Intermediate phases in binary and ternary alloys: a new perspective on semi-empirical bond constraint theory

This paper extends the scope of semi-empirical bond constraint theory, (SEBCT) and uses this extension to provide quantitative insights into the atomic scale bonding interactions for the two transitions that bracket intermediate phases (IPs) in binary and ternary alloys. Reversibility windows have usually been defined in terms of the average bonding coordination, r(c) (also, N-av, r ), and show considerable scatter between different alloys when displayed in this way. This paper analyzes and plots these transitions in terms of the average number of bonding constraints/atom, n(c) (also C-av), and thereby provides important insights into the extent to which SEBCT must be modified by either extending, or contracting the force field with respect to the 2-body bond-stretching and 3-bond-bending valence forces of the original SEBCT formulation. These modifications include (i) broken bond-bending constraints that reduce nc below the level determined from stretching and bending constraints of the SEBCT, and (ii) additional forces due to repulsions between non-bonding lone-pair orbitals on two-fold coordinated Se, three-fold coordinated As, and terminal or one-fold coordinated I atoms that add additional constraints to the SEBCT counting. These modifications identify the bonding interactions that give rise to the scatter in the r(c)-based plots, and then use the IP plots based on rc to provide a way of determining whether broken or additional constraints move the window threshold, respectively above or below the SEBCT value of 2.4.