Diffusion equation for solute atoms under a temperature gradient

By combining Wirtz's equation and the phenomenological diffusion equation f or carbon under a temperature gradient, J(C) = -(DCNC/RT) [del(mu(C))(T) *Q(C)del T/T], Shewmon proposed the relation, *Q(C) = -epsilon(C)(m), where , *Q(C) and epsilon(C)(m) are the heat of transfer and the migration enthal py of carbon in a-iron. In this paper, it is pointed out that (1) the vecto r space in which Wirtz's and the phenomenological diffusion equation are de fined is not the same, (2) hence, it is not allowed theoretically to combin e directly these two equations to obtain the relation, *Q(C) = -epsilon(C)( m). Showing a correct equation to be combined with Wirtz's equation, the co rrect diffusion equation for solute atoms under a temperature gradient is d erived.