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Register a new userDimensionalities and multiplicities determination of crystal nets
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Low-dimensional materials have attracted significant attentions over the past decade. To discover new low-dimensional materials, high-throughout screening methods have been applied in different materials databases. For this purpose, the reliability of dimensionality identification is therefore highly important. In this work, we find that the existence of self-penetrating nets may lead to incorrect results by previous methods. In stead of this, we use the quotient graph to analysis the topologies of structures and compute their dimensionalities. Based on the quotient graph, we can calculate not only the dimensionality but also the multiplicity of self-penetrating structures. As a demonstration, we screened the Crystallography Open Database using our method and found hundreds of structures with different dimensionalities and high multiplicities up to eleven.
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The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distortion and stress regularization at a dislocation core and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for the consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We also compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.
We propose an approach for exploiting machine learning to approximate electronic fields in crystalline solids subjected to deformation. Strain engineering is emerging as a widely used method for tuning the properties of materials, and this requires repeated density functional theory calculations of the unit cell subjected to strain. Repeated unit cell calculations are also required for multi-resolution studies of defects in crystalline solids. We propose an approach that uses data from such calculations to train a carefully architected machine learning approximation. We demonstrate the approach on magnesium, a promising light-weight structural material: we show that we can predict the energy and electronic fields to the level of chemical accuracy, and even capture lattice instabilities.
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and materials property prediction. Previous work has used machine learning models such as neural networks and support vector machines combined with composition features for lattice constant prediction and has achieved a maximum performance for cubic structures with an average $R^2$ of 0.82. Other models tailored for special materials family of a fixed form such as ABX3 perovskites can achieve much higher performance due to the homogeneity of the structures. However, these models trained with small datasets are usually not applicable to generic lattice parameter prediction of materials with diverse compositions. Herein, we report MLatticeABC, a random forest machine learning model with a new descriptor set for lattice unit cell edge length ($a,b,c$) prediction which achieves an R2 score of 0.979 for lattice parameter $a$ of cubic crystals and significant performance improvement for other crystal systems as well. Source code and trained models can be freely accessed at https://github.com/usccolumbia/MLatticeABC
Crystal structure prediction is now playing an increasingly important role in discovery of new materials. Global optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) have been combined with first principle free energy calculations to predict crystal structures given composition or only a chemical system. While these approaches can exploit certain crystal patterns such as symmetry and periodicity in their search process, they usually do not exploit the large amount of implicit rules and constraints of atom configurations embodied in the large number of known crystal structures. They currently can only handle crystal structure prediction of relatively small systems. Inspired by the knowledge-rich protein structure prediction approach, herein we explore whether known geometric constraints such as the atomic contact map of a target crystal material can help predict its structure given its space group information. We propose a global optimization based algorithm, CMCrystal, for crystal structure reconstruction based on atomic contact maps. Based on extensive experiments using six global optimization algorithms, we show that it is viable to reconstruct the crystal structure given the atomic contact map for some crystal materials but more constraints are needed for other target materials to achieve successful reconstruction. This implies that atomic interaction information learned from existing materials can be used to improve crystal structure prediction.
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