2024 年 119 巻 1 号 論文ID: 240220
Knowledge of the viscosity of melts and liquids at high pressure conditions is essential to understand the mobility of magmas and other liquids in the Earth’s interior. The falling sphere viscosity measurement in large volume press using synchrotron X-ray imaging is one of the most powerful techniques for investigating the viscosities of melts and liquids at high pressure and high temperature conditions. Despite capability of the in-situ X-ray radiography falling sphere viscosity measurement strongly depends on the speed of X-ray imaging, common imaging setups are limited to speed of ∼ 30-60 frames/second (fps), which hamper proper viscosity measurements on low viscous melts and liquids. In this study, we developed a new high-speed X-ray imaging setup up to 5000 fps combined with 1500-ton multi-anvil press at the BL04B1 beamline in the SPring-8. By using the high-speed X-ray imaging with the frame rate of 1000 fps, we succeeded to determine low viscosity value of 0.0081 (±0.0011) Pa s in calcite (CaCO3) liquid at ∼ 4.7 GPa and ∼ 1925 °C. The high-speed X-ray imaging combined with 1500-ton multi-anvil press at the BL04B1 beamline would expand capability of falling sphere viscosity measurement of low viscous liquids at high pressure conditions of deep mantle.
Viscosity is the most fundamental transport property controlling migration processes of magmas and liquids in the Earth’s interior. Extensive studies on viscosity of silicate melts have been conducted at ambient pressure, and models have been proposed to calculate viscosities of magmas with various compositions under high temperature conditions (e.g., Hui and Zhang, 2007; Giordano et al., 2008; Langhammer et al., 2022). In addition, efforts have been made to understand effect of pressure on the viscosity of silicate melts or other liquids. In-situ X-ray radiography falling sphere viscosity measurement is one of the most well-established techniques used to investigate viscosity of liquids at high pressure conditions (e.g., Kanzaki et al., 1987; Dobson et al., 2000; Suzuki et al., 2002; Brizard et al., 2005; Liebske et al., 2005; Kono et al., 2013; Sakamaki et al., 2013; Kono et al., 2014a, 2014b, 2015; Kono, 2018; Xie et al., 2020). Using this technique, the viscosity of melt (η) can be calculated from the terminal velocity of falling sphere (ν) by using the Stokes’ equation as follows:
| \begin{equation} \eta = \frac{g d_{\text{s}}^{2}(\rho_{\text{s}} - \rho_{\text{m}})}{18\nu} \end{equation} | (1), |
where ρ and d are density and diameter, with subscripts s and m denoting properties of probing sphere and melt, respectively. In order to accurately determine viscosity based on equation (1), precise determination of the terminal velocity (ν) is therefore critical.
Synchrotron X-ray imaging enables us to monitor the trajectory of the falling sphere with time, during in situ high pressure and high temperature experiments in large volume press, which allows for a precise determination of the terminal velocity and the resultant viscosity of melts. Previous falling sphere viscosity measurements using synchrotron X-ray imaging in multi-anvil press have been conducted using an X-ray imaging speed of ∼ 30-60 frames/second (fps) to investigate viscosities of polymerized silicate melts with relatively high viscosity (e.g., Suzuki et al., 2002; Sakamaki et al., 2013). These techniques are however difficult to apply to the investigation of low viscosity liquids such as liquid metals and salts. For instance, previous studies that investigated viscosities of low viscous liquid iron alloys (4-20 mPa s) could only use 2-4 images (e.g., Dobson et al., 2000), which makes it difficult to precisely determine the terminal velocity of the falling sphere in such measurements, and hence would likely results in large uncertainties in the calculated viscosity.
In order to overcome such limitations, high-speed X-ray imaging with the imaging rates of up to 5000 fps was recently developed at the 16-BM-B beamline in the Advanced Photon Source, USA (e.g., Kono et al., 2013, 2014a, 2014b, 2015; Kono, 2018). The high-speed X-ray imaging opened new way to investigate viscosity of low viscous liquids such as liquid salts (Kono et al., 2013), carbonate melts (Kono et al., 2014a), and liquid Fe-S (Kono et al., 2015). On the other hand, the 16-BM-B beamline is only equipped with a small Paris-Edinburgh press, which has a limited range of available pressures. Use of large volume multi-anvil press apparatus may expand capability of the falling sphere viscosity measurement to a wide range of pressure conditions (Liebske et al., 2005; Xie et al., 2020). In this letter, we report the development of a high-speed X-ray imaging setup combined with the 1500-ton multi-anvil press (SPEED-1500) at the BL04B1 beamline in SPring-8, and discuss its capability for measuring the viscosity of low viscous liquid using the falling sphere methods.
High-speed X-ray imaging combined with multi-anvil large volume press experiment was conducted at the BL04B1 beamline in SPring-8. A high-speed camera (Photon FASTCAM Mini AX100) with a capable recording frame rate of 4000 fps by full image size of 1024 × 1024, and at higher frame rate by reduced image size (for example, the maximum image size of 1027 × 768 at 5000 fps and 640 × 480 at 12500 fps) was installed at the BL04B1 beamline. The high-speed camera equips 32GB memory, which enables us to record images of 1024 × 1024 size, continuously, for 21.8 s, at 1000 fps frame rate. The high-speed camera was placed on a newly installed camera stage with a scintillator mount and lens system, which locates just behind the 1500-ton multi-anvil press (SPEED1500) (Fig. 1). We use a 100 µm thick Ce-doped GAGG (gadolinium aluminum gallium garnet) as the scintillator, which provided high brightness for high-speed X-ray imaging. The pixel resolution was 4.0 um/pixel using 5 times infinity-corrected objective lenses. The full field of view is 4.0 × 4.0 mm.
A high-pressure experiment was carried out in the 1500-ton multi-anvil press, SPEED1500 located at the beamline BL04B1. The cell assembly consisted of tungsten carbide anvils with the truncation edge length (TEL) of 8 mm, and 17% CoO + MgO octahedron pressure medium with edge length of 14 mm (Fig. 2). The pressure medium was built in three parts in order to place the sample capsule vertically to the falling direction of the metallic sphere. The top and bottom caps are made of ZrO2 for thermal insulation, and we used rhenium foil heater for high temperature experiment. Temperature during the X-ray imaging experiment was determined from a power-temperature relationship, calibrated in a separate experiment using the identical cell assembly equipped with a W97%Re3%-W75%Re25% thermocouple placed at the sample position in the center of the rhenium heater. A pellet of sample was put into a graphite capsule, and Pt sphere was placed in the upper part of the sample.
Falling sphere viscosity measurement was conducted for CaCO3 sample. The viscosity of CaCO3 liquid is reported to be very low (0.0059-0.0067 Pa s at the pressure and temperature conditions of 0.9-6.2 GPa and 1380-1790 °C; Kono et al., 2014a) among those of known magma compositions. CaCO3 liquid, which is therefore an adequate candidate for assessing the capability of the falling sphere techniques to measure the viscosity of low-viscosity melts, using high-speed X-ray imaging in the multi-anvil press. Falling sphere viscosity measurement on CaCO3 liquid was conducted at the frame rate of 1000 fps (exposure time of 1.0 ms). We conducted the falling sphere viscosity measurement of CaCO3 liquid at a condition of the press oil load of 300 ton and the heating power of 750 W, which corresponds to the pressure and temperature conditions of ∼ 4.7 GPa and ∼ 1925 °C based on estimations from separate calibration experiments. It is important to note that we increased temperature at the rate of 100 °C par minute until ∼ 1500 °C and then heated to ∼ 1925 °C instantly by changing heating power directly from 612 to 750 W. Since the melting temperature of CaCO3 is ∼ 1650 °C at ∼ 5 GPa (Suito et al., 2001), the Pt sphere might fell at lower temperature than the estimated temperature of ∼ 1925 °C.
Figure 3 shows X-ray radiography images of a 150 µm Pt sphere embedded in the CaCO3 sample in the multi-anvil cell. In order to investigate the capability of high-speed X-ray imaging through the multi-anvil cell, we collected the images with varying exposure time of 1.0, 0.5, and 0.2 ms (corresponding camera frame rate of 1000, 2000, and 5000 fps, respectively). These high frame rates are required to obtain enough data points for accurate monitoring of the falling sphere trajectory in low viscous liquids such as carbonate melts, molten salts, and water (Fig. 10.2 in Kono, 2018). The results show clear X-ray radiography image of the Pt sphere in the multi-anvil cell even at the shortest exposure time of 0.2 ms, implying the possibility of carrying out the falling sphere viscosity measurement by using 5000 fps high-speed X-ray imaging in the multi-anvil cell.
Figure 4a shows a series of selected images of the falling Pt sphere in CaCO3 liquid at every 5 ms. The Pt sphere starts to fall at ∼ 190 ms, and fall through the sample within 40 ms period. The analyzed results of the falling distance and falling velocity of Pt sphere in CaCO3 liquid are shown in Figure 4b. Although the distance versus time plot in Figure 4b appears to show a large linear segment, the time derivatives show gradual acceleration of falling velocity with time. The falling velocity reaches a constant maximum (terminal velocity) at 21.5 mm/s in a limited time frames of 228-234 ms. As the result, viscosity of CaCO3 liquid at ∼ 4.7 GPa and ∼ 1925 °C is calculated as η = 0.0081 ± 0.0011 Pa s by using the equation (1) with the following parameters: densities of CaCO3 liquid and Pt sphere of 2.6 and 21.45 g/cm3, respectively, diameter of the Pt sphere of 0.15 ± 0.02 mm, and the correction factors for wall effect (F) (Faxén, 1922) and end effect (E) (Maude, 1961). Our obtained viscosity result of the CaCO3 liquid is similar to that reported in previous experimental study (Kono et al., 2014a) (η = 0.0060 ± 0.0003 Pa s at 4.8 GPa and 1770 °C) and that calculated by first principles molecular dynamics calculation (Du et al., 2018) (η = ∼ 0.006 Pa s at ∼ 5 GPa and 1727 °C), and therefore our viscosity result confirms the capability of the falling sphere viscosity measurement using high-speed X-ray imaging in multi-anvil press at the BL04B1 beamline to measure properly the viscosity of low-viscosity melts such as CaCO3 melt. The slight difference of the viscosity obtained in this study and reported in Kono et al. (2014a) might be due to uncertainty of temperature. In addition, slight ellipticity of the Pt sphere may be another source of the uncertainty in viscosity determination. The Pt sphere showed the longest diameter of 0.17 mm and the shortest diameter of 0.13 mm. The different size yielded the uncertainty of the viscosity of ±0.0011 Pa s.
It has been known that the camera frame rate strongly affects the precision of the terminal velocity of the falling sphere (e.g., Kono et al., 2014a). In Figure 5, we simulated the falling sphere trajectory using the data in Figure 4b with reduced frame rates of 200 fps (Fig. 5a) and 50 fps (Fig. 5b). The number of observable images decreases with reducing frame rate, and in case of the frame rate of 50 fps, only 4 images can be obtained in 60 ms experimental time frame. Although determination of the terminal velocity through linear fitting of the falling distance versus time data has been a commonly used methodology in the previous studies, linear fittings of the data in Figures 5a and 5b yield falling velocity of 18.2 and 13.6 mm/s, respectively, which are 15 and 37% lower than the terminal velocity determined by the frame rate of 1000 fps (Fig. 4b). The data indicate that substantial oversampling by using enough high-speed imaging and confirmation of constant falling velocity region by time derivative analysis is important for accurate measurement of terminal velocity of falling sphere and the resultant viscosity particularly for low viscous liquids. The time derivative analysis with the data collected with the frame rate of 1000 fps shows a constant velocity at the time frames of 228-234 ms (Fig. 4b), indicating that the frame rate of 1000 fps is sufficient to determine the terminal velocity of the carbonate melt having the lower viscosity of 0.0081 Pa s.
In conclusion, our newly established setup at the BL04B1 beamline, in SPring-8, enables us to conduct high-speed X-ray imaging in multi-anvil press at an imaging rate up to 5000 fps (2 ms exposure time). These techniques currently enable us to investigate viscosity of low viscous liquids in large volume multi-anvil press at higher pressure conditions than the smaller Paris-Edinburgh press used in previous studies. The 1500-ton multi-anvil press at the BL04B1 beamline has been used for high-pressure experiment at the pressure conditions of the Earth’s lower mantle (>23 GPa). Combination of our developed high-speed X-ray imaging and large volume multi-anvil press technique would provide further opportunity to investigate viscosity of low viscous liquids at high pressure conditions of the Earth’s mantle.
The experiments were performed at the BL04B1 beamline (JASRI Proposal Nos. 2019A0069 and 2021B1222) of SPring-8.
