Calculation of Thermal Expansion Coefficient of Rare Earth Zirconate System at High Temperature by First Principles

Compounds of rare earth zirconates with pyrochlore structure are candidates for the application of thermal barrier coatings of next generation. In order to modify the mechanic properties and maintain the low thermal conductivity, other trivalent rare-earth element substitution is commonly used. Presently, investigation on the evaluation of the property of thermal expansion is attracting more attention. In this paper, a feature parameter of thermal expansion coefficient at high temperature (α_∞) was proposed by combining Grüneisen's equation and the Debye heat capacity model. Using α_∞ model, the thermal expansion property of different compounds can be easily figured out by first principles. Firstly, α_∞ of ZrO₂, HfO₂, were calculated, and results are in good agreement with the experimental data from the literature. Moreover, α_∞ of La₂Zr₂O₇, Pr₂Zr₂O₇, Gd₂Zr₂O₇, and Dy₂Zr₂O₇ were calculated, and results demonstrated that the model of α_∞ is a useful tool to predict the thermal expansion coefficient at high temperature. Finally, Gd₂Zr₂O₇ with 4 different Yb dopant concentrations (Gd_1-xYb_x)₂Zr₂O₇ (x = 0, 0.125, 0.3125, 0.5) were calculated. Comparing with the experimental data from the literature, the calculation results showed the same tendency with the increasing of Yb concentration.