Anharmonic vibration and forbidden reflexions in silicon and germanium

Abstract

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 V j (r) = V 0 , j + ½ α j ( x 2 + y 2 + z 2 ) + β j xvz required to satisfy the T d symmetry of the atomic sites. Values of the α -parameter, derived from the characteristic temperatures Θ M of Ge and Si, are similar to the results for α 0 and α F found in the vibration analysis of neutron data for the fluorite structures UO 2 and CaF 2 (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 UO 2 and CaF 2 . The resultant predictions for Bragg scattering at temperatures in excess of Θ M 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.