Earth and Planetary Science Letters 258 (2007) 561 – 568
www.elsevier.com/locate/epsl
Rutile saturation in hydrous siliceous melts and its bearing on
Ti-thermometry of quartz and zircon
Leslie A. Hayden ⁎, E. Bruce Watson
Department of Earth & Environmental Sciences, Rensselaer Polytechnic Institute, 110 8th St Troy, NY 12180 USA
Received 17 January 2007; received in revised form 1 April 2007; accepted 5 April 2007
Available online 19 April 2007
Editor: R.W. Carlson
Abstract
The TiO2 solubility of rutile-saturated hydrous siliceous melts has been investigated at P = 1 GPa and T = 650–1000 °C for
several representative felsic compositions. The dissolution of a rutile crystal into a TiO2 undersaturated melt provides information
on both TiO2 solubility and Ti diffusion. Results of this study confirm that TiO2 solubility is strongly dependent on both
temperature and melt composition, but not on the amount of H2O present. For a given T, TiO2 content decreases as the melts
become more felsic. The solubility of TiO2 is given by:
logðTi; ppmÞ ¼ 7:95 5305
þ 0:124FM
T
where T is in K and FM is a melt composition parameter,
FM ¼
1 Na þ K þ 2ðCa þ Mg þ FeÞ
:
Si
Al
in which the chemical symbols represent cation fractions.
Results of dissolution experiments yield an activation energy (E ) for Ti transport in a hydrous felsic melt of 186 ± 27 kJ/mol and
a frequency factor, Do, of 3.6 ± 1.2 m2/s. These results suggest an activation energy similar to that established for Zr diffusion in
similar melts, but with Ti diffusion rates 2–3 orders of magnitude faster.
Both TiO2 solubility and Ti diffusion have important applications in geothermometry, particularly in light of new thermometers
calibrated for the incorporation of Ti into quartz and zircon. Rutile saturation is improbable in the types of melts where these
thermometers are most likely to be useful, and therefore it is important that rutile solubility behavior in these melts to be wellconstrained. TiO2 activities in silicic melts at typical magmatic temperatures are generally 0.6 or higher, implying that Ti
thermometry of out-of-context zircons will rarely underestimate zircon crystallization temperature by more than ∼ 50 °C.
© 2007 Elsevier B.V. All rights reserved.
Keywords: rutile; solubility; diffusion; quartz; zircon; thermometry
⁎ Corresponding author. Tel.: +1 518 276 6474; fax: +1 518 276
2012.
E-mail addresses: haydel@rpi.edu (L.A. Hayden),
watsoe@rpi.edu (E.B. Watson).
0012-821X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2007.04.020
1. Introduction
The systematic incorporation of titanium into quartz
and zircon has generated two new geothermometers with
562
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
the potential to be powerful tools in crustal petrology. The
calibration of these thermometers requires the coexistence
of rutile with quartz or zircon, a scenario that rarely occurs
in the types of melts where these thermometers are most
likely to be applied. This has resulted in the need to
constrain rutile saturation behavior in hydrous siliceous
melts in order to better define the actual TiO2 activity in
melts where rutile is not present. Here we present the
results of an investigation of rutile solubility as a function
of melt composition and temperature over the range of
650–1000 °C at 1 GPa utilizing an approach that also
yields information on Ti diffusion.
Table 1
Electron probe microanalysis of glass starting materials
SiO2
TiO2
Al2O3
FeO
MgO
CaO
Na2O
K2O
FM
ASI a
Na/K
a
2. Experimental
2.1. General approach—thermodynamic analysis
Trondhjemite
S-type granite
LCO
Intermediate mix
70.94
0.23
14.99
1.35
0.72
3.46
5.96
1.44
2.17
0.968
6.289
75.45
0.12
15.85
0.55
0.16
0.48
2.84
1.80
0.79
1.246
2.398
75.64
0.10
13.62
0.70
0.07
0.35
3.34
2.26
0.96
1.066
2.247
73.29
0.17
14.31
1.03
0.391
.91
4.65
1.85
1.44
1.046
3.820
Alumina Saturation Index, molar Al2O3/(CaO + Na2O + K2O).
where γ is the activity coefficient and X is the mole
fraction of TiO2 in the melt, and ΔGo is the standard
state free energy change for the dissolution reaction, R is
the gas constant and T is absolute temperature. If gmelt
TiO2 is
assumed to be constant, then because of the dependence
of Keq on 1/T we should expect the log–linear
relationship between Ti concentration in the melt and
inverse absolute temperature, as seen in the Ryerson–
Watson (R–W) model [1].
commercially grown rutile crystals. Both the trondhjemite
and S-type peraluminous granite were prepared from
oxides, ground under ethanol, and then subjected to three
fusion cycles in a Pt crucible at 1400 °C. The intermediate
composition glass powder was prepared by mixing equal
amounts of finely ground trondhjemite and Lake County
Obsidian (LCO), which was also fused at 1400 °C. The
glasses were inspected to make sure that no TiO2
remained undissolved following the fusion cycles.
These particular melts were chosen because they not
only cover a compositional range in terms of Si content
but also have chemically distinct features that may affect
rutile solubility, such as a high Na/K ratio in trondhjemite
and the strongly peraluminous S-type granite.
All experiments were run in a piston–cylinder
apparatus under hydrous conditions using the assembly
illustrated in Fig. 1. A welded pressure-sealing capsule of
either Pt, Au, or Ag60Pd40 was inserted into an oxidized Ni
cylinder with several wells. A synthetic, polished rutile
crystal was placed in the bottom of the capsule, which was
then tightly packed with one of the four powdered silicate
glasses. Distilled H2O (2–15 wt.%) was added with a
syringe, then a metal gasket was placed on top, followed
by an oxidized Ni lid. The sample was placed within the
assembly so that the center of the capsule would be at the
‘hot spot’ during the run. Assemblies consisted of NaCl
and Pyrex® sleeves with internal filler pieces of crushable
MgO, Pyrex®, and fired pyrophyllite. All experiments
were run in a 19 mm diameter assembly. Run temperatures
were monitored using a W97Re3–W75Re25 thermocouple.
All experiments were run at 1 GPa, over a temperature
range of 650–1200 °C and for durations of 2–336 h.
2.2. Experimental details
2.3. Analysis
Both natural and synthetic siliceous glasses were used
as starting materials in this study (Table 1), along with
The Cameca SX 100 electron microprobe was used
for all analyses of Ti in hydrous glasses. Analyses were
This project expands on the previous work by
Ryerson and Watson [1] and Green and Adam [2] on
rutile saturation in magmas. The overall objective of this
study was to determine the amount of the dissolved
essential structural constituent (ESC), TiO2, required to
saturate felsic melts of various compositions in the
accessory mineral of interest, in this case rutile. Rutile
saturation represents the simplest possible case in which
a single oxide, TiO2, is the only ESC.
If the saturation of a melt in rutile is expressed at
equilibrium by TiOrutile
X TiOmelt
then the equilibrium
2
2
constant is
Keq ¼
amelt
½TiO2 melt
TiO2
¼ rutile
:
½TiO2 rutile aTiO2
ð1Þ
f1, so
Because rutile is essentially pure TiO2, arutile
TiO2
Kiamelt
,
and
thus
TiO2
melt
melt
amelt
TiO2 ¼ gTiO2 d XTiO2 ¼ exp
DGo
RT
ð2Þ
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
563
Fig. 1. Piston–cylinder assembly (left) and capsule design (right).
performed with a 40 μm beam at 15 kV accelerating
potential and sample currents ranging from 35–55 nA
for Ti and 10 nA for major elements. Kα X-rays were
collected through TAP crystals for Al, Si, Na and Mg;
through LPET crystals for K, Ca, and Ti; and through an
LiF crystal for Fe. Acquisition times were 60 s for Ti and
20 s for major elements, except Na and K; these
elements are quite mobile in hydrous glasses under the
electron beam and were measured first and for only 10 s
to minimize losses. In order to confirm accurate
measurement of Na and K, a test series was run which
involved repeat analysis of the same spot. After three
repeat analyses, Na and K values remained constant,
which indicated that they were not being lost during
analysis. Dissolved H2O was estimated by difference
from a 100% total, which served to confirm the
measured amounts of H2O added to the capsules prior
to the experiments. During X-ray acquisition, two of the
five spectrometers were devoted to simultaneous
counting of the Ti peak, and the peaks were averaged
at the end of the analysis to obtain a concentration.
These analytical procedures resulted in a detection limit
of ∼ 50 ppm Ti, which was well below the Ti
concentrations in the lowest temperature experiments
(where Ti ≈ 300 ppm). Although Ti detectability was not
an analytical problem, the potential for secondary
fluorescence of Ti was a concern that needed to be
addressed. Analytical problems were encountered in
preliminary experiments that involved growth of rutile
crystals from glassy starting materials that had been predoped with (dissolved) TiO2. Attempts were made to
analyze the glass following precipitation of rutile, but
Table 2
Microprobe analyses of selected rutile-saturated glasses
Run No.
RS10
RS8
RS13
RS16
RS11
RS9
RS14
Starting composition
Trondhjemite
T (°C)
1000
900
800
700
1000
900
800
1000
900
800
1000
900
800
SiO2
TiO2
Al2O3
FeO
MgO
CaO
Na2O
K2O
H2O
Total
FM
65.33
0.99
13.92
0.58
0.51
3.19
4.59
1.39
9.50
100
1.874
66.44
0.70
14.25
0.65
0.57
3.21
4.28
1.48
8.42
100
1.810
68.34
0.23
12.99
0.23
0.59
3.06
5.08
1.51
7.97
100
1.976
70.07
0.09
14.05
0.35
0.17
1.96
5.33
1.54
6.44
100
1.569
70.93
0.84
14.59
0.41
0.15
0.94
2.55
3.56
6.03
100
0.787
70.56
0.61
14.19
0.3
0.17
0.97
2.33
3.75
7.12
100
0.807
71.41
0.2
13.22
0.02
0.24
1.06
2.77
4.21
6.87
100
0.792
71.17
0.54
13.32
0.27
0.06
0.43
3.14
2.55
8.06
100
0.970
71.82
0.39
13.44
0.2
0.08
0.57
3.14
2.35
8.01
100
0.952
72.09
0.2
13.91
0.03
0.13
0.57
3.41
2.51
7.15
100
0.966
68.1
0.79
14.26
0.55
0.41
1.97
4.1
1.93
7.89
100
1.495
68.5
0.64
13.06
0.22
0.35
1.81
4.2
2
9.22
100
1.500
68.75
0.25
13.49
0.22
0.29
1.9
4.45
2.11
8.54
100
1.521
S-type granite
RS12
RS21
RS15
LCO
Normalized to 100%. H2O calculated by difference. Average of 15–30 analysis spots.
RS25
RS26
RS27
Intermediate mix
564
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
Fig. 2. Least-squares multi-variable calibration of rutile solubility
model for siliceous melts. Solid line represents the solubility curve for
a melt of FM = 1.5 based on the solubility equation.
the crystals were very small and dispersed throughout
the glass, which led to significant secondary fluorescence of Ti in rutile during analysis of nearby glass. This
led to the current experimental design involving the
dissolution of a large single crystal at one end of the
capsule. To avoid secondary fluorescence effects near
the rutile crystal, analytical traverses were initiated at
least 100–150 μm from the crystal/glass interface,
extending roughly along the axis of the generally
cylindrical sample to capture the entire diffusion profile.
Analyses were made every ∼ 100 um, to obtain
approximately 35–40 data points along the length of
the sample and to avoid overlap of analysis spots.
Continuous analytical traverses were not possible in
experiments run at temperatures below the liquidus of
major phases; in these cases the glass was analyzed in
selected spots near the rutile under the same operating
conditions described above. Complete EMP analyses for
selected runs are given in Table 2.
rutile solubility employs the parameter FM, which also
proved suitable for describing the solubility behavior in
this study. FM is a compositional parameter given by
where chemical symbols repFM ¼ Si1 d NaþKþ2ðCaþMgþFeÞ
Al
resent cation fractions. The quasi-thermodynamic rationale for the parameter is given by Watson and Harrison [6]
and Ryerson and Watson [1].
The solubility data are generally coherent and the
variations with temperature and melt composition are
highly systematic. As seen in Figs. 2 and 3, there is, as
expected, indeed a log–linear relationship between Ti
concentration and T- 1. A new solubility model for rutile
was determined by a multi-variable least squares analysis
for temperature and melt composition for 31 experiments
and is given as
5305ðF103Þ
T
þ 0:124ðF0:023ÞFM
logðTi; ppmÞ ¼ 7:95ðF0:09Þ ð3Þ
(1σ errors) which provides a good fit to the data. This
extended portion of the R–W model deviates somewhat
from the original version; for example, a melt with an FM
value of 1.5 at 750 °C is expected to have a saturation
value of ∼ 900 ppm Ti compared to ∼1800 ppm Ti as
predicted by the original R–W model. However, it is
important to bear in mind that the R–W calibration was
for much more mafic melt compositions, and the
application to the silicic melts of interest here requires
significant extrapolation. Given the differences between
the two models, the question arises of how far beyond the
range of compositions covered in this study can the
Hayden–Watson (H–W) model be safely extrapolated?
The difference between the two models is primarily the
result of the overall fit of data in the R–W model being
3. Results and discussion
3.1. Rutile solubility
The solubility of rutile was obtained by the dissolution
of a rutile crystal and subsequent diffusion of TiO2 into the
melt. The estimated titanium concentration at the crystal–
melt interface, Co, is the amount of Ti that can be
dissolved in the melt at the run temperature. Complete
results are given in Fig. 2. Because of the variable H2O
content of the 30+ experiments, values have been
normalized to correspond to an anhydrous melt. Rutile
solubility is a function of both temperature and melt
composition, so a compositional parameter is required to
systematically describe the results. The R–W model for
Fig. 3. Log–linear dependence of rutile solubility on inverse absolute
temperature for various melt compositions in experiments run above
melt liquidus (800–1000 °C).
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
heavily influenced by the high temperature data for
mafic compositions (FM ≥ 4). There are clearly two
distinct trend lines in the R–W data; one for hightemperature mafic compositions and a second for lower
temperature silicic compositions. The combination
of these silicic low-temperature R–W data with the
new H–W data would form a consistent band of data
over the entire spectrum of silicic compositions. Thus the
H–W solubility model can be safely extrapolated to
silicic compositions beyond the scope of this study.
3.2. Effect of composition on TiO2 solubility
The dependence of TiO2 solubility on FM is illustrated
in Fig. 4. For a given temperature, TiO2 solubility
increases as FM increases, or as the melt becomes more
basic. For a given melt composition as represented by FM,
rutile solubility increases with temperature. The compositional effects are greater at higher temperatures, with
solubility values converging as melts approach the
liquidus. As previously mentioned, the starting glass
compositions were selected not only for their range of FM
values but also because they represented variety in both
alkali composition (mole fraction Na/K) and in alumina
saturation index, or ASI (mole fraction Al2O3/[CaO +
Na2O + K2O]). It does not appear that the Na/K value
alone is a factor in determining TiO2 solubility at a given
temperature. As expected, TiO2 solubility does show a
relationship with ASI, where solubility is relatively
constant for ASI N 1, then shows a significant increase
as the melt transitions to an alumina-undersaturated state.
This is the result of a TiO2 dissolution mechanism that
involves the complexation of titanate with mono- and
divalent cations present in excess of that required for
charge balance of Al3+ in 4-fold coordination [3].
3.3. Effect of H2O on TiO2 solubility
The rutile solubility model of Ryerson and Watson
[1] adequately described both anhydrous and hydrous
data without explicitly including H2O melt contents, and
it was thus concluded that H2O has little effect on rutile
solubility. All of the experiments in this study were
hydrous, including melts both saturated and undersaturated in H2O, and the results were also sufficiently well
modeled without including a parameter for H2O content,
suggesting little or no effect on solubility. Several
experiments were conducted to specifically examine the
effect of variable water content on rutile solubility. RS37 and -38 were run with the S-type granite composition
at 900 °C and 1 GPa for durations of 2.5–100 h with
water contents of ∼12 and ∼ 7 wt.%, respectively (with
12 wt.% being the approximate solubility of H2O in the
melt at these conditions). RS-41 and -42 were also run in
S-type granite at the same P–T conditions but with
water contents of ∼2.5 and ∼4 wt.%, respectively. Runs
RS-9 and -20 had also been run in S-type granite at
900 °C and contained ∼ 9 and ∼ 6 wt.% H 2O
respectively. Results of these experiments confirm that
water content does not have a significant effect on rutile
solubility over the range examined.
3.4. Diffusion
In experiments run at temperatures above the majorphase liquidus, dissolution of the large rutile crystal
resulted in a Ti concentration profile in the glass that is
characteristic of diffusion as the transport mechanism
(Fig. 5a). These profiles provide information necessary
to calculate diffusion coefficients for Ti in these melts.
Because of interference from major mineral phases, not
all experiments yielded systematic diffusion profiles.
There is also significant scatter in the diffusivity values,
and the data gleaned from this study should be
considered preliminary.
To compute a diffusion coefficient from the data, the
experiments were assumed to conform to the following
boundary conditions: the rutile/melt interface at x = 0 is
fixed; the rutile and melt are semi-infinite regions, with
the glass having some uniform background concentration. The solution of Fick's Second Law for these initial
and boundary conditions is given by
Cðx;tÞ ¼ Co þ ðCb Co Þerf
Fig. 4. Effect of melt composition (FM) on rutile solubility.
565
x
pffiffiffiffiffi
2 Dt
ð4Þ
where C(x,t) is the concentration of Ti at a distance x
from the crystal–glass interface at time t, Co is the
566
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
Fig. 5. Example of diffusion profile in glass. Run RS-11, standard error
function fit. R2 = 0.9979 (a) Linearized profile of run RS-11 (b).
solubility of Ti in the melt, Cb is the initial background
concentration of Ti in the melt, and D is the diffusion
coefficient. The assumption of a stationary boundary is
not entirely accurate, since the Ti present in the melt has
become available as a result of the dissolution of the
rutile. However, this proves to be insignificant here as
the movement of the boundary is extremely small
compared to the length of the diffusion profile.
In addition to computing D by fitting the profile to
Eq. (4), we have also linearized the profile by inverting
the data through the error function. Concentration data
are recast as
erf 1
Cx;t Co
x
¼ pffiffiffiffiffi
Cb Co
2 Dt
ð5Þ
where the solubility, Co, is a variable within a limited
range. These transformed data are plotted against x and
the fit of the line is determined by a least squares
regression. The data are reduced using a succession of
trial Co values close to the value measured by EMP. The
value of Co that yields a zero intercept of the line is the
Ti solubility in the melt. Once the value of Co is
determined,
pffiffiffiffiffiffiffiffi the slope of the corresponding line is equal
to 1= 4Dt , and determination of D requires only the
known value of t. This data treatment is shown in
Fig. 5b.
Calculated values of D and their associated errors are
given in Table 3 and shown in Fig. 6. All diffusion
experiments contained between ∼ 5 and 12 wt.% H2O.
The effect of variable H2O content on diffusivity is not
likely to be significant under these experimental
conditions. Previous work by Watson [4,5] indicates
that most of the increase in log D occurs over the first 2–
3 wt.% of dissolved H2O before reaching a plateau
between 4 and 6 wt.%. Therefore water content was not a
variable of concern in characterizing Ti diffusion in these
melts. These data define the Arrhenius relationship
D = Doexp(− E/RT), in which the activation energy, E, is
equal to 186 ± 27 kJ/mol and the frequency factor, Do, is
3.6 ± 1.2 m2/s.
Both titanium and zirconium are important trace
elements in thermometry of granitic rocks. The solubility
and diffusion behavior of Zr in hydrous granitic melts has
been well characterized [4,6]. It is worth noting that the
preliminary data for diffusivity of Ti indicates that
diffusion is 2–3 orders of magnitude faster than that of
Zr (Fig. 6). The implications of Zr being the slower
diffusing species are significant to the crystallization
thermometer for Ti in zircon recently developed by
Watson et al. [7]. Zircon growth from a melt is rate-limited
by Zr diffusion. Ti diffusion is faster and therefore Ti can
diffuse away from the advancing crystal–melt interface of
the growing zircon, precluding accumulation of dissolved
Ti and local rutile saturation in the diffusive boundary
layer [8] and thus precluding disequilibrium in Ti
partitioning between the zircon and the melt.
Table 3
Diffusivity of Ti
Experiment
Temperature
(°C)
Duration
(h)
Diffusivity
(m2/s)
RS-8
RS-9
RS-11
RS-15
RS-25
RS-27
RS-28
RS-29
RS-31
RS-36
900
900
1000
800
1000
800
1200
1200
850
950
100
100
20
336
24
72
2
2
48
25
2.23E− 12 ± 2.85E− 13
7.00E− 13 ± 6.57E− 14
4.97E− 12 ± 1.54E− 13
9.05E− 13 ± 2.51E− 13
1.59E− 12 ± 2.23E− 13
1.42E− 13 ± 3.44E− 14
1.27E− 10 ± 2.16E− 11
1.34E− 10 ± 7.25E− 11
1.07E− 12 ± 1.75E− 13
1.36E− 12 ± 8.11E−14
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
567
4. Applications to Ti thermometry
Table 4
TiO2 activities of select rocks
While there are few direct thermometry applications
of this work due to the infrequent occurrence of rutile in
igneous systems, it has important implications for the
recently developed geothermometers based on Ti
incorporation in quartz and zircon.
The Ti-in-quartz (or TitaniQ) [9] and Ti-in-zircon
thermometers [7,10,11] are two experimentally based
geothermometers that define a log–linear relationship
between Ti concentration in the respective mineral and
inverse absolute temperature. Each geothermometer was
calibrated in the presence of rutile, thus with aTiO2 = 1.
The most accurate application of these thermometers to
rutile-absent systems requires accounting for sub-unity
aTiO2, which can be constrained by the solubility model
and presented here. The thermometers when adjusted for
a rutile-absent system are
Sample
TiO2 glass
(ppm)
FM
T range
(°C)
aTiO2
Taylor Creek
rhyolite [13]
Taupo[14]
Alid volcanics
[15]
Yellowstone
melt incl. [16]
Bishop Tuff
rhyolite I [9]
Bishop Tuff
rhyolite II [9]
Lund [17]
Fraction [17]
Toiyabe [17]
Hiko [17]
Fish Canyon [17]
Vista lava [17]
1103
1.45
775–840
0.66 ± 0.28
3000
1200
2.01
1.91
810–860
840–900
1.16 ± 0.34
0.34 ± 0.11
1567
1.64
800–900
0.58 ± 0.38
425
1.5
730
0.60
900
1.5
800
0.58
890
497
656
844
802
648
1.4
1.4
1.4
1.6
1.5
1.5
754–814
734–786
754–762
748–763
746–772
739–783
0.70 ± 0.28
0.51 ± 0.18
0.69 ± 0.03
0.86 ± 0.08
0.81 ± 0.13
0.64 ± 0.19
3765
T ð CÞ ¼
273
h Qtz i
XTi
log aTiO 5:69
-
ð6Þ
2
and
T ð-CÞ ¼
4800
273
log½XTiZrc þ log½aSiO2 log½aTiO2 5:711
ð7Þ
for Ti-in-quartz and Ti-in-zircon, respectively.
As seen in Eq. (6), the Ti-in-quartz thermometer is
relatively straightforward in terms of the adjustment for
the aTiO2 of the system. In the case of the Bishop Tuff
rhyolite, there is good agreement between the aTiO2
predicted by the solubility model (0.58–0.60), the aTiO2
Fig. 6. Diffusivity of Ti vs. Zr in comparable melts. Zr diffusion data
from Harrison and Watson ([4]).
The first group of rocks are amongst those used in the calibration of the
Ti-in-zircon thermometer of Watson and Harrison [10]. The range of
TiO2 activities were calculated using the new solubility model and
published data for TiO2 content of glasses, major element compositions, and approximate known temperature ranges. The second group
of rocks are rhyolites which were analyzed by EMP at RPI. The range
of crystallization temperatures for these rocks are based on Ti-in-quartz
and Zr-in-sphene thermometry [17].
determined empirically by Wark, et al. [12], and the
estimated aTiO2 based on Fe–Ti oxide pairs (0.63 ± 0.03).
The Ti-in-zircon thermometer has important implications for understanding the conditions of the Hadean
Earth [10], in addition to its more general applications to
thermometry of crustal rocks. These Hadean zircons are
no longer associated with their original host material, and
their coexistence with rutile cannot be established.
Additionally, given the nature of the application,
magma temperature is unknown. However, generally
speaking, magma temperature is well correlated with
magma composition, as described by a melt's FM value.
If FM is known, magmatic temperature can be inferred
and the corresponding rutile solubility can be read off of
the contours (see [10], supporting online materials for
further discussion). This aTiO2 should be consistent with
any other constraints based on the presence or absence of
other Ti-bearing minerals such as ilmenite or sphene.
The common occurrence of these Ti-bearing phases
indicates that aTiO2 is typically fairly high in most rocks.
However the assumption of aTiO2 =1 to rutile-absent crustal
rocks or detrital zircons can result in temperature estimates
that are too low by as much as ∼70 °C for an actual
aTiO2 = 0.5. This is particularly significant when considering
the implications of the crystallization temperatures of the
568
L.A. Hayden, E.B. Watson / Earth and Planetary Science Letters 258 (2007) 561–568
Hadean zircons in regards to the conditions of the early
Earth. The refined rutile solubility model not only allows
for a more accurate estimate of aTiO2 to specific systems,
but when applied to a wide variety of representative rocks,
confirms that for most igneous and metamorphic rocks
existing today, generally aTiO2 ≥ 0.5 (Table 4). In order to
calculate aTiO2 for glassy compositions, the temperature of
the melt must be known or approximated and the FM must
be determined from major element analysis. The solubility
model will yield the amount of Ti required for melt
saturation at the given conditions, and aTiO2 is determined
by assuming Henrian behavior—i.e., dividing the measured levels of Ti in the glass by the amount required for
Tiglass
saturation, aTiO2 ¼ Timeasured
:
glass
saturated
5. Conclusions
The principal conclusions of this study are:
1) The saturation behavior of titanium in hydrous
siliceous melts over the temperature range 650° to
1000 °C deviates somewhat from the Ryerson–Watson
model, which was calibrated for more mafic compositions. Solubility data from this study are systematic and
can be modeled as a function of temperature and melt
composition using the parameter FM.
2) Variable water content does not appear to have affect
TiO2 solubility. Melts ranging from water saturated
(∼ 12 wt.%) down to ∼ 2 wt.% H2O showed virtually
no difference in TiO2 melt concentrations.
3) Diffusion coefficients calculated from titanium concentration profiles adjacent to a rutile/melt interface
produce a (preliminary) activation energy (E) of 186 ±
27 kJ/mol and frequency factor (Do) of 3.6± 1.2 m2/s for
systems containing at least ∼5% H2O. This activation
energy is quite similar to that reported for zirconium
diffusion in hydrous granitic melts [4], however for a
given temperature Ti diffusion is 2–3 orders of
magnitude faster than Zr diffusion.
4) TiO2 activities in silicic melts at typical magmatic
temperatures are generally 0.6 or higher, which
means that Ti thermometry of out-of-context zircons
will rarely underestimate zircon crystallization temperature by more than ∼ 50 °C.
Acknowledgements
This work was supported by the National Science
Foundation under grant number EAR 0440228 to E.B.
Watson.
Appendix A. Supplementary data
Supplementary data associated with this article can
be found, in the online version, at doi:10.1016/j.
epsl.2007.04.020.
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