Analysis of dislocation mechanism for melting of elements: Pressure dependence

In the framework of melting as a dislocation-mediated phase transition we d erive an equation for the pressure dependence of the melting temperatures o f the elements valid up to pressures of order their ambient bulk moduli. Me lting 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 gase s (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These ca lculated melting curves are in good agreement with existing data. We also d iscuss the apparent equivalence of our melting relation and the Lindemann c riterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest i tself in a new relation between the Gruneisen constant, bulk and shear modu li, and the pressure derivative of the shear modulus. (C) 2000 American Ins titute of Physics. [S0021-8979(00)03624-0].