We are pleased to introduce the collection, 2022 Retrospective: Computational Materials Science. This collection aims to showcase original research and review-based papers on the most exciting developments of the past couple of years.The work presented here highlights the broad diversity of research performed across the section, and aims to put a spotlight on the main areas of interest. All research presented here seeks to display strong advances in theory, experiment, and methodology with applications to compelling problems.Authors are encouraged to showcase their most recent discoveries and to kickstart scientific discourse around them.

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Frontiers in Materials

Computational Materials Science

2022 Retrospective: Computational Materials Science

In this work, the hot deformation behavior and microstructure evolution of ZK60 alloy are investigated. Meanwhile, constructive models and hot processing maps of ZK60 alloy during thermal tension are also established. Toward these ends, thermal tensile tests were performed at elevated deformation temperatures (523 K–673 K) and wide-ranging strain rates (0.0005 <mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to 0.1 <mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). The findings indicated that as the tensile temperature increases and the strain rate decreases, the flow stress exhibited a decrease. To better evaluate the flow behavior of the alloy, Arrhenius model coupled strain effects and particle swarm optimization support vector machine (PSO-SVM) regression model are developed. Both the developed Arrhenius model and PSO-SVM regression model could depict the flow stress of the hot deformation ZK60 alloy. However, the results comparison revealed that the PSO-SVM regression model provides a more accurate prediction of the stress in the studied alloy with the AARE and R of 1.12% and 0.9984, respectively. The microstructure observation revealed that the primary softening mechanism in the alloy is predominantly dynamic recrystallization (DRX). Using the created hot processing map, the stability processing areas for this alloy were concentrated in the range of 573 K–653 K with a strain rate of 0.001 s-1 to 0.08 s-1. The described model is implemented in the finite element software. Then, the wire-drawing process of ZK60 alloy is also simulated.

In this work, the hot deformation behavior and microstructure evolution of ZK60 alloy are investigated. Meanwhile, constructive models and hot processing maps of ZK60 alloy during thermal tension are also established. Toward these ends, thermal tensile tests were performed at elevated deformation temperatures (523 K–673 K) and wide-ranging strain rates (0.0005 <math id="m1"><mrow><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> to 0.1 <math id="m2"><mrow><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>). The findings indicated that as the tensile temperature increases and the strain rate decreases, the flow stress exhibited a decrease. To better evaluate the flow behavior of the alloy, Arrhenius model coupled strain effects and particle swarm optimization support vector machine (PSO-SVM) regression model are developed. Both the developed Arrhenius model and PSO-SVM regression model could depict the flow stress of the hot deformation ZK60 alloy. However, the results comparison revealed that the PSO-SVM regression model provides a more accurate prediction of the stress in the studied alloy with the AARE and R of 1.12% and 0.9984, respectively. The microstructure observation revealed that the primary softening mechanism in the alloy is predominantly dynamic recrystallization (DRX). Using the created hot processing map, the stability processing areas for this alloy were concentrated in the range of 573 K–653 K with a strain rate of 0.001 s-1 to 0.08 s-1. The described model is implemented in the finite element software. Then, the wire-drawing process of ZK60 alloy is also simulated.

Prediction of flow stress and microstructure evolution mechanism during thermal tensile process of ZK60 alloy

In this work we devise a theoretical and computational method to compute the elastic scattering of electrons from a non-spherical potential, such as in the case of molecules and molecular aggregates. Its main feature is represented by the ability of calculating accurate wave functions for continuum states of polycentric systems via the solution of the Lippmann-Schwinger equation, including both the correlation effects and multi-scattering interference terms, typically neglected in widely used approaches, such as the Mott theory. Within this framework, we calculate the purely elastic scattering matrix elements. As a test case, we apply our scheme to the modelling of electron-water elastic scattering. The Dirac-Hartree-Fock self-consistent field method is used to determine the non-spherical molecular potential projected on a functional space spanned by Gaussian basis set. By adding a number of multi-centric radially-arranged s-type Gaussian functions, whose exponents are system-dependent and optimized to reproduce the properties of the continuum electron wave function in different energy regions, we are able to achieve unprecedented access to the description of the low energy range of the spectrum (0.001 < E < 10 eV) up to keV, finding a good agreement with experimental data and previous theoretical results. To show the potential of our approach, we also compute the total elastic scattering cross section of electrons impinging on clusters of water molecules and zundel cation. Our method can be extended to deal with inelastic scattering events and heavy-charged particles.

In this work we devise a theoretical and computational method to compute the elastic scattering of electrons from a non-spherical potential, such as in the case of molecules and molecular aggregates. Its main feature is represented by the ability of calculating accurate wave functions for continuum states of polycentric systems via the solution of the Lippmann-Schwinger equation, including both the correlation effects and multi-scattering interference terms, typically neglected in widely used approaches, such as the Mott theory. Within this framework, we calculate the purely elastic scattering matrix elements. As a test case, we apply our scheme to the modelling of electron-water elastic scattering. The Dirac-Hartree-Fock self-consistent field method is used to determine the non-spherical molecular potential projected on a functional space spanned by Gaussian basis set. By adding a number of multi-centric radially-arranged s-type Gaussian functions, whose exponents are system-dependent and optimized to reproduce the properties of the continuum electron wave function in different energy regions, we are able to achieve unprecedented access to the description of the low energy range of the spectrum (0.001 &lt; E &lt; 10&nbsp;eV) up to keV, finding a good agreement with experimental data and previous theoretical results. To show the potential of our approach, we also compute the total elastic scattering cross section of electrons impinging on clusters of water molecules and zundel cation. Our method can be extended to deal with inelastic scattering events and heavy-charged particles.

Elastic scattering of electrons by water: An ab initio study

We introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability by training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). We show that this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier), and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, we demonstrate, that using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure relative importance of the contributing physical processes.

We introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability by training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). We show that this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier), and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, we demonstrate, that using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure relative importance of the contributing physical processes.

Emulating quantum dynamics with neural networks via knowledge distillation

One of the most interesting applications of the Monte Carlo method consists in the simulation of the energy loss spectrum of backscattered electrons when a solid target is bombarded with an electron beam of given kinetic energy. Knowing the elastic and inelastic scattering cross-sections of the electrons in their interaction with the atoms of the target, it is possible to calculate the probabilities of angular diffusion and the loss of kinetic energy for each collision between the electrons of the incident beam and the atoms of the target. In this way, it is possible to model the history of each electron following its trajectory and calculating its energy losses, its final energy, and the exit point from the target surface whether and where it exists. By averaging over a large number of trajectories, it is possible to obtain a spectrum representing the energy distribution of the backscattered electrons from any given solid target. This paper compares experimental and Monte Carlo data concerning reflection electron energy loss spectra. In particular, the paper is aimed at understanding the interplay between surface and bulk features for incident electrons in Al.

One of the most interesting applications of the Monte Carlo method consists in the simulation of the energy loss spectrum of backscattered electrons when a solid target is bombarded with an electron beam of given kinetic energy. Knowing the elastic and inelastic scattering cross-sections of the electrons in their interaction with the atoms of the target, it is possible to calculate the probabilities of angular diffusion and the loss of kinetic energy for each collision between the electrons of the incident beam and the atoms of the target. In this way, it is possible to model the history of each electron following its trajectory and calculating its energy losses, its final energy, and the exit point from the target surface whether and where it exists. By averaging over a large number of trajectories, it is possible to obtain a spectrum representing the energy distribution of the backscattered electrons from any given solid target. This paper compares experimental and Monte Carlo data concerning reflection electron energy loss spectra. In particular, the paper is aimed at understanding the interplay between surface and bulk features for incident electrons in Al.

Aluminum electron energy loss spectra. A comparison between Monte Carlo and experimental data

Machine learning and artificial intelligence (AI/ML) methods are beginning to have significant impact in chemistry and condensed matter physics. For example, deep learning methods have demonstrated new capabilities for high-throughput virtual screening, and global optimization approaches for inverse design of materials. Recently, a relatively new branch of AI/ML, deep generative models (GMs), provide additional promise as they encode material structure and/or properties into a latent space, and through exploration and manipulation of the latent space can generate new materials. These approaches learn representations of a material structure and its corresponding chemistry or physics to accelerate materials discovery, which differs from traditional AI/ML methods that use statistical and combinatorial screening of existing materials via distinct structure-property relationships. However, application of GMs to inorganic materials has been notably harder than organic molecules because inorganic structure is often more complex to encode. In this work we review recent innovations that have enabled GMs to accelerate inorganic materials discovery. We focus on different representations of material structure, their impact on inverse design strategies using variational autoencoders or generative adversarial networks, and highlight the potential of these approaches for discovering materials with targeted properties needed for technological innovation.

Machine learning and artificial intelligence (AI/ML) methods are beginning to have significant impact in chemistry and condensed matter physics. For example, deep learning methods have demonstrated new capabilities for high-throughput virtual screening, and global optimization approaches for inverse design of materials. Recently, a relatively new branch of AI/ML, deep generative models (GMs), provide additional promise as they encode material structure and/or properties into a latent space, and through exploration and manipulation of the latent space can generate new materials. These approaches learn representations of a material structure and its corresponding chemistry or physics to accelerate materials discovery, which differs from traditional AI/ML methods that use statistical and combinatorial screening of existing materials via distinct structure-property relationships. However, application of GMs to inorganic materials has been notably harder than organic molecules because inorganic structure is often more complex to encode. In this work we review recent innovations that have enabled GMs to accelerate inorganic materials discovery. We focus on different representations of material structure, their impact on inverse design strategies using variational autoencoders or generative adversarial networks, and highlight the potential of these approaches for discovering materials with targeted properties needed for technological innovation.

Deep Generative Models for Materials Discovery and Machine Learning-Accelerated Innovation

Zn–Ni electrophosphate coating is one of the most commonly used materials in industrial applications. The corrosion resistance of this coating is very important in order to achieve the minimum corrosion current of the Zn–Ni electrophosphate coating. This study described a new reliability simulation framework to determine the corrosion behavior of coating using a gene artificial neural network (ANN) to estimate the corrosion current of the coating. The input parameters of the model are temperature, pH of electroplating bath, current density, and Ni2+ concentration, and corrosion current defined as output. The effectiveness and accuracy of the model were checked by utilizing the absolute fraction of variance (R2 = 0.9999), mean absolute percentage error (MAPE = 0.0171), and root mean square error (RMSE= 0.0002). This is determined using the genetic algorithm (GA) and the optimum practice condition.

Zn–Ni electrophosphate coating is one of the most commonly used materials in industrial applications. The corrosion resistance of this coating is very important in order to achieve the minimum corrosion current of the Zn–Ni electrophosphate coating. This study described a new reliability simulation framework to determine the corrosion behavior of coating using a gene artificial neural network (ANN) to estimate the corrosion current of the coating. The input parameters of the model are temperature, pH of electroplating bath, current density, and Ni2+ concentration, and corrosion current defined as output. The effectiveness and accuracy of the model were checked by utilizing the absolute fraction of variance (R2 = 0.9999), mean absolute percentage error (MAPE = 0.0171), and root mean square error (RMSE= 0.0002). This is determined using the genetic algorithm (GA) and the optimum practice condition.

Application of Artificial Neural Networks for Corrosion Behavior of Ni–Zn Electrophosphate Coating on Galvanized Steel and Gene Expression Programming Models

With the advancement of artificial intelligence and machine learning methods, autonomous approaches are recognized to have great potential for performing more efficient scattering experiments. In our view, it is crucial for such approaches to provide thorough evidence about respective performance improvements in order to increase acceptance within a scientific community. Therefore, we propose a benchmarking procedure designed as a cost-benefit analysis that is applicable to any scattering method sequentially collecting data during an experiment. For a given approach, the performance assessment is based on how much benefit, given a certain cost budget, it is able to acquire in predefined test cases. Different approaches thus get a chance for comparison and can make their advantages explicit and visible. Key components of the procedure, i.e., cost measures, benefit measures, and test cases, are made precise for the setting of three-axes spectrometry (TAS) as an illustration. Finally, we discuss neglected aspects and possible extensions for the TAS setting and comment on the procedure’s applicability to other scattering methods. A Python implementation of the procedure to simplify its utilization by interested researchers from the field is also provided.

With the advancement of artificial intelligence and machine learning methods, autonomous approaches are recognized to have great potential for performing more efficient scattering experiments. In our view, it is crucial for such approaches to provide thorough evidence about respective performance improvements in order to increase acceptance within a scientific community. Therefore, we propose a benchmarking procedure designed as a cost-benefit analysis that is applicable to any scattering method sequentially collecting data during an experiment. For a given approach, the performance assessment is based on how much benefit, given a certain cost budget, it is able to acquire in predefined test cases. Different approaches thus get a chance for comparison and can make their advantages explicit and visible. Key components of the procedure, i.e., cost measures, benefit measures, and test cases, are made precise for the setting of three-axes spectrometry (TAS) as an illustration. Finally, we discuss neglected aspects and possible extensions for the TAS setting and comment on the procedure&#x2019;s applicability to other scattering methods. A Python implementation of the procedure to simplify its utilization by interested researchers from the field is also provided.