Estimation of inter-atomic force constants and phonon dispersion using correlation effects among thermal displacement of atoms in Ge

Neutron diffraction measurements have been performed on powder Ge at 6, 150 and 300 K. Oscillatory diffuse scattering intensity is clearly observed at 150 and 300 K. The diffuse scattering theory including correlation effects among thermal displacements of atoms is applied to background function in the Rietveld analysis. The inter-atomic distance and temperature dependence of the values of correlation effects are discussed. The force constants among the first, second and third nearest neighboring atoms in Ge are obtained from the values of correlation effects and Debye-Waller temperature parameters. A phonon dispersion spectrum in Λ [111] direction for Ge crystal has also been calculated at 80 K using inter-atomic force constants and the crystal structure.