Exchange equilibria
Exchange equilibria can be fruitful sources of thermodynamic data for end-members which only occur as solid solutions. They are of most practical use when the two solid solutions are relatively simple (e.g. just Fe-Mg mixing in each) and where the mixing properties of at least one is well known. In more complex solutions, the uncertainties may be too large to make these equilibria useful for extracting thermodynamic data. The effects of non-ideality were assessed by preprocessing the data, fitting the measured distribution coefficients as a function of mineral Fe:Mg ratio, and/or Ca-content.
Phases whose enthalpies rely on Fe-Mg exchange equilibria are ankerite, annite, Fe-celadonite, hedenbergite, magnesioferrite, Fe-anthophyllite, daphnite, Fe-sapphirine, Fe-carpholite, Fe-sudoite and Fe-talc. Experimental partition data of Dalton & Wood (1993) at 1000°C on olivine-carbonate experiments were used to derive data for ankerite and to confirm the data for siderite. Taking a value for W(ol) =4.2 kJ leads to W(mag)=4.0 kJ and W(dol)=3.0 kJ (all values on a one-site basis). These values are also consistent with the lower-temperature partitioning data on dolomite-magnesite exchange (Rosenberg, 1967) and the natural data for dolomite-magnesite of Anovitz & Essene (1987).
The experimental data of Ferry & Spear (1978) on the reaction py + ann = alm + phl were used together with W(gt)=0.8 kJ and W(bi)=3.0 kJ. The experiments of Perchuk & Lavrenteva (1983) are not consistent with this analysis, possibly because they involved much more aluminous biotites, and were not used. For hedenbergite, two sets of equilibria were used, those of Lindsley (1983) on 2hed + en = fs + 2di and those of Perkins & Vielzeuf (1992) on 2hed + fo = fa + 2di and are consistent with W(cpx)=2.5 and W(opx)=0.5. For magnesioferrite, the experiments of Jamieson & Roeder (1984) on the equilibrium fa + 2mft = 2mt + fo were used, and the value for ln K was taken directly from the analysis of Nell & Wood (1989). For Fe-anthophyllite, the partitioning data were taken from natural assemblages at low-temperature granulite grade (5 kbar, 725°C) for the equilibrium 7en + 2fanth = 2anth + 7fs.
For daphnite, the Fe-Mg partitioning between garnet and chlorite and between chlorite and biotite used in HP90 are consistent with the analysis of a larger suite of samples by Dickenson & Hewitt (1986). Therefore the daphnite enthalpy has been derived from partitioning using the expression of Dickenson & Hewitt (in Laird, 1989) for the reaction 5alm + 3clin = 5py + 3daph, and from the equilibrium 5phl + 3daph = 5ann + 3clin (Laird, 1989). As a mutual check on such equilibria, the natural chlorite-actinolite partitioning (Laird, 1982) for the equilibrium clin + fact = tr + daph was also fitted successfully. This last reaction makes a link back to hedenbergite via the experiments of Ernst (1966) on the reaction 2fact = 3fa + 5q + 4hed + 2H2O discussed above, and shows that the exchange data in the laboratory at high temperatures, the end-member experiments and the low-temperature natural exchange data are all mutually compatible.
Data for Fe-sapphirine were taken from the cordierite-sapphirine partitioning in Waters (1986) for the reaction 4spr7 + 7fcrd = 4fspr + 7crd. The data for Fe-osumilite were taken from the study of Holland et al. (1996a) using the partitioning of osumilite with orthopyroxene and with cordierite. The entropy of Fe-osumilite has been corrected to 762 J/mol by incorporation of the magnetic contribution erroneously omitted in Holland et al. (1996a). For Fe-talc the natural partitioning in eclogites from Chinner & Dixon (1974), Chopin & Monie (1984) and Miller (1986) for talc-chloritoid pairs was used. Data for ferrocarpholite were derived from natural partitioning between chloritoid and carpholite using analyses from Seidel & Okrusch (1977) and Theye et al. (1992). Finally, the enthalpy for Fe-sudoite is taken from the sudoite-chlorite partitioning measured by Theye et al. (1992).
Experimental and natural partitioning data have also been used to check for consistency, rather than in deriving enthalpies, in several other equilibria. Good agreement of the data set is found with the garnet-olivine data of O'Neill & Wood (1979) and Hackler & Wood (1989), the olivine-orthopyroxene experiments of von Seckendorff & O'Neill (1993), the garnet-orthopyroxene experiments of Lee & Ganguly (1988), the garnet-cordierite experiments of Perchuk & Lavrenteva (1983) and the biotite-orthopyroxene experiments of Fonarev & Konilov (1986). The olivine-spinel exchange experiments of Engi (1983) and Jamieson & Roeder (1984) are not reproduced well with the current data set, the problem possibly stemming from the variable disordering state in the spinels.
271) 2mag + fa = fo + 2sid (Dalton & Wood, 1993)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-1.32 - 20.0 1000 6.06 8.42 -1.25 0.17 1 (6.21 <-> 8.27)
cH = 6.55 (sd 0.88) 2
within bracket
uH = 0.22, d/s = 5.3, h = 0.14
272) 2dol + fa = fo + 2ank (Dalton & Wood, 1993)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-1.48 - 20.0 1000 10.70 13.47 -1.52 0.49 1 (10.75 <-> 13.42)
cH = 12.48 (sd 2.58) 2
within bracket
uH = 0.22, d/s = 6.4, h = 0.72
* dol + sid = ank + mag (Anovitz & Essene, 1987)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-0.35 - 4.0 400 2.00 3.11 -0.42 0.47 ** NOT USED **
cH = 2.97 (sd 1.32) 3
273) dol + sid = ank + mag (Rosenberg, 1967)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-0.43 - 3.0 500 2.22 4.71 -0.35 0.41 1 (2.41 <-> 4.52)
cH = 2.97 (sd 1.32) 2
within bracket
uH = 0.26, d/s = 4.8, h = 0.30
* en + 2ank = 2dol + fs (Natural., Klein, 1978)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
1.80 - 8.0 600 -16.59 -12.92 -1.15 0.40 0.71 ** NOT USED **
cH = -4.60 (sd 2.58) 2
274) py + ann = alm + phl (Ferry & Spear, 1978)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
5.08 - 2.0 550 -56.36 -54.07 5.11 0.29 1 (-56.18 <-> -54.66)
4.76 - 2.0 600 -58.03 -54.46 4.65 0.27 cH = -55.41 (sd 1.00) 2
4.26 - 2.0 650 -56.64 -54.48 4.24 0.26 within bracket
3.82 - 2.0 700 -56.48 -53.42 3.88 0.25 uH = 0.43, d/s = 2.2, h = 0.80
3.71 - 2.0 745 -58.80 -54.23 3.58 0.24
3.42 - 2.0 800 -59.48 -54.37 3.25 0.22
* py + ann = alm + phl (Perchuk & Lavrenteva, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
3.57 - 6.0 700 -53.69 -49.79 -0.21 4.02 0.25 ** NOT USED **
2.97 - 6.0 750 -51.36 -47.27 -0.48 3.69 0.23 cH = -55.41 (sd 1.00)
2.43 - 6.0 800 -49.04 -44.75 -0.71 3.39 0.22
275) 3fcrd + 2py = 3crd + 2alm (Perchuk & Lavrenteva, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
11.52 - 6.0 700 -145.07 -134.95 11.55 0.38 1 (-141.67 <-> -135.49)
9.73 - 6.0 800 -143.89 -133.16 9.92 0.34 cH = -140.21 (sd 1.54) 2
8.27 - 6.0 900 -143.16 -131.37 8.58 0.32 within bracket
7.03 - 6.0 1000 -142.21 -129.50 7.45 0.29 uH = 0.74, d/s = 4.9, h = 0.05
276) alm + 3cel = py + 3fcel (Green & Hellman, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-0.83 - 20.0 975 1025 20.45 21.39 1000 102 1 (20.50 <-> 21.34)
cH = 20.92 (sd 0.96) 2
within bracket
uH = 0.29, d/s = 1.7, h = 1.00
277) 2hed + en = fs + 2di (Lindsley, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0.33 - 15.0 990 -12.65 -10.47 -0.25 0.68 0.24 1 (-12.55 <-> -11.76)
0.66 - 15.0 910 -16.94 -10.93 0.80 0.26 cH = -15.26 (sd 1.27) 3
0.68 - 15.0 810 -13.78 -11.65 -0.16 0.96 0.28 too low
uH = 0.21, d/s = 2.4, h = 0.32
278) 2hed + fo = fa + 2di (Perkins & Vielzeuf, 1992)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
1.60 - 10.5 1000 -25.59 -21.81 1.55 0.24 1 (-25.25 <-> -22.15)
cH = -23.14 (sd 1.27)
within bracket
uH = 0.44, d/s = 4.3, h = 0.52
* fs + fo = en + fa (Matsui & Nishizawa, 1974)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0.75 - 27.0 1000 -5.63 -3.17 -0.21 1.08 0.03 ** NOT USED **
cH = -7.88 (sd 0.13) 2
279) fs + fo = en + fa (von Seckendorff & O'Neill, 1993)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0.94 - 15.0 900 -8.21 -6.71 0.99 0.03 1 (-7.75 <-> -6.83)
0.88 - 15.0 1000 -7.96 -6.68 0.93 0.03 cH = -7.88 (sd 0.13) 2
0.80 - 15.0 1150 -7.88 -6.30 -0.00 0.87 0.02 too low but OK
uH = 0.22, d/s = 2.6, h = 0.03
280) 2py + 3fa = 2alm + 3fo (O'Neill & Wood, 1979)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
2.04 - 27.0 1000 -44.10 -37.67 1.93 0.29 1 (-43.69 <-> -39.30)
1.74 - 27.0 1100 -45.02 -37.98 1.58 0.27 cH = -39.74 (sd 1.55) 2
1.49 - 27.0 1200 -45.89 -38.69 1.28 0.25 within bracket
1.25 - 27.0 1300 -46.69 -38.88 1.02 0.24 uH = 0.55, d/s = 4.7, h = 0.16
281) 2py + 3fa = 2alm + 3fo (Hackler & Wood, 1989)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
1.20 - 9.1 1000 -42.39 -35.86 1.26 0.29 1 (-42.42 <-> -35.83)
cH = -39.74 (sd 1.55) 2
within bracket
uH = 0.46, d/s = 7.1, h = 0.04
* 2py + 3fs = 2alm + 3en (Lee & Ganguly, 1988)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
4.71 - 20.0 980 -68.64 -57.15 4.76 0.29 ** NOT USED **
4.43 - 25.0 1055 -66.18 -53.44 4.75 0.28 cH = -63.39 (sd 1.53)
4.25 - 25.0 1105 -67.04 -53.46 4.52 0.27
3.66 - 25.0 1205 -65.02 -50.68 4.11 0.25
* 2py + 3fs = 2alm + 3en (Kawasaki & Matsui, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
5.04 - 45.0 1100 -57.15 -49.51 -0.55 5.92 0.27 ** NOT USED **
4.04 - 45.0 1300 -55.08 -45.28 -0.64 5.05 0.23 cH = -63.39 (sd 1.53)
* 2py + 3fs = 2alm + 3en (Harley, 1984)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
2.98 - 27.0 1200 -54.73 -40.51 -0.71 4.26 0.25 ** NOT USED **
2.80 - 23.0 1200 -55.70 -41.81 -0.63 3.99 0.25 cH = -63.39 (sd 1.53)
2.98 - 18.0 1150 -60.02 -46.29 -0.28 3.84 0.26
3.49 - 18.0 1050 -60.51 -49.08 -0.26 4.27 0.28
3.99 - 13.5 975 -65.43 -55.15 4.29 0.29
4.29 - 7.5 900 -68.68 -59.54 4.22 0.31
* 2herc + fo = 2sp + fa (Jamieson & Roeder, 1984)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-0.06 - 0.0 1300 0.39 2.19 -0.70 -0.83 0.11 ** NOT USED **
cH = 11.37 (sd 0.71) 2
* 2herc + fo = 2sp + fa (Engi, 1983)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-0.60 - 1.0 700 4.80 9.58 -0.22 -1.11 0.17 ** NOT USED **
-0.31 - 1.0 800 4.09 6.02 -0.60 -1.01 0.16 cH = 11.37 (sd 0.71)
-0.79 - 1.0 900 4.10 15.69 -0.94 0.14
282) fa + 2mft = 2mt + fo (Jamieson & Roeder, 1984)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
3.61 - 0.0 1300 -42.10 -47.40 3.53 0.64 2 (-45.06 <-> -44.44)
cH = -43.64 (sd 4.19) 2
too high but OK
uH = 0.27, d/s = -10.0, h = 0.64
283) 3en + 2ann = 2phl + 3fs (Fonarev & Konilov, 1986)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
2.59 - 4.9 700 -50.43 -43.39 2.66 0.58 1 (-48.18 <-> -43.55)
2.01 - 4.9 750 -48.34 -40.49 2.37 0.56 cH = -47.44 (sd 2.36) 2
1.82 - 4.9 800 -48.42 -41.36 2.11 0.53 within bracket
uH = 0.40, d/s = 6.1, h = 0.18
284) fact + 5di = tr + 5hed (Natural Kd)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0 - 6.0 600 0.10 8.82 -0.89 1.49 0.56 1 (0.92 <-> 8.00)
cH = -6.34 (sd 2.04) 2
too low
uH = 1.05, d/s = 4.2, h = 0.06
285) 7en + 2fanth = 2anth + 7fs (Natural Kd)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0 - 5.0 725 20.19 37.70 0.00 4.16 1 (21.37 <-> 36.52)
cH = 28.95 (sd 17.26) 2
within bracket
uH = 1.71, d/s = 5.1, h = 1.00
286) 3tr + 5fgl = 5gl + 3fact (Natural Kd)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
0 - 10.0 400 3.20 17.25 -0.83 2.09 4.59 1 (2.88 <-> 17.57)
cH = -1.46 (sd 12.85) 2
too low but OK
uH = 0.93, d/s = 7.5, h = 0.59
287) 2acm + pa + 2q = 3ab + hem + H2O (Natural Tauern)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
1.16 0 10.0 8.0 450 66.05 74.21 8.99 3.80 1 (66.78 <-> 73.48)
cH = 70.13 (sd 7.63) 2
within bracket
uH = 0.94, d/s = 4.3, h = 1.00
288) 5alm + 3clin = 5py + 3daph (Dickenson & Hewitt, 1986; Laird, 1989)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-34.81 - 7.0 450 222.72 244.95 -33.30 2.77 1 (224.14 <-> 236.20)
-31.46 - 7.0 500 218.29 237.62 -30.96 2.59 cH = 224.71 (sd 8.32) 2
-29.98 - 7.0 550 222.04 242.06 -28.91 2.43 within bracket
uH = 1.81, d/s = 4.1, h = 0.47
289) 5phl + 3daph = 5ann + 3clin (Laird, 1989)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
2.03 - 6.0 550 49.27 62.64 2.55 2.54 1 (50.00 <-> 61.91)
cH = 52.36 (sd 8.69) 2
within bracket
uH = 1.21, d/s = 5.5, h = 0.41
290) clin + fact = tr + daph (Laird, 1982)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
2.66 - 7.0 420 -26.64 -21.72 2.35 1.07 1 (-26.72 <-> -21.64)
cH = -22.40 (sd 3.08) 2
within bracket
uH = 0.33, d/s = 7.4, h = 0.28
291) 4spr7 + 7fcrd = 4fspr + 7crd (Waters, 1986)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
12.75 - 5.5 800 -142.65 -172.89 12.75 10.33 2 (-158.94 <-> -156.59)
cH = -157.78 (sd 46.09) 2
within bracket
uH = 1.00, d/s = -15.1, h = 1.00
292) 3fctd + ta = 3mctd + fta (Chinner & Dixon, 1974; Chopin & Monie, 1984; Miller, 1986)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-7.94 - 20.0 550 620 50.41 55.17 -53 497 68 5 (44.81 <-> 48.85)
-7.69 - 18.0 470 550 44.00 49.28 513 70 cH = 46.83 (sd 2.33) 2
-6.97 - 20.0 560 620 44.39 47.99 601 78 within bracket
uH = 0.55, d/s = -2.2, h = 1.00
293) mcar + fctd = fcar + mctd (Natural, Seidel & Okrusch, 1977; Theye et al., 1992)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-1.92 - 7.0 330 430 9.08 10.60 423 64 5 (10.00 <-> 10.99)
-1.95 - 9.0 320 380 9.09 10.02 31 411 64 cH = 10.49 (sd 0.49) 2
-2.09 - 10.0 370 430 10.64 11.64 -9 361 58 within bracket
-2.04 - 17.0 420 480 11.23 12.21 -46 374 60 uH = 0.24, d/s = -2.6, h = 1.00
294) 5sud + 2daph = 5fsud + 2clin (Theye et al., 1992)
ln_K x(CO2) P(kbar) T(C) H(low) H(high) miss calc 2sd summary
-7.53 - 10.0 375 425 54.14 58.31 400 92 1 (54.53 <-> 57.92)
cH = 56.23 (sd 3.86) 2
within bracket
uH = 0.95, d/s = 2.2, h = 1.00
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