The effect of isotopes on lattice heat conduction II. Solid helium

The thermal conductivity of solid mixtures of the helium isotopes has been determined from 1°K to near the melting temperatures. In the hexagonal close-packed phase, pure 4He and three 4He-rich mixtures were measured at three different pressures of formation (60, 90 and 140 atm) and pure 3He and six 3He-rich mixtures at a single pressure of formation (145 atm). The results are analysed on the basis of Callaway’s relaxation-time theory, and a consistent explanation is obtained if the relaxation rate for three-phonon normal processes is assumed to be proportional to w2T2. Scattering of phonons by the isotopic impurities is greater than corresponds to the mass difference alone and the additional scattering is attributed to the effect of lattice strain around the impurity. Although the magnitude of this effect is considerably less than has been calculated, its variation with pressure is as predicted. These conclusions are supported by consideration of the behaviour of the conductivity in the limit of low isotopic concentration, when the calculated conductivity is independent of the form of the relaxation rate for normal processes.