Geothermobarometry

See http://plate-tectonic.narod.ru/metpetrographylinks.html
C http://ijolite.geology.uiuc.edu/08SprgClass/geo436/lectures.html

I. Thermodynamics revisited

A. Definitions

-Recall goal of met. pet. is to determine Tand P conditions a rock has experienced.
-Geothermometry = determining T based on equilibrium distribution of elements between co-existing minerals
-Geobarometry = determining P
-Geothermobarometry = determining both

B. Gibbs free energy

-G = H - T S
-Now we add the change in G due to variations in composition:P:G at a given P,T = H - TS + V dP + RT ln K
-K = distribution coefficient: determined experimentally by microprobe; ratio of the concentrations expressed as mole fractions

II. Garnet-biotite exchange geothermometer

A. Reaction: Alm + Phl = Pyp + Ann

-K = (X of Fe in biotite)*(X of Mg in garnet)/ (X of Mg in biotite)*(X of Fe in garnet) = (Mg/Fe) in garnet / (Mg/Fe) in biotite
-Experimental data gives Mg/Fe data at equilibrium at specific temperatures, at P = 0.207 GPa, so equation above reduces to : 0 = H - TS + RT ln KD; or ln K = H/R (1/T) - S/R = straight line in ln K vs. 1/T; see plot ln KD vs. 1/T. Fit a line to data

B. This only applies at the experimental pressure. To extend it to other pressures, need to modify eqn:
-0 = H - TS + PV + 3 RT ln K
-Then ln K = (-H - P V) / 3R * (1/T) + S / 3R: slope of line = -2108 => H = 52.09 kJ/mol; Y-intercept = 0.7811 => S = 19.506 J/K mol
-Then 0 = 52090 - 19.506 T + 2.494 P + 3*8.3144*T* ln KD
Solving for T = (52090 + 2.494 P) / ( 19.506 - 12.943 ln K) - 273

-Plot of contours of K on a PT diagram.
-Steep slope => highly sensitive to T

III. Geobarometers

A. GASP geobarometer

-Reaction: 3An = Grs + 2Ky + Q
-Similar experimental data plotted: from this, get H and S, then plug into equation: 0=-48357 + 150.66 T - 0.6608 P + 8.3144 T ln K (P in MPa, T in kelvin); T = (48357 + 0.6608 P) / (150.66 + 8.3144 ln K) - 273 (P in MPa, T in celsius)
-Here K is the true equilibrium constant = (X of Grs in Grt)3 / (X of An in Plag)3: assuming ideal solutions in garnet and plagioclase; exponents come from details of the chemical reaction and the ideal solution model
-contours of K plotted:

-Shallower slope than contours in previous diagram
-Better sensitivity to P
-Still, requires that you know T from a geothermometer.

B. A more accurate geobarometer

-Grt + Rt = Il + Ky + Q
-Solid solutions: Alm in Grt and Hm in Il: K = (activity of Hm in Il)3 / (activity of Alm in Grt) where activity is the "thermodynamically effective concentration".
-See Figure on handout: plot of contours of log K for T and P: reaction is almost independent of T; T need not be known accurately for this geobarometer to be used.
C. Combined geothermobarometers

-If X of Alm in Grt = 0.88 and X of An in Bt = 0.62, then T = 625 oC and P = 0.43 GPa

C. Sources of error in GTB

-Disequilibrium : equilibrium cannot be proved - only supported; zoned minerals: which zone(s) are coeval; check chemographic diagram for crossing tie-lines; check for consistency in partitioning (i.e., constant K for mineral(s) of interest)
-Retrograde metamorphism / polymetamorphism: continuous reactions occur prograde AND retrograde => calculated T might not be max T, but T where reaction ceases = closing temperature; ion-exchange reaction effects; net transfer reaction effects
-Poorly designed experiments to calibrate GTB
-Extra components in natural systems
-Extrapolation beyond experimental range (some apply only within limits)
-Oxidation state of Fe