Oxidation of carbon compounds by silica-derived oxygen within impact-induced vapor plumes
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 2 July 2010
Accepted: 18 December 2012
Published: 23 August 2013
Impact-induced vapor plumes produce a variety of chemical species, which may play an important role in the evolution of planetary surface environments. In most previous theoretical studies on chemical reactions within impact-induced vapor plumes, only volatile components are considered. Chemical reactions between silicates and volatile components have been neglected. In particular, silica (SiO2) is important because it is the dominant component of silicates. Reactions between silica and carbon under static and carbon-rich “metallurgic” conditions (C/SiO2 ≫ 1) are known to occur to produce CO and SiC. Actual impact vapor plumes, however, cool dynamically and have carbon-poor “meteoritic” composition (C/SiO2 ≪ 1). Reactions under such conditions have not been investigated, and final products in such reaction systems are not known well. Although CO and SiO are thermodynamically stable at high temperatures under carbon-poor conditions, C and SiO2 are stable at low temperatures. Thus, CO may not be able to survive the rapidly cooling process of vapor plumes. In this study, we conduct laser pulse vaporization (LPV) experiments and thermodynamic calculations to examine whether interactions between carbon and silica occur in rapidly cooling vapor plumes with meteoritic chemical compositions. The experimental results indicate that even in rapidly cooling vapor plumes with meteoritic compounds are rather efficiently oxidized by silica-derived oxygen and that substantial amounts of both CO2 and CO are produced. The calculation results also suggest that those oxidation reactions seen in LPV experiments might occur in planetary-scale vapor plumes regardless of impact velocity as long as silicates vaporize.
When a hypervelocity impact occurs on a planetary surface, an impact-induced vapor plume is generated. Many chemical species are produced within impact vapor plumes and are released into the atmosphere of planets. These species may have played an important role in planetary climates and abiotic synthesis of organic materials (e.g., Fegley et al., 1986; Mukhin et al., 1989; Kasting, 1990; Chyba and Sagan, 1992; Kress and McKay, 2004). Thus, it is important to understand the molecular composition of products within impact-induced vapor plumes. Because of the complexity of chemical reactions in vapor plumes, however, the composition of produced gases within vapor plumes is poorly known. Among the complex chemical reactions, chemical reactions between silicates and carbon compounds are expected to play a particularly important role, but they have not been investigated extensively.
There are few studies that estimate the molecular composition of gases produced within impact-induced vapor plumes from asteroidal compositions (i.e., meteoritic), which contain silicates much more than comets. Such estimation would be very difficult because the effect of silicates is not understood well. Previous theoretical studies on gases produced within vapor plumes generated by a comet impact consider chemical reactions within only volatile elements of comets, such as C, H, O, N, and S, in calculating the molecular composition of produced gas; silicate components are removed from the calculation (e.g., McKay et al., 1989; Kress and McKay, 2004; Ishimaru et al., 2005; Hashimoto et al., 2007). This simplification appears to be appropriate for as a first-order approximation, since silicates are refractory and are expected to condense at temperatures much higher than the quenching temperatures of volatile species. However, if oxygen derived from thermally decomposed silicates participates in the chemical reactions among carbon compounds in impact-induced vapor plumes, the composition and the oxidation state of produced gases may differ greatly from the molecular composition predicted by calculations that neglect the oxidation effect of silicates.
Laser pulse vaporization experiments on terrestrial rocks and chondrites by Mukhin et al. (1989) show that the gas products in vapor plumes are composed mainly of oxidized species, such as CO and CO2, with small amounts of reduced species, such as hydrocarbons, HCN, and aldehydes. They proposed that this is because oxygen derived from thermal decomposition of silicates oxidized carbon. The proposed reaction between carbon and silicate-derived oxygen, however, has not been investigated extensively. They suggest that thermal decomposition of silicates in vapor plumes leads to high oxygen fugacity at high temperatures (Gerasimov, 1987; Gerasimov et al., 1987), and this oxygen would react with carbon to produce CO or CO2. Nevertheless, silicate-derived oxygen might recombine back to silicates and not to CO or CO2, as mentioned above. Since Mukhin et al. (1989) used complex natural samples (terrestrial rocks and chondrites), it is difficult to specify what reactions occur. Furthermore, since oxygen might be contained in the form of volatile components, such as water, carbonates and sulfates, the effect of oxidization by silicate-derived oxygen cannot be separated from that by volatile-derived oxygen. Such uncertainties in main oxidizing agent, reaction path, and possible effect of water and hydroxyls will prevent us from investigating the conditions for this oxidation process and its reaction rate, which are very important for applying to real-world impact events on planetary surfaces.
In particular, silica (SiO2) is a very important species because it is the dominant component of silicates and would control the overall thermodynamic parameters of vaporization of silicates (e.g., Gerasimov et al., 1998). Actually, the reactions between silica and carbon have been studied for many years because of their industrial importance, such as the production of iron, silicon, and silicon carbide. Experiments have shown that SiO2 reacts with C to generate SiC and CO under such “metallurgic” conditions, C/SiO2 ≫ 1 (e.g., Klinger et al., 1966; Biernacki and Wotzak, 1989a). This is consistent with thermodynamic equilibrium calculations, which indicate that SiC and CO are stable at high temperatures. The reactions under such conditions are known to proceed via solid-solid and solid-vapor reaction paths in a well-controlled and static reaction cells or furnaces (Biernacki and Wotzak, 1989b; Klinger et al., 1966). These studies show that carbon is oxidized by silica-derived oxygen. Thus, silica cannot be readily excluded from the consideration of the composition of gases produced within impact-induced vapor plumes. Reactions in actual impact vapor plumes, however, may be greatly different from those in static metallurgic conditions. First, such reactions would be influenced by rapid cooling due to adiabatic expansion of vapor plumes. Second, the composition of the reaction system is not “metallurgic” (C/SiO2 ≫ 1) but “meteoritic” (C/SiO2 ≪ 1) that is produced by silicate-rich impactors. Reactions in such dynamic rapidly cooling reaction systems with a meteoritic composition have not been intensively studied before, and final products in such reaction systems have not been known either. Thermodynamic equilibrium calculations indicate that gaseous SiO and CO are generated at high temperatures under such C/SiO2 ≫ 1 conditions. For example, under 1 bar condition, SiO and CO can coexist stably at >2000 K. However, at <2000 K SiO2 and C are stable, and neither SiO nor CO can exist stably. This means that although SiO and CO may be formed at a high temperature, they would react to yield SiO2 and C if the thermal equilibrium is maintained during the cooling of vapor plumes down to <2000 K. It is not known whether SiO and CO can survive the adiabatic cooling of vapor plumes. In other words, it is not clear that SiO2 can be an efficient oxidizing agent in impact-induced vapor clouds.
Thus, in this study we investigate the reaction between silica and carbon compounds under meteoritic conditions (C/SiO2 ≪ 1). We conduct both laser pulse vaporization (LPV) experiments and thermodynamic calculations to examine whether oxygen derived from SiO2 reacts with carbon within large-scale vapor plumes. Instead of complicated reaction systems, we consider simple reaction systems that simulate impacts of carbonaceous chondritic projectiles to investigate the effect of carbon oxidation by silica-derived oxygen. In both experiments and thermodynamic calculations, we consider reaction systems consisting of silica (SiO2) and polyethylene (PE). First, we conduct LPV experiments, which have been used to simulate impact vaporization (e.g., Mukhin et al., 1989; Kadono et al., 2002; Managadze et al., 2003; Sugita et al., 2003; Ohno et al., 2004) and measure whether CO and/or CO2 are produced in even carbon-poor reaction systems. We use artificial samples, mixtures of silica powder and polyethylene powder, for investigating the effect of silica-derived oxygen. Since polyethylene is composed only of C and H ([CH2]n), production of CO or CO2 will indicate that silica-derived oxygen reacts with carbon in polyethylene. We also examine the effect of target mixing ratio of silica on the yields of CO and CO2 systematically. This set of experiments will also confirm whether silica-derived oxygen reacts with carbon. Furthermore, LPV experiments in different laser beam diameters and different laser intensities are performed to examine the robustness of the experimental results. Second, we perform thermodynamic equilibrium calculations that simulate reactions within vapor plumes and compare the results of thermodynamic equilibrium calculations and the results of LPV experiments.
We conducted laser pulse vaporization (LPV) experiments using polyethylene-silica (PE-SiO2) targets with different silica mixing ratios to investigate the effect of silica-derived oxygen on the yields of carbon compounds. Similar LPV experiments were repeated under different laser irradiation conditions to examine the robustness of the results.
2.1 Experimental methods
Note that the laser we used does not have a very flat beam profile. As long as the beam profile is constant, however, we can obtain data on the effect of laser intensity and beam size to final gas composition. Laser beam pattern, nevertheless, may actually change when the output energy and frequency of the laser unit are changed. Thus, instead of changing the output energy of the laser unit itself, we controlled the output laser energy by using different numbers of beam splitters for different runs. This way the output energy and frequency of the laser always stay the same, ensuring the laser beam pattern be the same. Consequently, the result of experiments can be compared safely among different laser intensities despite the inhomogeneous laser energy distribution within the beam.
Mixing ratio and C/O ratio of polyethylene-silica targets.
silica/polyethylene (mass ratio)
silica/polyethylene (mole ratio)
O/C (mole ratio)
Because polyethylene consists only of C and H, either CO or CO2 cannot be produced from a pure polyethylene target. If there were other oxygen sources, such as water adsorption on the surface of targets, CO and CO2 would be produced. However, neither CO nor CO2 were detected from the LPV experiments using polyethylene-only targets. This indicates that there is no substantial amount of water adsorption on the surface of targets or that such a possible reaction between absorbed water and carbon is not efficient.
2.2 Experimental results
In the main experiments, we first fixed the laser irradiation condition (i.e., 1 mm in beam diameter and 1×109 W/cm2 in laser intensity) and investigated the effect of the SiO2 ratio of targets on the composition of produced gases. If silica-derived oxygen is used in the reaction with carbon compounds, the yields of the oxygen-bearing carbon species, CO and/or CO2, will increase as the silica ratio of targets increases.
Note that the C2H2/CH4 does not depend on target silica ratio (solid line of Fig. 3(a4)). This strange behavior of hydrocarbons is also reported in the previous LPV experiments by Gerasimov (2002), which shows that the ratios of hydrocarbons are almost the same regardless of the experimental conditions. He suggested that Fischer-Tropsch type catalytic reactions, which produce hydrocarbons from CO and H2 on the surface of nano-scale condensed particles, may occur. The same type reactions may occur in our experiments as well. Another possible hydrocarbon source is the polyethylene melts generated by laser irradiation. Hydrocarbons may degassed from the melts. Although we cannot tell which process may be the case at this point, both possible case would suggest that most of the hydrocarbons detected in our experiments are not gas-phase reaction products within vapor plumes but produced by subsequent catalytic reactions or secondary degassing from melts around the ablation crater. This would further support that the main carbon-bearing species produced within high-temperature vapor plumes are most likely CO and CO2.
For all the laser beam diameters and laser intensities we examined, CO and CO2 are produced. Furthermore, those are always the dominant carbon-bearing species produced within the vapor plumes in this study. The dependence of the CO/CH4, CO2/CH4, and CO2/CO ratios on the target composition (the O/C ratio of target) is also the same as the nominal case of 1 mm laser beam diameter and 1×109 W/cm2 of laser intensity (Figs. 3(a) and 4(a)). These results indicate that the reaction between silica-derived oxygen and carbon in polyethylene is not limited to only one specific experimental condition but is applicable to multiple experimental conditions; implying the possibility that the same reaction may occur under a rather wide range of conditions. This suggests that even in meteoritic carbon-poor reaction systems silica-derived oxygen oxidizes carbon compounds within vapor plumes to produce CO and CO2.
Here, it is noted that the CO/CH4, CO2/CH4, and CO2/CO ratios decrease as laser beam diameter increases (Fig. 3(b1) to (b3)) and that the CO/CH4, CO2/CH4, and CO2/CO ratios decrease as laser intensity increases (Fig. 4(b1) to (b3)). We will discuss these dependences in Section 3.2 comparing with the results of thermodynamic calculations.
3. Thermodynamic Equilibrium Calculations
Experimental results discussed in the previous section show that carbon compounds are oxidized by silica-derived oxygen within vapor plumes by the LPV experiments. In this section we discuss whether the results of LPV experiments can be accounted for by a simple thermodynamic model. Thermodynamic calculations are carried out (Section 3.1), and the results are compared with the results of LPV experiments (Section 3.2).
We carried out thermodynamic equilibrium calculations using Gibbs free energy minimization method (e.g., Prigogine and Defay, 1954) to simulate LPV experiments described in the previous section and to estimate the composition of products.
In our calculations, the following assumptions were used. (1) Products are always in a chemical equilibrium. (2) Vapor plumes cool adiabatically. Thus, the temperature and pressure of the vapor plumes change along isentropic paths, whose entropies are determined by laser ablation. The composition of products is estimated along those pressure-temperature paths. (3) The composition of products is determined by a single quenching; all reactions quench at one quenching temperature. Quenching temperature is the temperature where chemical reaction rate and cooling rate of vapor plume become the same. Since the cooling rate of vapor plumes decreases as the scale of a vapor plume increases, quenching temperature decreases as the scale of a vapor plume increases. In general, quenching temperature of reactions within vapor plumes of LPV experiments (i.e., millimeter-scale vapor plumes) is estimated to be ~3000 K and that of vapor plumes produced by impactors several kilometers in diameter is ~2000 K (e.g., Gerasimov et al., 1998). In our calculation, the composition of products is determined as a function of quenching temperature.
It is difficult to know exactly the entropy gained by laser ablation on PE-SiO2 targets. According to Sugita et al. (2003), gained entropy is ~10 kJ/K/kg for laser intensity 1.0×109 W/cm2 on a basalt target. Silica might absorb less energy than basalt because of its lower absorbance at the laser wavelength. Thus, we consider four adiabatic paths, S = 7, 8, 9, and 10 kJ/K/kg, along which the equilibrium composition is determined.
Species considered in the thermodynamic equilibrium calculation and thermodynamical data used.
SiO2 (l), SiO (g), SiO (s), Si (s), Si (g)
SiC (s), SiC (g)
CO2 (g), CO (g), CH4 (g), C2H2 (g), graphite (s)
Chase et al. (1985)
O (g), O2 (g), H (g), H2 (g), H2O (g)
The equilibrium compositions are determined by searching for the composition that gives the minimum Gibbs free energy at a given temperature and pressure. Then entropy is calculated using the determined composition. The composition along an isentropic path is determined as follows: First, we iteratively look for the pressure value whose entropy coincides with the entropy for a given isentropic curve at each temperature using our above-mentioned equilibrium calculation code. Then, we calculate the equilibrium composition for this pressure and temperature condition. When we repeat this calculation for different temperatures, we obtain the compositions along an isentropic path.
3.2 Calculation results and comparison with LPV experiments
In contrast, the observed plume scale dependence on the CO2/CO ratio cannot be reproduced by the model calculation. Increase in vapor plume scale leads to decrease in quenching temperature because the cooling rate with adi-abatic expansion for larger plumes is lower than that for smaller plumes. In the LPV experiments, the CO2/CO ratio slightly decreases as the scale of vapor plume increases (Fig. 3). However, the results of the thermodynamic calculations show that the CO2/CO ratio increases as quenching temperature decreases at high temperatures (Fig. 7). Furthermore, the CO2/CO ratios obtained in the LPV experiments are less than 0.09 (Figs. 3 and 4), which is smaller than the values obtained from the calculations by more than a factor of ten at probable quenching temperatures between 2500 and 3000 K (Fig. 7). Thus, other cooling processes in addition to adiabatic cooling may be needed to explain these trends of the CO2/CO ratio. Contours for the equilibrium CO2/CO ratio are shown in Fig. 6 along with the adiabatic p-T paths. Note that the CO2/CO ratio is the highest along the decomposition boundary curve of SiO2 and that the ratio is lower under conditions further away from the boundary curve. The pace of change in the CO2/CO ratio as a function of temperature depends on the difference in slope between the adiabatic path and the CO2/CO contour curve. Figure 6 also shows that when a vapor cools along an adiabatic path, the CO2/CO ratio increases before the path reaches the decomposition boundary. After reaching the decomposition boundary, the curve bends and becomes practically parallel to the contour curves. This is the reason why CO2/CO ratio increases as temperature decreases at higher temperatures (>~1500 K) as shown in Fig. 7. However, if the p-T paths deviate from the decomposition boundary of SiO2 at the end of cooling toward lower temperature conditions where the CO2/CO ratio decreases with decrease in temperature, decrease in the CO2/CO ratio will occur as observed in our experiments. Thus, mechanisms that cool vapor plumes more rapidly than adiabatic cooling for a given pressure decrease, such as radiative cooling and mixing with ambient atmosphere, would fill the gap between observed trends and an adiabatically cooling equilibrium model. Since vapor plume pressure at probable quenching temperatures (2500 to 3000 K) is much higher (10−2 to 1 bar, Fig. 7) than the ambient pressure in the LPV experiments (1×10−3 mbar), mixing between expanding vapor plumes and the ambient air is probably not efficient. In contrast, since the scale of the plumes in the LPV experiments is small, radiation may contribute to cooling efficiently. Thus, high radiation efficiency due to the smallness of plumes may account for the difference in the CO2/CO ratio between the results of the LPV experiments and the predictions of theoretical calculation that does not consider radiation.
The calculation results also indicate that SiO, O, and O2 are produced. However, those species are not detected in the actual LPV experiments. This experimental result might suggest that after reactions related to CO and CO2 have been quenched, reactions related to SiO, O, and O2 are still active (i.e., not single quenching) and that those species may be lost by SiO2 formation and condensation or some other mechanisms. This will be discussed in Section 4.1.
4.1 The fate of silica that released oxygen
Since oxygen released from silica is used in reactions with carbon, silica should be reduced. The thermodynamic equilibrium calculations indicate that SiO2 decomposes into gaseous SiO, O, and O2 at high temperatures. Thus, gaseous SiO remains after oxygen is used in reactions with carbon compounds. However, SiO, O, and O2 are not detected in the LPV experiments. This suggests that reactions related to these species are still active after reactions related to carbon-bearing species quench, and SiO might combine with O and O2 at low temperatures (i.e., not single quenching). However, since a part of oxygen combines with carbon, SiO is stoichiometrically more abundant than O and O2. Thus, it cannot be accounted for by these reactions alone. Other possibilities are that both solid SiO2 and metallic Si are generated through disproportionation reactions of SiO (e.g., Mamiya et al., 2001; Han et al., 2003) and that solid SiO is produced. Though solid SiO is known to be unstable at any temperature and atmospheric pressure (Brewer and Green, 1957), vapor condensates consist of metastable substances under some conditions (e.g., Nuth and Donn, 1982; Rietmeijer et al., 1999). Generation of reduced-state silicon, such as Si0, in LPV experiments is also reported although the elemental composition of the reaction system is considerably different from ours; more metallic elements, such as Ca, Mg and Al, are included (Dikov et al., 1996; Gerasimov et al., 1996). Those experiments suggest that disproportionation reactions generating reduced Si may occur within vapor plumes. What substances are generated could be revealed through the investigation of condensates generated by the LPV experiments. However, the recovered amount of the condensed matter is too little to analyze accurately. Improvement in a condensate-recovery method is needed for resolving this issue.
4.2 The effect of vapor plume scale and gained entropy
The scale of vapor plumes in LPV experiments is ~10−3–10−4 m while that of asteroidal and cometary impacts on surfaces of planets is typically up to 106 m. Quenching temperature of chemical reactions within vapor plumes decreases as the scale of vapor plumes increases. For example, quenching temperature is estimated to be ~3000 K for laboratory-scale plumes and ~2000 K for plumes produced by impacts of projectiles several kilometer in diameter (Gerasimov, 1998). In previous theoretical studies of impact-induced vapor plumes, silicate components are removed from calculations because those components are thought to be condensed completely because of low quenching temperature.
However, the results of thermodynamic calculations along isentropic pressure-temperature paths indicate that at least silica should not be removed from calculations. The results of calculations indicate that silica does not condense completely and that large amount of CO and CO2 are produced even at low temperatures (<2000 K) where the reactions quench in planetary-scale vapor plumes (Fig. 5). Why did not silica condense completely even at low temperatures? In Fig. 6, though each path goes through different point at high temperatures, all paths converge to almost the same curve at low temperatures. This curve is located approximately along the decomposition boundary of pure silica. Thus, adiabatic pressure-temperature paths are “trapped” by the silica decomposition boundary. Pressure decreases steeply as temperature decreases, and pressure and temperature conditions could not reach where silica completely condenses. Thus, silica does not condense completely, and oxidation of carbon by silica-derived oxygen occurs as long as plumes cool adiabatically. In general, planetary-scale vapor plumes that are larger than atmospheric scale height of planets cool adiabatically. Thus, oxidation of carbon by silica is likely to occur even in planetary-scale vapor plumes.
Entropy of impact-induced vapor plumes increases with impact velocity. As mentioned in Section 2.1, entropy gained by our LPV experiments are estimated to be ~10 kJ/K/kg, which corresponds to impacts with velocity of several tens of km/s to hundred km/s (Kadono et al., 2002; Sugita et al., 2003), which is higher than the mean impact velocity of asteroids to the Earth (Chyba, 1991). However, the results of thermodynamic equilibrium calculations along adiabatic pressure-temperature paths suggest that difference in entropy gained by impact does not so much affect the vapor composition at low quenching temperatures where the chemical reactions within planetary-scale vapor plumes are expected to quench (<2000 K). Adiabatic pressure-temperature paths converge to almost the same curve at low temperatures (Fig. 6), and the vapor composition becomes almost the same at low temperatures (Fig. 5). Thus, oxidation of carbon compounds by silica-derived oxygen may occur regardless of impact velocity as long as silica vaporizes.
Here it is noted that coexistence between vapor-phase SiO-O2 and condensed-phase SiO2 will continue down to extremely low-temperatures and pressures thermodynami-cally (e.g., Zel’dovich and Raiser, 1967). Thus, the SiO2-derived O2 continues to react with carbon-bearing species. However, such adiabatic expansion process would be interfered by other processes, such as radiative cooling or mixing with ambient atmosphere and cease in thermodynamic equilibration due to the low molecular density. Nevertheless, the tendency that oxygen derived from SiO2 play an important role in vaporized meteoritic materials will not be affected significantly by these processes.
We investigate experimentally and theoretically whether carbon is oxidized by oxygen derived from SiO2 within impact-induced carbon-poor vapor plumes.
First, we conducted laser pulse vaporization (LPV) experiments on polyethylene-silica mixture, which simulate hypervelocity impacts of carbonaceous chondritic im-pactors, to investigate whether silica-derived oxygen reacts with carbon compounds in laser-induced vapor plumes. Though polyethylene contains no oxygen, the produced gas from polyethylene-silica mixture contains significant amounts of CO and CO2. In addition, the production ratio of CO and CO2 monotonically increases as silica mixing ratio in targets increases. When the laser irradiation conditions (i.e., laser beam diameter and laser intensity) are changed, the trends do not change. These results unambiguously show that silica-derived oxygen reacts with carbon compounds within vapor plumes.
Second, we carried out the thermodynamic equilibrium calculations to examine whether the results of the LPV experiments could be explained thermodynamically. The calculation results indicate that both CO and CO2 are produced, and the amount of CO is larger than CO2 at the estimated quenching temperature of LPV vapor plumes. Those results are consistent with the results of LPV experiments. The dependence of vapor composition (CO2/CO ratio) on entropy gained by laser irradiation is explained by adiabatic cooling of vapor plumes. The dependence of vapor composition on plume scale seems not to be explained by adiabatic cooling only. Thus, additional cooling processes, such as radiative cooling may be important at laboratory-scale vapor plumes.
The calculation results also indicate that oxidation of carbon by silica-derived oxygen occurs even at low quenching temperatures (<2000 K) as long as plumes cool adiabatically. Thus, though quenching temperatures in those planetary-scale vapor plumes are lower than those in laboratory-scale vapor plumes, oxidation of carbon by silica-derived oxygen might occur. In addition, the calculation results indicate that isentropic pressure-temperature paths are converged to decomposition boundary of silica at low temperatures, and the composition of products are almost the same at those temperatures.
We conclude that carbon compounds in impactors are likely to be oxidized by oxygen derived from SiO2, the main component of silicate, within planetary-scale vapor plumes produced by hypervelocity impacts regardless of impact velocity as long as silica is vaporized.
The authors thank K. Kuramoto for insightful discussions during the early phase of this study. H. Yoshida for technical assistance in target preparation. We appreciate the constructive comments from Dr. M. V. Gerasimov and the anonymous reviewer. This research was partly supported by the Grant in Aide from Japan Society for the Promotion of Science.
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