How the Temperature and Composition Govern the Structure and Band Gap of Zr-Based Chalcogenide Perovskites: Insights from ML Accelerated AIMD

Abstract

The effects of temperature and composition on the structural and electronic properties of chalcogenide perovskite (CP) materials AZrX3 (A = Ba, Sr, Ca; X = S, Se) in the distorted perovskite (DP) phase are investigated using ab initio molecular dynamics (AIMD) accelerated by machine-learned force fields. Long-range van der Waals (vdW) interactions, incorporated into the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional using the DFT-D3 scheme, are found to be crucial for achieving correct predictions of structural parameters. Our calculations show that the distortion of the DP structure with respect to the parent cubic (C) phase, realized in the form of interoctahedral tilting, decreases with the increasing size of the A cations. The tendency for a gradual transformation of the DP-to-C phase with increasing temperature is shown to be strongly composition-dependent. The transformation temperature decreases with the size of cation A and increases with the size of anion X. Thus, within the range of the temperatures considered here (300–1200 K), a complete transformation is observed only for BaZrS3 (∼600 K) and BaZrSe3 (∼900 K). The computed band gap of CPs is shown to monotonically decrease with increasing temperature, and the magnitude of this decrease is found to be proportional to the extent of the thermally induced changes in the internal structure. Diverse factors affecting the magnitude of band gaps of CP materials are analyzed.

Thermal Stability of Chalcogenide Perovskites

“…Both compositions are stable as ternary compounds, and their thermodynamically most favorable phase is a DP orthorhombic phase. As we have shown in our recent theoretical studies, , upon heating to sufficiently high temperatures, the orthorhombic DP lattices of SrZrS 3 and BaZrS 3 can be sufficiently “softened” so that the increased thermal motion can eliminate the octahedral distortions and the lattice transitions to the more symmetric tetragonal or even cubic arrangement. The onset of this process is experimentally observed at ∼510 °C for BaZrS 3 and ∼410 °C for BaHfS 3 .…”

“… a The relative sizes of ions and bond lengths are shown in scale. The ionic radii were taken from ref . …”

“…In contrast, BaZrS 3 is known to crystallize in two crystal phases: a low temperature, T < 893 K (520 °C) distorted perovskite phase (orthorhombic, Pnma ) and a high temperature, T > 933 K (560 °C) tetragonal, I4 1 /acd phase . Within the structure, the small Zr 4+ cations ( r B = 0.72 Å) are octahedrally coordinated by six larger S 2– anions ( r X = 1.84 Å).…”

“…In the case of the BaZrS 3 and BaHfS 3 , the RT stable phase is the orthorhombic distorted perovskite (DP) phase. Upon heating to ∼510–530 °C, BaZrS 3 , and ∼410–430 °C, BaHfS 3 reversibly transition to a more symmetric tetragonal phase . In the case of SrZrS 3 and SrHfS 3 , the thermodynamically most stable phase at RT is the nonperovskite NL phase .…”

Overcoming the Chemical Complexity Bottleneck in on-the-Fly Machine Learned Molecular Dynamics Simulations

“…This failure mode is related to the uncertainty quantification and structure of the active learning loop. Typically, the error estimate from the Bayesian regression are assumed to be correlated with the actual root mean squared error, ,− although the error estimates are known to be poorly calibrated. However, we observe that in some cases the error estimates are not even correlated with the true error.…”