Investigation of the stability of the Si III and Ge III crystal structures using force constants

The metastable crystalline phases of Si and Ge, known as Si III and Ge III, offer an interesting test of the force constant models currently being applied to the study of amorphous Si and Ge, since they are made up of distorted tetrahedral bonds. It is found that, using force constants depending only on the bond lengths and angles (adjusted to fit the phonon spectrum of the diamond cubic structure by Singh and Dayal), minimisation of the total energy gives structures and densities fairly close to the observed values for these phases. However, the magnitude of the total energy, relative to the diamond cubic structure, appears to be much too large and some caution seems advisable in applying this or similar models to the calculation of the heat of crystallisation of amorphous semiconductors.