I would like to explain this question with following description.
The system (crystal) can be perturbed by pressure, temperature, etc. Then the crystal may undergoes structural transition (from one space group to another space group) depending on the energy minimization.
Thermodynamically structural transition can be divided into two types.
1. First order ( volume change during the transition is high)
2. Second order (volume change during the transition is small)
The XRD and Raman can be used to detect structural transition.
Is there any general relation between phonon softening and second order structural transition?
Dear Rajaji,
Raman spectroscopy is a best tool for characterizing the phase transition whether first order or second order.
First order phase transition: Crystal structure changes discontinuously (ex: graphite to diamond and not reversible)
Second order transition: Continuous changes in the crystal structure, effected with infinitesimal displacement of atomic positions (Reversible)
Second order transitions in which a Raman-active mode has the correct symmetry to induce the transition from one phase to the other. The mode termed a soft mode.
In the vicinity of the transition the soft mode frequency should behave as
w2 proportional to ∣T- Tc∣ or ∣P- Pc∣
Dear Kishore Kumar Madapu ,
Thanks for your answer. Your answer is about soft phonon mode.
Up to my knowledge, the soft phonon mode and phonon softening are entirely different phenomenon?
1. Soft phonon mode
Soft mode has to go to zero (frequency) in the transition point.
Eg: PbTiO3
2. Phonon softening
Phonon softening means just its frequency lowering with respect to perturbation. It need not undergo zero frequency in the transition point.
Once again, I would like to reframe my question here (for clarification) as follows:
What is the relation between phonon softening and second order structural transition?
Have a look on this paper.This is a very nice paper on soft modes and phase transitions. Hope it will useful for you.
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