Ti-in-quartz thermobarometry and TiO2 solubility in rhyolitic melts: New experiments and parametrization

Earth and Planetary Science Letters 538 (2020) 116213

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Ti-in-quartz thermobarometry and TiO2 solubility in rhyolitic melts: New experiments and parametrization Chao Zhang ∗,1 , Xiaoyan Li, Renat R. Almeev, Ingo Horn, Harald Behrens, Francois Holtz Institute of Mineralogy, Leibniz University Hannover, Callinstr. 3, 30167 Hannover, Germany

a r t i c l e

i n f o

Article history: Received 7 October 2019 Received in revised form 27 January 2020 Accepted 8 March 2020 Available online xxxx Editor: H. Handley Keywords: quartz titanium-in-quartz thermobarometry magmatic system rhyolite

a b s t r a c t The Ti-in-quartz thermobarometer has a wide potential for constraining crystallization pressure and temperature of quartz in natural geological systems. However, there is a long-lasting debate on the applicability of two models that were proposed previously, based on the equilibration of quartz with Ti-bearing aqueous fluids. In this study, the Ti-in-quartz thermobarometer was calibrated based on partitioning data of Ti between quartz and aluminosilicate melt in the pressure and temperature range of 0.5−4 kbar and 700−900 ◦ C, which are conditions relevant for high-silica magmas stored at crustal depths. For seventeen experiments, in which both quartz, rutile and high-silica glass are present as experimental products (i.e., activity of TiO2 in silicate melt equals to unity), the Ti concentrations in quartz can be modeled with the following equation: Qtz

log C Ti = 5.3226 − 1948.4/ T − 981.4 ∗ P 0.2 / T , Qtz

in which C Ti is the Ti concentration (ppm) in quartz, T is temperature in kelvin and P is pressure in kbar. Based on the data from this study and a previous work of Hayden and Watson (2007), we modeled the dependence of rutile (TiO2 ) solubility in silicic melt on temperature, pressure and melt composition, which can be expressed as liq)

log( S Ti = 6.5189 − 3006.5/ T − 461.0 ∗ P 0.2 / T + 0.1155 ∗ FM, liq

in which S Ti is Ti solubility (ppm) at rutile saturation and FM is a parameter accounting for melt compositional effect, computed as

FM = (Na + K + 2Ca + 2Mg + 2Fe)/(Si ∗ Al), in which the chemical symbols denote molar fractions of each cation. Combining the two models presented above as well as some additional experimental data at activity of TiO2 <1, and assuming an ideal behavior for the activity of TiO2 , the following Ti-in-quartz thermobarometer is proposed: Qtz

liq

log(C Ti /C Ti ) = −1.1963 + (1058.1 − 520.4 ∗ P 0.2 )/ T − 0.1155 ∗ FM, in which C Ti is Ti concentration (ppm) in melt. Assuming an uncertainty of input temperature of ±25 ◦ C, the corresponding pressure can be determined within ±0.2 kbar. However, the Ti concentrations in quartz liq

Qtz

liq

and glass need to be determined with a high precision. Typical values of the ratio C Ti /C Ti in natural systems vary in the range from ∼0.09 to ∼0.13, corresponding to a change of pressure from ∼5 to ∼1 kbar assuming a temperature of ∼800 ◦ C. The model above was applied to natural datasets obtained for several silicic eruptions (i.e. Oruanui Rhyolite, Early Bishop Tuff, Toba Tuff, Upper Bandelier Tuff). The analyses of quartz and glass inclusions in quartz indicate that the pre-eruptive magma storage pressures are mainly in the range 2–4 kbar. These pressures are consistent to or slightly higher than the maximum value estimated previously from the

* 1

Corresponding author. E-mail addresses: [email protected], [email protected] (C. Zhang). Present address: Department of Geology, Northwest University, 710069 Xi’an, China.

https://doi.org/10.1016/j.epsl.2020.116213 0012-821X/© 2020 Elsevier B.V. All rights reserved.

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C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

analysis of H2 O-CO2 in glass inclusions, indicating a possible post-entrapment loss of hydrogen from melt inclusions and that gas saturation provides a minimum estimation of pressure. © 2020 Elsevier B.V. All rights reserved.

1. Introduction

2. Methods

Pre-eruptive magma storage conditions are key information for understanding the mechanism of volcanic eruptions and evolution of the underlying magma plumbing systems (e.g., Bachmann and Huber, 2016; Putirka, 2017). Developments in petrological methods, particularly geothermobarometers based on mineral and melt compositions, have been widely employed to provide constraints on intensive variables (e.g., pressure, temperature and volatile activities) prevailing in magma reservoirs of volcanic systems (e.g., Andersen et al., 1993; Blundy and Cashman, 2008). Compared to basaltic and andesitic systems, much less thermobarometers are available for silicic systems, because suitable minerals (e.g., olivine, pyroxene and amphibole) that have been regularly involved in calibrating thermobarometers are lacking. In addition, due to potential loss of H from melt inclusion after entrapment (e.g., Severs et al., 2007; Tollan et al., 2019), gas saturation pressure estimated primarily based on measured H2 O concentration in rhyolitic melt inclusions, in which CO2 concentrations are usually extremely low (e.g. Liu et al., 2006), may significantly underestimate the depth of magma pre-eruption storage if raw data are used. Alternatively, Myers et al. (2016, 2018, 2019) restored H2 O contents in quartzhosted melt inclusions based on an assumed linear correlation between H2 O and incompatible elements, which would result in much appropriate estimation of gas saturation pressure. As one of the major phases in silicic magmas, quartz accommodates various trace elements (such as Ti, Al, Fe, K; Götze, 2009), and several experimental studies showed that the concentration of Ti in quartz is pressure- and temperature-dependent (Wark and Watson, 2006; Thomas et al., 2010; Huang and Audétat, 2012; Thomas et al., 2015). Combined with the geospeedmeter based on diffusion of Ti in quartz (Cherniak et al., 2007), concentrations and distribution patterns of Ti in quartz can potentially offer spectacular information about magma storage conditions and timescales relevant to magmatic events (e.g., Wark et al., 2007; Gualda et al., 2018; Shamloo and Till, 2019). Currently, there are two available independent calibrations of Ti-in-quartz thermobarometer, i.e. one from Thomas et al. (2010) and another one from Huang and Audétat (2012). However, they have large and irreconcilable discrepancies between each other, resulting in widespread confusion about the application of Ti-inquartz thermobarometer for geological issues (e.g., Wilson et al., 2012). Both calibrations are based on experiments in which Tibearing quartz was crystallized from H2 O-dominated fluids (i.e., hydrothermal quartz). Thomas et al. (2015) discussed critically the experimental design of Huang and Audétat (2012) and suggested that their approach may inevitably result in disequilibrium between newly formed quartz and fluid in terms of TiO2 activity. Other the other hand, the calibration of Thomas et al. (2010) was performed at pressures of 5–20 kbar, which does not cover the main range of storage pressures of silicic magmas in the continental crust that is usually below 5 kbar (e.g., Liu et al., 2006; Wilke et al., 2017). Considering that it is difficult to reconcile both datasets published so far, we decided to test another experimental approach, consisting in the crystallization of quartz from a silicate melt (rather than from a fluid). The experiments were designed to obtain quartz and co-existing Ti-bearing melt, as well as rutile in some cases. The experimental data are used to propose an improved Ti-in-quartz thermobarometer for rhyolitic magmas at crustal depths.

2.1. Starting materials For investing the solubility of Ti in igneous quartz, we performed crystallization experiments using four synthesized highsilica glasses containing different TiO2 contents. Except for TiO2 , these starting glasses have similar relative mass proportions for other present cations (Si, Al, Na and K). The normative Qz-AbOr (SiO2 -NaAlSi3 O8 -KAlSi3 O8 ) proportion is Qz70 -Ab20 -Or10 , and the glasses are peraluminous with an aluminum saturation index [calculated as molar ratio Al2 O3 /(Na2 O+K2 O)] of 1.6–1.8. The compositions are clearly in the primary field of quartz at watersaturated and water-undersaturated conditions (Tuttle and Bowen, 1958; Holtz et al., 1992b). Based on our long-term experience on crystallization in granitic systems, we expected relatively large quartz crystals using the experimental procedure described below. The starting glasses were synthesized by melting mixed powders of oxides (SiO2 , Al2 O3 , TiO2 ) and carbonates (Na2 CO3 , K2 CO3 ) in the desired proportion. The mixtures were melted in a platinum crucible at 1600 ◦ C in a muffle furnace for ca. 4 hours. The obtained glasses were subsequently crushed in a steel mortar and grinded in an agate mortar. The melting processes was repeated for four times in order to generate homogeneous starting glasses, which was subsequently confirmed by electron probe microanalysis (EPMA). The compositions of synthesized starting glasses are listed in Supplementary Table 1, and the adjusted TiO2 contents (0.26–3.26 wt%) were expected to generate both rutile-saturated and rutile-undersaturated systems considering the solubility of TiO2 in hydrous silicic melts. Our experiments were performed first using the starting glasses (S1 and S2) with the highest TiO2 contents (3.26 and 1.01 wt%), but the quartz crystals that were synthesized tended to contain rutile inclusions (Supplementary Fig. 1), which makes it impossible to obtain reliable analysis of Ti concentration in such quartz crystals. Therefore, experimental data using these two starting glasses are excluded and will not be discussed in this paper. Subsequently, we performed more experiments using the other two starting glasses (S3 and S4) with lower TiO2 contents (0.52 and 0.26 wt%, respectively), and the experimental products show quartz crystals without detectable rutile inclusions, so that reliable analytical data on Ti concentrations in quartz could be obtained (see details below). 2.2. Experimental approaches Dry starting glass powders were sealed together with water in Au capsules. Based on H2 O solubility data from literature (e.g., Holtz et al., 1995; Moore et al., 1998), the amounts of water added to the capsule were chosen to be slightly above the H2 O solubility (typically 2 wt% H2 O at 0.5 kbar and 12–13 wt% H2 O at 4 kbar) and to generate H2 O-saturated conditions for the planned experimental runs. Capsules were shut by arc welding, during which they were cooled with a surrounded wet paper dipped into liquid N2 aiming to avoid water loss. Welded capsules were then stored in a drying oven at 110 ◦ C for ca. 12 hours and weighed to check for leakage. Experiments at 700 and 800 ◦ C were performed in cold-seal pressure vessels (CSPV) pressurized with H2 O, while internally heated pressure vessels (IHPV) pressurized with Ar were used for experiments at 900 ◦ C. The experimental duration was 21 days at

Table 1 Experimental conditions and products, and compositions of produced quartz and glass. Starting glass

CH2 O (wt%)*

T (◦ C)

P (kbar)

Duration (day)

Phases#

3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-9 3-10 4-1 4-2 4-3 4-4 4-5 4-6 4-8 4-9 4-10 4-11a 4-11b 4-12a 4-12b

S3 S3 S3 S3 S3 S3 S3 S3 S3 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4

2.1 3.9 7.4 9.1 12.7 2.2 4.1 9.2 13.2 2.0 3.8 7.6 9.0 13.1 2.1 7.6 9.1 13.0 9.3 9.5 13.2 12.8

800 800 800 800 800 700 700 900 900 800 800 800 800 800 700 700 900 900 700 700 700 700

0.5 1.0 2.0 3.0 4.0 0.5 1.0 1.0 4.0 0.5 1.0 2.0 3.0 4.0 0.5 2.0 1.0 4.0 3.0 3.0 4.0 4.0

16 16 19 19 16 21 21 14 14 16 16 19 19 17 21 21 14 14 21 21 21 21

Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl, Gl,

Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz, Qtz,

Sil, Sil, Sil, Sil, Sil, Sil, Sil, Sil, Sil, Sil Sil Sil, Sil, Sil Sil, Sil, Sil Sil Sil, Sil, Sil, Sil,

Rt Rt Rt Rt Rt Rt Rt Rt Rt

Rt Rt Rt Rt

Rt Rt Rt Rt

Quartz (ppm±1SD)

Glass (wt%±1SD)

n

Ti

Al

n

SiO2

TiO2

Al2 O3

Na2 O

K2 O

Total

11 10 10 11 12 10 10 12 12 12 12 10 9 12 8 10 10 10 10 8 10 8

534±55 391±43 293±29 242±32 218±23 287±32 208±41 694±50 347±45 428±20 282±48 269±31 217±25 175±29 258±39 142±46 378±61 215±41 116±55 113±32 105±25 97±37

2447±252 1760±123 1649±251 1136±214 937±76 2137±173 2375±267 2353±254 1400±190 2781±203 2186±277 1587±194 1310±126 1009±184 2430±204 1289±142 2440±177 1462±85 1188±144 1085±78 900±85 1392±124

16 15 17 18 12 8 15 10 10 15 17 15 16 12 15 15 10 10 12 12 12 12

77.77±0.59 79.47±0.64 79.04±0.46 78.56±0.54 76.24±0.37 75.42±0.21 76.27±0.52 80.78±0.33 79.69±0.63 78.46±0.71 80.07±0.94 79.29±0.95 77.36±0.91 76.43±0.43 75.92±0.47 74.74±0.31 80.68±0.35 79.42±0.41 73.80±0.61 73.42±0.72 73.89±0.42 74.93±0.65

0.44±0.06 0.47±0.03 0.31±0.03 0.27±0.02 0.33±0.02 0.19±0.01 0.19±0.02 0.64±0.02 0.52±0.04 0.34±0.02 0.35±0.03 0.32±0.02 0.27±0.02 0.29±0.02 0.28±0.02 0.16±0.02 0.33±0.03 0.34±0.02 0.14±0.01 0.14±0.01 0.14±0.01 0.14±0.01

12.55±0.28 10.77±0.38 10.68±0.36 10.65±0.44 9.77±0.20 13.78±0.16 12.68±0.14 11.44±0.17 10.53±0.13 12.34±0.24 10.23±0.24 10.58±0.46 10.98±0.43 9.80±0.14 13.48±0.53 12.21±0.23 11.33±0.19 10.50±0.16 11.99±0.32 11.82±0.26 11.92±0.23 11.90±0.27

3.93±0.14 3.12±0.16 2.31±0.21 2.34±0.14 2.45±0.08 4.98±0.10 3.82±0.16 3.28±0.28 2.73±0.14 3.99±0.15 3.21±0.14 2.51±0.16 2.85±0.14 2.49±0.11 4.49±0.16 3.59±0.20 3.34±0.14 2.71±0.18 3.64±0.15 3.59±0.09 3.45±0.17 3.35±0.14

2.97±0.06 2.33±0.09 1.88±0.08 1.83±0.08 1.91±0.06 3.94±0.08 2.88±0.09 2.44±0.06 2.08±0.06 2.96±0.08 2.43±0.07 1.95±0.07 2.26±0.08 1.94±0.04 3.60±0.12 2.71±0.13 2.54±0.05 2.08±0.04 2.82±0.08 2.66±0.08 2.68±0.07 2.69±0.07

97.66 96.16 94.25 93.65 90.70 98.31 95.84 98.58 95.55 98.09 96.29 94.65 93.72 90.95 97.77 93.41 98.22 95.05 92.39 91.62 92.08 93.01

liq−Rt §

FM

aTiO2

1.034 0.908 0.682 0.684 0.779 1.276 0.996 0.906 0.807 1.057 0.982 0.739 0.831 0.790 1.161 0.965 0.938 0.804 1.008 0.990 0.956 0.935

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.79 0.76 1.0 1.0 0.87 1.0 1.0 0.52 0.66 1.0 1.0 1.0 1.0

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

Run

 Compositions of starting glasses are listed in Supplementary Table 1. ∗ Initial H O content added to starting glass. 2

#

Phase abbreviations: Gl, glass; Qtz, quartz; Sil, sillimanite; Rt, rutile.

§

For experiments with rutile as stable phase, aTiO2 =1.0; otherwise, aTiO2

liq−Rt

liq−Rt

is calculated based on glass TiO2 content (see text for explanation).

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Fig. 1. Representative BSE images of experimental products with coexisting quartz and rutile. (a) Run_3-5, performed using starting glass S3 at 800 ◦ C and 4 kbar for 16 days. (b) Run_4-3, performed using starting glass S4 at 800 ◦ C and 2 kbar for 19 days. See Table 1 for details about experimental conditions. Phase abbreviations: Gl, glass; Qtz, quartz; Rt, rutile; Sil, sillimanite.

700 ◦ C, 16–19 days at 800 ◦ C, and 14 days at 900 ◦ C. Our experiments were performed at five different pressures (i.e., 0.5, 1, 2, 3 and 4 kbar). With our experimental approach, pressure was first set to be the target pressure prior to heating, so that a polybaric formation of experimental product can be clearly excluded. Quenching in CSPV was achieved by using a flow of compressed air, and quenching in IHPV by dropping the capsule directly down to a cold zone at ∼50 ◦ C that can yield a quench rate of ∼150 ◦ C/s (Berndt et al., 2002). After the experiments, capsules were weighed again to check potential leakage, and solid products of successful runs were mounted in epoxy for analysis. 2.3. Analytical methods Experimental products were analyzed with electron probe microanalysis (EPMA) using a Cameca SX-100 electron microprobe equipped with five wavelength dispersive spectrometers and the PeakSight operating program at the Institute of Mineralogy, Leibniz University Hannover. The materials for calibration included wollastonite (for Si and Ca), synthetic oxides (Al2 O3 and TiO2 ), albite (for Na) and orthoclase (for K). For analyzing trace elements of Ti, Al, Na and K in quartz, a beam current of 120 nA and a beam size of 5 μm were used. Due to limited size of quartz crystals, EPMA has been always conducted at the crystal center. For analyzing compositions of experimental glasses, a beam current of 5 nA and a beam size of 10 μm was used. In both cases, an accelerating voltage of 15 keV was used. Acquisition time for Ti, Al, Na and K in quartz included 60 s on peak and 30 s on both-side backgrounds, and the detection limits were ∼38 ppm for Ti, ∼35 ppm for Al, ∼70 ppm for Na, and 45 ppm for K, respectively. Analyses of the reference quartz of Audétat et al. (2014) yielded Ti and Al concentrations that are consistent to recommended values within ±1σ (Supplementary Table 2). We also analyzed the reference rhyolitic glass VG-568, and the result is identical to that of Jarosewich et al. (1980) within ±1σ (see Supplementary Table 3). In order to verify the reliability of EPMA for trace elements in quartz, we also measured experimental products from two selected samples (Run_3-4 and Run_3-5; Table 1), which contains relatively large quartz crystals, with femtosecond laser ablation-inductively coupled plasma-mass spectrometry (fs-LA-ICP-MS) at the Institute of Mineralogy, Leibniz University Hannover. The laser ablation system was built based on a Spectra-Physics Solstice femtosecond laser operating in the deep UV at 194 nm, and the regenerative amplified system was pumped with 500 Hz generating a pulse energy of 70 mJ. Helium gas flow was used for transporting the ablated sample particles from the cell, subsequently mixed with argon gas, to the plasma torch. Analyses of element concentrations

were conducted using a ThermoScientific Element XR fast scanning sector field ICP-MS. The details of operation conditions and procedures were described in Horn et al. (2006). For our analyses, a constant repetition rate of 5 Hz was used, and the experimental quartz crystals were ablated by laser pulses with a spot size of ∼10 μm. No crack was formed around the crater of quartz after ablation. Data acquisition for each analysis was conducted with an overall time of 100 s, including ∼40 s for background (laser off) and ∼60 s for sample signal integration (laser on). SiO2 content of quartz was used as internal standard (29 Si), and the quantification of other elements was performed based on calibration from the NIST SRM 610 reference glass (Jochum et al., 2011). Data processing was performed using the SILLS program (Guillong et al., 2008). Detection limits for the measured quartz were ∼10 ppm for Ti, ∼8 ppm for Al, ∼15 ppm for Na, and ∼50 ppm for K. 3. Results 3.1. Experimental products Experimental conditions and products using the two low-Ti starting glasses (S3 and S4) are listed in Table 1). Representative back-scattered electron (BSE) images are shown in Fig. 1. All experimental samples contained glass, quartz and an aluminosilicate phase. The ratio of Al/Si in the aluminosilicate phase clearly shows that the chemical formulae of the phase is Al2 SiO5 and that should be sillimanite considering the P-T range of the experiments. For experimental runs using starting glass S3 (0.52 wt% TiO2 ), the products also include a Ti-oxide (described hereafter as rutile) at all investigated conditions of pressure (0.5–4 kbar) and temperature (700–900 ◦ C). In contrast, experimental products using starting glass S4 (0.26 wt% TiO2 ) are saturated with rutile at 700 ◦ C but undersaturated with rutile at 900 ◦ C, for all investigated pressures. In experiments performed at 800 ◦ C, rutile is present in the experimental products at 2 and 3 kbar but could not be detected at 0.5, 1 and 4 kbar. Quartz is usually present as euhedral crystals and many crystals have sizes of more than 10 μm (Fig. 1). Rutile, if present, and sillimanite usually occur as micrometer-size crystals surrounded by matrix glass but not enclosed in quartz. Cathodoluminescence (CL) images of quartz grains show homogeneous brightness distribution (Supplementary Fig. 2), implying that trace elements (particularly Ti and Al) in quartz are homogeneously distributed. Compositions of the produced quartz and glass (i.e., quenched silicate melt) were analyzed by EPMA and are listed in Table 1. The sum of analyses is always lower than 100% because of the presence of water in the glasses. Several glass standards with differ-

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

Fig. 2. Time-resolved fs-LA-ICP-MS signals for Run_3-5. (a) Quartz. (b) Glass. Note the smooth signal of laser-on stages, which demonstrates that there was no assimilation of glass in laser ablation of quartz.

ent water contents, determined by different methods (Karl Fischer titration or infrared spectroscopy), were also analyzed to estimate the water contents in the glasses using EPMA data. The difference to 100% is increasing with increasing pressure, which is consistent with the effect of pressure on increasing water solubility. SiO2 contents of the glasses are always lower than those of the starting glasses, and high temperature glasses have higher SiO2 contents than low temperature glasses, which is consistent with the higher crystal content (mainly quartz) that is observed at lower temperatures. The Na2 O and K2 O contents are the highest in the 700 ◦ C experiments as expected, because all the crystallized phases are free of alkalis (quartz, aluminosilicate and rutile) and their amounts are highest at the lowest temperature. The Na2 O/K2 O ratio in the glasses obtained after the crystallization vary between 1.25 and 1.35 and is identical within error to that in the starting glasses (Supplementary Fig. 3), indicating that feldspars did not crystallize, even for the experiments at 700 ◦ C. Based on the liquidus phase relationships in the system Qz-Ab-Or-H2 O established at water-saturated conditions in former studies (e.g., Tuttle and Bowen, 1958), feldspar could have been expected at 700 ◦ C and low pressures (0.5 and 1 kbar). However, the investigated systems are strongly peraluminous (saturated with respect to an aluminosilicate phase) and the presence of excess alumina, which was shown to decrease the liquidus temperature by 20 to 30 ◦ C at 2 kbar (Holtz et al., 1992a; Joyce and Voigt, 1994) and may explain this observation. Time-resolved spectra of fs-LA-ICP-MS for quartz and glass from Run_3-5 (Fig. 2) demonstrate that the intensities of major and trace elements in these two phases can be measured without interference from each other, particularly evidenced by the observation that the signal of Na in quartz (laser on) is indistinguishable from background (laser off) while Na concentration in glass is very high. Ti and Al concentrations in quartz from experiments Run_3-4 and Run_3-5 by fs-LA-ICP-MS are consistent with those measured by EPMA and thus confirm the reliability of EPMA in this study (Supplementary Table 4). 3.2. Ti-in-quartz The Ti concentrations determined in the synthesized quartz Qtz crystals (C Ti ) vary from 90 to 700 ppm (Table 1). The scattering of quartz and glass compositions in each experimental run is sup-

23

5

Na across the whole analysis for quartz, in both laser-off and

posed to reflect analytical uncertainties rather than disequilibriuminduced heterogeneities (see details below). As expected from previous experiments, the Ti concentrations in quartz measured from rutile-saturated experiments, hereafter referred as Ti-in-quartz solubility, shows an increase with increasing temperature at a given pressure (Fig. 3a) and an increase with decreasing pressure at a given temperature (Fig. 3b). In experiments that were not satuliq−Rt

rated with respect to rutile (aTiO2 <1; five experiments data from starting glass S4, see Table 1), the Ti concentrations in quartz are systematically lower than that observed in experiments using starting glass S3. The Al concentrations in quartz (Table 1) show a general negative correlation with pressure (Supplementary Fig. 4), and a rough positive correlation with temperature that could be expected at equilibrium conditions (e.g., Dennen et al., 1970). Since all experiments are saturated with respect to an aluminosilicate phase, the Al activity in the investigated systems is fixed and correlations that are observed indicate that the Al concentration in quartz could be used as a thermobarometer potentially. However, such a calibration is beyond the scope of this paper. 4. Discussion 4.1. Attainment of equilibrium The calibration of a Ti-in-quartz thermobarometer requires that experimental data reflect equilibrium distribution of Ti between quartz and silicate melt. Different independent observations indicate that conditions close to equilibrium were reached. In our experiments the Ti content of the melt is significantly higher than that of the quartz and possible problems leading to disequilibrium distribution of Ti may occur if this element cannot diffuse fast enough away from the interface quartz-melt. Thus, if disequilibrium occurs, the Ti contents in the quartz would be expected to be higher than the equilibrium value and the Ti-inquartz solubility overestimated. However, since the diffusion of Ti in silicate melt is expected to be similar to that of Si (e.g., Zhang et al., 2010), no uphill concentration profiles of Ti in the melt are expected to form during quartz growth. One possible test to check for disequilibrium Ti distribution is to compare experimental data obtained at different temperatures but identical pressure. Since the diffusivity of Ti in melt is lower in low T experiments, higher (disequilibrium) Ti concentrations at the melt-quartz interface are

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C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

expected at low T (700 ◦ C) if quartz is growing too fast due to undercooling. This would imply that the Ti concentrations in quartz from low T runs would be higher than those of high T runs. Our experimental products show systematically the opposite trend; Ti concentration in quartz is always higher in high T runs (in which Ti diffuses faster) and this behavior cannot be explained by disequilibrium features that could be due to slow diffusion processes (i.e., fast growth of quartz). The comparison of TiO2 activities deduced from the quartz on one hand and from the glasses on the other hand is also useful to discuss equilibrium distribution of Ti. For the five experimental runs without rutile (Table 1), we estimated the activities of liq−Rt

TiO2 relative to the saturation of rutile (aTiO2 ) using two independent approaches assuming an ideal activity model (i.e., activity liq

coefficient γTiO2 =1). One approach is to use the ratio of glass TiO2 content in rutile undersaturated runs (five experiments with starting glass S4, Table 1) over that in rutile saturated runs which were performed at the same P-T conditions (using starting glass S3). The other approach is to use the ratio of quartz Ti content in rutile undersaturated runs over that of quartz in the correspondliq−Rt

ing rutile saturated runs (Fig. 4a). The estimated aTiO2 values (see also Table 1) from these two independent approaches are in good agreement with each other (Fig. 4b), which indicates that the system has attained equilibrium in terms of Ti distribution between phases. Finally, other observations also indicate that strong kinetic problems are not expected in our experiments. (1) The distribution of mineral phases and glass is apparently homogeneous in the capsules. (2) The nucleation of quartz was not problematic (strong undercooling was not necessary for nucleation) which may be related to the finely ground glass powders used as starting material and to a preferential nucleation on the surface of the initial glass grains (e.g., Holtz et al., 1992b). In addition, the shape of the quartz crystals would be skeletal in case of strong undercooling (e.g. Becker et al., 1998), which is never observed in our experiments. (3) The glass compositions (including TiO2 content) along the whole capsule are identical within analytical error. (4) The systematics observed between the Al concentrations in quartz and pressure and temperature conditions indicate that trace element concentrations in quartz (Ti as well as Al) are not fortuitous. 4.2. Modelling the effect of temperature and pressure on Ti-in-quartz solubility at rutile saturated conditions Ti-in-quartz solubility data obtained at 700, 800 and 900 ◦ C indicate a linear evolution between the concentration of Ti in quartz Qtz (C Ti in ppm) and 1/T (Fig. 3a). Thus, according to the thermodynamic formulation discussed in Wark and Watson (2006) and Thomas et al. (2010), assuming an ideal mixing model for trace level of Ti4+ replacing Si4+ in quartz, the dependence of Ti-inquartz solubility on temperature for a given pressure can be written as: Qtz

log C Ti = a + b/ T

Fig. 3. Correlation of Ti concentration in quartz with temperature and pressure. The Qtz Qtz colored dots represent our experimental data. (a) Plot of logC Ti vs. 104 /T . logC Ti concentrations expected using the model of Thomas et al. (2010) are shown as light blue dotted lines, and those of Huang and Audétat (2012) are shown as light green dashed lines. The interpolation of our data is marked by the black lines. (b) Plot Qtz Qtz of logC Ti vs. P 0.2 . (c) Comparison of measured C Ti and calculated values using Qtz

Qtz

Eq. (3). Error bars for measured log C Ti and C Ti are ±1 SD. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

(1)

in which a and b are constants. To consider the effect of pressure, Thomas et al. (2010) applied a linear model whereas Huang and Audétat (2012) applied a non-linear model. In this study we favor a non-linear effect of pressure (see explanation below), and the experimental dataset on Ti-in-quartz solubility can be successfully reproduced by applying following equation: Qtz

log C Ti = c + d/ T + e · P f / T

(2)

in which c, d, e and f are constants. The experimental dataset obtained in this study can be described successfully (R 2 =0.99) with following values for c , d, eandf :

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

liq−Rt

Fig. 4. Estimation of aTiO2

7

for rutile undersaturated experiments. (a) Plots of TiO2 content in glass and Ti concentration in quartz for rutile saturated and undersaturated liq−Rt

runs. Simultaneous runs were performed at the same conditions but using different starting glasses (S3 as starting glass for experimental runs with aTiO2 =1, and S4 as starting glass for experimental runs with liq−Rt

vs. aTiO2

liq−Rt aTiO2 <1;

compositions of S3 and S4 are listed in Supplementary Table 1). (b) Comparison of estimated

liq−Rt aTiO2

from TiO2 in melt

from Ti in quartz. The dashed line is 1:1 line. Error bar is ±1 SD.

Qtz

log(C Ti ) = 5.3226 − 1948.4/ T − 981.4 ∗ P 0.2 / T

(3)

in which T is given in Kelvin and P in kbar (Fig. 3). The value of 0.2 for the constant f can be justified by the physical and chemical properties of quartz. The substitution of Ti for Si at the tetrahedral site in the quartz structure is directly controlled by the length and energy states of Ti-O and Si-O bonds, which is related to the thermal expansion and volume compression, and eventually dependent on the bulk modulus property of quartz (with phase transition) with respect to temperature and pressure. The volume thermal expansion coefficient of quartz is about 0.47*10−5 K−1 (Angel et al., 2017) and usually set as 0 in thermodynamic database (Holland and Powell, 2011), which could explain the simple linear relationship between Ti incorporation in quartz structure and 1/T in our equation. The first derivatives of the bulk modulus of various SiO2 minerals with pressure vary from 4.19 (coesite) to 6 (quartz) at ambient pressures (Holland and Powell, 2011), and a value of 5.07 for quartz has also been estimated (Angel et al., 2017). Here we adopt a constant value of 5 for quartz in our low-pressure experiments (≤4 kbar), and therefore acquire a reciprocal value of 0.2 as the exponent of pressure effect on volume compression. Our assumption is supported by the linear Ti plots of logC Qtz vs. P 0.2 (Fig. 3b) and the high regression quality of Eq. (3) (R2 = 0.99). As illustrated in Fig. 3c, the measured Qtz Qtz C Ti with 1 standard deviation (1SD) and the calculated C Ti via Eq. (3) based on experimental conditions are consistent with each other. Furthermore, the experimental pressures and temperatures are largely consistent with those calculated via Eq. (3) (see Supplementary Fig. 5), confirming its high prediction reliability. 4.3. Comparison with previous Ti-in-quartz thermobarometers There are currently two Ti-in-quartz thermobarometers calibrated experimentally by Thomas et al. (2010, 2015) and by Huang and Audétat (2012), both based on experiments conducted in hydrothermal systems (quartz-fluid system). The calibration experiments of Thomas et al. (2010) were performed by reacting aqueous fluids with oxide powders to form crystals of quartz and rutile as well as SiO2 - and TiO2 -saturated fluids, at pressures of 5, 10, 15, 20 kbar and temperatures of 600–1000 ◦ C. The calibration experiments of Huang and Audétat (2012) performed at 1, 2 and

10 kbar and 600–850 ◦ C were based on reactions between preexisting crystals of rutile and Ti-free quartz in the presence of aqueous vapor phase composed of water ± NaCl. Thomas et al. (2015) argued that the experimental design of Huang and Audétat (2012) may have inevitably resulted in disequilibrium between newly formed quartz and fluid in terms of TiO2 activity, explaining the discrepancy between the two datasets. As shown in Fig. 5, at rutile saturated conditions, these two calibrations show large and irreconcilable discrepancies in estimated temperature and pressure for a given Ti concentration in quartz. Within a pressure range of 0.5–5 kbar and in the temperature range of 700–900 ◦ C, the pressure estimated from the model derived in this study (Eq. (3)) is lower than that estimated from Thomas et al. (2010) but higher than that estimated from Huang and Audétat (2012). For instance, assuming 500 ppm Ti in quartz, a temperature of 800 ◦ C and rutile saturated conditions, the pressures estimated from the models of Thomas et al. (2010), of Huang and Audétat (2012) and of this study are 3.7, 0.2 and 2.0 kbar, respectively. The comparison between the three models is also Qtz illustrated in the diagram of logC Ti vs. 104 /T (Fig. 3a) and indicates that the discrepancy between the calibrations of Thomas et al. (2010) and Huang and Audétat (2012) should be primarily accounted for by the remarkable difference in modelling the effect of pressure. The effect of pressure on the Ti concentration in quartz determined from this study is intermediate between the two previous models. On the other hand, the comparison also shows that the effects of temperature on the Ti concentration in quartz is qualitatively similar in the three models. Three observations lead us consider that our experimental results may be closer to equilibrium conditions: (1) the experimental starting glasses already contain Ti. Thus, the medium from which quartz crystallizes does not need to be equilibrated with rutile via dissolution of this phase or via reaction of oxides in the first stage of the experiments; (2) the Ti concentration in quartz from experiments at rutile-saturated conditions but conducted from glasses with different initial Ti contents are identical within error; (3) the quartz growth rate that is controlled by diffusion of Si in the surrounding medium is expected to be much slower in silicate melts than in fluids. Since Si and Ti have similar diffusivities in silicate melts, disequilibrium Ti concentrations at the interface with

8

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

liq−Rt

Fig. 5. Plots of temperature vs. pressure showing experimental results (Exp.) and modeled Ti-in-quartz isopleths (Mod.) for rutile saturated conditions (aTiO2 = 1). (a) Plot for a wide range of pressure (0 to 20 kbar. (b) Plot for a narrow range of pressure (0–5 kbar). References: T2010 = Thomas et al. (2010); H2012 = Huang and Audétat (2012).

quartz are not expected. It is also emphasized that the influence of temperature on the solubility of rutile in silicate melts is much weaker than that in H2 O-dominated fluids (e.g., Hayden and Watson, 2007; Antignano and Manning, 2008). Therefore, problems due to different equilibration times of the medium from which quartz crystallizes (fluid vs. melt) are minimized with our experimental approach. liq−Rt

4.4. TiO2 solubility in silicic melt and estimation of aTiO2

In order to apply the Ti-in-quartz thermobarometer to rutile liq−Rt

undersaturated magmatic systems, the value of aTiO2 in the system needs to be constrained independently and several approaches have been proposed. Based on a previous work of Reid et al. (2011), Ghiorso and Gualda (2013) developed a thermodynamic approach, which utilizes compositions of spinel-ilmenite pairs to liq−Rt

predict the value of aTiO2 . However, magmas containing quartz are usually Fe-poor and the method of Ghiorso and Gualda (2013) can hardly be used in such cases. liq−Rt

Another approach to estimate aTiO2 is to determine TiO2 contents in silicate melts and to apply TiO2 solubility models at corresponding P-T conditions. There are plenty of experimental datasets involving coexisting silicate melt and rutile, mainly focusing on partitioning of trace elements between rutile and melt (e.g. Green and Pearson, 1987; Ryerson and Watson, 1987; Foley et al., 2000; Klemme et al., 2002, 2005; Xiong et al., 2005, 2011) and the complex effect of P and melt compositions on TiO2 solubility in silicate melt has been emphasized (e.g. Ryerson and Watson, 1987; Liu et al., 2007; Thomas and Watson, 2012). Green and Adam (2002) observed that TiO2 solubility systematically decreases by ca. 20–40% with increasing P from 0.5 to 1.5 kbar in andesitic and dacitic melts, indicating that P has an important effect on TiO2 solubility in silicate melt in this low pressure range. However, data from these experiments are not suitable for constraining a Ti-in-melt solubility model for crustal silicic systems that are supposed to be quartz saturated. For instance, the silicate melts investigated in Green and Pearson (1987) and Ryerson and Watson (1987) are mostly mafic and significantly different from a rhyolitic composition. The experiments of Klemme et al. (2002) and Xiong et al. (2011) were performed at pressures ≥1.5 GPa, which are too high to be realistic for crustal magma chambers. In this study, available data have been used to recalibrate the Ti-in-melt solubility model

for crustal silicic magmatic systems; it is however out of the scope of this study to present a Ti-in-melt solubility applicable for wider ranges of melt composition and pressure. Hayden and Watson (2007) calibrated a rutile solubility model for silicic melts at temperatures of 700–1000 ◦ C and 10 kbar, in which effects of temperature and melt composition were considered and quantified. Similarly, Kularatne and Audétat (2014) calibrated rutile solubility in hydrous silicic melts at 750–900 ◦ C and 2 kbar. We note discrepancies by comparing the measured TiO2 solubilities in our experiments in the range 0.5–4 kbar and the values predicted by the model of Hayden and Watson (2007) as well as by the model of Kularatne and Audétat (2014). As shown in Fig. 6a, the calculated TiO2 solubilities in melt using the model of Kularatne and Audétat (2014) tend to overestimate the experimental values obtained at high pressure by Hayden and Watson (2007) but to underestimate the values obtained at low pressure in this study. These differences indicate that the effect of P on TiO2 solubility may differ strongly between high- and low-pressure conditions. Additional problems may be related to the modeling of the effect of melt composition. For example, although Fe-free starting materials were used in the experiments of Kularatne and Audétat (2014), some of their experimental glasses show significant FeO contents up to 1.14 wt%. The possible effect of Fe is not addressed in Kularatne and Audétat (2014), but may be associated with formation of Fe-Ti oxide phases which would affect LA-ICPMS analyses of glass compositions (analysis of glass contaminated by small amounts of oxides). Therefore, in our recalibration of TiO2 solubility in silicic melt (see below), the data from Kularatne and Audétat (2014) are not used as input but only used for comparison. In order to improve the solubility model for TiO2 in silicic melts, following the thermodynamic basis discussed in Hayden and Watson (2007) but with additional consideration of the effect of pressure, we compiled data from this study and from Hayden and Watson (2007) and yielded a linear regression: liq)

log( S Ti = 6.5189 − 3006.5/ T − 461.0 ∗ P 0.2 / T

+ 0.1155 ∗ FM( R 2 = 0.93) liq

(4)

in which S Ti is Ti solubility (ppm) in silicate melt, and FM is a parameter reflecting the compositional effect. Following the formalism proposed by Hayden and Watson (2007), FM can be calculated using the following expression:

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

9

Fig. 6. Comparison of measured TiO2 solubilities in melt and calculated values from solubility models. (a) Calculation using the model of Kularatne and Audétat (2014). The solid grey lines denote discrepancies of ±50% relative from the 1:1 line. (b) Calculation using the model of this study (Eq. (8)). All TiO2 contents were normalized corresponding to 100 wt% of anhydrous glass. Melt compositions with high FeO contents (≥0.15 wt%) from Kularatne and Audétat (2014) are discarded (see text). The solid grey lines denote discrepancies of ±25% relative from the 1:1 line.

FM =

Na + K + 2(Ca + Mg + Fe) Si ∗ Al

(5)

in which chemical symbols represent cation molar fractions. The comparison of measured TiO2 solubility data and those calculated by the model of Eq. (4) is illustrated in Fig. 6b, which shows that the discrepancies are mostly less than ±25% in relative. Our model also reproduces the majority data of Kularatne and Audétat (2014) within an error of ±30% (note that these data were not used as input for the model). Therefore, we propose that the empirical model of Eq. (4) enables a reliable estimation of TiO2 solubility in silicic melts (SiO2 content >70 wt%; with anhydrous total normalized to 100 wt%) in the temperature and pressure range of 700–1000 ◦ C and 0.5–10 kbar. 4.5. Ti-in-quartz geothermobarometer for rutile undersaturated systems The previous Ti-in-quartz thermobarometers of Thomas et al. (2010) and Huang and Audétat (2012) have been widely applied in natural case studies based on measured Ti concentrations in quartz liq−Rt and estimated aTiO2 . Using our parametrization, Eq. (3) can be modified for the application to rutile undersaturated systems: Qtz

liq−Rt

log(C Ti /aTiO2 ) = 5.3226 − 1948.4/ T − 981.4 ∗ P 0.2 / T

(6)

Assuming an ideal activity model for Ti in silicate melts (i.e., liq liq−Rt activity coefficient γTiO2 = 1), aTiO2 can be constrained if the TiO2 content of the melt from which quartz crystallized is known. On liq−Rt the other hand, aTiO2 is the ratio between the TiO2 content of the liq

melt of interest (C Ti ) and the TiO2 content of the melt at rutile saturation (see Section 4.4):

liq

liq−Rt

liq

C Ti = S Ti ∗ aTiO2

(7)

By integrating the solubility model of rutile proposed above to Eq. (4), P or T can be constrained knowing the Ti content of quartz liq Qtz (C Ti ) and of the silicate melt (C Ti ) with the following equation: Qtz

liq

log(C Ti /C Ti ) = −1.1963 + (1058.1 − 520.4 ∗ P 0.2 )/ T

− 0.1155 ∗ FM

(8)

The formulation of Eq. (8) implies that P or T can be determined directly using the Ti concentrations of quartz and of a coexisting silicate melt (considered to be in equilibrium). Thus, Eq. (8) describes the partitioning of Ti between quartz and silicic melt and its dependence on temperature, pressure and melt composition. The application of the Ti-in-quartz thermobarometer requires either T or P to be known and previous applications show that the Ti-in-quartz thermobarometer is mainly used to constrain pressure, since temperature can often be estimated via an independent approach (e.g. Thomas et al., 2010; Huang and Audétat, 2012; liq−Rt

Thomas and Watson, 2012). An assumption or estimation of aTiO2 is not required but it is emphasized that this model is only valid if liq

Eq. (7) is satisfied, i.e. if the activity coefficient γTiO2 = 1, which is usually accepted in literature (e.g. Huang and Audétat, 2012; Wilson et al., 2012). In order to assess the uncertainty in pressure estimated using Eq. (3) and Eq. (8), we performed an error propagation calculation via Monte Carlo simulation taking into account uncertainties liq−Rt

Qtz

Qtz

liq

of input temperature, aTiO2 , C Ti and C Ti /C Ti . The results of error propagation, expressed in terms of standard deviation (SD), are illustrated in Supplementary Fig. 6, which indicates that (1) Qtz the error bar in estimated pressure decreases with increasing C Ti

10

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

Table 2 Estimation of crystallization conditions of natural quartz in volcanic eruptions. liq−Rt f TiO2

Eruption

References

T literature (◦ C)

P sat a (kbar)

P Al-H b (kbar)

nc

Qtz C Ti (ppm±1SD)

liq C Ti (ppm±1SD)

Qtz liq C /C Ti Ti (±1SD)

FMd (±1SD)

P e (kbar)

a

Oruanui Rhyolite

Liu et al. (2006) Wilson et al. (2012) Allan et al. (2017) Myers et al. (2019) Wallace et al. (1999) Anderson et al. (2000) Hildreth and Wilson (2007) Huang and Audétat (2012) Gualda and Ghiorso (2013) Jolles et al. (2019) Manley and Bacon (2000) Huang and Audétat (2012) Chesner and Luhr (2010) Huang and Audétat (2012) Warshaw and Smith (1988) Wilcock et al. (2013) Audétat (2013) Audétat (2013)

750–820

1.0–2.0

0.8–2.4

11

87±6

764±25

0.113±0.007

1.58±0.04

1.6–2.6

0.28–0.52

700–800

1.0–2.3

-

3

41±5

388±25

0.107±0.014

1.64±0.02

2.5–2.9

0.24–0.34

740–770

-

1.4–2.7

6

26±5

246±46

0.108±0.014

1.69±0.06

2.3–2.6

0.14–0.18

701–780

1.1–1.4

-

3

26±6

223±59

0.114±0.009

1.55±0.08

2.0–3.5

0.13–0.27

820–880

1.5–2.5

-

8

53±19

517±189

0.101±0.011

1.53±0.11

2.4–3.0

0.07–0.11

640–750

-

-

14

36±17

364±187

0.102±0.013

1.39±0.17

3.9–5.2

0.23–0.56

Early Bishop Tuff

Coso Volcanic Field Toba Tuff Upper Bandelier Tuff Tunnel Spring Tuff

a Pressure estimated via gas (H O and CO ) saturation in references. 2 2 b c d e

Pressure estimated via Al-in-hornblende barometer in references. Number of measured pairs of quartz and melt inclusion in references. FM is compositional parameter related to Ti saturation in silicate melt, calculated according to Hayden and Watson (2007). Pressure estimated based on Ti concentrations in paired quartz and melt inclusions, T literature and thermobarometer of Eq. (8).

f aliq−Rt range calculated based on measured Ti concentration in melt inclusion and TiO solubility in melt (Eq. (4)). 2 TiO2

Fig. 7. (a) Plot of Ti concentrations in pairs of quartz and glass inclusion from natural volcanic rocks. See Table 2 for data sources. (b) P -T covariation curves calculated using Qtz

liq

the thermobarometer of Eq. (8), for different C Ti /C Ti ratios (0.09, 0.11 and 0.13) and different FM values of silicate melt (1.5, 1.6 and 1.7). Solidus curve (grey curve) of the Qtz

liq

water-saturated granite system is after Johannes and Holtz (1996). The blue arrow indicates that isothermal decompression would result in increasing C Ti /C Ti . Qtz

liq

and C Ti /C Ti if they have fixed relative uncertainties, and (2) the Qtz

uncertainty is significantly dependent on the mean value of C Ti liq Qtz C Ti /C Ti

and tainty).

(i.e. the higher the mean value, the lower the uncer-

Qtz

liq

26 to 87 ppm, but it is interesting to note that the C Ti /C Ti ratios in samples from different eruptions, or from different eruptive products of the same eruption (e.g. Upper Bandelier Tuff, Tunnel Spring Tuff), are very similar at 0.11±0.02 (Fig. 7a). However, slight Qtz

liq

4.6. Application to the determination of magma storage conditions of silicic volcanic systems

variation in C Ti /C Ti ratio might reflect a significant change in temperature and/or pressure according to our Ti-in-Qtz-Melt thermobarometer. For example, assuming a constant temperature of 800 ◦ C for a given eruption with a common melt FM value within

For testing the new thermobarometer we have used data of six large silicic volcanic eruptions (i.e. Oruanui Rhyolite, Early Bishop Tuff, Coso Volcanic Field, Toba Tuff, Upper Bandelier Tuff, and Tunnel Spring Tuff) which are summarized Table 2, including the compositions of quartz and enclosed melt inclusion. The mean values of Ti concentration in quartz from these eruptions vary from

1.5–1.7, an increase in C Ti /C Ti from 0.09 to 0.13 roughly indicates a decrease in pressure from ∼5 to ∼1 kbar (Fig. 7b). Pressure constraints for four volcanic eruptions (i.e. Oruanui Rhyolite, Early Bishop Tuff, Toba Tuff, Upper Bandelier Tuff) are illustrated in Fig. 8, for which independently estimated temperatures, gas (H2 O-CO2 ) saturation pressures ( P sat ) and paired quartz-

Qtz

liq

C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

11

Fig. 8. P -T covariation curves calculated using the thermobarometer of Eq. (8) for four volcanic eruptions. The light blue area denotes uncertainty deriving from ±1SD of Qtz

liq

C Ti /C Ti . The grey solid curve represents the solidus of water-saturated granite system (after Johannes and Holtz, 1996). The green dashed line represents the maximum value of P sat [i.e., pressure estimated from gas (H2 O-CO2 ) saturation]. The dotted lines denote the range of reference temperature. See Table 2 for data sources.

glass compositions have been previously reported in literature (Table 2). The uncertainties of calculated P -T covariation curves are correspondingly determined by the standard deviation of measured Qtz

liq

C Ti /C Ti . Using the temperature estimated in literature for each eruption, the corresponding pressure can be estimated according to its P -T covariation curve ( P TiQ ). Fig. 8 shows that the P TiQ valQtz

liq

ues based on the mean values of C Ti /C Ti are 1.6–2.6 kbar for the Oruanui Rhyolite, 2.5–2.9 kbar for the Early Bishop Tuff, 2.0–3.5 kbar for the Toba Tuff and 2.4–3.0 kbar for the Upper Bandelier Tuff (Table 2). The estimated pressure-temperature ranges are well above the solidus curve of water-saturated granite system (Johannes and Holtz, 1996). These estimates of pressure are close to or slightly higher than the maximum value of P sat for each eruption. One possible explanation is that, P sat tends to underestimate quartz-melt equilibrium pressure as a result of post-entrapment loss of hydrogen from melt inclusions (Severs et al., 2007). Recently, the significance of such diffusion-controlled loss of water from volcanic quartz-hosted melt inclusions was also emphasized by Myers et al. (2016, 2018, 2019) who demonstrated that a large proportion of melt inclusions from Oruanui (20–100%) and Bishop (31–67%) have experienced hydrogen loss. In contrast, diffusion

rates of Ti in silicate melt and quartz are much slower (Cherniak et al., 2007; Zhang et al., 2010), implying negligible loss or gain of Ti for melt inclusions at post-entrapment stages. Therefore, we propose that the maximum value of P sat defines a lower limit of pressure for the entrapment of melt inclusion by quartz, while P TiQ yields more reliable estimations for the storage depth, if the equilibrium between melt inclusion and hosting quartz is achieved. 5. Conclusions Experiments designed to attain near-equilibrium conditions between felsic melt, quartz and rutile were used to re-calibrate the Ti-in-quartz thermobarometer at rutile-saturated conditions and the TiO2 solubility in melt, which are functions of both pressure and temperature. The combination of these two models allowed us to propose a new Ti-in-quartz thermobarometer without an inliq−Rt

dependent estimation of aTiO2 provided that Ti concentrations in quartz and in a coexisting melt are available. Applications of the Ti-in-quartz thermobarometer to natural cases indicate that it can be applied successfully applied to silicic eruptions by the analysis of quartz and melt inclusions hosted in quartz.

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C. Zhang et al. / Earth and Planetary Science Letters 538 (2020) 116213

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We thank Colin Wilson and Jörg Hermann for their thoughtful reviews that have substantially improved this paper. We also thank Heather Handley for her editorial handling. This work was supported by German Research Foundation (DFG) project HO1337/40 in the frame of ICDP program. Appendix A. Supplementary material Supplementary material related to this article can be found online at https://doi.org/10.1016/j.epsl.2020.116213. References Andersen, D., Lindsley, D., Davidson, P., 1993. QUILF: a Pascal program to assess equilibria among fe-mg-mn-ti oxides, pyroxenes, olivine, and quartz. Comput. Geosci. 19, 1333–1350. Angel, R.J., Alvaro, M., Miletich, R., Nestola, F., 2017. A simple and generalised P– T–V EoS for continuous phase transitions, implemented in EosFit and applied to quartz. Contrib. Mineral. Petrol. 172, 29. Antignano, A., Manning, C.E., 2008. Rutile solubility in H2 O, H2 O–SiO2 , and H2 O– NaAlSi3 O8 fluids at 0.7–2.0 GPa and 700–1000 C: implications for mobility of nominally insoluble elements. Chem. Geol. 255, 283–293. Audétat, A., Garbe-Schönberg, D., Kronz, A., Pettke, T., Rusk, B., Donovan, J.J., Lowers, H.A., 2014. Characterisation of a natural quartz crystal as a reference material for microanalytical determination of Ti, Al, Li, Fe, Mn, Ga and Ge. Geostand. Geoanal. Res. 39, 171–184. Bachmann, O., Huber, C., 2016. Silicic magma reservoirs in the Earth’s crust. Am. Mineral. 101, 2377–2404. 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. Contrib. Mineral. Petrol. 130, 213–224. Berndt, J., Liebske, C., Holtz, F., Freise, M., Nowak, M., Ziegenbein, D., Hurkuck, W., Koepke, J., 2002. A combined rapid-quench and H2-membrane setup for internally heated pressure vessels: description and application for water solubility in basaltic melts. Am. Mineral. 87, 1717–1726. Blundy, J., Cashman, K., 2008. Petrologic reconstruction of magmatic system variables and processes. Rev. Mineral. Geochem. 69, 179–239. Cherniak, D.J., Watson, E.B., Wark, D.A., 2007. Ti diffusion in quartz. Chem. Geol. 236, 65–74. Dennen, W., Blackburn, W., Quesada, A., 1970. Aluminum in quartz as a geothermometer. Contrib. Mineral. Petrol. 27, 332–342. Foley, S.F., Barth, M.G., Jenner, G.A., 2000. Rutile/melt partition coefficients for trace elements and an assessment of the influence of rutile on the trace element characteristics of subduction zone magmas. Geochim. Cosmochim. Acta 64, 933–938. Götze, J., 2009. Chemistry, textures and physical properties of quartz - geological interpretation and technical application. Mineral. Mag. 73, 645–671. Ghiorso, M., Gualda, G.R., 2013. A method for estimating the activity of titania in magmatic liquids from the compositions of coexisting rhombohedral and cubic iron–titanium oxides. Contrib. Mineral. Petrol. 165, 73–81. Green, T.H., Adam, J., 2002. Pressure effect on Ti- or P-rich accessory mineral saturation in evolved granitic melts with differing K2 O/Na2 O ratios. Lithos 61, 271–282. Green, T., Pearson, N., 1987. An experimental study of Nb and Ta partitioning between Ti-rich minerals and silicate liquids at high pressure and temperature. Geochim. Cosmochim. Acta 51, 55–62. Gualda, G.A.R., Gravley, D.M., Connor, M., Hollmann, B., Pamukcu, A.S., Bégué, F., Ghiorso, M.S., Deering, C.D., 2018. Climbing the crustal ladder: magma storagedepth evolution during a volcanic flare-up. Sci. Adv. 4, eaap7567. Guillong, M., Meier, D.L., Allan, M.M., Heinrich, C.A., Yardley, B.W., 2008. Appendix A6: SILLS: a Matlab-based program for the reduction of laser ablation ICPMS data of homogeneous materials and inclusions. Mineral. Assoc. Can. Short Course 40, 328–333. Hayden, L.A., Watson, E.B., 2007. Rutile saturation in hydrous siliceous melts and its bearing on Ti-thermometry of quartz and zircon. Earth Planet. Sci. Lett. 258, 561–568. Holland, T.J.B., Powell, R., 2011. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. J. Metamorph. Geol. 29, 333–383.

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