Water Vapor Pressure Dependence of Crystallization Kinetics of

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Water vapor pressure dependence of crystallization kinetics of amorphous forsterite Daiki Yamamoto, and Shogo Tachibana ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.8b00047 • Publication Date (Web): 22 Jun 2018 Downloaded from http://pubs.acs.org on June 24, 2018

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ACS Earth and Space Chemistry

Water vapor pressure dependence of crystallization kinetics of amorphous forsterite Daiki Yamamoto† and Shogo Tachibana†,# †

Department of Natural History Sciences, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan

KEYWORDS. Amorphous forsterite, Water vapor, Crystallization, Kinetics, Protoplanetary disks

ABSTRACT. Amorphous silicate dust grains, dominant solid components in the interstellar medium, are converted into crystalline silicate dust through thermal annealing in protoplanetary disks. Water vapor is a major reactive gas species in the protoplanetary disk, and it may affect the crystallization behavior of amorphous silicates. In this study, the water vapor pressure dependence of the crystallization kinetics of amorphous silicate with forsterite composition was investigated under controlled water vapor pressures ranging from ~1×10-9 bar to 5×10-3 bar at 923−1023 K. We found that the crystallization rate depends on the water vapor pressure and becomes faster at higher water vapor pressures. We also found that the activation energy and the pre-exponential factor for crystallization rate decreases with increasing water vapor pressure. Water molecules dissolving into amorphous forsterite cut atomic bonds such as Si-O-Si and MgO-Mg through a hydroxyl (-OH) formation reaction. Rearrangement of structural units cut by

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hydroxyls occurs with a smaller energetic barrier, and thus water vapor can act as a catalyst to promote crystallization of amorphous forsterite. Based on the experimental data, we conclude that the temperature required for crystallization of amorphous forsterite within the lifetime of protoplanetary disks is ~620−700 K irrespective of the water vapor pressure in the disk and that the observed crystalline forsterite dust in protoplanetary disks indicates the presence of dust annealed at temperatures above ~620−700 K. Extraterrestrial materials record various thermal events in the early Solar System (e.g. chondrule formation). Considering that meteoritic evidence indicates that the H2O/H2 ratio was enhanced over the canonical ratio in the early Solar System, the thermal evolution of amorphous forsterite dust during various thermal events in the early Solar System should be discussed taking the effect of water vapor pressure into account.

1. INTRODUCTION Silicate dust is a dominant solid component in astronomical environments. Infrared spectroscopic observations have shown that silicate dust in the interstellar medium is almost completely amorphous (~0.2 % crystalline fraction)1, while a combination of crystalline silicates is required to explain observed sharp infrared features detected in protoplanetary disks2. The mass fraction of crystalline silicate dust in protoplanetary disks lies between a few and 40 percent, and decreases with increasing heliocentric distance from the central star2. These lines of evidence suggest that amorphous silicates in the interstellar medium, which fall into a protoplanetary disk and accrete to the central star, transform into crystalline silicates due to thermal annealing in the disk. Therefore, the fraction, distribution and composition of crystalline and amorphous silicates in protoplanetary disks could provide constraints both on the thermal structure and evolution of the protoplanetary disks and on the evolution of dust in the disks.


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Laboratory studies of the thermal annealing of amorphous silicates with various chemical compositions have been carried out3−9 to understand the crystallization behavior of amorphous silicates in astronomical environments. These annealing experiments have been done under different heating conditions; for instance, in air8,9, in one atmosphere of oxygen gas5, and at total pressure of 5.0×10-5 bar3 and 10-9−10-10 bar4,6,7. However, the effect of the surrounding gas on crystallization has not yet been fully investigated. In this study, we focus on the effect of water vapor on crystallization of amorphous forsterite (Mg2SiO4), which is considered to be a dominant astronomical dust component2,10. Because water vapor can be a major reactive gas species in protoplanetary disks, it may affect the crystallization behavior of amorphous silicates. Jäger et al.11 found that amorphous magnesium silicate containing hydroxyls (-OH) in its structure crystallizes more rapidly (with a smaller activation energy) than dry amorphous magnesium silicates. This implies that not only OH in the amorphous structure but gaseous water may also affect the crystallization of amorphous silicate if H2O molecules dissolve into the amorphous structure. However, no experimental investigation regarding the effect of water vapor on the crystallization of astronomical amorphous silicates has been carried out. Here we performed annealing experiments of amorphous forsterite under different water vapor pressure conditions to obtain the crystallization kinetics of amorphous forsterite in the presence of water vapor and to discuss the role of water vapor for crystallization.

2. EXPERIMENTAL SECTION 2.1 Starting Material and Experimental Set-up. We used sub-micron-sized amorphous silicate grains with forsterite composition, synthesized by an induced thermal plasma method9,12, as a starting material (amorphous forsterite hereafter). The amorphous powder was synthesized by


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vaporizing staring materials (Mg(OH)2 and SiO2) in high-temperature plasma (~104 K), followed by quenching9,12. Transmission electron microscopy (TEM) observation shows that the amorphous forsterite has a spherical shape approximately 10−200 nm in diameter (~80 nm average diameter) (Figure 1). More detail characteristics of the starting material are described in the results section. Thermal annealing experiments of amorphous forsterite under various water vapor pressures (PH2O) were conducted using a gold-mirror vacuum furnace (Thermo-Riko GFA430VN). The gold-mirror vacuum furnace (Figure 2) consists of a quartz glass tube (36 mm in diameter and 450 mm in length) surrounded by an Inconel alloy coil heater and a gold-coated mirror tube, a pumping system (a turbo-molecular pump and a scroll pump), and a gas inlet for water vapor. The furnace temperature was measured and controlled by a type K thermocouple outside of the silicate glass tube. About 5 mg of amorphous forsterite powder was put in a platinum vessel, and placed in a silicate glass sample stand. Because the location of the thermocouple is not the same as the sample inside the silica glass tube, the temperature measured with the thermocouple was calibrated against the sample temperature using melting points of sodium chloride (800.4°C), potassium bromide (730°C), lithium bromide (547°C) and indium (156.6°C) placed at the same location as the sample inside the furnace. The linear regression between the thermocouple temperatures and the melting temperatures was used to anneal the sample at a desired temperature. The pressure inside the silica glass tube was measured with a Pirani/cold-cathode gauge (Pfeiffer PKR251) using a proper conversion factor for H2O.


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500 nm

50 nm

Figure 1. Typical TEM images and an electron diffraction pattern of the starting material.


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2.2 Experimental Procedure. Annealing experiments in low pressure H2O were conducted at PH2O of 5×10-3, 3×10-6 and 1×10-9 bar. For experiments at PH2O=5×10-3 bar, the stainless steel container enclosing deionized pure water was kept at room temperature, and the water vapor was supplied from the liquid water. The pumping system was connected to the furnace with a stainless tube (~3 mm in inner diameter) to reduce the pumping rate, and the pressure in the system was ~10-5 bar without the supply of water vapor. The water vapor pressure of 5×10-3 bar was obtained by controlling the needle valve of the water flow system (Figure 2). For experiments at PH2O=3×10-6 bar, deionized pure water ice was used as a water vapor source. A stainless steel container, in which deionized pure water is enclosed, was put in a freezer (-25°C) attached to the furnace (Figure 2). The flow rate of water vapor was adjusted by a needle valve, and a gas evacuation rate was adjusted by a butterfly valve attached to the pumping system. The water vapor pressure of 3×10-6 bar was obtained by the balance between the gas flow and evacuation rates. We also made experiments using H218O (97 atom %

18

O; Sigma-

Aldrich) ice as a water vapor source for comparison. In these experiments, after the water vapor pressure in the furnace stabilized at room temperature, the sample temperature was raised to the desired temperature in 20 minutes. The sample was heated for the desired duration, and was cooled down to room temperature in about 20 minutes. Experiments in vacuum were also carried out using the gold-mirror vacuum furnace without using the gas flow system. The pressure inside the furnace was typically 1×10-9 bar during heating. The main residual gas species was found to be water vapor with a quadrupole mass


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spectrometer (MKS e-Vision+), and the total pressure in the vacuum furnace (~1×10-9 bar) was regarded as the partial pressure of water vapor. All the experimental conditions are summarized in Table 1.


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Figure 2. A schematic illustration of the configuration of the gold-mirror vacuum furnace equipped with a gas flow system for the experiments at PH2O=3×10-6 bar. For experiments at PH2O=5×10-3 bar, water was kept at a room temperature and the furnace was connected to the turbo molecular pump with a ~3-mm diameter stainless tube instead of the butterfly valve. The gas flow system was not used for the experiments in vacuum (PH2O of 1×10-9 bar).


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Table 1. Crystallization timescales and the Avrami exponents obtained from the fitting of time evolution of the crystallization degrees. Errors represent 1σ standard error of the mean.

PH2O (bar)

1×10-9

3×10-6

5×10-3

Temperature (K)

τ (hour)

n

953

46.42 ± 2.00

1.53 ± 0.10

1003

4.30 ± 0.28

1.53 ± 0.15

1023

1.25 ± 0.05

1.39 ± 0.12

953

26.07 ± 1.63

1.12 ± 0.12

973

7.18 ± 0.27

1.82 ± 0.19

1003

2.41 ± 0.08

1.37 ± 0.09

923

15.32 ± 0.70

1.34 ± 0.09

953

4.97 ± 0.36

1.24 ± 0.13

973

2.67 ± 0.12

1.10 ± 0.08


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2.3 Sample Analysis. Infrared spectra of the starting materials and run products were obtained with a Fourier transform infrared spectrometer (JASCO FT-IR 4200) with a spectral resolution of 4 cm-1. We purged the infrared light path with dry nitrogen gas to reduce the effects of atmospheric H2O and CO2 vapor on the spectra. A sample (~0.4 mg) and ground KBr powder were mixed in an agate mortar with a weight ratio of 1:500, and the mixed powder (0.2 g) was pressed into a pellet (10 mm in diameter). One hundred scans were accumulated to obtain a sample spectrum in the wavenumber range of 350−7800 cm-1 (~1.3−28.6 µm). The starting materials and run products were also analyzed with X-ray powder diffraction (XRD; Rigaku Smart Lab) with Cu Kα radiation (λ=1.54178Å), micro-Raman spectroscopy (Acton SP-2750) and transmission electron microscopy (TEM; JEOL-2010). The samples were put into a hole (3 mm in diameter) on a reflection-free Si substrate for the XRD analysis. The XRD pattern of the reflection-free Si substrate was also obtained to subtract background X-ray signals from the obtained XRD patterns of the samples. The starting material was also analyzed on a glass sample holder with a large sample area (2 cm × 2 cm) for the detection of minor phases. Micro-Raman spectra of run products were obtained in a frequency range of 621−1168 cm-1 with a grating of 1800 lines/mm. The spectrometer was calibrated with spectral lines from a Neon lamp source. For TEM analyses, samples were dispersed in ethanol and a droplet of diluted solution was dripped onto a carbon covered copper TEM grid. The acceleration voltage was set to be 200 kV for the observations.

3. RESULTS 3.1 Starting Material. An infrared spectrum of the starting material shows two characteristic broad features centered at ~10 µm and ~18 µm (Figure 3), which are attributed to the Si-O


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stretching vibration and O-Si-O bending vibration modes, respectively. A broad infrared feature at 20 − 25 µm can also be seen in previous studies6,11,12, which could be attributed to a combination of the bending vibration and rotation modes of SiO4 and the Mg translation modes as an analogy of crystalline forsterite13,14. An XRD pattern shows a halo peak at 2θ~20−40° originating from the disordered structure of amorphous forsterite with small diffraction peaks attributed to crystalline forsterite (Figure 3). This indicates either that crystalline forsterite nuclei are present in the amorphous particles or that a small fraction of the starting particles is present as a crystalline state and mixed with the amorphous forsterite particles. A Raman spectrum of the starting material in the range of 650−1120 cm-1 showed no strong and sharp peaks of crystalline forsterite (Figure 3). The Raman spectrum can be deconvoluted into six Gaussian-Lorentzian shaped bands centered at ~719, 866, 918, 963, 1050, and 1097 cm-1. The most intense Raman band at ~866 cm-1 is produced by isolated SiO44- tetrahedra in forsterite glass, and the bands at ~918, 963 and 1097 cm-1 could be associated with dimers, trimmers and tetramers of SiO44- tetrahedra, respectively15−17. A small but obvious Raman band centered at ~719 cm-1 could reflect the bending vibration of the Si2O76dimer15−17. A Raman band at ~1050 cm-1 could be due to unknown contaminants in the starting material, and the peak disappeared after annealing of the starting material at 743 K for 6 hours in air, where the annealed sample was still amorphous.


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Absorbance

1

(a)

0.8 0.6 0.4 0.2 0 5 2×10

Counts per second

10

15 Wavelength (µm)

5

20

25

(b)

1.5×105 1×105 5×104

20

30 40 50 Diffraction angle 2θ (degree)

60

(c) Relative intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(2)

(1)

700

800

900

1000

1100

Raman shift (cm -1)

Figure 3. (a) An infrared spectra of the starting material. (b) An XRD pattern of the starting material obtained by using the glass sample holder. Diffraction peaks of crystalline forsterite are shown as closed circles. (c) Raman spectra of (1) the starting material and (2) amorphous


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forsterite heated at 743 K for 6 hours in air. The spectrum of the annealed sample was shifted upward arbitrarily. The Raman spectrum of the starting material was reproduced by a sum (red solid curve) of six Gaussian-Lorentzian shaped bands (dotted curves). A baseline of the Raman spectrum is shown as a dot-dashed line.


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3.2 Run Products. Infrared spectra of starting material and run products heated at 953 K under different water vapor pressures (1×10-9, 3×10-6, and 5×10-3 bar) are shown in Figure 4. Under all conditions, the spectra of the run products changed gradually with heating duration from broad features of amorphous forsterite to sharp peaks at ~10, 10.5, 11, 11.9, 16.2, 18.6, 19, 20.9, 21.4, and 22.7 µm, which correspond to the peak positions of spherical-shaped crystalline forsterite12. At PH2O~1×10-9 bar, sharp features of crystalline forsterite appeared to show no significant change for the first three hours, but became more prominent with time, and showed no further change after 90-hours of heating (Figure 4). Similar spectral evolution was observed for samples heated at 1003 and 1023 K, respectively, but more intense and sharper peaks of crystalline forsterite were observed at higher temperatures. This could be because annealing at a higher temperature resulted in a more ordered crystalline structure. At PH2O of 3×10-6 bar, amorphous forsterite also changed into crystalline forsterite with time (Figure 4). The time required for complete crystallization (~72 hours) was shorter than that at PH2O~1×10-9 bar (~90 hours). Crystallization of amorphous forsterite also occurred at PH2O of 5×10-3 bar with annealing (Figure 4), but the crystallization timescale (~12 hours) was shortest among the present conditions at 953 K. The amorphous forsterite heated at 953 K and 3×10-6 bar of H218O for 24 hours showed the appearance of crystalline forsterite, but all the peak positions of crystalline forsterite shifted to longer wavelengths (Figure 5), which is not the case for samples heated in the presence of isotopically-normal water vapor. XRD patterns of run products heated at 953 K and PH2O of 1×10-9, 3×10-6, and 5×10-3 bar are shown in Figure 6 with that of the starting amorphous forsterite. It is clearly seen that crystalline forsterite is the only phase formed during annealing and its peaks became more prominent with


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time. We also found that the amorphous forsterite halo peak at 2θ~20−40° weakened and finally disappeared with annealing.


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PH2O=1×10-9 bar

PH2O=3×10-6 bar

PH2O=5×10-3 bar

Absorbance (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5

10

15 20 wavelength (µm)

25 5

10


25 5

10


25

Figure 4. Infrared spectra of the starting material (0 hour) and run products heated at 953 K and PH2O of 1×10-9, 3×10-6, and 5×10-3 bar for different durations. The spectra are arbitrarily shifted in the vertical direction.


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Figure 5. Infrared spectra of run products heated at 953 K with isotopically-normal water vapor (H216O; dotted curve) and

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O-enriched water vapor (H218O; solid curve) of 3×10-6 bar for 24

hours.


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PH O=1×10-9 bar 2

PH O=3×10-6 bar 2

PH O=5×10-3 bar 2

Figure 6. XRD patterns of the starting material (0 hour) and run products heated at 953 K and PH2O of 1×10-9, 3×10-6, and 5×10-3 bar for different durations. The XRD patterns are arbitrarily shifted in the vertical direction. Closed circles indicate diffraction peaks of crystalline forsterite. The XRD pattern of the starting material was obtained by using the reflection-free Si substrate for direct comparison with the run products, and the peaks of crystalline forsterite (Figure 3(b)) are barely seen.


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4. DISCUSSION 4.1 Crystallization Kinetics. The infrared and XRD analyses of the run products clearly show that the phase appeared through annealing under all the conditions in the present study is crystalline forsterite (Figures 4−6). Fabian et al.5 conducted annealing experiments of forsterite smoke synthesized by laser ablation technique, and found that tridymite and amorphous SiO2 in addition to forsterite were crystallized because their starting material was chemically inhomogeneous. The appearance of only crystalline forsterite in the present study suggests that the starting material in this study is chemically homogeneous, and hereafter we discuss the kinetics of appearance of crystalline forsterite within the amorphous forsterite. The time evolution of crystallization of amorphous forsterite is quantitatively evaluated based on the absorption features in the wavelength range of 8−13 µm as in previous studies7,8. We assume that all of the spectra can be reproduced by the linear combination of those of amorphous forsterite and crystalline forsterite in accordance with the Lambert-Beer law;

Abssample = Absamor . Fo ⋅Camor . Fo + Abscryst. Fo ⋅Ccryst. Fo

(1)

,

where Abssample, Absamor. Fo and Abscryst. Fo are the absorbance of the sample, amorphous forsterite and crystalline forsterite, respectively, and Camor.

Fo

and Ccryst.

Fo

are the weight fractions of

amorphous forsterite and crystalline forsterite, respectively. The weight fractions of amorphous and crystalline forsterite are equal to their molar fractions because they have the same molecular weights. As mentioned above, the samples heated for longer durations than a certain time showed no further spectroscopic change in the infrared analysis and no amorphous forsterite halo in the XRD patterns. These results imply that the samples completely transformed into


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crystalline forsterite, but their spectral features such as peak sharpness and intensity at different temperatures and PH2O are different from each other. This is because infrared spectra are sensitive to grain size, shape, and short-range atomic ordering and annealing at different conditions resulted in different final crystallization states. Therefore, in this study, we assume that a sample heated for the longest duration at each condition has the most ordered crystalline structure and used as Abscryst.

Fo.

We used an infrared spectrum of the starting material as

Absamor.aFo, and the infrared spectrum of each sample was fitted with eq 1 using the least-square method to determine the degree of crystallization. Figure 7 shows a typical result of the spectral fitting. All the spectra of run products were successfully reproduced.


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×

Figure 7. A typical spectral fitting of a run product with eq 1. The blue solid curve represents the infrared spectrum of a sample heated at 953 K and PH2O of 1×10-9 bar for 24 hours. The dotted and dot-dashed curves show the spectra of the amorphous forsterite and crystalline forsterite (see the text for the definition), respectively. The red dotted solid curve is the fitted spectrum, and the residue of the fitting is shown as a dot-dot-dashed curve.


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The crystallization degrees of annealed samples at different temperature and PH2O conditions are shown as a function of heating duration in Figure 8. The time evolution of crystallization was the fitted with the Johnson-Mehl-Avrami (JMA) equation18,19 using the least-square method;

n x = 1− exp  − ( t τ )   ,

(2)

where x is the crystallization degree, t is heating duration, τ is a time constant for crystallization and n is the Avrami exponent that varies with the transformation mechanism involving nucleation and crystalline growth. Fitting curves are shown in Figure 8, and the fitting parameters are summarized in Table 1. It is clear that the time constant for crystallization τ becomes smaller with increasing temperature and PH2O. For instance, τ at 953 K and PH2O=5×10-3 bar is about one order of magnitude smaller than that at 953 K and PH2O~1×10-9 bar. This indicates that water vapor promotes crystallization of amorphous forsterite The reciprocal time constants for the crystallization (1/τ) under various PH2O conditions follow the Arrhenius relation;

1 τ = ν 0 exp ( −Ea RT ) ,

(3)

where ν0 is the pre-exponential factor, Ea is the activation energy for crystallization, R is the gas constant, and T is the absolute temperature. The activation energies for crystallization at PH2O of 1×10-9, 3×10-6, and 5×10-3 bar are ~414 ± 7, 357 ± 9, and 254 ± 10 kJ mol-1, respectively (Figure 9, Figure10; Table 2). The activation energy decreases with increasing PH2O, and this clearly


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suggests that water vapor plays a critical role in lowering the activation barrier for crystallization (Figure 10). The natural logarithm of the pre-exponential factors (ln ν0) at PH2O of 1×10-9, 3×10-6, and 5×10-3 bar are ~40.2, 33.8, and 22.2, respectively (Figure 9, Figure10; Table 2). A mean vibration frequency of the lattice in magnesium silicates (2.0 × 1013 s-1) or the intermediate value between the Si-O stretching and O-Si-O bending frequencies (2.5 × 1013 s-1) has been used as a reciprocal pre-exponential factor in some previous studies on the crystallization kinetics of amorphous magnesium silicates in space4,5,6,11,20,21, but our results clearly show that the preexponential factor is not constant and changes with PH2O (Figure 10) because the pre-exponential factor should include other factors in addition to the vibration frequency. The activation energy and the natural logarithm of the pre-exponential factor for crystallization of amorphous forsterite, synthesized by the induced thermal plasma method, in air are 233 ± 8 kJ mol-1 and 21, respectively9. These are broadly consistent with our experimental results (Figure 10) because PH2O in uncontrolled atmospheric air was likely to be in the range of ~10-2−10-3 bar. The Avrami exponent n at PH2O of 1×10-9, 3×10-6, and 5×10-3 bar lies between 1 and 1.5 (Table 1). Previous studies8,9 reported n ~1.5 for crystallization of amorphous olivine in air, and suggested that diffusion-controlled crystallization would proceed three-dimensionally from the pre-existing forsterite nuclei without nucleation. If crystalline forsterite nuclei are present in the starting material, the three-dimensional diffusion-controlled crystal growth from the pre-existing crystalline forsterite nuclei would be a possible crystallization mechanism of amorphous olivine under various water vapor pressure conditions. If this is the case, the activation energy obtained in this study should not contain the activation barrier for nucleation, but reflect that for crystal growth of crystalline forsterite. The Avrami exponent n at PH2O of 5×10-3 bar is slightly smaller and closer to ~1 than that at lower PH2O conditions (Table 1). This could also be explained by the


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increased contribution of nucleation and growth of crystalline forsterite from the grain surface at higher PH2O because a previous experimental study on crystallization of silicate glass particles22 showed that crystallization of silicate glass particles containing crystalline nuclei proceeds from the grain surface when n is close to 1. The amount of dissolved water should be larger at higher PH2O, which may lead to the effective nucleation and growth near the grain surface. The Avrami exponent and its PH2O dependence may indicate that the starting material is not a mixture of a small amount of crystalline particles and amorphous particles, but most of particles contain a small amount of crystalline nuclei.


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1 PH2O=1×10-9 bar 0.8 Crystallization degree

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

PH2O=3×10-6 bar

PH2O=5×10-3 bar

1023 K 1003 K

1003 K 973 K

973 K 953 K

953 K

953 K

923 K

0.4

0.2

0 -2 10

10-1

100 101 Log duration (hr)

102 10-2

10-1


102 10-1


102

Figure 8. The time evolution of crystallization of amorphous forsterite at PH2O of 1×10-9, 3×10-6, and 5×10-3 bar.


25


-8 PH O=1×10-9 bar 2

PH2O=3×10-6 bar

-9

PH2O=5×10-3 bar

Ln (1/τ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-10

-11

-12

-13 0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

-1

1000/T (K ) Figure 9. Arrhenius plots of the reciprocal time constants (1/τ) for crystallization of amorphous forsterite at PH2O of 1×10-9, 3×10-6, and 5×10-3 bar.


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Figure 10. Water vapor pressure dependences of the activation energy (solid circles) and the natural logarithm of the pre-exponential factor (solid squares) of the crystallization rate.


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Table 2. Activation energies and natural logarithms of the pre-exponential factors of the crystallization rate of amorphous forsterite. Errors represent 1σ standard error of the mean. PH2O (bar)

Activation energy (kJ mol-1)

ln ν0 (s-1)

1×10-9

414.4 ± 7.0

40.2

3×10-6

357.3 ± 9.4

33.8

5×10-3

253.7± 9.6

22.2


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4.2 Role of Water Vapor for Crystallization of Amorphous Forsterite. The present study clearly showed that water vapor acts as a catalyst for the crystallization of amorphous forsterite. Here we discuss the role of water vapor for crystallization. The Raman spectrum of the amorphous forsterite (Figure 3c) indicates that dimers, trimmers and tetramers of SiO44- are present in the amorphous structure. This Raman spectrum is in good agreement with that of forsterite-composition glass15,16,17. Neutron and synchrotron X-ray diffraction measurements of forsterite glass showed the presence of MgO4 and MgO5 polyhedra as a network former in the glass structure23,24. By analogy with the forsterite glass structure, the amorphous forsterite in this study also consists of the structural units of both isolated and polymerized SiO4 tetrahedra and MgOx (x=4, 5) polyhedra. In this case, Si-O-Si and Mg-O-Mg bonds in the amorphous structure can be cut to form the structure of crystalline forsterite with isolated SiO4 tetrahedra and MgO6 polyhedra. Water molecules can dissolve into silicate glass, and its solubility is roughly proportional to the square root of PH2O25,26. Dissolved water molecules diffuse through the amorphous structure, but also form hydroxyls (-OH)26,27. Hydroxyls are the dominant form of water molecules at low water concentration, and thus dissolved water molecules most probably cut Si-O-Si and Mg-O-Mg bonds in the amorphous forsterite to form hydroxyls. The peak shifts of the 10 µm-infrared feature of the sample heated at 3×10-6 bar of H218O vapor (Figure 5) may be evidence of the interaction between amorphous forsterite and water vapor. Water molecules dissolving into the amorphous forsterite should exchange oxygen isotopes with amorphous forsterite through the hydroxyl formation reaction (structural O + H2O = 2OH). In annealing experiments in the presence of H218O vapor, the isotopic exchange between the amorphous forsterite and H218O would result in the shift of peak positions to longer


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wavelengths because of the replacement of oxygen isotopes (16O-rich) with heavier oxygen isotopes (18O). Koike et al.12 showed that some infrared features of crystalline forsterite are sensitive to particle shape, whereas the peak position at 11.9 µm remains unchanged irrespective of particle shape. We observed that the peak at 11.9 µm also shifted to longer wavelength (~12.5 µm). The peak shifts observed in experiments with H218O vapor can thus be attributed to the isotopic effect on the vibration frequencies due to the interaction between the amorphous forsterite and H218O water molecules. We therefore conclude that water molecules diffusing into the amorphous structure cut atomic Si-O-Si and Mg-O-Mg bonds and promote the rearrangement of the structural units. The fraction of the structural units cut by hydroxyls increases with increasing the water vapor pressure due to the increase of dissolvable water molecules in the amorphous forsterite. Because the structural rearrangement takes place with a smaller energetic barrier for the structural units cut by hydroxyls, the amorphous forsterite annealed at higher PH2O can crystallize at a higher rate with smaller activation energy. We note that the activation energies obtained in this study are still larger than the typical activation energy of water diffusion in silicate glasses (~100 kJ mol-1)28,29, and thus the rate-limiting step for crystallization is not the diffusion of water molecules but the structural rearrangement in the amorphous forsterite. The infrared spectra of the samples heated at 3×10-6 bar of H218O vapor showed broader peaks than those of the samples heated in the presence of isotopically-normal water vapor (Figure 5). These broadened peaks can be explained by the presence of both Si-16O and Si-18O stretching vibrations in the silicate structure. Crystalline forsterite is a nominally anhydrous mineral, and the isotopic exchange between crystalline forsterite and water molecules does not easily occur. The presence of both Si-16O and Si-18O stretching vibrations in the crystalline forsterite structure


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suggests that a part of the amorphous forsterite crystallized with the aid of hydroxyls and other part crystallized without the aid of hydroxyls, which supports the idea of decrease of the activation energy for crystallization with increasing PH2O.

4.3 Implications for Crystallization of Amorphous Forsterite in Protoplanetary Disks. The total pressure of protoplanetary disks has not yet been well constrained, but that in the inner disk might be in the range of ~10-3 to 10-6 bar30. Considering the H2O/H2 ratio based on the solar abundance of elements31, the nominal PH2O in the disk inside the water snowline might range from ~10-6 to 10-9 bar. The H2O/H2 ratio in the gas phase can be enhanced by a factor of 10 in the protoplanetary disk by the accumulation of icy dust32,33, and such enrichment may be required to explain the oxygen isotopic difference of planetary materials compared to the Sun34. Moreover, the increase of the H2O/H2 ratio by a factor of 100 may be required to explain the fayalite contents of chondritic olivine grains35. If this is the case, PH2O in the disk may be as high as 10-4 bar. The crystallization timescales of amorphous forsterite at PH2O between 10-9−10-4 bar are shown in Figure 11. The minimum temperature required for crystallization of amorphous forsterite within the lifetime of protoplanetary disk gas (1-10 Myr)36 would be ~700 and ~620 K at PH2O of 10-9 and 10-4 bar, respectively. This critical temperature for crystallization is not very sensitive to PH2O, and thus we conclude that crystalline forsterite dust observed in protoplanetary disks (e.g. HD100504)37 experienced thermal annealing at temperatures above ~620−700 K irrespective of disk conditions. The crystallization timescale of amorphous forsterite at PH2O of 10-4 bar is 10−100 times shorter than that at PH2O of 10-9 bar at 700-900 K, which changes the survivability of amorphous forsterite dust during various thermal events that may have occurred in the early Solar System.


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Under enhanced H2O/H2 conditions, the lifetime of amorphous forsterite dust becomes significantly shorter than that at the nominal H2O/H2 ratio. For instance, if shock wave heating occurred in the icy region of the disk, water ice enrichment by a factor of ~700 relative to the canonical solar ratio could be possible38. The amorphous forsterite dust in such a post shock region may be preferentially crystallized. Detailed discussion on the crystallization of amorphous forsterite during various thermal events in the early Solar System is beyond the focus of the present study, but we propose that the effect of water vapor should be considered in quantitative discussions of the presence, survival, and lifetime of amorphous forsterite dust in extraterrestrial materials.


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Figure 11. E-folding timescales for crystallization of sub-micrometer-sized amorphous forsterite dust under different temperature and PH2O conditions. The estimated lifetime of gas in protoplanetary disks (1-10 Myr)36 is also shown for comparison.


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5. CONCLUSIONS The crystallization kinetics of amorphous forsterite sub-micron sized grains under various water vapor pressure (PH2O) conditions ranging from 1×10-9 to 5×10-3 bar were investigated in order to evaluate the effect of water vapor on crystallization. The time evolution of the crystallization degree inferred from the 10 µm infrared feature follows the Johnson-MehlAvrami equation with an Avrami exponent of 1 to 1.5. The crystallization rate, which is represented by a reciprocal of the crystallization timescale, is faster at higher temperatures and higher PH2O. The activation energy and the pre-exponential factor of the crystallization rate decrease with increasing PH2O; The activation energy of 414.4 ± 7.0 kJ mol-1 at PH2O= 1×10-9 bar decreases to 253.7 ± 9.6 kJ mol-1 at PH2O= 5×10-3 bar, and the natural logarithm of the pre-exponential factor (s-1) changes from 40.2 at PH2O= 1×10-9 bar to 22.2 at PH2O= 5×10-3 bar. These results clearly suggest that water vapor acts as a catalyst for the crystallization of amorphous forsterite. The rearrangement of the structural units can take place with a smaller energetic barrier in the presence of water vapor because water molecules dissolving into the amorphous structure cut Si-O-Si and Mg-O-Mg bonds through a hydroxyl formation reaction. Water vapor is the third most abundant gas species in protoplanetary disks, and its abundance can be enhanced by enrichment of icy dust grains. The critical temperature for crystallization of amorphous forsterite in protoplanetary disks is estimated to be ~620−700 K irrespective of disk physicochemical conditions. The timescale of crystallization depends on PH2O, and the effect of water vapor should be considered for quantitative discussions of the crystallization of amorphous forsterite dust during various thermal events recorded in extraterrestrial materials.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Present Address #

UTokyo Organization for Planetary Space Science, The University of Tokyo, Hongo, Tokyo

113-0033, Japan. ORCID Daiki Yamamoto (D. Y.): 0000-0001-6852-2954 Shogo Tachibana (S. T.): 0000-0002-4603-9440 Author Contributions D. Y. and S. T. designed the research, and D. Y. conducted all the experiments and sample analysis. D. Y. and S. T. discussed the data and wrote the paper. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The authors thank Akira Tsuchiyama for providing the amorphous forsterite powder, Junji Yamamoto and Kohei Takahata for Raman spectroscopy. The TEM analysis was carried out at the “Joint-use Facilities: Laboratory of Nano-Micro Material Analysis”, Hokkaido University, supported by “Material Analysis and Structure Analysis Open Unit (MASAOU)”. This work was supported by Ministry of Education, Sports, Science and Technology KAKENHI Grant.


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For TOC only;


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Water Vapor Pressure Dependence of Crystallization Kinetics of

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