Local disorder in crystalline and amorphous germanium

Abstract

Anharmonic contributions to the pair potential of near-neighbor interactions of crystalline and amorphous germanium have been determined by temperature-dependent x-ray absorption fine structure measurements. The measurements have been carried out at the K edge of Ge in the temperature range 77\char21{}450 K and analyzed by the cumulant method. In c-Ge the temperature dependence of the first four cumulants has been determined for the first three coordination shells. The radial distribution function of the nearest-neighbor atoms has been found Gaussian in the examined temperature range; the second and third shell distance distributions show a symmetric but non-Gaussian behavior even below the Debye temperature. Cumulants have been related to the force constants of the effective pair potential. The harmonic contribution to thermal disorder has been extracted from the second cumulant for each coordination shell and compared with the mean square relative displacements calculated by harmonic models of lattice dynamics; experimental results are in good agreement with theoretical calculations. In amorphous germanium the first shell radial distribution function is asymmetric even at the lowest temperatures. Static and dynamic effects to the local disorder have been separately determined and compared with the results of previous studies.