Melting Is Well-Known, but Is It Also Well-Understood?

Abstract

Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is wellknown and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

Ising Paradigm in Isobaric Ensembles

“…While the transition between solid and fluid phases is well-known experimentally since long ago, its statistical-mechanical characterization remains an outstanding question to the theory of condensed matter [52]. The theory of topological order is able to describe melting in d = 2 [53], while classical density functional theory has proven efficient for computing solid-fluid phase diagrams [54].…”

Temperature and Degrees of Freedom of Potential Energy vs Its Kinetic Counterparts and Their Roles in Decoding Phase Transition

“…[4][5][6][7][8] Various models, like KTHNY theory [9][10][11][12][13] for two dimensional materials, 14 the Lindmann index 15 , and Trouton's rule 16 aid in understanding phase transition mechanisms. There have been several excellent review articles about the phase transition with different applications 14,[17][18][19][20][21] and we will not repeat the work here.…”