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?
