On the distribution of carbon in martensite

Abstract

The statistical-mechanics of a generalized perfect lattice gas is used to describe the distribution of interstitial solute atoms in martensite. In untempered martensite, partitioning of mobile interstitial carbon occurs between normal octahedral interstitial sites and those distorted sites around immobile dislocations. The statistics adopted acknowledge the finite number of each kind of site per unit volume of martensite. The dislocation density, fraction of twinned martensite, and the arrangement of dislocations are all input variables in the calculations. The principal quantities calculated are the fraction of carbon atoms segregated to dislocations and the fraction of distorted sites occupied as functions of the carbon content and substructure. The equilibrium distribution of carbon is also determined for tempering conditions where either ∈-carbide or cementite may precipitate. Here, the change in the solubility limit of ferrite with dislocation density is predicted. In untempered low carbon martensites (at 300°K) 85 pct of the carbon will be segregated to dislocations at equilibrium. This value decreases to 60 pct in an 0.80 wt pct C steel. Less than 5 pct of the distorted sites are filled when the dislocation distribution is uniform. Much higher concentrations occur when the long range stresses of the dislocations are relaxed and the mean carbon/dislocation interaction energy increases. Analogous results are presented for the equilibrium among carbides, normal sites, and distorted sites. The predictions of the lattice gas model are in agreement with numerous independent experimental observations.