Elastic Properties of Monoclinic \hbox {ZrO}_{2} at Finite Temperatures Via First Principles

The structural and elastic properties of orthorhombic $\hbox {ZrO}_{2}\,(m\hbox {-ZrO}_{2})$ as a function of temperature are investigated by the generalized gradient approximation (GGA) correction scheme in the framework of density functional theory (DFT) and the quasi-harmonic Debye model. The thirteen independent elastic constants of $m\hbox {-ZrO}_{2}$ at temperatures to 3200 K are theoretically investigated for the first time. It is found that with increasing temperature, all elastic constants change, especially $C_{35}\hbox { and }C_{25}$ change rapidly in the temperature range of 1400 K to 1600 K and 2200 K to 2600 K, respectively. We also obtain the bulk modulus $B$ , shear modulus $G$ , Young’s moduli $E$ , as well as Poisson’s ratio $\sigma $ of $m\hbox {-ZrO}_{2}$ at high temperatures. Our work suggests that it is very important to predict the melting properties of materials via the elastic constants at temperatures.