ORIENTATION AND TEMPERATURE DEPENDENCE OF THE Cd K-SHELL EXAFS OF SINGLE CRYSTAL Cd METAL : FIRST EXAFS OBSERVATION OF R2

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ORIENTATION AND TEMPERATURE

DEPENDENCE OF THE Cd K-SHELL EXAFS OF SINGLE CRYSTAL Cd METAL : FIRST EXAFS

OBSERVATION OF R2

A. Hitchcock, J. Garrett, T. Tyliszczak

To cite this version:

A. Hitchcock, J. Garrett, T. Tyliszczak. ORIENTATION AND TEMPERATURE DEPEN- DENCE OF THE Cd K-SHELL EXAFS OF SINGLE CRYSTAL Cd METAL : FIRST EXAFS OBSERVATION OF R2. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-1081-C8-1084.

�10.1051/jphyscol:19868211�. �jpa-00226123�

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JOURNAL DE PHYSIQUE

C o l l o q u e C8, s u p p l e m e n t au n o 1 2 , Tome 47, d g c e r n b r e 1 9 8 6

ORIENTATION AND TEMPERATURE DEPENDENCE OF THE Cd K-SHELL EXAFS OF SINGLE CRYSTAL Cd METAL : FIRST EXAFS OBSERVATION OF R2

A.P. HITCHCOCK, J . D . GARRETT and T . TYLISZCZAK

Institute for Materials Research, McMaster University, Hamilton, Canada, L8S 4 M 1

A b s t r a c t

-

The K-shell X-ray a b s o r p t i o n spectrum of a Cd s i n g l e c r y s t a l h a s been measured a t temperatures from 4 t o 300K w i t h t h e c r y s t 2 1 i n two o r i e n t a t i o n s

-

one o p t i m i z i n g EXAFS from t h e f i r s t Cd d i s t a n c e (R1 = 2.97A), t h e o t h e r o p t i m i z i n g EXAFS from t h e second Cd d i s t a n c e (R2 = 3.291). C l e a r evidence i s o b t a i n e d f o r R2 a l t h o u g h i t s v i s i b i l i t y v a r i e s g r e a t l y w i t h temperature on account of t h e l a r g e a n i s o t r o p y i n t h e thermal motion. The Debye-Waller f a c t o r s f o r t h e thermal motion a l o n g R1 and R2 a r e d e r i v e d and compared t o theory.

I

-

INTRODUCTION

The l o c a l s t r u c t u r e around each Cd atom i n t h e d i s t o r t e d hexagonal close-packed s t r u c t u r e of Cd m e t a l c o n s i s t s of 6 n e a r e s t neighbours a t 2.971 (R1) i n t h e b a s a l p l a n e (along t h e 5 o r

b

d i r e c t i o n s ) and 6 neighbours a t 3.291 (R2) a t a n a n g l e of 30' t o t h e 2 a x i s ( s e e Fig.

.

The problem t h a t t h i s work a d d r e s s e s i s t h e v i s i b i l i t y

'B

of t h e second s h e l l (3.29 ) d i s t a n c e i n Cd K-shell extended X-ray a b s o r p t i o n f i n e s t r u c t u r e (EXAFS). The K-shell photoabsorption spectrum of s i n g l e c r y s t a l Cd was f i r s t r e p o r t e d by Weber /1/ who r e c o r d e d s p e c t r a a t b o t h 300 and 83K w i t h u n p o l a r i z e d X-rays i n c i d e n t a l o n g e i t h e r t h e 5 d i r e c t i o n , where t h e R1 c o n t r i b u t i o n w i l l b e z e r o , o r t h e 2 d i r e c t i o n , where t h e R1 c o n t r i b u t i o n w i l l b e maximum b u t c o n t r i b u t i o n s from b o t h t h e R1 and R2 d i s t a n c e s w i l l occur. Weber / I / observed t h a t t h e EXAFS i n t e n s i t y was s m a l l e r w i t h t h e X-rays i n c i d e n t a l o n g

a

t h a n a l o n g

c

b u t t h e r e were no a p p a r e n t

changes i n t h e p e r i o d i c i t y o r b a s i c shape of t h e extended f i n e s t r u c t u r e between t h e two o r i e n t a t i o n s . No d e t a i l e d a n a l y s i s of t h e EXAFS was done. I n 1983, Thulke and Rabe /2/ r e p o r t e d t h e Cd K EXAFS of p o l y c r y s t a l l i n e Cd a t 77K which showed a symmetr- i c f i r s t peak i n t h e F o u r i e r t r a n s f o r m (FT) w i t h no s i g n s of R2 e i t h e r a s an asymm- e t r y o r a s e p a r a t e peak. Thulke and Rabe /2/ a t t r i b u t e d t h e absence of d e t e c t i b l e R2 s i g n a l t o a l a r g e thermal motion and t h u s l a r g e Debye-Waller f a c t o r (a) f o r t h i s s i g n a l .

I n o r d e r t o f u r t h e r i n v e s t i g a t e t h e i n t r i g u i n g q u e s t i o n a s t o whether o r n o t EXAFS c a n d e t e c t t h e R2 d i s t a n c e of Cd we have s t u d i e d t h e temperature dependence of t h e Cd K-shell EXAFS of s i n g l e c r y s t a l Cd over temperatures from 4K t o 300K w i t h o r i e n t a - t i o n s chosen t o o p t i m i z e t h e R1 and R;! EXAFS s i g n a l . O r i e n t a t i o n dependent EXAFS i s w e l l known t o provide a d d i t i o n a l s t r u c t u r a l i n f o r m a t i o n a s e x e m p l i f i e d i n t h e s t u d y by Brown e t , a l 131 of t h e o r i e n t a t i o n dependence of t h e EXAFS of s i n g l e c r y s t a l Zn, which has a s i m i l a r d i s t o r t e d hexagonal close-packed s t r u c t u r e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868211

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C8-1082 JOURNAL DE PHYSIQUE

I1

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EXPERIMENTAL

The Cd s i n g l e c r y s t a l s were o b t a i n e d from a shaped p i e c e of Cd metal, 50um t h i c k . This was sandwiched between two g l a s s s l i d e s w i t h 50um s p a c e r s ,

melted and Bridgeman cooled over a ~ e r i o d of 1 2 hours. The o r i e n t a t i o n of s e v e r a l of t h e l a r g e r c r y s t a l s was determined by t r a n s m i s s i o n Laue. The c r y s t a l chosen f o r s t u d y was about 3 x 5 m 2 w i t h i t s c a x i s a t 10' t o t h e s u r f a c e normal. I t was masked off w i t h l e a d t o a s i z e of 1 x 2 m F , clamped between two copper p l a t e s f a s t e n e d t o t h e bottom of a s i n g l e s t a g e c r y o s t a t , surrounded by a Be cup and immersed i n l i q u i d helium. Measurements a t temperatures h i g h e r t h a n 4K were c a r r i e d o u t o v e r s e v e r a l half-hour p e r i o d s w h i l e t h e c r y a s t a t was warming up.

The Cd K-shell s p e c t r a (26.6

-

27.7 keV) were recorded on t h e C2 beam l i n e a t CHESS w i t h t h e X-rays i n c i d e n t a l o n g e i t h e r t h e 5 a x i s

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v e c t o r i n t h e b a s a l p l a n e a l o n g t h e R1 d i r e c t i o n , denoted R1*), o r w i t h t b e X-rays i n c i d e n t 60' o f f t h e

c

^{a x i s}

(g

v e c t o r a t 30' t o t h e b a s a l p l a n e , denoted R ~ * ) ( s e e Fig. 2 ) . With 100% p o l a r i z e d X-rays and a m o n o c r y s t a l l i n e sample, K-shell EXAFS can b e d e s c r i b e d by / 4 / :

where t h e d i r e c t i o n t o t h e i t h neighbour w i t h EXAFS component Xi(k) makes an a n g l e

ei

w i t h t h e X-ray p o l a r i z a t i o n v e c t o r , and +(k) [Ai(k)] i s t h e b a c k s c a t t e r i n g amplitude [phase s h i f t ] a s a f u n c t i o n of wavenumber (k) from each of t h e neighbour- i n g atoms of t y p e i, which a r e l o c a t e d a t a d i s t a n c e r i and have a mean-square r e l a t i v e displacement of 0 2 . The 3cos2€I f a c t o r a v e r a g e s t o 1 f o r p o l y c r y s t a l l i n e samples. For t h e R ~ * measurements t h i s f a c t o r i s e q u a l t o 1.5 f o r R and 0.33 f o r R2 (assuming 100% p o l a r i s a t i o n and a p e r f e c t s i n g l e c r y s t a l ) . For the R2* measurements t h e 3coe.20 f a c t o r i s 0.375 f o r R1 and 1.72 f o r RZ. Thus i n t h e f i r s t c a s e t h e Rl component w i l l dominate w h i l e i n t h e second c a s e , t h e R2 component s h o u l d b e s t r o n g e r . The extended f i n e s t r u c t u r e was e x t r a c t e d by s u b t r a c t i n g a 4-section c u b i c s p l i n e background, normalizing t o t h e edge jump and c o n v e r t i n g from energy t o wavenumber. The o r i g i n of t h e k-scale (Eo), i n i t i a l l y chosen a s t h e mid-point of t h e edge jump, was optimized d u r i n g a n a l y s i s which used F o u r i e r f i l t e r i n g followed by c u r v e - f i t t i n g a p p l i e d t o kl-weighted d a t a , according t o s t a n d a r d procedures /5/.

111

-

RESULTS AND DISCUSSION

The kl-weighted EXAFS e x t r a c t e d from t h e Cd K a b s o r p t i o n s p e c t r a recorded a t 4K i n t h e R1* and R ~ * o r i e n t a t i o n s and t h e transforms of t h i s d a t a a r e p r e s e n t e d i n Fig. 1, a l o n g w i t h t h e r e s u l t s a t room temperature. The prominent side-lobe observed i n a l l

Fig. 1: kL-weighted EXAFS and magnitudes of t h e F o u r i e r t r a n s f o r m s (FT) o b t a i n e d from t h e Cd K-shell EXAFS of s i n g l e c r y s t a l Cd record- e d i n t h e R1* and R1*

o r i e n t a t i o n s a t 4 and 300K.

Radial Distance (A)

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transforms a t 2.2;* ( I * s i g n i f i e s phase s h i f t e d d i s t a n c e ) i s a s s o c i a t e d w i t h t h e s t r u c t u r e d b a c k s c a t t e r i n g amplitude f u n c t i o n of heavy atoms 161. A s expected, t h e R ~ * d a t a i s t o t a l l y dominate$ by R1 s i g n a l which produces a symmetric f i r s t s h e l l peak i n t h e t r a n s f o r m a t 2.78". I n t h e R ~ * geometry t h e R1 component s t i l l dominates, even though t h e R2 s i g n a l should be weighted 5 times t h a t of t h e R1 s i g n a l i f t h e o r i e n t a t i o n i s c o r r e c t and t h e X-rays 100% p o l a r i z e d . Although t h e r e i s no c l e a r evidence of

%

i n t h e 300K spectrum, t h e

%

s i g n a l does produce a prominent shoulder on t h e main peak a t 4K. I n a d d i t i o n , t h e r e i s a s h i f t i n t h e p e r i o d i c i t y of t h e k ~ ( k ) s i g n a l r e l a t i v e t o t h e 4K R ~ * d a t a which c a n b e s e e n i n t h e o v e r p l o t and t h e r e i s a d i s t i n c t b e a t p a t t e r n between t h e R1 and R2 components a s evidenced by t h e damped i n t e n s i t y and i r r e g u l a r p a t t e r n between 5 and 7x-(-1 i n t h e 4K spectrum.

The magnitude of t h e R1 s i g n a l i n t h e

%*

spectrum i s about 60% of t h a t i n t h e R ~ * s p e c t r a recorded a t similar temperatures. According t o t h e p r e d i c t e d p o l a r i z a t i o n dependence t h i s r a t i o should b e o n l y 25%. The a d d i t i o n a l R1 s i g n a l can b e explained by misalignment from t h e d e s i r e d o r i e n t a t i o n d u r i n g measurements, incomplete p o l a r - i z a t i o n of t h e X-rays o r i m p e r f e c t c r y s t a l l i n i t y of t h e Cd sample. A l l of t h e s e f a c t o r s probably c o n t r i b u t e t o some e x t e n t . An approximate R2 component was o b t a i n e d a t v a r i o u s temperatures by s u b t r a c t i n g 0.6 R ~ * from t h e R ~ * EXAFS. The t r a n s f o r m s of t h e s e s u b t r a c t e d s p e c t r a (Fig. 2) i n d i c a t e t h a t t h e R2 s i g n a l i n Cd m e t a l d e c r e a s e s v e r y r a p i d l y w i t h i n c r e a s i n g temperature. Above l O O K i t i s very d i f f i c u l t t o d e t e c t

%.

I n t e r e s t i n g l y a t 4K t h e h i g h e r s h e l l s of surrounding cadmiums become more v i s i b l e i n t h i s p r e s e n t a t i o n .

I n o r d e r t o q u a n t i f y t h e e f f e c t of a n i s o t r o p i c thermal motion on t h e EXAFS of Cd, multiparameter f i t s were made t o t h e F o u r i e r - f i l t e r e d f i r s t - s h e l l EXAFS d a t a from measurements a t a range of temperatures between 4 and 300K. The model amplitude and phase s h i f t f u n c t i o n s were o b t a i n e d from a n experimental R1 Cd b a c k s c a t t e r i n g s i g n a l d e r i v e d from I . O ~ ( R ~ *

-

0.12 R ~ * ) . The d i s t a n c e s d e r i v e d f o r b o t h R1 (2.963(8)11 averaged over a l l d a t a ) and R2 (3.220(12)1 averaged over a l l d a t a ) a r e s m a l l e r by 0.011 (R1) and 0.061 (R2) t h a n t h e c r y s t a l l o g r a p h i c v a l u e s . The d i f f e r e n c e s may b e a t t r i b u t e d t o t h e l i m i t a t i o n s of an a n a l y s i s based on a Gaussian p a i r d i s t r i b u t i o n b e i n g a p p l i e d t o a n anharmonic system 171. The number of n e a r e s t neighbours, N 1 i s 6+1 a t a l l temperatures. However t h e N2 v a l u e s a r e c o n s i s t e n t l y t o o low by more t h a n a f a c t o r of 2. Since our a n a l y s i s t r e a t s t h e R1 and

%

d i r e c t i o n s s i m i l a r l y and produces a r e a s o n a b l e N1 v a l u e , t h e 50% e r r o r i n N s u g g e s t s t h a t t h e a n h a r m o n i c i t i e s i n t h e two d i r e c t i o n s a r e a p p r e c i a b l y d i f f e r e n t . sowever, we do n o t b e l i e v e t h i s can b e t h e complete s t o r y s i n c e a n N2 v a l u e of only 321 was o b t a i n e d from t h e lZ2* d a t a

Fig. 2: FT magnitude s p e c t r a of t h e

weighted d i f f e r e n c e ( x R ~ *

-

0 . 6 ~ ~ ~ ~ ) of t h e s i n g l e c r y s t a l Cd EXAFS a s a

A

LZ

-

f u n c t i o n of temperature. This s i g n a l

u approximates t h a t from b a c k s c a t t e r i n g

i n t h e R2 d i r e c t i o n only. The i n s e t shows t h e d i s t o r t e d hexagonal c l o s z

a packed s t r y c t u r e of Cd (R1 2.9738, R2 = 3.2918) and t h e d i r e c t ~ o n s of X-ray i n c i d e n c e f o r t h e two c r y s t a l o r i e n t a t i o n s s t u d i e d .

l . . . . I . . . . I . . . . I . . . . J 0

Radial Oistonce (A)

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C8-1081 JOURNAL DE

PHYSIQUE

a t 4K, where anharmonicity e f f e c t s on t h e EXAFS amplitudes should b e minimal.

The mean-square r e l a t i v e displacements ( ~ 0 ~ ) d e r i v e d from t h e curve f i t s f o r b o t h R1 and R2 components (measured r e l a t i v e t o t h e 4K v a l u e f o r t h e R1 component) a r e p l o t t - e d a s a f u n c t i o n of temperature i n Fig. 3. These v a l u e s a r e compared t o t h e v a l u e s of A I J ~ c a l c u l a t e d by t h e c o r r e l a t e d Debye model / 8 / w i t h Debye temperatures of 200K and 140K f o r t h e R1 and R2 components r e s p e c t i v e l y , which were chosen f o r b e s t f i t of t h e c a l c u l a t e d curve t o t h e d a t a . They a r e somewhat h i g h e r t h a n t h o s e of 164K and 107K c a l c u l a t e d from X-ray d i f f r a c t i o n /9/ b u t lower t h a n t h e v a l u e s of 214K and 160K o b t a i n e d from thermal expansion d a t a

/ l o / .

A t l e a s t some of t h e discrepancy between t h e c a l c u l a t e d and observed temperature dependence i s probably due t o t h e assumptions of no s t a t i c d i s o r d e r and s t r i c t l y harmonic motion. A well-known e f f e c t of a p p l y i n g an EXAFS a n a l y s i s based on a Gaussian d i s t r i b u t i o n t o systems w i t h a p p r e c i a b l e d i s o r d e r o r anharmonicity i s t o produce d i s t a n c e s t h a t d e c r e a s e w i t h i n c r e a s i n g temperature r a t h e r t h a n i n c r e a s i n g a s r e q u i r e d by thermal expansion /7/.

This e f f e c t i s observed i n t h e p r e s e n t a n a l y s i s g i v i n g c l e a r evidence t h a t t h e Cd-Cd p o t e n t i a l i s anharmonic. Neglect of anharmonicity i n EXAFS a n a l y s i s u n d e r e s t i m a t e s o a s w e l l a s R

I l l / .

Thus i f t h e a n a l y s i s was modified t o account f o r non-Gaussian d i s t a n c e d i s t r i b u t i o n s one would e x p e c t h i g h e r a v a l u e s . This would produce an even b e t t e r agreement w i t h t h e c o r r e l a t e d Debye model, s u g g e s t i n g t h a t t h e Debye tempera- t u r e s of Cd a r e lower t h a n we have e s t i m a t e d and a r e s i m i l a r t o t h e v a l u e s from X-ray d i f f r a c t i o n 191. Non-gaussian p a i r d i s t r i b u t i o n can be taken i n t o account i n a more r i g o r o u s a n a l y s i s by s e v e r a l approaches i n c l u d i n g cumulant a n a l y s i s o r by f i t s t o assumed models of t h e p a i r d i s t r i b u t i o n s . Analysis of our d a t a a l o n g t h e s e l i n e s i s p r e s e n t l y i n p r o g r e s s .

/6/ Rabe, P., Tolkiehn, G. and Werner, A., J. Phys. C: S o l i d S t a t e Phys.

12

(1979) 899.

I " ' . . ' ' . . . ' . . '

^J

/7/ Eisenberger, P. and Brown, G.S., Sol. S t . Comm.

2

(1979) 481.

/8/ Beni, G. and Platzman, P.M., Phys. Rev. B g (1976) 1514.

191 B r i n d l e y , ^G.W. and Ridley, P., Proc. Roy. Soc. (London)

51

(1939) 73.

/lo/

Owen, F.A. and Roberts, E.W., P h i l . Mag.

2

(1936) -290.

/11/ C r o z i e r , E.D. and Seary, A.J., Can. J. Phys.

58

(1980) 1388.

* O _

r.

2c 30-

" 7 .

5

1 ⁰ - R; d i r . Debye model of Beni and P l a t z -

" 20-

man /8/ c a l c u l a t e d f o r t h e

N known R1 and R2 d i s t a n c e s w i t h

l o L Debye temperatures of 200K and

140K r e s p e c t i v e l y .

0

- ^-

I . . . . I . . . . I -

0 100 200 300

Temperature (K)

REFERENCES

/ I / Weber, W.M., Phys. L e t t . A 2 (1967) 590.

/2/ Thulke, W. and Rabe, P., J. Phys. C: S o l i d S t a t e Phys.

16

(1983) L955.

/3/ Brown, G.S., Eisenberger, P. and Schmidt, P., Sol. S t a t e Comm.

3

(1977) 201.

/4/ Teo, B.K. and Lee, P.A., J. Am. Chem. Soc.

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(1979) 2815.

/5/ Lee, P.A., C i t r i n , P.H. Eisenberger, P. and Kincaid, B.M., Rev. Mod. Phys.

2

(1981) 769.

-

C ~ I

-

^single^crystal

R I R Z

• + - R; d l r .

Fig. 3: Temperature dependence of ha2 f o r R1 and of Cd metal o b t a i n e d from non-1 n e a r l e a s t

"2