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

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. This book presents a survey of all the theoretical techniques needed to calculate a pressure-temperature phase diagram of a pure metal, or a composition-temperature phase diagram of a binary alloy, from first principles, that is, starting with the Hamiltonian of the system and with no other input except the atomic mass and the atomic number. The text begins with the elementary approach to the effective ionic forces in metals and alloys based on the pseudopotential and linear-response theories. The greater part of the book is concerned with the s, p-bonded or simple metals to which these theories apply. Transition and rare-earth metals and the tight-binding or band-theory methods required to describe them are treated only briefly. The statistical-mechanical and lattice-dynamical methods used to describe the liquid state and a vibrating crystal at finite temperatures are developed in detail. All scientists concerned with the structural and thermal properties of metals and alloys should find this book of interest. Front Matter....Pages I-XI Introduction....Pages 1-33 Interatomic Forces in Metals and Alloys....Pages 34-66 Phase Stability of Crystalline Metals....Pages 67-101 Structure and Thermodynamics of Liquid Metals....Pages 102-132 The pT Phase Diagram of Pure Metals....Pages 133-144 Alloy Formation and Stability....Pages 145-168 Solid Substitutional Alloys....Pages 169-206 Intermetallic Compounds....Pages 207-240 Liquid Alloys....Pages 241-281 Alloy Phase Diagrams....Pages 282-291 Beyond the Phase Diagram: The Formation and Properties of Metastable Phases....Pages 292-312 Conclusions and Outlook....Pages 313-314 Back Matter....Pages 315-404