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STRUCTURAL CHARACTERIZATION OF
NON-CRYSTALLINE MATERIALS BY THE
ANOMALOUS (RESONANCE) X-RAY SCATTERING
Y. Waseda
To cite this version:
STRUCTURAL CHARACTERIZATION OF NON-CRYSTALLINE MATERIALS BY T H E ANOMALOUS ( R E S O N A N C E ) X-RAY S C A T T E R I N G
Y. Waseda
Research I n s t i t u t e of Mineral Dressing and MetalZurgy ( S E N K E N ) ,
Tohoku University, Sendai 980, Japan
REsum6
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La d i f f u s i o n a n o m a l e d e s r a y o n s X a s s o c i E e 2 l ' u t i l i s a - t i o n d ' u n e s o u r c e b l a n c h e i n t e n s e e s t d E c r i t e e t ses m 6 r i t e s a n a - l y s t s e n r e l a t i o n a v e c l e problGme d e l ' o r d r e c h i m i q u e 2 c o u r t e d i s t a n c e d a n s l e s m a t E r i a u x n o n - c r i s t a l l i n s . A b s t r a c t The r e l a t i v e m e r i t o f t h e a n o m a l o u s x - r a y s c a t t e r i n g a n d i t s p o t e n t i a l p o w e r c o u p l e d w i t h a w h i t e x - r a y s o u r c e h a s b e e n d e s c r i b e d w i t h r e s p e c t t o t h e d e t e r m i n a t i o n o f t h e l o c a l c h e m i c a l e n v i r o n m e n t a r o u n d a s p e c i f i c a t o m a s a f u n c t i o n o f r a d i a l d i s t a n c e i n n o n - c r y s t a l l i n e m a t e r i a l s w i t h s u f f i c i e n t r e l i a b i l i t y . I - INTRODUCTION T h e p a s t t e n y e a r s o r s o h a v e b e e n a r e m a r k a b l e g r o w t h i n t h e s u b j e c t s o f t h e s t r u c t u r e a n d v a r i o u s p r o p e r t i e s o f n o n - c r y s t a l l i n e m a t e r i a l s s u c h a s l i q u i d s a n d g l a s s e s a t a m i c r o s c o p i c l e v e l , b e c a u s e o f t h e n o v e l t y o f p h y s i c s m a i n 1 y r e l a t e d t o t h e p a r t i c u l a r n o n - p e r i o d i c i t y i n t h e i r a t o m i c a r r a n g e m e n t s . F o r q u a n t i t a t i v e d i s c u s s i o n o n o n a d i r e c t l i n k b e t w e e n t h e a t o m i c s c a l e s t r u c t u r e a n d t h e i r c h a r a c t e r i s t i c p r o p e r t i e s , a k n o w l e d g e o f t h e f i n e s t r u c t u r e , s a y t h e n e a r n e i g h b o r c o r r e l a t i o n s o f t h e i n d i v i d u a l c h e m i c a l c o n s t i t u e n t s i s s t r o n g l y r e q u i r e d i n m u l t i - c o m p o n e n t n o n - c r y s t a l l i n e m a t e r i a l s . The m a i n p u r p o s e o f t h i s p a p e r i s t o p r e s e n t t h e u s e f u l n e s s o f t h e a n o m a l o u s ( r e s o n a n c e ) x - r a y s c a t t e r i n g ( h e r e a f t e r t o b e r e f e r r e d t o a s A X S ) method, p a r t i c u l a r l y f o r d e t e r m i n i n g t h e l o c a l c h e m i c a l e n v i r o n - ment a r o u n d a s p e c i f i c a t o m a s a f u n c t i o n o f r a d i a l d i s t a n c e i n non- c r y s t a l l i n e m a t e r i a l s .I1
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FUNDAMENTALS OF THE ANOMALOUS X-RAY SCATTERINGC8-294
JOURNAL
DE
PHYSIQUEenergy of incident x-rays, as exemplified by Yig.1 using the Ni atom as an example.
The measurements with several energies in the close vicinity of the absorption edge enables us to offer information about local chemi- cal environment around a specific atom in non-crystalline materials. Such energy derivative technique of the anomalous x-ray scattering is found to be about an order of magnitude better than the direct anoma- lous x-ray scattering (frequently referred to as the multi-wavelength technique)/l,2/ and has recently received much attention. The essen- tial equations are given below using a binary non-crystalline materials for simplification.
The structurally sensitive part of the coherent x-ray scattering intensity for a binary (A-B) non-crystalline system can be described by the following form.
2 2 2 2
I (qrE) =cAfA(q,E)aAA(q) +cBfB (qIE)aBB (q)
+2c,c,fA(qlE) f, (q,E) aAB (q) (1)
where ci is the atomic fraction of the i-th component and ai iq) is the partial structure factors in the Faber-Ziman's form /3/. Wzen the energy of the incident x-rays is tuned to close vicinity of the absor- ption edge of the A-component, the variation detected in intensity may be attributed o n l y t o the change in the atomic scattering factor
fA(q,E). Thus one can obtain the following equation.
Hence the quantity of AIA(q) or [ ~ I ( q , E ) / a E l q ~ a s s o c i a t e d with the A-
component contains information of two partla1 structure factors, aAA(q) and aAB(q) and its Fourier transform expressed by the following equation gives the average distribution function of A and B atoms
around A atom without complete separation of partial functions.
This idea can be readily extended to a multi-component non-crystalline system. In other words, the environmental structure around a specific atom can be evaluated from the measurement using the energy derivative
technique of the AXS / 4 / .
I11 - EXPERIMENTALS
The energies below the absorption edge are usually employed for the AXS measurements to prevent strong fluorescent radiation from sample and then the present our intension focuses o n the change in the real
part of the anomalous dispersion term f' as shown in Fig.1. The value
of f' for most of the elements is typically 15-25 % of the standard
atomic scattering factor f0 at the K shell absorption
,
and f' appearsto be substantially larger value (over 50 % ) at the L-shell absor-
ption. However, as long as we use only characteristic K a radiations produced by the sealed tube x-ray targets, the change arising from the
anomalous dispersion effect is not larger than about 10 %, because the
x-ray generator or the synchrotron radiation and an appropriate mono- chromator appear t o hold promise in reducing such difficulty by enabling us to use the energy in which the anomalous dispersion effect
is the greatest.
F i g . 2 shows the in-house AXS facility newly constructed in SENKEN, Tohoku University. Using a rotating anode RIGAKU x-ray genera-
tor with a gold target, fluxes of o v e r
lo7
photons/sec h a v e beeno b t a i n e d i n t h e d e s i r e d energy between 6 and 1 2 k e V with a b o u t a 1 0 e V
bandpass, coupled with a bent and grounded Ge(ll1) monochromator crystal (25 x 50 x 0.3 mm3, 2R=640 mm). Although fluxes drop by less than two orders of magnitude, the energy up to 36 k e v can be tuned
using higher order reflections from a Ge(1 I I ) o r Ge(220) crystal in
this in-house AXS facility. The x-ray scattering intensity are measured by a intrinsic Ge solid state detector (SSD), in order to
separate or accurately correct the fluorescent components of Ka and K B
and the Compton scattering intensity The incident beam intensity is monitored by measuring the Compton scattering intensity from a Kapton (polyimide) tape placed in the incident beam path. The sample chamber and the x-ray path are f i l l e d by the He gas for reducing the air scattering. A similar experimental set-up has also been used with the synchrotron radiation source/5/.
IV - EXAMPLES OF STRUCTURAL CHARACTERIZATION BY THE AXS
A f e w r e c e n t r e s u l t s o b t a i n e d by t h e A X S a r e g i v e n b e l o w f o r convenience of the fuller understanding of the effectiveness of this
atively new method.
The x-ray scattering intensity for the M o ~ o Nglass was ~ ~ ~
E l k 0 V 1
Fig.1 Energy dependence of the anomalous dispersion terms f' and f" for Ni atom calculated by the relativistic quantum mechanics/4/.
- 1
,
,
[
,
Fig.2 In-house AXS facility at SENKEN,o I 2 Tohoku University, Sendai, Japan.
C8-296. JOURNAL DE PHYSIQUE
systematically measured at several energies near the K-absorption edges, 20.004 keV for Mo atom and 8.333 keV for Ni atom. The resultant x-ray scattering intensity significantly depends upon the incident x- ray energy, as exemplified by the case of the Mo-edge in Fig.3. This observation clearly indicates good sensitivity attributed to the variation in the real component of the Mo anomalous dispersion factor f'. Further analysis including the correction for absorption, air scattering, fluorescent radiation, multiple scattering and Compton scattering has been made with respect the the experimental data obtained at several energies and the total structure factor and the environmental structure factors around Mo atom or around Ni atom were determined. These data processing have been reported in detail /5/ and need not repeat description here. By using the Fourier transformation
of eq.(3), the environmental partial RDFs, pMo(r) and p Ni(r) can be
evaluated as given by Fig.4.
As is well-known, the environmental structure information around a specific atom can be evaluated by the EXAFS or XANES measurements.. H o w e v e r , the A X S is much more straight f o r w a r d , a t l e a s t , theoretically. For example, the theoretical difficulties associated with the electron phase shifts and mean free path still make it impossible to obtain reliable information from the EXAFS measurement a l o n e , particularly for systems with unknown structure like non-
crystal line materials as already streesed by Lee et a 1 / 6 / . Whereas
the AXS does not require information of phase shifts and mean free path. In addition, one of the advantages of the AXS over the EXAFS
OX) 025
,.
*
0.20 v 0 a a 015*
0 0.10*
-
z
0.05 a 0Fig.3 Energy dependence of x-ray Fig.4 The environmental partial
scattering intensity of the M O ~ distribution functions pMo(r) and ~
Ni50 glass measured at energies ~ ~ i ( r ) in the Mo50Ni50 glass
near the Mo-edge. The values of determined by the A X S / ~ / with the
f' are -4.57 for E=19.781 keV EXAFS data for the same material
missed by the EXAFS method, because the cut-off (usually 3-5 A-I) in the l o w wave vector region and thus the EXAFS provides information mainly related to the first nearest neighbor only at the present time. In other words, only the AXS measurement gives the local chemical environment including not only 1st but also 2nd and 3rd near neighbor atomic correlations (so-called middle range ordering) as easily seen i n t h e r e s u l t s o f Fig.4. I t m a y b e w o r t h m e n t i o n i n g f o r n o n - crystalline materials that, the AXS gives better coordination numbers, whereas the EXAFS provides direct information regarding the nature of the atomic pair for the peaks /6/. Thus, the AXS data could supplement the EXAFS data or vice versa.The characteristic absorption edges of various elements are known to be separated, at least several hundred
eV, so that the data collected by the energy derivative technique- of
the AXS is quite feasible within the energy range of about 100-200 e V near the absorption edge with sufficient atomic sensitivity. However, the disadvantage due to the limited high q-region available (say qVax value less than about 7 A-I) is unavoidable, unless a reasonably hlgh energy absorption edge is employed. In such a case, a careful inter- pretation of the resultant RDF is required, although there have been
some modified techniques / 4 / .
V - CONCLUDING REMARKS
The AXS method for applying structural characterization of non- crystalline materials has not yet been completed. Nevertheless, the presently a v a i l a b l e information with several selected examples apparently indicates that the AXS method should basically work well and its potential power, in the present author's view, may not be overemphasized. For considering many factors, the AXS method w i l l bring about a significant breakthrough in the present unsolved dif- ficulty by permitting the accurate evaluation of the local chemical environment around a specific atom as a function of radial distance in multi-component non-crystalline materials in the near future. This may be particularly true when the AXS data is coupled with the EXAFS data. The financial support in 1985 from the Hyuga-Hosai Science Foundation (Iron and Steel Institute of Japan) should be greatly appreciated.
REFERENCES
/I/ Shevchik, N. J., Phil. Mag.
35
(1977) 805 and 1289./ 2 / Munro, R. G., Phys. Rev.
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(1982) 5037./3/ Faber, T. E. and Ziman, J. M., Phil. Mag.
a
(1965) 153./4/ Waseda, Y., Novel Application of Anomalous (Resonance) X-ray Scat-
tering for Structural Characterization of nisordered Materials, Springer-Verlag, Heidelberg, (1984).
/5/ Aur, S., Kofalt, D., Waseda, Y., Egami, T., Chen, H. S., Teo, B.
K. and Wang, R., Solid. State Commun.,
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(1983) 1 1 1 ./6/ Lee, P. A., Citrin, P. H., Eisenberger, P. and Kincaid, B. M.,
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(1 981 ) 761./7/ Teo, B. K., Chen, H. S., Wang, R. and Antonio, M. R., J. Non-
