Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si). DFT study

Abstract

Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si) compounds have all been computed from first principles. All compounds are ductile according to Pugh’s ratio, Cauchy’s pressure, and Poisson’s ratio values. Based on the Born stability criteria, each MPdZ compound is mechanically stable. The high machinability index values of TiPdSn and ZrPdSi indicate their high quality of machinability. The hardness of the compounds is between 5.5 and 8.0 GPa, and the highest hardness is found in the HfPdSn (7.966 GPa) compound. The computed Kleinman parameter indicates that the bond stretching for all MPdZ compounds is minimal. The anisotropy indices incorporating graphical presentation indicate all MPdZ compounds are anisotropic. Young’s modulus elastic anisotropy is less compared to the Zener anisotropy index, equivalent Zener anisotropy measure, and anisotropy ratio of the maximum and minimum shear moduli. Prominent anisotropy for sound velocities is observed in HfPdSi, ZrPdSi, and TiPdSi compounds. With the exception of TiPdGe, other compounds in this work are dynamically stable due to the lack of imaginary phonon modes. HfPdSn, ZrPdSn, and TiPdSn have narrow energy band gaps among the compounds that were studied.