The solid solution is treated as a ternary solution of clinozoisite, Fe-epidote and an ordered epidote solid solution, using the approach outlined in Holland & Powell (1996 Am Min). Here, Al and Fe3 are assumed to mix on only the M1 and M3 sites, with a strong tendency for Fe3 to order onto the M3 site. The model used is an extension of that used by Bird & Helgeson (1980) to incorporate non-ideal mixing.

The ideal activities of the three end-members are written

where pcz is the proportion of the cz end-member etc. The activity coefficients arefound from the simple regular solution expressions for the ternary solid solution among cz, fep and ep end-members. The degree of order, given by Q = XFeM3 - XFeM1 = pep is found by substituting the activities into the equilibrium constant for the internal equilibrium cz + fep = 2ep. The enthalpy of this reaction is -26.1 kJ, and the values for Wcz-fep, Wcz-ep and Wfep-ep are 15.4, 0.0 and 3.0 kJ/mol respectively, derived from the known values of the order parameter Q from Dollase (1973) and the experimental reversals of Liou (1973), Holdaway (1972), Jenkins et al. (1983) as well as consideration of natural zoisite-clinozoisite partitioning data. While the derived enthalpies of ep and fep depend on this mixing model, that of cz does not.

The calculated activities at 400 and 600°C are given below.

Coded up for THERMOCALC:

% ======================  Epidote symmetric formalism (cz-ep-fep) ======================
epid   3
 
    fep       1     2     0  2  1  1  1  2  1     0  2  1  1 -1  2  1
       gamma  3    
         15.4 0  0    1  1    1  2    1  2 -1  1  1  2  1      1  2 -1  1 -1  2  1   % W(cz-fep)
          0   0  0    1  1   -1  2    0  1  2  2  1      1  2 -1  1 -1  2  1         % W(cz-ep)
          3   0  0    1  1    1  2    0  1  2  2  1      1  2 -1  1  1  2  1         % W(fep-ep)
       bulk   1  1    0  1  1  1 
 
    cz        1     2     1  2 -1  1 -1  2  1     1  2 -1  1  1  2  1
       gamma  3   
         15.4 0  0    1  1    1  2    0  2  1  1  1  2  1      0  2  1  1 -1  2  1   % W(cz-fep)
          0   0  0    1  1    1  2    0  1  2  2  1      0  2  1  1  1  2  1         % W(cz-ep)
          3   0  0    1  1   -1  2    0  1  2  2  1      0  2  1  1 -1  2  1         % W(fep-ep)
          bulk  1  1    1  1  -1  1 
 
    ep        1     2     0  2  1  1  1  2  1     1  2 -1  1  1  2  1
       gamma  3   
         15.4 0  0    1  1   -1  2    0  2  1  1 -1  2  1      1  2 -1  1 -1  2  1  % W(cz-fep) 
          0   0  0    1  1    1  2    1  2 -1  1 -1  2  1      1  1 -2  2  1        % W(cz-ep)
          3   0  0    1  1    1  2    0  2  1  1 -1  2  1      1  1 -2  2  1        % W(fep-ep)
 
    x(ep) 0.5
    N(ep) 0.015   0  0.5