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ANALYSIS OF BOND STRENGTHS OF ARSENIC AND ARSENIC CHALCOGEN COMPOUNDS USING
THE TEMPERATURE DEPENDENCE OF THE EXAFS
C. Yang, M. Paesler, D. Sayers
To cite this version:
C. Yang, M. Paesler, D. Sayers. ANALYSIS OF BOND STRENGTHS OF ARSENIC AND ARSENIC CHALCOGEN COMPOUNDS USING THE TEMPERATURE DEPENDENCE OF THE EXAFS.
Journal de Physique Colloques, 1986, 47 (C8), pp.C8-391-C8-394. �10.1051/jphyscol:1986877�. �jpa-
00226199�
JOURNAL DE PHYSIQUE
Colloque C8, suppl6ment au n o 12, Tome 47, dgcembre 1986
ANALYSIS OF BOND STRENGTHS OF ARSENIC AND ARSENIC CHALCOGEN COMPOUNDS USING THE TEMPERATURE DEPENDENCE OF THE EXAFS
C.Y. YANG, M.A. PAESLER and D.E. SAYERS
Department of Physics, North Carolina State University, Raleigh, NC 27695-8202, U.S.A.
ABSTRACT
We p r e s e n t a study of t h e temperature dependence of t h e EXAFS of c r y s t a l l i n e ( c - ) A s . As2S3 and As4S4, amorphous ( a - ) A s and g l a s s y (g-) As2S3. Based on a n E i n s t e i n mode, we f i n d t h a t f o r the f i r s t s h e l l of t h e s e m a t e r i a l s , the mean square r e l a t i v e displacement (MSRD) i s r e l a t e d t o the b o n d - s t r e t c h i n g f o r c e c o n s t a n t . Our r e s u l t i n d i c a t e s t h a t A s - A s bonds i n c- A s a r e about 17% s o f t e r than those i n a- As. The s t r e t c h i n g f o r c e s of t h e As-S bonds i n c- and g- As2S3 a r e q u i t e s i m i l a r . The c a l c u l a t i o n of bond s t r e n g t h s i n c- As4S4 shows t h a t As-S bonds a r e about 30%
s t r o n g e r t h a n A s - A s bonds. T h i s work underscores t h e f a c t t h a t temperature de- pendent EXAFS d a t a may be used to provide i n f o r m a t i o n about t h e n a t u r e and, i n p a r t i c u l a r , t h e s t r e n g t h of l o c a l bonding.
INTRODUCTION
Although t h e advantage of t a k i n g EXAFS d a t a a t low temperatures has been rec- ognized f o r y e a r s , the e f f e c t s of thermal motion have r e c e i v e d r e l a t i v e l y l i t t l e a t t e n t i o n . Measurement of t h e temperature dependence of EXAFS i s , t h e r e f o r e , a t - t r a c t i v e i n i t s own r i g h t , n o t only because i t l e a d s t o important s t r u c t u r a l i n f o r - mation, b u t because i t a l s o p r o v i d e s an imporved understanding of t h e EXAFS tech- nique. An important i s s u e i n t h i s study of the MSRD i s the d e t e r m i n a t i o n of the microscopic p h y s i c a l parameters t h a t can be o b t a i n e d from such measurements. We p r e s e n t , i n t h i s paper, temperature-dependent EXAFS i n v e s t i g a t i o n s of c- (rhombohe- d r a l ) and a- A s , c- (orpiment) and g-As2S3 and c- ( r e a l g a r ) As4S4. Two major f e a - t u r e s of t h e s e s o l i d s a r e t h a t t h e i r l o c a l bonding is based upon molecular u n i t s and t h e i r optic-mode f r e q u e n c i e s a r e dominated by t h e s h o r t range i n t e r a c t i o n s . Our r e s u l t s u g g e s t s [ l ] t h a t t h e thermal v i b r a t i o n s of p a i r s of atmos measured by EXAFS i n t h e f i r s t s h e l l of t h e s e m a t e r i a l s a r e r e l a t e d t o bond s t r e t c h i n g modes which, i n t u r n , provide an e m p i r i c a l assement of t h e bond s t r e n g t h .
EXPERIMENTAL
EXAFS measurements were performed a t the NSLS on t h e X-11A beam l i n e with an S i (111) double c r y s t a l monocromator a t t h e As K-edge. The samples were s e p a r a t e l y ground t o f i n e powders and placed on kapton tape. Various t h i c k n e s s e s of uniform samples were measured t o avoid t h i c k n e s s e f f e c t s . Transmission measurements on c- A s , c- As2S3 and c- As4S4 were made a t 15, 8 0 , 145, 300 K u s i n g a d i s p l e x cryo- s t a t . The a - A s and g- As2S3 were measured a t 80 K and room temperature.
RESULTS AND DISCUSSION
Using s t a n d a r d techniques, the f i r s t s h e l l of EXAFS can be i s o l a t e d by F o u r i e r f i l t e r i n g . I n t h e c a s e s of c- A s , a- A s , c- and g- AsZS3, t h e MSRD, u 2 ( ~ ) i s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986877
JOURNAL DE PHYSIQUE
=-As ( dotdash line)
)
i
c-As,S4 As-As bonds (solid line)
As-S bonds (dotdesh line)
Temperature (K)
Fig. 1 Changes with temperature of the MSRD, a 2 , of the f i r s t s h e l l of ( a ) As-As bonds i n c- and a - As (b) As-S bonds i n c- and g- As2S3 and ( c ) As-As and As-S bonds i n c- As4S4. The l i n e s represent E i n s t e i n model f i t s to the data. A s i g n i f i c a n t d i f f e r e n c e between the MSRD of As-As and t h a t of As-S bonds i n c- AsbS4 can be seen. The a2 of As-As i n ( c ) and ( a ) and of As-S i n ( c ) and (b) a r e
s i m i l a r . Of i n t e r e s t i s the f a c t t h a t u2 i s sometimes not only s h e l l dependent b u t a l s o p a i r dependent.
determined using t h e r a t i o method. For c- As4S4 w i t h the presence of two As-S bonds and one A s - A s bond i n t h e same s h e l l , t h e c o n t r i b u t i o n s from each bond i s ob- t a i n e d u s i n g phase c o r r e c t e d F o u r i e r transforms [ 2 ] followed by f i t t i n g i n k- space using r e f e r e n c e compounds. I n o r d e r t o remove t h e a m b i g u i t i e s a r i s i n g from l a r g e numbers of f i t t i n g parameters, we s y n t h e s i z e t h e measured d a t a by s u b t r a c t i n g t h e c o n t r i b u t i o n from each bond using t h e f i t t i n g r e s u l t s . A f t e r such d a t a p r o c e s s i n g , we apply t h e phase c o r r e c t e d F o u r i e r transform a g a i n on each of t h e r e s i d u a l spec- t r a . Hence, t h e accuracy of f i t t i n g r e s u l t s can be monitored by t h i s s y n t h e s i s i n both k-space and r-space. The d e t a i l s of d a t a a n a l y s i s a r e d e s c r i b e d e l s e w h e r e . [ l ]
Since 02(T) from EXAFS i s a measure of t h e r e l a t i v e motion a l o n g t h e bond d i r e c t i o n between t h e absorbing and b a c k s c a t t e r i n g atom, t h e s h o r t range c o r r e l a - a t i o n of motion i s dominated by t h e o p t i c a l phonons. I n our s t u d y , i n o r d e r t o f i t t h e temperature dependence of a2(T) i n t h e f i r s t s h e l l , t h e E i n s t e i n approximation i s used n o t only because i t h a s a simple form, b u t a l s o because t h e o p t i c a l modes dominate. The E i n s t e i n approximation [ 3 ] g i v e s
where !J is the reduced mass, kg i s the Boltzmann's c o n s t a n t , and WE i s the E i n s t e i n frequency. The r e s u l t s a r e shown i n Fig. 1.
I n c u r r e n t EXAFS t h e o r i e s [ 3 ] i t is assumed t h a t a2(T) measured by EXAFS i s r e l a t e d t o a l o c a l , p r o j e c t e d d e n s i t y of modes. Hence, t h e r e should be a c l o s e connection between EXAFS measurement and t h e reduced Raman spectrum. I n o r d e r t o d i s c o v e r what microscopic p h y s i c a l parameters can be o b t a i n e d from t h e measurement of t h e temperature dependence of EXAFS i t i s h e l p f u l t o compare EXAFS s t u d i e s and Raman spectroscopy. A comparison of t h e E i n s t e i n v i b r a t i o n a l frequency, VE = u E / 2 ~ ~ d e r i v e d from EXAFS and v i b r a t i o n a l frequency o b t a i n e d from Raman s p e c t r a
i s shown i n Table 1. I t can be seen t h a t t h e E i n s t e i n v i b r a t i o n a l f r e q u e n c i e s a r e q u i t e c l o s e t o t h e symmetrical s t r e t c h i n g modes.
Although measurements of the temperature dependence of EXAFS cannot p r o v i d e t h e same d e t a i l t h a t Raman measurements can, i t g i v e s an easy way t o i d e n t i f y l o c a l v i b r a t i o n s w i t h r e s p e c t t o t h e main bond-stretching modes. A s t r e n g t h of t h e EXAFS technique i s i t s a b i l i t y t o determine l o c a l dynamical information about each type of atom i n a v a r i e t y of forms such a s f o r h i g h l y d i s o r d e r e d o r d i l u t e samples f o r which t r a d i t i o n a l v i b r a t i o n a l techniques have d i f f i c u l t i e s .
Upon comparing t h e EXAFS and Raman r e s u l t s , i t is e v i d e n t t h a t VE can be i n t e r p r e t e d a s t h e average of t h e s t r e t c h i n g mode f r e q u e n c i e s . From t h i s assump- t i o n a n e m p i r i c a l measure of bond s t r e n g t h i n a r s e n i c and a r s e n i c chalcogen com- pounds can be made. The e f f e c t i v e bond-stre t c h i n g f o r c e cons t a u t derf ved from EXAFS can be w r i t t e n a s
Table 1. Comparison of t h e E i n s t e i n V i b r a t i o n a l Frequencies VE and Raman Symmetrical S t r e t c h i n g Frequencies US.
-
M a t e r i a l Bonding vE(cm-l) vS(cm-1)
c- A s A s - A s 216
*
5 205a-As A s - A s 234
*
5 235c-Asps3 As-S 332
*
5 354g-As2S3 As-S 330
*
5 340c- AsqSq A s - A s 222
*
10 220As-S 342 i 10 354
JOURNAL DE PHYSIQUE
The r a t i o of t h e e f f e c t i v e b o n d - s t r e t c h i n g f o r c e c o n s t a n t s between a- and c- A s is a b o u t 1.17. T h a t i s , t h e A s - A s bonds i n c - A s a r e a b o u t 17% s o f t e r t h a t t h o s e i n a- A s . T h i s d i f f e r e n c e between c- and a- A s i s a l s o c o n s i s t e n t w i t h t h e s i z e of
t h e i r o p t i c a l gaps. The r e s u l t s f o r t h e As-S bond s t r e n g t h s i n c- and g- As2S3 can be used t o e x p l a i n q u a n t i t i v e l y t h e s i m i l a r i t i e s between t h e main s t r e t c h i n g f o r c e s . The c a l c u l a t i o n of bond s t r e n g t h s of t h e h e t e r o p o l a r and homopolar bonding i n c- As4S4 shows t h a t As-S bonds a r e a b o u t 30% s t r o n g e r than t h e A s - A s bonds.
CONCLUSION
Our s t u d y shows t h a t t h e thermal motions of p a i r of atoms i n a r s e n i c and a r s e n i c c h a l c o g e n compounds measured from EXAFS i n t h e f i r s t s h e l l a r e a t t r i b u t e d
t o b o n d - s t r e t c h i n g f o r c e s . The agreement between t h e EXAFS and Raman measurements i s q u i t e r e s p e c t a b l e . T h i s work u n d e r s c o r e s t h a t f a c t t h a t t e m p e r a t u r e dependent EXAFS d a t a may be used t o p r o v i d e i n f o r m a t i o n a b o u t t h e n a t u r e , i . e . t h e s t r e n g t h , of t h e l o c a l bonding.
ACKNOWLEDGEMENTS
S u p p o r t f o r t h e development of beamline X-11A a t NSLS and p a r t i a l s u p p o r t f o r t h i s r e s e a r c h was provided by t h e Department of Energy under c o n t r a c t DE-AS05-80- ER10742. P a r t i a l s u p p o r t f o r t h i s r e s e a r c h was a l s o provided by t h e N a t i o n a l S c i e n c e Foundation under g r a n t DMR-8407265.
REFERENCES
1. C. Y. Yang, M. A. P a e s l e r and D. E. S a y e r s , s u b m i t t e d t o Phys Rev B.
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Penner-Hahn ( S p r i n g e r - V e r l a g , New York, 1984).
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