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First-principles calculations of equilibrium silicon isotope fractionation in metamorphic silicate minerals
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ScienceDirect Solid Earth Sciences 4 (2019) 142e149 www.elsevier.com/locate/SESCI
First-principles calculations of equilibrium silicon isotope fractionation in metamorphic silicate minerals Yuanhong Li a, Wenzhong Wang b, Chen Zhou a, Fang Huang a,c,* a
CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, 230026, China b Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, China c CAS Center for Excellence in Comparative Planetology, University of Science and Technology of China, Hefei, 230026, China Received 10 September 2019; revised 24 September 2019; accepted 24 September 2019 Available online 27 November 2019
Abstract In this study, silicon isotope fractionation factors for metamorphic silicate including muscovite, epidote, and kyanite are calculated using first-principles methods based on density-functional theory. The reduced partition function ratio (103lnb) of 30Si/28Si decreases in the order of muscovite > epidote z kyanite. Combining with previous calculations, our results show that the equilibrium silicon isotope fractionation factors are correlated with average SieO bond length. These results predict that measurable Si isotope fractionation can occur during metamorphic fluid activities. At 1000 K, the calculated 103lna values for quartzeepidote, quartzekyanite, and quartzemuscovite are 0.51‰, 0.49‰, and 0.08‰, respectively. The calculation results are generally consistent with the observed Si isotopic data in two metamorphic eclogite-vein systems, showing that our work can provide useful information in investigating the Si isotope fractionation in metamorphic fluid evolution. Copyright © 2019, Guangzhou Institute of Geochemistry. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Si isotopes; First-principles calculation; Metamorphic fluid
1. Introduction Silicon is one of the most important elements in the Earth’s crust and mantle, and it constitutes the skeleton of silicate minerals in the form of silicon-oxygen polyhedrons. Silicon has three stable isotopes: 28Si, 29Si, and 30Si. The wide distribution of silicon in the lithosphere, hydrosphere, and biosphere makes Si isotopes a potentially useful tool to study a number of fundamental geochemical processes. Studies of Si isotopes have been carried on for more than half a century (Reynolds and Verhoogen, 1953; Grant, 1954; Allenby, 1954;
* Corresponding author. CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, 230026, China. E-mail address: [email protected] (F. Huang). Peer review under responsibility of Guangzhou Institute of Geochemistry.
Epstein and Taylor, 1970; Douthitt, 1982; Ding et al., 1996). During the last decade, owing to the development of Si isotope analytical techniques using MC-ICP-MS, there is great progress on the studies of Si isotope geochemistry. High precision Si isotope measurements have unraveled significant Si isotope fractionations during planetary core formation (Georg et al., 2007; Fitoussi et al., 2009; Chakrabarti and Jacobsen, 2010; Armytage et al., 2011; Fitoussi and Bourdon, 2012; Pringle et al., 2013; Zambardi et al., 2013) and evolution of mantle and continental crust (Savage et al., 2010, 2011, 2012, 2013). For better understanding the mechanisms of Si isotope fractionations during different geochemical processes, the equilibrium Si isotope fractionation factors among the rockforming minerals are essential. In previous studies, the equilibrium Si isotope fractionation between various kinds of common silicate minerals have been calculated by using the density functional theory (DFT), and their results show that
https://doi.org/10.1016/j.sesci.2019.09.004 2451-912X/Copyright © 2019, Guangzhou Institute of Geochemistry. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NCND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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the equilibrium fractionation factors are related to multiple controlling factors such as temperature, pressure, and cation composition (Meheut et al., 2009; Huang et al., 2014; Meheut and Schauble, 2014). As one of the major medium of mass exchange between the crust and the mantle, subduction zone fluids play a crucial role in global elemental cycling (McCulloch and Gamble, 1991; Scambelluri and Philippot, 2001; Manning, 2004; Hermann et al., 2006; Bebout, 2007). Silicon is one of the major solutes in subduction zone fluids (Manning, 2018), and greatly influence the physical and chemical properties of the fluids (Shen and Keppler, 1997; Bureau and Keppler, 1999). Therefore, it is important to study the behavior of Si during fluid evolution processes. Si isotopes in the crystallized products of subduction zone fluids may be a promising tool in the investigation of this problem. However, theoretical studies for Si isotope fractionation are rare for minerals that are commonly formed in high-temperature metamorphic fluid systems. This impedes the application of Si isotopes in studies of Si migration and isotope fractionation during metamorphic fluid activities. In this work, the equilibrium fractionation factors of Si isotopes between three typical metamorphic silicate minerals in veins, including epidote, muscovite, and kyanite are calculated using first-principles methods based on density-functional theory. The goal of this study is to constrain the Si isotope fractionation during the crystallization of HP-UHP metamorphic fluids. Furthermore, combining with the Si isotopic measurement data for the silicate minerals within two metamorphic eclogite-vein systems, the mechanism of Si isotope fractionation during metamorphic fluid activities are discussed.
where the asterisk denotes the heavier isotope; ui ¼ hcui/kBT, c is the speed of light; ui is the vibrational frequency of the ith mode; h and kB are the Planck and Boltzmann constants, respectively; T is the temperature in Kelvin; and N is the number of atoms in the unit cell. Quantum ESPRESSO (an open source software package based on DFT, plane waves, and pseudopotentials) was used to calculate the electronic structures and phonon frequencies of epidote, muscovite, and kyanite (Giannozzi et al., 2009). The calculation details were similar to those used in previous studies (Huang et al., 2013, 2014; Wu et al., 2015; Qin et al., 2016; Wang et al., 2017a, 2017b). The Local Density Approximation (LDA) was used in the calculations for exchange-correlation functions, which provides good predictions for mineral structures, thermodynamic properties, and phonon characteristics (e.g., Wentzcovitch et al., 2010; Huang et al., 2013). The plane-wave cutoff energy was 70 Ry. The pseudopotentials employed for calcium, aluminum, silicon, and oxygen were the same as those used by Huang et al. (2013), whereas those of hydrogen and iron were taken from Yang et al. (2017) and Wang et al. (2017b), respectively. A N1 N2 N3 grid whose dimensions depend on the size of the mineral unit cell were used to calculate the Brillouin zone summations over different electronic states. Crystal structures were optimized using variable cell shape molecular dynamics (Wentzcovitch, 1991). The residual forces acting on every atom were less than 1 104 Ry/Bohr, and unit-cell stresses were less than 0.5 kbar. Using the density functional perturbation theory, the dynamical matrices were calculated on a regular q mesh and then interpolated on a dense q mesh (Table 1) to obtain the vibrational density of each mineral.
2. Methods
3. Results
The substitution of isotopes with different masses into crystal lattices changes their vibrational frequencies, which control the equilibrium fractionation factors of stable isotopes (Bigeleisen and Mayer, 1947; Urey, 1947). The degree of equilibrium isotope fractionation of an element X between phases A and B is usually expressed as 103lnaAeB, where aAeB (defined as RA/RB) is the isotope fractionation factor between A and B. When B is an ideal gas of X atom, the fractionation factor can be represented by the reduced partition function ratio (b): aAeB ¼ bA/bB. For a crystal, the b value can be calculated as follows:
We calculated the equilibrium Si isotope fractionation factors (103lnaSi) for three major minerals in HPeUHP veins: epidote, kyanite, and muscovite. Their relaxed crystal structures are shown in Fig. 1. The calculated crystal lattice parameters of muscovite, kyanite, and epidote are listed in Table 2, and agree well with experimental data. The calculated parameters are generally slightly smaller (with one exception) than the experimental data, the discrepancies are within 2% for lattice constants, and 4% for volumes (Table 2). This is consistent with previous studies, in which the equilibrium volumes are usually slightly underestimated by LDA static calculation (Huang et al., 2013, 2014; Qin et al., 2016). However, the vibrational effect can generally increase the equilibrium volume by ~2% at 0 GPa and 300 K (Wu and
b¼
Y3N u
1
e2ui 1 eui ui 1 eui e12ui i
i
Table 1 K mesh used for Brillouin zone summations over electronic states, regular q mesh used for real space force constant matrix, and dense q mesh used for the reduced partitions function ratio. Mineral
Formulas
K mesh
Regular q mesh
Dense q mesh
Muscovite Epidote Kyanite
KAl2(AlSi3O10) (OH)2 Ca2Al2Fe(SiO4) (Si2O7)O(OH) Al2SiO5
421 121 444
111 121 111
111 121 111
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Fig. 1. Crystal structures of epidote, kyanite, and muscovite. O atom is shown in red. The dark blue structure is SiO4 tetrahedron formed by one Si atom and four O atoms, and the gray structure is octahedron formed by one Al atom and six O atoms.
Table 2 The crystal lattice parameters optimized at volume corresponding to zero pressure of static first-principles calculation compared with experiment measurements (reported in unit cell). Mineral
a(Å)
b(Å)
c(Å)
a( )
b( )
g( )
V (Å3)
Muscovite
5.132 5.199 1.29 8.860 8.891 8.890 0.34 7.053 7.124 1.00
8.911 9.027 1.28 5.589 5.624 5.637 0.74 7.780 7.856 0.97
20.154 20.106 0.24 10.006 10.164 10.160 1.54 5.509 5.577 1.22
90 90
95.686 95.782 0.1 114.918 115.44 115.432 0.5 101.103 101.15 0.05
90 90
917.152 938.715 2.30 449.340 458.950 459.786 2.18 284.655 293.978 3.17
Epidote
Kyanite
90 90 90 90 89.99 0.01
90 90 90 106 105.95 0.05
This study Experimenta Error (%) This study Experimentb Experimentc Error (%) This study Experimentd Error (%)
Data sources for experimental studies. a Richardson and Richardson (1982). b Giuli et al. (1999). c Nagashima and Akasada (2010). d Comodi et al. (1997).
Wentzcovitch, 2007; Huang et al., 2013). Therefore, when vibrational effect is taken into account, the difference between the calculated volumes and experimental data is expected to be ~1% (Wentzcovitch et al., 2010). There is also a good match between the experimental peak position and the calculated
frequencies of epidote (Fig. 2), indicating the reliability of our calculations. The temperature-dependent variations in 103lnbSi and 3 10 lnaSi between quartz and other minerals are shown in Fig. 3, in which 103lnaAeB ¼ 103ln(bA/bB) z d30SiA e
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Fig. 2. The calculated vibrational frequencies of epidote compared with Raman and measurement. Experimental Raman data are from rruff. info/ R100129 supplied by William W. Pinch. The short vertical lines in red show the positions of Raman active in spectrum.
d30SiB ¼ D30SiAeB, and d30SiA ¼ [(30Si/28Si)A/(30Si/28Si)s3 tandard e 1] 1000 (‰). The parameters of the polynomial fitting of 10 lnbSi 3 and 10 lnaSi are given in Tables 3 and 4, respectively, in which the data of quartz was quoted from Qin et al. (2016). The errors of the calculated volumes and bond length do not affect the result of 103lna because the offsets of 103lnb are systematic and can be canceled out as 103lnaAeB ¼ 103lnbA e 103lnbB (Huang et al., 2013). Our results confirm that the Si isotope composition of muscovite is very close to quartz, but significantly heavier compared with epidote and kyanite in equilibrium. At 1000 K, the calculated 103lnaSi(quartzemusco3 3 vite), 10 lnaSi(quartzekyanite) and 10 lnaSi(quartzeepidote) are 0.08, 0.49, and 0.51, respectively. In Meheut et al. (2007), the influence of the choice of the cut-off energy for the phonon energy calculations was discussed, and their result proves that the influence is negligible for the calculated fractionation factors. The pressure effect on Si isotope fractionation factors is negligible compared with Mg and O isotopes (Wu et al., 2015). Furthermore, the anharmonic effect is expected to be large only if the mass of the atom is small and the bond environment is strongly asymmetric (Meheut et al., 2009), so it should not play an important role in our case. In conclusion, the overall uncertainties of the 103lnbSi and 103lnaSi is expected to be smaller than the analytical error of Si isotopes at present (~0.07‰, 2SD). 4. Discussion Generally, equilibrium isotope fractionations are controlled by bond lengths and energies, which are related to bond strengths. Shorter chemical bonds have higher bond strengths and higher vibrational frequencies, which preferentially incorporate heavy isotopes relative to the longer, weaker bonds (Urey, 1947; Schauble, 2004; Young et al., 2009).
Fig. 3. (A) Calculated equilibrium reduced partition function (103lnb) vs. 106/ T2 (T is temperature in Kelvin) for 30Si/28Si of epidote (ep), kyanite (ky), and muscovite (mus) at 0 GPa. (B) Calculated 103lnaqz-minerals of Si isotopes in this study. The data are in Tables 3 and 4
The mechanisms that control the equilibrium Si isotope fractionation have been investigated for several decades. Theoretical calculations done by Grant (1954) suggested that the equilibrium Si isotope fractionations are controlled by the polymerization degrees of the SiO4 4 tetrahedra in the silicates. However, Meheut et al. (2009) calculated the equilibrium O and Si isotope fractionation of quartz, enstatite, forsterite, kaolinite, and lizardite, and showed that Si fractionation factor is not only dependent on the polymerization degrees, but also many other factors. For example, minerals with same polymerization degree can have different fractionation properties (such as kaolinite and lizardite), showing the complex structural controls over equilibrium Si isotope fractionations. Meheut and Schauble (2014) made a further calculation on fractionation factors for Si isotopes in phyllosilicates (pyrophyllite and talc), albite and pyrope with first-principles methods based on density-functional theory. Their results suggest that Si isotope fractionation is correlated with stoichiometry and correlated with SieO bond length. In their
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Table 3 Fitting parameters of calculated reduced partition function ratios of30Si/28Si (103lnb) and the average SieO bond lengths. Fitting equation: 103lnb ¼ ax3þbx2þcx, where x ¼ 106/T2, T is temperature in Kelvin. The temperature range for fitting is 675e1675 K. Minerals
Formulas
a
b
c
Bond lengths (Å)
Muscovite Epidote Kyanite Quartz * Data source: * Qin et al.
KAl2(AlSi3O10) (OH)2 Ca2Al2Fe(SiO4) (Si2O7)O(OH) Al2SiO5 SiO2 (2016).
0.0087 0.0074 0.0068 0.0092
0.2221 0.1968 0.1904 0.2275
8.0312 7.5792 7.5996 8.1207
1.623 1.630 1.636 1.617
Table 4 Fitting parameters of calculated fractionation factors of30Si/28Si (103lna) between quartz and other minerals. Fitting equation: 103lna ¼ ax3þbx2þcx, where x ¼ 106/T2, T is temperature in Kelvin. The temperature range for fitting is 675e1675 K. Mineral pairs
a
b
c
Qz-Mus Qz-Ep Qz-Ky
0.0005 0.0018 0.0024
0.0054 0.0307 0.0371
0.0895 0.5415 0.5211
opinion, cations with lower electronegativity have higher effect on Si isotope fractionation (Meheut and Schauble, 2014). In Huang et al. (2014), Si isotope fractionation factors for mantle minerals (olivine, wadsleyite, ringwoodite, pyroxenes, pyrope, majorite, and Mg-perovskite) show significant Si isotope fractionation between minerals with different Si coordination numbers. Qin et al. (2016) calculated equilibrium fractionation factors for Si isotopes between common silicate minerals in granites, showing that 103lna values for 30Si/28Si are controlled mainly by the average SieO bond length, an interpretation that was first proposed by Meheut and Schauble (2014). We also found that 103lnb values for 30Si/28Si ratios are linearly correlated with the average SieO bond lengths of minerals except in epidote (Fig. 4). This outlier may be due to other factors, such as polyhedral distortion and the electronegativity of the second closest atoms relative to Si.
Fig. 4. The negative correlation between 103lnbSi and the average SieO bond lengths at 1000 K. The data for grey dots are from Qin et al. (2016).
During crystallization of metamorphic fluids, different kinds of minerals can be formed (Castelli et al., 1998; Becker et al., 1999; Hermann et al., 2006; John et al., 2008), this may change the Si isotope composition of the fluids. Theoretical calculations of the equilibrium Si isotope fractionations between fluid-minerals and mineral-minerals are helpful in speculating the Si isotopic variation during fluid evolution. Dupuis et al. (2015) calculated equilibrium Si isotope fractionation factors of quartz and dissolved silicic acid (H4SiO4 and H3SiO 4 ), and found that quartz has a heavier Si isotopic composition than that of aqueous H4SiO4, with a 30Si fractionation factor of 0.15 ± 0.03‰ at 300 K. He and Liu (2015) calculated equilibrium Si isotope fractionation factors between quartz, orthosilicic acid, and adsorption Si on Feoxyhydroxide surface. The result reveals that quartz is enriched in heavy Si isotopes than H4SiO4(aq), and Si isotopes are also significantly fractionated (3.0‰) between the adsorbed Si and aqueous H4SiO4. They also proposed that significant kinetic isotope effect (KIE) can take place during the formation of amorphous silica, leading to the enrichment of light Si isotopes in amorphous silica (He and Liu, 2015). The results in Dupuis et al. (2015) are consistent with the experimental data of Pollington et al. (2016), in which Si isotope fractionation between quartz and aqueous solutions under controlled thermal and chemical conditions was reported. However, the data in Dupuis et al. (2015) and Pollington et al. (2016) do not agree well with natural observations in low-temperature systems, in which the quartz precipitation is dominated by kinetic, rather than equilibrium processes. But under high-temperature conditions, equilibrium crystallization of metamorphic fluids should be more likely. When the temperature reaches to 1000 K, the equilibrium Si isotope fractionation between quartz and fluid is 0.15 ± 0.03‰ by using the relationship: 1000lna30Siquartzefluid ¼ (0.15 ± 0.03) 106/T2 derived in Pollington et al. (2016). Combining with the calculated D30Siquartzemineral values in this study, the D30Sifluidemineral can be obtained as 0.07‰, 0.34‰, and 0.36‰, for muscovite, kyanite, and epidote, respectively. Together with calculated results for other common minerals in crystallization products of metamorphic fluids (for example, veins) such as diopside (Qin et al., 2016) and pyrope (Huang et al., 2014), the Si isotopic evolution pattern of the fluid can be deduced by the mineral composition of the crystallization products. For example, forming of Si-rich veins (such as quartz veins) may lead to decrease in the d30Si value of the residual fluids, because these veins usually have high quartz content. But for veins that are mainly composed by
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epidote, kyanite, and garnet (Spandler and Hermann, 2006; John et al., 2008; Guo et al., 2012, 2015a), as these minerals all have Si isotope compositions lighter than fluids, the d30Si value of the residual fluids could rise. Due to the difficulties in directly analyzing subduction zone metamorphic fluids, determining the Si isotopic composition of these fluids is still challenging. For this reason, the fractionation of Si isotopes in metamorphic fluid systems are poorly understood. Several studies have reported the Si isotope composition of hydrothermal quartz or silica (Geilert et al., 2015; Brengman et al., 2016; Kleine et al., 2018), which can still provide some useful information for Si isotope fractionations during fluid activities. Brengman et al. (2016) presented micro-scale d30Si heterogeneity of quartz in brecciated pillow basalt, recrystallized chert, and chert clasts in Isua Greenstone Belt, the quartz amygdules in brecciated pillow basalt, indicating the KIE effect during quartz precipitation under hydrothermal conditions. Kleine et al. (2018) measured Si isotope composition of hydrothermal quartz and silica polymorphs in Iceland, showing that fluid activities such as fluiderock interaction, cooling, boiling, changes in composition of fluids can cause large Si isotope fractionation. The mechanisms of Si isotope fractionation can be different in various conditions. Equilibrium fractionation may be the dominant mechanism during higher temperature (~200e400 C) hydrothermal activities, but kinetic fractionation is more obvious under lower temperatures (Kleine et al., 2018). The data in Kleine et al. (2018) indicate that under higher temperature, first-principles calculation can provide reliable constraints on the Si isotope fractionation during crystallization of quartz. It could also be useful in investigating mineral crystallization processes in metamorphic fluid systems. As the crystallized products of fluids, veins in metamorphic rocks can retain valuable information. In order to examine whether the calculated equilibrium Si isotope fractionations are applicable in natural systems, we measured the Si isotope composition of silicate minerals within two metamorphic eclogitevein systems (Ganghe and Hualiangting) for comparison. The two systems are located in the Dabie orogen, eastern China, and the veins were formed after crystallization of HP-UHP fluids that were released by breakdown of lawsonite in the host eclogite. The PT conditions were 2.8e3.0 GPa, 650e680 C for Ganghe veins (Guo et al., 2012) and 2.7e3.0 GPa, 660e720 C for Hualiangting veins (Guo et al., 2015a). The veins mainly consist of epidote, omphacite, quartz, kyanite, amphibole, garnet, muscovite, and other minor minerals, and more details are reported in Guo et al. (2012, 2014, 2015a, 2015b). The results show that the average Si isotope fractionations between minerals in the two systems are D30Siquartzeepidote ¼ 0.43‰, 30 D Siquartzekyanite ¼ 0.40‰, D30Siquartzemuscovite ¼ 0.00‰ for the Ganghe samples, and D30Siquartzeepidote ¼ 0.44‰, and D30Siquartzekyanite ¼ 0.42‰ for the Hualiangting samples (Li et al., 2019), the analytical errors for each minerals are within 0.06‰ (2SD). The calculated 103lna values for 30Si/28Si for quartzeepidote, quartzekyanite, and quartzemuscovite at
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1000 K in this study are 0.51‰, 0.49‰, and 0.08‰, respectively, which are generally in agreement with the measured values. The discrepancies between the calculated and measured values are within 0.09‰, which are significantly smaller than that in low-T systems (Dupuis et al., 2015; Pollington et al., 2016). The similarity between the calculated fractionation factors and the measured data suggests that equilibrium processes were dominant during vein-mineral crystallization, indicating the effectiveness of our calculated results in clarifying the mechanism of Si isotope fractionation during metamorphic fluid evolution. If the veins were formed under Si isotope equilibrium, then the correlation of d30Siquartz versus d30Simineral should fall on a line with a slope of ~1 for, which corresponds to a certain temperature. This could help us estimate the crystallization temperature. As an attempt, two mineral pairs (quartz-epidote and quartz-kyanite) in the Ganghe and Hualiangting samples are plotted on the d30Siquartzd30Simineral figures with calculated fractionation lines (Fig. 5). The d30Siquartz values are linearly correlated with d30Siminerals following the equilibrium fractionation lines around 800 C for both minerals. This result is about 100 C higher than the temperature derived from the mineralogical study (Guo et al., 2012, 2015a), which may be
Fig. 5. d30Si for mineral pairs of quartz-epidote (A) and quartz-kyanite (B) in the Ganghe and Hualiangting samples, showing the predicted peak temperature during the fluid evolution processes by the Si isotopes geothermometer. The temperature gradients are based on the first-principles calculations in this study.
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due to minor influence of kinetic processes such as chemical and thermal diffusion (Richter et al., 2009; Huang et al., 2010; Kleine et al., 2018) or the uncertainty of elemental thermometers. 5. Conclusions Equilibrium Si isotope fractionation factors for metamorphic minerals (muscovite, epidote, and kyanite) are calculated using first-principles calculations. The results indicate that the sequence of 30Si enrichment follows the order of muscovite > epidote z kyanite, and the Si isotope fractionation between muscovite and quartz is limited (~0.08‰ at 1000 K). The Si isotope fractionation factors of the calculated minerals are affected by mineral structure, especially the average SieO bond length. The calculated results can be compared with the measured Si isotope data of minerals within two eclogitevein system in the Dabie orogen, China. The measured data are generally consistent with the calculated equilibrium Si isotope fractionation factors, suggesting that the Si isotope fractionation between these minerals were likely dominated by equilibrium fractionation during crystallization from the fluids. Conflict of interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work is financially supported by the Natural Science Foundation of China (41873009 and 41630206). We thank Xiaobin Cao, an anonymous reviewer, and Editor-in-Chief Weidong Sun for their comments and suggestions, which greatly improved the manuscript. References Allenby, R.J., 1954. Determination of the isotopic ratios of silicon in rocks. Geochem. Cosmochim. Acta 5 (1), 40e48. Armytage, R.M.G., Georg, R.B., Savage, P.S., Williams, H.M., Halliday, A.N., 2011. Silicon isotopes in meteorites and planetary core formation. Geochem. Cosmochim. Acta 75, 3662e3676. Bebout, G.E., 2007. Metamorphic chemical geodynamics of subduction zones. Earth Planet. Sci. Lett. 260, 373e393. Becker, H., Jochum, K.P., Carlson, R.W., 1999. Constraints from high-pressure veins in eclogites on the composition of hydrous fluids in subduction zones. Chem. Geol. 160, 291e308. Bigeleisen, J., Mayer, M.G., 1947. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 15, 261e267. Brengman, L.A., Fedo, C.M., Whitehouse, M.J., 2016. Micro scale silicon isotope heterogeneity observed in hydrothermal quartz precipitates from the >3.7 Ga Isua Greenstone Belt, SW Greenland. Terra. Nova 28, 70e75. Bureau, H., Keppler, H., 1999. Complete miscibility between silicate melts and hydrous fluids in the upper mantle: experimental evidence and geochemical implications. Earth Planet. Sci. Lett. 165, 187e196.
Castelli, D., Rolfo, F., Compagnoni, R., Xu, S., 1998. Metamorphic veins with kyanite, zoisite and quartz in the Zhu-Jia-Chong eclogite, Dabie Shan, China. Isl. Arc 7, 159e173. Chakrabarti, R., Jacobsen, S.B., 2010. Silicon isotopes in the inner Solar System: implications for core formation, solar nebular processes and partial melting. Geochem. Cosmochim. Acta 74, 6921e6933. Comodi, P., Zanazzi, P.F., Poli, S., 1997. High-pressure behavior of kyanite: compressibility and structural deformation. Am. Mineral. 82, 452e459. Ding, T., Jiang, S., Wan, D., Li, Y., Li, J., Song, H., Liu, Z., Yao, X., 1996. Silicon Isotope Geochemistry. Geological Publishing House, Beijing. Douthitt, C.B., 1982. The geochemistry of the stable isotopes of silicon. Geochem. Cosmochim. Acta 46, 1449e1458. Dupuis, R., Benoit, M., Nardin, E., Meheut, M., 2015. Fractionation of silicon isotopes in liquids: the importance of configurational disorder. Chem. Geol. 396, 239e254. Epstein, S., Taylor Jr., H.P., 1970. 18O/16O, 30Si/28Si, D/H, and 13C/12C studies of lunar rocks and minerals. Science 167, 533e535. Fitoussi, C., Bourdon, B., Kleine, T., Oberli, F., Reynolds, B.C., 2009. Si isotope systematics of meteorites and terrestrial peridotites: implications forMg/Si fractionation in the solar nebula and for Si in the Earth’s core. Earth Planet. Sci. Lett. 287, 77e85. Fitoussi, C., Bourdon, B., 2012. Silicon isotope evidence against an enstatite chondrite earth. Science 335, 1477e1480. Geilert, S., Vroon, P.Z., Keller, N.S., Gudbransson, S., Stefansson, A., van Bergen, M.J., 2015. Silicon isotope fractionation during silica precipitation from hot-springs waters: evidence from the Geysir hydrothermal flfluid. Iceland. Geochim. Cosmochim. Acta 164, 403e427. Georg, R.B., Halliday, A.N., Schauble, E.A., Reynolds, B.C., 2007. Silicon in the Earth’s core. Nature 447, 1102e1106. Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., 2009. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502. Giuli, G., Bonazzi, P., Menchetti, S., 1999. Al-Fe disorder in synthetic epidotes: a single-crystal X-ray diffraction study. Am. Mineral. 84, 933e936. Grant, F.S., 1954. The geological significance of variations in the abundances of the isotopes of silicon in rocks. Geochem. Cosmochim. Acta 5, 225e242. Guo, S., Ye, K., Chen, Y., Liu, J., Mao, Q., Ma, Y., 2012. Fluiderock interaction and element mobilization in UHP metabasalt: constraints from an omphaciteeepidote vein and host eclogites in the Dabie orogen. Lithos 136e139, 145e167. Guo, S., Ye, K., Yang, Y., Chen, Y., Zhang, L., Liu, J., Mao, Q., Ma, Y., 2014. In situ Sr isotopic analyses of epidote: tracing the sources of multi-stage fluids in ultrahigh-pressure eclogite (Ganghe, Dabie terrane). Contrib. Mineral. Petrol. 167, 975. Guo, S., Chen, Y., Ye, K., Su, B., Yang, Y., Zhang, L., Liu, J., Mao, Q., 2015a. Formation of multiple high-pressure veins in ultrahigh-pressure eclogite (Hualiangting, Dabie terrane, China): fluid source, element transfer, and closed-system metamorphic veining. Chem. Geol. 417, 238e260. Guo, S., Ye, K., Cheng, N., Chen, Y., Su, B., Liu, J., 2015b. Metamorphic P-T trajectory and multi-stage fluid events of vein-bearing UHP eclogites from the Dabie terrane: insights from compositional zonations of key minerals. Int. Geol. Rev. 9e10, 1077e1102. He, H.T., Liu, Y., 2015. Silicon isotope fractionation during the precipitation of quartz and the adsorption of H4SiO4(aq) on Fe(III)-oxyhydroxide surfaces. Chin. J. Geochem. 34 (4), 459e468. Hermann, J., Spandler, C., Hack, A., Korsakov, A., 2006. Aqueous fluids and hydrous melts in high-pressure and ultra-high pressure rocks: implications for element transfer in subduction zones. Lithos 92, 399e417. Huang, F., Chakraborty, P., Lundstrom, C.C., Holmden, C., Glessner, J.J., Kieffer, S.W., Lesher, C.E., 2010. Isotope fractionation in silicate melts by thermal diffusion. Nature 464, 396e400. Huang, F., Chen, L., Wu, Z., Wang, W., 2013. First-principles calculations of equilibrium Mg isotope fractionations between garnet, clinopyroxene, orthopyroxene, and olivine: implications for Mg isotope thermometry. Earth Planet. Sci. Lett. 367, 61e70.
Y. Li et al. / Solid Earth Sciences 4 (2019) 142e149 Huang, F., Wu, Z., Huang, S., Wu, F., 2014. First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals. Geochem. Cosmochim. Acta 140, 509e520. John, T., Klemd, R., Gao, J., Garbe-Sch€onberg, C.-D., 2008. Trace-element mobilization in slabs due to non steady-state fluiderock interaction: constraints from an eclogite-facies transport vein in blueschist (Tianshan, China). Lithos 103, 1e24. Kleine, B.I., Stefansson, A., Halldorsson, S.A., Whitehouse, M.J., J onasson, K., 2018. Silicon and oxygen isotopes unravel quartz formation processes in the Icelandic crust. Geochem. Perspect. Lett. 5e11. Li, Y., Yu, H., Gu, X., Guo, S., Huang, F., 2019. Silicon isotopic compositions of metamorphic fluids. Young Scientist Forum of Earth Science Abstract 2 (3) (in Chinese). Manning, C., 2004. The chemistry of subduction-zone fluids. Earth Planet. Sci. Lett. 223, 1e16. Manning, C.E., 2018. Fluids of the lower crust: deep is different. Annu. Rev. Earth Planet Sci. 46, 67e97. McCulloch, M.T., Gamble, J.A., 1991. Geochemical and geodynamical constraints on subduction zone magmatism. Earth Planet. Sci. Lett. 102, 358e374. Meheut, M., Lazzeri, M., Balan, E., Mauri, F., 2007. Equilibrium isotopic fractionation in the kaolinite, quartz, water system: prediction from fifirstprinciples density-functional theory. Geochem. Cosmochim. Acta 71, 3170e3181. Meheut, M., Lazzeri, M., Balan, E., Mauri, F., 2009. Structural control over equilibrium silicon and oxygen isotopic fractionation: a first-principles density-functional theory study. Chem. Geol. 258, 28e37. Meheut, M., Schauble, E.A., 2014. Silicon isotope fractionation in silicate minerals: insights from first-principles models of phyllosilicates, albite and pyrope. Geochem. Cosmochim. Acta 134, 137e154. Nagashima, M., Akasada, M., 2010. X-ray Rietveld and 57Fe Mossbauer studies of epidote and piemontite on the join Ca2Al2FeSi3O12(OH) e Ca2Al2MnSi3O12(OH) formed by hydrothermal synthesis. Am. Mineral. 95, 1237e1246. Pollington, A.D., Kozdon, R., Anovitz, L.M., Georg, R.B., Spicuzza, M.J., Valley, J.W., 2016. Experimental calibration of silicon and oxygen isotope fractionations between quartz and water at 250 C by in situ microanalysis of experimental products and application to zoned low d30Si quartz overgrowthsChem. Or. Geol. 421, 127e142. Pringle, E.A., Savage, P.S., Badro, J., Barrat, J.-A., Moynier, F., 2013. Redox state during core formation on asteroid 4-Vesta. Earth Planet. Sci. Lett. 373, 75e82. Qin, T., Wu, F., Wu, Z., Huang, F., 2016. First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz, albite, anorthite, and zircon. Contrib. Mineral. Petrol. 171, 91. Reynolds, J.H., Verhoogen, J., 1953. Natural variations in the isotopic constitution of silicon. Geochem. Cosmochim. Acta 3, 224e234. Richardson, S.M., Richardson, J.W., 1982. Crystal structure of a pink muscovite from Acher’s Post, Kenya: implication for reverse pleochroism in dioctahedral micas. Am. Mineral. 67, 69e75. Richter, F.M., Dauphas, N., Teng, F.-Z., 2009. Nontraditional fractionation of non-traditional isotopes: evaporation, chemical diffusion and Soret diffusion. Chem. Geol. 258, 92e103.
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ScienceDirect Solid Earth Sciences 4 (2019) 142e149 www.elsevier.com/locate/SESCI
First-principles calculations of equilibrium silicon isotope fractionation in metamorphic silicate minerals Yuanhong Li a, Wenzhong Wang b, Chen Zhou a, Fang Huang a,c,* a
CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, 230026, China b Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, China c CAS Center for Excellence in Comparative Planetology, University of Science and Technology of China, Hefei, 230026, China Received 10 September 2019; revised 24 September 2019; accepted 24 September 2019 Available online 27 November 2019
Abstract In this study, silicon isotope fractionation factors for metamorphic silicate including muscovite, epidote, and kyanite are calculated using first-principles methods based on density-functional theory. The reduced partition function ratio (103lnb) of 30Si/28Si decreases in the order of muscovite > epidote z kyanite. Combining with previous calculations, our results show that the equilibrium silicon isotope fractionation factors are correlated with average SieO bond length. These results predict that measurable Si isotope fractionation can occur during metamorphic fluid activities. At 1000 K, the calculated 103lna values for quartzeepidote, quartzekyanite, and quartzemuscovite are 0.51‰, 0.49‰, and 0.08‰, respectively. The calculation results are generally consistent with the observed Si isotopic data in two metamorphic eclogite-vein systems, showing that our work can provide useful information in investigating the Si isotope fractionation in metamorphic fluid evolution. Copyright © 2019, Guangzhou Institute of Geochemistry. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Si isotopes; First-principles calculation; Metamorphic fluid
1. Introduction Silicon is one of the most important elements in the Earth’s crust and mantle, and it constitutes the skeleton of silicate minerals in the form of silicon-oxygen polyhedrons. Silicon has three stable isotopes: 28Si, 29Si, and 30Si. The wide distribution of silicon in the lithosphere, hydrosphere, and biosphere makes Si isotopes a potentially useful tool to study a number of fundamental geochemical processes. Studies of Si isotopes have been carried on for more than half a century (Reynolds and Verhoogen, 1953; Grant, 1954; Allenby, 1954;
* Corresponding author. CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, 230026, China. E-mail address: [email protected] (F. Huang). Peer review under responsibility of Guangzhou Institute of Geochemistry.
Epstein and Taylor, 1970; Douthitt, 1982; Ding et al., 1996). During the last decade, owing to the development of Si isotope analytical techniques using MC-ICP-MS, there is great progress on the studies of Si isotope geochemistry. High precision Si isotope measurements have unraveled significant Si isotope fractionations during planetary core formation (Georg et al., 2007; Fitoussi et al., 2009; Chakrabarti and Jacobsen, 2010; Armytage et al., 2011; Fitoussi and Bourdon, 2012; Pringle et al., 2013; Zambardi et al., 2013) and evolution of mantle and continental crust (Savage et al., 2010, 2011, 2012, 2013). For better understanding the mechanisms of Si isotope fractionations during different geochemical processes, the equilibrium Si isotope fractionation factors among the rockforming minerals are essential. In previous studies, the equilibrium Si isotope fractionation between various kinds of common silicate minerals have been calculated by using the density functional theory (DFT), and their results show that
https://doi.org/10.1016/j.sesci.2019.09.004 2451-912X/Copyright © 2019, Guangzhou Institute of Geochemistry. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NCND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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the equilibrium fractionation factors are related to multiple controlling factors such as temperature, pressure, and cation composition (Meheut et al., 2009; Huang et al., 2014; Meheut and Schauble, 2014). As one of the major medium of mass exchange between the crust and the mantle, subduction zone fluids play a crucial role in global elemental cycling (McCulloch and Gamble, 1991; Scambelluri and Philippot, 2001; Manning, 2004; Hermann et al., 2006; Bebout, 2007). Silicon is one of the major solutes in subduction zone fluids (Manning, 2018), and greatly influence the physical and chemical properties of the fluids (Shen and Keppler, 1997; Bureau and Keppler, 1999). Therefore, it is important to study the behavior of Si during fluid evolution processes. Si isotopes in the crystallized products of subduction zone fluids may be a promising tool in the investigation of this problem. However, theoretical studies for Si isotope fractionation are rare for minerals that are commonly formed in high-temperature metamorphic fluid systems. This impedes the application of Si isotopes in studies of Si migration and isotope fractionation during metamorphic fluid activities. In this work, the equilibrium fractionation factors of Si isotopes between three typical metamorphic silicate minerals in veins, including epidote, muscovite, and kyanite are calculated using first-principles methods based on density-functional theory. The goal of this study is to constrain the Si isotope fractionation during the crystallization of HP-UHP metamorphic fluids. Furthermore, combining with the Si isotopic measurement data for the silicate minerals within two metamorphic eclogite-vein systems, the mechanism of Si isotope fractionation during metamorphic fluid activities are discussed.
where the asterisk denotes the heavier isotope; ui ¼ hcui/kBT, c is the speed of light; ui is the vibrational frequency of the ith mode; h and kB are the Planck and Boltzmann constants, respectively; T is the temperature in Kelvin; and N is the number of atoms in the unit cell. Quantum ESPRESSO (an open source software package based on DFT, plane waves, and pseudopotentials) was used to calculate the electronic structures and phonon frequencies of epidote, muscovite, and kyanite (Giannozzi et al., 2009). The calculation details were similar to those used in previous studies (Huang et al., 2013, 2014; Wu et al., 2015; Qin et al., 2016; Wang et al., 2017a, 2017b). The Local Density Approximation (LDA) was used in the calculations for exchange-correlation functions, which provides good predictions for mineral structures, thermodynamic properties, and phonon characteristics (e.g., Wentzcovitch et al., 2010; Huang et al., 2013). The plane-wave cutoff energy was 70 Ry. The pseudopotentials employed for calcium, aluminum, silicon, and oxygen were the same as those used by Huang et al. (2013), whereas those of hydrogen and iron were taken from Yang et al. (2017) and Wang et al. (2017b), respectively. A N1 N2 N3 grid whose dimensions depend on the size of the mineral unit cell were used to calculate the Brillouin zone summations over different electronic states. Crystal structures were optimized using variable cell shape molecular dynamics (Wentzcovitch, 1991). The residual forces acting on every atom were less than 1 104 Ry/Bohr, and unit-cell stresses were less than 0.5 kbar. Using the density functional perturbation theory, the dynamical matrices were calculated on a regular q mesh and then interpolated on a dense q mesh (Table 1) to obtain the vibrational density of each mineral.
2. Methods
3. Results
The substitution of isotopes with different masses into crystal lattices changes their vibrational frequencies, which control the equilibrium fractionation factors of stable isotopes (Bigeleisen and Mayer, 1947; Urey, 1947). The degree of equilibrium isotope fractionation of an element X between phases A and B is usually expressed as 103lnaAeB, where aAeB (defined as RA/RB) is the isotope fractionation factor between A and B. When B is an ideal gas of X atom, the fractionation factor can be represented by the reduced partition function ratio (b): aAeB ¼ bA/bB. For a crystal, the b value can be calculated as follows:
We calculated the equilibrium Si isotope fractionation factors (103lnaSi) for three major minerals in HPeUHP veins: epidote, kyanite, and muscovite. Their relaxed crystal structures are shown in Fig. 1. The calculated crystal lattice parameters of muscovite, kyanite, and epidote are listed in Table 2, and agree well with experimental data. The calculated parameters are generally slightly smaller (with one exception) than the experimental data, the discrepancies are within 2% for lattice constants, and 4% for volumes (Table 2). This is consistent with previous studies, in which the equilibrium volumes are usually slightly underestimated by LDA static calculation (Huang et al., 2013, 2014; Qin et al., 2016). However, the vibrational effect can generally increase the equilibrium volume by ~2% at 0 GPa and 300 K (Wu and
b¼
Y3N u
1
e2ui 1 eui ui 1 eui e12ui i
i
Table 1 K mesh used for Brillouin zone summations over electronic states, regular q mesh used for real space force constant matrix, and dense q mesh used for the reduced partitions function ratio. Mineral
Formulas
K mesh
Regular q mesh
Dense q mesh
Muscovite Epidote Kyanite
KAl2(AlSi3O10) (OH)2 Ca2Al2Fe(SiO4) (Si2O7)O(OH) Al2SiO5
421 121 444
111 121 111
111 121 111
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Fig. 1. Crystal structures of epidote, kyanite, and muscovite. O atom is shown in red. The dark blue structure is SiO4 tetrahedron formed by one Si atom and four O atoms, and the gray structure is octahedron formed by one Al atom and six O atoms.
Table 2 The crystal lattice parameters optimized at volume corresponding to zero pressure of static first-principles calculation compared with experiment measurements (reported in unit cell). Mineral
a(Å)
b(Å)
c(Å)
a( )
b( )
g( )
V (Å3)
Muscovite
5.132 5.199 1.29 8.860 8.891 8.890 0.34 7.053 7.124 1.00
8.911 9.027 1.28 5.589 5.624 5.637 0.74 7.780 7.856 0.97
20.154 20.106 0.24 10.006 10.164 10.160 1.54 5.509 5.577 1.22
90 90
95.686 95.782 0.1 114.918 115.44 115.432 0.5 101.103 101.15 0.05
90 90
917.152 938.715 2.30 449.340 458.950 459.786 2.18 284.655 293.978 3.17
Epidote
Kyanite
90 90 90 90 89.99 0.01
90 90 90 106 105.95 0.05
This study Experimenta Error (%) This study Experimentb Experimentc Error (%) This study Experimentd Error (%)
Data sources for experimental studies. a Richardson and Richardson (1982). b Giuli et al. (1999). c Nagashima and Akasada (2010). d Comodi et al. (1997).
Wentzcovitch, 2007; Huang et al., 2013). Therefore, when vibrational effect is taken into account, the difference between the calculated volumes and experimental data is expected to be ~1% (Wentzcovitch et al., 2010). There is also a good match between the experimental peak position and the calculated
frequencies of epidote (Fig. 2), indicating the reliability of our calculations. The temperature-dependent variations in 103lnbSi and 3 10 lnaSi between quartz and other minerals are shown in Fig. 3, in which 103lnaAeB ¼ 103ln(bA/bB) z d30SiA e
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Fig. 2. The calculated vibrational frequencies of epidote compared with Raman and measurement. Experimental Raman data are from rruff. info/ R100129 supplied by William W. Pinch. The short vertical lines in red show the positions of Raman active in spectrum.
d30SiB ¼ D30SiAeB, and d30SiA ¼ [(30Si/28Si)A/(30Si/28Si)s3 tandard e 1] 1000 (‰). The parameters of the polynomial fitting of 10 lnbSi 3 and 10 lnaSi are given in Tables 3 and 4, respectively, in which the data of quartz was quoted from Qin et al. (2016). The errors of the calculated volumes and bond length do not affect the result of 103lna because the offsets of 103lnb are systematic and can be canceled out as 103lnaAeB ¼ 103lnbA e 103lnbB (Huang et al., 2013). Our results confirm that the Si isotope composition of muscovite is very close to quartz, but significantly heavier compared with epidote and kyanite in equilibrium. At 1000 K, the calculated 103lnaSi(quartzemusco3 3 vite), 10 lnaSi(quartzekyanite) and 10 lnaSi(quartzeepidote) are 0.08, 0.49, and 0.51, respectively. In Meheut et al. (2007), the influence of the choice of the cut-off energy for the phonon energy calculations was discussed, and their result proves that the influence is negligible for the calculated fractionation factors. The pressure effect on Si isotope fractionation factors is negligible compared with Mg and O isotopes (Wu et al., 2015). Furthermore, the anharmonic effect is expected to be large only if the mass of the atom is small and the bond environment is strongly asymmetric (Meheut et al., 2009), so it should not play an important role in our case. In conclusion, the overall uncertainties of the 103lnbSi and 103lnaSi is expected to be smaller than the analytical error of Si isotopes at present (~0.07‰, 2SD). 4. Discussion Generally, equilibrium isotope fractionations are controlled by bond lengths and energies, which are related to bond strengths. Shorter chemical bonds have higher bond strengths and higher vibrational frequencies, which preferentially incorporate heavy isotopes relative to the longer, weaker bonds (Urey, 1947; Schauble, 2004; Young et al., 2009).
Fig. 3. (A) Calculated equilibrium reduced partition function (103lnb) vs. 106/ T2 (T is temperature in Kelvin) for 30Si/28Si of epidote (ep), kyanite (ky), and muscovite (mus) at 0 GPa. (B) Calculated 103lnaqz-minerals of Si isotopes in this study. The data are in Tables 3 and 4
The mechanisms that control the equilibrium Si isotope fractionation have been investigated for several decades. Theoretical calculations done by Grant (1954) suggested that the equilibrium Si isotope fractionations are controlled by the polymerization degrees of the SiO4 4 tetrahedra in the silicates. However, Meheut et al. (2009) calculated the equilibrium O and Si isotope fractionation of quartz, enstatite, forsterite, kaolinite, and lizardite, and showed that Si fractionation factor is not only dependent on the polymerization degrees, but also many other factors. For example, minerals with same polymerization degree can have different fractionation properties (such as kaolinite and lizardite), showing the complex structural controls over equilibrium Si isotope fractionations. Meheut and Schauble (2014) made a further calculation on fractionation factors for Si isotopes in phyllosilicates (pyrophyllite and talc), albite and pyrope with first-principles methods based on density-functional theory. Their results suggest that Si isotope fractionation is correlated with stoichiometry and correlated with SieO bond length. In their
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Table 3 Fitting parameters of calculated reduced partition function ratios of30Si/28Si (103lnb) and the average SieO bond lengths. Fitting equation: 103lnb ¼ ax3þbx2þcx, where x ¼ 106/T2, T is temperature in Kelvin. The temperature range for fitting is 675e1675 K. Minerals
Formulas
a
b
c
Bond lengths (Å)
Muscovite Epidote Kyanite Quartz * Data source: * Qin et al.
KAl2(AlSi3O10) (OH)2 Ca2Al2Fe(SiO4) (Si2O7)O(OH) Al2SiO5 SiO2 (2016).
0.0087 0.0074 0.0068 0.0092
0.2221 0.1968 0.1904 0.2275
8.0312 7.5792 7.5996 8.1207
1.623 1.630 1.636 1.617
Table 4 Fitting parameters of calculated fractionation factors of30Si/28Si (103lna) between quartz and other minerals. Fitting equation: 103lna ¼ ax3þbx2þcx, where x ¼ 106/T2, T is temperature in Kelvin. The temperature range for fitting is 675e1675 K. Mineral pairs
a
b
c
Qz-Mus Qz-Ep Qz-Ky
0.0005 0.0018 0.0024
0.0054 0.0307 0.0371
0.0895 0.5415 0.5211
opinion, cations with lower electronegativity have higher effect on Si isotope fractionation (Meheut and Schauble, 2014). In Huang et al. (2014), Si isotope fractionation factors for mantle minerals (olivine, wadsleyite, ringwoodite, pyroxenes, pyrope, majorite, and Mg-perovskite) show significant Si isotope fractionation between minerals with different Si coordination numbers. Qin et al. (2016) calculated equilibrium fractionation factors for Si isotopes between common silicate minerals in granites, showing that 103lna values for 30Si/28Si are controlled mainly by the average SieO bond length, an interpretation that was first proposed by Meheut and Schauble (2014). We also found that 103lnb values for 30Si/28Si ratios are linearly correlated with the average SieO bond lengths of minerals except in epidote (Fig. 4). This outlier may be due to other factors, such as polyhedral distortion and the electronegativity of the second closest atoms relative to Si.
Fig. 4. The negative correlation between 103lnbSi and the average SieO bond lengths at 1000 K. The data for grey dots are from Qin et al. (2016).
During crystallization of metamorphic fluids, different kinds of minerals can be formed (Castelli et al., 1998; Becker et al., 1999; Hermann et al., 2006; John et al., 2008), this may change the Si isotope composition of the fluids. Theoretical calculations of the equilibrium Si isotope fractionations between fluid-minerals and mineral-minerals are helpful in speculating the Si isotopic variation during fluid evolution. Dupuis et al. (2015) calculated equilibrium Si isotope fractionation factors of quartz and dissolved silicic acid (H4SiO4 and H3SiO 4 ), and found that quartz has a heavier Si isotopic composition than that of aqueous H4SiO4, with a 30Si fractionation factor of 0.15 ± 0.03‰ at 300 K. He and Liu (2015) calculated equilibrium Si isotope fractionation factors between quartz, orthosilicic acid, and adsorption Si on Feoxyhydroxide surface. The result reveals that quartz is enriched in heavy Si isotopes than H4SiO4(aq), and Si isotopes are also significantly fractionated (3.0‰) between the adsorbed Si and aqueous H4SiO4. They also proposed that significant kinetic isotope effect (KIE) can take place during the formation of amorphous silica, leading to the enrichment of light Si isotopes in amorphous silica (He and Liu, 2015). The results in Dupuis et al. (2015) are consistent with the experimental data of Pollington et al. (2016), in which Si isotope fractionation between quartz and aqueous solutions under controlled thermal and chemical conditions was reported. However, the data in Dupuis et al. (2015) and Pollington et al. (2016) do not agree well with natural observations in low-temperature systems, in which the quartz precipitation is dominated by kinetic, rather than equilibrium processes. But under high-temperature conditions, equilibrium crystallization of metamorphic fluids should be more likely. When the temperature reaches to 1000 K, the equilibrium Si isotope fractionation between quartz and fluid is 0.15 ± 0.03‰ by using the relationship: 1000lna30Siquartzefluid ¼ (0.15 ± 0.03) 106/T2 derived in Pollington et al. (2016). Combining with the calculated D30Siquartzemineral values in this study, the D30Sifluidemineral can be obtained as 0.07‰, 0.34‰, and 0.36‰, for muscovite, kyanite, and epidote, respectively. Together with calculated results for other common minerals in crystallization products of metamorphic fluids (for example, veins) such as diopside (Qin et al., 2016) and pyrope (Huang et al., 2014), the Si isotopic evolution pattern of the fluid can be deduced by the mineral composition of the crystallization products. For example, forming of Si-rich veins (such as quartz veins) may lead to decrease in the d30Si value of the residual fluids, because these veins usually have high quartz content. But for veins that are mainly composed by
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epidote, kyanite, and garnet (Spandler and Hermann, 2006; John et al., 2008; Guo et al., 2012, 2015a), as these minerals all have Si isotope compositions lighter than fluids, the d30Si value of the residual fluids could rise. Due to the difficulties in directly analyzing subduction zone metamorphic fluids, determining the Si isotopic composition of these fluids is still challenging. For this reason, the fractionation of Si isotopes in metamorphic fluid systems are poorly understood. Several studies have reported the Si isotope composition of hydrothermal quartz or silica (Geilert et al., 2015; Brengman et al., 2016; Kleine et al., 2018), which can still provide some useful information for Si isotope fractionations during fluid activities. Brengman et al. (2016) presented micro-scale d30Si heterogeneity of quartz in brecciated pillow basalt, recrystallized chert, and chert clasts in Isua Greenstone Belt, the quartz amygdules in brecciated pillow basalt, indicating the KIE effect during quartz precipitation under hydrothermal conditions. Kleine et al. (2018) measured Si isotope composition of hydrothermal quartz and silica polymorphs in Iceland, showing that fluid activities such as fluiderock interaction, cooling, boiling, changes in composition of fluids can cause large Si isotope fractionation. The mechanisms of Si isotope fractionation can be different in various conditions. Equilibrium fractionation may be the dominant mechanism during higher temperature (~200e400 C) hydrothermal activities, but kinetic fractionation is more obvious under lower temperatures (Kleine et al., 2018). The data in Kleine et al. (2018) indicate that under higher temperature, first-principles calculation can provide reliable constraints on the Si isotope fractionation during crystallization of quartz. It could also be useful in investigating mineral crystallization processes in metamorphic fluid systems. As the crystallized products of fluids, veins in metamorphic rocks can retain valuable information. In order to examine whether the calculated equilibrium Si isotope fractionations are applicable in natural systems, we measured the Si isotope composition of silicate minerals within two metamorphic eclogitevein systems (Ganghe and Hualiangting) for comparison. The two systems are located in the Dabie orogen, eastern China, and the veins were formed after crystallization of HP-UHP fluids that were released by breakdown of lawsonite in the host eclogite. The PT conditions were 2.8e3.0 GPa, 650e680 C for Ganghe veins (Guo et al., 2012) and 2.7e3.0 GPa, 660e720 C for Hualiangting veins (Guo et al., 2015a). The veins mainly consist of epidote, omphacite, quartz, kyanite, amphibole, garnet, muscovite, and other minor minerals, and more details are reported in Guo et al. (2012, 2014, 2015a, 2015b). The results show that the average Si isotope fractionations between minerals in the two systems are D30Siquartzeepidote ¼ 0.43‰, 30 D Siquartzekyanite ¼ 0.40‰, D30Siquartzemuscovite ¼ 0.00‰ for the Ganghe samples, and D30Siquartzeepidote ¼ 0.44‰, and D30Siquartzekyanite ¼ 0.42‰ for the Hualiangting samples (Li et al., 2019), the analytical errors for each minerals are within 0.06‰ (2SD). The calculated 103lna values for 30Si/28Si for quartzeepidote, quartzekyanite, and quartzemuscovite at
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1000 K in this study are 0.51‰, 0.49‰, and 0.08‰, respectively, which are generally in agreement with the measured values. The discrepancies between the calculated and measured values are within 0.09‰, which are significantly smaller than that in low-T systems (Dupuis et al., 2015; Pollington et al., 2016). The similarity between the calculated fractionation factors and the measured data suggests that equilibrium processes were dominant during vein-mineral crystallization, indicating the effectiveness of our calculated results in clarifying the mechanism of Si isotope fractionation during metamorphic fluid evolution. If the veins were formed under Si isotope equilibrium, then the correlation of d30Siquartz versus d30Simineral should fall on a line with a slope of ~1 for, which corresponds to a certain temperature. This could help us estimate the crystallization temperature. As an attempt, two mineral pairs (quartz-epidote and quartz-kyanite) in the Ganghe and Hualiangting samples are plotted on the d30Siquartzd30Simineral figures with calculated fractionation lines (Fig. 5). The d30Siquartz values are linearly correlated with d30Siminerals following the equilibrium fractionation lines around 800 C for both minerals. This result is about 100 C higher than the temperature derived from the mineralogical study (Guo et al., 2012, 2015a), which may be
Fig. 5. d30Si for mineral pairs of quartz-epidote (A) and quartz-kyanite (B) in the Ganghe and Hualiangting samples, showing the predicted peak temperature during the fluid evolution processes by the Si isotopes geothermometer. The temperature gradients are based on the first-principles calculations in this study.
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due to minor influence of kinetic processes such as chemical and thermal diffusion (Richter et al., 2009; Huang et al., 2010; Kleine et al., 2018) or the uncertainty of elemental thermometers. 5. Conclusions Equilibrium Si isotope fractionation factors for metamorphic minerals (muscovite, epidote, and kyanite) are calculated using first-principles calculations. The results indicate that the sequence of 30Si enrichment follows the order of muscovite > epidote z kyanite, and the Si isotope fractionation between muscovite and quartz is limited (~0.08‰ at 1000 K). The Si isotope fractionation factors of the calculated minerals are affected by mineral structure, especially the average SieO bond length. The calculated results can be compared with the measured Si isotope data of minerals within two eclogitevein system in the Dabie orogen, China. The measured data are generally consistent with the calculated equilibrium Si isotope fractionation factors, suggesting that the Si isotope fractionation between these minerals were likely dominated by equilibrium fractionation during crystallization from the fluids. Conflict of interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work is financially supported by the Natural Science Foundation of China (41873009 and 41630206). We thank Xiaobin Cao, an anonymous reviewer, and Editor-in-Chief Weidong Sun for their comments and suggestions, which greatly improved the manuscript. References Allenby, R.J., 1954. Determination of the isotopic ratios of silicon in rocks. Geochem. Cosmochim. Acta 5 (1), 40e48. Armytage, R.M.G., Georg, R.B., Savage, P.S., Williams, H.M., Halliday, A.N., 2011. Silicon isotopes in meteorites and planetary core formation. Geochem. Cosmochim. Acta 75, 3662e3676. Bebout, G.E., 2007. Metamorphic chemical geodynamics of subduction zones. Earth Planet. Sci. Lett. 260, 373e393. Becker, H., Jochum, K.P., Carlson, R.W., 1999. Constraints from high-pressure veins in eclogites on the composition of hydrous fluids in subduction zones. Chem. Geol. 160, 291e308. Bigeleisen, J., Mayer, M.G., 1947. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 15, 261e267. Brengman, L.A., Fedo, C.M., Whitehouse, M.J., 2016. Micro scale silicon isotope heterogeneity observed in hydrothermal quartz precipitates from the >3.7 Ga Isua Greenstone Belt, SW Greenland. Terra. Nova 28, 70e75. Bureau, H., Keppler, H., 1999. Complete miscibility between silicate melts and hydrous fluids in the upper mantle: experimental evidence and geochemical implications. Earth Planet. Sci. Lett. 165, 187e196.
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