Coupling of phase transition, anharmonicity, and thermal transport in CaSnF$_6$

Abstract

Understanding the coupling between structural phase transitions and thermal transport is essential for designing functional materials with tunable properties. Here, we investigate this interplay in CaSnF$_6$ by combining first-principles calculations with a machine-learned neuroevolution potential that enables large-scale molecular dynamics simulations across a wide temperature range. The simulations accurately capture the first-order structural phase transition and associated lattice dynamics. We show that the negative thermal expansion originates from low-energy rigid unit modes involving cooperative rotations of corner-sharing [CaF$_6$]$^{4-}$ octahedra, which induce bond-angle bending and volume contraction. At the same time, strong anharmonicity, dominated by four-phonon scattering, plays a central role in suppressing lattice thermal conductivity ($κ_L$). Crucially, non-equilibrium simulations reveal a pronounced non-monotonic anomaly in $κ_L$ near the phase transition, deviating from the conventional $\sim 1/T^α$ behavior and providing direct transport evidence of lattice reconstruction. These results establish a unified mechanism linking lattice geometry, anharmonic vibrational dynamics, and thermal transport, and highlight the potential of machine-learned potentials for bridging atomic-scale phase transitions with macroscopic transport properties.

Figures (6)

• Figure 1: The crystal structures of (a) low temperature phase (rhombohedral) and (b) high temperature phase (cubic) of CaSnF$_6$. (d) and (e) are the electron localization function (ELF) plot of rhombohedral and cubic CaSnF$_6$. The phonon dispersion of cubic CaSnF$_6$ (c) without thermal expansion (w/o TE) and (f) with thermal expansion (w/ TE). The color scale (blue to red) represents the temperature variation from 250 K to 600 K. The phonon dispersions are calculated from NEP-MD trajectories.
• Figure 2: Phonon transport characteristics of CaSnF$_6$ obtained from AIMD trajectories. (a) Mode-resolved phonon scattering rates at 300 K. (b) Temperature-dependent heat capacity (left axis) and mode Grüneisen parameters (right axis) over 250--600 K. (c) Phonon group velocities at 300 K. (d) Frequency-resolved contribution to the cross-plane thermal conductivity $\kappa_c$ at 300 K, projected onto phonon mode pairs ($\omega_s$, $\omega_{s'}$).
• Figure 3: Thermal transport properties of CaSnF$_6$. (a) Spectral and cumulative thermal $\kappa_L$ as a function of phonon frequency. (b) Cumulative $\kappa_L$ as a function of phonon mean free path (MFP). (c) Decomposition of $\kappa_L$ into particle-like ($\kappa_p$) and glass-like ($\kappa_c$) components, with $\kappa_L = \kappa_p + \kappa_c$. (d) Comparison of $\kappa_L$ obtained from different theoretical approaches. Calculations in (a-c) are based on NEPMD trajectories.
• Figure 4: (a) System potential energy as a function of temperature, showing an abrupt change near 143 K indicative of a first-order structural phase transition. (b) Temperature-dependent pressure along the three lattice directions. (c) Lattice parameter along the a-axis as a function of temperature, exhibiting positive thermal expansion below 143 K and negative thermal expansion above 143 K. (d) Total supercell volume as a function of temperature.
• Figure 5: (a) Temperature dependence of the Ca-F-Sn bond angle. (b) Phonon dispersion projected with mode-resolved Grüneisen parameters. (c-e) Vibrational patterns of the three lowest-frequency optical modes ($o_1$, $o_2$, $o_3$) at the $\Gamma$ point.