Zero thermal expansion in cubic MgZrF₆

Isotropic zero thermal expansion (ZTE) is rare but intriguing physical property in materials. Here, we report an isotropic ZTE property in a double ReO₃-type compound of MgZrF₆, which exhibits a negligible value of coefficient of thermal expansion (α_l = −7.94 × 10⁻⁷ K⁻¹ (XRD), α_l = −4.22 × 10⁻⁷ K⁻¹ (dilatometry), 300-675 K). The ZTE mechanism of MgZrF₆ is understood by the joint studies of temperature dependence of crystal structure and lattice dynamics. Interestingly, different magnitudes of atomic displacement parameters (ADPs) for the fluorine atoms in MZrF₆ (M = Ca, Ni, Mg) are found. The strong temperature sensitivity of ADPs demonstrates intensive transverse thermal vibration of fluorine atoms, which contributes essentially to the negative thermal expansion of CaZrF₆. By contrast, for NiZrF₆ with positive thermal expansion, the temperature response of ADPs is weak. Moderate transverse thermal vibration takes place in MgZrF₆, and ZTE appears. Furthermore, lattice dynamics of MgZrF₆ is studied by temperature-dependent Raman spectroscopy, which reveals the ZTE mechanism. In particular, the F_2g and A_g modes, corresponding to the bending and stretching vibrations of fluorine atoms, respectively, neither soften nor harden over the whole temperature range, which is correlated with the isotropic ZTE property of MgZrF₆.