Melting as a dislocation-mediated phase transition

Abstract

We present a theory of the melting of elemental solids as a dislocation-mediated phase transition. We model dislocations near melt as non-interacting closed strings on a lattice. In this framework we derive simple expressions for the melting temperature and latent heat of fusion that depend on the dislocation density at melt. We use experimental data for more than half the elements in the Periodic Table to determine the dislocation density from both relations. Melting temperatures yield a dislocation density of (0.61 ± 0.20) b −2 , in good agreement with the density obtained from latent heats, (0.66 ± 0.11) b −2 , where b is the length of the smallest perfect-dislocation Burgers vector. Melting corresponds to the situation where, on average, half of the atoms are within a dislocation core.

Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

“…The values of the initial bulk and shear moduli and their derivatives in the BPS model are from Guinan and Steinberg (1974). The remaining parameters for the BPS model are from Burakovsky and Preston (2000) and Burakovsky et al (2000b). Burakovsky et al (2000a).…”

Melting and related precursor cooperative phenomena in chemically bonded assemblies

“…Following PK, who restricted their model to but two possible molecular orientations, separated by a suitable energy barrier (for n orientations with n > 2, see ref [5]) we summarize using the notation employed in the book by Ubbelohde [7], the phenomenological equations for the two order parameters Q and S, namely Though in ref [1], modest contact was established with solid H 2 and the halogens, it has subsequently come to the author's attention that very relevant proton magnetic resonance (PMR) experiments are recorded in the older literature for the solid tetramethyls already referred to. We refer here especially to the study [8] [16] and Burakovsky and co-workers [17,18]. Here we shall report on the subsequent study of Matthai and March [19] who have emphasized especially the common features shared by the treatments of KJ and Burakovsky et al…”

“…Turning to the second area, that of melting and mechanical properties of d-electron transition metals, important regularities are emerging from two models [15,17] which rest heavily on a mechanism of melting that is dislocation mediated. Their essential shape, as emphasized here (see also [19]), is summarized in eqns(3.1) and (3.2) and a further consequence, of course approximate, is subsumed into eqn(3.3), which is now structure independent.…”

“…where G is the shear modulus, while S LA denotes the structure-dependent part of the Los Alamos (LA) group of Burakovsky et al Table 3 Burakovsky et al [17] have also used the dislocation-mediated model to estimate the enthalpy of such an approach, and hence to obtain the latent heat of fusion L m as an enthalpy difference.…”

“…One of these, which shows promise of bridging two areas treated separately in the present study, is that of molecular nitrogen physisorbed on graphite. Cooling below 30K, such an assembly is known to exhibit an orientational phase transition [35; see also 36], and further theoretical studies here are obviously highly worthwhile.Turning to the second area, that of melting and mechanical properties of d-electron transition metals, important regularities are emerging from two models [15,17] which rest heavily on a mechanism of melting that is dislocation mediated. Their essential shape, as emphasized here (see also [19]), is summarized in eqns(3.1) and (3.2) and a further consequence, of course approximate, is subsumed into eqn(3.3), which is now structure independent.…”