Soft phonons reconstructions structural phase transitions

Soft phonons reconstructions structural phase transitions 

In the process of surface formation, there may exist positions k in reciprocal space where the frequency of a vibration is so deeply modified, as a consequence of bond-breaking, that it vanishes. The mode becomes unstable and one speaks of a soft phonon. The atoms are no longer pulled back to their equilibrium positions. A new periodicity, characterized by the wave vector k, shows up in low-energy electron or helium atom diffraction experiments. The mechanism of phonon softening was suggested to explain some reconstructions observed on metal surfaces (Blandin et al, 1973 Fasolino et al, 1980 Pick, 1990). When a true structural phase transition occurs at a temperature Tc, the frequency of the soft mode decreases as the temperature decreases in the fluctuative regime (T Tc). Below the critical temperature Tc, superstructure satellites appear. Such phenomena were, for example, observed by Ernst et al. (1987) on W(OOl), by diffraction of heUum atoms. They are also present in quasi-one-dimensional conductors which display a Peierls transition. One should nevertheless remember that there exist structural phase transitions that are not driven by soft phonons. 

On SrTi03((X)l), Prade et al. (1993) have calculated the relaxation strength, the origin of the reconstruction and the vibration dynamics, using Born s model, with an account of the ionic polarization by the shell model. They have analyzed the manifestation of the anti-ferrodisplacive phase transition at the surface, a transition which involves rotations of TiOe octahedra and which induces a doubling of the lattice parameters. Introducing in their model force constants which vary with temperature. 

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Soft phonons reconstructions structural phase transitions... 

A basic concept in the reconstruction theory of solid surfaces is the soft phonon approach of displacive structural transitions. An essential property of these structural phase transitions is the existence of an order parameter which... 

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