On the cumulant analysis of EXAFS in crystalline solids

The analysis of temperature-dependent EXAFS spectra based on the cumulant e xpansion is critically reviewed, seeking for accurate relations between EXA FS parameters and physical properties of crystals. The treatment is based o n the distinction between the real and effective distribution of distances, and is divided into three logical steps. (a) The connection between lattic e dynamics and cumulants C-n* of the real distribution is studied and the e xtent of the usual approximations are numerically evaluated. Atomic vibrati ons perpendicular to the bond direction make the EXAFS thermal expansion la rger than the crystallographic one; the difference is connected to a shift of the effective pair potential rather than to its asymmetry. Peculiar info rmation on lattice dynamics of crystals can be obtained from accurate EXAFS measurements and their cumulant analysis. (b) The differences between cumu lants of the real and effective distribution (C-n* and C-n, respectively) a re calculated for various physically realistic distributions. The largest d iscrepancy concerns the first cumulant: C-1* measures the thermal expansion of the interatomic bond, while C-1 is a better estimate of the crystallogr aphic thermal expansion. (c) The convergence properties of the cumulant ser ies are discussed and some phenomenological procedures are suggested to mon itor and possibly work out the connected failures of the cumulant method. B enefits and risks of the use of an effective pair potential are at last deb ated.