# Notes on Statistical Thermodynamics by Frenkel D.

By Frenkel D.

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N ) . 3 Enthalpy of Mixing and the Activity Coefficient, ~ 45 Thus, the total Gibbs energy of ideal mixing becomes G t~ = n~, x i G ~ ~ X i l n X i = a m e c h m i x + A G idealmix, i=l (14b) i=I where G~~ is the Gibbs energy of the mineral end-member i in its given standard state, hence being identical to the standard state chemical potential of i, /-tl~ (cf. Appendix 2). The first sum in eq. 14b is the energy contribution that is due to purely mechanical mixing (cf. sect. 2) between the end-members and is referred to as the mechanical Gibbs energy of mixing, Gn'ch''~ .

X gr WE lb: Calculate the ideal mixing activities of the biotite end-members phlogopite ( KMg(Mg2)Si 2 (SiAI)O,, (OH)2), annite ( K Fe(Fe2)Si 2(SiAl)O,,, (OH)2), eastonite ( K Mg(Mg al)Si~_ (alz)Qo (OH)2), siderophyllite K Fe( Feal) Si2 (Al)z O,, (OH)~. and Na-phlogopite ( NaMg(Mg2)Si 2(SiAt)O~o (OH)2) from the given biotite analysis. oxide. . . . 37 Many iron-bearing minerals contain ferrous (Fe 2§ and ferric (Fe 3+) iron. Unfortunately, microprobe analyses can not distinguish between the two oxidation states, and the total iron content of a mineral is estimated as ferrous iron.

Biotite has two different octahedral sites, M1 and M2, which occur in the ratio 2:1, with the s m a l l e r M1 site being preferentially occupied by three- and 30 2 Thermodynamics of Solid Solutions fourvalent cations. 17. 075. The remaining space on M1 are Xve~. on M1, X~p,~ Ml = 1 - ( X ~ l + xMIF:" + XrM~) = 0 . 414. 396. The two M1 sites are now completely occupied. The commonly made assumption that the Fe2+-Mg distribution between discrete structural sites is identical, ie. x z -" g-'biotite (eg.