Abstract
Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.
Highlights
Academic Editor: Luis M.Is there an intermediate state of matter between harmonic crystals and amorphous glasses? Below, we describe such state and identify key properties that lead to structural instabilities and symmetry-breaking phase transition, such as the large athermal atomic displacements away from high-symmetry crystallographic positions, a dimpled atomic potential with multiple local minima (MLM), and a time-dependent pattern in the occupied neighborhoods of the local potential-energy minima (LPEM).Here, in particular, we identify specific features in the potential-energy (PE) surface that lead a given solid to exhibit polymorphic behavior, which can be either stationary or dynamic
We provide reliable means to address these anharmonic states and to estimate the energetics and temperatures associated with the solid–solid symmetry-breaking phase transition for such polymorphic solids with MLM potentials
We verified that a 54-atom structure is a LPEM with a stable phonon spectrum (Figure 2b in [20]), and we found that its phonon density of states (DOS) compares well to that obtained from neutron-scattering experiment [44], see Figure 7
Summary
If the transformation barriers are low compared to the thermal energy of atomic motion in a solid with a dimpled atomic potential, multiple neighborhoods of local PE minima are visited by an ergodic atomic motion in a “dynamically polymorphic” phase In this phase, a diffraction pattern of a periodic crystal coexists with vibrational properties of a phonon glass. (color online) Schematic 1D potentials with an average lattice constant a and barriers EB for (a) harmonic PE (parabolic below EH ), (b) dimpled case with 2 local minima per basin (here, El ≡ EL ), where at kT < EL , each atom (filled circle) is displaced (arrow) from the high-symmetry unstable position (open circle), and (c) glass-like amorphous case. In Appendix B, we consider methods for predicting vibrational spectra at various atomic displacements, related to temperature
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