Chemical embrittlement of Fe grain boundaries: P and the P-Mo couple

Density functional theory is used in an embedded-cluster scheme to study the electronic effects of P and the P-Mo couple upon the chemical embrittlement of Fe grain boundaries. The results obtained for P alone in a model grain boundary (GB) are consistent with its observed behaviour as a chemical embrittling agent. Total energies calculated for P-Fe clusters indicate a lower free energy for P in a free surface (FS) relative to the GB, in agreement with the Rice-Wang thermodynamic model of intergranular embrittlement. It is found that the chemical interactions between the P and surrounding Fe atoms are similar in both environments but tend to favour the GB configuration. However, it is also found that the structural rearrangement of the GB when P is introduced leads to a sufficiently large reconstruction energy that, overall, the FS configuration is energetically favoured. The results obtained for P-Mo are consistent with the observed behaviour of Mo as a cohesion enhancer; total energies indicate that, when Mo is added to an Fe GB containing P, the embrittlement process is effectively reversed. Although Mo appears to increase somewhat the embrittling potency of P, this is more than compensated by its direct cohesion-enhancing effect at the GB. The underlying physical phenomena responsible for these energy differences are examined in detail using analytical and graphical techniques.