The lattice spectrum and specific heat of diamond

Summary

The new view of crystal dynamics developed by Sir C. V. Raman indicates that the diamond lattice has eight distinct normal frequencies of vibration which comprise forty-five out of the forty-eight degrees of freedom of the atoms present in a group of eight lattice cells, while the remaining three degrees of freedom represent the elastic vibrations of lower frequency. These eight frequencies of atomic vibrations are actually observed in the Raman spectrum recorded by Dr. R. S. Krishnan and in the luminescence and the absorption spectra in the visible region investigated by Dr. P. G. N. Nayar and (Miss) Anna Mani. The modes corresponding to the observed frequencies and their respective degeneracies have been ascertained from the theoretical formulæ given by Bhagavantam and Chelam. The elastic constants have been calculated from the spectroscopic data with the aid of the same formulæ. The calculated and experimental values of the bulk modulus agree well. The thermal energy of diamond has been evaluated from the spectroscopically observed frequencies and the known degeneracies, the three degrees of freedom not covered by these frequencies being considered as an elastic spectrum for which a formula of the Debye type with greatly reduced characteristic temperature is an approximate representation. The theoretical and experimental results agree throughout the whole range of temperature and particularly well in the temperature range between 200 and 1100° K. where the thermal energy content is principally determined by the optical frequencies of vibration.