On May 30, 2006, at 11:40 PM, Lijun Zhang wrote: > Dear all, > I am doing some calculations on the phase transition induced by > lattice > instability. With increasing pressures, I found that a Raman active > phonon > softens to zero, the same as behaviors in the ferroelectricity. An > elastic > instability also appears upon compression, signaled by a sound > velocity > going to zero. However, the former extremely precedes the latter, > thus I > conclude that the phase transition is driven by the phonon > instability. Is it > right?
NO, it is not. For two reasons, which are somewhat related to one another. First, the phonon instability is usually coupled to the phonon instability, so that the phase transformation usually results from a distortion pattern which involves both the shape of the unit cell (elastic) and the atomic positions within the unit cell (phonon). As a consequence of this, the transition is usuall first- order, i.e. it occurs before any mode (either phonon-like or elastic) actually softens. Phonon or sound-velocity softening just signal the onset of an instability. In order to study the structural stability of the crystal as a function of pressure, you should study how the enthalpy (E+PV) of the systems depends on the "order parameters" of the transition for different values of the pressure. Good order parameter would obviously be the atomic distortion patterns corresponding to the soft phonon mode and the components of the strain corresponding to the vanishing sound velocity. I am sure this is discussed in many different places. The references were what I have understood in this business is explained is: M. Buongiorno Nardelli, S. Baroni, and P. Giannozzi, Phys. Rev. B 51, 8060 (1995). M. Buongiorno Nardelli, S. Baroni, and P. Giannozzi, Phys. Rev. Lett., 69, 1069 (1992). Hope this helps SB > If true, how to search for the stable high pressure phase through the > eigenvectors of the unstable mode? > Any reply will be appreciated. > Lijun Zhang > > Mp3???-??????? --- Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) Please, if possible, don't send me MS Word or PowerPoint attachments Why? See: http://www.gnu.org/philosophy/no-word-attachments.html -------------- next part -------------- An HTML attachment was scrubbed... URL: /pipermail/attachments/20060531/f34a5953/attachment.htm
