Application of the numerical model of temperature-dependent thermal conductivity in Ca$_{1-x}$Y$_x$F$_{2+x}$ heterovalent solid solution nanocomposites

A series of Ca$_{1-x}$Y$_x$F$_{2+x}$ solid solution $x$ = 0.0005, 0.003, 0.007, 0.013, 0.02, 0.03, 0.04 single crystals were grown using the Bridgman method. The thermal conductivity of single crystals was measured using the absolute method of longitudinal heat flow in the range of 50 – 300 K. With an increase in the concentration of yttrium fluoride in the solid solution, a transition is observed from the temperature dependence characteristic of single crystals to a monotonically increasing one with increasing temperature, which is characteristic of disordered media. This behavior is associated with the scattering of phonons on nanosized clusters of defects present in the solid solution. Within the framework of a two-component model, including a superposition of thermal resistance coefficients from ordered and disordered media, a system of equations was obtained that provides a quantitative description of the experiment.