THERMODYNAMICS OF NONCONVERGENT CATION ORDERING IN MINERALS .3. ORDER-PARAMETER COUPLING IN POTASSIUM-FELDSPAR

The thermodynamic consequences of Al-Si ordering in potassium feldspar under equilibrium condition have been described quantitatively using a Landau free energy expansion in two order parameters. The first order parameter, Q(t), relates to nonconvergent ordering between T1 and T2 sites and the second, Q(od), relates to the symmetry-breaking ordering between T1o and T1m sites. Strong interactions occur between the two order parameters, as described by a term in lambdaQ(t)Q(od)2, and the form of the resulting expansion is G = -hQ(t) + 1/2a(t)(T - T(ct))Q(t)2 + 1/6c(t)Q(t)6 + 1/2a(od)(T - T(cod))Q(od)2 + 1/6c(od)Q(od)6 + lambdaQ(t)Q(od)2. The coupling coefficient, lambda, was assumed to be temperature dependent, as lambda = -20.13T, and a favored set of values for the coefficients is h = 1650 J/mol, a(t) = 22.28 J/mol.K, T(ct) = 586 K, c(t) = 14700 J/mol, a(od) = 41.09 J/mol.K, T(cod) = 239 K, and c(od) = 9818 J/mol. The monoclinic reversible triclinic transition temperature was assumed to be 753 K. Equilibrium variations of Q(t) and Q(od) calculated from the expansion give small changes in energy associated with Q(t) ordering in the stability field of monoclinic crystals. The monoclinic reversible triclinic transition is first order, with a jump in Q(od) from 0 to 0.94, a jump in Q(t) from 0.40 to 0.95, a latent heat of 7.2 kJ/mol, and a latent entropy of 9.5 J/mol.K. Below the transition, relatively large energy changes accompany Q(t) and Q(od) ordering. Coupling between Q(t) and Q(od) appears to outweigh coupling between Q(od) and the triclinic strain in crystals with the modulated orthoclase structure, with the result that both Q(t) and Q(od) may be close to being homogeneous in orthoclase and adularia.