Lattice vibrational spectrum of germanium

The Born-von Karman theory of crystal dynamics has been applied to the diamond structure, and the most general force system involving interactions between each atom and its first through sixth order neighbors has been derived. The macroscopic elastic constants and the frequencies of selected lattice vibrational modes have been expressed in terms of the 21 independent parameters entering into this force system. It will be shown that the experimental elastic constants and lattice frequencies along the [100] and [111] axes cannot be fitted to force models based only on general 1° and 2° neighbor interactions. The addition of general 3° and 4° neighbor interactions does not improve the situation, but the further addition of 5° (and higher order) neighbor interactions does. It is possible to obtain physically plausible force models which fit all the data considered within experimental error by the use of onlv general 1° throueh 5° interactions. The nature and the limitations of the derived force models Gili be discussed.