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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.

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what exactly is the difference between these types of stabilities

Elastically stable means that scaling the unit cell in either direction (while preserving the fractional coordinates of the atoms) increases the energy.

Dynamically stable, usually referred to as 'kinetically' stable, means that all of the atoms are trapped within local energy minima and will therefore remain in place (at sufficiently low temperatures).

what implications would this have for the materials?

If kinetically unstable then the structure will be very transient, undergoing a phase transition (most likely melting) within a picosecond time-scale.

Since each compound is elastically and energetically stable, would it still be possible to fabricate, even if it is predicted to be dynamically unstable?

Yes, but to reiterate: it won't last long! One way to generate an elastically stable but kinetically unstable structure is to excite the electrons on a sufficiently short timescale, e.g. using a laser. This is actually what happens when you fire lasers with high fluences at silicon: the electrons become excited so the bonding becomes metallic (elastically stable), but this destroys the directionality of the bonding which causes the structure to melt within a picosecond (kinetically unstable). I can provide citations if you require.

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