Phys Chem Minerals (2001) 28: 52±56

Ó Springer-Verlag 2001

ORIGINAL PAPER

A. Manceau á M. L. Schlegel

Texture effect on polarized EXAFS amplitude

Received: 3 February 2000 / Accepted: 26 July 2000

Abstract Application of polarized extended X-ray absorption ®ne structure (P-EXAFS) spectroscopy to thin ®lms of ®ne-grained minerals is emerging as a powerful method to investigate the in-plane and out-ofplane local structure of phyllosilicates. Mineral platelets have no preferential orientation in the plane of the ®lm, and their c* axes are oriented essentially along the ®lm normal. The angular dependence of the EXAFS amplitude critically depends on the orientation distribution of c* axes due to mosaic spread. The e€ect of ®lm texture on EXAFS amplitude has been calculated as a function of the mosaic spread, the orientation of the electric ®eld vector, and the crystallographic orientation of the atomic pair. Calculations show that the reduction in amplitude for partially ordered ®lms is more important when the electric ®eld vector is perpendicular to the ®lm plane. For phyllosilicates, no signi®cant deviation from single crystal dichroism occurs when the mosaic spread is less than ‹20±25° half-width at half-maximum (HWHM) for parallel measurement, and ‹15±20° HWHM for normal measurement. Graphs are given for correcting EXAFS-derived coordination numbers for texture e€ects. Key words Polarized EXAFS á P-EXAFS á EXAFS á X-ray absorption spectroscopy á Texture á Orientation distribution

Introduction In extended X-ray absorption ®ne structure (EXAFS) spectroscopy angularly resolved structural information can be obtained through analysis of the angular dependence of absorption spectra for anisotropic samples. A. Manceau (&) á M. L. Schlegel Environmental Geochemistry Group, LGIT-IRIGM, University Joseph Fourier and CNRS, BP 53, 38041 Grenoble cedex 9, France e-mail: [email protected]

Originally, polarized EXAFS (P-EXAFS) was applied to single crystals (Brown et al. 1977; Kutzler et al. 1981; Manceau et al. 1988, 1990; Waychunas and Brown 1990), and this technique was recently extended to thin ®lms of ®ne-grained layered minerals (Manceau et al. 1998). P-EXAFS probes the local structure of layered minerals between two di€erent directional limits, parallel and perpendicular to the (001) plane, by varying the angle between the electric ®eld vector (E) and the layer plane of a single crystal, or the surface of a thin ®lm. In the case of smectites, highly ordered ®lms can be prepared, which allows precise probing of their threedimensional local structure without loss of spatial resolution as compared to single crystals. However, the dichroism of P-EXAFS spectra can be diminished by an imperfect ®lm texture. Therefore, quantitative determination of the orientation distribution (OD) of individual crystallites in the ®lm is necessary to accurately determine coordination numbers, and to localize scattering atoms relative to the polarization direction. Generally, the OD of a ®lm is quanti®ed by X-ray di€raction (Schulz 1949; Bunge 1981). Texture analyses of smectite ®lms showed that a and b layer axes of crystallites have no preferential orientation in the plane of the ®lm and, consequently, that the complete OD could be obtained by measuring uniquely the misalignment of particles o€ the ®lm plane. The dispersion of c* axes can be modeled correctly with a Gaussian distribution function centered on the ®lm normal. In previous studies of smectites (Manceau et al. 1998; Schlegel et al. 1999; Manceau et al. 2000a, b), the half-width at half-maximum (HWHM) of the Gaussian distribution ranged from 10° to 22°, and its e€ect on EXAFS-derived coordination numbers was neglected. Indeed, preliminary calculations (Manceau et al. 1999) suggested that the texture e€ect was insigni®cant for HWHM 10 (Benfatto et al. 1989). Therefore, the importance of the deviation from the usual plane-wave limit can be neglected in the analysis of the EXAFS contribution (k > 3 AÊ)1) of nearest (R » 3 AÊ) and higher distance cationic shells in phyllosilicates. Angular dependence for partially ordered ®lms In practice, the particle packing is always disrupted to some degree, and the distribution of c* axes of individual particles around the ®lm normal has to be introduced in Eq. (1). The angular dependence of apparent coordination numbers then becomes (Dittmer and Dau 1998): Napp ˆ N with Iord ˆ

R p=2 0

1=2N …3 cos2 b

1†…3 cos2 a

…3 cos2 a 1†P …a† sin a da : R p=2 2 0 P …a† sin a da

2†Iord

…5†

…6†

The function Iord accounts for the particle disorder, and its value is one for perfectly ordered ®lms and zero for an isotropic sample. P …a† represents the pro®le-shape function used to model the distribution of c* axes around the ®lm normal. P …a† ˆ exp… a2 ln 2=X2 †

…7†

for a Gaussian distribution, where W is the HWHM of the mosaic spread.

Numerical application

Fig. 1 Vectors and angles relevant for P-EXAFS measurements on thin ®lms of ®ne-grained layered minerals. E is the electric ®eld vector, F is the ®lm normal, P is the particle normal, and Ri is the vector connecting the X-ray absorbing and the backscattering i atom. a is the angle between E and the ®lm plane (experimental angle), hi is the angle between E and Ri, and b is the angle between Ri and P. In a perfectly vectorially ordered ®lm, P and F are aligned

Equation (6) was solved numerically because the integral in the numerator has no analytical solution. Figure 2a shows that Iord(W) does not vary linearly with the mosaic spread. The disorder parameter has little sensitivity to W when the texture strength is high and low but a high sensitivity in the 15° < W < 30° interval. Experimental W values measured on di€erent ®lm preparations of nontronite and hectorite smectites are reported in Fig. 2b. Except for the two most well-oriented samples, which have an HWHM as low as 10° and 12.5°, all

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Fig. 2 a Plot of the order function (Iord) against the ®lm mosaic spread (W). b Calculation of Iord values for smectite ®lms studied by P-EXAFS. W values were determined by texture goniometry and are taken from Manceau et al. (1998, 2000a, b) and Schlegel et al. (1999, 2000)

others are located in the region where Iord(W) varies rapidly, and almost linearly, with W. This result demonstrates the importance of preparing highly oriented ®lms, because Iord increases by as much as 30% when the mosaic spread decreases by only 10° in the 15°±25° W interval. The e€ect of Iord on Napp was determined by calculating Napp/N for the in-plane and out-of-plane orientations of the electric ®eld vector. The two-variable Napp =N ˆ f…b; X† functions for a ˆ 0° and 90° are plotted in Fig. 3a, b. The most salient feature of these functions is their sheaf shape. For any b, Napp/N is almost independent of the texture strength for W < 10°. Beyond this threshold, the higher the W value and the closer b is to 90° or 0°, the more the iso-Napp/N lines are bent, meaning that the angular dependence of EXAFS spectra decreases. For b ˆ 54.7°, Napp/N is independent of W because at this magic angle, hcos2 hi ˆ 1=3 and Napp ˆ N. In practice, these graphs have two purposes. First, they can be used to correct Napp determined by ®tting EXAFS spectra from texture e€ects when b is known. Second, the b crystallographic angle of a particular atomic shell can be obtained from experimental

N90 =N35 and N0 =N35 ratios. An application can be found in Schlegel et al. (2000), where Napp and b EXAFS values for the two most disordered ®lm samples presented in Fig. 2a (W ˆ 23.2° and 24.2°) were corrected for texture e€ects. The variation of Napp resulting from the mosaic spread can be calculated from D…Napp =N † ˆ …Napp =N †X …Napp =N †Xˆ0 . Figure 3c, d shows that D…Napp =N † is systematically greater when the electric ®eld vector or the atomic pair is oriented perpendicularly (a ˆ 90°, b ˆ 0°) to the basal plane of particles. Therefore, an important conclusion is that the perpendicular orientation is more sensitive to texture e€ects than the parallel orientation. How the previous theoretical considerations apply to phyllosilicate ®lms is examined next. The structure of phyllosilicates consists of an octahedral sheet attached to two tetrahedral sheets (Fig. 4). All octahedral sites are occupied in trioctahedral structures and two thirds in dioctahedral structures. Sixfold coordinated cations are surrounded by three (dioctahedral framework) or six (trioctahedral framework) nearest cations (Oct) in the octahedral sheet (boct ˆ 90°) and by four nearest Si, Al atoms (Tet) in tetrahedral sheets (btet » 32°). From Eq. (4), the contribution of the Oct shell is cancelled ? ‰Napp (Oct) ˆ 0Š, and that of the Tet shell selected ? (Tet) ˆ 8:6Š, in the normal orientation. Conversely, ‰Napp when the polarization vector is parallel to the ®lm plane, the Oct contribution is preferentially reinforced k ‰Napp (Oct) ˆ 4:5 or 9Š, and the Tet contribution becomes k small ‰Napp (Tet) ˆ 1:7Š. The dependence of Napp on W for the Oct and Tet atomic shells of trioctahedral phyllosilicate is represented in Fig. 5. Napp logically converges to crystallographic values (NOct ˆ 6, NTet ˆ 4) when the particle disorder increases. In keeping with the previous ®nding from Fig. 3, the loss of dichroicity is more important in the normal than in the parallel orientation. ? For instance, at W ˆ 20°, NTet is 13% (7.5 vs. 8.6) and k NOct is 7% (8.4 vs. 9), below their values at W ˆ 0°. Since the precision on N by EXAFS is at best 10%, one sees k that NOct has relatively little sensitivity to W. At a ˆ 90°, ? not only does NTet decrease by 13% but, more impor? tantly, NOct increases from 0 to 1.3, and this additional atomic contribution no longer can be neglected during the least-squares ®tting of EXAFS spectra.

Concluding remarks The calculations presented here show that the angular dependence of EXAFS contributions is signi®cantly perturbed when the mosaic spread of crystallites in ®lms is greater than ‹20±25° HWHM for parallel measurements and ‹15±20° HWHM for normal measurements. In practice, one must scrutinize any P-EXAFS measurement made on clay ®lms because the mosaic structure obtained with smectites, whose platelets are known to orient themselves well, is comprised typically between 10 and 25°. To ascertain whether the texture e€ect is insigni®cant, and to account for this possible e€ect in the

55

Fig. 3 Plot of Napp/N as a function of the orientation of the atomic pair (b), and of the ®lm mosaic spread (W) for the in-plane orientation (a ˆ 0°) a, and the out-of-plane orientation (a ˆ 90°) b. Plot of D…Napp =N † ˆ …Napp =N†X …Napp =N †Xˆ0 as a function of b and W for a ˆ 0° c and a ˆ 90° d

Fig. 4 Idealized structure of a phyllosilicate. Oct and Tet denote octahedrally and tetrahedrally coordinated cations, respectively

quantitative analysis of EXAFS spectra, the texture strength of the ®lm sample should be measured by texture goniometry. However, in some cases this technique may not yield the entire orientation distribution of the

Fig. 5 Apparent number (Napp) of nearest cations in the octahedral and tetrahedral sheets of trioctahedral phyllosilicates as a function of the ®lm mosaic spread, and for the parallel (a ˆ 0°) and the normal (a ˆ 90°) orientations of the electric ®eld vector. N(Oct) ˆ 6, k k ? N(Tet) ˆ 4, Napp (Oct) ˆ 9, Napp (Tet) ˆ 1:7, Napp (Oct) ˆ 0, ? Napp (Tet) ˆ 8:6

metal-containing particles, and hence of the X-ray absorber-backscatterer atom pairs, in the ®lm. This can happen when the sample contains poorly crystallized

56

material amorphous to X-ray di€raction, or when the X-ray absorber is partitioned between several mineral phases, as in most natural samples (Manceau et al. 2000c). Acknowledgements The authors J.F. Farges for their reviews.

acknowledge

H.

Dau

and

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