Vibrational Amplitudes in Germanium and Silicon

Abstract

From the temperature dependence of x-ray Bragg reflections, Debye temperatures related to vibrational amplitudes ${\ensuremath{\Theta}}_{M}$ of 290\ifmmode\pm\else\textpm\fi{}5\ifmmode^\circ\else\textdegree\fi{}K and 543\ifmmode\pm\else\textpm\fi{}8\ifmmode^\circ\else\textdegree\fi{}K were determined for germanium and silicon, respectively. These are lower by about 20% than the corresponding specific-heat Debye temperatures ${\ensuremath{\Theta}}_{D}$ and consequently give mean square amplitudes 40% greater than those calculated from specific heat measurements.The large difference between the two types of Debye temperatures can be explained in terms of the normal mode frequency spectrum. The low ${\ensuremath{\Theta}}_{M}$ values result because the lower frequency modes contribute proportionally more to the vibrational amplitudes than to the specific heat.