From the temperature dependence of x-ray Bragg reflections, Debye temperatures related to vibrational amplitudes ${\Theta }_M$ of 290±5°K and 543±8°K were determined for germanium and silicon, respectively. These are lower by about 20% than the corresponding specific-heat Debye temperatures ${\Theta }_D$ 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 ${\Theta }_M$ values result because the lower frequency modes contribute proportionally more to the vibrational amplitudes than to the specific heat.

• Received 7 March 1962

DOI:https://doi.org/10.1103/PhysRev.127.690