Speaking of biotite tangents, the thermodynamic properties of Ti, vacancy substitutions, and solid solution of muscovite also remain unclear.  One would expect that these problems would be exacerbated at higher T.  Below is what I wrote in a review paper (Essene, 2009).

     "Determination of the Ti formula in a given biotite requires measurement of both FeO and total Fe as well as H2O, and even then one cannot distinguish Ti-1Si1 from Ti-1(Al)IV-2(Fe2+)1Si2 without additional structural information.  One cannot simply assume all Fe2+ in biotite even in graphitic schists because of the documented significant (8-15%) Fe3+ found in Mössbauer in biotite by Guidotti and Dyar (1991).  A complex biotite composition means the major mechanism for Ti is ambiguous because reactions can be written among postulated biotite species, including the above Ti exchanges, as well as Al-oxy or Fe3+-oxy and vacancy as dioctahedral solid solution, [ ]2R3+=3R2+ (Bohlen et al. 1980; Rancourt et al. 2001).  The latter substitution is fixed for Al vs. Mg + Fe2+ in both micas when muscovite coexists with biotite.  Patiño Douce (1993) postulated an octahedral site vacancy substitution for Ti, [ ]Ti=2R2+, but there is no way to distinguish it from a vacancy engendered by dioctahedral Al or Fe3+ substitution.  The correlation of octahedral site vacancy with increasing Ti (Patiño Douce 1993) is potentially flawed: a false vacancy in Ti-oxy biotite is generated by a 22 O normalization.  Consider the formula of a Ti-oxy biotite, K2TiFe4.5Al0.5Si5.5Al2.5O20(OH)2O2, which must be normalized to 23 O!  Erroneously normalizing to 22 O yields K1.91Ti0.96Fe4.30Al0.12[ ]0.62Si5.26Al2.74O20(OH)4 on an anhydrous basis, apparently closer to a dioctahedral than a trioctahedral mica, but only because it was misnormalized."

    "Electron microprobe data alone cannot be used to predict the VI occupancy in biotite (Afifi and Essene 1988).  The only reliable way to normalize titanian biotite is to measure Fe3+/Fe2+ as well as H2O and apply an anion normalization (Bohlen et al. 1980; Sassi et al. 2008).  One cannot evaluate alternative substitutions in biotite or muscovite with an electron microprobe analysis when also granting the possibility of Fe3+.  Atomic plots such as those shown by Sassi et al. (2008) are not persuasive of a particular substitution even with complete analyses of biotite because they represent projections from multicomponent biotite space onto two dimensions.  Thus, Ti-oxy substitution cannot be resolved from Al- or Fe-oxy, nor Ti-vacancy from Al- or Fe3+-vacancy substitutions.  Structure refinements of 10 biotite grains from medium grade metapelites show 6-24% vacancies ordered into the M1 octahedral site and 0-15% vacancies in the K site of the biotite crystals, as well as 7-12% trioctahedral substitution in four muscovite crystals that coexist with the refined biotite grains (Brigatti et al. 2008).  Reasonable crystal-chemical assumptions were made in reaching this result, including placing all Ti and AlVI in the M2 site of biotite.  The data indicate limited but significant mutual solid solution of biotite and muscovite in peraluminous metapelites and granites (Brigatti et al. 2000, 2008)."