Intergranular segregation and ordering effect: A mixed Monte Carlo mean-field approach

Abstract

Segregation in the $\ensuremath{\Sigma}=5$ (310) 〈001〉 symmetric tilt grain boundary (GB) is investigated with Monte Carlo simulations for the Cu(Ag) system. Due to the specific structure of the GB plane, a two-dimensional (2D) ordered structure is found for this alloy, which has, however, a strong tendency to phase separation in the bulk. Matching the Monte Carlo results on a lattice gas model (LGM) allows a detailed analysis of the stability of this 2D compound and reveals that the 2D long-range-order parameter can have a nonmonotonic temperature dependence. Moreover, the LGM analysis shows the existence of a multilayer phase transition in the first layers near the GB plane, which can be viewed as a generalized Fowler-Guggenheim transition. During this transition, the Ag concentrations of the four planes adjacent to the GB plane jump from a very low value to a value almost equal to 1. However, a detailed study at the vicinity of the bulk solubility limit shows that this transition is not followed by others and thus no GB wetting is predicted at the temperature considered. Finally, the LGM matching allows us to estimate the influence of vibrational entropy on the GB segregation. This segregation vibrational entropy is found to be very inhomogeneous, being a large contribution to the segregation free enthalpy for a specific site of the GB plane and negligible for other sites.