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 Colloques, 1986, 47 (C8), pp.C8-75-C8-78. <10.1051/jphyscol:1986812>. <jpa00226018>
HAL Id: jpa-00226018
https://hal.archives-ouvertes.fr/jpa-00226018
Submitted on 1 Jan 1986
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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, IFF, 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
and 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 elements 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 .
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
The e r r o r s 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 influence o f systematic errors i n t h e data anslysis. For
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 (one type o f neighbours 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 A1-CU.
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 next
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 model a r e n o t i d e n t i c a l d i t h t h e absorber and 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
absorbers, (11) those w i t h i d e n t i c a l absorbers 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 scatterers.
Table 1 g i v e s a l i s t c f t h e systems 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
JOURNAL DE PHYSIQUE
C8-76
f i r s t s h e l l was s e p a r a t e d by 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 ,
DyPd
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
ErPd3 and HfPd3 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 and p h J s e s e x z i a c t e d
,
absorber
backscatterer
systems
AZ
I.
(a
Pt, Au
A1
PtA12, AuA12
0.008
Mn, Fe, Ni, Zn
S
MnS, FeS2, NiS2, ZnS
0.007
Y,
S
YS, ZrS2
0.006
Fe, Ni, Ge, As
Zr
Ni
FeNi3, Ni, GeNi3, AsNi
0.007
Gd, Tb, Dy
Ga
0.005
Er, Lu
Se
GdGa2, TbGa2, DyGa
2
ErSe, LuSe
Gd, Dy, Er, Lu, Hf
Pd
0.007
Al, S i
111.
Al,
S
Al,
S
-
Ga, Se, Y
YGa2, YSe, YH2
Ga, Se
ErGa2, ErSe
Y,
YH2, YPd3, YIn3
Pd, I n
Rh, Pd
ZrRh3, ZrPd3
Tb, Ho, Er
BiTb, BiHo, BiEr
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,
Rh, Pd
YPd3, ZrRh3
0.008
Zr
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 ) and 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
errors 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 i n 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
phases 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 by 0.022 8 compared t o
t 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 number 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 , beinc; o n l y 0.005
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 when 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 model a n d t h e system t o be 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
and BiEr anelyzea with t h e amplitudes and phases derived from
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 model.
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
number N l o f t h e f i r s t s h e l l when 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 model and t h e system t o b e a n a l y z e d d i f f e r from o n e a n o t h e r .
a
Fig. 1
E r r o r s A rl i n t h e f i r s t i n t e r atomic d i s t a n c e rl v e r s u s A Z
f o r ( I ) systems with i d e n t i c a l
backscatterers (Pd), f o r (11)
s y s t e m s w i t h i d e n t i c a l abs o r b e r s ( B i ) and f o r (111)
systems with different absorbers
and b a c k s c a t t e r e r s . For ins 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
analyzed with t h e phases
and amplitudes e x t r a c t e d
f r o m LuPdj.
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 have 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 . The
r e s u l t s of t h e f i t s a r e given i n table 2
JOURNAL DE PHYSIQUE
m o d e l f o r Ag
A
Ag:
z
N1
Rh
-2
-.0.9
Pd
1
-
12.1
T a b l e 2 C o o r d i n a t i o n number N a n d D e b y e - W a l l e r
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 .
2
f a c t o r 6 0 1 i n Ag
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 . The 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 be summarized as 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 compounds 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
backscatterers a r e neighbouring elements i n t h e p e r i o d i c
t a b l e t o those o f t h e system t o b e analyzed.
2. The e r r o r A r
i n t h e i n t e r a t ~ m i cd 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 dcar! 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 system t o b e analyzed. I n t h i s case 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 phase. 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 because t h e e r r o r s i n t h e f i t
parameters f o r t h e f i r s t s h e l l t e n d t o generate e r r o r s i n
t h e parameters o f t h e second s h e l l , even i f a c o r r e c t model
( 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. The 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
elements i n t h e p e r i o d i c t a b l e enlarges considerably t h e use
o f m o d e l compounds i n EXAFS d a t a a n a l y s i s .
REFERENCES
LEE, P.A.,
Rev. Mod.
/I/
/2/
C I T R I N , P.H.,
EISENBERGER,
Phys. 53, 7 6 9 ( 1 9 8 1 )
P.9
KINCAID,
B-M-,
STERN, E.A.,
HEALD, S.M.,
i n Handbook 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.