2元合金鋳物の凝固過程に対する非平衡熱力学的取扱い

Abstract

The purpose of the present paper is to theoretically calculate the solidification process of alloy castings. The equations of the rate of the reactions and the conservations of mass and energy have been derived by expressing the solidification process of binary alloy, in which only primary crystals are solidified, in terms of two reactions, A (in liq.) =A(in sol.) and B(in liq.)=B(in sol.), and also by regarding it as a process of growth of crystals dispersed in the melt. These equations transform into the foundamental equations which describe the solidification process of a binary alloy casting when the related properties are given as known functions of temperature and concentration. In the present paper most of the properties are regarded to be constant. But, the activities and partial enthalpies of the components are estimated from the phase diagram on the assumption that Raoult’s law is valid in solid and Henry’s law in liquid. The foundamental equations consisting of four simultaneous non-linear partial differential equations have four unknown functions, that is, temperature, concentrations in solid and in liquid and fraction of solidification.As an example of the calculation, a solidification process of an Al-4.5% Cu plate in the metal mold has been calculated by the finite difference method, and distributions of temperature, concentration and fraction of solidification, and their variations with time have been obtained. These data indicate a mush mode of the solidification, the near-equilibrium condition of concentration and temperature, and less segregation than expected. The motion of the liquid phase and the behavior of the nucleus, which are neglected in the present calculation, may have a great influence on the mode of solidification and on the segregation.