Anharmonic vibration and forbidden reflexions in silicon and germanium

An appraisal is given of antisymmetric features of vibrational anharmonicity in Ge and Si which could be manifested by Bragg reflexions in neutron diffraction studies conducted at elevated temperatures. The discussion is based on the generalized structure factor and the implications of effective one-particle potentials of the form Vj(r) = V0,j + ½αj(x2 + y2 + z2) + βjxvz required to satisfy the Td symmetry of the atomic sites. Values of the α-parameter, derived from the characteristic temperatures ΘM of Ge and Si, are similar to the results for α0 and αF found in the vibration analysis of neutron data for the fluorite structures UO2 and CaF2 (Dawson, Hurley & Maslen 1967). This α-similarity is used to develop a ‘fluorite-like’ appraisal of possible vibrational anharmonicity in Ge and Si by assuming a β-parameter which satisfies the ratio |β|/α ~ 1.3 Å-1 found earlier for both UO2 and CaF2. The resultant predictions for Bragg scattering at temperatures in excess of ΘM are examined for the conditions relevant to both mosaic and perfect crystal specimens. It is shown that the two types of specimen offer different opportunities for detecting anharmonic phenomena, and that the perfect specimen could manifest strong scattering associated with the ‘forbidden’ reflexions 666 and 864 in experiments conducted at high temperatures.