Thermodynamics of Cottrell atmospheres tested by atomistic simulations

Abstract

Solute atoms can segregate to elastically deformed lattice regions around a dislocation and form an equilibrium distribution called the Cottrell atmosphere. We compare two approaches to describe Cottrell atmospheres. In the Eshelby theory, the solid solution is represented by a composite material obtained by insertion of misfitting elastic spheres (solute atoms) into an elastic matrix (solvent). The theory proposed by Larché and Cahn (LC) treats the solution as an elastic continuum and describes elasto-chemical equilibrium using the concept of open-system elastic coefficients. The two theories are based on significantly different concepts and diverge in some of their predictions, particularly regarding the existence of screening of dislocation stress fields by atmospheres. To evaluate predictive capabilities of the two theories, we perform atomistic computer simulations of Al segregation on a dislocation in Ni. The results confirm the existence of hydrostatic stress screening in good agreement with the LC theory. The composition field is also in much better agreement with the LC prediction than with the Eshelby theory. However, the simulations confirm the logarithmic divergence of the total amount of solute segregation as expected from the Eshelby theory, whereas the LC theory predicts the total segregation to be zero. Several other aspects of the two theories are analyzed. Possible non-linear extensions of the LC theory are outlined.