At low temperatures, the behaviour of structural phase transitions is modified by the influence of quantum fluctuations. Such fluctuations enhance the stability of the high-symmetry phase, reducing the observed transition temperature. The effect on phase diagrams of temperature versus some other control parameter (e.g. pressure or chemical composition) is described. A simple low-temperature extension of Landau theory is used, where the extent of quantum mechanical effects is characterized by a saturation temperature . The theory is used to model the phase diagrams of the mineral anorthoclase , the ferroelectric materials ( for the 20 K transition), and SbSI . The saturation temperature is related to the extent to which changes in the hard phonon modes influence the transition mechanism.