15 - Limit of stability and critical phenomena

Summary

Transformations and transitions

In Chapter 12 we were mainly concerned with the question whether a transformation is sharp or gradual. The difference between those cases is very practical and straight-forward. It is based on a one-dimensional phase diagram where the only axis represents the quantity that is being varied. If that diagram shows a two-phase field of some extension between the two one-phase fields, then the transformation between the two phases will be gradual. If the two-phase field has no extension, then the transformation will be sharp. For a unary system with a transformation this will happen if one varies a potential, e.g. T. The Gibbs energy is a continuous function of T across the sharp transformation but its derivatives, yielding S and V, show discontinuous jumps. This is why the phase boundaries separate when a molar axis is introduced (see Figs 9.1 and 9.2). In other cases there is no such separation because the first-order derivatives are zero. A typical example is found in a ferromagnetic substance, which gradually loses its magnetization as the temperature is increased. At the Curie temperature it reaches zero and the substance has thus become paramagnetic. There is no temperature where ferromagnetic and paramagnetic regions coexist in a pure substance, not even if one varies a molar quantity.