In Chapter 3, we mainly focus on the fundamentals of typical mesoscale simulation methods, which can provide a bridge between atomistic structures and macroscopic properties of materials. Among many mesoscale simulation methods, the phase-field and cellular automaton methods are extremely popular and powerful for simulating microstructure evolution. Consequently, we first give a detailed introduction on the fundamentals of the two methods, briefly describing some other mesoscale simulation methods, such as level set and front tracking. After that, application examples using individual mesoscale simulation methods and integrations of the phase-field method with other simulation methods such as atomistic simulation, crystal plasticity, CALPHAD, and machine learning are described in detail. Finally, a case study for design of high-energy-density polymer nanocomposites using the phase-field method is very briefly presented.

In Chapter 11, first an introduction to cutting tools is presented, followed by case studies for two hard coatings. For the TiAlN PVD coating case, we describe how to adjust the formation of metastable phase, select the deposition temperature, and manipulate microstructure to obtain desired mechanical properties through first-principles calculations and thermodynamic calculations. The deposition of the TiAlN/TiN and TiAlN/ZrN multilayer guided by first-principles calculations is also briefly mentioned. For the TiCN CVD coating, we demonstrate that computed CVD phase diagrams can accurately describe phases and their compositions under the given temperature, total pressure, and pressures of various gases. Subsequently, computational fluid dynamics (CFD) is used to provide temperature field, velocity, and distributions of various gases inside the CVD reactor. From that information, calculations-designed experiments were conducted and TiCN coatings were deposited highly efficiently. These simulation-driven designs for the hard coatings have found industrial applications in just two years, much quicker compared to the costly experimental approach.

An accurate analysis of the stress evolution in a metal line loaded with an electric current requires solution of a number of coupled partial differential equations (PDEs). The continuity equations, describing the evolution of concentrations of vacancies and plated atoms along the line, are linked with the force balance equation yielding the elastic stress evolution due to interaction of the metal line volumetric deformation with the rigid confinement. The electric current density distribution is found by solving the corresponding Laplace equation. Accounting for the polycrystalline structure of the metals used as conductors in on-chip interconnects, and proper consideration of a variety of venues for diffusion of vacancies, such as grain boundaries and interfaces with liners and capping layers, requires a comprehensive 2D or 3D analysis. Following void nucleation, which happens when the tensile stress reaches a critical value, the void shape and size are described by a combination of the Cahn–Hilliard and Allen–Kahn equations with the phase-field formalism. Detailed description of these coupled PDEs and results of their solution for a number of cases using finite element analysis (FEA) are demonstrated in this chapter. A good fit between simulation results and measurements is demonstrated throughout the chapter.