Diffusion Equation for Solute Atoms under a Temperature Gradient

By combining Wirtz’s equation and the phenomenological diffusion equation for carbon under a temperature gradient, JC=−(DCNC⁄RT)[∇(μC)T+*QC∇T⁄T], Shewmon proposed the relation, *QC=−εCm, where, *QC and εCm are the heat of transfer and the migration enthalpy of carbon in α-iron. In this paper, it is pointed out that (1) the vector space in which Wirtz’s and the phenomenological diffusion equation are defined is not the same, (2) hence, it is not allowed theoretically to combine directly these two equations to obtain the relation, *QC=−εCm. Showing a correct equation to be combined with Wirtz’s equation, the correct diffusion equation for solute atoms under a temperature gradient is derived.