Configuration averaging of X-ray absorption spectra of disordered systems within the augmented-space full multiple-scattering formalism

Abstract

We present a formulation of the full multiple-scattering theory of X-ray absorption spectroscopy (XAS) for disordered systems based on the augmented-space method of Mookerjee. Both substitutional (chemical) and thermal (vibrational) disorder are cast, on the same footing, as exact matrix elements of a non-random operator acting on an enlarged Hilbert space. The configuration-averaged scattering-path operator is thereby obtained by inverting a non-random secular matrix, with no expansion in scattering paths, without recourse to the single-site approximation and without any assumption on the shape of the disorder distribution. This is what the quantitative analysis of the near-edge region requires: XANES lies where the multiple-scattering series does not converge, so that a treatment of disorder tied to a path expansion is unavailable there. The inversion is carried out by a continued-fraction (Lanczos) recursion, which accesses the required matrix element without constructing the full configuration basis or diagonalising the augmented operator. The operator Debye-Waller factor of the harmonic theory is recovered as the Gaussian special case, and anharmonic disorder is included with no additional machinery, through the moments of a non-Gaussian displacement distribution. Where the series does converge, the construction also settles a question of principle: for statistically independent site variables, replacing each t-matrix by its configuration average is exact only for scattering paths in which every site occurs once, and for paths that revisit a site we obtain the exact second-order correction.