Model calculations of the effective phase factors for extended absorption fine-structure measurements on oxidized aluminum and silicon

Abstract

Model calculations are made of the effective phase factors for surface extended x-ray-absorption fine-structure (SEXAFS) and extended appearance-potential fine-structure (EAPFS) measurements on oxidized aluminum and silicon surfaces. The potentials used in this work have a muffin-tin form and were constructed from overlapping atomic and/or ionic charge densities. Plots are made of these effective phase factors as a function of the momentum, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ of the extended x-ray absorption fine structure (EXAFS)-like electron. These plots exhibit a "breakover" between a high- and low-momentum region at $k\ensuremath{\simeq}3\ensuremath{-}4$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. For these oxide systems the analyzed SEXAFS data extend into this breakover region while the analyzed EAPFS data lie entirely in the well-behaved, high-momentum region. Extrapolating from the high-momentum region into the low-momentum region could lead to underestimating the O---Al and O---Si bond lengths. This is consistent with the differences noted in analyzing the SEXAFS data using extrapolated theoretical phase shifts and experimental phase shifts determined from bulk standards. The model calculations do not agree well with the experimental results over the fairly low-momentum range of the SEXAFS data but do seem to give reasonable bond-length determinations using the higher-momentum range of the EAPFS data.