Phase Transitions
Phase Transitions can be classified thermodynamically on the basis of which derivative of the free energy is discontinuous at the phase transition as the P or T is varied through the transition:
- First-order phase transitions are characterised by a jump in the volume at the phase transition. Within EosFit the appropriate way to fit data with a first-order phase transition is just to fit the data of the two phases seperately. The example of kalsilite shows you how to do this.
- Second-order transitions have no jump in the volume at the transition, but there is jump in the value of the second derivative of the free energy, which means the bulk modulus and the thermal expansion coefficient has a jump in value at the transition.
- It is also possible for materials to exhibit behaviour intermediate between the classical 'first-order' and 'second-order' transitions. These are often simply described as 'continuous transitions'. There is no jump in the volume at the transition, but the volume and its P and T derivatives evolve continuously away from the transition point. Landau theory has been developed to successfully model such transitions. Within EosFit we provide a very simplified Landau-type model that enables data containing a continuous transition to be modeled or fit with a single Eos combined with a refineable model of the transition behaviour. The theory is described in this section, and a worked example is provided. For a full description of the concepts of spontaneous strain at structural phase transitions, see Carpenter and Salje (1988).