Elucidating the High-Pressure Phases of MAPbBr3 Using a Machine Learning Force Field

TL;DR

This work addresses the challenge of understanding pressure-induced phase behavior in the hybrid perovskite MAPbBr3, where conventional AIMD is limited by time and length scales. It introduces a DeepMD-based MLFF trained with DP-GEN concurrent learning to enable large-scale, long-time MD under pressure, and validates the model against known phase sequences and experimental observations. The simulations reproduce the $α$ phase with a triple-well tilt PES $a^0a^0a^0$, the $β$ phase with MA sublattice doubling arising from an in-phase tilt pattern $a^+a^+a^+$, and the $γ$ phase with long-range MA ordering and polar/anti-polar domain formation characterized by $a^+b^0b^0$ tilts and strong host–guest coupling. The results highlight the crucial role of octahedral tilting and host–guest interactions in governing phase stability and dynamics, reveal domain lifetimes exceeding 50 ps at higher pressures, and demonstrate the value of MLFFs for exploring pressure-induced phenomena in hybrid perovskites with-scale and timescale access beyond AIMD.

Abstract

High-pressure phases of the hybrid perovskite MAPbBr3 have been investigated in detail using a novel machine learning force field (MLFF). MLFF simulations successfully reproduce the sequence of pressure-induced phase transitions from the $α$ ($Pm\bar{3}m$) to the $β$ ($Im\bar{3}$) and finally the $γ$ ($Pnma$/$Pmn2_1$) phase. In the $α$ phase, the simulations confirm the triple-well character of the potential energy surface for octahedral tilting shedding light into the local dynamic distortions. In the $β$ phase, our simulations reveal MA sublattice doubling yielding both orientationally disordered and ordered MA ions mirroring experimental observation. This mixed-order phase results from locally frustrated host-guest couplings arising from the in-phase octahedral tilt system ($a^+a^+a^+$). In the high-pressure $γ$ phase, we confirm the formation of polar and anti-polar domains, with the latter have higher lifetimes and persist for over 50 ps at pressures above 1.5 GPa. By elucidating the behavior of various phases of MAPbBr3, this work provides a fundamental understanding of how host-guest interactions and octahedral tilting govern the material's properties. Further, the importance of time scales and length scales in characterizing these phases is emphasized.

Figures (7)

• Figure 1: a) Comparison of cell parameters obtained from our MLFF MD simulations with previous experimentsjaffeHighPressureSingleCrystalStructures2016liangReassigningPressureInducedPhase2022zhangEffectsNonhydrostaticStress2017yesudhasCouplingOrganicCation2020 and simulationsmaityStabilizingPolarDomains2023. The colors denote the directions a, b or c and the symbols denote separate experiments/simulations. The b-axis of the $Pmn2_1$ phase obtained in Ref. liangReassigningPressureInducedPhase2022 has been halved from its original value for comparison purposes as a cell doubling occurs in this direction compared to the $Pnma$ phase reported by other studies. The value of lattice parameter $a$ in the $Pm\bar{3}m$ phase in Ref. wangPressureInducedPhaseTransformation2015a is very different from other works (8.44 $\AA$) and hence is not included. b) Average of the global order parameter associated with the lattice, $\xi_{s^\pm}^{lat}$ at various pressures, where $s = a, b$ or $c$ denotes the coupling direction.
• Figure 2: Histogram on a sphere surface depicting the orientational distribution of MA for each phase where each point represents a unique MA orientation ($\theta$, $\phi$). The arrows on the right shows the positive a, b and c axes directions to denote the regions in the histogram oriented towards the face centers along these directions. The high-symmetry orientations are marked with blue, green, and red circles denoting face-to-face, body-diagonal, and edge-diagonal configurations, respectively. The negative directions as well as other pressures histograms are shown in the SI.
• Figure 3: Intermediate pressure MA ordering. a) Orientational distribution of each MA in the $2\times2\times2$ supercell formed after cell doubling. b) Ensemble averages of the intermediate pressure global order parameter, $\xi^{\beta}$ corresponding to the origin with the maximum value. Inset: Schematic representing the orientational ordering of each of the MA.
• Figure 4: Preference for MA alignment towards horizontal and vertical axis arising as a result of anti-clockwise (positive) and clock-wise (negative) tilts respectively.
• Figure 5: Distributions of tilt patterns (a) and the associated MA orientation distributions (b) for the four groups of unitcells in the simulation cell displaying a distinct orientational MA alignment. Here the tilt patterns were obtained by normalizing a vector composed of the tilts along the three directions as $\vec{K}=[\eta_a^{lat}, \eta_b^{lat}, \eta_c^{lat}]$ and converting them to polar coordinates, ($\theta$, $\phi$). Each tilt component $\eta_s^{lat}$ is obtained as the magnitude of unitcell lattice tilt order parameter $\vec{\eta}_s^{lat}$