The thermal energy of crystalline solids: Alkali halides
The character table for rock-salt derived from the theory of groups applied to the unit cell containing four atoms of sodium and four atoms of chlorine, gives eight triply degenerate normal modes of vibrations. One of them corresponds to the translations of the cell as a whole, two are infra-red active and Raman inactive, and five are inactive both in the Raman and the infra-red. The overtones of the latter five modes should however, appear in the Raman effect. This analysis of the vibration spectrum of the rock-salt structure gives a complete explanation of the infra-red absorption spectra of the alkali halides observed by Barnes and the Raman spectrum of rock-salt obtained by Fermi and Rasetti. The two infra-red absorption maxima at 161 and 247 cm.−1 are taken as the two fundamental frequencies and the five frequencies at 228, 272, 298, 346 and 366 cm.−1 identified from the Raman spectrum reproduced by Fermi and Rasetti, are assumed to be the first overtones of the remaining five frequencies of the lattice. The latter also shows three broad bands with peak frequencies of 81, 42 and 20 cm.−1 These are shown to be the octaves of the superlattice frequencies of the second, third and fourth orders.
A general expression is derived for the thermal energy of cubic crystals of the rock-salt type in terms of the lattice and superlattice frequencies. The expression is evaluated for rock-salt and sylvine for a wide range of temperatures which in the case of sylvine is 3° to 285° absolute. Two of the lattice frequencies for sylvine are given by the infra-red spectrum and the others are deduced from those of rock-salt. The calculated values in either case are in reasonable agreement with experimental data, showing that the thermal energy of crystalline solids is satisfactorily explained on the basis of the ideas indicated in the foregoing paper by Sir C. V. Raman and developed further in the present communication.