- © The Mineralogical Society Of America
Phonon spectra respond, in principle, to any change of the crystal structure or lattice imperfections of a material. Traditionally optical soft modes, which can show relatively large variations, have been widely used for the analysis of displacive phase transitions. A soft mode is a particular mode of vibration of the high symmetry phase, whose frequency tends towards zero as the critical point is approached. In other cases the variations can be small; typical examples are the weak phonon renormalization of high temperature superconductors at the superconducting phase transition or isosymmetric phase transitions. Typical relative changes Δω/ω of phonon frequencies which do not directly correspond to characteristic response modes (such as soft modes) are between 0.001 and 0.02. Similar changes are observed for the intensities of phonon signals and, rather often, for the spectral line widths.
Although such relative changes are small, their absolute values (e.g., 5 cm−1 for a phonon signal at 500 cm−1) can be well resolved experimentally by most Raman and infrared spectrometers (ca. 0.1 cm−1). Over the last two decades, several phase transitions were either first discovered or analyzed in detail using the renormalization of optical phonon signals as the primary analytical tool which was named ‘hard mode spectroscopy’ (Petzelt and Dvorak 1976; Bismayer 1988; Güttler et al. 1989; Bismayer 1990; Salje and Yagil 1996; Zhang et al. 1996, 1999; Salje and Bismayer 1997).
Following the phenomenological theory of structural phase transitions by Landau and Lifshitz (1979) the order parameter Q is non-zero below the transition point and increases on cooling (in the case of temperature as state variable) according to Q(T) ~ |T−Tc|β with a critical exponent β. In terms of thermodynamics, the soft mode theory relates directly …