Hard mode Spectroscopy: Experimental studies of structural phase transitions

Abstract

The frequencies of phonons with energies well above those of corresponding soft modes depend on the evolution of the structural order parameter as a function of temperature, pressure or chemical composition. The relative changes of the phonon frequencies are usually below 2% of their total energies (hence “hard modes” in contrast to “soft modes”) which allows the treatment of the coupling between the phonon frequencies ω and the order parameter Q in perturbation theory

The exponent m = 1, or 2 is determined by symmetry considerations. For modes which are optically active at T > T_c one finds B ≪ A in most cases.

Similar correlations are given for the Raman scattering cross sections and the intensities of infrared absorption signals.

The correlation length of hard modes is, in general, comparable with that of bond distances so that the order parameter is measured on an atomistic length scale. This property of Hard Mode Infrared Spectroscopy allows the quantitative investigation of short range order, local incommensurations, soliton densities etc. Examples of experimental studies are discussed.

Key Words:

• Raman spectroscopy
• infrared spectroscopy
• hard modes
• lattice dynamics
• structural phase transitions