Interaction between a solute atmosphere and material defects in solid solutions has long been of fundamental importance to many engineering applications.  We develop a systematic modeling framework on the basis of statistical mechanics foundations which enables us to capture response of a solute atmosphere around a material defect in the absence or presence of an external loading, and further allows us to compute the energetic driving forces on a material defect.  In contrast to the available continuum frameworks for modeling solid solutions, the effect of image stresses both on the solute (re)distribution in the solid and also on the configurational forces on the defect are taken into consideration.  Modeling solute atmosphere as a distribution of misfitting inclusions, the enthalpy of a solid solution is first worked out accounting for the interaction of the solutes with their self-stress field, including their image stresses, as well as with the stress field of an external loading.  Considering a set of lattice points representing interstitial sites in a host solid, Monte Carlo simulations are used for exploring various arrangements of solutes at any given temperature, and for any arrangement, the stress field of the solutes is found by solving the corresponding elasticity problem using a combination of analytical and numerical methods.  The configurational forces on a defect are determined through taking ensemble averages of the well-established path independent integrals of elasticity which are first computed for each microstate independently and then averaged over all arrangements arising in MC simulations.  MC simulations reveal the emergence of a transition temperature below which solutes tend to for a precipitate close to a free surface of the solid.  It is further shown that image stresses, usually unaccounted for in the available continuum frameworks, once interacting with the stress field of an external loading lead to a concentration-dependent change in the configurational forces which does not dies down to zero even when the solid dimensions grow indefinitely large provided that the solute concentration remains finite.

Statistical mechanics based modeling of solute atmospheres around material defects: voids and cracks and the role of image stresses

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