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:

% ==================   Epidotes   ========================
epi 3   
      x(ep)   0.5
      N(ep)   0.015  range 0 0.5       % where N = Q/2

%-------------------------------------------------------------------

p(cz)    1  1    1  2 -1  x -1  N
p(ep)    1  1    0  2  1  x  1  N
p(fep)   1  1    0  1  2  N

% --------------------------------------------------
   sf

   W(czep)         0  0  0  
   W(czfep)     15.4  0  0 
   W(almpy)        3  0  0  
   
% --------------------------------------------------
   4   % 4 "site fractions"
   
   xFeM1   1  1    0  2  1  x  1  N
   
   xAlM1   1  1    1  2 -1  x -1  N   
      
   xFeM3   1  1    0  2  1  x -1  N

   xAlM3   1  1    1  2 -1  x  1  N
   
% --------------------------------------------------
% ideal mixing activities
   
 cz      1  2      xAlM1  1  xAlM3   1     % may only involve "site fractions"

 ep      1  2      xFeM1  1  xAlM3   1
      
 fep     1  2      xFeM1  1  xFeM3   1


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