Preface

A unified introduction to the theory of anisotropic elasticity for static defects in crystals is presented. The term “defects” is interpreted broadly to include defects of zero, one, two, and three dimensionality: included are

• Point defects (vacancies, self-interstitials, solute atoms, and small clusters of these species),

• Line defects (dislocations),

• Planar defects (homophase and heterophase interfaces),

• Volume defects (inhomogeneities and inclusions).

The book is an outgrowth of a graduate course on “Defects in Crystals” offered by the author for many years at the Massachusetts Institute of Technology, and its purpose is to provide an introduction to current methods of solving defect elasticity problems through the use of anisotropic linear elasticity theory. Emphasis is put on methods rather than a wide range of applications and results. The theory generally allows multiple approaches to a given problem, and a particular effort is made to formulate and compare alternative treatments.

Anisotropic linear elasticity is employed throughout. This is now practicable because of significant advances in the theory of anisotropic elasticity for crystal defects that have been made over the last 35 years or so, including the development of Green's functions for unit point forces in infinite anisotropic spaces, half-spaces and joined dissimilar half-spaces. The use of anisotropic theory (rather than the simpler isotropic theory) is important, since, even though the results obtained by employing the two approaches often agree to within 25%, or so, there are many phenomena that depend entirely on elastic anisotropy. Unfortunately, however, the results obtained with the anisotropic theory are usually in the form of lengthy integrals that can be evaluated only using numerical methods and so lack transparency. To assist with this difficulty, isotropic elasticity is employed in parallel treatments of many problems where sufficiently simple conditions are assumed so that tractable analytic solutions can be obtained that are more transparent physically. Sections in the book where isotropic elasticity is employed are clearly distinguished to avoid confusion.