Determination of bond lengths, atomic mean-square relative displacements, and local thermal expansion by means of soft-x-ray photoabsorption.

Abstract

Temperature-dependent extended x-ray-absorption fine-structure (EXAFS) measurements at the oxygen and fluorine K edges of CuO, ${\mathrm{Cu}}_{2}$O, ZnO, ${\mathrm{CaF}}_{2}$, and LiF have been performed. We present an EXAFS analysis of bulk samples in the soft-x-ray region of h\ensuremath{\nu}\ensuremath{\le}1500 eV determining the moments of the radial pair distribution function (RDF) of the oxygen and fluorine nearest-neighbor bonds by use of the conventional cumulant expansion method, i.e., coordination numbers, bond lengths, atomic mean-square, and mean-cubic relative displacements of the RDF. It is shown that high-quality K\ensuremath{\alpha}-fluorescence-yield measurements, analyzed in combination with theoretical standards, allow a determination of nearest-neighbor distances within 0.015 \AA{} and of coordination numbers with 10--20 % accuracy. Using quantum-mechanical models for the description of the atomic motions, the EXAFS Debye and Einstein temperatures, as well as the local thermal expansion of the bond under consideration, are obtained. In particular, these quantities for ${\mathrm{CaF}}_{2}$ are found to be in good agreement with those measured by other techniques. In contrast to the fluorides, no thermal expansion could be observed up to room temperature for the transition-metal oxides, which confirms a recent finding of enhanced anharmonicity in the low-Z adsorbate-surface interaction. A detailed compilation is given of the majority of EXAFS studies from the literature where moments of the RDF higher than the second one are reported. For these compounds the local thermal expansion is quantum mechanically calculated in contrast to previous calculations that were performed in the classical limit. Debye temperatures and the local thermal expansion measured by EXAFS and other techniques agree well for fcc metals. For binary compounds like alkali halides or superionic conductors a deviation up to 100% can be found.