Fundamentally, materials derive their properties from the interaction between their constituent atoms. These basic interactions make the atoms assemble in a particular crystalline structure. The same interactions also define how the atoms prefer to arrange themselves in the dislocation core. Therefore, to understand the behavior of dislocations, it is necessary and sufficient to study the collective behavior of atoms in crystals populated by dislocations. This chapter introduces the basic methodology of atomistic simulations that will be applied to the studies of dislocations in the following chapters. Section 1 discusses the nature of interatomic interactions and introduces empirical models that describe these interactions with various degrees of accuracy. Section 2 introduces the significance of the Boltzmann distribution that describes statistical properties of a collection of interacting atoms in thermal equilibrium. This section sets the stage for a subsequent discussion of basic computational methods to be used throughout this book. Section 3 covers the methods for energy minimization. Sections 4 and 5 give a concise introduction to Monte Carlo and molecular dynamics methods. When put close together, atoms interact by exerting forces on each other. Depending on the atomic species, some interatomic interactions are relatively easy to describe, while others can be very complicated. This variability stems from the quantum mechanical motion and interaction of electrons [15, 16]. Henceforth, rigorous treatment of interatomic interactions should be based on a solution of Schrödinger’s equation for interacting electrons, which is usually referred to as the first principles or ab initio theory. Numerical calculations based on first principles are computationally very expensive and can only deal with a relatively small number of atoms. In the context of dislocation modelling, relevant behaviors often involve many thousands of atoms and can only be approached using much less sophisticated but more computationally efficient models. Even though we do not use it in this book, it is useful to bear in mind that the first principles theory provides a useful starting point for constructing approximate but efficient models that are needed to study large-scale problems involving many atoms.
Deformation potential extraction and computationally efficient mobility calculations in silicon from first principles
