Cumulant analysis of the extended x-ray-absorption fine structure of β-AgI

The extended x-ray-absorption fine structure (EXAFS) at the K edge of silver has been measured in β-AgI at different temperatures in the range T=23–410 K. Amplitude and phase of the first-shell EXAFS have been separately analyzed in terms of cumulant expansion within the photoelectron wave-vector range k=2.5–16.5 A${\mathrm{̊}}^{\mathrm{-}1}$ taking the 23-K spectrum as reference. Tests on EXAFS simulated from excluded-volume-model distributions have been performed to check the convergence of the cumulant series and the correspondence between polynomial coefficients obtained from EXAFS analysis and exact cumulants. The cumulant series of the Ag-I distance distribution is convergent within the k and T ranges considered; below 300 K the polynomial coefficients are a good estimate of the exact cumulants; above 300 K the exact cumulants can be obtained by extrapolating the behavior of the polynomial coefficients below 300 K. The distributions of distances calculated from the cumulants are consistent with those obtained for β-AgI by other authors through a real-space analysis of EXAFS. The mean-square relative displacement is largely insensitive to anharmonicity as a consequence of the high degree of correlation of the motion of silver and iodine nearest neighbors.