Analysis of dislocation mechanism for melting of elements: Pressure dependence

Abstract

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Grüneisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.

Analytic model of the Grüneisen parameter all densities

“…Finally, we note that our model for γ can be used to calculate shear moduli along the solidus using Eq. (8) and the formula G(ρ, T m (ρ))/(ρ · T m (ρ)) = constant [43]. Table 1 vs. the experimental data [40] and the results of calculations [44] (larger points).…”

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

“…Table 2 shows the parameters used in the melting temperature models of copper. Figure 3 shows a comparison of the two melting temperature models along with experimental data from Burakovsky et al (2000a) (shown as open circles). An initial density ρ 0 of 8930 kg/m 3 has been used in the model calculations.…”

“…The remaining parameters for the BPS model are from Burakovsky and Preston (2000) and Burakovsky et al (2000b). Burakovsky et al (2000a). The original sources of the experimental data can be found in the above citation.…”

“…An alternative melting relation that is based on dislocation-mediated phase transitions is the Burakovsky-Preston-Silbar (BPS) model (Burakovsky et al (2000a)). The BPS model has the form…”

“…We also evaluate the associated shear modulus models of Varshni (1970), Steinberg et al (1980), and Nadal and Le Poac (2003). The melting temperature models of Steinberg et al (1980) and Burakovsky et al (2000a) are also examined. A temperature-dependent specific heat relation is used to compute specific heats and a form of the Mie-Grüneisen equation of state that assumes a linear slope for the Hugoniot curve are also evaluated.…”