More Accurate Formulas for Determination of Absolute Atom Concentration Using Electron Energy-Loss Spectroscopy.

Abstract

When the value of the dispersion coefficient is "greatly different from 0.5," as is the case for "free-electron" materials such as sodium (Na), the approximate expression for the volume plasmon critical wave vector (PCV) used by Hadji stops being valid and a different, more precise, expression must be used. Here a more accurate PCV formula is used to get a more accurate expression for plasmon scattering cross-section per atom (PSCA) species. This PSCA is then employed to calculate some physical quantities for several "free-electron" materials and together with the techniques from the quoted paper to determine values for physical quantities from amorphous silicon (a-Si) experimental data. The program source used to obtain these values is supplied. Any valid formula for the PSCA species is, in fact, relevant for use together with the two quoted techniques. The PCV and the dispersion coefficient have upper limits. Negative dispersion coefficient values are allowed. A PCV-related dimensionless universal function that can represent all ideal "free-electron" materials is given. "Not greatly different from 0.5" is mathematically expressed.