Long-range order instead of phase separation in large lattice-mismatch isovalent AX-BX systems

Large atomic size mismatch between compounds discourages their binding into a common lattice because of the ensuing cost in strain energy. This central paradigm in the theory of isovalent alloys long used to disqualify alloys with highly mismatched components from technological use is clearly broken by the occurrence of stable spontaneous long-range order in mixtures of alkali halides with as much as 40% size mismatch (e.g., LiF-CsF). Our theoretical analysis of these failures uncovered a different design principle for stable alloys: very large atomic size mismatch can lead to spontaneous ordering if the large (small) components have the ability to raise (lower) their coordination number (CN) within the mixed phase. This heuristic design principle has led us to explore via first-principles structure search a few very largely mismatched binary systems whose components have a propensity for CN disproportionation. We find ordered structures for BeO-BaO (37% size mismatch) and BeO-SrO (30%), and ordering in LiCl-KCl (20%), whereas BN-InN (33%) is found to lower its positive formation enthalpy by similar to 60% when CN disproportionation is allowed. This new design principle could be used to explore phases unsuspected to order by the common paradigm of strain instability.