Materials Science is an extremely broad field covering metals, semiconductors,
ceramics, and polymers, just to mention a few. Its study is dominated by the
fabrication of specimens and the characterization of their properties. A
relatively small portion of the field is devoted to phase transformation, the dynamic
process by which in the present context a liquid is frozen or a solid is melted.
This book is devoted to the study of liquid (melt)-solid transformations of
atomically rough materials: metals or semiconductors, including model organ-
ics like plastic crystals. The emphasis is on the use of instability behavior as a
means of understanding those processes that ultimately determine the micro-
structure of a crystalline solid. The fundamental building block of this study
is the Mullins-Sekerka instability of a front, which gives conditions for the
growth of infinitesimal disturbances of a soild-liquid front. This is generalized
in many ways: into the nonlinear regime, including thermodynamic
disequilibrium, anisotropic material properties, and effects of convection in the liquid.
Cellular, eutectic, and dendritic behaviors are discussed. The emphasis is on
dynamic phenomena rather than equilibria. In a sense then, it concerns
"physiology" rather than "anatomy."