**Abstract:** The one-dimensional Ising (regular solution) model is a first-order statistical mechanical approximation to real muscovite-montmorillonite mixed layer clays. The model assumes a constant excess interaction energy, *w*, between the unlike layers;
w=
w
ab
−
1
2
(
w
aa
+
w
bb
).
Exact solution of the model, applicable to infinitely long chains, can be given by the quasi-chemical formula
N
aa
¯
N
bb
¯
/
N
bb
¯
2
=(
1
4
) exp (2w/kT)
where *N _{ab}* is the equilibrium value of the number of

Using the Ising model, the values of *w/kT* and µ_{i}/*kT* (where µ_{i} is the excess chemical potential of the ith type of layers) were calculated for three clays whose probability of layer succession, *p _{ij}*, had been evaluated by the MacEwan method. For two muscovite-montmorillonite mixed layer clays,

For thin plates of equal numbers of *a, b* layers, a correction factor [(*N* − 2)/*N*]^{2} (where *N* = *N _{a}* +

Application of the Ising model to real crystals depends on our ability to correlate X-ray diffraction patterns with run sequences in crystals. Computer calculations of expected diffraction patterns for thin crystals having various values of *N _{a}* and

*Clays and Clay Minerals*; 1967 v. 15; no. 1; p. 49; DOI: 10.1346/CCMN.1967.0150106

© 1967, The Clay Minerals Society

Clay Minerals Society (www.clays.org)