The free energy of mechanically unstable phases

Abstract

Phase diagrams provide ‘roadmaps' to the possible states of matter. Their determination traditionally rests on the assumption that all phases, even unstable ones, have well-defined free energies under all conditions. However, this assumption is commonly violated in condensed phases due to mechanical instabilities. This long-standing problem impedes thermodynamic database development, as pragmatic attempts at solving this problem involve delicate extrapolations that are highly nonunique and that lack an underlying theoretical justification. Here we propose an efficient computational solution to this problem that has a simple interpretation, both as a topological partitioning of atomic configuration space and as a minimally constrained physical system. Our natural scheme smoothly extends the free energy of stable phases, without relying on extrapolation, thus enabling a formal assessment of widely used extrapolation schemes.

Triaxial-Stress-Induced Homogeneous Hysteresis-Free First-Order Phase Transformations with Stable Intermediate Phases

“…On the applied side, stress hysteresis and the corresponding energy dissipation, as well as interfacial stresses should be reduced for many PT-related applications, like for shape memory alloys for actuation or medical applications [2,3,4] or caloric materials [4,5]. On the fundamental side, it is of interest to stabilize intermediate structures along the transformation path and study their properties [10], with the expectation that they may be unique. Also, significant reduction of the PT pressure by applying nonhydrostatic stresses is of basic and applied interests [1,6,7], but it is still not connected to lattice instabilities.…”

Epicycle method for elasticity limit calculations

“…It has recently been shown [4] that the point of lowest energy at the onset of mechanical instability (as identified with the proposed method) provides a logically consistent definition of the energy of a mechanically unstable phase. For completeness and clarity, we summarize the main features of this approach below (refer to Fig.…”

“…The inflection point calculations presented in [4] relied on the nudged elastic band method (NEB) [23], which has two drawbacks in the context of inflection point calculations. First, this approach demands rather large-scale calculations in which multiple copies of the whole system are being simultaneously optimized to map out the path along the elastic band.…”

“…The task of identifying a solid's onset of mechanical instability [1,2] arises in many problems in materials science and condensed matter physics, from the determination of the failure mechanisms [3] to the consistent assignment of free energies to mechanically unstable phases [4].…”

“…We consider the interesting case of the failure mechanism of graphene under tension [3]. We also devote special attention to the calculation of (free) energies of mechanically unstable phases [4] and exploit the accuracy of the proposed method to analyze in detail how the calculated quantities vary smoothly with…”