How Isotopes Obscure the Anisotropic Phonon Umklapp Scattering in Dielectrics

Abstract

Calculations of the thermal conductivity of h.c.p. 4He, doped with up to 1 % 3He, are presented using a Debye relaxation-time approach. The results are analysed to extract information on the exponents in the anisotropic phonon Umklapp relaxation rate. The results show that even if 1 % of 3He is present the exponents may be measured to within 7 % of their undoped value. Consequently, anisotropic phonon Umklapp parameters may be determined in crystals where natural isotopes exist