Lectures on Phase Field

Description

This open access textbook fills a gap, in that it introduces readers to the theory and applications of the Phase-Field technique. Phase Field, over the years, has emerged as a standard tool for materials research, just as the Finite-Element technique has in structure mechanics.  Whereas the few existing textbooks on this topic are intended for advanced readers, this one is made accessible to the widest possible audience, through an engaging, lecture format. The content grows out of a course the authors teach for graduate students at Ruhr-University Bochum. Even readers who may, at first, have no clue at all what a “Phase Field” is and for what it is used, are invited on a journey from general physics of thermodynamics and wave mechanics, through applications in all fields of materials science, up to the central questions of physical being. On this journey all the necessary techniques are detailed, mostly formulated in a mathematical language easily understood by engineers and natural scientists. Preface Reference Contents Part I The Phase-Field Method 1 Introduction 1.1 What Is a Phase Field? 1.2 What Is the Purpose of Phase Field? 1.3 History of the Phase-Field Method 1.3.1 Microscopic Phase Field 1.3.2 The Problem of Scale 1.4 Mesoscopic Phase-Field Model 1.4.1 Applications References 2 Analytics 2.1 The Problem of Propagating a Wave Front on a Numerical Grid 2.2 Equation of Motion for the Phase Field 2.3 Traveling-Wave Solution for the Double-Well Potential 2.4 Interpretation of the Phase-Field Equation 2.5 Phase-Field Equation and Traveling-Wave Solution for the Double-Obstacle Potential 2.6 Gibbs–Thomson Limit of the Phase-Field Equation 2.7 Exercises References 3 Capillarity 3.1 Curvature of a Phase-Field Contour 3.2 Anisotropy of Interface Energy 3.2.1 Interface-Energy Anisotropy: PhenomenologicalPicture 3.2.2 Interface-Energy Anisotropy: Phase-Field Picture 3.3 Exercises References 4 Temperature 4.1 Thermodynamically Consistent Derivation of the Phase-Field Equation Coupled to Temperature 4.2 Thin-Interface Limit 4.3 Exercises References 5 Concentration 5.1 Phase Field and Solute Concentration 5.2 Finite Interface Dissipation Model 5.3 Multicomponent Alloy Transformation 5.4 Exercises References 6 Multi-Phase-Field Approach 6.1 Phase-Field Functional for Multiple Phases 6.2 Double Obstacle versus Double Well in Multi Phase Field 6.3 Multi-Phase-Field Equation 6.4 Exercise References 7 Stress–Strain and Fluid Flow 7.1 Coupling to Stress and Strain 7.2 Coupling to Fluid Flow 7.3 Exercises References 8 Quantum Phase Field 8.1 Introverted Picture of Mass and Space 8.2 Formal Definition of Quantum Phase Fields 8.3 Volume Energy of One Doublon 8.4 Multidimensional Interpretation 8.5 Symmetry Breaking in Condensed Matter and Elementary Particle Physics 8.6 Exercises References Part II OpenPhase 9 Tutorial 1: OpenPhase 9.1 Introduction to the OpenPhase Software Package 9.1.1 Features 9.2 Download 9.3 Installation 9.3.1 System Requirements Minimum System Requirements 9.3.2 Installing the Prerequisites The GCC Compiler FFTW 9.3.3 OpenPhase (Compilation) 9.3.4 Update OpenPhase 9.3.5 OpenPhase Application Structure of an OpenPhase Application Compile Your Application Run Your Application 9.4 The Input File Structure 9.4.1 Step by Step Through the ProjectInput File RunTimeControl Settings BoundaryConditions 10 Tutorial 2: OpenPhase Examples 10.1 Normal Grain Growth 10.1.1 Simulation Example Step by Step Through the Source Code Results 10.2 Dendritic Solidification 10.2.1 Simulation Example Step by Step Through the Source Code Results Reference Appendix A A.1 Simple Dendrite Code Index