The Equations of Materials

This book describes some of the important equations of materials and the scientists who derived them. It is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. The book is pitched at the level of a final year school student or a first year undergraduate who has been studying the physical sciences and is thinking of specialising into materials science and/or materials engineering, but it should also appeal to many other scientists at other stages of their career. It requires a working knowledge of school maths, mainly algebra and simple calculus, but nothing more complex. It is dedicated to a number of propositions, as follows:1. The most important equations are often simple and easily explained;2. The most important equations are often experimental, confirmed time and again;3. The most important equations have been derived by remarkable scientists who lived interesting lives. Each chapter covers a single equation and materials subject. Chapters are structured in three sections: first, a description of the equation itself; second, a short biography of the scientist after whom it is named; and third, a discussion of some of the ramifications and applications of the equation. The biographical sections intertwine the personal and professional life of the scientist with contemporary political and scientific developments. Topics included are: Bravais lattices and crystals; the Bernal packing and liquids and glasses; the Hume-Rothery rules and alloys; Bragg's law and diffraction; the Abbe limit and microscopy; Pauli's exclusion principle and spectroscopy; the Gibbs phase rule and phases; Boltzmann's equation and thermodynamics; the Arrhenius equation and reactions; Ellingham diagrams and extraction; the Gibbs-Thomson equation and surfaces; Fick's laws and diffusion; the Scheil equation and solidification; the Avrami equation and phase transformations; Hooke's law and elasticity; the Burgers vector and plasticity; Griffith's equation and fracture; the Fermi level and electrical properties; the Curie point and magnetic properties; and Snell's law and optical properties. This new and more comprehensive second edition contains seven new chapters and updated versions of the original thirteen chapters. The new chapters expand and develop upon the following sections: structure of materials now includes liquids and alloys as well as crystals, assessment techniques now cover microscopy and spectroscopy as well as diffraction. Sections on reactions are extended to include extraction as well as thermodynamics and kinetics and the section on properties now discusses magnetic and optical behaviour, as well as mechanical and electrical properties.