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EXPERIMANTAL X-RAY RESONANT RAMAN STUDY OF NICKEL
S. Manninen, P. Suortti, M. Cooper, J. Chomilier, G. Loupias
To cite this version:
S. Manninen, P. Suortti, M. Cooper, J. Chomilier, G. Loupias. EXPERIMANTAL X-RAY RESO-
NANT RAMAN STUDY OF NICKEL. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-827-C9-
830. �10.1051/jphyscol:19879146�. �jpa-00227257�
JOURNAL D E PHYSIQUE
Colloque C9, supplement au n 0 1 2 , Tome 48, decembre 1987
EXPERIMANTAL X-RAY RESONANT RAMAN STUDY OF NICKEL
S. MANNINEN, P. SUORTTI, M.
J.COOPER* ,
J.CHOMILIER* * and G. L O U P I A S * * , * * *
Department of Physics, University of Helsinki, SF-00170 Helsinki, Finland
* ~ e p a r t m e n t of Physics, University of Warwick, GB-Coventry CV4 7AL, Great-Britain
**Laboratoire de Mineralogie-Cristallographie, UPMC, T 16, 4 , Place Jussieu, F-75252 Paris Cedex 0 5 , France
* * * L U R E , Bdt. 2090, Universite Paris-Sud, F-91405 Orsay Cedex France
RESUME
Les i n t e n s i t e s e t l e rendement d e d i f f u s i o n Raman o n t b t b mesur6s j u s t e en d e s s o u s d u s e u i l K du n i c k e l ,
l a
o c l e phbnomene d e v i e n t r 6 s o n n a n t . Le rayonnement s y n c h r o t r o n s t a v e r e B t r e une s o u r c e p e r f o r m a n t e p o u r d e t e l l e s e x p & r i e n c e s , e t d e s m e s u r e sa
h a u t e r b s o l u t i o n , a v e c un c r i s t a l a n a l y s e u r , p e r m e t t r o n t d ' o b t e n i r d e s i n f o r m a t i o n s s u r l a d e n s i t 6 d ' b t a t s .ABSTRACT
KL a n d KM Raman s c a t t e r i n g i n t e n s i t i e s have b e e n r e c o r d e d j u s t below t h s K a b s o r p t i o n e d g e o f n i c k e l , where t h e r e s o n a n c e o c c u r s , a n d t h e y i e l d h a s been d e t e r m i n e d . S y n c h r o t r o n r a d i a t i o n r e v e a l s t o b e a s u i t a b l e s o u r c e of p h o t o n s f o r t h i s s t u d y , a n d h i g h r e s o l u t i o n m e a s u r e m e n t s , w i t h a n a n a l y z i n g c r y s t a l , a r e e x p e c t e d t o p r o v i d e more i n f o r m a t i o n s a b o u t t h e d e n s i t y of s t a t e s .
KL o r KM r e s o n a n t Raman s c a t t e r i n g (RRS) o c c u r s when t h e e n e r g y of t h e i n c i d e n t x - r a y p h o t o n i s j u s t below t h e K a b s o r p t i o n t h r e s h o l d o f t h e t a r g e t . It p r o c e e d s by a v i r t u a l K - s h e l l h o l e i n t h e i n t e r m e d i a t e s t a t e t o a f i n a l s t a t e i n which t h e r e i s a n L - s h e l l o r M-shell h o l e , a n e l e c t r o n i n t h e continuum, and ar e m i t t e d p h o t o n . The p r o c e s s i s shown s c h e m a t i c a l l y i n F i g . 1. As t h e photon e n e r g y , ha1, a p p r o a c h e s t h e t h r e s h o l d K-shell b i n d i n g e n e r g y h a l s , t h e s c a t t e r e d i n t e n s i t y i n c r e a s e s a p p r o x i m a t e l y a s A E - ~ where AE = h ( Q l s
-
al)L Energy d i a g r a m of a KL r e s o n a n t Raman
ha2
s c a t t e r i n g . ha1 i s t h e i n c i d e n t photoni
e n e r g y . Qls and QZp a r e t h e 1s and 2p"01 b i n d i n g e n e r g i e s . The a v a i l a b l e e n e r g y - - -
1
- - - - - - - i s s h a r e d by t h e o u t g o i n g photon ( h a 2 )hw
and t h e e j e c t e d e l e c t r o n ( h a ) .The s p e c t r u m i s c o n t i n u o u s b e c a u s e t h e p h o t o n and t h e e l e c t r o n s h a r e t h e a v a i l a b l e e n e r g y , ha1- where hW2pdenotes t h e f i n a l h o l e e n e r g y . I n t e r m s of s e m i c l a s s i c a l r a d i a t i o n t h e o r y , t h e s c a t t e r i n g o c c u r s t h r o u g h t h e p.A t e r m i n s e c o n d o r d e r ( 1 , 2 ) , n o t t h e t e r m which a c c o u n t s f o r e l a s t i c , Compton and normal Raman s c a t t e r i n g ( 3 ) .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879146
C9-828 J O U R N A L D E PHYSIQUE
Above t h e t h r e s h o l d , where
w2
( o u t g o i n g p h o t o n e n e r g y ) h a s a L o r e n t z i a n d i s t r i b u t i o n c e n t e r e d a t n l s t h e i n t e g r a t e d c r o s s s e c t i o n d o l d n f o l l o w s t h e d e n s i t y o f s t a t e s a s a f u n c t i o n of t h e e n e r g y o f t h e e j e c t e d e l e c t r o n , h a , and d o t d n i s c o n v o l u t e d by t h i s L o r e n t z i a n of w i d t h T l s . If t h e d e n s i t y of s t a t e s were a s i m p l e s t e p f u n c t i o n , t h e c r o s s s e c t i o n a t AE=O would b e one h a l f t h a t f o r f u l l f l u o r e s c e n c e , i . e.
4x (dcr/dQKL = 0 . 5 ols
(als)
(1)w h e r e GIs
( a l s )
i s t h e K L c o n t r i b u t i o n t o t h e p h o t o e l e c t r i c a b s o r p t i o n c o e f f i c i e n t . When AE i s l a r g e r t h a n Tls t h e r e s o n a n t c r o s s s e c t i o n r e d u c e s t o a s i m p l e h y p e r b o l i c e x p r e s s i o n , andl-1 .7
(als
+w)
( d ~ ~ l d n ) ~ ~ = ols (nls+w) ( 2 )
E Z ~ A E
wls
The c r o s s s e c t i o n i s i n d e p e n d e n t of t h e s c a t t e r i n g a n g l e and t h e p o l a r i z a t i o n s t a t e of t h e i n c i d e n t beam i n t h i s n o n r e l a t i v i s t i c a p p r o x i m a t i o n (4).
We measured t h e r e s o n a n t Raman y i e l d - t h a t i s t h e r a t i o of x - r a y e m i s s i o r i n t h e KL a n d KM p r o c e s s e s t o a b s o r p t i o n - a s w e l l a s t h e a b s o l u t e c r o s s s e c t i o r t h r o u g h t h e t r a n s i t i o n from RRS t o x - r a y f l u o r e s c e n c e . P r e v i o u s measurements ( 5 ) o f t h e y i e l d h a v e b e e n r e s t r i c t e d t o c h a r a c t e r i s t i c x - r a y e n e r g i e s b u t s y n c h r o t r o n r a d i a t i o n i s t h e o b v i o u s s o u r c e f o r s u c h a s t u d y n o t o n l y b e c a u s e of i t s t u n e a b i l i t y b u t a l s o of i t s p o l a r i z a t i o n ; it means t h a t e l a s t i c a n d Compton s c a t t e r i n g c a n b e s u p p r e s s e d b y c h o o s i n g a s c a t t e r i n g a n g l e of 90' i n t h e s t o r a g e r i n g ' s o r b i t a l p l a n e . R a d i a t i o n from LURE-DCI was c o l l i m a t e d down t o a c r o s s s e c t i o n 0 . 5 mm h i g h b y 8 mm w i d e . The r e s o l u t i o n o f t h e ( 2 2 0 ) s i l i c o c c h a n n e l - c u t monochromator was 1 e V a t 8 kev and t h e f l u x was of t h e o r d e r of 1 0 ' p h o t o n s / s e c o n t o t h e n i c k e l s a m p l e s . An i o n i z a t i o n chamber m o n i t o r e d t h e i n c i d e n t beam and a n i n t r i n s i c s i l i c o n d e t e c t o r which had a r e s o l u t i o n of 170 eV a t 8 kev d e t e c t e d t h e s c a t t e r e d r a d i a t i o n . The s o l i d s t a t e d e t e c t o r h a d c o n s t a n t e f f i c i e n c y ( 1 0 0 % ) a c r o s s t h e i n c i d e n t e n e r g y r a n g e 8200-8350 eV ( t h e N i K - a b s o r p t i o n edge i s c e n t e r e d a t 8333 e V ) . The e n e r g y s t e p was 1 eV j u s t arounc t h e a b s o r p t i o n t h r e s h o l d and 250 s e c were s u f f i c i e n t t o a c c u m u l a t e a p p r o x i m a t e l y
l o 5
c o u n t s u n d e r t h e KL and KM l i n e s . The e n e r g y s c a l e was c o m p l e t e d by measuring t h e n i c k e l a b s o r p t i o n e d g e , g i v i n g a n a c c u r a c y b e t t e r t h a n 0 . 5 eV t o t h e p o s i t i o n of t h e t h r e s h o l d e n e r g y .T h r e e s a m p l e s w e r e s t u d i e d : a (100) s i n g l e c r y s t a l s l i c e , a powder d i s c , b o t h " t h i c k " a n d measured i n symmetric r e f l e c t i o n , a n d a 2 5 p n p o l y c r y s t a l l i n e f o i l f o r s y m m e t r i c t r a n s m i s s i o n . T h r e e t y p i c a l s p e c t r a a r e r e p r o d u c e d f o r i l l u s t r a t i o n i n F i g . 2 . Two f e a t u r e s a r e r e a d i l y e v i d e n t ; f i r s t l y t h e r a p i d i n c r e a s e of i n t e n s i t y a s t h e i n c i d e n t e n e r g y a p p r o a c h e s t h e Is b i n d i n g e n e r g y and s e c o n d l y t h e s h i f t of t h e RRS peak, a s i t s maximum v a l u e i s w l - n 2 p , t o w a r d s t h e l i m i t i n g K - f l u o r e s c e n c e e m i s s i o n e n e r g y a t t h e t h r e s h o l d .
The i n t e g r a t e d i n t e n s i t i e s c a n n o t b e u s e d d i r e c t l y t o c a l c u l a t e t h e KM:KL r a t i o o r t h e r e s o n a n t Raman y i e l d b e c a u s e t h e y may i n c l u d e o t h e r s p u r i o u s s c a t t e r i n g c o n t r i b u t i o n s u c h a s e l a s t i c s c a t t e r i n g , o r N i f l u o r e s c e n c e e x c i t e d by t h e f i r s t harmonic of t h e monochromator. Some c o n t r i b u t i o n t h r o u g h t h e t e r m i s p o s s i b l e ; f i r s t l y , t h e beam i s n o t 100% p o l a r i z e d , a n d s e c o n d l y , t h e a n g u l a r a p e r t u r e of t h e d e t e c t o r a l l o w s some s c a t t e r i n g of t h e p a r a l l e l p o l a r i z a t i o n . The KM l i n e i s n o t s e p a r a t e l y r e s o l v e d from t h e TDS ( t h e r m a l d i f f u s e s c a t t e r i n g ) by t h e s o l i d s t a t e d e t e c t o r (Q2p=120 e V ) . F o r t u n a t e l y t h e e n e r g y v a r i a t i o n of TDS i n n i c k e l a t x - r a y e n e r g i e s i s w e l l known ( 6 ) ; t h e r e f o r e it was measured a t lower e n e r g i e s where t h e r e i s no RRS i n t e n s i t y and t h e r e s u l t e x t r a p o l a t e d t o t h e range o f i n t e r e s t . At 10 eV below t h e f l u o r e s c e n c e t h r e s h o l d TDS c o n t r i b u t e s a few p e r c e n t t o t h e measured KM i n t e n s i t y . I t i s e v i d e n t from F i g . 2 t h a t t h e r e s o n a n t Raman l i n e s w i l l o v e r l a p a n y f l u o r e s c e n c e e m i s s i o n s e x c i t e d i n t h e t a r g e t by monochromator h a r m o n i c s . The f l u o r e s c e n t i n t e n s i t i e s were d e t e r m i n e d a t s e v e r a l e n e r g i e s i n t h e r a n g e 7000 (RRS n e g l i g i b l e ) t o 8000 eV ( t h e c o n t r i b u t i o n s a r e s e p a r a b l e ) a n d t h e n e x t r a p o l a t e d t o t h e measurement r a n g e , t a k i n g i n t o account
F i g . 3 . K - s h e l l c o n t r i b u t i o n t o t h e a b s o r p t i o n c o e f f i c i e n t of N i . F i g . 2 . KL-RRS s p e c t r a of n i c k e l w i t h Experiment (open c i r c l e s ) , and
d i f f e r e n t i n c i d e n t e n e r g i e s ; c a l c u l a t e d from t h e d e n s i t y of
7700, 8250 and 8300 e v . 2p s t a t e s ( 9 )
t h e v a r i a t i o n of sample a b s o r p t i o n and s o u r c e f l u x w i t h e n e r g y . The c o n t r i b u t i o n t o e a c h RRS peak was a few p e r c e n t a t 10 eV below t h e t h r e s h o l d .
The h o l e i n t h e K - s h e l l c a n b e f i l l e d w i t h o u t t h e e m i s s i o n of a photon, t h r o u g h t h e c o m p e t i n g Auger p r o c e s s . I f ( d d d n ) , i s t h e K - s h e l l p h o t o e l e c t r i c a b s o r p t i o n c r o s s s e c t i o n , t h e n t h e r e s o n a n t Raman y i e l d WRRS i s s i m p l y t h e r a t i o :
oRRs
= ( d ~ f d n ) , ~ / ( d d d ~ ) ~ ( 3 )The y i e l d c a n b e e x p r e s s e d i n t e r m s o f t h e i n c i d e n t , n i , a n d s c a t t e r e d , n,, p h o t o n f l u x e s , i n t h e c a s e of a t h i c k sample i n r e f l e c t i o n :
s ~ R R S P K ( ~ ~ )
where K K ( w l ) i s t h e K - s h e l l a b s o r p t i o n c o e f f i c i e n t , p ( a l ) a n d ~ ( 0 ) ~ ) a r e t h e t o t a l a t t e n u a t i o n c o e f f i c i e n t s f o r t h e incoming and o u t g o i n g beams. Thus t h e y i e l d can b e c a l c u l a t e d w i t h an a c c u r a c y d e p e n d e n t upon t h e d e t e r m i n a t i o n of t h e i n c i d e n t f l u x and t h e u n c e r t a i n t y i n t h e a b s o r p t i o n c o e f f i c i e n t s . I n t h i s a n a l y s i s t h e f o r m e r of t h e s e problems was c i r c u m v e n t e d by m e a s u r i n g t h e f l u o r e s c e n c e i n t e n s i t y a t s e v e r a l e n e r g i e s j u s t above t h e t h r e s h o l d a n d u s i n g t h e f a c t t h a t t h e f l u o r e s c e n c e y i e l d ,
w K ,
i s a w e l l d e t e r m i n e d q u a n t i t y . The a t t e n u a t i o n c o e f f i c i e n t s where d e d u c e d from a measurement o f t h e i n t e n s i t y t r a n s m i t t e d t h r o u g h a 6 pn n i c k e l f o i l a s t h e monochromator was s c a n n e d between 8100 and 8400 e v . The v a l u e s g i v e n i n t h e I n t e r n a t i o n a l t a b l e s f o r x - r a y c r y s t a l l o g r a p h y were u s e d a s r e f e r e n c e s ( 7 ) . The r e s u l t s a r e n o t s e n s i t i v e t o t h e c h o i c e s o f t h e r e f e r e n c e v a l u e s a s l o n g a s t h e s e v a l u e s a r e c o m p a t i b l e . The measured v a l u e 0 . 4 3 2 + 0 . 0 0 6 ( 2 ) a g r e e s w e l l w i t h a c a l c u l a t e d v a l u e o f 0 . 4 3 3 b a s e d upon a H a r t r e e - F o c k - S l a t e r (HFS) c a l c u l a t i o n ( 8 ).
B e f o r e t h e K - s h e l l a b s o r p t i o n c r o s s s e c t i o n c a n b e a n a l y z e d , t h e c o n t r i b u t i o n o f t h e h i g h e r s h e l l s must b e s u b t r a c t e d from t h e measured t o t a l
C9-830 JOURNAL
DE
PHYSIQUEa b s o r p t i o n c o e f f i c i e n t . The s u b t r a c t i o n i s b a s e d on a n e x t r a p o l a t i o n from t h e t a b u l a t e d v a l u e s t h a t d o n o t i n c l u d e t h e e f f e c t s of t h e r e s o n a n t s c a t t e r i n g below t h e K e d g e , b u t f o l l o w a s i m p l e power l a w . The r e s u l t i n g e x p r e s s i o n f o r t h e h i g h e r s h e l l c o n t r i b u t i o n i s :
(p/p),,, = 48.83 (8041 ~ v / E ) ~ - ~ ~ cm2g-1 ( 5 )
The r e s u l t of s u b t r a c t i o n , i . e . t h e K - s h e l l c o n t r i b u t i o n t o t h e a b s o r p t i o r c o e f f i c i e n t , i s shown i n F i g . 3 . Below t h e a b o r p t i o n edge, t h e v a l u e s a r e l a r g e r t h a n t h o s e d u e t o t h e s t e p (pKlp)= 90 cm2g-l a t AE=O, which i s i n f e r r e d from t h e d e n s i t y o f p s t a t e s , c a l c u l a t e d from n u m e r i c a l i n t e g r a t i o n b a s e d on d a t a from r e f 9, b u t f o l l o w c l o s e l y t h e c u r v e a f t e r t h e e f f e c t of t h e d e n s i t y of p s t a t e s above t h e e d g e i s t a k e n i n t o a c c o u n t . The y i e l d a n d t h e KL:KM r a t i o were t h e n c a l u c l a t e d a n d t h e r e s u l t s were t r a n s f o r m e d i n t o t h e s c a t t e r i n g c r o s s s e c t i o n u s i n g e q . ( 3 ) .
The r a d i a t i v e y i e l d f i r s t i n c r e a s e s s l i g h t l y when t h e i n c i d e n t e n e r g y d e c r e a s e s below t h e t h r e s h o l d e n e r g y , b u t f r o m a b o u t AE=-15 eV t h e y i e l d f a l l s s t e a d i l y w i t h AE. U n f o r t u n a t e l y , t h e u n c e r t a i n t i e s o f t h e measurement a r e t o c l a r g e t o a l l o w f i r m c o n c l u s i o n s . A s m a l l d r i f t i n t h e e n e r g y s c a l e ( a b o u t 0 . 2 eV) i s enough t o c a u s e t h e a p p a r e n t i n c r e a s e o f W K between +5 a n d -10 eV, and d e p e n d s c r i t i c a l l y on t h e c o r r e c t n e s s o f t h e s u b t r a c t i o n o f t h e h i g h e r s h e l l s c o n t r i b u t i o n from t h e measured (p/p).
T h e r e a r e no t h e o r e t i c a l c a l c u l a t i o n s of WRRS, a n d no o b v i o u s r e a s o n why t h e v a l u e f o r f l u o r e s c e n c e , aK, s h o u l d p r e v a i l f a r below t h e K e d g e . The need of r e l i a b l e e x p e r i m e n t a l d a t a i s t h e r e f o r e e v i d e n t . The q u a l i t y o f t h e p r e s e n t d a t a c o u l d b e improved i n v a r i o u s ways. R a d i a t i o n from a m u l t i p o l e w i g g l e r i s l i n e a r l y p o l a r i z e d a l s o o u t s i d e t h a t from a b e n d i n g magnet s o u r c e . The u s e of a S i (311) monochromator would make t h e harmonic c o n t a m i n a t i o n a l m o s t n e g l i g i b l e and a l s c i m p r o v e t h e e n e r g y r e s o l u t i o n . The K - s h e l l a b s o r p t i o n c r o s s s e c t i o n c a n b e s e p a r a t e d f r o m t h e t o t a l a t t e n u a t i o n c o e f f i c i e n t , i f t h e measurements c o v e r a s u f f i c i e n t l y l a r g e e n e r g y r a n g e below t h e K e d g e . T h e o r e t i c a l v a l u e s o f ( p / ~ ) ~ can b e c a l c u l a t e d , if t h e d e n s i t y of 2 p s t a t e s a n d t h e t r a n s i t i o n p r o b a b i l i t i e s a r e known. The c o n t r i b u t i o n of RRS t o t h 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 l a r g e i n t h e i m m e d i a t e n e i g h b o r h o o d o f t h e a b s o r p t i o n t h r e s h o l d a n d it i s i m p o r t a n t t c e s t a b l i s h w h e t h e r t h e s i m p l e t h e o r y d e v e l o p e d h e r e i s v a l i d i n o t h e r m a t e r i a l s w i t h d i f f e r e n t d e n s i t i e s of s t a t e s . I t i s e x p e c t e d t h a t h i g h r e s o l u t i o n s t u d i e s o f t h e s p e c t r a l d i s t r i b u t i o n c u r r e n t l y b e i n g p l a n n e d w i l l y i e l d much more i n f o r m a t i o n a b o u t t h e r e s o n a n t Raman s c a t t e r i n g p r o c e s s . I t i s a l s o l i k e l y t h a t h i g h - r e s o l u t i o n s t u d i e s w i l l r e v e a l a s t r u c t u r e s i m i l a r t o EXAFS phenomena due t c t h e b a c k s c a t t e r i n g of t h e e j e c t e d e l e c t r o n s . I n t h e f i r s t measurement u s i n g a c u r v e d c r y s t a l s p e c t r o m e t e r w i t h a m o d e r a t e r e s o l u t i o n (20 eV a t Cu K a ) , t h e s e t y p e s o f o s c i l l a t i o n s a r e r e a l l y s e e n ( 1 0 ) . C o r r e l a t i o n e f f e c t s a r e a l s o p o t e n t i a l l y i m p o r t a n t i n t h i s t w o - e l e c t r o n p r o c e s s .
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