From Hamiltonians to Phase Diagrams: The Electronic and Statistical-Mechanical Theory of Sp-Bonded Metals and Alloys

ISBN-13: 9783642830600 / Angielski / Miękka / 2011 / 404 str.

J. Rgen Hafner

Opis

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.

Spis treści

1. Introduction.- 1.1 Why This Book Was Written and What It Contains.- 1.2 The Thermodynamic Origin of Phase Diagrams.- 1.2.1 First-Order Transitions Without Compositional Change — The pT Phase Diagram.- 1.2.2 First-Order Transitions with Compositional Change — The Alloy Phase Diagram.- 1.2.3 Second-Order Transitions.- 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.- 1.9.1 Effective Medium Approximations.- 1.9.2 The Recursion Method and Related Techniques.- 1.10 Configurational Thermodynamics of Solids and Liquids.- 1.10.1 Order-Disorder Transitions.- 1.10.2 From the Interatomic Force Law to the Structure of a Liquid.- 1.10.3 Order-Parameter Approach to Freezing and Melting.- 2. Interatomic Forces in Metals and Alloys.- 2.1 Pseudopotentials.- 2.1.1 The Operator Approach.- 2.1.2 The Scattering Approach.- 2.1.3 Model Potentials.- 2.2 Response Theory.- 2.2.1 Nonlocality.- 2.2.2 Screening Beyond the Random Phase Approximation.- 2.3 Effective Pair Potentials in Pure Metals.- 2.4 Effective Pair Potentials in Binary Alloys.- 2.4.1 Chemical Compression.- 2.4.2 Chemical Ordering.- 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.- 3.1.1 An Excursion into Transition-Metal Cohesion.- 3.2 Structural Stability.- 3.3 Trends in Crystal Structures.- 3.3.1 A Brief Remark on Transition Metal Structures.- 3.3.2 The Crystal Structures of the Lanthanides.- 3.3.3 Charge-Density Analysis of Bonding.- 3.4 Pressure-Induced Phase Changes.- 3.5 Thermodynamics of Crystalline Metals.- 3.5.1 Harmonic Lattice Dynamics.- 3.5.2 Anharmonicity.- 3.5.3 Variational Method for Calculating Thermodynamic Properties (Gibbs-Bogoljubov Method).- 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.- 4.3.1 Thermodynamic Variational Method for Liquids (Gibbs-Bogoljubov Method).- 4.3.2 Repulsive Forces: Weeks-Chandler-Andersen Theory.- 4.3.3 Attractive Forces: Random Phase Approximation, Optimized Random Phase Approximation and Mean Spherical Approximation.- 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.- 6.1.1 Criteria for Solubility in Homovalent Systems.- 6.1.2 Variations of the Atomic Volume in Heterovalent Alloy Systems.- 6.1.3 The Chemical Potential Model for the Heat of Formation.- 6.1.4 Band Picture for Simple-Metal Alloys.- 6.1.5 Real-Space Picture for Alloy Formation.- 6.1.6 A Brief Summary.- 6.2 Miedema’s Semiempirical Theory of Alloy Formation.- 6.2.1 Microscopic Interpretation of Miedema’s Alloying Rules: Simple Metals.- 6.2.2 Microscopic Interpretation of Miedema’s Alloying Rules: Transition Metals.- 7. Solid Substitutional Alloys.- 7.1 Primary Solid Solutions.- 7.1.1 The Homovalent Case.- 7.1.2 The Heterovalent Case.- 7.2 Hume-Rothery Phases.- 7.3 Static Lattice Distortions.- 7.4 Ordering in Substitutional Alloys.- 7.4.1 Long-Range Order.- 7.4.2 Short-Range Order.- 7.4.3 Ordering in Substitutional Transition-Metal Alloys..- 7.5 Thermodynamics of Alloys.- 7.5.1 Lattice Dynamics of Substitutional Alloys.- 7.5.2 Thermodynamic Perturbation Theory.- 7.5.3 Vibrational Dynamics and the Ordering Transition..- 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).- 8.4.1 Heat and Volume of Formation of Laves Phases.- 8.4.2 Structural Stability of Laves Phases.- 8.4.3 Other Topologically Close-Packed Compounds.- 8.4.4 Charge-Density Analysis of Bonding.- 8.4.5 Lattice Dynamics of Topologically Close-Packed Compounds.- 8.5 Intermetallic Phases with Large Band-Structure Stabilization.- 8.5.1 Charge-Density Analysis of Bonding in Zintl Phases.- 8.5.2 Lattice Dynamics of Zintl Phases.- 9. Liquid Alloys.- 9.1 Computer Simulations of Binary Liquid Alloys.- 9.2 Thermodynamic Variational Calculations.- 9.2.1 Systems with a Nearly Ideal Mixing Behaviour.- 9.2.2 Liquid Alloys with Strong Chemical Short-Range Order.- 9.2.3 Liquid Alloys with a Miscibility Gap.- 9.3 Thermodynamic Perturbation Theory.- 9.3.1 Repulsive Forces: Weeks-Chandler-Andersen Theory.- 9.3.2 Long-Range Forces: Optimized-Random-Phase Approximation.- 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.- 10.2.1 Melting Extrema.- 10.2.2 Eutectic Diagrams.- 10.2.3 Compound Formation.- 10.2.4 Phase Separation in the Liquid State.- 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.- 11.1.1 Glass-Forming Ability.- 11.1.2 Atomic Structure of Metallic Glasses.- 11.1.3 Elementary Excitations in 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 Integral Equations 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.