Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Negative Thermal Expansion, Response to Pressure and Phase Transitions in CaTiF6

Strong volume negative thermal expansion over a wide temperature range typically only occurs in ReO₃-type fluorides that retain an ideal cubic structure to very low temperatures, such as ScF₃, CaZrF₆, CaHfF₆, and CaNbF₆. CaTiF₆ was examined in an effort to expand this small family of materials. However, it undergoes a cubic ( Fm3̅ m) to rhombohedral ( R3̅) transition on cooling to ∼120 K, with a minimum volume coefficient of thermal expansion (CTE) close to -42 ppm K^-1 at 180 K and a CTE of about -32 ppm K^-1 at room temperature. On compression at ambient temperature, the material remains cubic to ∼0.25 GPa with K₀ = 29(1) GPa and K'₀ = -50(5). Cubic CaTiF₆ is elastically softer and shows more pronounced pressure induced softening, than both CaZrF₆ and CaNbF₆. In sharp contrast to both CaZrF₆ and CaNbF₆, CaTiF₆ undergoes a first-order pressure induced octahedral tilting transition to a rhombohedral phase ( R3̅) on compression above 0.25 GPa, which is closely related to that seen in ScF₃. Just above the transition pressure, this phase is elastically very soft with a bulk modulus of only ∼4 GPa as octahedral tilting associated with a reduction in the Ca-F-Ti angles provides a low energy pathway for volume reduction. This volume reduction mechanism leads to highly anisotropic elastic properties, with the rhombohedral phase displaying both a low bulk modulus and negative linear compressibility parallel to the crystallographic c-axis for pressures below ∼2.5 GPa. At ∼3 GPa, a further phase transition to a poorly ordered phase occurs.

Crystal structures, phase transitions and thermal expansion properties of NaZr2(PO4)3–SrZr4(PO4)6 solid solutions

Structures and phase transitions depending on compositions and temperature between R3̄c and R3̄ in Na_(2−2x)Sr_x[ ]_xZr₄(PO₄)₆ have been investigated.