The thermal conductivity of dielectric crystals: the effect of isotopes

Abstract

Measurements of the thermal conductivity of TiO$_{2}$, KCl, LiF and of three types of diamond below room temperature are reported. Although the first three crystals were very pure there are great deviations from the form of conductivity curve predicted by Peierls for perfect crystals. A consideration of these and other results suggests that the conductivity of many crystals which have been measured is limited by the existence of more than one isotopic species of the chemical elements involved. These give rise to irregularities in the arrangement of atomic mass in the crystals and are a source of phonon scattering. A theory of this effect is given and is compared with the experimental results for the nine substances for which there are sufficient data. The agreement is satisfactory; only for diamond does it appear necessary to invoke impurities as well as isotopes to explain the observed conductivity.