Science Record

28 Fo ZiFy + Z2F2 + ++", (3)

where the Z’s denote the coordination numbers and the F’s are to be determined. From this it is obvious that Fy is the free energy when all interaction encizics vanish and thus may be written down immediately. To find Fy; F,,°+:, it is also pointed out in the said paper that all we have to do is to find the free energy F for-certain pseudo-lattices for which all Z except a few vanish.

Such a calculation is now envisaged. It is easily seen that the coefficients F for those Z in (1), (2) are closed forms of the Boltzmann factors, and to get their explicit expressions, the only troublesome work is to solve for an _ algebraic equation of the 3rd or 4th degree. Such expressions will not be written out here'’), as they are all cumbersome. By using suitable combination of the F’s, we get configurational free energy of binary solid solutions of the type AB, with or without next nearest neighbour interactions, with or without long-distance order, of solid solutions on a face-centred lattice, etc.

One may also discuss quasi-chemical formulas based on the above method. We point out first that if we neglect all the coordination numbers except the lowest (i.e. the average number of nearest neighbours of a site), we obtain the quasi-chemical formula for the different number X of pairs of nearest neighbours, quite independently of the number of components present in the solution. Thus for 2, 7=1, 2,--* (¢@7), we get

2 4 exp ((—2V i; + Vis + Vi /kT} (4)

with obvious meanings for the notations. Next, we include higher coordination numbers and obtain in this way natural extensions of the quasi-chemical formulas. Thus after including the next coordination number, the new quasichemical formula for a binary solid solution on a face-centred lattice becomes

nf A S ae X44 = X44 + 3X (4,) + 3x Ca)

Ko = 2X5 + 6x"( A BP Ox (a) (5)

ar A * (3 ae

Xa)? EX’ CSs)E | Go) Kako (Ax (A) x°(P) x’ CA)

= exp {((=—2V an + Vad = Vee) /RT}, (6)

Xep = Xpa + axa A) =

2(Xi4ga + Xun) = —36NO4, 2(X4s + Xan) = —36NOz, (7)