Shry: Application of Canonical Augmentation to the Atomic Substitution Problem

Abstract

A common approach for studying a solid solution or disordered system within a periodic ab initio framework is to create a supercell in which certain amounts of target elements are substituted with other elements. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from many substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. Our developed Python software package, which is called Shry (Suite for High-throughput generation of models with atomic substitutions implemented by Python), allows the selection of only symmetry-inequivalent structures from the vast number of candidates based on the canonical augmentation algorithm. Shry is implemented in Python 3 and uses the CIF format as the standard for both reading and writing the reference and generated sets of substituted structures. Shry can be integrated into another Python program as a module or can be used as a stand-alone program. The implementation was verified through a comparison with other codes with the same functionality, based on the total numbers of symmetry-inequivalent structures, and also on the equivalencies of the output structures themselves. The provided crystal structure data used for the verification are expected to be useful for benchmarking other codes and also developing new algorithms in the future.

Feature Space of XRD Patterns Constructed by an Autoencoder

“…[ 4 ] For the ten different concentrations considered here ( Table 1 ), we have recorded 150 XRD patterns corresponding to inequivalent symmetries analyzed with the space‐group clustering tool. [ 37 ] There is a variation in the number of non‐equivalent structures depending on concentration, which causes the imbalance in the training data. In fact, as we will see later in detail, for the case of Sm 1 Zr 0 Fe 1 1Ti 1 , this imbalance results in low prediction accuracy for this composition as a special case.…”

“…In some compositions, clusters are concentrated in a narrow region, while others are widely spread (e.g., Sm 1.0 Zr 0.0 Fe 10.0 Ti 2.0 ). This reflects the variation in the number of irreducible structures [4,37] for each composition, as described below. Even for the same composition, there are several inequivalent structures (irreducible structures) in terms of the space group, depending on which sites are substituted.…”

Evolution of Yb3+ Speciation in Cl–/Br–- and Yb3+/Gd3+-Alloyed Quantum-Cutting Lead-Halide Perovskite Nanocrystals

“…We assumed, furthermore, that both Yb Pb and V Pb exist in their nominal charge states and constrained our simulation cells to be charge-neutral by only allowing for multiples of the fully compensated complex 2Yb Pb + V Pb , whether dissociated or not. We employed the SHRY software library 37 to enumerate symmetrically distinct Yb Pb −V Pb configurations under this charge-balance constraint. Given the minimum supercell sizes required to fit the longest conformation of these Pb-sublattice defect configurations, we subsequently used random uniform enumeration of the Cl−Br-site decorations.…”

Machine learning-aided band gap prediction of semiconductors with low concentration doping

“…As an example, the number of possible configurations for A 0.5 Pb 0.5 Te systems with a 2 Â 2 Â 2 supercell will be reduced from 601 080 390 to 404 582 after an elimination process using symmetrical operations. 40 In detail, space group operations (symmetrical operations) are performed on each configuration starting from the first configuration in the order of the labels to traverse its equivalent configurations. The labels corresponding to the equivalent configurations are found and removed in list L. The above steps are repeated until all equivalent configurations except one in list L have been eliminated during traversal.…”