Science Record

SCIENCE RECORD New Ser. Vol. III, No. 1, 1959

PHYSICS

CONFIGURATIONAL PARTITION FUNCTION OF SOLID SOLUTIONS*

T. S. Cuanc (4A %)**

(Institute of Mathematics, Academia Sinica)

In an earlier paper'!, it is proved that the configurational free energy F of regular solid solutions is linear in certain coordination numbers defined through the so-called neighbour matrices. To be precise, we let hee, Pec» “" "5 be defined as functions of the sites c, c as follows:

he? = 1 if c, ¢ are nearest neighbours, 0 if otherwise, Hee = 1 if c, ¢ are next nearest neighbours,

= 0 if otherwise,

The coordination numbers are then

NS Red's

ND Reel Reel? betel’ 5

NS Reet heel? Rete!’ 5

NZ ect Rect Rettteh delta! 5 (1)

etc., where N denotes the total number of sites and the summation is taken over all positions of c, ¢’,:--, with the understanding that they are never “equal”. If we wish to study the long-distance order, we divide sites among various sublattices and denote points on them by a, a’,---, 5, b’,--+, and then the relevant coordination numbers are

(2N)* 2 das, (2N)1 3 Ras da’s baa" 5 (2)

etc., a, a@,**: being again always unequal,---. The right hand sides of (1), (2) are characterized by the fact that the term under the summation sign is an irreducible product in the suffices, i.e. not divisible into two or more parts with one or no suffix in common. Thus we may write F as

*Received Nov, 21, 1958, **Member of Academia Sinica,