From Hamiltonians to Phase Diagrams: The Electronic and Statistical-Mechanical Theory of sp-Bonded Metals and Alloys(70 Springer Series in Solid-State Sciences)

The development of the modern theory of metals and alloys has coincided with great advances in quantum-mechanical many-body theory, in electronic structure calculations, in theories of lattice dynamics and of the configura- tional thermodynamics of crystals, in liquid-state theory, and in the theory of phase transformations. For a long time all these different fields expanded quite independently, but now their overlap has become sufficiently large that they are beginning to form the basis of a comprehensive first-principles the- ory of the cohesive, structural, and thermodynamical properties of metals and alloys in the crystalline as well as in the liquid state. Today, we can set out from the quantum-mechanical many-body Hamiltonian of the system of electrons and ions, and, following the path laid out by generations of the- oreticians, we can progress far enough to calculate a pressure-temperature phase diagram of a metal or a composition-temperature phase diagram of a binary alloy by methods which are essentially rigorous and from first prin- ciples. This book was written with the intention of confronting the materials scientist, the metallurgist, the physical chemist, but also the experimen- tal and theoretical condensed-matter physicist, with this new and exciting possibility. Of course there are limitations to such a vast undertaking as this. The selection of the theories and techniques to be discussed, as well as the way in which they are presented, are necessarily biased by personal inclination and personal expertise.

Table of Contents:
1. Introduction.- 1.1 Why This Book Was Written and What It Contains.- 1.2 The Thermodynamic Origin of Phase Diagrams.- 1.3 Adiabatic Decoupling of the Ionic and Electronic Degrees of Freedom.- 1.4 The One-Electron Approximation.- 1.5 Tightly-Bound and Nearly-Free Electrons; Potentials and Pseudopotentials.- 1.6 Response Theory and Interatomic Interactions.- 1.7 The Statistical Mechanics of a Vibrating Lattice.- 1.8 Periodic, Aperiodic and Quasi-Periodic Structures.- 1.9 Elementary Excitations in Aperiodic Structures.- 1.10 Configurational Thermodynamics of Solids and Liquids.- 2. Interatomic Forces in Metals and Alloys.- 2.1 Pseudopotentials.- 2.2 Response Theory.- 2.3 Effective Pair Potentials in Pure Metals.- 2.4 Effective Pair Potentials in Binary Alloys.- 2.5 Interatomic Forces in Non-Simple Metals and Alloys.- 2.6 Beyond Perturbation Theory.- 3. Phase Stability of Crystalline Metals.- 3.1 Simple-Metal Cohesion.- 3.2 Structural Stability.- 3.3 Trends in Crystal Structures.- 3.4 Pressure-Induced Phase Changes.- 3.5 Thermodynamics of Crystalline Metals.- 3.6 Temperature-Induced Phase Changes.- 4. Structure and Thermodynamics of Liquid Metals.- 4.1 Computer Simulations.- 4.2 Integral Equation Approach.- 4.3 Thermodynamic Perturbation Theories.- 4.4 Trends in Liquid Structures.- 4.5 Expanded Fluid Metals.- 4.6 Structure and Thermodynamics of Liquid Transition and Rare-Earth Metals.- 4.7 Atomic Motion in Liquid Metals.- 5. The pT Phase Diagram of Pure Metals.- 5.1 Solid-Liquid Trnasitions: The Total Energy Approach.- 5.2 Microscopic Theories of Melting and Freezing.- 5.3 The Liquid-Vapour Transition.- 6. Alloy Formation and Stability.- 6.1 Nearly-Free-Electron Approach to Alloy Formation.- 6.2 Miedema’s Semiempirical Theory of Alloy Formation.- 7. Solid SubstitutionalAlloys.- 7.1 Primary Solid Solutions.- 7.2 Hume-Rothery Phases.- 7.3 Static Lattice Distortions.- 7.4 Ordering in Substitutional Alloys.- 7.5 Thermodynamics of Alloys.- 8. Intermetallic Compounds.- 8.1 Structure Maps.- 8.2 Empirical Pair-Potential Analysis of Intermetallic Phases.- 8.3 Classification of Intermetallic Phases According to Building Principles and Properties.- 8.4 Topologically Close-Packed Intermetallic Compounds (Frank-Kasper Phases).- 8.5 Intermetallic Phases with Large Band-Structure Stabilization.- 9. Liquid Alloys.- 9.1 Computer Simulations of Binary Liquid Alloys.- 9.2 Thermodynamic Variational Calculations.- 9.3 Thermodynamic Perturbation Theory.- 9.4 Structure and Thermodynamics of Liquid Transition-Metal Alloys.- 9.5 Collective Excitations in Liquid Alloys.- 10. Alloy Phase Diagrams.- 10.1 First Principles Calculations of Alloy Phase Diagrams.- 10.2 Chemical Short-Range Order and Alloy Phase Diagrams.- 10.3 Molecular Theory of the Freezing of Liquid Alloys.- 11. Beyond the Phase Diagram: The Formation and Properties of Metastable Phases.- 11.1 Amorphous Alloys — Metallic Glasses.- 11.2 Quasi-Crystals.- 12. Conclusions and Outlook.- Appendices.- A. Density-Functional Pseudopotentials.- A.1 Optimized Pseudopotentials — the Operator Approach.- A.2 Norm-Conserving Pseudopotentials — the Scattering Approach.- B. Linear Response Theroy.- C. Electrostatic Energies of Crystals and Liquids.- C.1 The Madelung Constants of the Elemental Structures.- C.2 The Madelung Constants of Binary Alloys and Intermetallic Compounds.- C.3 Electrostatic Energies of Model Liquids and Liquid Mixtures.- D. Liquid State Theory: Integral Equations, Variational Principles and Exactly Soluble Models.- D.1 Correlation Functions and Equations of State.- D.2 IntegralEquations and Variational Principles for the Total and Direct Correlation Functions.- D.3 Analytical Solutions for Model Liquids and Mixtures.- D.3.1 Solution of the PY Equation for the Hard-Sphere Fluid.- D.3.2 Solution of the PY Equation for Hard-Sphere Mixtures.- D.3.3 The Solution of the MSA for Charged Hard Spheres with Yukawa Interactions.- D.3.4 The Solution of the MSA for a Symmetric Mixture of Charged Hard Spheres with Yukawa Interactions.- References.