Thermal Conductivity of Isotopic Mixtures of Solid Helium

The thermal conductivity of solid He⁴ containing zero, 0.56, 1.38, and 2.8 He³ has been measured as a function of temperature from 1.1 to 2.1^∘{}K. For pure He⁴, the results are in satisfactory agreement with those of Webb, Wilkinson, and Wilks. The addition of 1.38% He³, at a sample density ρ=0.208 g cm^-3 caused a decrease in thermal conductivity by a factor of 5 at 1.1^∘{}K. The additional thermal resistance caused by adding He³ was substantially independent of temperature, rather than proportional to temperature, as would be expected from isotropically distributed point scatterers. Agreement with Klemens' theory in magnitude and temperature dependence can be obtained by assuming the He³ to be arranged on lines in the solid. Possible mechanisms to explain these results are discussed.