JOURNAL OF PETROLOGY
VOLUME 40
NUMBER 10
PAGES 1497–1507
1999
Experimental Study of the Effect of
Temperature on Water Solubility in
Natural Rhyolite Melt to 100 MPa
SHIGERU YAMASHITA∗
INSTITUTE FOR STUDY OF THE EARTH’S INTERIOR, OKAYAMA UNIVERSITY, MISASA, TOTTORI 682-0193, JAPAN
RECEIVED AUGUST 9, 1998; REVISED TYPESCRIPT ACCEPTED APRIL 29, 1999
The effect of temperature on water solubility in rhyolite melt was
experimentally determined at 850–1200°C and 22–100 MPa.
A natural high-silica rhyolite glass was equilibrated with pure
water vapor, and the water content in the quenched glass was
determined by IR spectroscopy. The results demonstrate that water
solubility in rhyolite melt has a negative temperature dependence,
which becomes weaker at high temperatures and low water contents.
This temperature dependence can be modeled adequately on the
basis of ideal mixing of water species and anhydrous rhyolite melt
components. The model reproduces both the present and previously
published solubility data for water in rhyolitic melts to 100 MPa
and over a wide range of temperature from near the solidus to
1200°C, thereby permitting calculation of water saturation under
varying temperature conditions. At 50–100 MPa, an increase in
the fraction of excess water as a result of a rise in temperature can
cause a four- to eight-fold increase in the fractional amount of
volumetric expansion above that caused by pure thermal expansion,
per unit temperature rise. Thus, the negative temperature dependence
of water solubility could be of fundamental importance in the
development of gravitational instability in shallow, water-saturated
silicic magma chambers.
A negative temperature dependence of water solubility
in rhyolitic melts has been repeatedly documented at
pressures below ~400 MPa (Tuttle & Bowen, 1958;
Burnham & Jahns, 1962; Karsten et al., 1982; Holtz et
al., 1995). Many thermodynamic models for the computation of water solubility in natural silicate melts are
now available (Nicholls, 1980; Burnham & Nekvasil,
1986; Silver et al., 1990; Papale, 1997; Moore et al., 1998),
but their use for reproducing the negative temperature
dependence of water solubility in rhyolitic melts is not
straightforward. Most of the previously published solubility experiments on natural silicate melts or synthetic
analogs were performed over a limited range of temperature (e.g. Hamilton et al., 1964; Silver et al., 1990), or
more frequently, at pressure and temperature conditions
arbitrarily chosen to follow the water-saturated liquidus
of each starting composition (e.g. Tuttle & Bowen, 1958;
Burnham & Jahns, 1962). This, together with large
uncertainties in the solubility measurements of earlier
works, has resulted in insufficient data coverage of temperature–composition space, making it difficult to model
precisely the effect of temperature on water solubility in
a silicate melt of interest (Nicholls, 1980; Papale, 1997).
The primary goal of this study was to develop a
thermodynamic model for computing water solubility in
shallow rhyolitic melts over a wide range of temperature
from near the solidus to above the liquidus. For this
purpose, I performed a series of high-precision experimental determinations of water solubility in rhyolite
melt as a function of temperature between 850 and
1200°C and at pressures of 22–100 MPa. This dataset
constrains the calorimetric property of the water solution
reaction, which is critical for modeling the temperature
dependence of water solubility.
∗Telephone: +81-858-43-3738. Fax: +81-858-43-3450.
e-mail: [email protected]
 Oxford University Press 1999
magma chamber; melting experiment; rhyolite melt; temperature dependence; water solubility
KEY WORDS:
INTRODUCTION
JOURNAL OF PETROLOGY
VOLUME 40
NUMBER 10
OCTOBER 1999
Al2O3/(CaO + Na2O + K2O) of 1·08 in molar proportion. Replicate microprobe analyses confirmed that
the sample is homogeneous in composition.
Table 1: Composition of starting
material
High-silica rhyolite WOBS
Melting experiments
(wt %)1
SiO2
77·38 ± 0·07
TiO2
0·17 ± 0·04
Al2O3
12·33 ± 0·11
FeO∗
1·26 ± 0·04
MnO
0·05 ± 0·01
MgO
0·17 ± 0·02
CaO
1·11 ± 0·03
Na2O
3·39 ± 0·09
K2 O
3·58 ± 0·04
P2O5
0·01 ± 0·01
Water2
Total
0·12 ± 0·01
99·57
(kg/mol)
Formula weight3
0·03231
1
Major element composition was determined by electron
microprobe analyses with defocused beam of 10 lm, beam
current of 1·2 nA, and acceleration voltage of 15 kV (average
± 1r of eight spot analyses, all iron as FeO).
2
Water content was determined by micro-IR spectroscopy
(average ± 1r of five spot analyses); none of the IR absorption bands related to dissolved CO2 were detected.
3
Formula weight of anhydrous composition was calculated
on a one oxygen basis.
One advantage of this approach is the ability to fully
quantify water saturation in shallow silicic magmas under
varying temperature conditions. Water saturation in a
melt causes formation of bubbles of excess water, resulting
in an increase of volume and a decrease of bulk density
in a magma (Huppert et al., 1982). I use the new solubility
model to compute the increase of excess water as a result
of temperature rise in a rhyolite melt, and provide a
new constraint on the development of thermally driven
gravitational instability in water-saturated silicic magma
chambers.
EXPERIMENTAL TECHNIQUES
Starting material
The starting material for the melting experiments was a
high-silica rhyolite sample (WOBS) collected from the
Taupo Volcanic Zone, New Zealand. The sample is
aphyric obsidian composed entirely of fresh glass. Neither
quench crystals nor bubbles were observed under a
microscope. The chemical composition of the sample is
presented in Table 1; it is slightly peraluminous with
Cylindrical fragments prepared from the rhyolite sample,
WOBS, were equilibrated with pure water vapor at
above-liquidus conditions in a Kobelco internally heated
pressure vessel. Pure Ar gas was used as the pressure
medium, and the double capsule method (Sisson & Grove,
1993) was employed to control the oxygen fugacity in
the experiments. The inner capsule was an Au25Pd-lined
Pt tube (1·5 mm diameter, ~8 mm length) containing a
single cylindrical fragment (~10 mg) of WOBS and
deionized water. The outer capsule was a Pt tube (4·7 mm
diameter, 15–20 mm length) containing Ni powder and
additional deionized water as a buffering assemblage.
The inner capsule was crimped and twisted at its end,
but not welded, to ensure that the NNO (Ni–NiO)buffered water vapor was in contact with the charge.
Additional unbuffered experiments were also carried out
using the single capsule method with an Au25Pd tube
(2·7 mm diameter, 10–15 mm length) as the container
for a cylindrical fragment (10–30 mg) of WOBS and
deionized water.
The capsule was hung by Mo wire in the hot spot of
a Mo furnace within the pressure vessel, and held for
24–96 h at the desired pressure and temperature conditions. At the end of the run, the hanging wire was
broken with a surging current, thereby letting the capsule
fall into the cold (<300°C) bottom of the vessel. This
procedure made it possible to quench the capsule nearly
isobarically. Pressures were measured with a strain-gauge
pressure transducer. Temperatures were monitored with
a W5Re–W26Re thermocouple, which was calibrated to
the melting point of Au at 100 MPa (1069°C; Mitra et
al., 1967). To calibrate the temperature gradient across
the sample, thin Au wires vertically spaced 5 mm apart
were hung in the hot spot of the furnace, and then
pressurized and heated. This procedure was repeated
over a range of temperatures chosen to blanket the
melting point of Au, and it was found that the temperature
gradient was less than 10°C over the length of capsule.
After quenching, the capsules were punctured under
a microscope and heated for ~10 min at 110°C in an
oven. The presence of free water vapor in the capsules
was confirmed by either a water spill upon puncturing
or weight loss upon heating. Each glass product was then
carefully removed from its capsule for the determination
of water content by micro-IR spectroscopy. The upper
surface of the glass product was convex toward the void
space in the capsule, but the other surface was in direct
contact with the inner capsule wall. The water spill came
1498
YAMASHITA
WATER SOLUBILITY IN RHYOLITE MELT
out of the void space adjacent to the upper surface of
the glass product. These observations suggest that the
vast portion of water vapor migrated upwards at the
beginning of the experiment; hence, the rhyolite melt
was in contact with water vapor only at its upper surface.
The presence of both NiO and Ni was confirmed
under a microscope after quenching, indicating that the
oxygen fugacity was successfully controlled along the
NNO buffer in the double capsule experiments. The
nucleation of NiO indicates that hydrogen generated in
the buffer assemblage was transferred to the pressure
medium through the outer capsule wall. This means that
in the single capsule experiments, the oxygen fugacity in
the capsule was greater than the NNO buffer. Vapor in
the system H–O is essentially pure water at oxygen
fugacities along or greater than the NNO buffer (Ohmoto
& Kerrick, 1977; Holloway & Wood, 1988). Thus, all
melting experiments were performed under the presence
of pure water vapor.
Determination of water contents of glass
products
Water contents of glass products were determined by
micro-IR spectroscopy, following the method of Yamashita et al. (1997). Each glass product was mounted in
orthodontic resin and doubly polished. Micro-IR spectroscopy was carried out using a Jasco Janssen Fourier
transform IR spectrometer with a Cassegrain beam condenser, a broad band HgCdTe detector, a Ge-coated
KBr beam splitter, a W light source, and a beam path
purged continuously with dry N2. The IR beam passed
through a 100 lm × 100 lm sample spot by adjusting
an aperture window. At least three spots were analyzed
on each sample to test for homogeneity.
The water contents (both H2Omolecular and OH group
as H2O) of samples were determined using the 1·9 lm
band (fundamental stretching–bending of H2Omolecular) and
2·2 lm band (fundamental stretching–bending of OH
group). With these absorption bands, the water concentration of a sample is given by the following equation
(Lambert–Beer’s law):
0·01802 Abs1·9 Abs2·2
Water (wt %)=100×
+
dq
e1·9
e2·2
where d is the sample thickness (m), q is the sample
density (kg/m3), Abs1·9 and Abs2·2 are the absorption
peak heights of individual bands (absorbance), and e1·9
and e2·2 are the molar absorption coefficients of individual bands (m3/mol per m). Sample thickness was
measured with a Mitsutoyo Litematic 318 displacement
gauge with an accuracy of ±2 lm. Sample density was
assumed to be constant at 2350 kg/m3, on the basis of
the density measurements of hydrous rhyolite glasses
described below. The absorption peak heights of the 1·9
lm and 2·2 lm bands were determined by subtracting
two computer-fitted Gaussian background peaks (one at
~1·8 lm and the other at ~1·0 lm). The molar absorption
coefficients were calibrated to nine standard rhyolite
glasses (water contents 1·14–4·45 wt %) that had also
been synthesized from the sample WOBS. A constant
value of each molar absorption coefficient worked well;
I obtained optimum values of 0·158 ± 0·005 m3/mol
per m and 0·199 ± 0·009 m3/mol per m for e1·9 and
e2·2, respectively, using an iterative calculation (Fig. 1).
In this calibration, the densities of the standard rhyolite
glasses were measured using Archimedes’ principle in
toluene with a precision of ±50 kg/m3. The glass density
possesses rather little variation (2320–2410 kg/m3), a
range that is comparable with the precision of the measurements. Precision of the micro-IR spectroscopy was
estimated for each sample by propagating the uncertainties in sample thickness (±2 lm), sample density
(±50 kg/cm3), absorption peak heights (±0·001), and
molar absorption coefficients (±0·005 for the 1·9 lm
band and ±0·009 for the 2·2 lm band) into the calculation of water content.
The calibrated value of e1·9 agrees with that previously
reported by Silver et al. (1990) in rhyolite glasses, but the
e2·2 value is ~15% greater than the Silver et al. (1990)
calibration. This disagreement is possibly due to either
a variability of the molar absorption coefficients stemming
from the anhydrous composition dependence (e.g. Silver
et al., 1990) or an interlaboratory bias stemming from
the background subtraction process. In any case, the use
of the molar absorption coefficients calibrated here is not
hampered, because neither of these possibilities affects
the conclusions of this study.
RESULTS
Table 2 shows the results of water solubility experiments
for the rhyolite WOBS melts. The run products were
optically homogeneous glasses with one exception: the
50 MPa/850°C run product that contains sporadic very
tiny crystals. All glass products were completely bubblefree under a microscope.
Achievement of equilibrium
All glass products listed in Table 2 are homogeneous
in dissolved water content, which strongly suggests the
achievement of melt–water vapor equilibrium. The absence of bubbles in the glass products suggests that
there was no water exsolution upon quenching. These
interpretations are reinforced by an additional solubility
experiment of shorter duration (Fig. 2). The glass product
1499
JOURNAL OF PETROLOGY
VOLUME 40
NUMBER 10
OCTOBER 1999
Effects of pressure and temperature on
water solubility
Figures 3 and 4 display the effects of pressure and
temperature on water solubility in WOBS melt. Also
shown is a projection of the water solubility surface
modeled to fit the present dataset (described below). The
water solubility in WOBS melt decreases rapidly with
decreasing pressure at constant temperature (Fig. 3). The
water solubility also decreases with rising temperature at
constant pressure (Fig. 4). Therefore, the water solubility
has a negative temperature dependence over the range
of pressure and temperature investigated. Figure 4 also
suggests that the negative temperature dependence of
the water solubility becomes weaker as temperature rises
and as pressure decreases. The origin of this phenomenon
is discussed below.
Fig. 1. Calibration of molar absorption coefficients for the 1·9 lm
and 2·2 lm bands of hydrous rhyolite glasses. These glasses were
synthesized from deionized water and dehydrated powder of the
rhyolite sample WOBS under water-undersaturated conditions, using
an internally heated pressure vessel and a piston cylinder apparatus.
Error bars indicate standard deviation (1r) of micro-IR spectroscopy
for replicate analyses of each glass. The molar absorption coefficients
were calibrated based on the water contents of the glasses as measured
by manometry (1·14, 1·46, 1·95, 2·76, 3·65, and 4·45 wt %) or calculated
from the weight proportion of loaded water to loaded powder (2·11,
2·73, and 3·28 wt %). The manometry was carried out using a method
modified after Yamashita et al. (1997): the intrinsic water was extracted
by stepwise heating under vacuum; the sample was held at a certain
temperature, at which the commencement of significant dehydration
was detected with a Pirani gauge (the samples with 1·14 and 1·46 wt
% water at 700°C, and the samples with >1·95 wt % water at
450–500°C), until the dehydration was completed, and then heated to
~1000°C.
of a 4 h run at 30 MPa/1200°C has water concentrations
decreasing toward the sample bottom, whereas the glass
product of a 69 h run at the same pressure and temperature condition is homogeneous within analytical precision. The average water content of the glass product
of the 69 h run (1·53 wt %; Table 2) was taken to be
the equilibrium value at that pressure and temperature
condition. Then, assuming instantaneous equilibrium between the upper surface of melt and water vapor, the
water concentration gradient of the 4 h run glass is
consistent with the diffusive transfer of water into a semiinfinite anhydrous medium with a diffusion coefficient of
10–10 m2/s. This value lies approximately on a hightemperature extrapolation of the Arrhenius plot for the
diffusion coefficient of water in rhyolitic melts (Karsten
et al., 1982). It is thus very likely that diffusive transfer
of water into the initially anhydrous WOBS melt (0·12
wt %; Table 1) governs the water concentration of the
glass products in the solubility experiments. Once the
water concentration has reached the equilibrium value
everywhere, further diffusive transfer of water (hence
nucleation and growth of bubbles) should not occur.
THERMODYNAMIC MODELING
Basic equations
In the model developed here, hydrous rhyolite melt is
treated as the system H2Omolecular(melt)–OH(melt)–
O(melt), following Silver & Stolper (1985), and ideal
mixing of these three components is assumed.
The melt–water vapor equilibrium is governed by the
following two reactions:
Water(vapour)↔H2Omolecular(melt)
(heterogeneous equilibrium) (1)
H2Omolecular(melt)+O(melt)↔2OH(melt)
(homogeneous equilibrium) (2)
The pressure and temperature dependence of heterogeneous equilibrium (1) can be written in the form
ln
XHm2O(P,T )
DHohetero,1bar 1 1
− −
=A1bar,Tr−
v
fwater(P,T )
R
T Tr
P
1
VHo,m
(P,T )dP
2O
RT
(3)
1
where XHm2O(P,T ) is the mole fraction of H2Omolecular(melt)
per one oxygen formula along the water solubility surface,
v
(P,T ) is the fugacity of pure water vapor,
fwater
DHohetero,1bar is the enthalpy change taken to be independent
(P,T ) is the molar volume of
of temperature, and VHo,m
2O
H2Omolecular(melt). A1bar,Tr is the numerical constant defined
v
), where XHm2O,1bar,Tr is the mole
by ln(XHm2O,1bar,Tr/fwater,1bar,T
r
fraction of H2Omolecular(melt) soluble into melt at 1 bar
and a reference temperature Tr sufficiently high for water
vapor to exist as a perfect gas.
1500
1501
100
100
100
100
wobsA8/5
wobsA10B6
wobsA10B3
wobsA10B8
850
900
1000
1200
1200
850
1000
1200
850
900
1000
1200
1000
1200
1200
T (°C)
94
68
48
24
24
87
48
24
96
52
48
24
48
69
24
NNO
NNO
NNO
>NNO
NNO
NNO
>NNO
>NNO
NNO
NNO
NNO
NNO
>NNO
>NNO
>NNO
Time (h) fo2
876
902
941
995
965
633
668
695
464
471
482
497
293
299
219
(bar)
v
a
f water
L+V
L+V
L+V
L+V
L+V
L+V
L+V
L+V
L+V+S
L+V
L+V
L+V
L+V
L+V
L+V
Product
H2Omolecularb
2·82±0·04
2·80±0·01
2·63±0·03
2·28±0·09
2·17±0·05
2·16±0·02
1·90±0·10
1·68±0·04
1·65±0·02
1·59±0·01
1·41±0·03
1·22±0·02
0·92±0·03
0·75±0·03
0·58±0·01
(wt %)
OH groupb
1·15±0·02
1·00±0·03
0·97±0·01
1·06±0·05
1·04±0·03
1·07±0·01
1·05±0·05
1·01±0·02
1·01±0·01
0·95±0·01
0·96±0·01
0·90±0·02
0·88±0·02
0·77±0·06
0·77±0·03
(wt %)
Waterb
3·97±0·06
3·80±0·03
3·61±0·03
3·34±0·13
3·21±0·04
3·24±0·03
2·95±0·15
2·68±0·06
2·66±0·03
2·54±0·01
2·38±0·04
2·12±0·03
1·80±0·04
1·53±0·08
1·35±0·03
(wt %)
Squared X waterb
0·0690±0·0009
0·0661±0·0005
0·0629±0·0006
0·0583±0·0023
0·0562±0·0006
0·0566±0·0004
0·0517±0·0025
0·0471±0·0011
0·0466±0·0005
0·0446±0·0001
0·0419±0·0007
0·0373±0·0005
0·0317±0·0008
0·0270±0·0014
0·0240±0·0005
(mol. fract.)
(6)
(4)
(4)
(3)
(8)
(5)
(5)
(3)
(6)
(5)
(5)
(7)
(4)
(5)
(3)
(n)
d
d
d
s
d
d
s
s
d
d
d
d
s
s
s
Remarksc
b
calculated based on a modified Redlich–Kwong equation of state (Holloway, 1977).
H2Omolecular and OH group contents in quenched glass were determined by micro-IR spectroscopy, using 1·9 lm and 2·2 lm bands (OH group content is given as
the amount of water dissolved as OH); water content was determined from sum of H2Omolecular and OH group; mole fraction of water (one oxygen basis) was
calculated based on the anhydrous formula weight of 0·03231 kg/mol of high-silica rhyolite WOBS; all data are given in the form average ± 1r of n spot analyses
for an individual run product.
c
s, single capsule experiment (unbuffered); d, double capsule experiment (NNO-buffered).
a
97
wobsA10B1
50
wobsA10B11
70
50
wobsA10B4
wobsA10B12
50
wobsA10B5
70
50
wobsA10B2
wobsA6/8
30
wobsA6/2
70
30
wobsA8/8
22
wobsA8/7
P (MPa)
wobsA6/4
Run no.
Table 2: Results of water solubility experiments
YAMASHITA
WATER SOLUBILITY IN RHYOLITE MELT
JOURNAL OF PETROLOGY
VOLUME 40
Fig. 2. Water concentration in quenched glass products of water
solubility experiments for different duration times at the same pressure
and temperature condition (30 MPa and 1200°C). Error bars indicate
analytical precision of micro-IR spectroscopy. The water in the glass
product of the 69 h run is homogeneously distributed within analytical
precision, whereas the 4 h run glass possesses a water concentration
gradient, which suggests that diffusive transfer of water into the melt
governs the water concentration of the quenched glass product.
NUMBER 10
OCTOBER 1999
Fig. 4. Water solubility in rhyolite WOBS melt as a function of
temperature. Also projected (dotted lines) is the water solubility surface
modeled to fit the data. Two of the solubility data (22 MPa/1200°C
and 97 MPa/1200°C) are not shown for convenience of presentation.
The mole fraction of H2Omolecular(melt) can be related
to the mole fraction of water (melt) by homogeneous
equilibrium (2) (Silver & Stolper, 1985):
m
XHm2O=Xwater
− 0·5− 0·25−
m
m 2
Xwater
−Xwater
Khomo=
Fig. 3. Water solubility in rhyolite WOBS melt as a function of pressure.
Error bars indicate analytical precision of micro-IR spectroscopy. Also
shown (dotted lines) is the water solubility surface modeled to fit the
data.
Recent progress in the understanding of equilibration
kinetics of hydrous silicate melts has revealed that homogeneous equilibrium (2) possesses a strong temperature
dependence. Consequently, the water speciation measured by IR spectroscopy in quenched glasses represents,
to some degree, rapid re-equilibration upon quenching
(Dingwell & Webb, 1990; Zhang et al., 1997). This
makes it very difficult to determine the mole fraction of
H2Omolecular(melt) along a water solubility surface on the
basis of any direct information obtained from the
quenched glass products. This difficulty prevents simple
adaptation of equation (3) for thermodynamic modeling
of the water solubility surface.
m 2
OH
m
m
H2O O
X
X
X
Khomo−4
Khomo
(4a)
Khomo−4
Khomo
0·5
DHohomo DSohomo
+
RT
R
=exp −
(4b)
m
is the mole fraction of water (melt) per one
where Xwater
m
m
oxygen formula defined by Xwater
=XHm2O+0·5XOH
,
o
o
DHhomo is the enthalpy change, and DShomo is the entropy
change. Both DHohomo and DSohomo are assumed to be
independent of pressure and temperature, and hence
homogeneous equilibrium (2) is also assumed to be independent of pressure. This latter assumption requires
that the volume change upon reaction is negligible; the
molar volume of H2Omolecular(melt) has the same quantity
as that of water(melt). Recently, Ochs & Lange (1997a,
1997b) experimentally established the equation of state
of water dissolved in melts in the system Na2O–
K2O–CaO–Al2O3–SiO2. Their equation of state is used
for calculation of the W(P,T) term that appears below.
Substituting equations (4a) and (4b) into equation (3)
yields a volume-explicit form of the water solubility
equation:
DHohetero,1bar 1 1
− −
R
T Tr
W(P,T )=A1bar,Tr−
ln
where
1502
m
U(Xwater
(P,T ),T,DHohomo,DSohomo)
v
fwater
(P,T )
(5)
YAMASHITA
WATER SOLUBILITY IN RHYOLITE MELT
P
Table 3: Model parameters
1
o,m
W(P,T )o
Vwater
(P,T )dP
RT
and
m
U(Xwater
(P,T ),T,DHohomo,DSohomo)o
DHohomo DSohomo
−4
+
RT
R
DHohomo DSohomo
+
RT
R
exp −
0·5
m
m
(Xwater
(P,T )−Xwater
(P,T )2)
DHohomo DSohomo
+
−4
RT
R
DSo
DHo
exp − homo+ homo
RT
R
.
m
In the above equations, Xwater
(P,T ) is the water solubility
in mole fraction per one oxygen formula at a given
pressure and temperature.
Optimization of model parameters
Using the Taylor series expansion, we can approximate
equation (5) to be a linear function of small changes in
the model parameters A1bar,Tr, DHohetero,1bar, DHohomo, and
DSohomo:
W(P,T )=Wo(P,T )+
∂Wo(P,T )
dA1bar.Tr+
∂A1bar,Tr
∂Wo(P,T )
∂Wo(P,T )
dDHohetero,1bar+
dDHohomo+ (6)
o
∂DHhetero,1bar
∂DHohomo
−25·3 ± 4·8 kJ/mol
DHohomo
25·8 ± 11·8 kJ
DSohomo
6·0 ± 8·7 J/K
Vo,m
water(P,T)
9·65 × 10–3T (K) – 3·61 × 10–4P (bar)
Standard errors (1r) were estimated by covariance matrix
method.
exp −
−10·52 ± 0·08 at T r = 1473 K
+ 10·80 (Ochs & Lange, 1997b)
m
Xwater
(P,T )− 0·5− 0·25−
exp −
A1bar,T
DHohetero,1bar
r
1
∂Wo(P,T )
dDSohomo
∂DSohomo
where Wo(P,T ) is the term calculated from equation (5)
using first approximations of A1bar,Tr, DHohetero,1bar, DHohomo,
m
(P,T ).
and DSohomo at a given Xwater
I minimized the sum of the unweighted squares of
residuals of equation (6) for the experimental dataset
(Table 2) using an iterative approach, which yielded
optimum values of A1bar,Tr, DHohetero,1bar, DHohomo, and
DSohomo. Standard errors (1r) of the optimized model
parameters were estimated by the covariance matrix
method, assuming that all data points have the same
v
(P,T ) were calculated by
variance. The values of fwater
using a modified Redlich–Kwong equation of state (Holloway, 1977). The iteration converged upon A1bar,Tr =
–10·52 ± 0·08 at Tr = 1473 K, DHohetero,1bar = –25·3 ±
4·8 kJ/mol, DHohomo = 25·8 ± 11·8 kJ, and DSohomo =
6·0 ± 8·7 J/K. The water solubility surface calculated
with these parameters reproduces the experimental results
for the rhyolite WOBS melt (Figs 3 and 4). The values
of all model parameters employed are listed in Table 3.
It is worth remembering that the model is based on
the assumption of pressure-independent homogeneous
equilibrium (2). This assumption appears to be valid at
relatively low pressures (i.e. below 100 MPa) because of
the successful fitting of the model parameters to the
experimental dataset. Although the DHohomo and DSohomo
values are poorly constrained, the Khomo values computed
by equation (4b) with the optimum values of DHohomo and
DSohomo fall on a high-temperature extrapolation of those
obtained by structural relaxation studies of hydrous rhyolite melts over the pressure range 0·1–150 MPa (Dingwell & Webb, 1990; Zhang et al. , 1997), within 1r error.
This agreement provides a compelling validation of the
assumption of pressure independence of homogeneous
equilibrium (2) over the range of investigated pressure.
Moreover, Ochs & Lange (1997a) showed that their
equation of state for water dissolved in silicate melts is
independent of the concentration of water, and hence is
insensitive to the speciation of water. This implies a
negligible volume change for homogeneous reaction equilibrium (2) and, therefore, an expected pressure independence for this equilibrium. Accordingly, the
optimum values of the model parameters A1bar,Tr,
DHohetero,1bar, DHohomo, and DSohomo (Table 3) are probably
valid to 100 MPa, but their use is not recommended at
elevated pressures.
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Calorimetric significance along water
solubility surface
The experimental results suggest that the negative temperature dependence of the water solubility is weaker at
lower pressures and at higher temperatures (Fig. 4). A
key to understanding this phenomenon is the calorimetric
contribution of homogeneous equilibrium (2), which is
m
strongly influenced by Xwater
(P,T ) and temperature.
Figure 5 shows a P–T projection of the water solubility
surface computed with the model parameters for WOBS
melt. The projection includes a low-temperature extrapolation of the modeled solubility surface and approximates the positions of the water-saturated liquidus
m
and solidus. The ∂P/∂T slopes at constant Xwater
(P,T ) are
positive, but their magnitudes change remarkably as a
m
(P,T ) and temperature; the ∂P/∂T slope
function of Xwater
m
becomes gentler as Xwater
(P,T ) decreases and as temm
perature rises. The ∂P/∂T slope at constant Xwater
(P,T ) is
expressed by the Clapeyron equation:
∂P
∂T
Xm
water
=
L
TDV(P,T )
(7)
where L is the latent heat of solution of water in rhyolite
melt, and DV(P,T) is the volume change. The nearly
m
zero ∂P/∂T slope at lower Xwater
(P,T ) and higher temperature is a consequence of increasing DV(P,T) and
decreasing L, where the absolute values of both are
negative. The increase in DV(P,T) with decreasing presm
(P,T )] occurs because
sure [hence with decreasing Xwater
water vapor has a greater compressibility than water
dissolved in the melt. The decrease in L arises from
the changing calorimetric contribution of homogeneous
equilibrium (2) to L. Under the assumption of ideal
mixing (no heat of mixing), the latent heat, L, can be
written in a simple linear form:
L=DHohetero+HDHohomo
(8)
where
m
(P,T )−XHm2O(P,T )
Xwater
.
m
Xwater
(P,T )
Ho
In the above equations, H is the fraction of water that
has been converted to OH groups by homogeneous
equilibrium (2). It is seen from equation (4a) that
m
XHm2O(P,T ) approaches zero as Xwater
(P,T )→0. Thus H
m
approaches unity as Xwater(P,T )→0, which thereby yields
the maximum contribution of DHohomo to L. It is also
expected from equation (4b) that H approaches unity at
very high temperatures. As homogeneous equilibrium (2)
is endothermic, whereas heterogeneous equilibrium (1)
m
(P,T )
is exothermic (Table 3), L must decrease as Xwater
decreases and as temperature rises. At this time, it is
difficult to provide further quantitative constraints on
Fig. 5. P–T projection of the water solubility surface modeled for
rhyolite WOBS melt. Contour lines are P–T trajectories of constant
water solubility at 0·2 wt % intervals. The lines labeled L and S
approximate the positions of the water-saturated liquidus and solidus,
respectively, which were estimated from available phase diagrams
(Tuttle & Bowen, 1958; James & Hamilton, 1969).
the L values because the standard errors of the model
parameters are too large.
EVALUATION OF MODEL
Comparison with compiled data
Figure 6 shows a compilation of water solubility data in
rhyolitic melts determined by previous workers along or
above the liquidus to 100 MPa (high-silica rhyolite KS,
Silver et al., 1990; haplogranite TM, Tuttle & Bowen,
1958; Harding pegmatite HP, Burnham & Jahns, 1962;
haplogranite AOQ, Holtz et al., 1995). To avoid any bias
stemming from minor compositional difference among
these starting materials, each solubility datum was recalculated to mole fraction of water per one oxygen
formula. Projection of the water solubility surface
modeled for the rhyolite WOBS melt is also shown for
comparison. The CIPW norm projection of KS, HP,
TM, AOQ, and WOBS into the system Qz–
Ab–Or–An–H2O is shown in Fig. 7. Also shown are the
liquidus phase boundaries in the system at 100 MPa,
under water-saturated condition (Tuttle & Bowen, 1958;
James & Hamilton, 1969), and these boundaries do not
change much at lower pressures.
The experimental determinations of water solubility in
the KS, HP, and TM melts fall to the low-temperature
side relative to this study; some of them are below the
liquidus of the WOBS melt (Figs 5 and 6). Overall, these
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YAMASHITA
WATER SOLUBILITY IN RHYOLITE MELT
Fig. 6. Water solubility in melts for a variety of rhyolitic compositions
(high-silica rhyolite KS, Silver et al., 1990; haplogranite TM, Tuttle
& Bowen, 1958; Harding pegmatite HP, Burnham & Jahns, 1962;
haplogranite AOQ, Holtz et al., 1995). Each datum was recalculated
to mole fraction of water per one oxygen formula. Error bars were
taken from the literature. Also projected (dotted lines) is the water
solubility surface computed with the model parameters optimized for
rhyolite WOBS melt. Some of the solubility data (symbols labeled by
the numbers indicating pressures in MPa) fall off the model solubility
surface.
degree of crystallization. This agreement, therefore, suggests that at pressures below 100 MPa, the model can
be extended to temperatures near the solidus whenever
the compositional effect on water solubility (Holtz et al.,
1995) can be avoided.
Holtz et al. (1995) attempted to determine water solubility in rhyolitic melt (AOQ in Fig. 7) well above the
liquidus. Figure 6 demonstrates that their experimental
data are also broadly concordant with the model solubility
surface fitted to the WOBS melt. Holtz et al. (1995) showed
that in the system Qz–Ab–Or–H2O, the water solubility
increases with increasing amounts of normative Ab component in the melt, a component that becomes significant
above 100 MPa. Thus the overall agreement between the
compiled data and the model solubility surface (Fig. 6)
is understandable because of the rather limited range of
normative Ab component among the five starting materials
(<10 wt %; Fig. 7) and the relatively low-pressure conditions (below 100 MPa). It is noteworthy that the anhydrous compositions of KS, HP, TM, AOQ and WOBS
span the range of common natural rhyolites (Tuttle &
Bowen, 1958, fig. 41). The solubility model presented here
is, therefore, capable of predicting water solubility in natural rhyolitic melts to 100 MPa, over a wide range of
temperature from near the solidus (~700°C) to 1200°C.
Comparison with other water solubility
models
Fig. 7. The CIPW norm projection (wt %) of rhyolitic rocks or
synthetic oxide mixtures used as starting materials in water solubility
experiments (high-silica rhyolite WOBS, this study; high-silica rhyolite
KS, Silver et al., 1990; Harding pegmatite HP, Burnham & Jahns,
1962; haplogranite TM, Tuttle & Bowen, 1958; haplogranite AOQ,
Holtz et al., 1995). Also projected are liquidus phase boundaries under
water-saturated conditions at 100 MPa (Tuttle & Bowen, 1958; James
& Hamilton, 1969). Thermal minima of the system at pressures to 100
MPa are approximated by the position of TM.
solubility data show general agreement with the lowtemperature extrapolation of the model solubility surface
fitted to the WOBS melt, within the analytical precision
reported by the researchers (Fig. 6). The rhyolite WOBS
is close to the thermal minima in the system Qz–
Ab–Or–An–H2O at pressures below 100 MPa, and so
are KS, HP, and TM (Fig. 7), so that its anhydrous melt
composition would remain in the vicinity of the other
three starting materials regardless of temperature or
The water solubility model proposed by Burnham and his
coworkers (Burnham & Davis, 1974; Burnham & Nekvasil,
1986) has been widely used by petrologists for the computation of water solubility in silicate melts for a variety of
compositions. Figure 8 shows a projection of the water
solubility surfaces for WOBS melt computed by both the
present model and the Burnham model. It is seen in Fig. 8
that the Burnham model gives a poorer fit to both the
present and previously published solubility data in rhyolitic
melts below 100 MPa. For example, let us consider the
magnitude of the temperature dependence of water solubility. According to the present model, water solubility in
rhyolitic melts decreases by ~1·3 wt % as temperature rises
from 700°C to 1200°C at 100 MPa. The Burnham model,
on the other hand, predicts a decline in solubility of only
~0·4 wt % for the same rise in temperature, which is onethird of the temperature dependence obtained in this study.
Such a large discrepancy probably stems from the fact
that the Burnham model depends on the activity coefficient
of water dissolved into melt (both H2Omolecular and OH
group as OH group), which was formulated as a function
of pressure and temperature by integrating the molar volume of water (melt) with respect to pressure over a range
from 100 to 1000 MPa and 700 to 1100°C. In this integration, the Burnham model utilizes an empirical equation of state for water (melt) (Burnham & Davis, 1971),
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JOURNAL OF PETROLOGY
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NUMBER 10
OCTOBER 1999
solubility model presented here permits a quantitative
evaluation of how such a phenomenon can be a significant
magmatic process.
The fractional volume increase per unit temperature
rise, f(P,T ), is given by solving the following equation
numerically:
f(P,T )=
1
Xj(P,T )Vj(P,T )
Xj(P,T+dT )Vj(P,T+dT )−Xj(P,T )Vj(P,T )
Fig. 8. The water solubility surface computed with the model parameters optimized in this study is compared with the water solubility
surface computed by two other methods (Burnham & Nekvasil, 1986;
Moore et al., 1998). All solubility surfaces were computed for the same
anhydrous composition, the rhyolite WOBS, in mole fraction per one
oxygen formula. Actual water solubility data in rhyolitic melts (WOBS,
KS, HP, TM and AOQ melt) are also shown by large filled circles for
comparison.
but this equation of state greatly overestimates the molar
volume of water (melt) below 200 MPa and above 1000°C
(Ochs & Lange, 1997a). This, in turn, results in the overestimation of the activity coefficient of water dissolved into
melts under relatively low-pressure and high-temperature
conditions, and hence the greater water solubility and
smaller temperature dependence (Fig. 8).
Also shown in Fig. 8 is a more recent water solubility
model proposed by Moore et al. (1998), which is applicable
to 300 MPa over the temperature range 700–1200°C.
Their model and the present model give equally good fits
to the solubility data. Moore et al. (1998) treated hydrous
silicate melts as a mixture of water (both H2Omolecular and
OH group as OH group) and anhydrous elemental oxide
compounds, but they did not address the non-ideal behavior of the mixture expected from such a treatment.
Thus their solubility model is rather empirical, but its
algebraically simple form makes it easy to use.
PETROLOGIC IMPLICATION
Silicic magmas stagnant at shallow crustal chambers are
not only cooled by conductive heat loss, but are also heated
from below by underplating of hotter mafic magmas (e.g.
Hildreth, 1981). When such a silicic magma is saturated
with respect to water, the fraction of water vapor exsolved
increases with rising temperature as a result of the negative
temperature dependence of water solubility in a rhyolitic
melt portion (Fig. 5). The exsolution of water vapor causes
an increase of the volume of the magma as a result of
formation of water vapor bubbles, which thereby can affect
the magnitude of thermal expansion of the magma. The
dT
(9)
where Xj(P,T ) are the mole fractions of anhydrous rhyolite
melt, water dissolved into the melt, and water vapor,
Vj(P,T ) are the molar volume of each of them, and dT
is a small increment of temperature. For simplicity, I have
treated the silicic magma as a closed system consisting of
hydrous rhyolite melt and water vapor. In this case, using
the solubility model presented above, it was possible to
compute the mole fractions of anhydrous rhyolite melt,
water dissolved into the melt and water vapor, at the
pressure, temperature and bulk water content of interest.
The molar volume of each component was computed by
available equations of state (Holloway, 1977; Lange,
1997; Ochs & Lange, 1997a, 1997b).
For any temperature increment over the temperature
range from near the solidus to 900°C, the calculated f(P,
T ) value remains approximately constant at ~5 × 10–4/
K at 50 MPa (~2 km depth), or ~4 × 10–4/K at 100
MPa (~4 km depth), whenever the melt is water saturated
and the mass fraction of pre-existing water vapor does
not exceed 10–3, a maximum value permissible in mechanically stable magma chambers (Blake, 1984; Tait et al.,
1989). The fractional volume increase as a result of pure
thermal expansion (i.e. when the water solubility remains
unchanged regardless of temperature) calculated for such
a system is ~6 × 10–5 to ~9 × 10–5/K at 50 MPa,
depending primarily on the mass fraction of pre-existing
water vapor, or ~8 × 10–5 to ~1 × 10–4/K at 100 MPa.
Thus, the contribution of the negative temperature dependence of water solubility is large enough to increase
the fractional amount of volumetric expansion four to
eight times greater than the pure thermal expansion, per
unit temperature rise.
This argument is valid when the temperature changes
over a limited portion of a magma chamber, because
the calculation is based on the assumption that the
pressure remains unchanged when the temperature and
volume change, regardless of mechanical property of
chamber wall [equation (9)]. Such a situation can, indeed,
occur in a thermal boundary layer which is being
thickened by conductive heat transfer in a rhyolite melt–
water vapor system (Brandeis & Jaupart, 1986). The
Rayleigh number of the layer is proportional to f(P,
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YAMASHITA
WATER SOLUBILITY IN RHYOLITE MELT
T)DTd 3, where DT is the temperature difference across
the layer and d is the layer thickness. It is then envisaged
that to achieve a critical value of the Rayleigh number,
the layer thickness, d, can be halved by the contribution of
the negative temperature dependence of water solubility.
This can, in turn, cause a quarter-fold decrease in the
time scale of the development of gravitational instability
of the layer, as the layer thickness is proportional to the
square root of time. Therefore, the negative temperature
dependence of water solubility is of fundamental importance for better understanding of convection phenomena
in shallow, water-saturated silicic magma chambers.
ACKNOWLEDGEMENTS
I thank Yoshie Ogo, Kazuhito Ozawa, Michael Walter
and Atsushi Yasuda for their helpful comments. Reviews
by Victor Kress, Rebecca Lange and Gordon Moore
significantly improved this manuscript. This study was
supported by Grant-in-Aid for Scientific Research (No.
09740396) from the Ministry of Education, Science and
Culture of Japan.
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