First-principles approaches and models for crystal defect energetics in metallic alloys

Abstract

Many physical and mechanical properties of metallic alloys are sensitive to the formation and migration of crystal defects such as vacancies, dislocations, stacking faults, and grain boundaries. Those defect behaviors are intrinsically governed by the energetics associated with the distortion, breaking, and reforming of chemical bonds at the atomistic level. As such, first-principles calculations based on density functional theory, which accurately describe the energies and electronic structures of interatomic bonding, have been widely applied to study the formation and migration energetics of crystal defects in various alloy systems. This review article aims to provide a brief summary of the contemporary approaches and models associated with first-principles calculations for accurate modeling and prediction of energetics of various crystal defects in metallic alloys. The review also highlights the recent progress in the development of physics- or/and data-driven-based surrogate models for more efficient predictions of defect energies with first-principles accuracy in a broad range of alloy systems. Last but not least, some of the remaining challenges and issues associated with the first-principles modeling of crystal defects are discussed, along with recommendations for possible solutions.

Introduction

Most of the time, the crystal lattice of a metallic alloy is inevitably imperfect with disruptions of lattice periodicity induced by the presence of crystal defects. In fact, rather than seeking for the perfect, defect-free alloys, the thousand-year development history of metallic alloys in human civilization is accompanied and to some extent driven by the progress in understanding and controlling the behaviors of crystal defects. This can even be traced back to the bronze and iron ages at when our ancestors already learned how to pin dislocations with solutes and other crystal defects to make a stronger hoe or a sharper blade, although they were not clear of the exact strengthening mechanism behind it. The critical roles of crystal defects in determining various alloy properties have been revealed by modern physical metallurgy, from which we learned how the strengths and ductility of metals and alloys could be modified by understanding the defect behaviors such as dislocation motion, twin nucleation, and grain boundary (GB) sliding [1], how the oxidation and corrosion resistance could be improved by understanding the interactions between the crystal defects and reactive atoms, molecules, and ions [2], [3], how the radiation tolerance could be improved by understanding the migration and aggregation kinetics of point defects [4], and more. Moreover, our knowledge of crystal defects in metallic alloys still keeps growing every day due to the tones of active research in the field, from which emerging concepts, theories, models, and approaches are developed one after another to refresh our understanding of the current alloys and to expedite the design and development of new alloys.

The behaviors of crystal defects in metallic alloys are usually complex and inherently across multiple time and length scales. Nevertheless, most of the defect behaviors are governed by the energetics associated with defect formation and migration at the atomistic scale. For example, the dislocation glide in the metals with high lattice friction stress is determined by the migration energy barrier of a part of dislocation moving from one Peierls valley to another at the atomistic level [5], [6]. The formation and migration processes of crystal defects are commonly associated with the distortion, breaking, and reforming of the chemical bonds between atoms. By providing an accurate description of those interatomic bonding responses, first-principles calculations based on density functional theory (DFT) are thus an ideal tool to study the energetics of defect formation and migration at the atomistic scale. The first attempt was made thirty years ago. In the early 1990 s, the DFT-based codes started to become powerful enough to allow first-principles calculations of vacancy formation energies in pure simple metals such as Al and Li [7], [8], and later on in transition metals [9]. Five years later, first-principles calculations of GB became real, from which people, for the first time, developed an in-depth understanding of impurity-induced intergranular embrittlement at the electronic level [10]. The atomic structure of dislocation core, which classic elasticity theory fails to predict, was revealed by first-principles calculations in 2002, solving a long-term debate about the core structure of the screw dislocation in body-cubic-center (bcc) metals [11].

Building upon those milestones, great efforts have been made in the past to develop various first-principles-based models and approaches for accurate modeling and prediction of crystal defect energetics. In this review, we attempt to provide an overview of the first-principles-based modeling methods that are widely adopted for the computation of the formation and migration energies of different types of crystal defects, and to discuss the issues of those methods to address the possible structural and chemical complexity in the defect configurations in complex metallic systems. We also review the efforts in the recent works on resolving those issues via integration of first-principles calculations with physics- and data-driven-based surrogate models. Finally, we provide a summary and an outlook for the future advancement of the first-principles-based approaches and models for modeling crystal defect energetics in metallic alloys.