CCDCGAN: Inverse design of crystal structures

Autonomous materials discovery with desired properties is one of the ultimate goals for modern materials science. Applying the deep learning techniques, we have developed a generative model which can predict distinct stable crystal structures by optimizing the formation energy in the latent space. It is demonstrated that the optimization of physical properties can be integrated into the generative model as on-top screening or backwards propagator, both with their own advantages. Applying the generative models on the binary Bi-Se system reveals that distinct crystal structures can be obtained covering the whole composition range, and the phases on the convex hull can be reproduced after the generated structures are fully relaxed to the equilibrium. The method can be extended to multicomponent systems for multi-objective optimization, which paves the way to achieve the inverse design of materials with optimal properties.Comment: 14 pages, 3 figure

Representations of Materials for Machine Learning

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such relations for design. However, to build these connections, materials data must be translated into a numerical form, called a representation, that can be processed by a machine learning model. Datasets in materials science vary in format (ranging from images to spectra), size, and fidelity. Predictive models vary in scope and property of interests. Here, we review context-dependent strategies for constructing representations that enable the use of materials as inputs or outputs of machine learning models. Furthermore, we discuss how modern ML techniques can learn representations from data and transfer chemical and physical information between tasks. Finally, we outline high-impact questions that have not been fully resolved and thus, require further investigation.Comment: 20 pages, 5 figures, To Appear in Annual Review of Materials Research 5

Analysis of crystallographic texture information by the hyperspherical harmonic expansion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 223-230).The field of texture analysis is fundamentally concerned with measuring and analyzing the distribution of crystalline orientations in a given polycrystalline material. Traditionally, the orientation distribution function describing crystallographic orientation information is written as a linear combination of the generalized spherical harmonics. Since the use of generalized spherical harmonics requires that orientations be described by sets of Euler angles, the field of texture analysis suffers from the inherent limitations of Euler angles. These include difficulty of presentation and interpretation, discontinuous changes in the description of a changing orientation, and singularities in many equations of Euler angles. An alternative expansion of the orientation distribution function as a linear combination of the hyperspherical harmonics is therefore proposed, with the advantage that this expansion allows rotations to be described by angles that directly relate to the axis and angle of a rotation. Apart from the straightforward and intuitive presentation of orientation statistics that this allows, the utility of the hyperspherical harmonic expansion rests on the fact that the orientation distribution function inherits the useful mathematical properties of the hyperspherical harmonics. The relationship of the hyperspherical harmonics to the three- and four-dimensional rotation groups is investigated, and expressions for the matrix elements of the irreducible representatives of these rotation groups as linear combinations of the hyperspherical harmonics are found.(cont.) These expressions allow an addition formula for the hyperspherical harmonics to be derived, and provide the means to write a simple conversion between the generalized spherical harmonic and hyperspherical harmonic expansions. This allows results derived via the hyperspherical harmonic expansion to be related to the texture analysis literature. Furthermore, a procedure for calculating the symmetrized hyperspherical harmonics consistent with crystal and sample symmetries is indicated, and used to perform the expansion of an orientation distribution function significantly more efficiently. The capability of the hyperspherical harmonic expansion to provide results not traditionally accessible is demonstrated by the generalization of the Mackenzie distribution to arbitrary textures. Finally, further areas where the application of the hyperspherical harmonic expansion is expected to advance the field of texture analysis are discussed.by Jeremy K. Mason.Ph.D

Microstructure sensitive design: a tool for exploiting material anisotropy in mechanical design

A new mathematical framework called Microstructure Sensitive Design (MSD) was recently developed to facilitate solutions to inverse problems in microstructure design where the goal is to identify the complete set of relevant microstructures that are predicted to satisfy a set of designer specified criteria for effective properties or performance. In this work, MSD has been successfully applied to a few design case studies involving polycrystalline metals and continuous fiber reinforced composites (CFRC). The solutions obtained are, as expected, strongly influenced by the selected homogenization theories. In the case studies presented here, elementary first-order theories are used for both the polycrystalline metals and the continuous fiber reinforced composites. In the composite case, elementary first-order theories spanning two length scales have been selected to obtain effective properties of continuous fiber reinforced composite material systems. Having selected these first-order theories, we proceeded to demonstrate the viability of applying the MSD framework to designing optimal orientation distributions in both polycrystalline metals and continuous fiber reinforced composites for the selected mechanical design problems. Specifically, the mechanical design case study used in this work involved maximizing the load carrying capacity of an orthotropic plate with a circular hole and loaded in in-plane tension. MSD results for this case study show a potential improvement of 27% in nickel polycrystals and 267% improvement in AS4-Epoxy composites investigated in this study. Additionally the mechanical design of a pressure vessel containing a partially through axial flaw is examined; the potential improvement in energy dissipated during crack growth is 31%.Ph.D., Materials Science and Engineering -- Drexel University, 200

Site-Net: Using global self-attention and real-space supercells to capture long-range interactions in crystal structures

Site-Net is a transformer architecture that models the periodic crystal structures of inorganic materials as a labelled point set of atoms and relies entirely on global self-attention and geometric information to guide learning. Site-Net processes standard crystallographic information files to generate a large real-space supercell, and the importance of interactions between all atomic sites is flexibly learned by the model for the prediction task presented. The attention mechanism is probed to reveal Site-Net can learn long-range interactions in crystal structures, and that specific attention heads become specialized to deal with primarily short- or long-range interactions. We perform a preliminary hyperparameter search and train Site-Net using a single graphics processing unit (GPU), and show Site-Net achieves state-of-the-art performance on a standard band gap regression task.Comment: 23 pages, 13 figure

Homogenization of Maxwell's equations in periodic composites

We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a computationally-efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically-measurable quantities rather than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some color figures in this preprint may be easier to read because here we utilize solid color lines, which are indistinguishable in black-and-white printin