Thermodynamics of phase transitions in current-carrying conductors

This work studies the thermodynamics of phase transitions of the first kind in current-carrying conductors when these transitions are accompanied by a sharp change of the electrical conductivity. It is shown that the critical current in the normal conductor, i.e., the current that generates the critical pressure, may be considerably lower than is generally believed. The reason for the lower value of the critical current is the shift of the whole curve of phase equilibrium in the presence of a strong electric current. This shift arises due to the additional work performed against ponderomotive forces, which prevents the formation of the nucleus of a phase with the lower value of electric conductivity. In case of the van der Waals model of the critical state the value of the critical current calculated taking into account the shift of the phase equilibrium curve is 2-3 times less than the critical current determined when this shift is neglected. It is shown that under these conditions there occurs a splitting of the phase-equilibrium curve into two separate curves for direct and inverse phase transitions. Depending upon the mutual location of both curves two opposite situations may occur. The first case is that of regular hysteresis when there exists a domain of stability of both phases and the realization of a particular phase is determined by the initial conditions and the direction of the process. In the second case there exists a region where both phases are unstable. This region is considered as a domain of the fragmentation of material into small particles. This work determines various thermodynamic parameters: latent heat of the phase transition, shift of the phase-equilibrium curve, and the size of the critical nucleus. It is shown that the value of the shift of the phase-equilibrium curve under the current densities employed in the experiments with exploding wires is of order 1. A mechanism for the formation of small particles is suggested and theoretical results are compared with experimental data.