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Identification of crystal structures is a crucial stage in the exploration of novel functional materials. This procedure is usually time-consuming and can be false-positive or false-negative. This necessitates a significant level of expert proficiency in the field of crystallography and, especially, requires deep experience in perovskite - related structures of hybrid perovskites. Our work is devoted to the machine learning classification of structure types of hybrid lead halides based on available X-ray diffraction data. Here, we proposed a simple approach to quickly identify of dimensionality of inorganic substructures, types of lead halide polyhedra connectivity and structure types using common powder XRD data and ML - decision tree classification model. The average accuracy of our ML algorithm in predicting the dimensionality of inorganic substructure, type of connection of lead halide and inorganic substructure topology by theoretically calculated XRD pattern among 14 most common structure types reaches 0.86+-0.05, 0.827+-0.028 and 0.71+-0.05, respectively. The validation of our decision tree classification ML model on experimental XRD data shows the accuracies of 1.0 and 0.82 for the dimension and structure type prediction. Thus, our approach can significantly simplify and accelerate the interpretation of highly complicated XRD data for hybrid lead halides.

Metal halide perovskites APbX3 (A+ = FA+ (formamidinium), MA+ (methylammonium) or Cs+, X- = I-, Br-) are considered as prominent innovative components in nowadays perovskite solar cells. Crystallization of these materials is often complicated by the formation of various phases with the same stoichiometry but structural types deviating from perovskites such as well-known the hexagonal delta FAPbI3 polytype. Such phases are rarely placed in the focus of device engineering due to their unattractive optoelectronic properties while they are, indeed, highly important because they influence on the optoelectronic properties and efficiency of final devices. However, the total number of such phases has not been yet discovered and the complete configurational space of the polytypes and their band structures have not been studied systematically. In this work, we predicted and described all possible hexagonal polytypes of hybrid lead halides with the APbI3 composition using the group theory approach, also we analyzed theoretically the relationship between the configuration of close-packed layers in polytypes and their band gap using DFT calculations. Two main factors affecting the bandgap were found including the ratio of cubic (c) and hexagonal (h) close-packed layers and the thickness of blocks of cubic layers in the structures. We also show that the dependence of the band gap on the ratio of cubic (c) and hexagonal (h) layers in these structures are non-linear. We believe that the presence of such polytypes in the perovskite matrix might be a reason for a decrease in the charge carrier mobility and therefore it would be an obstacle for efficient charge transport causing negative consequences for the efficiency of solar cell devices.

The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so precise description of host-guest interactions is essential for high-throughput screening aimed at ranking the most promising candidates. However, highly accurate ab initio calculations cannot be routinely applied to model thousands of structures due to the demanding computational costs. On the other side, methods based on force field (FF) parametrization suffer from low transferability. To resolve this accuracy-efficiency dilemma, we apply the machine learning (ML) approach. The trained models reproduce atom-in-material quantities, including partial charges, polarizabilities, dispersion coefficients, quantum Drude oscillator and electron cloud parameters within the accuracy of underlying density functional theory method. The aforementioned FF precursors make it possible to thoroughly describe non-covalent interactions typical for MOF-adsorbate systems: electrostatic, dispersion, polarization, and short-range repulsion. The presented approach can also significantly facilitate hybrid atomistic simulations/ML workflows., Comment: 15 pages, 4 figures, 1 table, 125 references

The unprecedented structural flexibility and diversity of inorganic frameworks of layered hybrid halide perovskites (LHHPs) rise up a wide range of useful optoelectronic properties thus predetermining the extraordinary high interest to this family of materials. Nevertheless, the influence of different types of distortions of their inorganic framework on key physical properties such as band gap has not yet been quantitatively identified. We provided a systematic study of the relationships between LHHPs' band gaps and six main structural descriptors of inorganic framework, including interlayer distances (dint), in-plane and out-of-plane distortion angles in layers of octahedra ({\theta}in,{\theta}out), layer shift factor (LSF), axial and equatorial Pb-I bond distances (dax,deq). Using the set on the selected structural distortions we realized the inverse materials design based on multi-step DFT and machine learning approach to search LHHPs with target values of the band gap. The analysis of calculated descriptors band gap dependences for the wide range of generated model structures of (100) single-layered LHHPs results in the following descending order of their importance:dint > {\theta}in > dax > LSFmin > {\theta}out > deq > LSFmax, and also implies a strong interaction value for some pairs of structural descriptors. Moreover,we found that the structures with completely different distortions of inorganic framework can have similar band gap, as illustrated by a number of both experimental and model structures.

Asceding interest of the scientific community in layered hybrid halide perovskites (LHHPs) as materials for innovative photovoltaic and optoelectronic applications led to unprecedented expansion of this family of compounds, reaching now several hundred refined structures. Despite the unique structural diversity of LHHPs, traditional approaches of describing their structures, such as dividing into Dion-Jacobson (DJ) or Ruddlesden-Popper (RP) phases for mostt structures are ambiguous and unquantifiable. Here, we introduced a quantitative layer shift factor (LSF) for a univocal classification and quantitative comparison of the structures. We also developed an algorithm for automatic calculation of the LSF for such structures. We demonstrate the application of the proposed approach for an analysis of correlations between LSF and band gap to reveal "structure-property" relationships. Our study gives a simple and useful approach to classify of either the layered perovskite-like structures or other layered compounds composed of layers of vertex-connected octahedra as a structural unit.

We describe a first open-access database of experimentally investigated hybrid organic-inorganic materials with two-dimensional (2D) perovskite-like crystal structure. The database includes 515 compounds, containing 180 different organic cations, 10 metals (Pb, Sn, Bi, Cd, Cu, Fe, Ge, Mn, Pd, Sb) and 3 halogens (I, Br, Cl) known so far and will be regularly updated. The database contains a geometrical and crystal chemical analysis of the structures, which are useful to reveal quantitative structure-property relationships for this class of compounds. We show that the penetration depth of spacer organic cation into the inorganic layer and M-X-M bond angles increase in the number of inorganic layers (n). The machine learning model is developed and trained on the database, for the prediction of a band gap with accuracy within 0.1 eV. Another machine learning model is trained for the prediction of atomic partial charges with accuracy within 0.01 e. We show that the predicted values of band gaps decrease with an increase of the n and with an increase of M-X-M angles for single-layered perovskites. In general, the proposed database and machine learning models are shown to be useful tools for the rational design of new 2D hybrid perovskite materials.

The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the dust phase and the difference in the spatial distributions of individual fractions of dust particles in the computational domain. The developed technique allows us to reproduce concentrations from one to three fractions of dust particles in each cell in the computational domain. Each of the three fractions of dust particles is mapped to one of the main channels of the RGB palette. The intensity of the color shade is set to be proportional to the relative concentration of dust particles in this fraction. The final image for a polydisperse mixture is obtained by adding images in each of the three color channels. To visualize the degree of polydispersity, I propose depicting the spatial distribution of the entropy of the dust mixture. The definition of the entropy of a mixture is generalized to take into account the states of a mixture with zero number of particles in the mixture. They correspond to dust-free sections of the computational domain (voids). The proposed method for visualizing the polydispersity of a mixture of particles is demonstrated using the example of dynamic numerical modeling of the spatial features of dust structures formed in turbulent gas-dust flows and in flows with shock waves.