[Pw_forum] Questions about a soft Raman active phonon

[Stefano Baroni]

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疯狂搜-新歌热歌高速下

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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