The purpose of this book is to fill something of a gap. In general, thermodynamics has been a great success and has provided a means of understanding and predicting material behavior of almost all kinds at the macroscopic level. Even when thermodynamic statements were limited to equilibrium states they were widely useful, and with extension to nonequilibrium states almost all behaviors that a person might observe directly became accessible to theory. But there has been and is one resistive point: if a cylinder of material is more strongly compressed along its length than radially, it is in a nonequilibrium state no matter how ideal its condition in other respects, and the effect of this type of nonequilibrium has not been successfully explored. The physical consequences are, of course, well known; the cylinder deforms in ways successfully described in almost all respects by the methods of continuum mechanics. But the chemical consequences are less well known. For example, suppose the cylinder contains iron and is surrounded by some second iron-bearing phase; suppose further that before the cylinder is compressed axially, the cylinder and its surroundings are in equilibrium. When the axial compression is imposed, how is the equilibrium disturbed and what processes begin to run? The purpose of the book is to provide the outline of a comprehensive approach to this question. The question has been discussed extensively in technical journals and in complicated ways. The stimulus for this book is the belief that the topic need not be so complicated. There are two equations that describe the stresses in the cylinder that have up to now not been used; using these neglected equations provides a point of view not taken by other writers, and it is the fresh point of view that permits certain simplicities to be seen (the key equations are 6.3 and 8.10). Of course, we make headway only to a limited extent; not all problems are answered, not all complications are resolved. The existence of a central and unresolvable complication is recognized toward the end of this overview, in the section on Continuum Behavior and Atoms.
Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales