Complex phase diagrams

Abstract

This paper is an assembly of a number of results that originate in thermodynamics except that thermodynamics here includes Landau's generalization of the thermodynamic potentials as a functional. The results focus on crossing phase boundaries, listing the sum rules around the crossing point and discussing various different possible terms in the Ginzburg–Landau free energy, along with their consequences.

Keywords:

• phase diagrams
• Ehrenfest relations
• Ginzburg–Landau free energy

Notes

Note

1. The proof here is based on “reductio ad absurdum”. It shows that assumption of three second order lines coming to a point leads to a contradiction. At the time the proof was published, the only way out of the contradiction seemed to be to claim that at least one of the boundaries must be first order. In light of more recent discussion of much higher order phase transitions (see Kumar and Saxena [1]), it seems more natural to simply state that all three lines cannot be second order.

2. In [13] the phase diagram of superconducting UPt₃ has been determined by measuring the coefficient of thermal expansion. Also see in a different context [23].

3. In [14] there are eight rules for a phase diagram near a tricritical point.