Occupational groups similar

Careful consideration of the composition of the group may increase discussion by combining participants from similar occupational groups. 

Fig. 1. Electronic states [or iron-group atoms, showing number of states as qualitative [unction of electronic energy. Electrons in band A are paired with similar electrons of neighboring atoms to form bonds. Electrons in band B are d electrons with small interatomic interaction they remain unpaired until the band is half-filled. The shaded area represents occupancy of the states by electrons in nickel, with 0.6 electron lacking from a completely filled B band. (States corresponding to occupancy of bond orbitals by unshared electron pairs are not shown in the diagram.)...

The same structure is formed in a number of binary (or ternary) phases, for which a random distribution of the two (or three) atomic species in the two equivalent sites is possible. Typical examples are the (3-Cu-Zn phase (in which the equivalent 0,0,0 A, A, A positions are occupied by Cu and Zn with a 50% probability) and the (3-Cu-Al phase having a composition around Cu3A1 (in which the two crystal sites are similarly occupied, on average by Cu, with a 75% occupation probability, and by Al, with a 25% occupation probability). A number of these phases can be included within the group of the Hume-Rothery phases (see 4.4.5). 

We say that the sites are identical in a weak sense whenever the three PFs 0(1,0,0), 0(0,1,0), and 0(0,0, 1) have the same value. This is identical to the requirement that the single-site intrinsic constant is the same for any specific site. In this case we can replace these three PFs by three times one representative PF, as is done on the rhs of Eq. (2.2.22). We shall say that the sites are identical in a strict sense whenever the PF of any given occupation number is independent of the specific group of occupied sites. For instance, in an equilateral triangle all PFs with two sites occupied are equal. Hence we can replace the sum on the rhs of Eq. (2.2.23) by three times one representative PF. This cannot be done, in general, for a linear arrangement of the three sites, in which case 0(1,1,0) is different from 0(1,0,1), even when the sites are identical in the weak sense (see Chapter 5). Similarly, for... 

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