Combined EXAFS and powder diffraction analysis

ELSEVIER

Physica B 208&209 (1995) 129-134

Combined EXAFS and powder diffraction analysis N. Binsted*, M.T. Weller, J. Evans Department of Chemistry, University of Southampton, Southampton S09 5NH, UK

Abstract

A method has been developed which allows the simultaneous refinement of X-ray powder diffraction data and one or more EXAFS spectra from the same sample using a single coordinate description of the structure. The positional parameters of the atoms are refined together with isotropic thermal factors, peak shape and amplitude parameters, and the EXAFS energy zeros for each absorption edge. Where correlations between shells can be calculated, as with Cu for which Debye theory can be used, EXAFS mean square displacements can be derived from the isotropic thermal factors, otherwise these must be introduced as separate variables. The program determines the point symmetry and radial coordinates of each site occupied by an atom for which EXAFS data are available, allowing a full multiple scattering calculation to be performed for each site. Mixed or partial occupancy of sites is permitted. The method allows us to determine accurately the position of oxygen and other light atoms in materials where the diffraction pattern is dominated by heavy atoms, and to determine the occupancy of sites where elements of similar scattering amplitude are involved. Results are particularly good where the EXAFS of several absorbing atoms are available.

1. Introduction

The techniques of EXAFS and X-ray powder diffraction (XRD) have often been combined in the study of materials. In most cases this is due to the complementarity of the techniques rather than a simply a confirmatory role. One aspect often utilised is that the short-range order seen by EXAFS contrasts with the long-range order seen by XRD. This has been used in real time QUEXAFS studies of crystallisation of amorphous materials and other solid state reactions [1, 2"1. However, even with well ordered crystalline materials there are differences in the information available from the two techniques. The atom-specific nature of EXAFS allows the determination of minor or trace elements within the structure I-3, 4]. In this situation EXAFS measurements may be made after the bulk properties have been well

* Corresponding author.

established by powder diffraction studies yielding site coordinates and cell parameters. EXAFS may then reveal the site occupancies of minor components. Another EXAFS application of considerable importance is the determination of the positional coordinates of major elements within crystalline materials where specific site coordinates or occupancies are not well resolved by XRD alone. In such cases EXAFS may provide significant additional information allowing a unique determination of the structure where ambiguities occur in the XRD data. Previously Currie et al. [5, 6] have used EXAFS data to resolve the identity of I and group IV element (M') sites in mixed metal periodates using EXAFS spectra associated with both edges. A limitation of this method was that the discrepancy in M ' - O and I - O distances between the techniques was not resolved. Although in principal a unique solution could be obtained should a third EXAFS spectra be obtained, using triangulation techniques, a more general solution, adopted here, is to

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N. Binsted et al./ Physica B 208&209 (1995) 129-134

refine both the XRD and EXAFS spectra simultaneously. This has a number of additional advantages. One advantage is that no additional structural variables need be introduced in order to describe the EXAFS distances, even when very many shells are fitted, thus the method is a far more rigorous test of a structural model than either of the techniques performed independently and should lead to a better determined refinement. Provided some means of weighting the EXAFS and XRD contributions can be agreed, it should also allow a better assessment of errors. The idea of combining information from other techniques with XRD data has been applied to combined X-ray and neutron diffraction analysis [7-9].

Least squares refinement during the combined EXAFS and XRD curve fitting involves minimisation of the weighted sum of squares of residuals employing nonlinear least squares routine VA05A in the Harwell library. The quantity minimised is given by Wexafs(~exafs -~ W x r d ~ x r d.

The EXAFS contribution is given by N

~xaf.~ = ~ 1/o-~(z~P(k) -- z~h(k))2 .

(2)

i

ze~P(k) and z'h(k) are the experimental and theoretical

EXAFS. We normally define a by

2. Theory and method

k7

1/ai -

Our EXAFS method is based on the fast spherical wave formalism [10, 11]. Multiple scattering (MS) to fifth order is included but in general we only use third-order scattering involving no more than two scattering atoms. Phaseshift calculations have been described previously [12]. The XRD calculations are based on the DBW code of Wiles et al. [13]. Results presented here employ a pseudo-Voigt peak shape and a refinable quadratic background. When combining the two techniques, it is important to consider systematic differences between them. In particular systematic errors arise in the EXAFS distances because of the approximations used in calculating the phaseshifts, and in the treatment of thermal disorder. We include the centroid correction of Tranquada and Ingalls [141 in our theory, as failure to do so will result in systematically short distances. If necessary this term can be multiplied by an adjustable coefficient, to compensate for systematic errors. Alternatively all distances can be scaled by a constant factor. We aim to remove the need for these terms but they are currently useful in revealing sources of error. The structural model is first defined as for a Rietveld analysis, in terms of a space group, positional coordinates and occupancies. For each atom for which EXAFS spectra are available, the program calculates the radial distribution up to a pre-defined limit (normally 5 to 10/~). If necessary several clusters will be generated for each structurally unique site occupied by the atom in question. Mixed or partially occupied sites are permitted. For each cluster, the program determines the point group. This allows the table of coordinates to be reduced to a set of shell coordinates and occupation numbers, and a point group operator. This allows efficient treatment of multiple scattering making full use of symmetry. The XRD and EXAFS theories may then be calculated.

(l)

~ jNkjn Izy*P(k)l

(3)

'

where n is selected to give an envelope of approximately constant amplitude for k " X ~ P ( k ) . Similarly the XRD contribution is given by ~bxrd = ~ 1/y~,,p(y~,,p __ y~h)2.

(4)

i

So far we have found Wexafs= Wxrd= 0.5 to give reasonable results. We also define an R-factor: N R = ~ 1/~r,(IzTP(k) i

Z~h(k)l)× 100%

(5)

which gives a meaningful indication of the quality of fit to the EXAFS data in k-space. Similar expressions widely used to assess XRD data, Rwp and RBragg, are given in Ref. [15]. Statistical criteria are discussed in more detail elsewhere. In addition to the structural parameters required to describe the model, other parameters refined are the XRD isotropic thermal parameters, peak shape and background parameters, scale factor and zero offset. For the EXAFS, Debye-Waller factors A ( = 2a 2) are refined in groups typically the first few strongly correlated values are treated separately except for closely spaced shells, while for remote atoms all atoms of similar Z are treated similarly. The EXAFS energy zero EF (one per spectrum), the coefficient of the centroid correction and optionally one or more phaseshift parameters are refined. Examples of the latter are a global interstitial potential term (VO) or individual muffin-tin radii. The program also allows constraints for molecular groups or nearest neighbour distances to be applied [ 16].

N. Binsted et al. / Physica B 208&209 (1995) 129-134 |

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Fig. 1. EXAFS fits to the Ge-K edge (left) and I K-edge (right) of RbGelO6.

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2e* Fig. 2. Profile fit to the powder diffraction data from RbGelO6. Dots are observed intensities,the upper continuous line the calculated profile and the lower continuous line the difference.Tick marks show the reflection positions.

3. Results Results are presented here for two well-characterised compounds, Cu metal and CuO and for the compound RbGelO6 I-5, 6]. EXAFS and XRD fits for the latter are given in Figs. 1 and 2, respectively.

metal oxide structures and we are currently reviewing the way these terms are calculated. In order to obtain meaningful Debye-Waller factors it would be desirable to use just a single isotropic thermal parameter for each site. In order to derive EXAFS Debye-Waller factors however, it is necessary to calculate the correlations (c) between them as they are related 1-17] by

3.1. Cu

0-2_i = (aft 2 + 0-•2)(1 - c),

FCC Cu provides a simple test of the program as only one structural parameter, the cell parameter a can be refined. A reasonable quality of fit was obtained for data to 10g, the best fit required some adjustment of phaseshifts and scaling of the EXAFS distances relative to the XRD distances of 0.998. For the first shell this corresponded to an error of 0.005. The most accurate published values give 2.556/~. We believe some of the lack of fit to be due to the treatment of disorder in MS calculations [16] which is inappropriate for metals or

where 0-o~2is the uncorrelated mean square amplitude of vibration given by 0 -0 o 2 =

Biso/(8/t2).

(6)

(7)

is the isotropic thermal factor. In the case of Cu metal both the correlations and the 0- values were calculated by Debye theory [17], using the Debye temperature of Cu of 343 K. These values gave excellent agreement with the EXAFS, provided a small and physically reasonable adjustment to the overall amplitude factor Bis o

N. Binsted et al./ Physica B 208&209 (1995) 129-134

AFAC was allowed. The XRD data fitted only if the monochromator coefficient (CuK~I from a quartz monochromator was employed) was adjusted from 0.8 to 0.6. This implies that the overall Lorentz, polarisation and absorption correction, or its 20 dependence is not quite correct. 3.2. CuO

CuO is monoclinic, with space group C2/c and with one adjustable positional parameter - the oxygen y-coordinate. The structure was fitted to 6.8 A resulting in 62 shells; 2968 MS paths were included. Structure was present beyond this limit but was ignored. A EXAFS R factor of 22.5 signified a moderately good fit - most of the lack of fit was associated with peaks with a substantial MS contribution and we again suspect the treatment of the disorder is the cause. The XRD Rwv was 15.0%, which was almost identical to a refinement in which the EXAFS data was excluded. Fitting the EXAFS required slightly different Cu and O muffin-tin radii from default values and the centroid coefficient refined to 0.69 rather than its ideal value of 1. This is equivalent to a discrepancy of 0.001/~ in the first shell distance. The structural parameters obtained were (with literature values [18] in square brackets) a = 4 . 6 9 1 5 [4.6837(5)], b = 3 . 4 2 1 0 [3.4226(5)], c = 5.1334 [5.1288(6)] .A, fl = 99.43 [99.54(1?)] and Or = 0.4154 [0.4184(13)].

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Previously the XRD results gave 1.82 and 1.78 A. The refinement gave an Rwp of 17.7% compared to a previous value of 17.0%. The overall EXAFS R-factor of 22.4% was comparable with the previous values of 23.9% and 21.3% for the individual EXAFS refinements but the data range used here does not extend to quite such low energy as previously. It was not necessary to include any additional structural parameters to account for systematic errors so the XRD and EXAFS derived distances are identical.

4. Discussion The results show that an acceptable fit can be obtained to both XRD and EXAFS data using a single structural model. Systematic errors in EXAFS distances can be described by a single additional parameter which gives rise to corrections well within the accepted accuracy of the EXAFS technique. The EXAFS fit is sometimes significantly poorer than when many individual shell distances are allowed to vary, but, provided some optimisation of phaseshifts is performed, a reasonable fit can be obtained to the whole spectrum, including the MS contributions. Normally the quality of the fit to the XRD data is only slighlty affected by the constraints introduced by the EXAFS data but the positional parameters of some light atoms may be substantially changed.

3.3. R b G e l 0 6

Acknowledgements The previously published spectra [5,6] were reanalysed using the new program. In this case both the Ge and I K-edge spectra were used. As the core-hole lifetimes for the two edges are very different [19] it was necessary to introduce an additional variable to account for this. This was achieved by an approximate correction to the imaginary part of the phaseshifts [10]: A3(6,) = 2Iv, d~(6,). dE

(8)

With a correction to the imaginary part of the potential lv for each spectrum n. Here 6t is the real phaseshift, the photoelectron energy. This allows the same scattering atom phaseshifts, calculated assuming an intermediate core-hole lifetime to be used for both spectra, although the excited central atom will of course be unique to each spectrum. The refinement yielded a new O coordinate of (0.6363(l), 0.0018(12), 0.3443(8)). This confirms that the G e - O distance (1.889(1)/~) is slightly longer than the I O distance (1.878(1) A) as found previously. The previous EXAFS values were 1.90 and 1.87 A, respectively.

We thank Drs. D.B. Currie, W. Levason, R.J. Oldroyd and G. Sankar for providing data and previous analysis, and to EPSRC for funding.

References [1] A.J. Dent, G.N. Greaves, J.W. Couves and J.M. Thomas, in: Synchrotron Radiation and Dynamic Phenomena, ed. A. Beswick (1991) 631. [2] (3. Sankar, P.A. Wright, S. Natarajan, J.M. Thomas, (3.N. (3reaves, A. Dent, B. Dobson, C.A. Ramsdale and R.H. Jones, J. Phys. Chem. 97 (1993) 9550. [3] P.D. Battle, C.R.A. Catlow, A.V. Chadwick, G.N. Greaves and L.M. Moroney, J. de Physique C 8 (1986) 669. [-4] J.M. Charnock, C.D. Garner, R.A.D. Patrick and D.J. Vaughan, J. Solid State Chem. 82 (1989) 279. [-5] D.B. Currie, W. Levason, R.D. Oldroyd and M.T. Weller, J. Mater. Chem. 3 (1993) 447. [6] D.B. Currie, W. Levason, R.D. Oldroyd and M.T. Weller, J. Mater. Chem. 4 (1994) 1. [7] I.J. Picketing, M. Sansone, J. Marsch and G.N. George, J. Am. Chem. Soc. 115 (1993) 6302.

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[8] I.J. Pickering, M. Sansone, J. Marsch and G.N. George, Jpn. J. Appl. Phys. 32-2 (1993) 206. [9] GSAS. A.L. Larsen and R.B. von Dreele, Los Alamos National Laboratory. [10] S.J. Gurman, N. Binsted and I. Ross, J. Phys. C 17 (1984) 143. [11] S.J. Gurman, N. Binsted and I. Ross, J. Phys. C 19 (1986) 1845. [12] N. Binsted and D. Norman, Phys. Rev. B 49 (19941 15531. [13] D.B. Wiles, A. Sakthivel and R.A. Young, Georgia Institute of Technology (1991).

[14] J.M. Tranquada and R. lngalls, Phys. Rev. B 28 (1983) 3520. [15] R.A. Young, The Rietveld Method (International Union of Crystallography/Oxford University Press, Oxford, 1993). [16] N. Binsted, R.W. Strange and S.S. Hasnain, Biochemistry 31 (1992) 12117. [17] G. Beni and P.M. Platzman, Phys. Rev. B 14 (1976) 1514; W. Bohmer and P. Rabe, J. Phys. C 12 (1979) 2465. [18] S. Asbrink and L.J. Lorrby, Acta Crystallogr. B 24 (1982) 1968. [19] O. Keski-Rahkonen and M.O. Krause, Atomic Data Nuclear Data Tables 14 (1974) 140.