Ultrahigh‐Pressure Acoustic Velocities of Aluminous Silicate Glass up to 155 GPa With Implications for the Structure and Dynamics of the Deep Terrestrial Magma Ocean

We have carried out in situ high‐pressure acoustic velocity measurements of (Fe2+, Al)‐bearing MgSiO3 glass up to pressures of 155 GPa, which confirmed a distinct pressure‐induced trend change in the transverse acoustic velocity (VS) profile around 98 GPa, likely caused by the Si‐O coordination number (CN) change from 6 to 6+. Although it has been reported that the substitution of Fe2+ in MgSiO3 glass induces almost linear velocity reduction up to ∼160 GPa, we revealed that the VS profile of (Fe2+, Al)‐bearing MgSiO3 becomes anomalously steeper above ∼100 GPa and eventually came to be equivalent to MgSiO3 glass above ∼125 GPa. This implies the incorporation of Al into Fe‐bearing MgSiO3 glass significantly facilitates making it far elastically stiffer and thus the densification under pressures well within the Earth's lower mantle. Our results indicate the possible presence of stiff and highly dense silicate melts in deep MOs in the rocky terrestrial planets.

Silicate glasses have alternatively been extensively studied as promising analog materials to silicate melts, which in fact showed similarities in various high-pressure physical properties including the change in Si-O coordination number (CN) among silicate glass and silicate melt (Benmore et al., 2010;Karki et al., 2018;Kono et al., 2020;Lin et al., 2007;Mashino et al., 2022;Meade et al., 1992;Morard et al., 2020;Murakami & Bass, 2010Murakami et al., 2019;Ohira et al., 2016;Petitgirard et al., 2015Petitgirard et al., , 2017Prescher et al., 2017;Sanloup et al., 2013;Sato & Funamori, 2008;Zeidler et al., 2014). Recent experimental progress in the acoustic velocity measurements using Brillouin scattering spectroscopy makes it possible to explore the structural changes of silicate glasses under ultra-high pressure conditions approaching to ∼200 GPa and has shown the possible Si-O CN change from 6 to 6 + under extreme pressure conditions above ∼100 GPa (Mashino et al., 2022;Murakami & Bass, 2010Ohira et al., 2016), which has been subsequently confirmed by in situ high-pressure X-ray diffraction studies on SiO 2 glass (Kono et al., 2020;Murakami et al., 2019;Prescher et al., 2017). Although previous Brillouin scattering studies on Si-enriched silicate glasses such as MgSiO 3 and Fe-bearing MgSiO 3 have reported the structural changes of Si-O CN from 6 to 6 + above 100 GPa and shown that the substitution of Fe 2+ in MgSiO 3 glass induces almost linear acoustic velocity reduction over a wide range of pressures to ∼160 GPa (Mashino et al., 2022;Murakami & Bass, 2011), it still remains unknown as to how the silicate melt/glass with more realistic chemical composition in the terrestrial planets structurally evolves under deep MO conditions. Although it is well known that the solution of Al 2 O 3 in silicate melts/glasses results in significant changes in their physical properties under ambient pressure (Mysen, 2021), the effect of Al 2 O 3 in the silicate glasses/melts on the elasticity under ultrahigh pressures corresponding to deep terrestrial MOs has been unclarified.
Here, we conducted in situ high-pressure acoustic wave velocity measurements of (Fe 2+ , Al)-bearing MgSiO 3 glass using the Brillouin spectroscopic technique combined with diamond anvil cell (DAC) high-pressure apparatus up to pressures of 155 GPa to bring new insights into the structural evolution of the silicate melts with pressure/depth corresponding to the deep MO. Results suggest that the transverse acoustic wave velocity profile of (Fe, Al)-silicate glass becomes anomalously steeper above 98 GPa and eventually came to be equivalent to that of pure MgSiO 3 glass above ∼125 GPa. This implies that the incorporation of Al into Fe 2+ -bearing MgSiO 3 glass significantly facilitates making it far elastically stiffer and thus the possible densification under pressures above ∼100 GPa which indicates the possible existence of ultra-stiff and dense silicate melts under deep MO conditions of the terrestrial planets.

Sample Preparation and Characterization
The starting material for the synthesis of (Fe 2+ , Al)-bearing MgSiO 3 glass (hereafter referred to as (Fe, Al)-silicate glass) was the mixture of MgO, 57 Fe 2 O 3 , Al 2 O 3 , and SiO 2 powders. The mixture was cold compressed along with a loop made of 50 μm thick platinum wire inside the cylindrical volume of sample powder and sintered at a temperature of 1000°C. Then it was melted and reduced in a vertical gas-mixing furnace at 1600°C for 2 hr. Oxygen fugacity was adjusted using a mixture of H 2 and CO 2 to a value of two log-units below fayalite-magnetite-quartz (FMQ) buffer at approximately log(fO 2 ) = −6.57. The melted sample was subsequently quenched by letting it drop into the water. The quenched sample was crushed into pieces for further characterization. The wavelength dispersive X-ray spectroscopy (WDS) measurement was performed to check the chemical homogeneity on two polished pieces using electron microprobe analysis with a JEOL JXA-8230 at ETH. The results of these measurements are shown in Table S1 of Supporting Information S1 and the values Fare the averages of 25 points. Data shows the incorporation of Fe and Al by 7 and 9 atomic% in MgSiO 3 -glass and the chemical formula Mg 0.92 Fe 0.07 Si 0.93 Al 0.09 O 3 . The samples were then examined by Mössbauer spectroscopic measurement performed at Bayerisches Geoinstitut in Germany using a 57 Co source in Rh matrix with the nominal activity of 1.85 GBq. The velocity scale is referenced to α-Fe. The Mössbauer spectrum of our synthesized (Fe, Al)-silicate glass is shown in Figure S1 of Supporting Information S1. Deconvolution of the spectrum yields two doublets for Fe 2+ with central shifts of 1.093 ± 0.078 mm/s (deep green doublet) and 0.934 ± 0.092 mm/s (cyan doublet), respectively and are consistent with the literature (Dyar, 1985;Mysen & Richet, 2019). The area covered by the ferric iron is below the detection limit of Fe 3+ /Fe = 0.05 ± 0.04, hence our synthesized glass mainly consists of ferrous iron.

DAC Preparation
A pair of beveled diamond anvils with a culet flat 120 μm was utilized to generate high pressure in a symmetric cell. The crushed piece was loaded into the central hole of about 60-70 μm in diameter made on a pre-indented Re gasket of the thickness of 40 μm by laser drilling. No pressure-transmitting medium was used. To check the effect of deviatoric stress with pressure, we have compared the full width at half maxima (FWHM) of the Brillouin peaks as shown in Figure S2 of Supporting Information S1. No systematic broadening of the peaks was observed in our measurements with pressure, which excludes the possibility of the presence of significant deviatoric stress in our sample chamber. The pressure was determined using the Raman T 2g mode shift of the diamond anvil (Akahama & Kawamura, 2007) by measuring several points around the central area of the sample where the probe laser for Brillouin scattering measurements was irradiated. Since there was a little change in pressure (maximum ± 2 GPa) after Brillouin scattering measurements, for reporting we took the average of 6 pressures measured before and after experiments.

Brillouin Scattering Measurements
The high-pressure in situ acoustic wave velocities were obtained using the Brillouin scattering spectroscopic measurement system at ETH Zurich. To probe our sample, we used a micro-focused (∼10 μm) diode-pumped laser beam with a wavelength of 532 nm (Verdi V6) from Coherent. The scattered light from the center of the sample was collected and passed through a Sandercock-type six-pass Fabry-Perót interferometer and recorded with a multichannel analyzer (GHOST v.7.0.0, The Table Stable Ltd.) (Sandercock, 1970). Symmetric scattering geometry with a ∼50° external scattering angle was maintained in all measurements and the angle was calibrated using a doubly polished borosilicate crown glass (BK7) (Murakami et al., 2009). In a symmetric scattering geometry, the velocity V of an acoustic wave can be calculated without any prior knowledge of the sample refractive index following the relation (Whitfield et al., 1976 where λ is the laser wavelength (532 nm), θ is the external scattering angle, and i denotes one of the acoustic modes. In our measurements, we collected a total of 53 points from 8.4 to 155 GPa in two runs with pressure increments of 1-6 GPa. We could not go beyond 155 GPa due to the diamond failure. The acquisition time was adjusted in each pressure point to get very sharp Brillouin peaks. Generally, the acquisition time increases with pressure and it was from 2 to 5 hr in this study. We used the Gaussian function to fit the peaks. Figure 1 shows the representative Brillouin spectra at 21.5, 108, and 155 GPa, which show very sharp Stoke and anti-Stoke lines even at the highest pressure point. The evolution of Vs of (Fe, Al)-silicate glass with pressure up to 155 GPa is shown in Figure 2 together with the relevant silicate glasses reported in the previous experimental studies (Huang et al., 2022;Mashino et al., 2022;Murakami & Bass, 2011). The longitudinal acoustic peaks (V P ) are observed to merge with the V S of the diamond above 37 GPa. Although the pressure conditions where we could observe the V P were limited, we found the overall trend change of the V P goes smoothly and is well synchronized with that of V S as shown in Figure S3 of Supporting Information S1. All the V S and V P data together with the FWHM values are listed in Table 1.

Results
The entire V S data set was then fitted by a fourth-order polynomial function to evaluate the trend change in the V S profile with pressure, which shows a remarkably good fit with an adjusted R 2 of 0.9989. This fitting result is found to be very satisfactory with respect to MgSiO 3 glass with R 2 ∼ 0.9985 (Murakami & Bass, 2011), Fe 2+ bearing MgSiO 3 glass with R 2 ∼ 0.9987 (Mashino et al., 2022), and pyrolite glass with R 2 ∼ 0.9950 (Huang et al., 2022). By following the same procedure as the previous Brillouin studies, the pressure condition where the change in the velocity profile occurs was then determined by the point where the second derivative of the fitted function with respect to pressure ( 2 / 2 ) becomes maximum (hereafter referred to as inflection pressure). The resultant inflection pressure was then found to be at 98 GPa as shown in Figure S4 of Supporting Information S1, which is 35 GPa lower than that of MgSiO 3 glass and 43 GPa lower than that of SiO 2 glass (Murakami & Bass, 2010. The gradient of the fitted curve, / , decreases gradually in the pressure range 8.4-98 GPa from 55 to 6 (m/sec)/GPa followed by a significant increment by approximately 50% to 9.1 (m/sec)/GPa above 98 GPa. While the Vs trend in the present study is observed to be highly consistent within 1.7% and 0.3% with respect to pyrolite and Fe 2+ bearing MgSiO 3 glasses (Huang et al., 2022;Mashino et al., 2022), respectively up to the inflection point at 98 GPa, the Vs profile above inflection pressure becomes far steeper than that of other ferrous glasses and deviates up to ∼4% at the maximum pressure point we explored, which eventually came to be equivalent to that of pure MgSiO 3 glass (Murakami & Bass, 2011) above ∼125 GPa.

Pressure-Induced Si-O Coordination Number Change
Previous studies using in situ high-pressure Brillouin scattering spectroscopy on various silicate glasses including SiO 2 , Al-bearing SiO 2 , hydrous SiO 2 , MgSiO 3 , and Fe-bearing MgSiO 3 glasses (Mashino et al., 2022;Murakami, 2018;Murakami & Bass, 2010Ohira et al., 2016) have suggested that the trend changes in the acoustic velocity profile of silicate glasses as a function of pressure could primarily synchronize with the change in the Si-O CN (Sato & Funamori, 2008). This interpretation is in fact in good agreement with the theoretical studies (Brazhkin et al., 2011;Karki et al., 2007;Zeidler et al., 2014) and also the recent experimental works on SiO 2 glass obtained up to pressures of ∼200 GPa (Kono et al., 2020;Murakami et al., 2019;Prescher et al., 2017). More importantly, most of those previous high-pressure Brillouin studies have observed a trend change in the acoustic velocity profile above ∼100 GPa. Based on the criterion mentioned above, it has been suggested that the trend change in the acoustic velocity of silicate glasses with pressure so far observed above ∼100 GPa corresponds to the Si-O CN changes from 6 to 6 + (Mashino et al., 2022;Murakami, 2018;Murakami & Bass, 2010Ohira et al., 2016). The emergence of this ultrahigh-pressure densification process involved in the higher CN above 6 is also supported by the recent high-pressure experimental and theoretical works on GeO 2 glass (Brazhkin et al., 2011;Kono et al., 2016;Petitgirard et al., 2019) considered as a promising low-pressure analog material to SiO 2 glass.

Reduction of the Inflection Pressure
From the current regression analysis, we find the velocity profile of (Fe, Al)-silicate glass can be divided into two distinct pressure regimes: (a) from 8.4 to 98 GPa, and (b) 98 GPa to high pressure. The absence of any sharp anomaly in the velocity profile in the pressure regime (a) implies a gradual change in the Si-O CN from 4 to 6 similar to MgSiO 3 and Fe 2+ bearing MgSiO 3 glass (Mashino et al., 2022;Murakami & Bass, 2011). The V S trend is ∼3.6% lower than that of MgSiO 3 glass on average in this pressure regime. The shear velocity (V S ) depends on the shear modulus (G) and density (ρ) of the sample as V S = √(G/ρ). Since the chemical compositions of pyrolytic, Fe-bearing, and (Fe, Al)-silicate glasses are slightly different, that may have effect on both G and ρ. The pyrolytic glass velocity is 1.7% lower than (Fe, Al)-silicate glass up to 98 GPa most likely because it contains 3 wt% higher FeO and also heavy Ca, which explain reduction of V S by increased density of the pyrolytic glass. A very careful look at Figure 2 reveals that V S of Fe-bearing glass becomes lower at least up to 22 GPa, and it could be explained by the higher density of Fe-bearing glass with respect to (Fe, Al)-silicate glass as it contains 3.8 wt% higher FeO. However, above 22 GPa V S of (Fe, Al)-silicate glass is very similar up to 98 GPa, which could be induced by the coupled effect of G and ρ due to the different CN environment of Fe and Al. In pressure regime (b), 6 + coordinated Si-O would be dominated in the structure. Although the substitution of Fe 2+ in MgSiO 3 glass induces almost linear velocity reduction even beyond the inflection pressure up to at least ∼160 GPa (Mashino et al., 2022), (Fe, Al)-silicate glass shows an anomalously steeper velocity profile in the pressure regime (b). The inflection pressures and linear fit to the V S data after the inflection pressures for different silicate glasses are shown in Figure S5 and Table S2 of Supporting Information S1. From those data, we found that the Mg has very little effect on the reduction of the inflection pressure, while Al 2 O 3 and H 2 O were observed to be very effective. A large decrease in the inflection pressure is recently observed in Fe 2+ -bearing MgSiO 3 , which indicates that Fe 2+ is acting as network former and Fe-O CN might have undergone to the higher than 6 prior to that of Si-O. In fact very recent spin polarized calculations on pyrolite melt, the average CN of Fe-O reaches 6 above 25 GPa and in the core-mantle boundary (CMB) conditions it is 6-7 (Solomatova & Caracas, 2019). One experimental study on the Al 2 O 3 -SiO 2 glass showed an average Al-O CN increase from 4 to 6 above 20 GPa, and from 6 to >6 ∼110 GPa (Ohira et al., 2019), while theoretical calculations on the model basaltic melt, pyrolite glass and melt a gradual increase is predicted with higher than 6 CN in the pressure range 60-80 GPa (Bajgain et al., 2015(Bajgain et al., , 2022Solomatova & Caracas, 2019) and reaching 7 toward the CMB conditions. It is therefore evident that both Fe-O and Al-O undergo the higher CN much earlier than Si-O and have a large effect on the reduction of the inflection pressure. To realize the quantitative molar effect of Al 2 O 3 and FeO on the inflection pressure, we have summarized previous Brillouin measurements data with our data in Figure 3. Assuming the linear decrement of the inflection pressure with threshold intercept with respect to mol% of Al 2 O 3 as per Ohira et al. (2016), it should be reduced by 11.5 GPa for 4.2 mol% of Al 2 O 3 . The molar percentage reported here is with respect to 1 mol of parent glasses (SiO 2 /MgSiO 3 ). Furthermore given the linear reduction of inflection pressure with respect to FeO mol% according to Mashino et al. (2022), a further pressure reduction by ∼16.2 GPa is expected for 7.2 mol% of FeO in our sample. Hence an expected total reduction in pressure will be ∼28 GPa, which means the inflection pressure in our sample would be at ∼105 GPa, which is fairly consistent with our actual observed pressure at ∼98 GPa. The fact that such a small amount of Al and Fe 2+ facilitates the reduction of inflection pressure implies

Effect of Al on the Elasticity and Densification Mechanisms
By definition, the acoustic velocity gradient of materials with pressure (hereafter referred to as the slope) primarily indicates how materials become stiffer with pressure, which indirectly offers us insights into the stiffness and densification mechanisms of materials. While the slope of Fe 2+ -bearing MgSiO 3 glass is 8% less than pure MgSiO 3 (Mashino et al., 2022;Murakami & Bass, 2011), 20.5 mol% of Al 2 O 3 -bearing SiO 2 glass shows almost 14% higher slope with respect to simplest SiO 2 glass (Murakami & Bass, 2010;Ohira et al., 2016) after the inflection pressure,which is evident that Al could make SiO 2 glass much stiffer with pressure. Our results support that Al acts as network former and undergoes the higher coordination (>6 + ) at much lower pressure than Si as predicted by various studies for different glasses/melts (Bajgain et al., 2015(Bajgain et al., , 2022Ohira et al., 2019;Solomatova & Caracas, 2019). So we could assume that when the pressure is increased from the inflection point, the fraction of 6 + in (Fe, Al)-silicate glass is expected to increase faster than in MgSiO 3 glass because Si undergoes a CN change following Al, and Fe 2+ . Hence the higher CN of Al and Fe makes the slope of (Fe, Al)-silicate glass larger than MgSiO 3 glass. Very recent high-pressure experimental studies up to 42 GPa in the system of Al 2 O 3 -MgSiO 3 also showed that the incorporation of Al makes MgSiO 3 glass much stiffer (Wei et al., 2022) although they did not quantify the effect of Al 2 O 3 on the elasticity. The identification of an anomalously steeper slope for (Fe, Al)-silicate glass above ∼98 GPa strongly indicates that the incorporation of Al into Fe-bearing MgSiO 3 glass significantly facilitates making it elastically stiffer along with a unique densification mechanism possibly associated with Si-O CN change beyond 6, which could have a significant effect on the structural evolution in a deep terrestrial MO of silicate melts having the realistic composition with molar Mg/Si ratio ∼1 for the massive terrestrial exoplanets. Although further experimentation is surely needed to clarify as to whether the structural analogy between glasses and melts really work. Previous high-pressure and high-temperature element partitioning measurements between silicate melts and solids have shown that the silicate melts in equilibrium with a peridotitic/chondritic lower mantle should have higher Al 2 O 3 contents with ∼13-30 mol% and FeO with ∼15-22 mol% (Andrault et al., 2012;Ghosh & Karki, 2016;Nomura et al., 2011;Ohira et al., 2016Ohira et al., , 2019Pradhan et al., 2015). With these higher molar % of Al 2 O 3 and FeO could shift the inflection pressure to much lower pressure, which will be well within the Earth's lower mantle pressure regime. This essentially indicates a potential emergence of elastically stiffer and denser silicate melts than previously expected well within the lower mantle conditions.

Implications for the Dynamics and Structure of Deep MO
Because the extensive melting of the protoplanets and the formation of deep MOs are believed to be indispensable processes after the accretion of the terrestrial planetary bodies from the cloud of gas and dust, the emergence of such elastically stiff and dense silicate melts in deep MO would be a fairly common feature for the rocky terrestrial planets such as super-Earths. Very recent in situ ultrahigh-pressure X-ray diffraction measurements of silicate glass to 200 GPa combined with ab-initio molecular dynamic simulation in fact showed the significant decrease in Si-O-Si bond angle above ∼100 GPa highly indicative of the presence of OSi 3 tricluster and OSi 4 tetracluster . Therefore, our experimental finding of anomalously steeper slope for (Fe, Al)-silicate glass above ∼98 GPa most likely associated with Si-O CN change from 6 to 6 + strongly indicates the significant modification of the Si-O bond properties hence the network structure of such melts upon structural transition at much lower pressure. The potential presence of highly dense silicate melts in deep terrestrial MOs may imply a deep isolated gravitationally stable silicate melts layer located at a greater depth than 100 GPa, which should offer important insights into the MO convection, gravitational stability of silicate melts in the course of MO crystallization, and the mantle stratification of the Si-enriched rocky terrestrial planets. Further experimental verification on this issue is obviously needed by in situ viscosity and density measurements of silicate melt under relevant pressure conditions though it is extremely difficult to implement such experiments even with state-of-the-art techniques at this point.

Data Availability Statement
All the acoustic wave velocity data presented in Table 1 can be found at https://doi.org/10.17632/4dh4g4jx4v.1. The experimental datasets are also available at https://doi.org/10.17632/4dh4g4jx4v.1.