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American Mineralogist, Volume 76, pages 477-492, 1991
Plagioclase-melt equilibria in hydrous systems
Tooo B. HousH,* Jauns F. LunnDepartment of Earth and Planetary Sciences, Washington University, St. Louis, Missouri 63130, U.S.A.
Ansrucr
Although plagioclase is the most common minera! in crustal rocks, plagioclase-meltequilibrium relationships in hydrous silicate systems are poorly understood. This study isbased on analyses of 54 new plagioclase-melt pairs produced in HrO-saturated experimentson natural andesite and basalt in the pressure range of 1-4 kbar.We combined these datawith Hro-saturated data from the literature, and we evaluated the quality of availableactivity-composition models for silicate melts by calculating equilibrium constants for theexchange of albite and anorthite components between plagioclase and melt as functionsof reciprocal temperature. Plagioclase-melt equilibrium relationships are shown to bestrongly dependent on both the temperature and the HrO content of the melt. Because theHrO content of natural melts is generally not known, we present two expressions thatrelate the temperature of the system to the HrO content ofthe melt, one for albite exchangeand the other for anorthite exchange. Successful application ofthese relationships to nat-ural rocks requires both a good estimate of preeruptive temperature and knowledge of theequilibrium plagioclase and melt compositions. Under optimal conditions, the uncertain-ties in estimated HrO contents are 0.54 and 0.33 wto/o for the albite and anorthite exchangeequations, respectively.
INrnooucrroN
Plagioclase is the most common mineral found in ig-neous rocks and crystallizes from silicate melts over awide range of temperatures, pressures, and HrO contents.Bowen (1913) demonsrrated the form of the liquidus-sol-idus loop in the system albite-anorthite at I bar, andYoder et al. (1957) showed the strong thermal depressionof the loop, with little change in shape, at 5-kbar HrOpressure. These relationships pointed toward the possi-bility of using the compositions of coexisting plagioclaseand glass in volcanic rocks to deduce the temperature ofequilibration and the HrO content of the melt. This im-portant goal has remained elusive largely because of apaucity of experimental plagioclase-glass pairs for HrO-bearing natural compositions and because of limitationsin available activity-composition models for silicate melts.Recent years have seen the publication ofcoexisting phasecompositions for a significant number of hydrous exper-imental charges (Helz, 1976; Baker and Eggler, 1987;Rutherford et al., 1985; Conrad et al., 1988), along witha variety of models for silicate melts (Ghiorso et al., 1983;Nielsen and Dlrgatr, I 983; Bumham and Nekvasil, 1986).This study is based on a set of 54 plagioclase-melt pairsproduced in HrO-saturated experiments using natural an-desites and basalts in the pressure range of l-4 kbar. Wecombined these data with HrO-saturated pairs from
I Present address: Department of Earth, Atmospheric, andPlanetary Sciences, Massachusetts Institute of Technology,Cambridge, Massachusetts 02139, U.S.A.
0003-o04x/91/03044477s02.00 477
Rutherford et al. (1985) in order to evaluate the availableactivity-composition models for silicate melts by calcu-lating equilibrium constants for exchange of albite andanorthite components between melt and plagioclase asfunctions of reciprocal temperature. We present expres-sions that can be used to calculate the HrO contents ofmelts from natural plagioclase-glass pairs if the temper-ature can be independently estimated.
Pnnvrous woRK
A variety of plagioclase-melt geothermometers havebeen proposed that are applicable to low-pressure, an-hydrous conditions. These geothermometers are basedupon the rather extensive set of coexisting plagioclase-melt pairs from experimental studies at l-bar pressure.These geothermometers primarily differ in the nature ofthe activity-composition model adopted for the silicatemelt and include purely empirical formulations (Smith,1983; Glazner, 1984), two-site quasi-lattice models(Drake, 1976; Nielsen and Dungan, 1983), and the reg-ular-solution model of Ghiorso et al. (1983). These geo-thermometers calibrated at I bar are generally able topredict temperatures of plagioclase-melt equilibration towithin 10-30'C.
Relatively few models have been proposed for equilib-ria between plagioclase and hydrous silicate melts. Bestknown are the model of Kudo and Weill (1970) and itssubsequent modification by Mathez (1973, 1974). TheKudo-Weill formulation assumed a regular-solutionmodel for the silicate melt and was calibrated using phase
478 HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
TABLE 1, Major element analyses of starting materials
St. comp. A1Technique: XRF
Chich6n trachyandesite erupted in 1982 (Luhr et al.,1984); G, a synthetic gel corresponding to a Ti-Mn-P-free equivalent of the 1982 trachyandesite; B, Jorullo ba-salt JOR-44 erupted in 1759 (Luhr and Carmichael, 1985);and A2, andesite COL-40 erupted from Volc6n Colimain 1975 (Luhr and Carmichael, 1990). As described inLuhr (1990), compositions Al and B were converted toglasses at I bar, and these glasses were used in the exper-iments. Major element compositions and CIPW normsfor the Al and B glasses, the gel G, and the rock powderof A2 are given in Table l. For compositions Al, G, andB, S was added to the ground glass or gel (3 wto/o SON inthe form of the stable S-bearing mineral: pyrrhotite forthe FMQ buffer and anhydrite for the MNH and MTHbuffers. S was not added to composition A2, which con-tains only the natural sulfur content of approximately 0.1wto/o equivalent SOr. Prior to crimping and welding ofloaded sample capsules, distilled HrO was added in quan-tities sufrcient to assure vapor saturation at the experi-mental pressure: 5 wto/o HrO atl kbar, l0 wt0/0 at2kbarand 2.5 kbar, and 15 wt0/0 at 4 kbar. Fugacities of allimportant gas species at experimental conditions for sam-ples of compositions Al, G, and B are given in Luhr(1990). Although these samples are S bearing, fugacitiesof all S gas species were less than 15 bars in all sampleassemblies, and the samples were close to the conditionPrro: P,.o,. The vapor phase for the nearly S-free com-position A2 was essentially pure HrO. The duration ofeach experiment in hours, and the temperature, pressure,and O buffer are listed in Table 2. All experiments wereconducted as crystallization experiments, with tempera-ture frrst taken to 1000 "C for 30 min, followed by manualcooling to the temperature of the experiment at an ap-proximate rate of 200 "C/h. This technique generally pro-duced relatively coarse-grained (10 to > 100 pm) texturesof homogeneous phases that were ideal for analysis ofboth glass and crystals. Phase assemblages for all chargesof compositions Al, G, and B are given in Luhr (1990).Backscattered electron images of representative plagio-clase and glass textural relationships for each ofthe fourstarting compositions are shown in Figure l.
MrcnopnonE TECHNTeUES
The experimental glasses were analyzed using the ARLSEMQ electron microprobe at the U.S. Geological Sur-vey, Reston, Virginia. Analytical techniques and correc-tions for alkali loss are discussed in Luhr (1990). Ten to12 individual spot analyses were typically collected forglass in each experimental sample. Spatially related com-positional variations were not detected in any sample.The number of spots analyzed and mean and one stan-dard deviation values are listed in Luhr (1990).
Plagioclase was analyzed on two different microprobes,the ARL-SEMQ at the U.S.G.S. in Reston and the JEOL733 at Washington University.All analyses were con-ducted using natural feldspars as standards along withBence-Albee interelement corrections. An acceleratingpotential of 15 kV, a beam current of20 nA, and a de-
G B A 2XRF XRF WC
sio,Tio,Al2o3FerO3'MnOMgoCaONaroK"oPro.
Total
qorADandihyolmtilap
57.53o.71
18.956.600 .192.277 .144 .122.820.38
100.71
3.8016.6734.8624.896.719 . 1 20.00l o l
1 .350.88
(srt"A)58.600.00
1 8 .186.150.002.156.644.772.850.00
99.34CIPW norm (wt%)
2 . 1 116.8440.3619.781 1 .006.970.001 .780.000.00
52.33 60.070.84 0.64
16.13 17 .918.30 5.810.14 0 .119.37 3.048.39 5.943.31 4.64o.72 1.340.13 0.20
99.66 99.70
0.00 9.464.26 7 92
28.01 39.2627.03 24.0911.04 3.3418.85 1 1 .795.51 0-002.41 r.681 .60 1.220.30 0.46
Nofe.-St. comp. : starting com@sitions A1, G, B, and A2 as describedin the text. A2 was not converted to glass; it was loaded into capsules asfine rock powder. Technique: XRF : X-ray fluorescence analysis of glassdisk prepared from fusion using a ratio of nine parts lithium tetraborate toone part glass or gel mix; WC : wet chernistry (analyst, l.S.E. Carmichael).CIPW norms calculated assuming + Fe*) : 0.2
- Total Fe as FerO3.
relations in synthetic systems at l-bar pressure (Bowen,1913, 1915; Prince, 1943), unpublished data for HrO-saturated granitic compositions at 500 and 1000 barspressure, and 5-kbar data for the HrO-saturated albite-anorthite binary (Yoder et al., 1957). As discussed below,the Kudo-Weill model performs poorly in predicting theknown HrO pressures for the experimental data used inthis study, pointing to the need for reformulation of aplagioclase-melt geothermometer.
ExpnnrunNTAL DESTcN
The materials studied and experimental techniques aredescribed in detail by Luhr (1990) and will be discussedonly briefly here. The experiments were performed at theU.S. Geological Survey in Reston, Virginia, using an in-ternally heated pressure vessel with Ar gas as the pressuremedium. Most experiments were conducted using a grid-like array oftemperature (800, 850, 900, 950, and 1000qC) and pressure (2 and 4 kbar) conditions. Fewer exper-iments were conducted at pressures of I and 2.5 kbar.Temperatures reported in this study are believed to beaccurate to +3 oC, and pressures are probably accurateto +50 bars. Oxygen fugacity was buffered using one ofthree diferent HrO-saturated solid O buffers in a doubleAu capsule arrangement: FMQ, fayalite-magnetite-quartz;MNH, manganosite-hausmanite; and MTH, magnetite-hematite.
Four different starting compositions from the subduc-tion-related Mexican Volcanic Belt were studied: Al, El
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
Fig. l. Backscattered electron photomicrographs ofrepresentative plagioclase and glass textures. (A) no. 213, starting compo-sition Al, 850 "C, 4 kbar, MNH buffer; (B) no. l2l, starting composition B, 950"C,2 kbar, MTH; (C) no. 167, starting compositionG, 850 "C, 2 kbar, MNH; (D) no. 285, starting composition A2, 900'C, I kbar, MNH. A 100-pm scale bar is in the lower leftcorner of A, C, and D, the upper right in B. Abbreviations of phases: p, plagioclase; g, glass; h, hornblende; t, titanomaFetite; a,anhydrite; c, clinopyroxene; o, orthopyroxene.
479
focused spot l0 pm in diameter were used on both probes.On-peak, mean atomic number background correctionswere used at Reston, and off-peakbackground correctionswere used at Washington University. In order to assureconsistency from experiment to experiment and betweenthe two microprobes, all plagioclase analyses were nor-malized to an in-experiment standard, a well-analyzedand stoichiometric natural bytownite from Crystal Bay,Minnesota (Anrrn). Ten to 12 individual spot analyseswere typically collected for plagischse in each sample.The number of spots analyzed and mean and one stan-dard deviation values are given for each plagioclase inTable 2. Plagioclase is relatively homogeneous in mostsamples, without any sigrificant variations related to po-sition in the sample or rim-core location in a single crys-tal. The degree of homogeneity is indicated by the meanof all standard deviations for An content of 3.2 tl.5mol0/0. In order to test for consistencv between the two
microprobes, plagioclases from four samples (nos. 139,169,ll9,l7l) were analyzed on each machine (Table 2).These pairs of analyses are very similar, on average dif-fering by only 0.35 molo/o An, well within the one stan-dard deviation values.
Trrn .lr,nrrn-lNoRTHrrE BTNARy pRoJEcrroN
The well-known liquidus-solidus loop for the albite-anorthite system at l-bar pressure (Bowen, l9l3) is shownin Figure 2, along with the loop for 5-kbar HrO pressure(Yoder et al., 1957). The latter has a very sirnilar shapebut is shifted downward in temperature by 350-400 "C.Wyllie (1963) and Morse (1980) showed that when l-barplagioclase-melt compositions are projected onto the al-bite-anorthite binary from the diopside-plagioclase co-tectic in the ternary system diopside-albite-anorthite, theliquidus-solidus loop collapses to a very narow temper-ature range of approximately 100 "C (Fig. 2). A similar
480 HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
TABLE 2. Electron microprobe analyses of experimental plagioclase
Sample no.St. Comp.Hours:r0c):P (bars):O. buffer:H,O (wt%):
Spots:Probe:
sio,Alro3FerOs'CaONaroK.O
Total
sio,Alro3FerO3"CaONaroKrO
siAIFeCaNaKmd% An
Sample no.St. Comp.Hours:rfc):P (bars):O, buffer:H.O (wt%):
Spots:Probe:
sio,Alro3Fe2O3t
CaONa2OKrO
Total
sio,Al,o3Fe2O3'CaONa2OKrO
SiAIFeCaNaKmol% An
1 1 ' t 2 1 2W.U. U.S.G.S U.S.G.S57.09 56.88 56.8826.65 25.06 26.530.44 0.97 0.638.15 8.97 9.046.29 5.91 6.020.82 0.61 0.68
99.45 98.40 99.78
1 2 1 2 1 2w.u. u.s.G.s u.s.G.s55.67 54.72 54.8127 .86 27.87 28.010.47 0.60 0.69
10.07 10.54 1 0.545.60 s.3s 5.490.40 0.40 0.47
100.07 99.48 100.01
153AI102800
2000FMQ6.02
0.97o.570.090.730.420.08
149A1
48800
2000MNH5.98
105A196
8002000MTH5.95
0.880.430.090.650.310.14
263A168
8002500MNH6.52
1 0W.U.57.5026.670.458.805.700.79
99.90
1.090.480.050.550.190.07
0.670.580.080.500.270.03
268A143
8002500MTH6.49
1 0w.u.57.7327.410.469.225.520.82
1 0 1 . 1 6
193A1
60800
4000MTH8.30
144A148
8502000FMO6.04
0.540.750.060.570.250.07
165A1
81850
2000MNHs.99
Mean analyses
218A1
co800
4000FMQ8.25
203A1
80800
4000MNH8.24
9 1 0W.U. W.U.56.12 54.6228.06 27.930.24 0.44
10.02 10.225.52 5.400.41 0.40
100.37 99.02
185A1
1 5900
2000FMO6.08
One standard deviation value3
0.830.930.200.450.320.09
Formulao based on I O atoms
0.39 0.590.36 0.360.03 0.040.38 0.440.27 0.210.04 0.07
2.515 2.4891.483 1 .5000.008 0.0150.481 0.4990.480 0.4770.023 0.023
48.9 49.9
1 .270.700.060.730.430.17
0.770.570.070.550.310.10
o.720.810.040.750.370.10
2.578 2.602 2.5661 .419 1 .351 1 .4110.015 0.033 0.0210.395 0.439 0.4370.551 0.524 0.5270.047 0.036 0.039
39.7 44.0 43.6
139A1
72850
2000MTH5.99
1 1U.S.G.S55.3627.570.72
10.035.490.49
99.66
0.670.540.040.450.250.06
2.5071.4720.0250.4870.4820.028
48.8
2.5821.4120.0150.4230.4960.045
4.i1.9
213A184
8504000MNH8.19
2.5631.4340.0150.4380.4750.046
45.7
208A144
8504000MTH8.22
169A168
9002000MNH6.05
0.620.540.040.450.200.50
2.507 2.485 2.4791.480 1.492 1.4940.016 0.021 0.0230.486 0.513 0.51 10.489 0.471 0.4820.023 0.023 0.027
48.7 50.9 50.1
139 228A146
8504000FMQ8.24
1 0 1 0w.u. w.u.51.25 50.9730.48 29.860.31 0.59
12.93 12.904.05 4.010.21 0.21
99.22 98.53
169 114A148
9002000MTH6.05
104A1
72950
2000MNH5.98
0.60 0.660.48 0.600.05 0.060.53 0.470.23 0.260.05 0.03
1 0W.U.54.6927.490.74
10.155.510.51
99.09
0.310.39o.120.310.180.04
2.4951.4780.0250.4960.4880.030
49.0
0.580.380.070.260.140.03
1 . 1 40.430.040.460.330.02
2.3071.6920.0190.6280.3690.012
62.2
0.540.470.090.290.150.03
0.670.430.040.440.240.05
Mean analyses
1 1W.U.49.8631.020.54
12.664.120.21
98.40
1 0 1 2W.U. U.S.G.S.53.05 51.2030.39 29.23o.42 0.80
12.30 12.594.39 4.220.28 0.29
r 00.82 98.33
1 0 1 t 1 2w.u. u.s.G.s. u.s.G.s.51.71 52.82 48.9829.75 29.37 31.190.81 0.83 1.10
12.65 12.15 14.684.18 4.61 3.020.26 0.31 0.17
99.36 100.10 99.14
One standard deviation valueg
Formulae based on I O atoms
2.347 2.3541 .646 1.6250.011 0.0210.635 0.6380.360 0.3s90.012 0.012
63.0 63.2
2.385 2.3711.61 1 1 .5960.014 0.0280.592 0.6250.382 0.3790.016 0.017
59.8 61.2
2.368 2.398 2.2631 .606 1.572 1 .6990.028 0.028 0.0380.621 0.591 0.7270.371 0.406 0.2710.015 0.01 8 0.010
61.6 58.2 72.1
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 481
f aete 2-Continued
Sample no.St. Comp.Hours:r('c):P (bars):O, buffer:H,O (wt%):
Spots:Probe:
sio,Al2o3Fer03*CaONazOKrO
Total
sio,Al,o3FerO3'CaONaroKrO
siAIFeCaNaKmol% An
Sample no.St. Comp.Hours:r(€):P(bars):O. buffer:H.O (wt%):
Spots:Probe:
sio,Al2o3FerO3"CaONaroK'O
Total
sio,AlrosFe.O".CaONaroKrO
SiAIFeCaNaKmolo/o An
1 1 9 1 1 9A136
9502000MTH5.98
1 2 9U.S.G,S. W.U.
49.06 49.4031.10 30.891 .13 1 .22
14.87 14.583.06 3.120.18 0 .17
99.41 99.39
270 220B B43 56
800 8002500 4000MTH FMO6.43 8.04
1 1 1 0W,U. W.U.57.02 56.2128.41 28.160.43 0.23
10.36 10.245.35 5.740.18 0 .15
101 .75 100.73
205B80
8004000MNH8.12
195B60
8004000MTH8.12
1 2 1 0w.u. w.u.55.60 54.8428.25 28.820.37 0.36
10.39 1 1 .085.66 5.370.16 0 .13
100.43 100.60
108B96
8002000MTH5.84
Msan analyses
9 1 2 1 2w.u. u.s.G.s. u.s.G.s.53.60 57.06 56.2529.10 26.71 27.200.45 0.56 0.62
11 .55 9.04 9.714.88 6.32 6.010.17 0 .18 0 .19
99.75 99.87 99.98
155B102800
2000FMQ5.95
152B48
8002000MNH5.81
265B68
8002s00MNH6.43
1 0W.U.51.9329.300.58
12.514.340.10
98.77
1.290.710.080.900.480.02
2.3871.5880.0200.6160.3870.006
61.1
121B36
9502000MTHs.89
1.521 . 1 30.100.920.410.04
One standard deviation Yalueg
0.350.430.070.280.150.02
146B48
8502000FMQ6.01
29.440.66
1 1.485.090.15
2.4491.5210.0230.s580.4480.009
55.0
0.450.140.040.310.140.02
168B81
8502000MNH5.91
0.910.850.060.720.400.04
1.960.960.071 . 1 50.530.04
0.760.310.030.340.210.03
0.610.410.060.430.3t!0.03
0.940.580.070.57o.210.16
0.830.380.050.s30.3d10.02
0.77 1.930.46 1.1 10.06 0.130.41 1.490.26 0.720.05 0.05
2.263 2.2771.691 1 .6790.039 0.0420.735 0.7200.274 0.2790.01 1 0.010
72.1 71.4
Formulae based on 8 O atoms
2.431 2.566 2.5331 .556 1 .416 1.4440.015 0.019 0.0210.562 0.435 0.4680.430 0.551 0.5250.010 0.010 0.01 1
56.1 43.7 46.7
2.495 2.4621.494 1.5250.012 0.0120.s00 0.5s10.493 0.4680.009 0.007
49.9 52.9
107 148G G96 48
800 8502000 2000MTH FMQ6.00 6.09
2.518 2.5111.479 1.4830.014 0.0080.490 0.4900.458 0.4970.010 0.009
51.2 49.2
141B72
8502000MTH5.88
230B46
8504000FMQ8.10
1 0W.U.52.3229.900.31
12.544.560.10
99.72
156G102800
2000FMQ6.10
151G48
8002000MNH6.05
215B84
8504000MNH8 .13
Mean analyseg
1 2 1 2 1 2u.s.G.s. u.s.G.s. u.s.G.s.
53.96 53.91 55.03
10 ' t2 13 12w.u. u.s.G.s. u.s.G.s. u.s.G.s.58.95 57.92 58.54 55.4826.55 25.05 25.69 27.660.42 0.70 0.67 0.628.00 8.02 7.72 10.156.79 6.54 6.92 5.710.87 0.87 0.82 0.41
101.59 99.11 100.36 100.0399.78 99.85 99.38
28.42 27.53
1 1 1 2w.u. u.s.G.s.51.77 49.1029.97 31.320.53 0.90
12.76 14.954.20 2.950.07 0.08
99.30 99.30
0.771 1 . 5 45.070 .15
0.6910.595.350 .19
1 . 1 30.620.070.830.510.04
One standard deviation values
0.660.370.o70.50o.230.02
0.880.400.110.580.330.02
2.4461.5200.0260.5610.4460.009
55.3
0.670.540.050.520.24o.o2
0.890.430.080.300.170.01
0.67o.470.100.450.200.05
Formulae based on I O atom3
0.59 0.990.47 0.580.05 0.100.40 0.550.21 0.240.08 0.10
2.605 2.6261.383 1 .339
0.014 0.0240.379 0.3900.582 0.5750.049 0.050
37.5 38.4
2.499 2.381't.474 1.6040.024 0.0110.515 0.61 10.471 0.4020.011 0.006
51.7 60.0
2.368 2.2641.616 1 .7020.018 0.0310.625 0.7390.373 0.2630.004 0.005
62.4 73.4
2.620 2.5041.355 1.4720.023 0.0210.370 0.4910.600 0.5000.047 0.024
36.4 48.4
T ABLE 2-Continued
Sample no.St. Comp.Hours:r('c):P (bars):O. buffer:H.O (wt7"):
Spots:Probe:
sio,Al,o3Fe2O3'CaONaroKrO
Total
sio,Al,O,FerO"*CaONa2OK.o
SiAIFeCaNaKmd% An
167u81
8502000MNH6.06
1 3W.U.56.0326.950.939.955.830.53
t 00.21
0.990.680.070.590.260.07
2.527't.4320.0320.4810.5090.030
47.1
Sample no. 210St. Comp. BHours: 44r(rc): 850P(bars): 4000O, buffer: MTHH.O (wto/"): 8.07
Spots: 11Probe: W.U.
sio, 52.90At,o3 29.95Fe2O3* O.52CaO 12.43NarO 4.51K,O 0.09
Total 100.39
sio, 0.45Alro, 0.36FerOs' 0.05CaO 0.35Na2O 0.26K,O 0.01
si 2.390Ar 1.595Fe 0.018Ca 0.602Na 0.395K 0.005molTo An 60.1
207 197A2 A280 60
800 8004000 4000MNH MTH
143G72
8502000MTH6.04
7W.U.
56.6926.430.819.266.250.52
99.96
1 . 1 00.580.070.48o.270-03
2.5571.406o.o27o.4470.5470.030
43.7
187B1 5
9002000FMQ6.O2
1 0w.u.52.5530.410.50
12.504.U0 . 1 1
100.41
0.680.360.060.500.270.02
2.3741 .6190.0170.6050.3800.006
61.0
1 0W.U.
57.3926.500.438.696.350.28
99.63
0.690.460.040.500.220.02
2.4031.5630.0250.6060.4050.006
59.6
8.00
1 0W.U.
55.5827.U0.399.625.87o.17
98.97
0.710.380.070.380.270.03
1 2U,S.G.S.52.3829.530.82
12.654.400.11
99.88
0.820.560.130.660.330.02
2.3841.5840.0280.6170.3880.006
61.0
7.98
1 2W.U.55.8827.790.469.736.170.15
100.19
0.57o.280.030.380.790.03
2w.u.53.2329.940.26't2.264.750.15
100.59
0.080.230.010.270.040.00
2.3991.5900.0090.5920.4150.009
58.3
103B72
9502000MNH5.93
't2u.s.G.s.48.8131.480.93
15.002.890.09
99.20
1 . 1 60.580.100.840.400.04
2.2541.7130.0320.7420.2590.005
73.8
217A284
8504000MNH8.O7
1 0W.U.52.7630.030.60
12.544.580.07
100.s9
0.630.250.040.250.150.01
2.3821.5980.0200.6060.4010.004
60.0
289A2
1 8900
1000FMO4.09
1 0w.u.56.0627.350.679.866.01o.22
100.17
1.380.950.091.040.540.05
2.5231.4510.0230.4750.5240.013
47.0
212A244
8s04000MTH8.07
1 0W.U.52.6829.850.70
12.354.660.07
100.30
0.510.510.050.180.160.02
2.38s1.5930.0240.s990.4090.004
59.2
285A2
22900
1000MNH4.06
1 0W.U,54.7528.550.68
10.965.394.21
100.55
1.901 . U0.061.460.810.06
2.621.5140.0230.5280.4700.012
52.3
0.57o.420.04o.41o.220.02
2.5271.4700.0070.4660.5190.010
46.9
0.290.400.050.290.130.02
222A2
56800
4000FMO8.'12
Mean analyses
1 0w.u.56.2527.750.219.695.960. ' t7
100.03
One standard deviation values
0.8it0.,130.060.430.330.04
Formulae baged on I O atoms
2.5831.4060.0150.4190.5540 .016
42.4
171B68
9002000MNH5.96
2@B't 1.3950
2000FMO6.08
1 0w.u.
50.1931.210.56
14.U9.440.08
99.82
0.310.320.040.230.080.01
2.2951.6820.0190.7030.3050.005
69.4
2.526 2.5121 .465 1.4730.013 0.01 60.468 0.4690.517 0.5380.010 0.009
47.1 46.2
171 116B48
9002000MTH5.91
Mean analyses
1 2 9u.s.G.s. w.u.52.53 52.5628.98 29.340.73 0.76
12.37 12.184.57 4.530.11 0 .1 1
99.28 99.47
One slandard deviatlon values
Formulae based on I O atoms
2.3981.5780.0260.5950.4000.006
59.4
/Vofe.'St. Comp : starting composition: A1, B, G, and A2 as described in the text. Hours: duration of experiment. O" buffer: O buffer used inexperiment: FMO, MNH, and MTH. H,O : H,O solubility limit calculated after Bumham and Nekvasil (1986) as described in the text. Spots: numberof spot analyses used to calculate mean and one standard deviation values. Probe indicates whicfr microprobe was used in analyzing plagioclase:W.U., JEOL 733 at Washington University; U.S.G.S., ARL SEMQ at Reston, Virginia. The value of mol% An : 100 x [Cal(Ca + Na + K)].
'Total Fe as FerOr.
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 483
collapse of the plagioclase-melt loop might be expectedfor projections of natural multicomponent systems. Inthe lower part ofFigure 2, we have plotted the projectedpositions of 54 experimental plagioclase and glass com-positions from this study along with other HrO-saturatedplagioclase-glass pairs from the literature: ten pairs formedat 5-kbar pressure from Helz (1976) and four pairs formedbetween 1250 bars and,2250 bars from Rutherford et al.(1985). The majority of these experimental data fromnatural rock compositions form distinct isobaric trendssimilar in slope to those for the 5-kbar binary system ofYoder et al. (1957). The projected compositions fromthese multicomponent systems are shifted downward intemperature by approximately 300 oC compared to thebinary system, such that the l-kbar projected data areessentially superimposed on the 5-kbar binary trends. TheHrO-saturated experimental glasses of this study, Ruth-erford et al. (1985), and Helz (1976) have only 57.8 +9.5wto/o normative albite * anorthite, but 92.4 +3.9 wto/onormative quartz + orthoclase + albite + anorthite. Forsystems containing large percentages of normative quartzand orthoclase, it appears that plagioclase-glass compo-sitions project onto the albite-anorthite binary with low-ered temperatures but without significant distortion ofthe binary loop topology (but see Johannes, 1984). Onthe contrary, systems with large percentages of normativediopside (and presumably other mafic constituents) leadto substantial collapse of the liquidus-solidus loop.
The set of 54 plagioclase-glass pairs from this studycontains considerable redundancy, owing to the use ofthree different O buffers and two to four different startingcompositions at each temperature-pressure condition. Thediferent O bufers were chosen to investigate effects on Ssolubility in the melt (Luhr, 1990) and compositional re-lationships among the melt and mafic minerals; these Obuffers should have little influence on plagioclase-meltequilibria. Likewise, the different bulk compositions ap-pear to have no significant effect on the projected plagro-clase-melt compositions. The great redundancy of the dataset, with up to nine different experiments at a single tem-perature-pressure condition, allowed us to evaluate eachexperiment for consistency with the total data set. Pla-gioclase or glass analyses, or both, from eight ofthe ex-periments of this study (nos. 108, 116, 149, 152, 155,193,203,265) fall offof the general compositional trends(Fig. 2: half-closed symbols). Seven of the eight aberrantcharges were conducted at 800 oC and are inferred toreflect disequilibrium at this lowest temperature condi-tion. As the slope of the isobaric curves is well defined athigher temperatures, there is little doubt about the ex-pected equilibrium plagioclase and glass compositions at800'C. These eight samples have been deleted from thefollowing analysis and from subsequent figures. Althoughthe data ofHelz (1976) are plotted on subsequent figures,these too have been deleted from the analysis becausethey deviate from trends displayed by the data of thisstudy and Rutherford et al. (1985). The possible cause ofthis deviation is the correction technique applied to ac-
this study
P (kbar): I 2 2.5 4 1.3 - 2.3 5S y m b o l : O O A t r I
Rutherford Helz
Fig. 2. Albite-anorthite binary diagram showing the l-barliquidus-solidus loop of Bowen (1913) and the 5-kbar HrO-sat-urated loop ofYoder et al. (1957). Also shown is the collapse ofthe loop when projected from diopside saturation in the systemdiopside-albite-anorthite (Wyllie, I 963; Morse, I 980). Symbolsshow plagioclase and projected glass compositions from thisstudy, Helz (1976), and Rutherford et al. (1985). Multicompo-nent glass compositions are plotted as lO0[normative anl(an *ab)1. Half closed symbols indicate the eight samples whose pla-gioclase or glass compositions deviate from the general trendsand are deleted from the modeling. Small numbers adjacent toopen squares indicate experimental pressures in kbar for datafrom Rutherford et aL (1985). Solid and dash-dot lines labeledI kbar,2 kbar, 2.5 kbar, 4 kbar, and 5 kbar indicate mean lociofprojected isobaric melt and plagioclase compositions, respec-tively.
count for alkali loss in the glass as a result of electron
bombardment during the microprobe analysis (Helz,
r976).
Tun Kuno-Wrrr.r, PLAGToCLASEGEOTHERMOMETER
In order to emphasize the need for reformulation ofplagioclase-melt equilibrium relationships for hydrous
30 50An mol%
484 HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
melts, we have plotted in Figure 3 the 60 available HrO-saturated plagioclase-glass pairs from this study, Helz(1976), and Rutherford et al. (1985) in the form ofy(?")vs. Z [see Kudo and Weill (1970) for the definition andcalculation of y(Dl. AIso shown are the linear regressioncurves of Kudo and Weill (1970) and Mathez (1973, 197 4)for anhydrous conditions and P"ro : 0.5 kbar, I kbar,and 5 kbar. Although the 1- to 5-kbar experimental datafall between the l- and S-kbar P"ro regression lines, mostpredicted P"ro values are significantly higher than the ex-perimental values at the given experimental temperature.Several possibilities can be put forward to explain theseproblems with the Kudo-Weill formulation. First, at thetime of their study, the significance of Na loss duringelectron beam bombardment of hydrous glasses was notwell appreciated. Kudo and Weill (1970) do not discussthis problem and do not give the specimen current atwhich the granitic glasses were analyzed, so this effect isCifficult to appraise in their data. Second, as discussedabove and pointed out by Wyllie (1963), Loomis (1979),and Morse (1980), plagioclase-melt relationships are dra-matically changed when melt compositions lie signifi-cantly off the binary. Accordingly, reliance of the Kudo-Weill (1970) formulations on data from simple systemsmay contribute to its failure when applied to natural mul-ticomponent systems.
Pr,,lcrocr,lsE-MEr,T EeurLrBRrA
We have approached the problem of plagioclase-meltequilibria by solving for the equilibrium constants of ex-change reactions for albite and anorthite components be-tween these two phases. Activities of albite and anorthitein plagioclase (aoo,o, and a*,o,) were calculated followingLindsley and Nekvasil (1989) and Fuhrman and Lindsley(1988). In treating melt components we have evaluatedthree different models for silicate melts, which we nowdiscuss in turn: the two-site quasi-lattice model of Niel-sen and Dungan (1983), the quasi-crystalline model ofBurnham and Nekvasil (1986), and the regular-solutionmodel of Ghiorso et al. (1983).
Two-site quasi-lattice model
We slightly modified the technique of Nielsen andDungan (1983) to account for the presence of minor MnOand SO, in the experimental glasses, and we speciated theglass compositions into network-forming componentsSiOr, NaAlOr, and KAlOr, and network-modifying com-ponents TiOr, AlOr r, FeO, MnO, MgO, CaO, and SOr.Activities of these components in the melt were then takenas equal to the mole fractions on the respective quasi-lattice sites. Each of the 60 HrO-saturated plagioclase-glass pairs was then used to calculate ln Koo and ln Ko",where
ln Ko : In 4oo,o, - ln X*,*or,*" - 3 ln X.,or."u
and
ln K* : ln 4an,o1 - ln X*o,", - 2ln Xoror r,"nn - 2X'or,"..
Figures 4a and 4b show plots of these equilibrium con-stants vs. reciprocal temperature. As also found by Drake(1976) and Nielsen and Dungan (1983) in the tempera-ture range ofthis study (<1000 "C), the data ofFigure 4show a systematic increase in ln K^o with reciprocal tem-perature, but considerable scatter for ln K^,.The poorquality of the anorthite reaction might reflect the fact thatCa is present in both diopsideJike and anorthiteJike meltmolecules, a possibility not accounted for by the two-sitequasi-lattice model (Drake, 1976). On Figure 4a, the lnK^o data show separate subparallel trends for the differentexperimental pressures, with the intercept increasing sys-tematically from 5 kbar to I kbar. The systematic low-ering of ln K^o with increasitg Pn o may reflect the in-creasing mole fraction of HrO in the melt. If theconcentration of HrO in the melt could be explicitly ac-counted for in the model, all data points might collapseonto a single line, as shown later for the regular-solutionmelt model of Ghiorso et al. (1983). It is not obvious,however, how to adapt the two-site quasi-lattice modelto hydrous conditions. The simplest approach is to as-sume that all HrO enters the melt on the network-mod-ifuing lattice. This will not cause any change in the molefractions of species on the network-forming site, howev-er, and since both melt-phase albite components are onthe network-forming site, this will similarly cause nochange in the calculated ln K^o. For this reason, the two-site quasi-lattice model was not pursued any further.
Quasi-crystalline model
The quasi-crystalline melt model of Burnham andNekvasil (1986) was designed to model activity-compo-sition relationships within the system quartz-feldspar-HrO. As described above, the 60 H2o-saturated glassesconsidered in our analysis have >900/o normative quartz* feldspars. Accordingly, we modified the method ofBurnham and Nekvasil (1986) to accommodate the re-maining components. CIPW norms were calculated foreach glass. In addition to q, or, ab, and an, the glassescontain normative di, hy, c, mt, il, hm, ru, and wo; S inthe glasses was calculated as normative pyrrhotite (po) oranhydrite (anhy) depending upon the O butrer. The nor-mative proportions were converted from wto/o to molefractions and then converted to molecules with eight Oatoms (or S atoms for po): 4q, or, al;., ab, 8/3c,8/3hy,dpy, 2mt, 8/3ilm, 8/3hm, 4ru, 8/3wo, 2arrhy, and 8po.Normative 8/3c was combined with normative 4q to formdehydroxylated pyrophyllite (dpy) as described by Burn-ham (1981: Table 9.2). After this normative speciationof the melt, components were combined in three groups:(l) albitelike: ab, an, or, dpy, 2mt,8/311,8/3hm, 8po,4ru, and 2anhy; (2) quartzlike: 4q; and (3) diopsidelike:4/3di, 8/3hy, and 8/3wo. HrO contents in the melt werethen calculated by summing the contributions of thesethree groups, treating albite- and quartzJike componentsas described by Burnham and Nekvasil (1986) and di-opside-like components as described by Eggler and Burn-ham (1984). HrO solubility values calculated in this fash-
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 485
I kbil
0.5 kbardry
T (K)
thisstudy Rutherford Helz
P (kba r ) : 1 2 2 .5 4 l , 3 -23 5S y m b o l : O O A t r l
Fig. 3. Plot of Kudo-Weill (1970) parameter y(7) vs. 7,showing experimental data of this study (46 pairs), Helz (1976:ten pairs), and Rutherford et al. (1985: four pairs), along withlinear regression lines of Kudo and Weill (1970) and Mathez(1973,1974) for dry conditions and Pr,o : 0.5 kbar, I kbar, and5 kbar.
ion for the glasses of this study were reported by Luhr(1990) and listed in Table 2; these were used in calculat-ing activity-composition relationships both for the quasi-crystalline model and for the regular-solution model dis-cussed in the following section.
Activities of albite and anorthite in the hydrous meltwere calculated as described by Burnham and Nekvasil(1986). First the mole fractions of Ab and An in the an-hydrous melt were calculated: X^0."- and Xo"."-, The ap-propriate eutectic compositions were calculated from Ta-ble 2a of Burnham and Nekvasil (1986): Xr,o."-(E) andXo","- (E). Using Table 2b or 2d of Burnham and Nekvasil(1986), the difference functions Xno.* - dAb.* and XAn,"-- aro,u were then calculated. From Xoo,"- and X*,"-, thecoresponding activities in the anhydrous melt were de-termined. Finally, these anhydrous activities were usedto calculate activities of Ab and An in the hydrous melt(aoo,n- and a*,o-) from Equations 5 and 6 of Burnhamand Nekvasil (1986).
The reaction constants for exchange of albite and an-orthite components between plagioclase and melt werethen determined as
ln Koo : ln 4oo,o, - ln 4oo,n-
and
ln Ko, : ln 4o^,o, - ln 4*,o-.
These values are plotted in Figure 5 vs. reciprocal tem-perature, with different symbols distinguishing experi-mental HrO pressures. Because the melt model of Burn-ham and Nekvasil (1986) explicitly accounts for HrO, alldata points should collapse onto a single line. This isclearly not the case. The data of Helz (1976) are system-atically shifted to higher ln K values as compared to the
E5 9.0 95 10.0
10000/T (K)
this study
P ( k b a r ) : 1 2 2 . 5 4 1 3 - 2 3 5S y m b o l : O a A t r l
Rutherford Helz
Fig. 4. Equilibrium constants for albite (a) and anorthite (b)plotted vs. reciprocal temperature, with melt components cal-culated according to the two-site quasiJattice model of Nielsenand Dungan (1983).
other data and are not included in the regression. Amongthe remaining data of this study and Rutherford et al.(1985), deviations from the regression lines are not sys-tematically related to HrO pressure or /o, (not shown).The standard errors ofthe regressions (109.7 K for ln K"o,75.5 K for ln K*) are quite large compared to thoseachieved with the regular-solution melt model describednext.
Regular-solution model
In applying the regular-solution melt model of Ghiorsoet al. (1983), we first subtracted CaO or Fe from the glassanalysis to balance the analyzed S as either anhydrite orpyrrhotite, depending upon the O buffer. These minorcomponents were not considered in the calculation. Theremaining oxide components were then normalized to100-HrO, the latter being the HrO solubility value (inwto/o) calculated according to Burnham and Nekvasil(1986), as described above. These wto/o oxide componentswere then converted to molecular proportions and spe-ciated into the eight O-atom molecules of Ghiorso et al.(1983; Table 4). Activity coefficients for the componentsNa,u,rSirrrOr, Ca4Si2O8, and SioOr in the hydrous melt were
1 z.ota
15
3.0
Vzs
10.58.0
l lt l
t r
r !I I
t r
c_o o l ta t ra
Ia
l .a
:l,i
486 HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
l5
t4
t t tva 1 2
< 2 5vt 2.o
v- 1 8
L7
l 5
1.0
- 4 54.
4.0iT
= J 5
5.0
3.0
this study Rutherford Helz
P ( k b a r ) : l 2 2 . 5 4 1 3 - 2 3 5S y m b o l : O O A A t r l
Fig. 5. Equilibrium constants for albite (a) and anorthite (b)plotted vs. reciprocal temperature, with melt components cal-culated according to the quasi-crystalline model ofBurnham andNekvasil (1986). Regression equations for the 50 plqgi66lasg-glass pairs ofthis study and Rutherford et al. (1985): ln Koo:-5.054 + 7597.7(l/7), R'? : 0.689, standard error of 109.7 K;ln K*: -4.546 + 8845.4(l/7"), R2 : 0.824, standard error of75.5 K.
calculated from Equation A3-16 using the binary inter-action parameters from Table A4-3 of Ghiorso et al.(1983). Activities for these components are simply theproduct of the mole fractions in the hydrous melt and theactivity coemcients. Combined with the activities of Aband An in plagioclase, these values were used to evaluatethe reaction constants
1 ?ln Koo : ln da6,o1 -
G ltt aNar6/3si8/3o8 -
G t" a*16t3og
{- f
ln arro, (l)
. I 3 .ln K* : ln d*,o' -
a t" dc"4si2os -
, t" aerr6,jos
3 .- 5ln
a.iao.. e)
These expressions are plotted vs. reciprocal temperaturein Figure 6, urith symbols distinguishing different exper-
9.0 95
10000/T (K)
this study
P ( k b a r ) : 1 2 2 . 5 4 1 3 - 2 3 5
S y m b o l : O O A t r l
Rutherford Helz
Fig. 6. Equilibrium constants for albite (a) and anorthite O)plotted vs. reciprocal temperature, with melt components cal-culated according to the regular-solution model ofGhiorso et al.(l 983). Regression equations for the 50 plagioclase-glass pairs ofthis study and Rutherford et al. (1985): tn Kou : -4.365 +18571.10/n, R, : 0.984, standard error of 20.6 K ln Ko" :-4.62'1 + 25689.8(l/7"), R2:0.993, standard error of 13.4 K.
imental HrO pressures. Again, deviations are noted forthe data of Helz (1976). For both expressions, the re-maining 50 HrO-saturated experimental data points con-form closely to a single line. Regression parameters aregiven in Figure 6. The quality ofthe regression fits (stan-dard errors: 20.6 K for ln Koo, 13.4 K for ln K*) indicatesthat the regular-solution formulation is highly successfulin modeling activity-composition relationships in hy-drous silicate melts.
In order to illustrate the universality ofthe albite andanorthite exchange reactions formulated with the regular-solution melt model, in Figure 7 we plot the 60 HrO-saturated data considered earlier along with 15 HrO-un-dersaturated plagioclase-glass pairs from Baker and Eggler(1987) and 76 pairs from l-bar anhydrous experiments(Grove and Bryan, 1983; Sack et al., 1987). The plot ofln Koo vs. reciprocal temperature in Figure 7a shows astrong linear correlatioR for all data, with a standard errorfor these 140 data points of l2.l K. The plot of ln K*vs. reciprocal temperature in Figure 7b shows somewhat
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 48',7
more scatter, especially at higher temperatures. In thisplot, the l-bar data appear to define a slightly differenttrend from the hydrous data. Nonetheless, the standarderror for the 140 data points is just 15.2 K.
In the following section, we apply the regular-solutionmelt model to the problem of determining the HrO con-tents of melts from compositions of coexisting plagioclaseand glass in volcanic rocks.
Esrrvr.lrroN oF H2O CoNTENTS
The reaction constants plotted in Figure 7 were calcu-lated using the compositions of coexisting plagioclase andglass determined with an electron microprobe and theexperimental HrO solubility values calculated after Burn-ham and Nekvasil (1986). Typically, however, the HrOcontent of a natural melt is not known, and thus the re-action constant cannot be correctly calculated. In this sec-tion we examine the effect of the HrO content of a meltupon the evaluation of plagioclase-melt equilibria usingthe melt solution model of Ghiorso et al. (1983) and theplagioclase activity model of Lindsley and Nekvasil (1 989)and Fuhrman and Lindsley (1988).
The HrO content of a melt affects the reaction con-stants ofEquations 1 and 2 through its effect on the ac-tivities of the melt components NarurrSirrrOr, CaoSirOr,A116,308, and SioOr. The activities of these componentsare calculated by multiplying the mole fractions of thecomponents by their respective activity coefficients which,for a hydrous melt, are given by:
R I l n 7 o : W,T,X,
+ R7ln(l - X*) (3)
(Eq. ,A'3-16; Ghiorso et al., 1983), where 7o is the activitycoefficient of melt component k, X,is the mole fraction(calculated on a hydrous basis) of component i, W,t is thebinary interaction coefficient between components i andj, and X* is the mole fraction of HrO in the melt. Sincethe HrO content of the melt is unknown, the hydrousmole fractions must be converted into anhydrous molefractions using the relationship: X': X,'(l - X*), where-{' is the mole fraction of component i calculated on ananhydrous basis. The activity of component i in the meltthus becomes
a,: Xi$ - X*)
I t f n
*rt#L? wk,X'{r - x) + w",,oX*i+H2o
2 w,.,xixj(r - x*)2
- fw' , " - ,xJ jy-x)i : l
7.0 75 8.0 85 9.0 95 10.0 10.5
10000/T (K)
this studySack& Baker&
Rutherford llelz Grove Eggler
P (kbar): 1 2 2.5 4 13 - 23 5 0.001 2-5 undersal.
S y m b o l : o a A A t r l * t r
Fig. 7. Equilibrium constants for albite (a) and anorthite (b)plotted vs. reciprocal temperature, with melt components cal-culated according to the regular-solution model ofGhiorso et al.(1983). Plots include the 60 H,O-saturated data points ofFigure6, along with the HrO-undersaturated data of Baker and Eggler(1987: l5 pairs, 1.7-2.0 wto/o H,O in melt, P,o,:2 and 5 kbar)'and the l-bar anhydrous data of Grove and Bryan (1983: 30pairs) and Sack et al. (1987: 45 pairs); the l-bar data are collec'tively labeled "sack and Grove." Regression equations for entiredata set, with 140 plagioclase-glass pairs: ln Koo : -4.059 +18213.9(l/7), R'z : 0.993, standard error of l2.l Ys ln K", :-l 1.488 + 33388.6(l/D, R'z : 0.989, standard error of 15.2 K.
The relationships between temperature and X* for pla-gioclase-melt equilibria can be determined by substitut-ing into Equations I and 2 the following: (a) Equation 4,(b) the analytical expressions for aAb,er and 4*,o, (Fuhrmanand Lindsley, 1988; Lindsley and Nekvasil, 1989), and(c) the relationship: ln K: m'(l/T") + b, where m and bare the regression coefficients from the plots of ln Koo andln K- vs. reciprocal temperature (Fig. 6). If we makethese substitutions and solve for temperature, we find
z(K, Ab) : IA + B(l - X*)2 - C(l - X*)- lltot * X*(l - X)D - X*EI/
lF + 2ln(1 - x*)l (5)r(K, An): [G + B(l - X)'z - H(l - X")
- r/te.^ * X*(l - X)D - X*n/IJ + 2ln(l - x-)1. (6)
The terms in these expressions are
IA : : l(W g,"b + PW6,^b)l2X'|,X$,(l - x'i")
t ( '
13
e"v 1 1E r o
5r 'g 1 6
t4
2'r'*' - +2?
l n
) ?
i,j+H2O
+ R?"ln(l (4)
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
+ XSJR"(+ - xr,,)l
+ (wxo- + PWKv)I(Xr+Xr - ZX*,1I
+ xgX,l"(j- xRo)l
t (W|,o" + PW6,^^)IXBJRK+ - Xp;b - 2xel)lz
+ (WX^o, + PWK^o,)|XMR"(+ - Xplb - 2xg,)l
+ (WXoo" + pwKb;[(X"rl"),(l - 2X*b)
+ xsx,i,(+- x*o)l+ (w\-oo + Pwk;l2x*bxR"(l - x*b)
+ xsJR'"(+ - x*o)l
t (wg,no* + PW5,^b^)IX8JR"; - 2xrDll
where XX'', Xf", and Xg. are the mole fractions of albite,anorthite, and orthoclase, respectively, in the plagioclase,and W and W are the binary and ternary interactioncoefficients for the plagioclase components,
E: * [r*
t*""'o"'3o3'H2o + ]'ouu''o"'"o
* |
t"'"''"'"]
F: bno * fr r" xfr"16z3sisz3os + fr rn Xk,u,,o,
+ f
rn x6i4o8 - lnx1b
+ f,{n a.^,tzxllxExl - xRt)
+ XS,rI^(;- xr',)l
+ I,Zibo,(XEI.),(l - 2x,ib) + XS"X"|"(:- XR!)l
+ w8,A"lX8*XtX; - xpib - 2xp;^)l
+ WSMi,;XSJ(,*(; - Xeib - 2X$l
+ Ws^b^^l(Xpi^),(l - 2x,lb) + XBX,i,(i- Xfl)l
+ WS^"^bl2XplbXRl(l - Xfl)
+ xs,x,,L(;- xRL)l
+ WSo,^b^^IXBJA(I - 2XR'.)11
c: !$wa^b + pw5,^b)lxlr"xg,(;- x,;.^ - 2xelb)l
* (WKoo, + PWKbJIX,;*Y*(;-
+ (w8,^ + PW5,^^)l2XE'1*.(l -
+ x,i*Y[t]'
* (wK^o, + Pwko,)l(xg),0 - 2x"l)
+ x,;,Y[,(;- xfl^)l
+ (WKoo, + PWKb;l2X*bXR',(1 - Xf'")
+ x,;*Yu(i- xR")
+ (wN"^b + PWK";I(XRL)'(1 - 2XR")
+ x,;,*Yd,(t- x*.)l
* (w&ooo" + PW',5,^btu)IXE'JR!(l - 2x'il1]
x*" - 2x$l
xR',)
- XR'J]
,:,*! 2 f ,,,*:*jit+H2O
r f ec : * L* i
wNa16'ljs44o2'ixl . + Z w^'u''o'''x"
i+H2O i+H2O
* l > w^^ Ig u,_, " -o.r.txil
t+}{2O
D: * 2 "*'*tr [ r n
": .L; } wc^4si2o'.ix'i +
t+H20
'1 S u/ -". l* e !
wt'oo''Xi)i+H2O
3 ? wo4u,,o,,,x',
i+lI2O
r: +[i
wCaas;2os,H2o * ]wo,,u,,o,,,,o
* | t""''"'"1J: be,, *
)h x'**"rr", *
; ln x'orru,ro,
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 489
X6,oo* - ln XRt"
1 1+ *11l&".[x,]J8,$- xf, - 2x1'o)
+ ws^bo,lxplvxg.tl - x'1" - 2X8,)l
+ W&A,I2X8,XR'"(I - X*)
+ x*,xe(+ - x*,Jl
+ ,zilo.Kx8r.) rtt - zxxs
+ xx"xa,(* - xR'Jl
+ WS^b^^I2XplbXl*(f - X*")
+ xR"rB.(+ - xxJl
+ ,I/LAb[(XR!),(| - 2X,A)
+ xR.FXs{* - xRJl
+ wg,^b^^IXE'JR"(1 - 2X*")11.
For given melt and plagioclase compositions, Equations5 and 6 define the temperature-HrO content relationshipfor the system (a Basic program that calculates these re-lationships is available from the authors upon request).
If an independent estimate of the temperature for thesystem can be made (e.9., coexisting Fe-Ti oxides), thenthe HrO content of the melt can be determined. Similarly,if the HrO content of the melt is known, then the tem-perature can be determined. We have calculated the HrOcontents of the 46 experimental product samples reportedhere, and in Rutherford et al. (1985) and Helz (1976),using Equations 5 and 6 and the experimental tempera-tures. These calculated HrO contents are plotted in Figure8 against the HrO solubility values calculated after Burn-ham and Nekvasil (1986), as discussed previously. Theagreement between the HrO contents is good, except forthe samples of Helz (1976). An estimate of the uncertain-ty associated with these calculations of HrO content canbe made if we assume that the reduced chi-squared (xi)equals one for the remaining 50 charges and solve for theappropriate o. This results in approximate uncertainties(lo) of 0.54 and 0.33 wto/o for the HrO contents of meltsas determined by the albite (Eq. 5) and anorthite (Eq. 6)equilibria, respectively.
Equations 5 and 6 have also been used to estimate theHrO contents of melts from four natural samples: rhyoda-cite pumice from the climatic eruption of Mount Maza-ma; dacitic pumice from the May 18, 1980, eruption ofMount St. Helens; the Fish Canyon Tufl and the trachy-andesite pumice from the 1982 eruption of El Chich6n.
13t2111098765
4
34 5 6 7 8 9 1 0
H2O (wtVo) Burnham and Nekvasil
this study Rutherford
P ( k b a r ) : 1 2 2 . 5 4 L 3 - 2 3S y m b o l : o a A A t r I
Fig. 8. Melt HrO contents calculated using Equations 5 and6 for albite (a) and anorthite (b) plotted vs. H'O solubility valuescalculated after Burnham and Nekvasil (1986) as discussed inthe text.
The results of these calculations are summarized in Ta-ble 3.
Bacon and Druitt (1988) and Druitt and Bacon (1989)reported analyses of matrix glass and plagioclase forrhyodacitic pumices from the climactic eruption of MountMzama, and Druitt and Bacon (1989) reported prerup-tive temperatures between 880 and 886 "C based on co-existing Fe-Ti oxide compositions. Plagioclase composi-tions within the rhyodacitic pumices varied widely fromAn' to Anuo, although most were less than Anoo (Druittand Bacon, 1989). Using a plagioclase composition ofAn35, the calculated HrO contents of the melt are 3.7 wto/o(Eq. 5) and 4.3 wt0/o (Eq. 6), and agree within error. Baconet al. (1988) examined glass inclusions within plagioclasephenocrysts using infrared spectroscopy and reported apreeruptive HrO content of approximately 4.5 wto/o forthe melt, easily within 1o error of the 4.3 wto/o calculatedusing Equation 6 and just over lo error from the 3.7 wto/ocalculated using Equation 5.
Rutherford et al. (1985) published analyses of matrixglass and glass inclusions in plagioclase from the tephraof the May 18, 1980 eruption of Mount St. Helens and
14
6 1 3E 1 2Erri ro
9
SrC7o6N s
- 4
+ f ro
c)
s'
N
490 HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA
TmLe 3. Calculated HrO contents for volcanic rocks
HrORemarks lrc) (Eq.5)
matrix glass and coexisting plagioclase from the FishCanyon Tuff. Johnson and Rutherford (1989), using thedata of Whitney and Stormer (1985), estimated that pre-eruptive temperatures were 760 + 30 'C based on coex-isting Fe-Ti oxide compositions. This uncertainty in thetemperature produces a range of calculated HrO contentsof the melt from 4.1 to 6.1 wto/o (Eq. 5) and3.3 to 4.7wto/o (Eq. 6). The two calculated HrO contents best agreeat 790 "C (4.1 wto/o, calculated from Eq. 5; 3.3 wto/0, cal-culated from Eq. 6). Whitney and Stormer (1985) esti-mated HrO contents of melts of the Fish Canyon Tuffbetween 4 and 6 wt0/0, based on comparison of observedmineral assemblages in the tuf with published phase re-lations. Similarly, Johnson and Rutherford (1989) con-ducted phase equilibrium experiments on a sample of theFish Canyon Tuff and estimated the HrO content of thenatural melt as 5 wtolo.
Luhr ot al. (1984) published compositions of matrixglass and plagioclase from the 1982 trachyandesite pum-ice from El Chich6n. For this case, relatively large un-certainties exist in both the equilibrium plagioclasecomposition and in the preeruptive temperature. Thepreeruptive temperature was estimated as between 750and 850 "C using stable isotope partitioning relationships(Rye et al., 1984). The best agreement between the cal-culated HrO contents was produced using the dominantplagioclase composition (Anor), which yielded relativelyhigh HrO contents in the melt, between 5.0 and 8.4 wto/odepending upon the temperature used.These estimates areconsistent with Hro contents in the melt of 6-8 wtyobased on electron microprobe totals for glass inclusionsof 93.5 wto/o (Luhr et al., 1984) and on experimental phase-equilibria constraints that indicate approximate HrO sat-uration at approximately 2 kbar pressrue (Carroll andRutherford, 1987; Luhr, 1990).
CoNcr-usroNs
We have modeled HrO-saturated plagioclase-meltequilibria by evaluating the equilibrium constants of ex-change reactions for albite and anorthite components be-tween plagioclase and melt for 46 new experimentalcharges in the pressure range of 1-4 kbar as well as fordata from the literature. Equilibrium constants were cal-culated using the plagioclase activity-composition modelof Fuhrman and Lindsley (1988) and Lindsley and Nek-vasil (1989), as well as three different silicate melt solu-tion models: the two-site quasi-lattice model of Nielsonand Dungan (1983), the quasi-crystalline model of Burn-ham and Nekvasil (1986), and the regular-solution modelof Ghiorso et al. (1983). Of these melt models, the reg-ular-solution model of Ghiorso et al. (1983) was the mostsuccessful in that it resulted in the lowest standard errorsfor regressions of ln K vs. reciprocal temperature. Thismodel was successfully extended to include published an-hydrous and HrO-undersaturated experimental data.
Not surprisingly, plagioclase-melt equilibria were shownto be strongly dependent upon temperature and the HrO
HP H,O(Eq. 6) (estimated)
Mount MazamaMount St. Helens
Fish Canyon Tuff
El Chich6n
An$*, mg'" 883An4s, gi 930Ans, gi 930An57, gi 930Anle, mg 930Ans, mg 930An57, rng 930sample 4f 730sample 4f 760sample 4t 790An36, mg 750An4, mg 750An4s, mg 750An.u, mg 800An*, mg 800An4e, mg 800Ane, mg 850An*, mg 850An1e, mg 850
4.3 4.52.7 3.44.32.5 3.44.32.3 3.44.32.9 3.44.32.7 3.,1-4.32.5 3.4-4.34.7 4-'63.9 4-63.3 4-68.7 6-88.1 6-87.7 6-87.1 6-86.6 6-86.2 6-85.8 6-85.3 6-a4.9 6-8
3.73.74.04.33.74.04.36.25.04.17.98.49.06.06.57.O4.55.05.4
Notej Sources of data: Mount Mazama: Bacon and Druitt (1988), Druittand Bacon (1989), Bacon et al. (1988); Mount St. Helens: Rutherford etal. (1985), Metzbacher and Eggler (1984); Fish Canyon Tuff: Whitney andStormer (1985), Johnson and Rutherford (1989); El Chich6n: Luhr et al.(1984), Rye et al. (1984).
'Composition of plagioclase used..- gi: glass inclusion; mg: matrix glass.t Plagioclase and glass compositions of sample 4 (Whitney and Storm-
er, 1985).
estimated the preeruptive temperature as 930 "C basedon coexisting Fe-Ti oxide compositions and experimentalphase relations. They also reported that plagisshse com-positions within these samples vary from Anon to Anrr.Depending upon the plagioclase composition used, thecalculated HrO content of the melt (at 930 "C) rangesfrom 3.7 to 4.3 wto/o (Eq. 5) and 2.3 to 2.9 wto/o (Eq. 6).These calculations illustrate the influence of variable pla-gioclase compositions in natural samples upon the cal-culated HrO content of the melt. For plagioclase of com-position Anon, the calculated HrO contents for both thematrix glass and melt inclusions of 3.7 wto/o (Eq. 5) and2.7 to 2.9 wto/o (Eq. 6) overlap at the 2o uncertainty.Rutherford et al. (1985) used the difference technique(1000/o - )oxides) for the glass inclusions to estimate thetotal volatile content (H,O + COr) of the Mount St. Hel-ens magma as 4.6 w0/0, and based on experimentally de-termined phase relationships, they estimated that PHro/(Prro * P.or) was 0.5 to 0.7. Using the thermodynamicdata for HrO from Burnham et al. (1969) and the melt-HrO activity relations of Burnham (1981) and Eggler andBurnham (1984), the P.ro/(Prro * P.or) values for theMount St. Helens magma convert to approximately 3.4to 4.3 wto/o HrO in the melt, which is broadly consistentwith the range of values calculated using Equations 5 and6. Similarly, Merzbacher and Eggler (1984) estimated HrOcontents of 3 to 4 wt9o for pyroclastic rocks from the May1980 eruption of Mount St. Helens by experimentallycalibrating the shift ofprojected cotectics with increasingHrO content.
Whitney and Stormer (1985) published analyses of the
HOUSH AND LUHR: PLAGIOCLASE-MELT EQUILIBRIA 491
content of the melt. The activities of the melt compo-nents were calculated using the experimental HrO con-tents, a parameter not generally known for natural sam-ples. For this reason, expressions are presented that relatethe temperature of the system to the mole fraction of HrOin the melt for both albite and anorthite equilibria, whichallow the HrO content of the melt to be estimated if thetemperature of the system is known. The application ofthese expressions to the experimental data suggests thatthese calculations have associated uncertainties on thecalculated HrO contents of approximately 0.54 and 0.33wto/o (lo) for the albite and anorthite equilibria, respec-tively.
Four examples of the calculation of HrO contents ofmelts are presented using natural samples. The complex-ities of these natural samples as reflected in large uncer-tainties in preeruptive temperature, or compositionallycomplex plagioclase, or both, may result in a large rangeof calcr lated HrO contents. Successful application of theserelationships requires both a good estimate of preeruptivetemperature and knowledge of the equilibrium plagio-clase and melt compositions.
AcxNowr,nncMENTs
The experimental work on which this study is based could not havebeen performed without the kindness and encouragement of Tren Hasel-ton, Rosalind Helz, Bob Rye, Gary Cygan, Steve Huebner, Phil Bethke,I.-M. Chou, and many other U.S.G.S. scientists. Jim McKee (U.S.G.S.,Reston) and Dan Kremser (Washington University) offered valuable ad-vice during rnicroprobe analysis. Reviews by Mark Ghiorso and AllenGlazner are sincerely appreciated. This work was supported by NSF grantsEAR-8414946 and EAR-8618872.
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492 HOUSH AND LUHR: PLAGIOCLASE.MELT EQUILIBRIA
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MaNuscnrrr RECETVED Mlv 3, 1990MlNuscrur"r AccEprED JaNulnv 14, 1991
