Thermodynamics of Crystalline Materials: From Nano to Macro (SpringerBriefs in Materials)

This book provides expert treatment of the use of the Calphad calculations for the study of crystal structures and thermodynamics relationships in phase diagram determination. After a short review of the relationships between crystal structures and the thermodynamics of materials, including all possible phase transformations, the book proceeds to a brief discussion of the methods for solving the stability hierarchy of different phases. Coverage includes both theoretical calculations and experimental methods based on classical thermodynamics, with emphasis on the latter. The experimental approach is mainly carried out using heat-exchange data associated with the transition of one form into another. It is demonstrated that the crystallographic properties must be associated with the phase transformations and should be taken into account. The role of X-ray crystallography therein is also discussed. Readers interested in carrying out related research will appreciate the detailed discussion and critical analysis of key results obtained by the author and his colleagues over the past five years. Acknowledgments General Introduction Basis and New Trends in Thermodynamics and Phase Diagrams Contents 1 General Considerations on Crystallography: Elements of Crystallography and Their Use in Thermodynamics of Phases 1.1 Introduction 1.2 Isomorphism and Phase Transitions 1.2.1 Reconstructive Transitions 1.2.2 Polytypism 1.3 The Periodic Network of Atoms in a Structure: Crystal Structure 1.3.1 Nodes 1.3.2 Lattice [12–13] 1.3.3 The Bravais Lattice 1.3.4 Lattice Centering and Face Centering (See Fig. 1.9) 1.3.5 The 14 Bravais Lattices 1.4 Symmetry in Crystals 1.4.1 Group of Symmetry and Lattice Symmetry 1.4.2 Space Group: Plans, Directions and Indices 1.4.3 The Nomenclature of the Crystal Structures 1.5 Crystallochemistry 1.6 Defects in Lattices and Structures 1.7 Linear and Volumic Defects 1.8 Lying Crystallography and Thermodynamics References 2 Thermodynamics of Materials and Basis 2.1 Introduction: The Modern Approach of Phase Diagrams 2.2 Basis and History. Heat Quantity, Temperature and System 2.3 Theoretical Background 2.3.1 External State Variables 2.3.2 Internal State Variables 2.4 Laws of Thermodynamics 2.4.1 The First Law of Thermodynamics 2.4.2 The Second Law of Thermodynamics 2.4.3 The Third Law of Thermodynamics 2.5 Entropy 2.6 Equilibrium 2.7 Definitions 2.8 Free Energy and the Free Energy Function 2.8.1 The Gibbs Energy Function for Pure Stoichiometric Substance 2.8.2 Mixtures, Solutions and Their Free Energy Functions 2.8.3 Relative Molar Quantities 2.8.4 Ideal Solutions 2.8.5 Real Solutions 2.9 Free Energy of Solutions 2.9.1 The Free Energy of Mixture of Phases 2.9.2 Gibbs Free Energy of Mixing 2.9.3 Entropy of Mixing 2.9.4 Enthalpy of Mixing 2.10 Heterogeneous Equilibrium. Phase Equilibria; Equilibria Between Phases 2.10.1 The Phase Rule 2.10.2 The Free Energy of Solutions 2.10.3 The Free Energy of Phases and Mixtures 2.11 Variation of the Solubility with Temperature 2.12 Conclusion References 3 Assessment of a Multicomponent System: The Ternary Space Model 3.1 Introduction 3.2 The Ternary Space Model 3.2.1 The Representation of Ternaries 3.2.2 The Situation with Compounds Existing in Binary Boundaries or Inside Ternary 3.3 Analysis of the Space Model 3.3.1 Isothermal Sections 3.3.2 Vertical Sections and Isopleth Sections 3.3.3 Liquidus Surfaces 3.4 Conclusion References 4 The CALPHAD Methodology: A Guide 4.1 Understanding Methodology 4.2 The Phase Model 4.3 Understanding the Software: The Software Architecture 4.4 Database and Calculation Modules 4.5 Creating the TDB File 4.6 Basic Calculations with TDB References 5 Ab Initio Calculations in the CALPHAD Methodology, the Quantic Simulations: Slight Description and Use in CALPHAD 5.1 Introduction. «An Introduction to Numerical Simulations in Order to Approach Specialized Works in This Field» 5.2 Resolution of the Schrödinger Equation 5.3 Case Study: The System Ti–Sn (Published in «CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry» (5.3)) 5.4 Conclusion References Conclusion Bibliography