I have a material that can crystallize in either a cubic or tetragonal polymorph depending on the synthesis. I used DFPT in VASP and calculated the phonon band structures. I see that the cubic has all positive frequencies, while the tetragonal has some negative (imaginary) frequencies. This leads me to believe that the cubic phase is at a local minimum on the potential energy surface, while the tetragonal is at a saddle point.

I thought the tetragonal might be stabilized by entropic contributions at finite temperature, so I used phonopy to plot the thermal properties. I was looking at the Helmholtz free energy vs temperature, and surprisingly at 0 K, the free energy of the tetragonal phase is slightly lower than the cubic. Once the temperature increases, a crossover happens, and the free energy of the cubic becomes lower.

My question is: why is the free energy of the tetragonal phase at 0 K lower than the cubic, when the tetragonal phase has negative phonon frequencies and the cubic does not?

  • $\begingroup$ Why a saddle point can't have lower energy in one system than the local (global) minimum of the other system? $\endgroup$ – Camps Feb 22 at 11:25
  • $\begingroup$ They are the same composition (or system). Just two different polymorphs that depend on the synthesis conditions. $\endgroup$ – DoubleKx Feb 22 at 21:56

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