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FOCUSSED MULTIPLE SCATTERING IN COMPRESSED ReO3
N. Alberding, E. Crozier, R. Ingalls, B. Houser
To cite this version:
N. Alberding, E. Crozier, R. Ingalls, B. Houser. FOCUSSED MULTIPLE SCATTERING IN COMPRESSED ReO3. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-681-C8-684.
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J O U R N A L D E P H Y S I Q U E
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FOCUSSED MULTIPLE SCATTERING IN COMPRESSED ReOj
N. A L B E R D I N G , E.D. C R O Z I E R , R. I N G A L L S * and B. HOUSER*
Department of Physics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6
' ~ e p a r t m e n t of Physics, University of Washington, Seattle, WA 98105, U.S.A.
~esume.- ReO, a une structure perovskite qui consiste en atomes de rhenium lies par ponts d'oxyggne. L'angle de liaison peut 6tre varie continuellement par application de pression superieure a 5.1 kbar, la pression critique d'une transition de phase subie par ce compose. Nous avons mesures des spectres EXAFS en fonction de pression jusqu'h 22 kbar. Les donnees sont reliees a l'amplitude de diffusion dtoxyg&ne, fO(P,k), qui depend sur l'angle de diffusion 0. Ces resultats experimentaux sont utils pour verifer les calculs theoriques de l'amplitude de diffusion d'oxygene. En plus, ils facilitent la determination de l'angle de pont dfoxyg&ne dans les structures indeterminees.
Abstract,-- ReO, is a Perovskite consisting of oxygen-bridged rhenium atoms.
The bridging angle can be continuously varied by application of pressure above a phase transition at 5.1 kbar. We have measured EXAFS spectra of ReO, as a function of pressure up to 22 kbar. The data are related to the angle-dependent oxygen scattering amplitude, fo(P,k). These experimental results are useful in verifying theoretical calculations and for analysing other systems in which the bridging angle is unknown.
I. Introduction
Phase transitions in the Perovskites are of continuing interest. Unlike some other Perovskites, ReO, is stable at atmospheric pressure at all temperatures. It consists of corner-linked oxygen octahedra with Re in the center of the octahedra (Fig. 1). Pictured as a simple cubic arrangement, Re is in the body center position and 0 in the face center position. The compound has metallic conductivity
approximately 1/5 that of copper. At room temperature it undergoes a second order phase transition at PC = 5.1 kbar [l]. The high pressure phase is much softer than the low pressure phase: the compressibility increases by nearly an order of magnitude at the transition. Neutron powder diffraction data show that the octahedra begin to tilt at PC and the tilt angle varies as ( P - P , ) ~ . ~ ~ ~ [2].
Fig. 1. Structure of ReO,. The corner positions of the Perovskite are vacant.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868128
C8-682 JOURNAL DE PHYSIQUE
As the octahedra rotate, the Re-0-Re chains kink, i.e, the bridging angle changes. The kinking of the chains can be monitored in the EXAFS spectra via
"focussed" multiple scattering through the intermediate oxygen atom. Thus the application of pressure provides a systematic means of changing the multiple scattering pathways and observing the effect on EXAFS spectra.
2. Experimental Technique
Samples were mounted in inconel washers 40 fim thick and compressed between boron-carbide tipped anvils. We used boron-carbide tips to avoid Bragg peaks caused by diamonds. An oil hydraulic pump controlled the pressure [ 3 ] .
The pressure was measured by analysing the spectrum of a RbCl sample included in the washer as a separate layer with the ReO, sample. At 5.2 kbar RbCl changes phasea transition easily seen in its edge structure. Above 5.2 kbar the Rb-C1 bond length, determined from EXAFS, is calibrated to give the pressure [ 4 ] .
X-ray absorption spectra of the rhenium L, edge and the rubidium K edge were recorded at the Stanford Synchrotron Radiation Laboratory on wiggler side station IV-1. The monochromator used two Si(220) crystals. The crystals were adjusted slightly off parallel-until only 50% of the maximum intensity was transmitted in order to reduce harmonics.
3. Data Analysis and Results
At atmospheric pressure one oxygen atom lies colinearly between two rhenium atoms. The scattering angle of the photoelectron at the oxygen atom is therefore 0.
The strong forward scattering of the intermediate oxygen atom amplifies the contribution from second nearest neighbour rhenium backscattering in the rhenium EXAFS spectrum. As the octahedra tilt with increasing pressure, the intervening oxygen atom moves out of the colinear position. The amplitude of the Re peak is then sharply reduced according to the angular dependence of the magnitude of the oxygen forward scattering amplitude [fo(~,k).l, where P is the scattering angle at 0.
Using the known pressure-dependence of 0, the Re shell of the EXAFS spectra can be related to fo(P,k).
To this end the formulation by Teo to describe focussed multiple scattering is useful [5,6].
FRe(k) is the magnitude of the rhenium backscattering amplitude and @Re(k) is the phase shift of the Re-Re absorbing-backscattering atom pair. h is the
photoelectron's mean-free path. $2 and o are functions of fo:
Although this formulation assumes a plane-wave approximation it gives a convenient method of relating fo(P,k) to experimental data.
The Re peak can be isolated in the Fourier transform then back-transformed to extract the amplitude and phase:
In practice, we found that the rhenium peak of the ReO, Fourier transform could be separated more easily if the raw spectra were first divided by the Re metal backscattering amplitude derived from Re metal spectra. The Fourier transforms of the EXAFS spectra of ReO, at several pressures are shown in Fig. 2.
Fig. 2. Fourier Transforms of the EXAFS spectra of ReO, at pressures of 0, 5.5 and 22 kbar, corresponding to bridging angles of 0, 5, and 12.5 degrees. The transforms are of k3x(k) over a range of 2 to 16 1 - I using a 10% Gaussian apodization.
4. Conclusions
Three factors contribute to the varration of A(k) with pressure: the change of fl reflected in Slo(p,k), change in the thermal disordeqwith pressure and change of the mean free path with pressure. We have analysed the Debye-Waller factor of the oxygen shell (Table 1). There is no significant change in it from the transition pressure to the highest pressure measured. The relative longitudinal motion of the Re-Re distance should be twice that of Re-0, i . e . negligible change above the PC.
The transverse motion is less easily monitored. Large transverse movements should cause a reduction in the overall amplitude, though the effect is much less than that for motion of similar size in the longitudinal direction. If considerable softening of the transverse modes occurs near PC the overall amplitude may be reduced at this pornt by at most 10-15%.
Pressure (kbar )
5.5 7 .O 8.0 9 .O 10.5 14.0
Table 1.
scattering angle P
(degrees) 5.0 6.0 7 .O 8.0 9.0 10.5
We are aware of no determinatiorl of the mean free path with pressure and see no reason to assume a significant variation.
With these assumptions:
similarly
These experimentally derived functions (Fig. 3) can be compared to the corresponding functions derived from theoretical calculations of fo(P,k). For example, the
calculations of Teo are in poor agreement with our experimental results. In particular, the amplitude, Q , predicted is too large. If used to analyse a system of unknown structure, Teo's oxygen scattering amplrtudes would yield too large an angle. The use of the Q and w functions experimentally derlved from Re03 EXAFS data is preferable if unknown structures are to be analysed for bridging angle.
JOURNAL DE PHYSIQUE
Fig. 3. The functions Q(P,k) and w(P,k) express the effect of focussed multiple scattering on the amplitude and phase of the EXAFS spectrum. They are simply related to the oxygen scattering amplitude fo(P,k). Curves shown represent values for k=8, 9, 10, . . . , 16 8-1. All points are compared with respect to the spectrum immediately before the transition (-5. kba8. The P=O points
relate to the spectrum immediately after the transition, -5.25 kbar.
Acknowledgments
The authors wish to acknowledge grants received from the National Sciences and Engineering Research Council, Canada and the U . S . Department of Energy, grant number DE-FGO6-84ER45163. The experimental work was done at the Stanford
Synchrotron Radiation Laboratory which is supported by the Department of Energy, Office of Basic Energy Sciences; and National Institute of Health, Biotechnology Research Program, Division of Research Resources.
References
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Batlogg B., Maines R.G. and Greenblatt M., P h y s i c s o f S o l i d s Under High P r e s s u r e (1981) 215.
[2] Jdrgensen, J.-E., J,orgensen J.P., Batlogg, B. and Remeike, J.P., P h y s . R e v . B 33 (1986) 4793.
[3] Ingalls, R. and Crozier, E.D., Whitmore, J.E., Seary A.J., and Tranquada, J.M., J . A p p l . P h y s . 5 1 (1980) 3158.
[4] Vaidya, S.N. and Kennedy, G.C., J . P h y s . Chem. S o l i d s 32 (1971) 951.
[5] Teo B.-K. J. Am. Chem. S o c . 103 (1981) 3990.
[6] Boland, J.J., Crane, S.E. and Baldeschwieler, J.D., J . Chem. P h y s . 77 (1982) 142. A polarization factor noted in this paper is not included in our treatment because it is negligible in nearly linear bridges.
