Crystal-Structure Matches in Solid-Solid Phase Transitions.

The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully exploits the translational and rotational symmetries and is independent of the choice of supercells. This is enabled by the use of the Hermite normal form, an analog of reduced echelon form for integer matrices. With its help, exhausting all CSMs is made possible, which goes beyond the conventional optimization schemes. In an example study of the martensitic transformation of steel, our enumeration algorithm finds many candidate CSMs with lower strains than known mechanisms. Two long-sought CSMs accounting for the most commonly observed Kurdjumov-Sachs orientation relationship and the Nishiyama-Wassermann orientation relationship are unveiled. Given the comprehensiveness and efficiency, our enumeration scheme provide a promising strategy for solid-solid phase transition mechanism research.

Complex phase diagram and supercritical matter.

The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.

Dynamic Nature of High-Pressure Ice VII.

Starting from Shannon's definition of dynamic entropy, we propose a theory to describe the rare-event-determined dynamic states in condensed matter and their transitions and apply it to high-pressure ice VII. A dynamic intensive quantity named dynamic field, rather than the conventional thermodynamic intensive quantities such as temperature and pressure, is taken as the controlling variable. The dynamic entropy versus dynamic field curve demonstrates two dynamic states in the stability region of ice VII and dynamic ice VII. Their microscopic differences were assigned to the dynamic patterns of proton transfer. This study puts a similar dynamical theory used in earlier studies of glass models on a simpler and more fundamental basis, which could be applied to describe the dynamic states of more realistic condensed matter systems.

Ferroelectric Problem beyond the Conventional Scaling Law.

Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g., defects and lattice strains) were often resorted to. Via first-principles based finite-temperature (T) simulations, we reveal that these abnormalities are intrinsic to their unusual symmetry breaking from bulk to thin film. Changes of the electronic structures result in different order parameters characterizing the FE phase transition in bulk and in thin films, and invalidation of the scaling law. Beyond the scaling law T_{c} limit, this mechanism can help predict materials that are promising for room-T ultrathin FE devices of broad interest.