Thermo-optic behaviour of solids

Summary

Making use of the dispersion formula given in the International Critical Tables, with absorption bands at λλ 0·0942 and 35·48 μ, and using the theory developed in Part I, the course of the variation ofdn/dt with wave-length has been satisfactorily explained from 0·185 to 6·5 μ. The dispersion formula however fails below 0·185 μ, and consequently two new formulæ have been developed holding down to 1300 Å. U., one of which uses dispersion frequencies at λλ 0·082, 0·1115 and 35·48 μ together with a non-unity constant in the expression forn ², while the other is of the Ketteler-Helmholtz type with four frequencies at λλ 0·045, 0·088, 0·1115 and 35·48μ. All the formulæ explain the variations ofdn/dt, in particular, as to why it increases algebraically as one proceeds both into the ultraviolet and the infra-red. The interesting fact emerges that the extreme ultraviolet frequency at λ 0·045 μ does not vary with temperature, while the proportionate variation of the one at 0·0888 μ is much less than that of the one at 0·1115 μ. This result becomes intelligible when one remembers that the deeper levels in the crystal would be less affected by temperature than the low-lying ones. Even the last one, although it is of the same order, is only one half of the proportionate variation of the infra-red lattice frequency. It is also found that the rate of variation of the ultraviolet frequencies is constant at different temperatures. In these respects, fluorspar differs from diamond and vitreous silica. The difference has been attributed to the fact that the binding in fluorspar is not purely covalent, but is also partly electrovalent.