Theoretical estimates of phosphorus concentration profiles across grain boundaries in Fe-P and Fe Ni-P systems

Abstract

The equilibrium “intergranular segregation extent (ISE)” of P in the above two alloy systems has been calculated on the basis of a model presented here. The ISE of P is defined as the monolayer thickness of a P-enriched bulk region adjacent to the grain boundary, where a normalized concentration of P is greater than one-tenth of that of the grain boundary. The model is in principle analogous to Ono's discrete lattice approach based on a simple regular solution model under the assumption of the nearest neighbor interaction of atoms. The ISE of P thus calculated is. irrespective of the Ni-concentration of the alloys, ~ one monolayer thick at most whatever magnitudes are chosen for the various parameters adopted within their limited ranges in the present model. This suggests that the equilibrium intergranular segregation of P occurs exclusively at grain boundaries per se in ferrous alloys.