 3

m o d i f i e r , s o t h a t t h e a v e r a g e c h a l c o g e n c o o r d i n a t i o n number i n c r e a s e s w i t h i n c r e a s i n g Cu c o n c e n t r a t i o n . I n n e t w o r k m o d i f i c a t i o n , t h e o p p o s i t e would t a k e p l a c e . kle w e r e a n x i o u s , t h e r e f v r e i t o s e e w h e t h e r t h i s was a more g e n e r a l phenomenon

w i t h t h e a d d i t i o n o f n o b l e m e t a l s t o amorphous s c m i c o n d u c t o r s .

I n a d d i t i o n , some o f t h e g l a s s e s i n t h e s y s t e m s s t u d i e d h e r e had t h e same c o m p o s i t i o n s a s t h o s e w h i c h must b e o b t a i n e d i n t h e p h o t o d o p i n g o f GeS2 and GeSeZ by Ag. C o n s e q u e n t l y , t h c s e r d f s t u d i e s a r e t h e f i r s t o f a s e r i e s o f s t r u c t u r a l s t u d i e s aimed a t u n d e r s t a n d i n g t h e p h o t o d o p i n g p r o c e s s . S i m i l a r l y , we h o p e t h a t t h e s e s t r u c t u r a l s t u d i e s w i l l y i e l d more u n d e r s t a n d i n g of t h c h i g h d i f f u s i o n r a t e s o f t h e n o b l e m e t a l s i n amorphous s e m i c o n d u c t o r s a n d C:le l a r g e c o n d u c t i v i t y i n c r e a s e s w h i c h t h e i r a d d i t i o n s c a u s e . F i n a l l y , t h e s e p a r t i c u l a r s y s t e m s h a v e l a r g e g l a s s - f o r m i n g r e g i o n s and Ag h a s a s u f f i c i e n t l y l a r g e a t o m i c number s o t h a t i t i s p o s s i b l e t o s e e t r e n d s w i t h c o m p o s i t i o n .

E x p e r i m e n t a l . - The g l a s s y s a m p l e s u s e d i n t h i s s t u d y w e r e p r e p a r e d t h r o u g h q u e n c h e s f r o m t h e m e l t , and t t ~ e i r d e n s i t i e s d e t e r m i n e d , i n t h e mqnners d e s c r i b e d by Rowland e t a l . ( 3 ) I n t h e s u l f u r s y s t e m , g l a s s e s were c h o s e n from t h e g l a s s - f o r m i n g r e g i o n d e f i n e d by F e l t z and Thieme ( 4 ) . To o u r k n o w l e d g e , t h i s r e g i o n i-n t h e s e l e n i u m s y s t e m h a s n o t y e t b e e n d e t e r m i n e d , s o t h a t t h i s work s e r v e s t o i n d i c a t e some p o r t i o n s o f i t .

Two d i f f e r e n t x - r a y d i f f r a c t o m e t e r s y s t e m s w e r e u s e d f o r a c q u i s i t i o n o f t h e C n t e n s i t y d a t a . One was a P i c k e r s y s t e m p r e v i o u s l y d e s c r i b e d by u s . The

o t h e r was a N o r e l c o s y s t e r p w i t h a d d i t i o n a l s l i t s p r o v i d e d t o a c h i e v e c o m p l e t e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814208

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C4-952 JOURNAL DE PHYSIQUE

e l i m i n a t i o n o f XB r a d i a t i o n . One s a m p l e , Ge Ag oSe 5 2 was r u n w i t h b o t h s y s t e m s . The f i r s t n e i g h b o r p e a k a r e a was 4 2 7 0 9 0 f r o r h 2 @ h e ' 2 a t a ' o n t h e P i c k e r s y s t e m

and 4 2 3 0 5 0 o n t h e N o r e l c o s y s t e m . Hcnce, we d o n o t b e l i e v e t h a t t h e r e a r e s i g n i f i c a n t s y s t e m a t i c d i f f e r e n c e s b c t w e c n t h e d a t a o b t a i n e d o n t h e two s y s t e m s . T h i s r e s u l t g i v e s some i d e a o f t h e r e p r o d u c i b i l i t y o f r d f a r e a s

o b t a i n e d u n d e r d i f f e r e n t c o n d i t i o n s . I t d o e s n o t , h o w e v e r , i n d i c a t e t h e a b s o l u t e e r r o r s i n c e t h i s c o u l d b e a f f e c t e d by unknown e r r o r s i n t h e a t o m i c s c a t t e r i n g f a c t o r c u r v e s u s e d i n t h e d a t a r e d u c t i o n s .

The x - r a y d i f f r a c t i o n d a t a w e r e a n a l y z e d t o o b t a i n 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 s a s d e s c r i b e d b y B e t t s e t a l . ( 5 ) , w i t h one s i g n i f i c a n t d i f f e r e n c e . The c o m p u t e r p r o g r a m h a s b e e n m o d i f i e d t o t a k e i n t o a c c o u n t t h e f a c t t h a t t h e r e i s f r e q u e n t l y a s m a l l c o n s t a n t b a c k g r o u n d c o u n t i n g r a t e i n t h e d i f f r a c t i o n

m e a s u r e m e n t s . T h i s c o n s t a n t b a c k g r o u n d r a t e was d e t e r m i n e d and s u b t r a c t e d u s i n g t h e method p r o p o s e d by F u o s s ( 6 ) .

I n a n a l y z i n g t h e r d f ' s , a r e a s u n d e r o v e r l a p p i n g p e a k s w e r e d e t e r m i n e d ~ i s i n g a c o m p u t e r p r o g r a m d e v e l o p e d t o f i t a s e r i e s o f G a u s s i a n p e a k s t o a n a p p r o p r i a t e c u r v e . F o l l o w i n g t h e s u g g e s t i o n o f Waser a n d Schomaker ( 7 ) t h a t Xo(R) s l l o u l d be s y m m e t r i c f o r i s o l a t c d p e a k s , we assumed Ro(R) t o be a sum o f o v e r l a p r i n g G a u s s i a n p e a k s . The p r o g r a m PRAXIS i s u s e d t o d e t e r m i n e t h e s e t o f p a r a m e t e r s f o r a s e t o f s u c h G a u s s i a n p e a k s w h i c h b e s t f i t t h e d a t a a c c o r d i n g t o t h e method o f l e a s t s q u a r e s . A r e a s qnd peak p o s i t i o n s a r e t h e n o b t a i n e d f o r t h e s e p a r a t e d p e a k s i n t h e f u n c t i o n 4nR2p(R)

.

The r d f peak c o r r e s p o n d i n g t o t h e f i r s t c o o r d i n a t i o n s h e l l c o u l d b e f i t by a s i n g l e G a u s s i a n f o r e a c h s a m p l e i n t h i s s t u d y . F o r t l i o s e w i t h Ag c o n t e n t i n e x c e s s o f 30 a t X , a n a d d i t i o n a l s m a l l peak c o u l d b e f i t < l o s e t o 3g. T h i s i s c o n s i s t e n t w i t h bond l e n g t h s f o r some o f t h e Ag-S b o n d s found i n c r y s t a l l i n e Ge AgSS ( 8 ) .

6

R e s u l t s and C o u c 1 u s i o n s . - T a b l e s 1 and 2 l i s t t h e r e s u l t s o f t h e s e s t u d i e s f o r t h e s u l f u r and s e l e n i u m s y s t e m s , r e s p e c t i v e l y . As x e and o t h e r s h a v e n o t e d r e p e a t e d l y , i t i s i m p o s s i b l e t o o b t a i n u n i q u e s t r u c t u r a l i n t e r p r e t a t i o n s o f t h e x-ray 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 s f o r complex p o l y a t o m i c g l a s s e s i n w h i c h t h e r e l e v a n t c o v a l e n t o r i o n i c r a d i i a r e a p p r o x i m a t e l y e q u a l o r d i f f e r by j u s t a few t e n t h s o f a n ang- s t r o m . To p r o g r e s s i n t h e a n a l y s i s , we w i l l make t h e s i m p l i f y i n g a s s u m p t i o n t h a t t h e o n l y t y p e s o f n e a r n e i g h b o r bonds p r e s e n t i n t h e g l a s s e s a r e g e r m a n i u m - c h a l c o g e n , germanium-germanium a n d s i l v e r - c h a l c o g e n . We w i l l a l s o assume t h a t t h e Ge i s a l w a y s f o u r f o l d c o o r d i n a t e d . Under t h e s e a s s u m p t i o n s , t h e a r e a o f t h e f i r s t n e i g h b o r p e a k i n t h e r d f i s g i v e n by

A = 2qGeaxzGezx + q G e ( l - a ) x ~ 2 G + 2 q ~ g Y z ~ g z ~ ' ( 1 )

H e r e , q j . a n d Z. a r c t h e n e a r n e i g h b o r c o o r d i n a t i o n number and a t o m i c number o f t h e s p e c i e s 3 , a i d t h e f r a c t i o n o f Ge a t o m s w h i c h a r e bonded t o c h a l c o g e n s w h i l e t h e f r a c t i o n o f Ge bonded t o Ge i s g i v e n by ( l - a ) .

A p a r t i c u l a r l y i n t e r e s t i n g f e a t u r e of t h e s u l f u r s y s t e m i s t h a t Z = 2ZS, s o t h a t t h e c a l c u l a t e d a r e a s a r e i n d e p e n d e n t o f t h e v a r i a b l e a . As a r e s u f f .

t h e s i l v e r c o o r d i n a t i o n nurpber c a n b e d e t e r m i n e d d i r e c t l y from t h e c o m p o s i t i o n and t h e o b s e r v e d f i r s t n e i g h b o r peak a r e a t h r o u g h t h e r e l a t i o n

The r e s u l t i n g q b a s e d on t h e assumed q = 4 a r e shown i n T a b l e 1 . I t i s e v i d e n t t h a t t h e y . r a n g e A E f r o m a p p r o x i m a t e l y 3 t o ? a n d i n c r e a s e w i t h i n c r e a s i n g y.

T h e s e low c o o r d i n a t i o n numbers may be t a k e n a s p r i m a f a c i e e v i d e n c e t h a t t h e s i l v e r - c h a l c o g e n b o n d i n g i s c o v a l e n t a n d t h e s i l v e r i s a c t i n g l i k e a n e t w o r k f o r m e r r a t h e r t h a n a n e t w o r k m o d i f i e r . F u r t h e r e v i d e n c e f o r t h i s v i ~ y p o i q t i s o b t a i n e d from t h e o b s e r v e d n e a r n e i g h b o r d i s t a n c e s . The sum o f t h e Ag -X i o n i c r a d i i a r e 3. 10 and 3 . 2 4 8 f o r S a n d S e , r e s p e c t i v e l y . I n t h e s e m a t e r i a l s , t h e a d d i t i o n o f Ag

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. 2 9 . 2 0 2420+120 2 . 4 8 4 . 0 ~ 0 . 4

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. 2 5 . 2 5 23502120 2 . 4 8 3 . 5 ~ 0 . 3

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i n t r o d u c e s i n t o t h e 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 a n e a r n e i g h b o r peak component i n t h e r e g i o n o f 2.4-2.78, w h i c h i s more t y p i c a l o f c o v a l e n t b o n d i n g . T h u s , b o t h t h e a r e a s and t h e d i s t a n c e s support t h e p i c t u r e o f c o u a l e n t s i l v e r bonding w i t h coor- d i n a t i o n numbers i n t h e range o f t h r e e t o f o u r . T h i s t y p e o f bonding i s t h e predominant banding o f s i l v e r i n t h e compounds Ag G e X 6 ( 8 ) . I t i s more d i f f i c u l t t o o b t a i n c o o r d i n a t i o n numbers f o r t h e Se syste.? *because Eq. ( 2 ) does n o t hold f o r t h i s s y s t e m . 'To proceed f u r t h e r , we w i l l make f u r t h e r s i m p l i t y i n g assumptions and d i s c u s s t h e consequences o f t h e r e s u l t i n g parameters. I n p a r t i c u l a r , f o r any v a l u e s o f X and y , we assume t h a t t h e v a l u e s o f t h e parameters q and a have t h e same v a l u e s f o r t h e s e l e n i u m g l a s s a s t h e y do f o r t h e s u l % : ~ S ; S ? X That i s , we are assuming t h a t t h e g l a s s e s o f t h e same t y p e s o f corppositions a r e e s s e n t i a l l y i s o s t r u c t u r a l . (We do n o t b e l i e v e t h a t t h e s e assumptions a r e s t r i c t l y v a l i d , b u t do t h i n k t h a t t h e t r e n d s t h e y b r i n g f o r t h a r e l i k e l y t o have v a l i d i t y . ) W i t h t h i s a s s u m p t i o n , i t i s r e a d i l y shown t h a t t h e parameter a i s g i v e n by t h e e q u a t i o n

R e s u l t s f o r t h e s e l e n i u m s y s t e m a r e presented i n T a b l e 2 , t o g e t h e r w i t h chalcogen c o o r d i n a t i o n numbers o b t a i n e d from t h e e x p r e s s i o n

The r e s u l t s f o r q i n Table 2 i n d i c a t e t h a t t h e chalcogen c o o r d i n a t i o n numbers X .

i n c r e a s e s t e a d i l y w i t h increasing Ag c o n c e n t r a t i o n . Such a t r e n d could b e r a t i o n - a l i z e d through t h e same t y p e s o f models put f o r t h by Hunter e t a l . ( 2 ) t o e x p l a i n t h e almost i d e n t i c a l t y p e s o f r e s u l t s i n t h e CU-As2Se3 s y s t e m . That i s , t h e Ag may be viewed a s h a v i n g a formal v a l e n c e o f -3 o r -4 when c o v a l e n t l y bonded by 4 and 3 c h a l c o g e n s , r e s p e c t i v e l y . These e l e c t r o n s would be t n a n s f e r r e d f o r m a l l y from t h e chalcogen atoms w h i c h , i n t u r n , would have p o s i t i v e formal v a l e n c e s and w o u l d , t h e r e f o r e , i n c r e a s e t h e i r c o o r d i n a t i o n numbers c o r r e s p o n d i n g l y i n k e e p i n g w i t h t h e 8-N r u l e , where N i s t h e formal number o f v a l e n c e e l e c t r o n s . T h i s i s j u s t

t h e o p p o s i t e o f what happens i n normal network m o d i f i c a t i o n i n which t h e m o d i f y i n g m e t a l atom g i v e s up e l e c t r o n s t o t h e oxygen o r c h a l c o g e n and reduces t h e coordina-

t i o n number. I f t h i s p i c t u r e i s c o r r e c t , one would a n t i c i p a t e t h a t t h e c o m p o s i t i o n average o f t h e c o o r d i n a t i o n numbers o f t h e e l e m e n t s i n t h e sample would be equal t o e i g h t minus t h e c o m p o s i t i o n average o f t h e number o f v a l e n c e e l e c t r o n s o f t h e atoms

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C4-954 JOURNAL DE PHYSIQUE

i n t h e s a m p l e , a s we f i n d w i t h i n e x p e r i m e n t a l e r r o r .

C o n s e q u e n t l y , i t a p p e a r s a s i f t h e a s s u m p t i o n s p r e s e n t e d above y i e l d a c o n s i s - t e n t p i c t u r e o f t h e s t r u c t u r e s o f t h e s e g l a s s e s even though t h a t p i c t u r e i s by no means u n i q u e . I n t h a t p i c t u r e , t h e s i l v e r i s c o v a l e n t l y c o o r d i n a t e d w i t h low coor- d i n a t i o n numbers o f t h e o r d e r o f t h r e e o r f o u r . The c h a l c o g e n c o o r d i n a t i o n numbers i n c r e a s e c o r r e s p o n d i n g l y t o m a i n t a i n a b a l a n c e o f f o r m a l c h a r g e and p e r f e c t p a i r i n g o f e l e c t r o n s . Such a p i c t u r e i s n o t o n e which l e a d s n a t u r a l l y t o s t a t e s i n t h e g a p : I n s t e a d , one would e x p e c t t h a t t h e v a l e n c e band i s broadened t o t a k e i n t o a c c o u n t t h e s e b o n d i n g p a t t e r n s .

We n o t e , a s w e l l , t h a t t h i s c o o r d i n a t i o n scheme i s c o n s i s t e n t w i t h t h o s e i n t h e c r y s t a l s AggGeX6. I n t h e s u l f u r compound, f o r example, t h e Ge i s s u r r o u n d e d by a n i r r e g u l a r t e i r a h e d r o n o f S atoms w i t h i n t e r a t o m i c d i s t a g c e s which r a n g e from 2.200 t o 2.227 A . T h e r e a r e no S-S bonds s h o r t e r t h a n 3 . 5 A . T h e r e a r e 8 i n e q u i v a - l e n t Ag s i t z s . Each Ag i s s u r r o u n d e d by 4 S a t o m s , b u t a t d i s t a n c e s which r a n g e from 2 . 5 t o 3 . 5 A. These d i s t a n c e s , however, f a l l i n t o :WO g r o u p s , t h o s e which a r e l e s s t h a n 2.76

1

and t h o s e which a r e g r e a t e r t h a n 2.94 A . The a v e r a g e c o o r d i n a t i o n number based o n t h o s e i n t h e f i r s t g r o u p i s 3.125, b u t two o f t h e e i g h t Ag atoms a r e f o u r - f o l d c o o r d i n a t e d , f i v e a r e t h r e e f o l d c o o r d i n a t e d and o n e i s t w o f o l d c o o r d i n a t e d w i t h i n t h i s d e f i n i t i o n : t h u s , t h e s i l v e r c o o r d i n a t i o n i s q u i t e v a r i a b l e .

Acknowledgements.- We e x p r e s s a p p r e c i a t i o n t o P. B a r n e t t o f t h e W h i r l p o o l Corpora- t i o n R e s e a r c h and E n g i n e e r i n g C e n t e r f o r a s s i s t a n c e i n d a t a a c q u i s i t i o n o n t h e i r x-ray d i f f r a c t o m e t e r and t o t h e U n i v e r s i t y o f N o t r e Dame G e o l o g i c a l L a b o r a t o r y f o r u s e of t h e i r Berman d e n s i t y b a l a n c e . T h i s work was s u p p o r t e d i n p a r t by t h e Natio- n a l S c i e n c e F o u n d a t i o n t h r o u e h G r a n t No. DMR 7908554AOI and t h e c e n t r a l f a c i l i t i e s o f t h e S t a n f o r d U n i v e r s i t y C e n t e r f o r H a t e r i a l s R e s e a r c h .

R e f e r e n c e s . -

1 . LIANG, K.S., BIENENSTOCK, A. and BATES, C. : Phys. Rev.

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2. HUNTER, S.H., BIENENSTOCK, A. and HAYES, T.M. : Proc. S e v e n t h I n t e r n a t . Conf. o n Amorphous and L i q u i d S e m i c o n d u c t o r s , Ed. S p e a r W.E. (1977) 78

3 . ROWLAND, S.C., RITLAND, F., HAFERBURNS, D. and BIENENSTOCK, A. : I b i d . , p. 135 4. FELTZ, A. and THIEME, C . : Z. Chem. 14 (1974) 32

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6. FUOSS, P. : Ph.D. T h e s i s , S t a n f o r d U n i v e r s i t y ( 1 9 8 0 ) , u n p u b l i s h e d 7. WASER, J . and SCHOMAKER, V. : Rev. Mod. Phys. 25 (1953) 671

8. EULENBERGER, G. : Monatsh. Chem. 108 (1977) 901