I am studying a group of materials using density functional theory. I am able to calculate elastic constants, phonon densities of states, and formation energies. The results imply that the materials are elastically stable, and also provide an energetically favorable configuration. However, for the phonon densities of states, there exist phonon modes at negative frequencies, which supposedly implies that the compound would be dynamically unstable.
My question is: what exactly is the difference between these types of stabilities, and what implications would this have for the materials? Since each compound is elastically and energetically stable, would it still be possible to fabricate, even if it is predicted to be dynamically unstable? My thoughts are that, perhaps the unstable phonon modes would be "frozen out" at low temperatures...but that's just a guess.
Any help or explanation with this would be greatly appreciated.