Isosymmetric structural phase transitions: phenomenology and examples

Structural phase transitions ('type 0') in which there is no change of space group or of the occupied Wyckoff sites contrast with others in which diffusionless transformation can occur in a single step between higher-and lower-symmetry space groups (type I), through a low-symmetry transition state between relatively higher-symmetry initial and final structures (type II), and those where the mechanism is necessarily more complex (type III). A phenomenological model shows that type 0 transitions are necessarily first order, and may terminate at a critical point. The corresponding supercritical behaviour is a 'crossover' or 'diffuse transition' in which there is no discontinuity in any free-energy derivative. However, the location of the crossover is precisely defined at a minimum in the second derivative of the free energy with respect to a suitable order parameter. Isosymmetric transitions and/or crossovers occur in important mineralogical systems (pyroxenes, feldspars and carbonates) and non-linear optic materials (KTiOPO 4 ). Non-monotonic variation of free-energy derivatives around the crossover can have a serious effect on the locations and slopes of phase equilibria in pressure-temperature space. Interaction between non-symmetry-breaking and symmetry-breaking order parameters appears to play a major role in stabilizing low-symmetry clinopyroxene and anorthite feldspar phases.