Mixing I and Br in Inorganic Perovskites: Atomistic Insights from Reactive Molecular Dynamics Simulations
Summary¶
The study extends a CsPbI\(_3\)-focused ReaxFF parametrization to CsPbBr\(_3\) and mixed CsPb(Br\(_x\)I\(_{1-x}\))\(_3\), training to VASP/ADF PBE + D3(BJ) data (equations of state, precursor phases, defect formation/migration, phase transitions). CMA-ES optimization in ParAMS/AMS 2022 minimizes a weighted SSE loss starting from prior Cs/Pb/I parameters and scaled Br interactions. Large NPT-style ReaxFF MD sweeps map temperature–composition behavior of pseudocubic lattice vectors and octahedral tilting, showing that Br substitution lowers the cubic-like transition temperature and couples to ~2 nm cooperative octahedral dynamics—consistent with strong effects at x ≤ ¼.
Methods¶
- Reference QM: VASP and ADF with PBE + D3(BJ); training properties include atomic charges, EOS of perovskite and non-perovskite phases, precursor EOS (CsX, PbX\(_2\)), defect energies/barriers, and phase transitions (Supporting Information Notes).
- ReaxFF fit: SSE objective with weights σ\(_i\); CMA-ES in ParAMS; initial Br parameters from scaled I-interaction starting points (SI Note 2).
- MD validation / phase diagrams: Gradual heating 100–700 K for compositions x = 0, ⅛, …, 1; monitor lattice vectors and octahedral orientation angles (θ\(_x\), θ\(_y\), θ\(_z\)); compare unit-cell volumes at 575 K to experiment within ~1% (Figure 2).
1 — NPT ReaxFF MD (phase mapping). Engine: LAMMPS + fitted ReaxFF; 3D PBC pseudocubic perovskite supercells at each halide composition x; NPT isotropic with Nose–Hoover/Berendsen-style thermostat + Parrinello/Berendsen-class barostat as in the article (GPa-scale isotropic pressure near 0). Integration timestep in fs (typically sub-1 fs for ReaxFF halide perovskites): JPCC Methods if not copied here. E-field, umbrella, MTD: N/A. Ramped 100–700 K anneal over multi-ns-scale (exact ps/ns equilibration and production / ramp duration: JPCC if not tabulated in this one-page blurb). Compositions x = 0, ⅛, …, 1. 2 — CMA-ES / ParAMS training: PBE + D3(BJ) VASP/ADF targets (first bullets). 3 — Static-only primary claim: N/A beyond training references.
Findings¶
- The fitted potential recovers DFT-ranked bulk stability ordering for CsPbI\(_3\) phases and positive mixing enthalpies for Br/I substitution (< ~1 kcal/mol per formula unit in their Table/figures), with noted discrepancies near x = ⅙ and ¼ linked to overstabilized mixed supercells (SI).
- Defect barriers—for example I vacancy migration ~4.8 kcal/mol (ReaxFF) vs ~7.0 kcal/mol (DFT)—track the training set reasonably, enabling kinetic discussions.
- Pure CsPbBr\(_3\) attains cubic-like averages at lower temperature than CsPbI\(_3\) in the simulations (~310 K vs ~430 K), with Br’s smaller ionic radius (~1.96 Å vs I ~2.20 Å) reducing lattice volumes and Goldschmidt tolerance-related behavior as discussed.
- For mixtures, most of the drop in cubic onset temperature occurs by x ≤ ¼, matching experimental narratives that small Br fractions strongly stabilize cubic-like halide perovskites; octahedral tilt correlations show coherence lengths up to ~2 nm, explaining long-range sensitivity to dilute Br.
The Pols–Tao–Calero–van Duin line thus treats halide mixing as both a thermodynamic and a dynamic problem: tilt coherence and defect migration are co-trained against DFT so that composition–temperature maps are not inferred from static energies alone. DFT vs ReaxFF defect barriers, T-dependent cubic-like onsets, and Br-dilution trends are the key sensitivity levers. JPCC line-edited VOR PDF is authoritative.
Limitations¶
PBE + D3(BJ) training biases transition temperatures low by ~50–100 K vs experiment; ReaxFF cannot capture electronic band properties.
Relevance to group¶
Continues the Eindhoven–van Duin halide perovskite ReaxFF line (Pols, Tao, Calero) for CsPb(Br\(_x\)I\(_{1-x}\))\(_3\) phase behavior.