Thermodynamic model of solute site preferences in ordered alloys

TL;DR

This paper develops a thermodynamic model based on the law of mass action to predict solute site preferences in ordered alloys, considering various defect combinations and deriving general rules for site occupancy behavior.

Contribution

It introduces a transparent formalism for defect concentrations without chemical potentials and explores site-preference phenomenology with algebraic and numerical methods.

Findings

Solute prefers sites of element deficiency.

Site preference switches with composition and energy differences.

Maximum interstitial occupancy occurs near stoichiometry.

Abstract

A thermodynamic model based on the law of mass action is used to calculate concentrations of elementary point defects and to determine site preferences of solute atoms in ordered alloys. Combinations of lattice vacancies, antisite atoms and host interstitials that form equilibrium defects are enumerated for the CsCl (B2) and Ni2Al3 structures. For CsCl, in addition to the two substitutional sites, a distorted tetrahedral interstitial site is considered. For Ni2Al3, the Ni site, two distinct Al sites and a vacant, insterstitial-type Ni-site are considered. An equation of constraint among concentrations of elementary defects is derived that is valid for any crystal structure. The concentration of a selected defect can be solved using the equation of constraint in conjunction with mass-action equations for defect combinations. The method leads directly to defect concentrations without the need to evaluate composition-dependent chemical potentials, resulting in a more transparent formalism. The model is used to explore the phenomenology of site-preferences of dilute ternary solute atoms. Findings are in agreement with previous treatments restricted to substitutional sites. General rules for how site-preferences depend on temperature and on composition in non-stoichiometric compounds are obtained through algebraic analysis and numerical simulations: (1) Solute S tends to occupy substitutional sites of the element in which there is a deficiency. (2) If the difference of energies of S on sites A and B is very positive or negative, then S will occupy site B or A exclusively, independent of composition. If the difference of site energies is intermediate, the solute will switch from one site to the other as the composition changes. (3) Solutes have a tendency to occupy interstitial or empty-lattice sites with a maximum site-fraction near the stoichiometric composition.