Thermal expansions of Ln ₂Zr ₂O ₇ (Ln = La, Nd, Sm, and Gd) pyrochlore

The thermal expansions of the rare earth zirconate (Ln ₂Zr ₂O ₇, Ln = La, Nd, Sm, and Gd) pyrochlore were studied by the Debye and quasi harmonic approximation combined with the first principles calculations. The difference between C _V and C _P was obtained. The temperature dependence of thermal expansions is mainly caused by the restoration of thermal energy due to phonon excitations at relatively a low temperature. When the temperature is much higher than Debye temperature, i.e., above 600 K for Ln ₂Zr ₂O ₇ compounds, the volumetric coefficient is increased linearly by increasing the temperature. The calculations are in good agreement with the experiments.