EXTENDED FINE STRUCTURE OF BRAGG REFLECTIVITY OF COPPER SULPHATE IN THE VICINITY OF COPPER K-EDGE

(1)

HAL Id: jpa-00227318

https://hal.archives-ouvertes.fr/jpa-00227318

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

EXTENDED FINE STRUCTURE OF BRAGG REFLECTIVITY OF COPPER SULPHATE IN THE

VICINITY OF COPPER K-EDGE

I. Arčon, A. Kodre, D. Glavič, M. Hribar

To cite this version:

I. Arčon, A. Kodre, D. Glavič, M. Hribar. EXTENDED FINE STRUCTURE OF BRAGG REFLEC-

TIVITY OF COPPER SULPHATE IN THE VICINITY OF COPPER K-EDGE. Journal de Physique

Colloques, 1987, 48 (C9), pp.C9-1105-C9-1108. �10.1051/jphyscol:19879200�. �jpa-00227318�

(2)

Colloque C9, supplbment au n012, Tome 48, dbcembre 1987

EXTENDED FINE STRUCTURE OF BRAGG REFLECTIVITY OF COPPER SULPHATE IN THE VICINITY OF COPPER K-EDGE

I.

AREON,

A. KODRE, D.

GLAVIE

and M. HRIBAR

Department of Physics of FNT and J. Stefan Institute,

E. Kardelj University of Ljubljana, YU-Ljubljana, Yugoslavia

ABSTRACT

-

The Bragg r e f l e c t i v i t y of a monocrystal of copper s u l p h a t e i n t h e energy r e g i o n around t h e K edge of copper i s examined f o r a n extended f i n e s t r u c t u r e similar t o EXAFS. A c a l c u l a t i o n based on a model of a mosaic c r y s t a l s h w s t h a t t h e s t r u c t u r e i s d e r i v e d frcm t h e EXAFS as w e l l a s frcm a n analogous e f f e c t i n t h e s c a t t e r i n g amplitude. The r e s u l t can b e brought t o t h e same form as EXAF'S, b u t w i t h d i t i o n a l phase s h i f t s . I n an e x p e r i m e n t a l ccmparison of t h e s t r u c t u r e t o t h e s t a n d a r d EXAFS of a t h i n copper s u l p h a t e p l a t e t h e e x i s t e n c e of phase s h i f t s i s confirmed.

INTRODUCTION

There have been s e v e r a l o b s e r v a t i o n s of t h e EXAFS-like s t r u c t u r e i n t h e Bragg r e f l e c t i v i t y of c r y s t a l s on t h e high-energy s i d e of a b s o r p t i o n edges of c o n s t i t u e n t atms [I-31. I n mosaic c r y s t a l s where both t h e i n c i d e n t and t h e r e f l e c t e d X-ray beam a r e mainly attenuated by photoabsorption t h e e f f e c t i s a p p a r e n t l y r e l a t e d t o t h e EXAFS i t s e l f , b u t a d i r e c t ccmparison h a s n o t been r e p o r t e d . T h e o r e t i c a l arguments a r e g i v e n [3-41 t h a t t h e a t e n u a t i o n of t h e beam as w e l l a s t h e s c a t t e r i n g p r c c e s e s c o n t r i b u t e t o t h e s t r u c t u r e .

I n t h e p r e s e n t paper e x p l i c i t r e s u l t s a r e d e r i v e d f o l l o w i n g t h e p a t h developed i n t h e t h e o r e t i c a l t r e a t m e n t of t o t a l r e f l e c t i o n s EXAFS 141. The e f f e c t w i l l be r e f e r r e d t o a s BREFS (Bragg r e f l e c t i v i t y extended f i n e s t r u c t u r e ) . Analogously t o

t h e r e l a t i v e a t t e n u a t i o n c o e f f i c i e n t i n EXAFS, t h e r e l a t i v e r e f l e c t i v i t y i s i n t r o d u c e d t o r e p r e s e n t BREFS: t h i s i s t h e o s c i l l a t o r y p a r t of t h e r e f l e c t i v i t y of t h e c r y s t a l normalised t o its smooth, s l m l y v a r y i n g average. These q u a n t i t i e s a r e u s u a l l y expressed i n k-space, i. e . a s f u n c t i o n of t h e p h o t o e l e c t r o n wavevector.

We measured t h e BREFS and EXAFS o n s c r y s t a l of copper s u l p h a t e a t t h e copper K edge.

The e x p e r i m e n t a l r e s u l t s are used t o test t h e t h e o r e t i c a l p r e d i c t i o n s . THE MODEL

The i n t e g r a t e d c o e f f i c i e n t of r e f l e c t i v i t y of a mosaic c r y s t a l

,. -

151 i s g i v e n by

where U d e n o t e s t h e f r e q u e n c y of t h e s c a t t e r e d wave, r t h e c l a s s i c a l e l e c t r o n r a d i u s , N t h e number of s c a t t e r i n g a t m s p e r u n i t v o l d e and u ( 8 ) t h e w e l l known

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879200

(3)

C9-1106 JOURNAL DE PHYSIQUE

a n g u l a r dependence of Bragg r e f l e c t i v i t y . The canponents of t h e atomic s c a t e r i n g f c c t o r are c w c t e d [ 6 ] by _- _.

f l ( q ) ;

-

L J ~ u ~ " ( ~ ) d(J

n o

0 % - 3 ( 2 )

and t h e a b s o r p t i o n c o e f f i c i e n t ( U ) is p r o p o r t i o n a l t o t h e imaginary p a r t of t h e s c a t t e r i n g f a c t o r

p ( u )

= 4

r,

c N f l l ( U ) (3)

U

Its o s c m a t o r y p a r t , t h e r e l a t i v e a t t e n u a t i o n c o e E c i e n t can, i n k-space, be deccmposed i n t o harmonic c o n t r i b u t i o n s of c o n s e c u t i v e s h e l l s of neighbour a t a n s :

. "

By d i f f e r e n t i a t i n g E q . ( l ) t h e r e l a t i o n between t h e s m a l l o s c i l l a t o r y p a r t s of

X

( k )

,

Af' and A f " is obtained:

7 7 r- -I

Xp'k) =

&%!- ₅₅

⁼l F ] A f i k ) +

1 ^3$j,9

^)]nrll(k) ⁽⁵⁾

The r e l a t i v e r e f l e c t i v i t y is expressed by t h e f i n e s t r u c t u r e of t h e canponents of t h e sceiltering f a c t o r . While Af" i s d i r e c t l y p r o p o r t i o n a l t o

X

( k ) , t h e i n t e g r a l o p e r a t o r d e f i n i n g A f l i n Eq.(2) r e d u c e s , w i t h i n t h e same l i n e a r aproximation, t o a n e g a t i v e d e r i v a t i v e of A f " i n t r o d u c i n g t h e phase s h i f t of 3T1/2. Conseqently, BREFS can be e x p r e s s e d as a sum of t h e same harmonic terms a s EXAFS:

where

( f"2

-

f t 2 ) g ( k ) =

and ( f1lZ+ yP)

Apart frcm t h e s m a l l i n c r e a s e of t h e amplitude, t h e s h e l l c o n t r i b u t i o n s of EXAFS a r e canbined t o BREFS w i t h a d d i t i o n a l phase s h i f t s .

THE EXPERIMENT

A monocrystal of copper s u l p h a t e p e n t a h y d r a t e (CuSO 5H 0 ) is i n s e r t e d f o r t h e B r a g c r y s t a l of t h e X-ray monochranator w i t h a c o n v & t i g n a l X-ray tube. A c r y s t a l p l a n e w i t h 2d = 0.964 nm i s used and t h e r e s o l u t i o n of 20 e V a t t h e copper K edge (8.980 keV) i s achieved i n t h e t h i r d o r d e r r e f l e c t i o n . The r e f l e c t e d beam i s a n a l y s e d by a G e d e t e c t o r t o d i s c r i m i n a t e t h e t h i r d o r d e r from o t h e r r e f l e c t i o n s and f r a n copper f l u o r e s c e n c e of t h e c r y s t a l . More t h a n 100 s c a n s of t h e 500 eV r e g i o n above t h e copper K edge a r e superinnposed t o e x t r a c t t h e s t r u c t u r e from t h e s t a t i s t i c a l n o i s e .

The r e l a t i v e r e f l e c t i v i t y i s obtained frcm t h e e x p e r i m e n t a l d a t a by s u b t r a c t i n g t h e smooth p r i n c i p a l p a r t d e f i n e d a s a b e s t f i t t h i r d - o r d e r polyncmial. The r e s u l t is shown i n Fig.1: f o r c l a r i t y , t h e s t a t i s t i c a l e r r o r i s only given f o r m e d a t a p o i n t , b e i n g c o n s t a n t over t h e r e g i o n . For a c a n p a r i s o n , t h e r e l a t i v e a t t e n u a t i o n c o e f f i c i e n t i s shcwn b e s i d e t h e BREFS: it i s t h e s t a n d a r d EXAFS of a t h i n copper s u l p h a t e p l a t e l e t measured on t h e same a p a r a t u s w i t h LiF (220) c r y s t a l i n t h e f i r s t o r d e r r e f l e c t i o n and i n t h e same r e s o l u t i o n and s t a t i s t i c s a s above.

CONCLUSION

Taking i n t o account t h e s i z e of t h e s t a t i s t i c a l n o i s e , t h e two s e t s of e x p e r i m e n t a l d a t a p o i n t s i n Fig.1 r u n remarkably w e l l i n parallel. I n copper s u l p h a t e [7] t h e EXAFS spectrum of t h e copper a t a n i s governed by t h e c o n t r i b u t i c n f r a n t h e f i r s t s h e l l of oxygen a t a n s : The sums of Eqs. ( 4 ) and ( 6 ) a r e d a n i n a t e d by a s i n g l e s i n e term, d i f f e r i n g only i n i t s phase. The a v e r a g e s i z e of a phase

(4)

Fig. 1 EXAFS spectrum (

+

) and t h e r e l a t i v e Bragg r e f l e c t i v i t y (BREFS) ( o ) a t a t t h e copper K edge.

Fig. 2. EXAFS spectrum ( + ) transformed accordingly t o Eq. 6. canpared t o t h e BREFS ( o ).

(5)

C9-1108 JOURNAL

DE

PHYSIQUE

s h i f t , a s can be estimated f r a n t h e p l o t , i s a l s o i n accord with t h e t h e o r e t i c a l v a l u e of+. 38 r a d (Eq. 6 b ) .

To make t h e t e s t more s t r i n g e n t , we transformed t h e experimental EXAFS spectrum with t h e help of Eq. (6) and with t h e phase s h i f t c a l c u l a t e d f r a n s c a t t e r i n g f a c t o r t a b l e s [ 8 ] , i n t o t h e BREFS spectrum. I n t h e c a l c u l a t i o n t h e v a l u e of 25.0 is adopted f o r

g ,

t h e normal d i s p e r s i m p a r t of f'

,

t o t a k e i n t o account t h e scattering a n g l e of 40 degrees: The r e s u l t , t c g e t h e r with t h e experimental BREFS i s s h a m i n Fig. 2.

It should be noted t h a t t h e a b s o l u t e v a l u e of t h e F o u r i e r transform, as routinely used t o i n t e r p r e t EXAFS s p e c t r a , d e s t r o y s t h e phase informaticn. Thus, BREFS and EXAFS a r e l a r g e l y e q u i v a l e n t when transformed t o r-space.

REFERENCES

1. S. I. SALEM, V. L. HALL: J. Phys. F , 10, (1980) 1627 2. V. PONOMAREV, A. TURUTIN:

ZTK

2, (1984) 391 .

3. V. PONOMAREV, A. TURUTIN: Vesti. Mosk. Univ. 2, (1984) 92 . 4. G. MARTENS, P. RABE: J Phys. 14, (1981) 1523.

5. R. W. JAMES: The O p t i c a l P r i n c i p l e s of t h e D i f f r a c t i o n of X-rays, G-Bell, London (1950).

6. T. KAWAMURA, T. FUKAMACHI: Jap. J. Appl. Phys. Suppl. 17-2, (1978) 2 2 4 . 7. R. W. JOINER: Chem. Phys. L e t t . 1, (1980) 162.