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Grain growth kinetics of majorite and stishovite in MORB
Physics of the Earth and Planetary Interiors 183 (2010) 183–189
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Grain growth kinetics of majorite and stishovite in MORB Daisuke Yamazaki ∗ , Takuya Matsuzaki, Takashi Yoshino Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193 Japan
a r t i c l e
i n f o
Article history: Received 14 July 2009 Received in revised form 4 August 2010 Accepted 28 September 2010 Guest Editors Daisuke Suetsugu Craig Bina Toru Inoue Douglas Wiens
a b s t r a c t Grain growth rates of majorite and stishovite, in their aggregates with MORB composition, were studied at 18 GPa and temperatures ranging from 1873 to 2223 K. The rates of grain growth were expressed by Gn − G0n = k0 t exp(−H ∗ /RT ) where G is the grain size at time t (s), and G0 is the initial grain size. We determined the grain growth kinetic parameters for majorite, where n = 9.1 ± 1.3, H* = 950 ± 249 kJ/mol, and log k0 = −32.5 ± 2.3 m9.1 /s for the graphite capsule and log k0 = −31.3 ± 3.9 m9.1 /s for the Re capsule. Kinetic parameters for stishovite were determined to be n = 6.6 ± 0.9, H* = 599 ± 226 kJ/mol, and log k0 = −30.6 ± 0.9 m6.6 /s for the graphite capsule and log k0 = −29.0 ± 1.1 m6.6 /s for the Re capsule. © 2010 Elsevier B.V. All rights reserved.
Editor Mark Jellinek Keywords: Grain size Majorite Stishovite High-pressure experiment
1. Introduction The subducting slab is mainly composed of two layers characterized by chemistry; one is a depleted peridotite layer and the other is an overlying garnetite layer with MORB composition (e.g., Ringwood, 1991). Thus the convection style of these two layers in the mantle is a key factor in understanding the dynamics and chemical heterogeneity of the mantle. One of the most profound problems is whether the garnetite layer is separated from the peridotite layer. If so, the garnet-rich mantle transition zone is formed above 660 km because the garnetite layer is denser than the surrounding mantle, but less dense than lower mantle materials (e.g., Anderson, 1979). If not, the garnetite layer sinks to the core–mantle boundary region with the peridotite layer (e.g., van der Hilst et al., 1997). Karato (1997) pointed out that the viscosity structure across the subducting slab was an important factor to evaluate with regard to the separation of the garnetite layer. For polycrystalline aggregates, the grain size of the constituent minerals is one of the most important parameters that determine rheological behavior. For example, it is well known that the transition between dislocation and diffusion creep during deformation
∗ Corresponding author. Tel.: +81 858 43 3741; fax: +81 858 43 2184. E-mail address: [email protected] (D. Yamazaki). 0031-9201/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2010.09.009
is essentially controlled by grain size (Frost and Ashby, 1982). Also, the viscosity in the diffusion creep regime is defined as a function of the grain size of the constituent materials (Raj and Ashby, 1971). Knowledge of grain growth is necessary in order to estimate the grain size of rocks constituting the slab and the resultant viscosity. Grain growth kinetics of major minerals forming peridotite layers (i.e., olivine, wadsleyite, ringwoodite, perovskite) have been studied extensively (Karato, 1989; Nishihara et al., 2006; Yamazaki et al., 1996, 2005). However, grain growth of majorite as the most dominant mineral of the garnetite layer is still unknown. Thus we conducted a series of high-pressure experiments at a pressure of 18 GPa, equivalent to a depth of the mantle transition zone, and temperatures of 1673–2273 K to determine the grain growth kinetics of majorite in majorite dominant rocks. 2. Experimental procedures We used two types of glass powders with compositions of pyrolite minus olivine and MORB as starting materials (Irifune and Ringwood, 1987) (Table 1). The pyrolite minus olivine powder was prepared according to the previous report (Irifune, 1987) and MORB powder was prepared by quenching method using a furnace at ambient pressure with oxygen control with CO2 + H2 gas (Kubo, personal communication). We employed a Kawai-type doublestage multianvil high-pressure apparatus (USSA-1000, -5000). We
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Table 1 Chemical composition of starting materials and run products. Py − Ol
MORB
SiO2 TiO2 Al2 O3 Cr2 O3 FeOc MgO CaO Na2 O Total
a
IR87
Stating material
Run product
IR87
Starting material
Run productb
50.32 0.57 16.06 – 7.67 10.48 13.03 1.87 100.00
50.16 (56) 0.54 (6) 15.27 (31) – 7.45 (36) 10.33 (29) 13.00 (27) 2.55 (16) 99.31
47.34 (92) 0.44 (10) 16.78 (36)
51.12 0.45 11.29 0.91 3.08 22.84 9.38 0.93 100.0
50.37 n.d. 12.53 0.97 3.02 22.21 9.59 0.77 98.76
51.47 (76) 0.38 (6) 11.61 (32) 0.91 (5) 2.89 (15) 23.26 (40) 9.32 (28) 0.82 (9) 100.67
8.41 (25) 11.33 (30) 14.34 (28) 1.76 (13) 100.44
Cation (O = 24) Si Ti Al Cr Fe2+ Mg Ca Na Total a b c
6.84 (9) 0.05 (1) 2.86 (6) – 1.02 (3) 2.44 (6) 2.22 (5) 0.49 (4) 15.93
7.14 (6) 0.04 (1) 1.90 (5) 0.10 (1) 0.34 (2) 4.81 (8) 1.38 (4) 0.22 (2) 15.93
Average composition of majorites (n = 117). n = 114. All iron is assumed to be ferrous iron.
Table 2 Variations of grain size and water content of run products conducted at 18 GPa. Except for run 1K648, all samples were undergone pre-heating at 1673 K for 30 min. Run no.
Temperature (K)
Time (h)
Graphite capsule
Re capsule
Grain size
Starting material: MORB 1K648 1673 1873 1K680a 1K838 1873 1K655 1873 2073 1K677a 1K847 2073 a 2273 5K968 1K843 2273 5K984 2273 5K988 2273 Starting material: Py − Ol 1K717 2073
Water (wt.%)
Mj (m)
St (m)
0.5 2 3 32 2 3 2 3 8 32
0.5 (0.3) 0.8 (0.4) 0.9 (0.4) 1.3 (0.7) 1.0 (0.5) 1.4 (0.7) 2.1 (1.0) 2.6 (1.5) 3.3 (1.8) 3.8 (2.2)
0.3 (0.1) 0.6 (0.2) 0.6 (0.3) 0.6 (0.2) 0.6 (0.3) 0.6 (0.3) 1.0 (0.4) 1.1 (0.5) 1.0 (0.3) 1.1 (0.5)
2
8.5 (5.2)
–
Grain size
Water (wt.%)
Mj (m)
St (m)
0.124 0.005 0.005 0.004 0.006 0.002 0.005 0.003 0.002 <0.001
1.2 (0.6) 2.6 (1.1) 2.6 (1.3) 2.9 (1.3) 2.3 (1.2) 3.0 (1.4) 2.7 (1.4) 3.8 (2.0) 4.4 (1.9) 4.7 (2.0)
0.6 (0.3) 1.0 (0.4) 1.1 (0.4) 1.2 (0.5) 1.1 (0.5) 1.2 (0.5) 1.2 (0.6) 1.3 (0.6) 1.8 (0.8) 1.7 (0.6)
0.135 0.032 0.016 0.008 0.012 0.012 0.020 0.004 0.003 0.002
n.d.
6.3 (3.7)
–
n.d.
Numbers in parentheses are uncertainties estimated from the 1 of grain size distributions. a These data were used as initial grain sizes.
used tungsten carbide (WC) cubes with a truncated edge length of 6 mm. In order to observe the effect of oxygen fugacity on grain growth, two samples – contained respectively within graphite and Re capsule – were used in each experimental run. A WRe3% –WRe25% thermocouple was placed between the two capsules in the center of the LaCrO3 furnace. The samples were compressed to 18 GPa at room temperature. Then the temperature was increased to a pre-annealing temperature of 1673 K for 30 min. At this stage, the starting glass was completely crystallized (run no. 1K648, Table 2). After the preannealing, temperature was increased to the desired range from 1873 to 2273 K for grain growth studies. Temperature was kept constant within 5–10 ◦ C of the desired value for time intervals of 2–32 h. The recovered sample charges were mounted in epoxy resin and polished with diamond powder and colloidal silica. X-ray micro-diffraction measurements were performed to identify the phases present and electron-prove micro-analyses were carried out to measure chemical composition (Table 1). Using a field emission scanning electron microscope (FE-SEM), the observation of microstructures, such as grain boundaries, were made on the
polished surface after chemical etching with 5% HF for several minutes to sharpen grain boundaries. Without etching, neither grain boundaries nor the individual grains were observed. Grain size measurements were made on the digitized FE-SEM images using the intercept method. Average grain size (G) was estimated from the measured average intercept length (L) using the relationship G = cL, where c is a constant value of 1.56 (Mendelson, 1969). The water content in the samples after experiments was determined by Fourier-transform infrared (FTIR) spectroscopy. A non-polarized IR beam of cross-section 100 m × 100 m was directed to the polycrystalline samples with thickness of 100–250 m. Background corrections of the absorbance spectra were carried out by a spline fit of the baseline, and water content was calculated using a calibration based on Paterson (1982). 3. Results Microstructural observations with FE-SEM and X-ray microdiffraction measurements revealed that the recovered samples with starting material of MORB were composed of two phases of majorite and stishovite without a minor phase (Fig. 1A–F). The
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Fig. 1. A secondary electron image of the recovered samples for MORB composition annealed at 1873 K for 3 h (run 1K838) with graphite capsule (A) and with Re capsule (B), at 2273 K for 3 h (run 1K843) with graphite capsule (C) and Re capsule (D), at 2273 K for 32 h (run 5K988) with graphite capsule (E) and with Re capsule (F), and sample with pyrolite minus olivine composition annealed at 2073 K for 2 h (run 1K717) with graphite capsule (G) and with Re capsule (H). All samples were etched with HF for clearer visualization of grain boundaries. It is difficult to observe grain boundary without etching. The pores were formed by the etching.
samples contained a substantial amount of stishovite (∼10%). In contrast, the recovered samples with starting composition of pyrolite minus olivine contained tiny amounts of stishovite (less than 1%) (Fig. 1G and H). Grain boundaries in both compositions showed almost straight lines or gentle curvatures but not wavy (Fig. 1) and homogeneous grain sizes (Fig. 2) with size distribution of the lognormal to LSW distribution in which a peak skews toward larger grain size (Lifshitz and Slyozov, 1961; Wagner, 1961). Stishovite grains of euhedral shape are commonly, but not exclusively, located on majorite grain boundaries. The grain sizes of both majorite and stishovite increased with increasing run duration and/or temperature, as shown in Fig. 1 and Table 2.
In Fig. 3, representative FTIR spectra of the samples are shown. Bands around ∼3110 cm−1 were observed in all samples in this study, which can be assigned to hydrous stishovite (Panero et al., 2003). The observed broad band around 3450 cm−1 suggests the presence of grain boundary water. Bolfan-Casanova et al. (2000) reported a sharp band around 3550 cm−1 for structural water of tetragonal garnet but a broad band at same position for cubic garnet. Our observations are consistent with the results of BolfanCasanova et al. (2000) and Yoshino et al. (2008, for the Al-bearing system). In an Al-free system, water prefers to partition into majorite rather than stishovite. For example, the partition coefficient of water between majorite and stishovite (Kmj /st ) is ∼270
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B
A
0.3
water content (wt.%)
normalized frequency
A
0.2
0.1
0.1
0.05
0
D
0.3 0
B
0.2
0.1
0
–1
0
1 –1
0
log (L/L ave)
1
log (L/L ave)
water content (wt.%)
normalized frequency
C
0.1
0.05
Fig. 2. Representative distributions of grain size for sample, (A) 1K838 with graphite capsule, (B) 1K838 with Re capsule, (C) 5K988 with graphite capsule and (D) 5K988 with Re capsule.
(Bolfan-Casanova et al., 2000). The water contents of samples with the Re capsule were systematically greater than those with graphite capsules (Table 2). The samples contained a high water content of ∼0.12 wt% after initial heating at 1673 K for 30 min. However, water content of those samples which were annealed continuously at higher temperature (1873–2273 K) for 2 h were drastically reduced to less than 0.03 wt%, and water content did not change with additional annealing (Fig. 4). Thus we assume that such trace amounts of water present in these samples should yield only negligible effects on the grain growth in this study, based on previous results on the effect of water content on the grain growth of wadsleyite (Nishihara et al., 2006). Averages of grain sizes with MORB starting composition (Table 2) were fitted to a rate equation for grain growth, expressed as Gn − G0n = kt, where G is the grain size at time t, G0 is the initial grain size at time t = 0, n is a grain growth exponent factor, and k
3550
3110
–1
absorption coeffi cient (cm )
30
20
10
0 4000
3500
3000
2500
Wavenumber (cm-1) Fig. 3. Representative FTIR spectra of samples: solid, dashed and dotted lines correspond to the sample numbers 5K988 (graphite capsule), 1K838 (Re capsule) and 1K648 (graphite capsule), respectively (see also Table 1). Arrows indicate the characteristic peaks of garnet at 3550 cm−1 and stishovite at 3110 cm−1 .
0
0
10
time (h)
20
30
Fig. 4. Change of water content with increasing annealing time. Graphite (A) and Re (B) capsules were used in the experiments. Circles, squares and triangles represent the water content at 2273, 2073, 1873 K, respectively. Data at t = 0 (diamonds) show the initial contents just after the initial annealing at 1673 K for 30 min.
is a rate constant. Here, the rate constant k represents the dependence of temperature in the Arrhenius relation and is expressed as k = k0 exp(−H* /RT), where k0 is the pre-exponential term depending on oxygen fugacity, H* is the activation enthalpy, R is the gas constant and T is the absolute temperature (e.g., Burke, 1949). In this study, G0 values are assumed to be the average grain size of samples annealed at target temperatures (1873, 2073 and 2273 K) for 2 h, respectively, to eliminate the effect of the change of water content during experiments (Fig. 4). Grain size evolution of majorite and stishovite with MORB starting composition, with increasing duration and/or temperature, are plotted in Figs. 5 and 6. A non-linear least square fitting to the grain growth law yielded grain growth kinetic parameters for majorite as follows: n = 9.1 ± 1.3, H* = 950 ± 249 kJ/mol, and log k0 = −32.5 ± 2.3 m9.1 /s for the graphite capsule and log k0 = −31.3 ± 3.9 m9.1 /s for the Re capsule. Kinetic parameters for stishovite were determined to be n = 6.6 ± 0.9, H* = 599 ± 226 kJ/mol, and log k0 = −30.6 ± 0.9 m6.6 /s for the graphite capsule and log k0 = −29.0 ± 1.1 m6.6 /s for the Re capsule. The grain size increased with increasing run duration in both samples for the graphite capsule and Re capsule, with grain sizes in the Re capsule systematically larger than those in the graphite capsule. However, the regression lines for the Re capsule somewhat deviate from those of the expected values displayed by the solid lines (Figs. 5 and 6). The grain size of majorite with starting composition of pyrolite minus olivine was much larger (3–8 times) than that of MORB at
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6
Grain size of Mj (µm)
Grain size (µm)
4
4
2
2
Mj 0 3
0 0
0.5
1
1.5
2
Grain size (µm)
Grain size of St (µm) Fig. 7. Comparison of grain sizes of majorite and stishovite. Best fitted line for the plots is shown.
2
the same experimental conditions by the comparison run 1K677 with 1K717 (Table 2).
1
4. Discussion St 0
0
10
20
30
time (h) Fig. 5. Variation of grain sizes of majorite (A) and stishovite (B) with increasing annealing time at different temperatures. Solid and open symbols correspond to the grain sizes for graphite and Re capsules, respectively. Circles, squares and triangles display the grain sizes at 2273, 2073 and 1873 K, respectively. Solid and dotted lines indicate the non-linear least square fit to the grain growth law for the data with graphite and Re capsules, respectively. Uncertainties are shown by error bars. On the error bar, small symbols display the upper and lower bounds of uncertainties for each data points using same symbol type with data points.
–45
–50
log G
n
n –G0
(m)
A
–55 Mj
–40
n
n
log G –G0 (m)
B
–45
St
–50
3
4
5
6
Log time (s) Fig. 6. Alternative plots of grain growth of majorite (A) and stishovite (B) with time. Symbols for data points and error bars are same as used in Fig. 5.
For the grain growth law, growth exponent, n, is considered to be a geometric factor, and it is theoretically expected to be 2 in the grain growth of a single phase (Burke, 1949). However, grain growth exponent, n, were reported to be more than 2 for the multiphase system. Microstructure of two phase system is classified into two types: one is dual-phase (duplex structure) and the other is dispersion structure. In the former, most of secondary phase locate on the grain boundary of dominant phase. On the other hand, the secondary phase located in the crystal of dominant phase as inclusion in dispersion structure. The aggregate of majorite plus stishovite in this study shows almost the dual-phase (duplex structure) as shown in Fig. 1. In this case, the secondary phase retards the grain boundary migration of the dominant phase, a process called Zener pinning (Nes et al., 1985). Both of grains of dominant and secondary phases grow each other, satisfying Zener’s relation, G = Cd/fm , where C is a constant, G and d are the grain sizes of dominant phase and secondary phase in steady state, respectively, f is the volume fraction of secondary phase and m is the exponential factor (∼1/3–1, Evans et al., 2001). In this study, although G/d is scattered, most of samples yielded almost constant ratio of G/d with 2.0–2.5, indicating that Zener’s relation was achieved in most of samples (Fig. 7). During annealing, coarsening of secondary phase can occur by Ostwald ripening to reduce total interfacial energy in the system. Smaller (high curvature) grains of secondary phase preferentially dissolve into the dominant phase and migrate to larger grain of secondary phase by diffusion process (Lifshitz and Slyozov, 1961). If coarsening is mainly contributed by Ostwald ripening, the grain size distribution shows the LSW distribution (Lifshitz and Slyozov, 1961; Wagner, 1961). The weak LSW grain size distribution in this study indicated that Ostwald ripening may be dominant mechanism for grain growth. Growth exponent, n, is considered to be 4 or 5 when the rate of Ostwald ripening is limited by grain boundary diffusion (two dimensional path) or pipe diffusion (one dimensional path), respectively (summarized in Ohuchi and Nakamura, 2007). The growth exponent, n, determined in this study is considerably larger than expected value for Ostwald ripening. One possibility to explain such large growth exponent is faceting effect
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Fig. 8. Comparison of present data and other mantle materials from the geological time scale at 1673 K with initial grain size, G0 = 0. Ol: olivine at 300 MPa (Karato, 1989), MgO at ambient pressure (Kapadia and Leopold, 1974), Fp: ferropericlase at 18 GPa (Tsujino and Nishihara, 2009), Wd: wadsleyite at 15 GPa (Nishihara et al., 2006), Rw: ringwoodite at 21 GPa (Yamazaki et al., 2005), Pc: periclase at 25 GPa (Yamazaki et al., 1996), Pv: MgSiO3 perovskite at 25 GPa (Yamazaki et al., 1996), Mj: majorite at 18 GPa [this study with graphite capsules], St: stishovite at 18 GPa [this study with graphite capsules]. Dotted lines indicate the grain growth in the single phase, whereas solid lines indicate the grain growth in the multiphase. Meshed time range corresponds to the timescales of the transition zone residence of subducting slab for subduction velocity of 1–10 cm/y. Uncertainties of grain size of majorite and stishovite are shown as dark meshed areas indicated by “Mj+”, “Mj−”, “St+” and “St−” for the upper and lower bounds, respectively.
buffer (Frost et al., 2001), while the oxygen fugacity with graphitediamond capsules was considerably lower than the QFM buffer. High oxygen fugacity introduces vacancies in cation sites and hence it enhances diffusivity of atoms. Our observation that grain growth with Re capsules is greater than growth with graphite-diamond capsules is consistent with the diffusion experiment (Yamazaki and Irifune, 2003). We extrapolated the grain growth data to the geological time scale, as shown in Fig. 7. Although the uncertainties of estimated grain sizes of majorite and stishovite are large due to scattered data points, it is clearly seen that the grain sizes of majorite and stishovite in their aggregates are much smaller than olivine, wadsleyite, ringwoodite and (Mg, Fe)O in the same time scale. On the other hand, the grain sizes of majorite and stishovite yield comparable sizes for perovskite and periclase in post-spinel. The grain sizes of multiphase rocks are several orders of magnitude smaller than those of single phase rocks in the geological time scale. This result indicates that grain sizes are significantly affected by the presence of the secondary phase with the pinning effect. Therefore, knowledge of grain growth in multiphase is important for the estimation of grain size and resultant rheogy of the mantle (Fig. 8). Acknowledgments The authors thank E. Ito, T. Katsura and A. Yoneda for their helpful comments, and T. Kubo and T. Irifune for providing the starting materials. T. Ota, Y. Shinoda and M. Okube are also acknowledged for their experimental support. Anonymous reviewers are also thanked to improve the manuscript. References
of stishovite. As shown in Fig. 1, stishovite grains show the euhedral shape of elongated rectangular and have straight crystal surface, indicating facet (low index plane). Therefore, grain growth of stishovite is probably controlled by development of flat surface due to the relatively stronger anisotropic surface energy. For crystals with strong anisotropy, the growth exponent, n, tends to become higher (Kazaryan et al., 2002; Yoshino and Yamazaki, 2007). From the experimental approach, growth exponent, n, in multi phase mantle rocks were determined in previous works. For grain growth of MgSiO3 perovskite and periclase in their aggregates, n values were determined to be 10.6 and 10.8, respectively (Yamazaki et al., 1996). In the diopside and enstatite system, n values ranged from ∼3 to 7 (Ohuchi and Nakamura, 2007), and n value is ∼5 in forsterite and enstatite system (Hiraga et al., 2010). This growth rate of forsterite in the aggregate of forsterite and enstatite is much lower than that of olivine in single phase (Karato, 1989). In metallurgy, Carpenter (1967) reported the growth exponent ranging from 3.2 to 9.3 for Au–Pt alloy. It is clear that the presence of a secondary phase causes a pinning effect and retards grain growth. Although the grain growth rate of majorite with pyrolite minus olivine composition could not be determined in this study, large discrepancies in grain size between the two starting compositions indicate that growth rates of majorite in the MORB composition are much lower than those in the pyrolite minus olivine composition. These results suggest that pinning with a secondary phase is effective in MORB compositions because of the ∼10% stishovite contents; whereas, the pinning effect is not valid in the pyrolite minus olivine system due to the very small amount of secondary phase. Grain growth rates are enhanced by oxygen fugacity because the fundamental process for mass transport for grain growth, shown in this study, is considered to be the diffusion of atoms through vacancy (e.g., Yan et al., 1977). The oxygen fugacity of samples with Re capsules were buffered by Re–ReO2 , close to the QMF
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Physics of the Earth and Planetary Interiors journal homepage: www.elsevier.com/locate/pepi
Grain growth kinetics of majorite and stishovite in MORB Daisuke Yamazaki ∗ , Takuya Matsuzaki, Takashi Yoshino Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193 Japan
a r t i c l e
i n f o
Article history: Received 14 July 2009 Received in revised form 4 August 2010 Accepted 28 September 2010 Guest Editors Daisuke Suetsugu Craig Bina Toru Inoue Douglas Wiens
a b s t r a c t Grain growth rates of majorite and stishovite, in their aggregates with MORB composition, were studied at 18 GPa and temperatures ranging from 1873 to 2223 K. The rates of grain growth were expressed by Gn − G0n = k0 t exp(−H ∗ /RT ) where G is the grain size at time t (s), and G0 is the initial grain size. We determined the grain growth kinetic parameters for majorite, where n = 9.1 ± 1.3, H* = 950 ± 249 kJ/mol, and log k0 = −32.5 ± 2.3 m9.1 /s for the graphite capsule and log k0 = −31.3 ± 3.9 m9.1 /s for the Re capsule. Kinetic parameters for stishovite were determined to be n = 6.6 ± 0.9, H* = 599 ± 226 kJ/mol, and log k0 = −30.6 ± 0.9 m6.6 /s for the graphite capsule and log k0 = −29.0 ± 1.1 m6.6 /s for the Re capsule. © 2010 Elsevier B.V. All rights reserved.
Editor Mark Jellinek Keywords: Grain size Majorite Stishovite High-pressure experiment
1. Introduction The subducting slab is mainly composed of two layers characterized by chemistry; one is a depleted peridotite layer and the other is an overlying garnetite layer with MORB composition (e.g., Ringwood, 1991). Thus the convection style of these two layers in the mantle is a key factor in understanding the dynamics and chemical heterogeneity of the mantle. One of the most profound problems is whether the garnetite layer is separated from the peridotite layer. If so, the garnet-rich mantle transition zone is formed above 660 km because the garnetite layer is denser than the surrounding mantle, but less dense than lower mantle materials (e.g., Anderson, 1979). If not, the garnetite layer sinks to the core–mantle boundary region with the peridotite layer (e.g., van der Hilst et al., 1997). Karato (1997) pointed out that the viscosity structure across the subducting slab was an important factor to evaluate with regard to the separation of the garnetite layer. For polycrystalline aggregates, the grain size of the constituent minerals is one of the most important parameters that determine rheological behavior. For example, it is well known that the transition between dislocation and diffusion creep during deformation
∗ Corresponding author. Tel.: +81 858 43 3741; fax: +81 858 43 2184. E-mail address: [email protected] (D. Yamazaki). 0031-9201/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2010.09.009
is essentially controlled by grain size (Frost and Ashby, 1982). Also, the viscosity in the diffusion creep regime is defined as a function of the grain size of the constituent materials (Raj and Ashby, 1971). Knowledge of grain growth is necessary in order to estimate the grain size of rocks constituting the slab and the resultant viscosity. Grain growth kinetics of major minerals forming peridotite layers (i.e., olivine, wadsleyite, ringwoodite, perovskite) have been studied extensively (Karato, 1989; Nishihara et al., 2006; Yamazaki et al., 1996, 2005). However, grain growth of majorite as the most dominant mineral of the garnetite layer is still unknown. Thus we conducted a series of high-pressure experiments at a pressure of 18 GPa, equivalent to a depth of the mantle transition zone, and temperatures of 1673–2273 K to determine the grain growth kinetics of majorite in majorite dominant rocks. 2. Experimental procedures We used two types of glass powders with compositions of pyrolite minus olivine and MORB as starting materials (Irifune and Ringwood, 1987) (Table 1). The pyrolite minus olivine powder was prepared according to the previous report (Irifune, 1987) and MORB powder was prepared by quenching method using a furnace at ambient pressure with oxygen control with CO2 + H2 gas (Kubo, personal communication). We employed a Kawai-type doublestage multianvil high-pressure apparatus (USSA-1000, -5000). We
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Table 1 Chemical composition of starting materials and run products. Py − Ol
MORB
SiO2 TiO2 Al2 O3 Cr2 O3 FeOc MgO CaO Na2 O Total
a
IR87
Stating material
Run product
IR87
Starting material
Run productb
50.32 0.57 16.06 – 7.67 10.48 13.03 1.87 100.00
50.16 (56) 0.54 (6) 15.27 (31) – 7.45 (36) 10.33 (29) 13.00 (27) 2.55 (16) 99.31
47.34 (92) 0.44 (10) 16.78 (36)
51.12 0.45 11.29 0.91 3.08 22.84 9.38 0.93 100.0
50.37 n.d. 12.53 0.97 3.02 22.21 9.59 0.77 98.76
51.47 (76) 0.38 (6) 11.61 (32) 0.91 (5) 2.89 (15) 23.26 (40) 9.32 (28) 0.82 (9) 100.67
8.41 (25) 11.33 (30) 14.34 (28) 1.76 (13) 100.44
Cation (O = 24) Si Ti Al Cr Fe2+ Mg Ca Na Total a b c
6.84 (9) 0.05 (1) 2.86 (6) – 1.02 (3) 2.44 (6) 2.22 (5) 0.49 (4) 15.93
7.14 (6) 0.04 (1) 1.90 (5) 0.10 (1) 0.34 (2) 4.81 (8) 1.38 (4) 0.22 (2) 15.93
Average composition of majorites (n = 117). n = 114. All iron is assumed to be ferrous iron.
Table 2 Variations of grain size and water content of run products conducted at 18 GPa. Except for run 1K648, all samples were undergone pre-heating at 1673 K for 30 min. Run no.
Temperature (K)
Time (h)
Graphite capsule
Re capsule
Grain size
Starting material: MORB 1K648 1673 1873 1K680a 1K838 1873 1K655 1873 2073 1K677a 1K847 2073 a 2273 5K968 1K843 2273 5K984 2273 5K988 2273 Starting material: Py − Ol 1K717 2073
Water (wt.%)
Mj (m)
St (m)
0.5 2 3 32 2 3 2 3 8 32
0.5 (0.3) 0.8 (0.4) 0.9 (0.4) 1.3 (0.7) 1.0 (0.5) 1.4 (0.7) 2.1 (1.0) 2.6 (1.5) 3.3 (1.8) 3.8 (2.2)
0.3 (0.1) 0.6 (0.2) 0.6 (0.3) 0.6 (0.2) 0.6 (0.3) 0.6 (0.3) 1.0 (0.4) 1.1 (0.5) 1.0 (0.3) 1.1 (0.5)
2
8.5 (5.2)
–
Grain size
Water (wt.%)
Mj (m)
St (m)
0.124 0.005 0.005 0.004 0.006 0.002 0.005 0.003 0.002 <0.001
1.2 (0.6) 2.6 (1.1) 2.6 (1.3) 2.9 (1.3) 2.3 (1.2) 3.0 (1.4) 2.7 (1.4) 3.8 (2.0) 4.4 (1.9) 4.7 (2.0)
0.6 (0.3) 1.0 (0.4) 1.1 (0.4) 1.2 (0.5) 1.1 (0.5) 1.2 (0.5) 1.2 (0.6) 1.3 (0.6) 1.8 (0.8) 1.7 (0.6)
0.135 0.032 0.016 0.008 0.012 0.012 0.020 0.004 0.003 0.002
n.d.
6.3 (3.7)
–
n.d.
Numbers in parentheses are uncertainties estimated from the 1 of grain size distributions. a These data were used as initial grain sizes.
used tungsten carbide (WC) cubes with a truncated edge length of 6 mm. In order to observe the effect of oxygen fugacity on grain growth, two samples – contained respectively within graphite and Re capsule – were used in each experimental run. A WRe3% –WRe25% thermocouple was placed between the two capsules in the center of the LaCrO3 furnace. The samples were compressed to 18 GPa at room temperature. Then the temperature was increased to a pre-annealing temperature of 1673 K for 30 min. At this stage, the starting glass was completely crystallized (run no. 1K648, Table 2). After the preannealing, temperature was increased to the desired range from 1873 to 2273 K for grain growth studies. Temperature was kept constant within 5–10 ◦ C of the desired value for time intervals of 2–32 h. The recovered sample charges were mounted in epoxy resin and polished with diamond powder and colloidal silica. X-ray micro-diffraction measurements were performed to identify the phases present and electron-prove micro-analyses were carried out to measure chemical composition (Table 1). Using a field emission scanning electron microscope (FE-SEM), the observation of microstructures, such as grain boundaries, were made on the
polished surface after chemical etching with 5% HF for several minutes to sharpen grain boundaries. Without etching, neither grain boundaries nor the individual grains were observed. Grain size measurements were made on the digitized FE-SEM images using the intercept method. Average grain size (G) was estimated from the measured average intercept length (L) using the relationship G = cL, where c is a constant value of 1.56 (Mendelson, 1969). The water content in the samples after experiments was determined by Fourier-transform infrared (FTIR) spectroscopy. A non-polarized IR beam of cross-section 100 m × 100 m was directed to the polycrystalline samples with thickness of 100–250 m. Background corrections of the absorbance spectra were carried out by a spline fit of the baseline, and water content was calculated using a calibration based on Paterson (1982). 3. Results Microstructural observations with FE-SEM and X-ray microdiffraction measurements revealed that the recovered samples with starting material of MORB were composed of two phases of majorite and stishovite without a minor phase (Fig. 1A–F). The
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Fig. 1. A secondary electron image of the recovered samples for MORB composition annealed at 1873 K for 3 h (run 1K838) with graphite capsule (A) and with Re capsule (B), at 2273 K for 3 h (run 1K843) with graphite capsule (C) and Re capsule (D), at 2273 K for 32 h (run 5K988) with graphite capsule (E) and with Re capsule (F), and sample with pyrolite minus olivine composition annealed at 2073 K for 2 h (run 1K717) with graphite capsule (G) and with Re capsule (H). All samples were etched with HF for clearer visualization of grain boundaries. It is difficult to observe grain boundary without etching. The pores were formed by the etching.
samples contained a substantial amount of stishovite (∼10%). In contrast, the recovered samples with starting composition of pyrolite minus olivine contained tiny amounts of stishovite (less than 1%) (Fig. 1G and H). Grain boundaries in both compositions showed almost straight lines or gentle curvatures but not wavy (Fig. 1) and homogeneous grain sizes (Fig. 2) with size distribution of the lognormal to LSW distribution in which a peak skews toward larger grain size (Lifshitz and Slyozov, 1961; Wagner, 1961). Stishovite grains of euhedral shape are commonly, but not exclusively, located on majorite grain boundaries. The grain sizes of both majorite and stishovite increased with increasing run duration and/or temperature, as shown in Fig. 1 and Table 2.
In Fig. 3, representative FTIR spectra of the samples are shown. Bands around ∼3110 cm−1 were observed in all samples in this study, which can be assigned to hydrous stishovite (Panero et al., 2003). The observed broad band around 3450 cm−1 suggests the presence of grain boundary water. Bolfan-Casanova et al. (2000) reported a sharp band around 3550 cm−1 for structural water of tetragonal garnet but a broad band at same position for cubic garnet. Our observations are consistent with the results of BolfanCasanova et al. (2000) and Yoshino et al. (2008, for the Al-bearing system). In an Al-free system, water prefers to partition into majorite rather than stishovite. For example, the partition coefficient of water between majorite and stishovite (Kmj /st ) is ∼270
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B
A
0.3
water content (wt.%)
normalized frequency
A
0.2
0.1
0.1
0.05
0
D
0.3 0
B
0.2
0.1
0
–1
0
1 –1
0
log (L/L ave)
1
log (L/L ave)
water content (wt.%)
normalized frequency
C
0.1
0.05
Fig. 2. Representative distributions of grain size for sample, (A) 1K838 with graphite capsule, (B) 1K838 with Re capsule, (C) 5K988 with graphite capsule and (D) 5K988 with Re capsule.
(Bolfan-Casanova et al., 2000). The water contents of samples with the Re capsule were systematically greater than those with graphite capsules (Table 2). The samples contained a high water content of ∼0.12 wt% after initial heating at 1673 K for 30 min. However, water content of those samples which were annealed continuously at higher temperature (1873–2273 K) for 2 h were drastically reduced to less than 0.03 wt%, and water content did not change with additional annealing (Fig. 4). Thus we assume that such trace amounts of water present in these samples should yield only negligible effects on the grain growth in this study, based on previous results on the effect of water content on the grain growth of wadsleyite (Nishihara et al., 2006). Averages of grain sizes with MORB starting composition (Table 2) were fitted to a rate equation for grain growth, expressed as Gn − G0n = kt, where G is the grain size at time t, G0 is the initial grain size at time t = 0, n is a grain growth exponent factor, and k
3550
3110
–1
absorption coeffi cient (cm )
30
20
10
0 4000
3500
3000
2500
Wavenumber (cm-1) Fig. 3. Representative FTIR spectra of samples: solid, dashed and dotted lines correspond to the sample numbers 5K988 (graphite capsule), 1K838 (Re capsule) and 1K648 (graphite capsule), respectively (see also Table 1). Arrows indicate the characteristic peaks of garnet at 3550 cm−1 and stishovite at 3110 cm−1 .
0
0
10
time (h)
20
30
Fig. 4. Change of water content with increasing annealing time. Graphite (A) and Re (B) capsules were used in the experiments. Circles, squares and triangles represent the water content at 2273, 2073, 1873 K, respectively. Data at t = 0 (diamonds) show the initial contents just after the initial annealing at 1673 K for 30 min.
is a rate constant. Here, the rate constant k represents the dependence of temperature in the Arrhenius relation and is expressed as k = k0 exp(−H* /RT), where k0 is the pre-exponential term depending on oxygen fugacity, H* is the activation enthalpy, R is the gas constant and T is the absolute temperature (e.g., Burke, 1949). In this study, G0 values are assumed to be the average grain size of samples annealed at target temperatures (1873, 2073 and 2273 K) for 2 h, respectively, to eliminate the effect of the change of water content during experiments (Fig. 4). Grain size evolution of majorite and stishovite with MORB starting composition, with increasing duration and/or temperature, are plotted in Figs. 5 and 6. A non-linear least square fitting to the grain growth law yielded grain growth kinetic parameters for majorite as follows: n = 9.1 ± 1.3, H* = 950 ± 249 kJ/mol, and log k0 = −32.5 ± 2.3 m9.1 /s for the graphite capsule and log k0 = −31.3 ± 3.9 m9.1 /s for the Re capsule. Kinetic parameters for stishovite were determined to be n = 6.6 ± 0.9, H* = 599 ± 226 kJ/mol, and log k0 = −30.6 ± 0.9 m6.6 /s for the graphite capsule and log k0 = −29.0 ± 1.1 m6.6 /s for the Re capsule. The grain size increased with increasing run duration in both samples for the graphite capsule and Re capsule, with grain sizes in the Re capsule systematically larger than those in the graphite capsule. However, the regression lines for the Re capsule somewhat deviate from those of the expected values displayed by the solid lines (Figs. 5 and 6). The grain size of majorite with starting composition of pyrolite minus olivine was much larger (3–8 times) than that of MORB at
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6
Grain size of Mj (µm)
Grain size (µm)
4
4
2
2
Mj 0 3
0 0
0.5
1
1.5
2
Grain size (µm)
Grain size of St (µm) Fig. 7. Comparison of grain sizes of majorite and stishovite. Best fitted line for the plots is shown.
2
the same experimental conditions by the comparison run 1K677 with 1K717 (Table 2).
1
4. Discussion St 0
0
10
20
30
time (h) Fig. 5. Variation of grain sizes of majorite (A) and stishovite (B) with increasing annealing time at different temperatures. Solid and open symbols correspond to the grain sizes for graphite and Re capsules, respectively. Circles, squares and triangles display the grain sizes at 2273, 2073 and 1873 K, respectively. Solid and dotted lines indicate the non-linear least square fit to the grain growth law for the data with graphite and Re capsules, respectively. Uncertainties are shown by error bars. On the error bar, small symbols display the upper and lower bounds of uncertainties for each data points using same symbol type with data points.
–45
–50
log G
n
n –G0
(m)
A
–55 Mj
–40
n
n
log G –G0 (m)
B
–45
St
–50
3
4
5
6
Log time (s) Fig. 6. Alternative plots of grain growth of majorite (A) and stishovite (B) with time. Symbols for data points and error bars are same as used in Fig. 5.
For the grain growth law, growth exponent, n, is considered to be a geometric factor, and it is theoretically expected to be 2 in the grain growth of a single phase (Burke, 1949). However, grain growth exponent, n, were reported to be more than 2 for the multiphase system. Microstructure of two phase system is classified into two types: one is dual-phase (duplex structure) and the other is dispersion structure. In the former, most of secondary phase locate on the grain boundary of dominant phase. On the other hand, the secondary phase located in the crystal of dominant phase as inclusion in dispersion structure. The aggregate of majorite plus stishovite in this study shows almost the dual-phase (duplex structure) as shown in Fig. 1. In this case, the secondary phase retards the grain boundary migration of the dominant phase, a process called Zener pinning (Nes et al., 1985). Both of grains of dominant and secondary phases grow each other, satisfying Zener’s relation, G = Cd/fm , where C is a constant, G and d are the grain sizes of dominant phase and secondary phase in steady state, respectively, f is the volume fraction of secondary phase and m is the exponential factor (∼1/3–1, Evans et al., 2001). In this study, although G/d is scattered, most of samples yielded almost constant ratio of G/d with 2.0–2.5, indicating that Zener’s relation was achieved in most of samples (Fig. 7). During annealing, coarsening of secondary phase can occur by Ostwald ripening to reduce total interfacial energy in the system. Smaller (high curvature) grains of secondary phase preferentially dissolve into the dominant phase and migrate to larger grain of secondary phase by diffusion process (Lifshitz and Slyozov, 1961). If coarsening is mainly contributed by Ostwald ripening, the grain size distribution shows the LSW distribution (Lifshitz and Slyozov, 1961; Wagner, 1961). The weak LSW grain size distribution in this study indicated that Ostwald ripening may be dominant mechanism for grain growth. Growth exponent, n, is considered to be 4 or 5 when the rate of Ostwald ripening is limited by grain boundary diffusion (two dimensional path) or pipe diffusion (one dimensional path), respectively (summarized in Ohuchi and Nakamura, 2007). The growth exponent, n, determined in this study is considerably larger than expected value for Ostwald ripening. One possibility to explain such large growth exponent is faceting effect
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Fig. 8. Comparison of present data and other mantle materials from the geological time scale at 1673 K with initial grain size, G0 = 0. Ol: olivine at 300 MPa (Karato, 1989), MgO at ambient pressure (Kapadia and Leopold, 1974), Fp: ferropericlase at 18 GPa (Tsujino and Nishihara, 2009), Wd: wadsleyite at 15 GPa (Nishihara et al., 2006), Rw: ringwoodite at 21 GPa (Yamazaki et al., 2005), Pc: periclase at 25 GPa (Yamazaki et al., 1996), Pv: MgSiO3 perovskite at 25 GPa (Yamazaki et al., 1996), Mj: majorite at 18 GPa [this study with graphite capsules], St: stishovite at 18 GPa [this study with graphite capsules]. Dotted lines indicate the grain growth in the single phase, whereas solid lines indicate the grain growth in the multiphase. Meshed time range corresponds to the timescales of the transition zone residence of subducting slab for subduction velocity of 1–10 cm/y. Uncertainties of grain size of majorite and stishovite are shown as dark meshed areas indicated by “Mj+”, “Mj−”, “St+” and “St−” for the upper and lower bounds, respectively.
buffer (Frost et al., 2001), while the oxygen fugacity with graphitediamond capsules was considerably lower than the QFM buffer. High oxygen fugacity introduces vacancies in cation sites and hence it enhances diffusivity of atoms. Our observation that grain growth with Re capsules is greater than growth with graphite-diamond capsules is consistent with the diffusion experiment (Yamazaki and Irifune, 2003). We extrapolated the grain growth data to the geological time scale, as shown in Fig. 7. Although the uncertainties of estimated grain sizes of majorite and stishovite are large due to scattered data points, it is clearly seen that the grain sizes of majorite and stishovite in their aggregates are much smaller than olivine, wadsleyite, ringwoodite and (Mg, Fe)O in the same time scale. On the other hand, the grain sizes of majorite and stishovite yield comparable sizes for perovskite and periclase in post-spinel. The grain sizes of multiphase rocks are several orders of magnitude smaller than those of single phase rocks in the geological time scale. This result indicates that grain sizes are significantly affected by the presence of the secondary phase with the pinning effect. Therefore, knowledge of grain growth in multiphase is important for the estimation of grain size and resultant rheogy of the mantle (Fig. 8). Acknowledgments The authors thank E. Ito, T. Katsura and A. Yoneda for their helpful comments, and T. Kubo and T. Irifune for providing the starting materials. T. Ota, Y. Shinoda and M. Okube are also acknowledged for their experimental support. Anonymous reviewers are also thanked to improve the manuscript. References
of stishovite. As shown in Fig. 1, stishovite grains show the euhedral shape of elongated rectangular and have straight crystal surface, indicating facet (low index plane). Therefore, grain growth of stishovite is probably controlled by development of flat surface due to the relatively stronger anisotropic surface energy. For crystals with strong anisotropy, the growth exponent, n, tends to become higher (Kazaryan et al., 2002; Yoshino and Yamazaki, 2007). From the experimental approach, growth exponent, n, in multi phase mantle rocks were determined in previous works. For grain growth of MgSiO3 perovskite and periclase in their aggregates, n values were determined to be 10.6 and 10.8, respectively (Yamazaki et al., 1996). In the diopside and enstatite system, n values ranged from ∼3 to 7 (Ohuchi and Nakamura, 2007), and n value is ∼5 in forsterite and enstatite system (Hiraga et al., 2010). This growth rate of forsterite in the aggregate of forsterite and enstatite is much lower than that of olivine in single phase (Karato, 1989). In metallurgy, Carpenter (1967) reported the growth exponent ranging from 3.2 to 9.3 for Au–Pt alloy. It is clear that the presence of a secondary phase causes a pinning effect and retards grain growth. Although the grain growth rate of majorite with pyrolite minus olivine composition could not be determined in this study, large discrepancies in grain size between the two starting compositions indicate that growth rates of majorite in the MORB composition are much lower than those in the pyrolite minus olivine composition. These results suggest that pinning with a secondary phase is effective in MORB compositions because of the ∼10% stishovite contents; whereas, the pinning effect is not valid in the pyrolite minus olivine system due to the very small amount of secondary phase. Grain growth rates are enhanced by oxygen fugacity because the fundamental process for mass transport for grain growth, shown in this study, is considered to be the diffusion of atoms through vacancy (e.g., Yan et al., 1977). The oxygen fugacity of samples with Re capsules were buffered by Re–ReO2 , close to the QMF
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