Anisotropy in elasticity, sound velocity, thermal conductivity, and thermodynamics properties of dodecaboride Zr_0.5Y_0.5B₁₂

Abstract

Solid solution of metal dodecaboride Zr 0.5 Y 0.5 B 12 is thermodynamically stable. The anisotropies of Zr 0.5 Y 0.5 B 12 in linear compressibility, Young's modulus, shear modulus, sound velocity, and minimum thermal conductivity are discussed. The linear compressibility shows slightly anisotropy, which arises from the atomic size mismatch between Zr and Y. Young's and shear modulus present significant anisotropy. The sound velocities show weak anisotropy in different planes, except the pure transverse mode v t in (010) plane, which shows isotropic. The minimum thermal conductivities in different planes are comparable and show very weak anisotropy. The effects of temperature and pressure on the thermal expansion coefficient, Debye temperature, and Grüneisen parameter are discussed based on the quasi-harmonic Debye model.