Diffusion-drift effect on grain boundary grooving

Diffusion-drift effect is a fast diffusion penetration along grain boundaries (GB) due to the concentration gradient and the force causing drift with the rate V = const. Earlier the problem was discussed with the use of two dimensionless parameters beta = root4Dt/delta and gamma = Vt/root4D(b)t where D and D-b are the coefficients of bulk and GB diffusion, delta is GB width and t is the time. In this paper a fresh portion of the solution is introduced into the denominator of 8 which is now equal to sdelta, where s is the segregation coefficient: s = C-b/C, where C and C-b are the bulk and GB concentrations of diffusant. The numerical solutions of the problem are obtained for different beta and gamma. These solutions are applied to the process of GB grooving. The region is limited of such beta, gamma-values when the drift flux predominates and the long step exists at GB solute concentration profiles. The main contradictions of the problem are discussed. If the drift effect is significant it may probably explain a cracks formation without external stresses.