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TRANSFERABILITY OF SCATTERING
AMPLITUDES AND PHASES IN EXAFS BETWEEN NEIGHBORING ELEMENTS IN THE PERIODIC
TABLE
B. Lengeler
To cite this version:
B. Lengeler. TRANSFERABILITY OF SCATTERING AMPLITUDES AND PHASES IN EXAFS
BETWEEN NEIGHBORING ELEMENTS IN THE PERIODIC TABLE. Journal de Physique Col-
loques, 1986, 47 (C8), pp.C8-75-C8-78. �10.1051/jphyscol:1986812�. �jpa-00226018�
JOURNAL DE PHYSIQUE
Colloque C8, suppl6ment au n o 12, Tome 47, d6cembre 1986
TRANSFERABILITY OF SCATTERING AMPLITUDES AND PHASES IN EXAFS BETWEEN NEIGHBORING ELEMENTS IN THE PERIODIC TABLE
B. LENGELER
Kernforschungsanlage Jiilich, I F F , Postfach 1913, 0-5170 Julich, F.R.G.
Abstract.-
M o d e l compounds c a n b e u s e d f o r EXAFS d a t a a n a l y s i s when t h e a b s o r b e r a n d b a c k s c a t t e r e r a r e n e i g h b o r i n g e l e m e n t s i n t h e p e r i o d i c t a b l e t o t h e a b s o r b e r and b a c k s c a t t e r e r s o f t h e s y s t e m t o be a n a l y s e d . The e r r o r s A r i n t h e i n t e r a t o m i c d i s t a n c e s a r e s m a l l and l i n e a r i n t h e d i f f e r e A c e AZ i n t h e a t o m i c numbers.
The b a c k s c a t t e r i n g a m p l i t u d e s and s c a t t e r i n g p h a s e s needed f o r d e t e r m i n i n g i n t e r a t o m i c d i s t a n c e s a n d c o o r d i n a t i o n numbers by EXAFS c a n e i t h e r be c a l c u l t a t e d o r t h e y c a n b e t a k e n f r o m m o d e l s y s t e m s /1,2/. The t r a n s f e r o f t h e a m p l i t u d e s and p h a s e s f r o m
a w e l l c h o s e n model t o t h e s y s t e m t o b e a n a l y z e d r e d u c e s c o r ~ s i d e r a b l y t h e i n f l u e n c e o f s y s t e m a t i c e r r o r s i n t h e d a t a a n s l y s i s . F o r
i n s t a n c e , o r d e r e d Cu Au i s a n e x c e l l e n t m o d e l f o r a d i l u t e CgAu a l l o y i n w h i c h t h e l J t t i c e d i s t o r t i o n a r o u n d t h e Au atoms s h o u l d b e d e t e r m i n e d , because t h e t w o s y s t e m s a r e c h e m i c a l l y v e r y s i m i l a r . U n f o r t u n a t e l y , t h e r e i s a g r e a t number o f a b s o r b e r - b a c k s c a t t e r e r p a i r s f o r w h i c h t h e r e e x i s t s n o a p p r o p r i a t e models. T h i s i s t r u e f o r t h o s e p a i r s w h i c h f a r m no o r d e r e d compounds a t a l l ('eg f o r Pd-Au) o r w h e r e none o f t h e compounds f o r m e d h a s w e l l d e f i n e d n e i g h b o r i n g s h e l l s ( o n e t y p e o f n e i g h b o u r s a t a w e l l d e f i n e d d i s t a n c e w e l l s e p a r a t e d f r o m o t h e r s h e l l s ) . An example o f t h e
s e c o n d g r o u p i s A 1 - C U . The q u e s t i o n now a r i s e s , u n d e r w h a t c o n d i t i o n s c a n m o d e l compounds b e chosen among e l e m e n t s w h i c h a r e n e i g h b o r s i n t h e p e r i o d i c t a b l e t o t h e a b s o r b e r A and t h e b a c k s c a t t e r e r B u n d e r c o n s i d e r a t i o n . F o r i n s t a n c e , c a n N i A l (CsC1 s t r u c t u r e ) be a m o d e l f o r d i l u t e QCu a n d c a n A u I n 2 (CaF s t r u c t u r e ) be a m o d e l f o r X A u ? T h i s p a p e r i s a b r i e f r e p o r ? on a d e t a i l e d i n v e s t i g a t i o n aimed a t d e t e r m i n i n g t h e e r r o r s A r l i n t h e n e x t
n e i g h b o r i n t e r a t o m i c d i s t a n c e r when t h e a b s o r b e r a n d b a c k s c a t t e r e r i n t h e m o d e l a r e n o t i d e n t i c a l d i t h t h e a b s o r b e r a n d b a c k s c a t t e r e r i n t h e s y s t e m t o be i n v e s t i g a t e d . Three g r o u p s o f s y s t e m s h a v e been z n a l y s e d : ( I ) t h o s e w i t h i d e n t i c a l b a c k s c a t t e r e r s b u t d i f f e r e n t a b s o r b e r s , ( 1 1 ) t h o s e w i t h i d e n t i c a l a b s o r b e r s b u t d i f f e r e n t
b a c k s c a t t e r e r s and ( 1 1 1 ) t h o s e w i t h d i f f e r e n t a b s o r b e r s and b a c k - s c a t t e r e r s .
T a b l e 1 g i v e s a l i s t c f t h e s y s t e m s i n v e s t i g a t e d .
The EXAFS s p e c t r a w e r e measured i n t r a n s m i s s i o n a t 77 K a t t h e Hamburger S y n c h r o t r o n s t r a h l u n g s l a b o r . S i ( 1 1 1 ) and S i ( 3 1 1 ) d o u b l e c r y s t a l n o n o c h r o m a t o r s w e r e used. Eo was c h o s e n a t t h e f i r s t i n f l e c t i o n p o i n t o f t h e a b s o r p t i o n edge. The c o n t r i b u t i o n o f t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986812
C8-76 JOURNAL DE PHYSIQUE
f i r s t s h e l l was s e p a r a t e d b y a window f u n c t i o n i n F o u r i e r space.
I n t e r a t o m i c d i s t a n c e s a n d c o o r d i n a t i o n numbers w e r e d e t e r m i n e d by means o f a n o n - l i n e a r l e a s t s q u a r e f j t t i n g 2 r o u t i n e . F o r i n s t a n c e , t h e f i r s t s h e l l c o n t r i b u t i o n i n t h e EXAFS X k o f GdPd
,
DyPdE r P d 3 a n d H f P d 3 w e r e f i t t e d w i t h t h e a m p l i t u d e s a n d p h J s e s e x z i a c t e d
absorber backscatterer systems
(a
A Z
I. Pt, Au A1 PtA12, AuA12 0.008
Mn, Fe, Ni, Zn S MnS, FeS2, NiS2, ZnS 0.007
Y, Zr S YS, ZrS2 0.006
Fe, Ni, Ge, As N i FeNi3, Ni, GeNi3, AsNi 0.007
Gd, Tb, Dy Ga GdGa2, TbGa2, DyGa
2 0.005
Er, Lu Se ErSe, LuSe 0.007
Gd, Dy, Er, Lu, Hf Pd
Al, S i Al, S Al, S Ga, Se, Y Ga, Se Y, Pd, I n Rh, Pd Tb, Ho, Er
-
YGa2, YSe, YH2 ErGa2, ErSe YH2, YPd3, YIn3 ZrRh3, ZrPd3 BiTb, BiHo, BiEr
111. Co, Ni, Cu, Ge Cc, Ni, Cu, Ge Co, Ni, Cu, Ge 0.011
Rh, Pd, Ag Rh, Pd, Ag Rh, Pd, Ag 0.011
Pt, AU Ni, Cu PtNi3, AuCu3 0.021
Y, Zr Rh, Pd YPd3, ZrRh3 0.008
T a b l e 1: Systems w i t h i d e n t i c a l b a c k s c a t t e r e r s ( I ) , w i t h i d e n t i c a l a b s o r b e r s ( 1 1 ) a n d w i t h d i f f e r e n t a b s o r b e r s a n d b a c k s c a t t e r e r s
( 1 1 1 ) . E r r o r s A r l i n t h e i n t e r a t o m i c d i s t a n c e p e r A Z = 1.
f r o m LuPd3. I n t h e s e c a s e s t h e f i t s w e r e e x c e l l e n t as a c o r ~ s e q u e n c e o f t h e s e s y s t e m s h a v i n g a l l t h e same b a c k s c a t t e r e r ( P d ) . The
e r r o r s A r i n t h e f i r s t i n t e r a t o m i c d i s t s n c e rl a r e g i v e n i n f i g u r e 1 . l ~ o r in s t a n c e , when a n a l y z e d w i t h t h e a m p l i t u d e s a n d p h a s e s t a k e n f r o m LuPd3 t h e f i r s t i n t e r a t o m i c d i s t s n c e Dy-Pd i n . D y P d 3 comes o u t t o o s m a l l i n t h e f i t b y 0.022
8
c o m p a r e d t ot h e r e s u l t known f r o m X - r a y d i f f r a c t i o n . N o t e t h e l i n e a r d e p e n d e n c e o f t h e e r r o r a r l o n AZ o v e r a w i d e r a n g e i n t h e v a r i a t i o n o f
t h e a t o m i c n u m b e r Z o f t h e a b s o r b e r . N o t e a l s o t h a t t h e e r r o r s a r e s m a l l a t a n a b s o l u t e s c a l e , b e i n c ; o n l y 0 . 0 0 5
a
p e r A Z = 1.We e x p e c t l a r g e r e r r o r s i n r w h e n t h e b a c k s c a t t e r e r s d i f f e r f r o m o n e a n o t h e r ( g r o u p I 1 a n 8 1 1 1 ) , b e c a u s e now p h a s e s a n d
a m p l i t u d e s a r e d i f f e r e n t i n t h e m o d e l a n d t h e s y s t e m t o b e a n a l y z e d . T h i s i s c o n f i r m e d b y t h e r e s u l t s q u o t e d i n t a b l e 1. A g a i n t h e e r r o r s a r l i n r a r e l i n e a r i n A Z a s s h o w n i n f i g u r e 1 f a r BiHo a n d B i E r a n e l y z e a w i t h t h e a m p l i t u d e s a n d p h a s e s d e r i v e d f r o m B i T b a n d f o r Co, N i a n d Ge a n a l y z e d w i t h t h e a m p l i d u d e s a n d p h a s e s d e r i v e d f r o m m e t a l l i c Cu. I t t u r n e d o u t t h a t t h e e r r o r A r i s n e g a t i v e when t h e a b s o r b e r o r t h e b a c k s c a t t e r e r i n t h e s y A t e m t o b e i n v e s t i g a t e d h a v e l o u e r a t o m i c n u m b e r Z ( i . e . AZ < 0 ) t h a n t h e c o r r e s p o n d i n g a b s o r b e r o r b a c k s c a t t e r e r i n t h e m o d e l .
We h a v e a l s o i n v e s t i g a t e d t h e e r r o r s i n d u c e d i n t h e c o o r d i n a t i o n n u m b e r N l o f t h e f i r s t s h e l l w h e n a b s o r b e r a n d b a c k s c a t t e r e r
i n t h e m o d e l a n d t h e s y s t e m t o b e a n a l y z e d d i f f e r f r o m o n e a n o t h e r .
F i g . 1
E r r o r s A r l i n t h e f i r s t i n t e r - a t o m i c d i s t a n c e r l v e r s u s A Z f o r ( I ) s y s t e m s w i t h i d e n t i c a l b a c k s c a t t e r e r s ( P d ) , f o r ( 1 1 ) s y s t e m s w i t h i d e n t i c a l a b - s o r b e r s ( B i ) a n d f o r ( 1 1 1 ) s y s t e m s w i t h d i f f e r e n t a b s o r b e r s a n d b a c k s c a t t e r e r s . F o r i n - s t a n c e , t h e EXAFS o f G d P d j a t t h e Gd L 3 e d g e h a v e b e e n a n a l y z e d w i t h t h e p h a s e s a n d a m p l i t u d e s e x t r a c t e d f r o m L u P d j .
I t i s w e l l known t h a t t h e e r r o r s i n t h e c o o r d i n a t i o n n u m b e r s a r e much l a r g e r t h a n t h o s e i n t h e d i s t a n c e s . T h i s i s t r u e h e r e t o o , e s p e c i a l l y when p o w d e r e d s a m p l e s a r e u s e d . On t h e o t h e r h a n d we h a v e o b t a i n e d v e r y s a t i s f a c t o r y r e s u l t s f o r f o i l s . T h e s i g n a l f r o m a Ag f o i l w a s a n a l y z e d w i t h Rh a n d Pd a s m o d e l . A l l t h r e e m e t s l s h a v e f c c s t r u c t u r e w i t h 1 2 n e a r e s t n e i g h b o u r s . T h e r e s u l t s o f t h e f i t s a r e g i v e n i n t a b l e 2
JOURNAL DE PHYSIQUE
m o d e l f o r Ag R h P d
A z
-
2-
1Ag: N1 -.0.9 12.1
T a b l e 2 C o o r d i n a t i o n n u m b e r N a n d D e b y e - W a l l e r f a c t o r 6 0 1 i n Ag 2 a n a l y z e d w i t h Rh a n d h d a s m o d e l .
The r e s u l t s a r e n o t a l w a y s a s s a t i s f a c t c r y a s i n t h i s c a s e , e s p e c i a l l y f o r l i g h t e l e m e n t s a s b a c k s c a t t e r e r s . T h e r e s u l t s o f t h e p r e s e n t i n v e s t i g a t i o n c a n b e s u m m a r i z e d a s f o l l o w s . 1. Due t o t h e weak d e p e n d e n c e o f t h e s c a t t e r i n g a m p l i t u d e s a n d p h a s e s o n t h e a t o m i c n u m b e r Z , m o d e l c o m p o u n d s f o r t h e EXAFS a n a l y s i s c a n b e u s e d i n w h i c h t h e a b s o r b e r a n d b a c k s c a t t e r e r s a r e n e i g h b o u r i n g e l e m e n t s i n t h e p e r i o d i c t a b l e t o t h o s e o f t h e s y s t e m t o b e a n a l y z e d .
2. T h e e r r o r A r i n t h e i n t e r a t ~ m i c d i s t a v c e i s s m a l l a n d l i n e a r i n ~ - 2 l a n d car! e a s i l y b e c o r r e c t e d ( t a b l e 1 )
3. I f p o s s i b l e , t h e m o d e l s h o u l d h a v e t h e same t y p e o f b a c k - s c a t t e r e r a s t h e s y s t e m t o b e a n a l y z e d . I n t h i s c a s e t h e e r r o r i s l i m i t e d t o t h e s c a t t e r i n g p h a s e . T h i s i s e s p e c i a l l y i m p o r t a n t i n t w o - s h e l l f i t s b e c a u s e t h e e r r o r s i n t h e f i t p a r a m e t e r s f o r t h e f i r s t s h e l l t e n d t o g e n e r a t e e r r o r s i n t h e p a r a m e t e r s o f t h e s e c o n d s h e l l , e v e n i f a c o r r e c t m o d e l ( w i t h AZ = 0 ) i s c h o s e n f o r t h e s e c o n d s h e l l c o n t r i b u t i o n .
4. T h e t r a n s f e r a b i l i t y o f p h a s e s a n d a m p l i t u d e s b e t w e e n n e i g h b o r i n g e l e m e n t s i n t h e p e r i o d i c t a b l e e n l a r g e s c o n s i d e r a b l y t h e u s e o f m o d e l c o m p o u n d s i n EXAFS d a t a a n a l y s i s .
REFERENCES
/I/ LEE, P.A., C I T R I N , P.H., EISENBERGER, P.9 K I N C A I D , B - M - , Rev. Mod. P h y s . 53, 7 6 9 ( 1 9 8 1 )
/ 2 / STERN, E.A., HEALD, S.M., i n H a n d b o o k o f S y n c h r o t r o n R a d i a t i o n ed. KOCH, E.E., N o r t h H o l l a n d ' ( 1 9 8 3 ) p 955.
