  Polymorphic solids of the same chemical composition can have different atomic
structures; in each polymorph atoms vibrate around a local potential energy
minimum (LPEM). If transformations to other structures have sufficiently high
enthalpy barriers, then each polymorph is either stable or metastable; it is
stationary and does not spontaneously change with time. But what happens, if
those barriers are low? As examples, we consider NiTi shape memory alloy
exhibiting a large elastocaloric effect, and selected elemental solids. We
suggest a model for dynamically polymorphic solids, where multiple LPEMs are
visited by ergodic motion of a single atom. We predict that upon cooling a
dynamically polymorphic phase should undergo a symmetry-breaking first-order
phase transition, accompanied by a finite change of the lattice entropy. We
discuss 3 methods used to calculate phonons in solids with non-harmonic dimpled
atomic potentials, and compare theoretical predictions to experiment.
