HAL Id: jpa-00227329
https://hal.archives-ouvertes.fr/jpa-00227329
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 pub- lished 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.
THE APPLICATIONS OF ANOMALOUS
DIFFRACTION IN POWDER DIFFRACTOMETRY
M. Laridjani, J. Sadoc
To cite this version:
M. Laridjani, J. Sadoc. THE APPLICATIONS OF ANOMALOUS DIFFRACTION IN POW- DER DIFFRACTOMETRY. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-1141-C9-1145.
�10.1051/jphyscol:19879209�. �jpa-00227329�
JOURNAL DE PHYSIQUE
Colloque C9, suppl6ment au n012, Tome 48, d6cembre 1987
THE APPLICATIONS OF ANOMALOUS DIFFRACTION I N POWDER DIFFRACTOMETRY
M. LARIDJANI and J.F. SADOC*
LURE, Bat. 2090, Universite Paris-Sud, F-91405 Orsay Cedex, France
'~aboratoire de Physique des Solides, Bdt. 510, Universite Paris-Sud, F-91405 Orsay Cedex, France
An atom scatters X-ray with an amplitude and a phase that can be represented by the complex number ; ftof (K,E) = fo (K)
+
f' (K,E)+if" (K, E)
.
fo(K) represents the atomic scattering factor for the radiations with frequencies smaller than the absorption edge frequencies. The anomalous scattering terms f' and f", which are functions of the wavelength, describe the in-phase an out phase components of the change due to finite binding energies of the electrons .in the atom. Near an absorption edge of an atom, where the x-ray energy is close to the binding energy of an inner shell electron both f' and f" vary rapidly with wavelength
,
f" jumps rapidly up to a maximum while f' dips and then rises again as the x-ray energy goes from below the edge to above it. The f" term results in breaking of Friedel's law, this effect has long been used to find the solution of the crystallographic phase problem. Very few applications were performed to show the useful aspect of anomalous dispersion on the powder dif f ractometry.
Even though the principle is simple and straight forword the implementation was not a trivia tasK. The main difficulty was to obtain reliable data. As the energy dependence of diffraction intensity is usually small then a very high accurancy of measurments were required. The recent availability of synchrotron radiation as a tunable source of x-ray, with very high intensity made it possible to use this effect to obtain structural information from a powder diffractometry. For this purpose a powder automated diffractometer has been designed to be adapted to such new sources (L.U.R.E. DCI).
This diffractometer consistes of three main parts :Goniometer
A vertical goniometer 8-28 with a resolution of 8=10/100. In order to avoid fluorescence and incoherent radiation, the scattered beam is recorded by an energy dispersive detector (supplied by SEPH) which is connected to a preamplifier and a pulse processor. The detector can rotate 360' around the goniometer's axis. A spatial set of slits complete the optical arrangment of goniometer.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879209
JOURNAL DE PHYSIQUE
Energy c a l i b r a t i o n
A s i l i c o n s i n g a l c r y s t a l ( 2 2 0 ) channel c u t monochromator i s used t o s e l e c t t h e needed e n e r g y . I t p r o v i d e s r a p i d t u n a b i l i t y o v e r a b r o a d s p e c t r a l r a n g e , n a r r o w b a n d w i d t h and a l m o s t c o n s t a n t exit-beam p o s i t i o n and d i r e c t i o n . A telecommand s e t of s l i t s i s mounted i n f r o n t of t h e monochromator which d e f i n e s a w h i t e beam. The energy c a l i b r a t i o n was performed by s t e p s c a n n i n g a c r o s s t h e a b s o r p t i o n edge of t h e element i n t h e specimen.
Fig ( A )
.
The precise calibration of energy by three different methods
The monitoring of t h i s system and t h e d a t a c o l l e c t i o n i s performed by a s e t of ATEC s t e p t r a n s l a t o r s , a microcomputer Goupil and a software.
This system allows t o s e t up t h e monochromator f o r t h e corresponding energy of t h e a b s o r p t i o n edge. The t r a n s m i t t e d i n t e n s i t y was recorded by a s o l i d s t a t e d e t e c t o r (SSD). F i g . (1) shows t h e s e n s i b i l i t y of SSD o b t a i n i n g an a b s o r p t i o n edge spectrum with a high q u a n t i t y
.
In t h i s spectrum, t h e s t r u c t u r e and t h e EXAFS s i g n a l a r e more pronounced than t h e ones obtained by o t h e r d e t e c t o r s . The easy s e l e c t i o n of wavelength permits s e v e r a l experiments t h a t a r e i m p r a c t i c a l with t h e X-ray tube.Instrumentation c o n t r o l , d a t a a c q u i s i t i o n and d a t a processing software Atomation and d a t a c o l l e c t i o n a r e provided by a microcomputer (Goupil 3) and a programmed m u l t i c h a n n e l l o g i c i e l ( M I K I ( 1 ) ) .The i n t e g r a t i o n of a c q u i s i t i o n c h a i n w i t h m i k i a l l o w s t o reduce considerably t h e experimental time without changing t h e r e s o l u t i o n ;
A menu-driven software system g i v e s , t h e power and f l e x i b i l i t y t o t a k e on t h e most demanding X-ray powder d i f f r a c t i o n a p p l i c a t i o n eg : auto-alignment of a goniometer ( c o r r e c t alignment of zero i s e s s e n t i a l f o r a t t a i n i n g an optimum r e s o l u t i o n and maximum i n t e n s i t y ) , energy s e l e c t i o n , powder d i f f r a c t o m e t r y , q u a l i t a t i v e a n a l y s i s of d a t a , i n t e r a c t i v e c o r r e c t i o n , i n t e r a c t i v e connexion with t h e computer c e n t r e . Thanks t o t h i s complex, t h e goniometer can be used f o r a 0-28scanning i n t r a n s m i s s i o n and r e f l e c t i o n geometry, 8 scan, 20 scan only and energy d i s p e r s i v e
.
This f l e x i b i l i t y g i v e s t h e p o s s i b i l i t y t o use a low temperature technique. The advantage of t h i s system i s t h a t t h e sample i s n o t t o be d i s p l a c e d d u r i n g t h e c o n v e r s i o n ; a c c o r d i n g t o t h e information we need t o g e t from t h e sample t h e geometrical conditions ( t r a n s m i s s i o n and r e f l e c t i o n mode) and o p t i c a l arrangement of goniometer.The e a s y wavelength s e l e c t ion permits t o o b t a i n t h e p a t t e r n s with t h e chosen wavelength near t h e a b s o r p t i o n edges, using t h e rapid change of t o t a l s c a t t e r i n g ( f t o t ) a s a f u n c t i o n of photon energy near t h e a b s o r p t i o n edge of one atomic s p e c i e s . In t h e r e s u l t we can s e p a r a t t h e mixture p a t t e r n by i n t r o d u c t i n g anomalous d i s p e r s i o n i n t o one of t h e phase. The examples below i n d i c a t e t h e u s e f u l n e s s of t h i s technique (anomalous d i f f r a c t i o n ) t o o b t a i n t h e e x t r a s t r u c t u r a l information on t h e d i s o r d e r and new m a t e r i a l s .
Examples
:I- Structure of amorphous solides :
a- Determination of total interference function
-
I { K ) - total atomic distribution functions W(R).
An amorphous a l l o y s u c h a s Cu Z r 2 h a s b e e n measured f o r t h r e e e n e r g i e s n e a r a n d below of Z r a n d n e a r t h e K a b s o r p t i o n e d g e of Cu.
Then t h e r e d u c e d i n t e r f e r e n c e f u n c t i o n F(K) = K [ I ( K ) - ~ ] i s d e r i v e d from I ( K , o ) w i t h t h e c o r r e c t i o n a n d n o r m a l i z a t i o n p r o c e d u r e ( f o r t h e d e t a i l s s e e r e f e r e n c e 4 )
.
$he r e d u c e r a d i a l d i s t r i b u t i o n f u n c t i o n ( R . D .F) -W ( R )-
i s t h e F o u r i e r t r a n s f o r m of t h e F(K) f u n c t i o n . F i g . ( 2 ) .
T h i s f i g u r e shows t h a t t h e c o n s e q u e n c e of u s i n g s y n c h r o t r o n r a d i a t i o n i s an immense improvement i n R . D . F . ' s o v e r t h o s e y i e l d e d i n c o n v e n t i o n a l X-ray t u b e e x p e r i m e n t . Such h i g h q u a l i t y o f R.D.F. i s a c h i e v e d due t o t h e f i n e q u a l i t y of t h e monochromatic beam a n d t h i s complex. As a r e s u l t , t h e e l a s t i c a n d i n e l a s t i c components o f t h e s c a t t e r e d X-ray beams c a n b e c h a r a c t e r i z e d c a r e f u l l y . So, i n h i g h ( K ) we c a n g e t a r e a l s i g n a l from t h e d i s o r d e r e d m a t e r i a l . T h i s p o s s i b i l i t y g i v e s a h o p e t o a c h i e v e a b e t t e r n o r m a l i z a t i o n o f R.D.F. a n d more c o n f i d e n t on t h e d e t a i l o b s e r v e d on t h i s f u n c t i o n . C o n s e q u e n t l y t h e R . D . F . d e r i v e d f r o m F ( K ) e x h i b i t s two w e l l r e s o l v e d p e a k c e n t e r e d a r o u n d 2 . 8 0 A w i t h o t h e r p e a k a t 3 . 1 0 A . T h e s e p e a k s a r e l o g i c a l l y a t t r i b u t e d t o Cu-Zr a n d Z r - Z r f i r s t n e i g h b o u r d i s t a n c e s which a r e s i m i l a r w i t h t h e Goldschmidt d i a m e t e r .
I n f i g u r e ( Z ) , w e c a n s e e t h e
e f f e c t o f e n e r g y d e p e n d i n g ~ K - I
p a r t i c u l a r l y i n c u r v e ( a ) where
(Es-ssssn
2, k.aP.1
t h e d i s t a n c e o f Cu-Zr i s (--17-
d i s a p e a r r i n g . Then, i t c a n b e ( L * ' 7 m w (lmr s h a p e ) D.r*rr.
a s s u m e d a s a p a r t i a l a t o m i c d i s t r i b u t i o n f u n c t i o n o f Z r - Z r .
I n s p i t e o f t h i s i m p o r t a n t a d v a n c e f o r o b t a i n i n g t o t a l R.D.F. t h e f u n d a m e n t a l problem o f i n t e r p r e t a t i o n r e m a i n s , when b i n a r y a l l o y s a r e a v a i l a b l e .
Fig(2)
.
The reduced radial distribution function CuZr2 corresponds t o the three energiesT h a t i s b e c a u s e e a c h R.D.F. peak m i g h t b e c o n t r i b u t e d w i t h t h e d i f f e r e n t a t o m i c p a i r s . I t i s u s u a l y i m p o s s i b l e t o u t i l i s e t h e peak p o s i t i o n s a n d a r e a s t o o b t a i n a u n i q u e s t r u c t u r a l i n t e r p r e t a i t o n f o r a d i r e c t comparison w i t h t h e model c a l c u l a t i o n . To remove t h i s a m b i g u i t y , t h e p a r t i a l a t o m i c d i s t r i b u t i o n f u n c t i o n i s i n d i s p e n s a b l e .
b- Determination of partial atomic distribution functions of amorphous material
I n b i n a r y a l l o y s (A-B), t h e t o t a l i n t e r f e r e n c e f u n c t i o n I ( K ) c a n b e e x p e r e s s e d a s :
I ( K ) Y i i ( K ) 1 1 1 ( K ) + Y 2 2 ( K ) I 2 2 ( K ) + Y 1 2 ( K ) I 1 2 (K) To d e d u c e t h e p a r t i a l i n t e r f e r e n c e f u n c t i o n s I i j (K), t h r e e d i f f e r e n t e x p e r i e m e n t s w i t h d i f f e r e n t e n e r g i e s a r e r e q u e s t e d i n which t h e v a l u e o f Y i j ( K ) a r e changed. I f t h e c o n t r i b u t i o n o f one e l e m e n t i n t h e b i n a r y a l l o y i s low ; o n l y two e x p e r i m e n t s are r e q u i r e d . So it i s p o s s i b l e t o assume a v e r y s i m p l e f u n c t i o n ( Y B B ) . Then b y i n v e r s i o n , t h e l i n e a r s y s t e m c a n b e s o l v e d w i t h two unkown f u n c t i o n s of A-A a n d A-B.
Below you c a n f i n d two examples o f amorphous a l l o y s Such a s C U ~ Y ( ~ ) FegQZrlo ( 3 1
C9-1144 JOURNAL DE PHYSIQUE
F i g . 3 , 4 show two p a r t i a l r a d i a l d i s t r i b u t i o n f u n c t i o n s W ( r ) of Fe-Fe and Fe-Zr, Cu-Cu and Cu-Y which a r e d e r i v e d from t h e p a r t i a l i n t e r f e r e n c e f u n c t i o n Y ( K ) . T h e s e f u n c t i o n s p e r m i t t o f i n d c h a r a c t e r i s t i c d i s t a n c e s Table ( 1 ) .
Fig.(3,4). The partial radial distribution WFe-Fe and WF,-Z,, WCu-Cu and WCumy
TABLE : I n t e r a t o m i c d i s t a n c e s i n amorphous CusY and Feso Z r l o
The c o o r d i n a t i o n numbers (Nc) f o r an Fe atom i n FegO Z r l o a r e : N F e - ~ , = l O . 2 N F , = l . 6 and NZr+,=14 .5 atoms. I n t h e c a s e o f CusY ; Ncu-cu =
10.4 NCu-Y = 2 . 8 ( i n t o t a l around
Cu 1 3 . 2 atoms) and Ny-cu=16.5 atoms. ---.. THEORETICAL
F i g u r e ( 5 ) shows how w e l l t h e t h e o r e t i c a l RDF matches w i t h t h e p a r t i a l a t o m i c d i s t r i b u t i o n f u n c t i o n of Fe-Fe.The t h e o r e t i c RDF' f o r p u r e I r o n i s o b t a i n e d from t h e curved s p a c e approch. The main i d e a i n t h i s approch i s t o i n t r o d u c e d i n o r d e r t o h a v e a f l a t s p a c e on
"average". ( 2 )
Fig.5, T h e partial radial distribution
f u n c t i o n of Fe-Fe f r o m a n amorphous FegOZr10
11- 1- :
The s t u d y o f new m a t e r i a l s u c h a s q u a s i c r y s t a l s i s t o be p e r f o r m e d by u s i n g t h e same e x p e r i m e n t s e t u p . F o r t h i s t y p e of m a t e r i a l two t y p e s o f Bragg l i n e s have been r e p o r t e d ; a ) t h e u s u a l powder p a t t e r n b ) a set o f continuum Bragg l i n e s which a r e . u s u a l l y immersed i n t h e background. I f t h e c l a s s i c a l method i s u s e d t h e continuum Bragg l i n e s c a n n o t be d i s t i n g u i s h e d from t h e background.
T h e r e f o r e t h i s new method must be used f o r s t u d y i n g such a s p e c t s
REFERENCES
1- P. LEBOUCHER, ANVAR Patent no 51337 (1985)
2- J.F. SADOC and R. MOSSERI, J. p~ysi&e
~ 8 ,
Supplkment au n012 46 (1985)3- M. LARIDJANI, J.F. SADOC and P. LEBOUCHER, 6th International Conference on Liquid and amorphous Metals, GARNISCH PARTENKIRCHEN, August 24-29 (1986)
4- M. LARIDJANI, J.F. SADOC and D. RAOUX, J. Non-Cryst.Solids 91(1987) 5- M. LARIDJANI, J.F. SADOC, Accepted by Mod. Phys. Lett. B(1987)
