Elasticity, slowness, thermal conductivity and their anisotropies of HfO<sub>2</sub> polymorphs
Abstract
The elasticity, slowness, thermal conductivity and theiranisotropiesoffourHfO<sub>2</sub> polymorphs are investigated based on density functional theory plane wave method with ultrasoft and norm-conserving pseudo-potentials. The elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio are obtained by first-principles calculations. The bonds properties of the four materials are analyzed through Poisson's ratio and Pugh modulus ratio (<italic>G</italic>/<italic>B</italic>). Both calculated values of elastic anisotropic ratios (<italic>A</italic><italic><sub>B</sub></italic>, <italic>A</italic><italic><sub>G</sub></italic> and <italic>A</italic><italic><sub>E</sub></italic>) and shear anisotropic factors (<italic>A</italic><sub>1</sub>, <italic>A</italic><sub>2</sub>and <italic>A</italic><sub>3</sub>) indicate the four HfO<sub>2</sub> being anisotropic. The details of anisotropies are demonstrated in 3D plots. Sound speed and minimum thermal conductivities along different directions are calculated. Slowness on <italic>XY</italic>, <italic>YZ</italic> and <italic>ZX</italic> faces are solved and plotted.
