## 4 Discussion  
In an _A_-_B_-_C_ system in which \(B\) has an intermediate size between \(A\) (larger atom) and \(C\) (smaller atom), there may exist a tendency to form the same ordered phase in the three constituting binary systems. This may cause irregular, somewhat triangular, shapes of homogeneity domains in isothermal sections. If the atom ordering obeys geometrical criterion, then the fact that \(B\) is smaller than \(A\) but larger than \(C\) causes a reversal of the ordering. When crossing the homogeneity domain, the \(B\) atom has to switch from the site it occupies when associated with \(A\) atoms to the other sites when associated with \(C\). Note that what is said about size and geometrical factors determining the site occupancies could be easily transposed to valence or electronic properties. We have shown that this behavior is not pure speculation but actually exists in a number of ternary systems. Of course, the three compounds do not necessarily exist as stable phases but the important point is that they are sufficiently close to stability to produce extensive homogeneity domains pointing in their direction. We have shown examples in which two compounds (_AC\({}_{x}\)_ and _BC\({}_{x}\)_: Zr-Nb-Fe, Zr-W-Re; _AB\({}_{x}\)_ and _BC\({}_{x}\)_: Mo-Re-Cr, Re-Cr-Co) or one compound (_AB\({}_{x}\)_: Cr-Mn-Si, Mo-Re-Ni) only was stable. Calculations could be made in any system for any type of phase but are worthwhile only if an odd homogeneity domain (or known inverse atomic distribution in the binaries, like in the Mo-Re-Cr and Re-Cr-Co systems) points to the possible existence of site reversal. We made a systematic scan of the Handbook of Ternary Alloys Phase Diagrams [29] to check for the occurrence of irregular homogeneity domains. The systems presented in this review are the only ones, to our knowledge, for which a detailed structural study of site reversal has been documented. Another interesting phase is the \(\gamma\) brass structure that has irregular homogeneity domains in many systems (e.g., Cd-Cu-Sn or Cu-Pt-Zn) but no detailed structural work showing that site reversal exists. Let us examine in which systems this phenomenon may be observed. These systems must differ strongly from the systems in which one observes a simple substitution (generally observed when two elements are similar and one is different from the two others) or no substitution at all (the three elements  
Figure 16: Calculated site occupancies for the \(\sigma\) phase at 1227 \({}^{\circ}\)C between Mo\({}_{2}\)Re and Cr\({}_{2}\)Ni. are very different). There should be a similar difference of radius/electronegativity between \(A\) and \(B\) and between \(B\) and \(C\) and the three compounds _ABx_, _ACx_, and _BCx_ should exist or be close to stability in the binary systems. This would exclude in principle the phases for which a strongly covalent bonding is involved or the bonding is metallic but very localized (systems with transition metals and rare earths). The irregular systems are therefore mainly systems associating three transition metals. We have presented only phases pertaining to the group of the topologically close-packed (TCP) phases. It seems that this type of structure favors this phenomenon. First, because the bonding has to be mainly metallic, second because transition metal systems are favored because they offer along the transition series wide and smooth variations of atomic radius and electronegativity. Finally, because there are not so many intermetallic phases in transition metal systems that are not TCP. Other phases are ordered structures from the _bcc_, _hcp_, or _fcc_ solid solutions. See, for example, the bow-shaped homogeneity domain of the _B2_ phase in the Al-Pd-Sc or Al-Ru-Sc systems. However, for _B2_ or _L10_, for example, there is no reversal since the two sites in the crystal structure are symmetrically equivalent. For other ordered phases like _L12_, the situation is more complex.