Unformatted text preview: JOURNAL OF PETROLOGY VOLUME 42 NUMBER 4 PAGES 673–683 2001 Calculation of Phase Relations Involving
Haplogranitic Melts Using an Internally
Consistent Thermodynamic Dataset
TIM HOLLAND1∗ AND ROGER POWELL2
1 DEPARTMENT OF EARTH SCIENCES, UNIVERSITY OF CAMBRIDGE, DOWNING STREET, CAMBRIDGE CB2 3EQ, UK 2 SCHOOL OF EARTH SCIENCES, UNIVERSITY OF MELBOURNE, PARKVILLE, VIC. 3052, AUSTRALIA RECEIVED OCTOBER 28, 1999; REVISED TYPESCRIPT ACCEPTED JUNE 23, 2000 A simple thermodynamic model is developed for silicate melts in
the system CaO–Na2O–K2O–Al2O3–SiO2–H2O (CNKASH). The
Holland & Powell ( Journal of Metamorphic Geology, 16,
289–302, 1998) internally consistent thermodynamic dataset is
extended via the incorporation of the experimentally determined
melting relationships in unary and binary subsystems of CNKASH.
The predictive capability of the model is evaluated via the experimental data in ternary and quaternary subsystems. The resulting
dataset, with the software THERMOCALC, is then used to
calculate melting relationships for haplogranitic compositions. Predictions of the P–T stabilities of assemblages in water-saturated
and -undersaturated bulk compositions are illustrated. It is now
possible to make useful calculations of the melting behaviour of
appropriate composition rocks under crustal conditions. The history of experimental investigation into the petrology of granites goes back to the days of N. L. Bowen
and colleagues, summarized in the classic monograph of
Tuttle & Bowen (1958) on the origin of granitic rocks
in the system NaAlSi3O8–KAlSi3O8–SiO2–H2O. Experimental and theoretical work continues, not only in
the ﬁeld of phase equilibrium studies but also on the
structure of melts and their viscosities, densities and
compositions as functions of pressure and temperature.
The results of much of this endeavour have been collected in the book by Johannes & Holtz (1996). Thermodynamic
approaches to calculating melting relations for basic
magmas and wet granitic systems have also been made
(e.g. Burnham, 1975; Nicholls, 1980; Berman & Brown,
1987; Stolper, 1989; Nekvasil, 1990; Ghiorso & Sack,
Metaluminous and peraluminous bulk compositions,
primarily in the silica-saturated portion of the haplogranitic system, CaO–Na2O–K2O–Al2O3–SiO2–H2O
(CNKASH), will be considered here. These include compositions made up of combinations of the end-member
components albite (NaAlSi3O8), K-feldspar (KAlSi3O8),
anorthite (CaAl2Si2O8), aluminosilicate (Al2SiO5), quartz
(SiO2) and water (H2O). The purpose of this study is to
extend the thermodynamic dataset of Holland & Powell
(1998) to allow prediction of melting relations involving
water-saturated and -undersaturated granitic melts. The
eﬀects of adding Fe and Mg will be addressed in a
forthcoming publication on beginning of melting in pelitic
and felsic rocks.
The approach followed in extending the thermodynamic dataset is to incorporate the experimentally
determined melting curves for each of the individual
minerals in CNKASH, dry and water saturated, as well
as in other binary subsystems. In this way the melt model
will be anchored in the overall system, particularly given
that there is a large volume of data in the unary and
binary subsystems. Also, the melt model will apply not
only to ‘granite’ melts but also to melts in the broader
CNKASH system. The model is validated by comparison
with experimental results in larger subsystems. With an
appropriate thermodynamic model, the advantage of ∗Corresponding author. Email: [email protected] Oxford University Press 2001 KEY WORDS: thermodynamics; melts; granite; dataset INTRODUCTION JOURNAL OF PETROLOGY VOLUME 42 being able to calculate melt equilibria is that the petrologist is not restricted to the P–T and composition
conditions under which experiments are performed, but
can consider any conditions within the range of applicability of the model. NUMBER 4 APRIL 2001 given suitable starting guesses for the compositions and
temperature. The formulation of G° follows Holland &
Powell (1998) whereas the equilibrium constants, K, use
the activities of the end-members
aqL = XqL(1−Xh2oL)
akspL = XkspL(1−Xh2oL)
ah2oL = X THE THERMODYNAMIC MODEL
The thermodynamic model adopted for the liquid is in
the spirit of Nicholls (1980), involving the macroscopic
mixing of a set of liquid end-members formulated, following Burnham (1975), on an eight-oxygen basis (with
the exception of H2O) and assuming that non-ideality is
accounted for by symmetrical interactions. The approach
used is similar to that of Ghiorso & Carmichael (1980)
and of Ghiorso & Sack (1995), although some assumptions
are rather diﬀerent; in particular: (1) the end-members
in the melt used are simple mineral-like units such as
albite (abL, NaAlSi3O8), K-feldspar (kspL, KAlSi3O8),
anorthite (anL, CaAl2Si2O8), quartz (qL, 4SiO2) and
sillimanite (silL, 8/5 Al2SiO5), rather than oxide and
multi-oxide units on a variable oxygen basis; (2) volumetric properties use the Murnaghan equation of state;
(3) partial molar volumes of H2O in the melt are modelled
using the recent data of Ochs & Lange (1997); (4) the
end-member liquid properties are calibrated entirely on
melting experiments on subsystems in NCKASH. One
of the principal goals of this model has been to describe
and predict phase relations in unary, binary, ternary and
quaternary subsystems as well as forming a basis for
prediction of more complex natural granitic melts involving addition of Fe and Mg. Although water is known
to exist as both hydroxyls and molecular water in silicate
melts (e.g. Silver & Stolper, 1989; Novak & Behrens,
1995) and the distribution of these species depends on
pressure and temperature, a macroscopic approach is
here used that considers total H2O in the form of the
single end-member, h2oL (H2O).
In using this model to calculate a feature such as the
minimum melting curve K-feldspar + quartz + H2O =
liquid in the system KAlSi3O8–SiO2–H2O, the melt phase
is described by the three end-members kspL, qL and
h2oL. Two compositional variables are required, and it
is convenient to choose two of the three end-member
proportions, denoted Xk (the third proportion being found
by diﬀerence, 1 − Xk). There are three independent
reactions between the end-members of the phases:
(1) 4q = qL;
(2) san = kspL;
(3) H2O = h2oL.
Writing the equilibrium relationships for each of these,
0 = G° + RTln K, the resulting set of non-linear
equations may be solved iteratively at a chosen pressure, qL
h2oL h2oL following Nicholls (1980), and the activity coeﬃcients, k,
are found from the regular solution model,
RT ln k =− (
i i − Xi )( j − Xj )Wij. j >i In the expression above, l = 1 if l = k and l = 0
if l ≠ k, and Wij is the macroscopic interaction energy
between end-members i and j (e.g. Powell & Holland,
1993). For more complex equilibria, for example in
NKASH, the independent reactions between the phases
will include ones to allow the equilibrium compositions
of the solids to be determined.
Application of the model to the granite system requires
calibration of the 15 binary regular solution energies
amongst the six end-members in the melt as well as the
thermodynamic properties of the six melt end-members
themselves. CALIBRATION OF THE MODEL
The model requires values for the heat capacity, volume,
thermal expansion, compressibility, entropy and enthalpy
for each end-member in the melt.
The heat capacities, based on the work of Stebbins et
al. (1984), of the melt end-members are taken from the
compilation of Holland & Powell (1998). The volumes,
thermal expansions and compressibilities were modiﬁed
from the tables in Ochs & Lange (1997), via the use of
a Murnaghan equation of state. with K′ set to four so as
to minimize the number of adjustable parameters required to satisfy the data. The properties for h2oL were
also obtained in the same way.
The compressibilities so derived required some adjustment in the next stage of data retrieval during which
the dry melting temperatures as a function of pressure
were used to constrain the thermodynamic data for abL,
kspL, anL, silL and qL. Fits to the melting experiments
were made by non-linear regression to determine optimum enthalpy of formation, entropy and bulk modulus
for each end-member to give best agreement between
calculated melting curves and experimental brackets (Fig.
1). In addition, literature values for enthalpy of fusion
(Lange & Carmichael, 1990) were used as further constraints in the least-squares analysis. The resulting set of 674 HOLLAND AND POWELL PHASE RELATIONS OF HAPLOGRANITIC MELTS Table 1: Thermodynamic properties of melt end-members
H H S V Cp Tfus Hfus qL −920·84 0·36 16·50 2·640 0·0825 −0·50 470 1726 9·8 anL −4257·70 0·89 52·00 10·206 0·4175 4·90 200 1557 134·9 kspL −3992·51 2·94 129·50 11·468 0·3673 6·00 260 1200 57·5 abL −3934·37 1·89 145·00 10·710 0·3585 4·50 390 1120 62·4 silL −2583·28 1·23 39·00 6·419 0·2376 1·00 300 1200 63·4 −295·71 0·10 45·50 1·414 0·0800 h2oL 107·9 40 — — H, enthalpy of formation from the elements; H, one standard deviation on the enthalpy of formation; S, entropy (in J/K); V,
volume; Cp, heat capacity (all properties at 1 bar and 298 K); , thermal expansion parameter; , bulk modulus (incompressibility) at 298 K. [See Holland & Powell, 1998 for details.] These parameters are incorporated in the updated version
of the dataset. The last two columns give the fusion temperature and calculated heat of fusion. Fig. 1. Calculated curves and experimental brackets for melting of
albite (ab), K-feldspar (ksp), anorthite (an), quartz (q) and cristobalite
(crst). Experimental brackets: ab (Boyd & England, 1963); ksp (Lindsley,
1966); an (Goldsmith, 1980); q & crst (Ostrovsky, 1966; Jackson, 1976). thermodynamic data is listed in Table 1, and diﬀers from
that of Holland & Powell (1998) because (1) the volume
behaviour of H2O is now based on Ochs & Lange
(1997) rather than Burnham & Davis (1971), and (2) the
enthalpies of fusion are now included as constraints. The
data for sillimanite melting are provisional and are based
on the suggested melting temperature (1200 ± 40°C) at
ambient pressure from Cameron (1977) and an estimate
of 1700–1750°C at 20 kbar from Holland & Carpenter
(1986). The agreement of calculated curves and experimental brackets in Fig. 1 shows that the thermodynamic data and formulation used here provide an
adequate description of the thermodynamics of melting
of these mineral end-members. The thermodynamic properties of the h2oL end-member were derived simultaneously from (1) the solubility
data for H2O in albitic melts, as measured by Goranson
(1931, 1932), Burnham & Jahns (1962), Morey & Hesselgesser (in Clark, 1966) and Behrens (1995), and (2) the
melting experiments of Goldsmith & Jenkins (1985).
There are two equilibrium relations, ab (solid) = abL
(liquid) and h2oL (liquid) = H2O (ﬂuid). The H2O
solubility experiments yield the entropy and enthalpy
of the h2oL end-member from the second equilibrium
relation, if the value for the regular solution parameter
Wab h2o is known (in subscripts to W, the L part of the
liquid end-member name will be omitted for ease of
reading, so that Wab h2o replaces WabL h2oL). The temperatures of the wet melting of albite depend on the
properties of the abL end-member (known from above)
and the value of Wab h2o. Simultaneous ﬁtting of the two
equilibria yields the values for Wab h2o in Table 2 and the
enthalpy and entropy of h2oL given in Table 1. It was
found that a small pressure dependence was required
for Wab h2o, a feature that probably incorporates the
cumulative errors and simpliﬁcations in the models used
here. Because the water contents of albitic melts are rather
insensitive to temperature, calculated water solubilities (at
1100°C) may be compared with experimental values at
a variety of temperatures in Fig. 2, where the agreement
is seen to be good, given the scatter in the measurements.
The predicted solubility of water in K-feldspar melts is
a little lower than that in albite melts (Fig. 3), in agreement
with the study of Behrens (1995).
The interaction energies in the qL–h2oL and anL–
h2oL binaries, Wq h2o and Wan h2o, were derived by adjusting their values to bring agreement with the wet
melting curves of quartz (Fig. 4) and anorthite (Fig. 5),
respectively. The value for Wksp h2o was derived from the
wet melting experiments of Goldsmith & Peterson (1990)
and, in the absence of any experimental constraint, the 675 JOURNAL OF PETROLOGY VOLUME 42 NUMBER 4 APRIL 2001 Table 2: Values for regular solution
parameters used in these calculations;
in the form Wij = a + bP
a (kJ) b (kJ/kbar) Wq ab 12 −0·4 Wq ksp −2 −0·5 Wq an −10 0 Wq sil 12 0 Wq h2o 15 0 Wab ksp −6 Wab an 0 Wab sil 12 0 Wab h2o 1 −0·2 Wksp an 0 −1·0 Wksp sil 12 0
0 Wksp h2o 11 Wan sil 12 0 Wan h2o 9 −0·85 Wsil h2o 16 Fig. 3. Calculated water solubility in albite and K-feldspar melts at
1100°C compared with experiments of Behrens (1995). 0 For Wab ksp in dry melts, a = −6 and b = 1·0. Fig. 4. Calculated curves and experimental brackets for wet melting
of quartz–cristobalite. Experimental data from Kennedy et al. (1962)
and Stewart (in Luth, 1976). Fig. 2. Calculated water solubility in albite melt at 1100°C compared
with experiments. G 38, Goranson (1938, in Clark, 1966); B 95,
Behrens (1995); B&J 62, Burnham & Jahns (1962); M&H 51, Morey
& Hesselgesser (1932, in Clark, 1966). value for Wsil h2o has been estimated. The interaction
energies among the components qL, abL, kspL and anL
were determined by ﬁtting the experimental eutectics for
binary joins involving dry and wet melting; for example, the wet melting curves of albite and K-feldspar are shown
in Figs 6 and 7. The calculated curves in Figs 2–7
show that a simple regular solution model is capable of
reproducing the shape of the experimental data. All
W values involving the silL end-member have been
estimated, in the absence of appropriate experimental
data to calibrate them, but this will introduce imperceptible errors in calculations because the proportion
of silL in granitic melts is always small (e.g. Joyce &
Voigt, 1994). Derived values of all of the interaction
energies are given in Table 2. 676 HOLLAND AND POWELL PHASE RELATIONS OF HAPLOGRANITIC MELTS Fig. 5. Calculated curves and experimental brackets for wet and dry
melting of anorthite. Data: dry melting, Goldsmith (1980); wet melting,
Yoder (1965) and Stewart (1967). Fig. 6. Calculated curves and experimental melting points for sanidine
(ﬁtted) and for sanidine + quartz (predicted). Β, Goranson (1931,
1932), Schairer & Bowen (1955), Yoder et al. (1957), Tuttle & Bowen
(1958), Boettcher & Wyllie (1969), Lambert et al. (1969), Spengler (in
Luth, 1976); Α, Shairer & Bowen (1947, 1955), Tuttle & Bowen (1958),
Shaw (1963), Luth et al. (1964), Boettcher & Wyllie (1969), Lambert et
al. (1969). Brackets: san, Goldsmith & Peterson (1990); san + q, Bohlen
et al. (1983). The mixing properties of alkali feldspars in this study
(albite–sanidine solutions) are taken directly from the
subregular model of Thompson & Waldbaum (1969). PREDICTIONS AND APPLICATIONS
OF THE THERMODYNAMIC MODEL
The calculated curves for wet melting are compared with
experimental data for sanidine + quartz in Fig. 6, albite Fig. 7. Calculated curves and experimental melting points for albite
(ﬁtted) and for albite + quartz (predicted). Β, Goranson (1931, 1932),
Schairer & Bowen (1947, 1956), Loder et al (1957), Tuttle & Bowen
(1958), Burnham & Jahns (1962), Luth et al. (1964), Morse (1970); Α,
Shairer & Bowen (1947, 1956), Tuttle & Bowen (1958), Shaw (1963),
Luth et al. (1964). Brackets: Goldsmith & Jenkins (1985). + quartz in Fig. 7, and albite + sanidine + quartz in
Fig. 8. As these data were not used in the calibration for
Tables 1 and 2, they provide a test of the predictive
capability of the model. The agreement between calculated and experimental melting temperatures in the
range 0–10 kbar is reasonable, especially when viewed
in the light of the scatter present between the various
experimental studies. The curves in Fig. 8 are simpliﬁed
in that the change from alkali feldspar to albite + sanidine
(solvus) and associated singularities are not shown here;
however, these features are discussed below with respect
to calculated phase diagrams such as in Fig. 11. An
additional test is to compare the predicted water contents
in a haplogranite melt of composition Qz28Ab38Or34
(weight percent basis) for which the experimental solubility data of Holtz et al. (1995) are available. Figure 9
shows that the model used here, involving a macroscopic
approach that ignores the details of the speciation of
water, reproduces the measured solubilities adequately,
particularly at lower pressures, but tends to underestimate
the solubility at higher pressure. The change in temperature dependence of solubility, with isopleths of positive slope at low pressures and negative slopes at higher
pressures (and high temperatures), is also predicted. It
should be noted that diﬀerent experimental studies (Goranson, 1931, 1932; Tuttle & Bowen, 1958; Luth et al.,
1964; Steiner et al., 1975; Holtz et al., 1992, 1995) disagree
by up to 1 wt % in absolute value for granitic melts.
Figure 10 shows a calculated P–T projection for the
KASH system involving feldspar (ksp), muscovite (mu),
quartz (q), sillimanite (sill), corundum (cor), liquid (liq)
and H2O. The locations of the two invariant points 677 JOURNAL OF PETROLOGY VOLUME 42 Fig. 8. Calculated curves and experimental melting points for albite
+ sanidine (ﬁtted) and for albite + sanidine + quartz (predicted). Α,
Schairer (1950), Yoder et al (1957), Tuttle & Bowen (1958), Luth et al.
(1964), Merrill et al. (1970); Φ, Tuttle & Bowen (1958), Luth et al.
(1964), Steiner et al. (1975). Singularity details at the intersections of
melting curves and the feldspar solvus have been omitted (see text). Fig. 9. Predicted solubility of water in haplogranitic melt of composition Qz28Ab38Or34 (wt %) compared with the experimental data of
Holtz et al. (1995). Calculated wet and dry solidus curves (minimum
melting) in bolder lines. (See text for discussion.) are in very good agreement with those experimentally
determined by Huang & Wyllie (1974, Fig. 3), and the
quartz-absent curve linking them, ksp + sill + H2O =
mu + liq, also has the same sense of curvature as
suggested by Huang & Wyllie. The minimum melting
curve in the peraluminous system ksp + q + sill + NUMBER 4 APRIL 2001 Fig. 10. A P–T projection of the univariant equilibria in KASH,
involving muscovite, quartz, K-feldspar, sillimanite, corundum, liquid
and H2O ﬂuid. H2O = liq is lowered by about 25° relative to that in
the haplogranite system (ksp + q + H2O = liq), in
agreement with experimental evidence ( Joyce & Voigt,
1994; Johannes & Holtz, 1996). The calculated position
of the ﬂuid-absent melting reaction mu + q = ksp +
sill + liq, which would play a major role in melting of
low-Na pelitic schists of low porosity, is also in excellent
agreement with the experimental data of Huang & Wyllie
Addition of Na to the KASH system dramatically
lowers the calculated temperatures of melting, and Fig.
11 shows the P–T projection calculated for muscovite +
albite + K-feldspar + quartz + sillimanite + corundum
+ liquid + H2O. The dashed lines show the reactions
in the KASH system from Fig. 10 for comparison.
Features to note are the azeotrope traces in the system
at temperatures above the alkali feldspar solvus crest, the
related singular points on the muscovite-absent reactions
at temperatures below the solvus crest [the reader is
referred to the discussion by Luth (1976, p. 339) or Morse
(1980, p. 397) for further details] and the singular point
on the albite-absent reaction (where quartz changes from
product to reactant with rising temperature). Dehydration
melting in pelitic rocks will begin at temperatures as low
as 650°C at 4 kbar to 750°C at 10 kbar, heralding the
change from muscovite schists to high-grade gneisses.
Figure 12 is a predicted ternary liquidus for ab–or–q
at 5 kbar, showing the calculated contours and azeotrope
traces. The experiments of Morse (1970) have the melting
loop and solvus just meeting on the feldspar join at this
pressure, whereas the thermodynamic model predicts 678 HOLLAND AND POWELL PHASE RELATIONS OF HAPLOGRANITIC MELTS Fig. 11. A P–T projection for KNASH, showing the relationship to
KASH equilibria. (Note the solvus top trace, and the azeotrope traces.)
The circles on the solidi mark complex singular relations that occur
over a very small range of P–T as a consequence of the intersection of
the shoulder of the alkali feldspar solvus with the solidus loop in the
vicinity of the azeotrope trace. Fig. 12. Predicted ternary liquidus for haplogranitic melts contoured
for temperature. The inset shows a ﬁeld of stability for muscovite +
liquid for the sillimanite-saturated system. that the solvus and the melting loop on the binary feldspar
join have just separated. The singular (critical) point on
the two-feldspar boundary at which the solvus meets the
melting loop is shown as a simple open circle. The inset
shows that adding excess alumina to the system at this
pressure introduces a ﬁeld of stability for muscovite +
liquid. The simplest way to see phase relationships in complex
systems is with pseudosections—phase diagrams showing
just those phase relationships experienced by a particular
bulk composition, or bulk composition line (e.g. Powell
et al., 1998). The following pseudosections are based on
a molar bulk composition: SiO2 = 75·00, Al2O3 =
18·32, K2O = 4·55, Na2O = 2·14. In the case of looking
at melting relationships, choice of H2O content in the
bulk composition is critical in that liquid has a strong
aﬃnity for H2O. The importance of H2O can be seen
in the T–XH2O pseudosection at 5 kbar in Fig. 13a, and
complemented by Fig. 13b, in which the H2O content
in the bulk composition runs from zero through to just
above H2O saturation at 850°C. The aﬃnity of H2O for
the liquid can be seen by the way the H2O saturation
line behaves once the solidus is crossed. The kick-back
of this line as muscovite melts out with rising temperature
is an interesting (but geologically irrelevant) feature. It is
interesting to note that the solidus temperature is not
very composition dependent at this pressure, but the melt
mode contours show that, as the amount of H2O in the
bulk composition decreases, the amount of melt decreases.
Nevertheless, this shows that heating a muscovite-bearing
ﬂuid-absent rock will cause it to melt at more or less the
same temperature as an H2O-saturated rock at this
pressure. Melting temperatures for ﬂuid-present and
ﬂuid-absent melting diverge considerably at higher pressures (Fig. 11). The relative complexity of the pseudosection between 650 and 700°C at relatively high H2O
contents relates to the H2O dependence of which
of quartz and K-feldspar disappears ﬁrst as melting
Considering a marginally H2O-saturated bulk composition heating up with no H2O inﬁltration (line A in
Fig. 13b), the solidus is the [cor, ksp] univariant in Fig.
11, but substantial melting occurs across the [cor, H2O]
univariant, and particularly the [cor, H2O, ab] divariant
immediately above it, across which muscovite is lost.
The solidus and the two dehydration-melting reactions
referred to above for this bulk composition are shown
rather more clearly in Fig. 14a. Such a migmatite may
lose its melt, in which case the residue composition moves
to the left in Fig. 13b as its H2O is removed with the
melt. With no melt loss the rock returns down the line
A. Signiﬁcantly, much of the crystallization of the liquid,
and consequent retrogression of such a migmatite, occurs
across [cor, H2O, ab] and [cor, H2O] under H2Oundersaturated conditions.
To see the P–T dependence of the equilibria in the
context of the importance of H2O, P–T pseudosections
corresponding to lines A and B in Fig. 13b are given in
Fig. 14a and b complemented by Fig. 14c. The diﬀerences
between Fig. 14a and b occur at temperatures above the
wet melting curves, where K-feldspar is stabilized in melts
to much higher temperatures (at higher pressure) in Fig. 679 JOURNAL OF PETROLOGY VOLUME 42 NUMBER 4 APRIL 2001 Fig. 13. (a) A temperature–XH2O diagram at 5 kbar, for molar bulk composition SiO2 = 75·00, Al2O3 = 18·32, K2O = 4·55, Na2O = 2·14,
with XH2O = 0 corresponding to H2O = 0, and XH2O = 1 corresponding to H2O = 30 (7·2 wt % H2O). (b) As for (a) but showing the H2O
saturation line, the solidus, dashed contours (roman labelling) giving melt modes (molar on a one-oxide basis), and unbroken contours (italic
labelling) giving h2oL proportions in the liquid (ph2oL). Weight percent H2O in the melt, to a close approximation, may be found as 1800ph2oL/
(260–242ph2oL). The line A corresponds to the composition used in constructing Fig. 14a. 14a. In this latter ﬁgure, the ﬂuid-absent melting reaction
mu + ab + q = ksp + sill + liq is responsible for the
ﬁrst appreciable melting with heating at pressures above
4 kbar. This is in contrast to the excess-H2O case, where
the ﬁrst appreciable melting occurs across the solidus
reaction mu + ab + q + H2O = sill + liq at 650°C,
at which point the albite is melted out. In Fig. 14a, for
the geologically more appropriate situation of a ﬁxed
H2O content leading to H2O-undersaturated conditions
for most super-solidus conditions, at moderate to higher
pressures the melt modes and melt water contents mirror
each other (Fig. 14c). However, at low pressure, the
water contents cut through to the solidus, whereas the
melt modes are closely spaced parallel to the solidus.
This decrease of solubility of H2O in the melt not only
gives the solidus its shape, but means that H2O saturation
of melts formed under H2O-undersaturated conditions
occurs at temperatures of some 20–70°C above the
minimum melting at pressures below 4 kbar. This implies
that such magmas will exsolve their H2O on decompression at greater depths (by some 2–3 km) than
given by the minimum melting curve. DISCUSSION
The assumptions and simpliﬁcations made in the model
are worth reiterating so that the limitations of the applicability of the thermodynamic model are appreciated: (1) the melt model is developed from a simple macroscopic viewpoint, particularly in neglecting the speciation
of water and the dissolved silicate in the accompanying
aqueous ﬂuid. No account is made of structural changes
in melts with pressure and temperature, as reﬂected,
for example, in viscosity changes, apart from letting
interaction energies be a function of pressure. As such,
there is an implicit assumption that the model applies to
Na–K-dominated largely polymerized melts.
(2) The volume behaviour is assumed to obey the
Murnaghan equation of state with an imposed constant
value of K′ = 4. Although this reproduces the silicate
melt volumes reported by Ochs & Lange (1997) in the
range 0–10 kbar, it may introduce error if extrapolated
to very high pressures for hydrous melts. The derived
values for the bulk modulus, as well as entropy and
enthalpy, for melt end-members derived from the melting
experiments may incorporate some errors introduced
through this assumption.
(3) It is assumed that the ﬂuid coexisting with the melt
phase is pure H2O. This is a reasonable assumption,
given that the silicate content of such ﬂuids remains very
small except close to the critical point for albite or quartz
(Kennedy et al., 1962; Shen & Keppler, 1997). If such
ﬂuids were to be described by mixing models, the tendency to unmix to ﬂuid + melt implies that activity is
larger than mole fraction, causing water activities to
remain close to unity in the aqueous component.
However, the values for the regular solution parameters 680 HOLLAND AND POWELL PHASE RELATIONS OF HAPLOGRANITIC MELTS Fig. 14. (a) A pseudosection for the same bulk composition as in Fig. 13 but with a ﬁxed H2O content. The molar composition used is SiO2 =
75·00, Al2O3 = 18·32, K2O = 4·55, Na2O = 2·14, with H2O = 12·75 (3·2 wt % H2O), corresponding to line A in Fig. 13b. (b) A pseudosection
as for (a) but for excess H2O (corresponding to line B in Fig 13b). (c) As for (a) but showing the solidus, dashed contours (roman labelling) giving
melt modes (molar on a one-oxide basis), and unbroken contours (italic labelling) giving h2oL proportions in the liquid. between silicate and h2oL end-members used in this
model will probably reﬂect the eﬀect of a slightly reduced
water activity stemming from the pressure-induced solubility of silicate in the ﬂuid.
The temperatures at which dry granitic rocks begin to
melt at high pressures has become a matter of debate
(Becker et al., 1998). The experimental results of Huang
& Wyllie (1975) indicate melting at the solidus at 1050°C
at 8 kbar, whereas more recent work (W. Johannes, personal communication, 1999) suggests that melting
occurs at >1050°C with 1 wt % water, and that extrapolation to dry conditions should yield a solidus nearly
90°C higher than this with a shallower dP/dT slope than
that proposed by Huang & Wyllie. In addition, Becker
et al. (1998) performed melting experiments at very low
water activities (aH2O = 0·07) at 5 kbar and found melting
temperatures (990°C) very similar to those encountered
by Huang & Wyllie in nominally dry runs. This led them 681 JOURNAL OF PETROLOGY VOLUME 42 to suggest that small amounts of water-containing gel in
the starting materials used by Huang & Wyllie might be
the explanation of their low melting temperatures. Our
calculations can shed further light in this debate. First,
calculated melting temperatures for dry melting of
quartz–albite and quartz–K-feldspar eutectics agree very
closely with the experiments of Luth (1968) up to 20 kbar.
Second, calculations for aH2O = 0·07 at 5 kbar reproduce
the results of Becker et al. (1998) within experimental
error, corroborating their inferences. Finally, the dry
granite solidus calculated in this study occurs at temperatures of 1130°C at 8 kbar (Fig. 9). The slope as well
as the position of our calculated granite solidus match
the extrapolation of W. Johannes & F. Holtz (personal
communication, 1999) remarkably well.
The model of melt thermodynamics presented here,
although rudimentary and preliminary in nature, appears
capable of reproducing the major features of the experimentally determined phase relations, and may be
used to investigate some of the complexities seen in
natural compositions. An extension of this model to
include Fe and Mg and to predict the melting behaviour
of pelitic schists and gneisses will be presented elsewhere. ACKNOWLEDGEMENTS
Alan Thompson, Francois Holtz and an anonymous
reviewer are thanked for helpful comments and suggestions. REFERENCES
Becker, A., Holtz, F. & Johannes, W. (1998). Liquidus temperatures
and phase compositions in the system Qz–Ab–Or at 5 kbar and
very low water activities. Contributions to Mineralogy and Petrology 130,
Behrens, H. (1995). Determination of water solubilities in high-viscosity
melts: an experimental study on NaAlSi3O8 melts. European Journal
of Mineralogy 7, 905–920.
Berman, R. G. & Brown, T. H. (1987). Development of models for
multicomponent melts: analysis of synthetic systems. In: Carmichael,
I. S. E. & Eugster, H. P. (eds) Thermodynamic Modelling of Geological
Materials: Minerals, Fluids and Melts. Mineralogical Society of America,
Reviews in Mineralogy 17, 405–442.
Boettcher, A. L. & Wyllie, P. J. (1969). Phase relationships in the system
NaAlSi3O8–SiO2–H2O to 35 kilobars pressure. American Journal of
Science 267, 875–909.
Bohlen, S. R., Boettcher, A. L., Wall, V. J. & Clemens, J. D. (1983).
Stability of phlogopite–quartz and sanidine–quartz: a model for
melting in the lower crust. Contributions to Mineralogy and Petrology 83,
Boyd, F. R. & England, J. L. (1963). The eﬀect of pressure on the
melting of diopside, CaMgSi2O6, and albite, NaAlSi3O8, in the range
up to 50 kilobars. Journal of Geophysical Research 68, 311–323.
Burnham, C. W. (1975). Water and magmas: a mixing model. Geochimica
et Cosmochimica Acta 39, 1077–1084. NUMBER 4 APRIL 2001 Burnham, C. W. & Davis, N. F. (1971). The role of H2O in silicate
melts: I. P–V–T relations in the system NaAlSi3O8–H2O to 10 kilobars
and 1000°C. American Journal of Science 270, 54–79.
Burnham, C. W. & Jahns, R. H. (1962). A method for determining
the solubility of water in silicate melts. American Journal of Science 260,
Cameron, W. E. (1977). Mullite: a substituted alumina. American Mineralogist 62, 747–755.
Clark, S. P. (1966). Solubility. In: Clark, S. P. (ed.) Handbook of Physical
Constants. Geological Society of America, Memoir 97, 415–436.
Ghiorso, M. S. & Carmichael, I. S. E. (1980). A regular solution model
for met-aluminous silicate liquids: applications to geothermometry,
immiscibility, and the source regions of basic magmas. Contributions
to Mineralogy and Petrology 71, 323–342.
Ghiorso, M. S. & Sack, R. O. (1995). Chemical mass transfer in
magmatic processes IV. A revised and internally consistent thermodynamic model for the interpretation and extrapolation of liquid–
solid equilibria in magmatic systems at elevated temperatures and
pressures. Contributions to Mineralogy and Petrology 119, 197–212.
Goldsmith, J. R. (1980). Thermal stability of dolomite at high temperatures and pressures. Journal of Geophysical Research 85, 6949–6954.
Goldsmith, J. R. & Jenkins, D. M. (1985). The hydrothermal melting
of low and high albite. American Mineralogist 70, 924–933.
Goldsmith, J. R. & Peterson, J. W. (1990). Hydrothermal melting
behaviour of KAlSi3O8 as microcline and sanidine. American Mineralogist 75, 1362–1369.
Goranson, R. W. (1931). The solubility of water in granitic magmas.
American Journal of Science 22, 481–502.
Goranson, R. W. (1932). Some notes on the melting of granite. American
Journal of Science 223, 227–236.
Holland, T. J. B. & Carpenter, M. A. (1986). Aluminium/silicon
disordering and melting in sillimanite at high pressures. Nature 320,
Holland, T. J. B. & Powell, R. (1998). An internally-consistent thermodynamic dataset for phases of petrological interest. Journal of Metamorphic Geology 16, 309–343.
Holtz, F., Behrens, H., Dingwell, D. B. & Taylor, R. (1992). Water
solubility in aluminosilicate melts of haplogranitic compositions at
2 kbar. Chemical Geology 96, 289–302.
Holtz, F., Behrens, H., Dingwell, D. B. & Johannes, W. (1995).
Water solubility in haplogranitic melts. Compositional, pressure and
temperature dependence. American Mineralogist 80, 94–108.
Huang, W. L. & Wyllie, P. J. (1974). Melting relations of muscovite
with quartz and sanidine in the K2O–Al2O3–SiO2–H2O system to
30 kilobars and an outline of paragonite melting relations. American
Journal of Science 274, 378–395.
Huang, W. L. & Wyllie, P. J. (1975). Melting reactions in the system
KAlSi3O8–NaAlSi3O8–SiO2–H2O to 35 kilobars, dry and with excess
water. Journal of Geology 83, 737–748.
Jackson, I. (1976). Melting of the silica isotypes SiO2, BeF2 and GeO2
at elevated pressures. Physics of the Earth and Planetary Interiors 13,
Johannes, W. & Holtz, F. (1996). Petrogenesis and Experimental Petrology of
Granitic Rocks. Berlin: Springer, 335 pp.
Joyce, D. B. & Voigt, D. E. (1994). A phase equilibrium study in the
system KAlSi3O8–NaAlSi3O8–SiO2–Al2SiO5–H2O and petrogenetic
interpretations. American Mineralogist 79, 504–512.
Kennedy, G. C., Wasserburg, G. J., Heard, H. C. & Newton, R. C.
(1962). The upper three-phase region in the system SiO2–H2O.
American Journal of Science 260, 501–521.
Lambert, I. B., Robertson, J. K. & Wyllie, P. J. (1969). Melting reactions
in the system KAlSi3O8–SiO2–H2O. American Journal of Science 267,
609–626. 682 HOLLAND AND POWELL PHASE RELATIONS OF HAPLOGRANITIC MELTS Lange, R. A. & Carmichael, I. S. E. (1990). Thermodynamic properties
of silicate liquids with emphasis on density, thermal expansion and
compressibility. In: Nicholls, J. & Russel, J. K. (eds) Modern Methods
of Igneous Petrology: Understanding Magmatic Processes. Mineralogical Society
of American, Reviews in Mineralogy 24, 25–59.
Lindsley, D. H. (1966). Melting relations of KAlSi3O8: eﬀect of pressure
up to 40 kb. American Mineralogist 51, 1793–1799.
Luth, W. C. (1968). The inﬂuence of pressure on the composition of
eutectic liquids in the binary systems sanidine–silica and albite–silica.
Carnegie Institution of Washington Yearbook 66, 480–484.
Luth, W. C. (1976). Granitic rocks. In: Bailey, D. K. & MacDonald,
R. (eds) The Evolution of the Crystalline Rocks. London: Academic Press,
Luth, W. C., Jahns, R. H. & Tuttle, O. F. (1964). The granite system
at pressures of 4 to 10 kilobars. Journal of Geophysical Research 69,
Merrill, R. B., Robertson, J. K. & Wyllie, P. J. (1970). Melting reactions
in the system NaAlSi3O8–KAlSi3O8–SiO2–H2O to 20 kilobars compared with results for other feldspar–quartz–H2O and rock–H2O
systems. Journal of Geology 78, 558–569.
Morse, S. A. (1970). Alkali feldspars with water at 5 kb pressure. Journal
of Petrology 11, 221–253.
Morse, S. A. (1980). Basalts and Phase Diagrams. Berlin: Springer.
Nekvasil, H. (1990). Reaction relations in the granite system: implications for trachytic and syenitic magmas. American Mineralogist 75,
Nicholls, J. (1980). A simple thermodynamic model for estimating the
solubility of H2O in magmas. Contributions to Mineralogy and Petrology
Novak, M. & Behrens, H. (1995). The speciation of water in granitic
glasses and melts determined by in situ near-infrared spectroscopy.
Geochimica et Cosmochimica Acta 59, 3445–3450.
Ochs, F. A. & Lange, R. A. (1997). The partial molar volume, thermal
expansivity, and compressibility of H2O in NaAlSi3O8 liquid: new
measurements and an internally consistent model. Contributions to
Mineralogy and Petrology 129, 155–165.
Ostrovsky, I. A. (1966). PT-diagram of the system SiO2–H2O. Geological
Journal 5, 127–134.
Powell, R. & Holland, T. J. B. (1993). On the formulation of simple
mixing models for complex phases. American Mineralogist 78, 1174–
1180. Powell, R., Holland, T. J. B. & Worley, B. (1998). Calculating phase
diagrams involving solid solutions via non-linear equations, with
examples using THERMOCALC. Journal of Metamorphic Geology 16,
Schairer, J. F. (1950). The alkali feldspar join in the system NaAlSi3O8–
KAlSi3O8–SiO2. Journal of Geology 58, 512–517.
Schairer, J. F. & Bowen, N. L. (1947). Melting relations in the systems
Na2O–Al2O3–SiO2 and K2O–Al2O3–SiO2. American Journal of Science
Schairer, J. F. & Bowen, N. L. (1955). The system K2O–Al2O3–SiO2.
American Journal of Science 253, 681–746.
Schairer, J. F. & Bowen, N. L. (1956). The system Na2O–Al2O3–SiO2.
American Journal of Science 254, 129–195.
Shaw, H. R. (1963). The four-phase curve sanidine–quartz–liquid–gas
between 500 and 4000 bars. American Mineralogist 48, 883–896.
Shen, A. H. & Keppler, H. (1997). Direct observation of complete
miscibility in the albite–H2O system. Nature 385, 710–712.
Silver, L. A. & Stolper, E. M. (1989). Water in albitic glasses. Journal
of Petrology 30, 667–710.
Stebbins, J. F., Carmichael, I. S. E. & Moret, L. H. (1984). Heat
capacities and entropies of silicate liquids and glasses. Contributions to
Mineralogy and Petrology 86, 131–148.
Steiner, J. C., Jahns, R. H. & Luth, W. C. (1975). Crystallization of
alkali feldspar and quartz in the haplogranite system NaAlSi3O8–
KAlSi3O8–SiO2–H2O at 4 kb. Geological Society of America Bulletin 86,
Stewart, D. B. (1967). Four phase curve in the system CaAl2Si2O8–
SiO2–H2O between 1 and 10 kilobars. Schweizerische Mineralogische und
Petrologische Mitteilungen 47, 35–39.
Stolper, E. M. (1989) Temperature-dependence of the speciation of
water in rhyolitic melts and glasses. American Mineralogist 74, 1247–
Thompson, J. B. & Waldbaum, D. R. (1969). Mixing properties of
sanidine crystalline solutions: (II) Calculations based on two-phase
data. American Mineralogist 54, 811–838.
Tuttle, O. F. & Bowen, N. L. (1958). Origin of Granite in the Light of
Experimental Studies in the System NaAlSi3O8–KAlSi3O8–SiO2–H2O. Geological Society of America, Memoir 74, 153 pp.
Yoder, H. S. (1965). Diopside–anorthite–water at ﬁve and ten kilobars
and its bearing on explosive volcanism. Carnegie Institution of Washington
Yearbook 64, 82–89.
Yoder, H. S., Stewart, D. B. & Smith, J. R. (1957). Feldspars. Carnegie
Institution of Washington Yearbook 56, 206–214. 683 ...
View Full Document