Atomistic mechanisms of phase transitions in all-temperature barocaloric material KPF$_6$

TL;DR

The study addresses the atomistic origins of the all-temperature barocaloric effect in KPF6 by combining first-principles calculations with a moment tensor potential–accelerated MD framework to map four phases (C, M-II, M-I, R) and their pressure-induced transitions. It reveals that strong fluorine orientational disorder in the cubic C phase, together with anharmonic lattice dynamics and cooperative PF6 rotations under pressure, drives transitions to the ordered R phase with low barriers, producing persistent isothermal entropy changes $S(p,T)=S_{vib}(p,T)+S_{ori}(p,T)$. Vibrational entropy dominates the total entropy, while orientational entropy is modulated by pressure, yielding an all-temperature BCE spanning 77–300 K that aligns with experiments. These insights offer design principles for BCE materials with broad operational temperature ranges and highlight the role of FOD and octahedral rotations in tuning caloric responses.

Abstract

Conventional barocaloric materials typically exhibit limited operating temperature ranges. In contrast, KPF$_6$ has recently been reported to achieve an exceptional all-temperature barocaloric effect (BCE) via pressure-driven phase transitions. Here, we elucidate the atomistic mechanisms underlying the phase transitions through first-principles calculations and machine-learning potential accelerated molecular dynamics simulations. We identify four distinct phases: the room-temperature cubic (C) plastic crystal characterized by strong fluorine orientational disorder (FOD) and anharmonicity, the intermediate-temperature monoclinic (M-II) phase with decreasing FOD, the low-temperature monoclinic (M-I) phase with suppressed FOD, and the fully ordered rhombohedral (R) phase under pressure. Phonon calculations confirm the dynamic stability of the M-II, M-I, and R phases at 0 K, whereas the C phase requires thermal fluctuations for stabilization. Under pressure, all the C, M-II, and M-I phases transform to the R phase, which are driven by cooperative PF$_6$ octahedral rotations coupled with lattice modulations. These pressure-induced phase transitions result in persistent isothermal entropy changes across a wide temperature range, thereby explaining the experimentally observed all-temperature BCE in this material. Hybrid functional calculations reveal wide-bandgap insulating behavior across all phases. This work deciphers the interplay between FOD, anharmonicity, and phase transitions in KPF$_6$, providing important insights for the design of BCE materials with broad operational temperature spans.

Figures (10)

• Figure 1: (a)-(d) Crystal structures of the four phases of KPF$_6$. (e) The experimentally-determined temperature-pressure phase diagram of KPF$_6$, adapted from Ref. LibingNC2025.
• Figure 2: (a) The kernel principal component analysis of training and validation structures. (b)-(d) MLP predicted energies, forces, and stress tensors against DFT results. The training and validation datasets are indicated by the blue and red points, respectively.
• Figure 3: Time evolution of the lattice parameter for the C phase during a MD simulation at 300 K and 0 GPa. Insets show the top view of the initial configuration obtained from PBEsol relaxation and the final equilibrated configuration from the MD simulation, highlighting the plastic crystal nature of the C phase characterized by significant orientational disorder of the fluorine atoms.
• Figure 4: Energy-volume curves for the M-I, M-II, and R phases of KPF$_6$, calculated at 0 K using the (a) PBEsol, (b) PBEsol+D3, and (c) SCAN functionals. (d)-(f) Corresponding enthalpy-pressure curves of the M-I and M-II phases relative to the R phase.
• Figure 5: Phonon dispersion relationships of the four phases of KPF$_6$ calculated using the MTP. (a) The M-I phase at 0 K and 0 GPa. (b) The M-II phase at 0 K and 0 GPa. (c) The C phase at 300 K and 0 GPa (obtained by the SSCHA method). (d) The R phase at 0 K and 1 GPa.