Intermediate phases in binary and ternary alloys How far can we go with a semi-empirical bond-constraint theory?

This paper extends the scope of semi-empirical bond constraint theory, SE BCT, and uses it provide quantitative information relative the two transitions that bracket intermediate phases in binary and ternary alloys. Reversibility windows have generally been defined in terms of the average bonding coordination, r_c (N_av, <r>), and show considerable scatter between different systems when displayed in this way. This paper designates these transitions in terms of the average number of bonding constraints/atom, n_c (C_av), and provides important insights into the extent to which SE BCT can be augmented and improved by considering i) broken bond-bending constraints, as well as ii) longer range forces beyond 2-body bond-stretching and 3-bond-bending valence forces of the original formulation.