[Paper Review] Coupling of phase transition, anharmonicity, and thermal transport in CaSnF$_6$

Daxue Hao, Hao Huang+3 more|arXiv (Cornell University)|Mar 25, 2026

Thermal Expansion and Ionic Conductivity0 citations

TL;DR

This study combines first-principles calculations with a neuroevolution potential to simulate CaSnF6, revealing how phase transition, lattice dynamics, and anharmonicity control thermal transport and negative thermal expansion. A pronounced non-monotonic κL anomaly is linked to lattice reconstruction near the phase boundary.

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.

Motivation & Objective

• Understand how structural phase transition affects lattice dynamics and thermal transport in CaSnF6.
• Quantify the roles of low-energy rigid unit modes and four-phonon scattering in thermal conductivity.
• Demonstrate the capability of machine-learned neuroevolution potentials for modeling phase transitions and transport.
• Provide transport-level evidence of lattice reconstruction during the phase transition.

Proposed method

• Use density functional theory with PAW pseudopotentials and PBEsol for accurate structural energetics.
• Train a neuroevolution potential (NEP) against DFT data for both low- and high-temperature phases via active learning.
• Compute lattice thermal conductivity (κL) using ShengBTE self-consistent solution of the BTE including 3- and 4-phonon scattering.
• Validate κL with Green-Kubo and homogeneous nonequilibrium MD (HNEMD) methods to cross-check transport results.
• Incorporate thermal expansion effects via NEP-MD trajectories and TDEP-derived force constants in BTE.
• Study phase transition by NPT-MD on large supercells to identify transition temperature and structural changes.

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

Experimental results

Research questions

• RQ1 What is the mechanism behind negative thermal expansion in CaSnF6 and how does it couple to lattice dynamics?
• RQ2 How do anharmonic phonon interactions, especially four-phonon processes, influence κL in CaSnF6 across temperatures?
• RQ3 Does CaSnF6 exhibit a measurable κL anomaly near its structural phase transition, and what is its nature?
• RQ4 Can a machine-learned potential accurately capture phase transitions and transport properties in CaSnF6 over a wide temperature range?

Key findings

• κL at 300 K is 7.02 W/mK from 3-phonon and 3.49 W/mK from 4-phonon contributions without thermal expansion; with expansion, κL becomes 5.23 W/mK (3ph) and 2.46 W/mK (4ph).
• HNEMD gives κL of 3.78 W/mK without expansion and 2.93 W/mK with expansion at 300 K, confirming enhanced scattering from volume contraction.
• CaSnF6 shows negative thermal expansion with αv = -14.67×10^-6 K^-1 in the high-temperature phase, in close agreement with experiment (-15.78×10^-6 K^-1).
• Low-frequency phonons (<100 cm^-1) contribute over 80% of κL, with a maximum cumulative κL MFP around 335 nm.
• Four-phonon scattering significantly suppresses κL, reducing 3ph+4ph results to less than half of 3ph-only predictions; expansion enhances low-frequency scattering and reduces κL.
• Near the phase transition (~143 K), κL exhibits a non-monotonic anomaly (decrease from 4.88 to 4.57 W/mK, then partial recovery to 4.70 W/mK), signaling lattice reconstruction.

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) Frequenc