Ultrahigh pressure structural changes in a 60 mol. % Al2O3-40 mol. % SiO2 glass
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Abstract
Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
). Our observations suggest an important role for aluminum in densification of aluminosilicate at the deep lower mantle, which might imply a dense aluminosilicate magma with negative buoyancy.Figures and Tables
Figure 1 Structure factors, S(Q), determined at the Q range up to 14 Å−1 and pair distribution functions, g(r), of the A40S glass up to 131 GPa. (a) S(Q) at ambient condition. (b-c) S(Q) at high pressures displayed by a vertical offset of 0.5 and 0.6 in (b) for experiment 1 and (c) for experiment 2, respectively. (d) g(r) at ambient condition. (e-f) g(r) at high pressures displayed by a vertical offset of 0.8 and 1.0 in (e) for experiment 1 and (f) for experiment 2, respectively. | Figure 2 The first (r1), second (r2), and third (r3) peak positions of g(r) of the A40S glass. (a) Red, blue, and black circles indicate the r1 determined in the high pressure experiments 1 and 2, and at ambient pressure, respectively. Triangles indicate the Si–O bond distance in SiO2 glass (Sato and Funamori, 2010). Open diamonds and squares indicate the Si–O and Al–O bond distance in CaAl2Si2O8 glass, respectively, simulated with 416 (black) and 208 (gray) atom simulation cells (Ghosh and Karki, 2018). The black dash lines are obtained from fitting for the Si–O and Al–O bond distances with CN = ~6. The light blue and orange lines are obtained from fitting the r1 of A40S glass at 35–102 GPa using the drSi–O(6CN)/dP and the drAl–O(6CN)/dP, respectively. The widths of lines indicate the fitting errors. (b) The r2 and r3 of the A40S glass determined in the experiments 1 (red) and 2 (blue), respectively. | Table 1 Experimental pressure conditions and the first (r1), second (r2), and third (r3) peak positions of g(r). |
Figure 1 | Figure 2 | Table 1 |
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Introduction
Pressure-induced structural change of silicate melts is one of the key factors in understanding the behaviour of silicate melts in the deep lower mantle to the core-mantle boundary (CMB), where the presence of silicate melt has been suggested by seismological studies as a cause of ultralow velocity zones (e.g., Garnero et al., 1998
Garnero, E.J., Revenaugh, J., Williams, Q., Lay, T., Kellogg, L.H. (1998) Ultralow velocity zone at the core-mantle boundary. In: Gurnis, M., Wysession, M.E., Knittle, E., Buffett, B.A. (Eds.) The core-mantle boundary region. The American Geophysical Union, Washington, D.C., 319–334.
). However, the structure of silicate melts at the ultrahigh pressure and high temperature conditions of the CMB is still poorly understood due to experimental challenges. Efforts have been made to understand pressure-induced structural changes in SiO2 glass, considered an analogue of silicate melts. Murakami and Bass (2010)Murakami, M., Bass, J.D. (2010) Spectroscopic evidence for ultrahigh-pressure polymorphism in SiO2 glass. Physical Review Letters 104, 025504.
found a kink in the pressure dependence of the shear wave velocity (dvS/dP) of a SiO2 glass at 140 GPa, and proposed a possible ultrahigh pressure structural change with an increase of the average Si–O coordination number (CN) to >6. Sato and Funamori (2010)Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
investigated the structure of SiO2 glass and reported a constant Si–O CN of 6 from 35 GPa to 102 GPa. On the other hand, a recent structure measurement on SiO2 glass up to 172 GPa showed a gradual increase of the average Si–O CN from 6 to higher than 6 above 50 GPa (Prescher et al., 2017Prescher, C., Prakapenka, V.B., Stefanski, J., Jahn, S., Skinner, L.B., Wang, Y. (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proceedings of the National Academy of Sciences of the United States of America 114, 10041–10046.
), while the trend of the gradual increase of Si–O CN is different from a sharp structural change as the kink observed in the dvS/dP (Murakami and Bass, 2010Murakami, M., Bass, J.D. (2010) Spectroscopic evidence for ultrahigh-pressure polymorphism in SiO2 glass. Physical Review Letters 104, 025504.
).Kinks in dvS/dP have also been observed in Al2O3–SiO2 glasses at 130 GPa (3.9 mol. % Al2O3–96.1 mol. % SiO2 glass) and at 116 GPa (20.5 mol. % Al2O3–79.5 mol. % SiO2 glass) (Ohira et al., 2016
Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
). Ohira et al. (2016)Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
suggested that incorporation of Al lowers the pressure condition of the ultrahigh pressure structural change, and indicated the role of aluminum in the structural change of aluminosilicate melts in the deep lower mantle. In fact, the composition of the melt generated by partial melting of a mid-ocean ridge basalt (MORB) at around 100 GPa contains a significant amount of Al2O3 (~20 wt. % or ~13 mol. %) (Pradhan et al., 2015Pradhan, G.K., Fiquet, G., Siebert, J., Auzende, A.-L., Morard, G., Antonangeli, D., Garbarino, G. (2015) Melting of MORB at core–mantle boundary. Earth and Planetary Science Letters 431, 247–255.
). Therefore, an understanding of the pressure-induced structural changes in aluminosilicate systems is important in determining the nature of such melts in the CMB region. However, direct structure measurements on aluminosilicate glasses have been limited to <30 GPa (e.g., Drewitt et al., 2015Drewitt, J.W.E., Jahn, S., Sanloup, C., de Grouchy, C., Garbarino, G., Hennet, L. (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. Journal of Physics: Condensed Matter 27, 105103.
), and pressure-induced structural changes of Al–O at the pressure condition in the deep lower mantle have not been experimentally studied. In this study, we experimentally determined the pair distribution functions of a 60 mol. % Al2O3–40 mol. % SiO2 glass (hereafter A40S glass) up to 131 GPa, and found an ultrahigh pressure structural change in this glass at pressures above 110 GPa.top
Structure Measurement up to 131 GPa
Figure 1 shows structure factors, S(Q), of the A40S glass up to 131 GPa (Fig. 1a–c), and the reduced pair distribution functions, g(r) (Fig. 1d–f). The first peak (r1) of g(r) is considered to represent the T–O (T = Al and Si) distance. Since Si–O and Al–O bond distances are very close (for example, 1.64 Å and 1.81 Å, respectively, in CaAl2Si2O8 glass calculated by Ghosh and Karki, 2018
Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
), these bond distances are not resolvable even in the measurements at ambient pressure (e.g., Okuno et al., 2005Okuno, M., Zotov, N., Schmücker, M., Schneider, H. (2005) Structure of SiO2–Al2O3 glasses: combined X-ray diffraction, IR and Raman studies. Journal of Non-Crystalline Solids 351, 1032–1038.
; Ohira et al., 2016Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
). Our observed r1 at ambient pressure (1.753 ± 0.004 Å) is consistent with that reported in a previous ambient pressure study (1.76 ± 0.01 Å with T–O CN of 4.3 ± 0.1; Okuno et al., 2005Okuno, M., Zotov, N., Schmücker, M., Schneider, H. (2005) Structure of SiO2–Al2O3 glasses: combined X-ray diffraction, IR and Raman studies. Journal of Non-Crystalline Solids 351, 1032–1038.
). At ambient pressure, we observed that there is a single second peak at ~3.1 Å with a shoulder peak at ~2.5 Å, while it changes to two distinct peaks above 16 GPa (r2 at ~2.5–2.6 Å and r3 at ~3.1–3.2 Å). The basic feature of g(r) in the A40S glass above 16 GPa is similar to that of SiO2 glass with 6-fold coordinated structure at high pressures (Sato and Funamori, 2010Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
; Prescher et al., 2017Prescher, C., Prakapenka, V.B., Stefanski, J., Jahn, S., Skinner, L.B., Wang, Y. (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proceedings of the National Academy of Sciences of the United States of America 114, 10041–10046.
), while the peak positions are different due to the difference between the Al–O and Si–O distances.Figure 2 shows pressure dependences of r1, r2, and r3 of the A40S glass, with the numerical data summarised in Table 1. r1 rapidly increases with increasing pressure at pressures below 16 GPa, and then almost linearly decreases with increasing pressure in the pressure range between 25 and 102 GPa (Fig. 2a). The slope of r1 changes with pressure at 25–102 GPa is similar to those of the Si–O bond distance in SiO2 glass with Si–O CN of ~6 at 35–102 GPa (Sato and Funamori, 2010
Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
) and Al–O bond distance in CaAl2Si2O8 glass with Al–O CN of ~6 at 41–105 GPa (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
) (Fig. 2a). We find that r1 starts to deviate from the linear compression trend above ~110 GPa and becomes constant at 110–121 GPa (Fig. 2a). The determined r2 and r3 values show some differences between the two experiments (up to 0.1 Å), while these are almost within the experimental errors. It is noted, however, that the experimental results from both runs show monotonous changes in r2 and r3 between 16 and 131 GPa (Fig. 2b).Table 1 Experimental pressure conditions and the first (r1), second (r2), and third (r3) peak positions of g(r).
Pressure | r1 | r2 | r3 |
(GPa) | (Å) | (Å) | (Å) |
Ambient | |||
0.0001 | 1.753 ± 0.004 | ||
Experiment 1 | |||
10.8 ± 0.7 | 1.805 ± 0.006 | ||
21.1 ± 1.1 | 1.809 ± 0.006 | 2.604 ± 0.040 | 3.213 ± 0.040 |
24.9 ± 1.2 | 1.811 ± 0.006 | 2.582 ± 0.040 | 3.206 ± 0.040 |
34.5 ± 1.7 | 1.806 ± 0.007 | 2.560 ± 0.040 | 3.182 ± 0.042 |
40.2 ± 1.7 | 1.801 ± 0.007 | 2.561 ± 0.040 | 3.208 ± 0.040 |
47.3 ± 2.9 | 1.793 ± 0.007 | 2.545 ± 0.041 | 3.184 ± 0.043 |
53.7 ± 3.3 | 1.790 ± 0.007 | 2.544 ± 0.041 | 3.186 ± 0.043 |
62.2 ± 2.3 | 1.787 ± 0.007 | 2.534 ± 0.040 | 3.184 ± 0.041 |
69.4 ± 2.5 | 1.775 ± 0.007 | 2.533 ± 0.040 | 3.165 ± 0.041 |
74.1 ± 3.2 | 1.775 ± 0.006 | 2.532 ± 0.040 | 3.175 ± 0.040 |
81.9 ± 3.1 | 1.771 ± 0.006 | 2.537 ± 0.040 | 3.192 ± 0.040 |
88.7 ± 2.8 | 1.767 ± 0.006 | 2.524 ± 0.040 | 3.172 ± 0.040 |
96.6 ± 2.7 | 1.760 ± 0.006 | 2.522 ± 0.040 | 3.154 ± 0.040 |
101.7 ± 3.3 | 1.754 ± 0.006 | 2.548 ± 0.040 | 3.185 ± 0.040 |
110.3 ± 4.3 | 1.752 ± 0.006 | 2.540 ± 0.040 | 3.175 ± 0.040 |
Experiment 2 | |||
3.7 ± 0.3 | 1.773 ± 0.006 | ||
15.5 ± 0.6 | 1.810 ± 0.006 | 2.601 ± 0.041 | 3.206 ± 0.041 |
37.4 ± 2.1 | 1.793 ± 0.007 | 2.510 ± 0.040 | 3.131 ± 0.040 |
45.8 ± 1.6 | 1.782 ± 0.006 | 2.515 ± 0.040 | 3.125 ± 0.040 |
57.8 ± 4.4 | 1.778 ± 0.007 | 2.502 ± 0.040 | 3.109 ± 0.040 |
65.6 ± 1.5 | 1.776 ± 0.007 | 2.480 ± 0.040 | 3.084 ± 0.040 |
86.3 ± 4.9 | 1.756 ± 0.007 | 2.486 ± 0.040 | 3.110 ± 0.041 |
91.4 ± 3.4 | 1.760 ± 0.007 | 2.485 ± 0.040 | 3.101 ± 0.040 |
108.1 ± 3.3 | 1.750 ± 0.006 | 2.474 ± 0.040 | 3.109 ± 0.040 |
113.9 ± 5.3 | 1.750 ± 0.007 | 2.492 ± 0.040 | 3.144 ± 0.040 |
120.9 ± 4.3 | 1.753 ± 0.006 | 2.481 ± 0.040 | 3.107 ± 0.040 |
130.8 ± 4.5 | 1.736 ± 0.006 | 2.473 ± 0.040 | 3.136 ± 0.040 |
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Discussion
The A40S glass has a significantly higher content of Al than Si (Al/Si = 3), and therefore the behaviour of r1 is considered to mainly represent the Al–O distance. In fact, our observed behaviour of r1 at low pressure (<25 GPa) is consistent with the behaviour of Al–O distance reported in previous studies. Drewitt et al. (2015)
Drewitt, J.W.E., Jahn, S., Sanloup, C., de Grouchy, C., Garbarino, G., Hennet, L. (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. Journal of Physics: Condensed Matter 27, 105103.
showed an increase in Al–O distance in CaAl2O4 glass with increasing pressure below 15 GPa, and then it displayed a slight decrease above 15 GPa. Along with the increase in Al–O distance, the average Al–O CN of CaAl2O4 glass increases from 4 at ambient pressure to 6 at ~23.5 GPa (Drewitt et al., 2015Drewitt, J.W.E., Jahn, S., Sanloup, C., de Grouchy, C., Garbarino, G., Hennet, L. (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. Journal of Physics: Condensed Matter 27, 105103.
). In addition, a recent simulation study for CaAl2Si2O8 glass found that the Al–O distance increases with increasing pressure below ~20 GPa together with an increase of average Al–O CN (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
) (Fig. 2a). The behaviour of the Al–O distance experimentally determined by Drewitt et al. (2015)Drewitt, J.W.E., Jahn, S., Sanloup, C., de Grouchy, C., Garbarino, G., Hennet, L. (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. Journal of Physics: Condensed Matter 27, 105103.
and calculated by Ghosh and Karki (2018)Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
is consistent with the change in r1 of the A40S glass obtained in this study (Fig. 2a). The increase of r1 below 16 GPa here is considered to represent an increase of Al–O CN from ~4 to 6. The pressure condition where the Al–O CN reaches 6 is markedly lower than the pressure where the Si–O CN in SiO2 glass reaches 6 (at ~35–50 GPa: Sato and Funamori, 2010Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
; Prescher et al., 2017Prescher, C., Prakapenka, V.B., Stefanski, J., Jahn, S., Skinner, L.B., Wang, Y. (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proceedings of the National Academy of Sciences of the United States of America 114, 10041–10046.
). Contrary to the behaviour of Al–O distance, Si–O distance decreases with increasing pressure up to ~10–20 GPa and then increases at ~20–35 GPa (Sato and Funamori, 2010Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
; Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
) (Fig. 2a), which is markedly different from our observed r1.Above 25 GPa, r1 linearly decreases with increasing pressure, while it starts to deviate from a linear trend above around 110 GPa (Fig. 2a), which implies an existence of another structural change under ultrahigh pressure conditions. We find that the slope of the r1 changes in the A40S glass at 25–102 GPa shows a trend similar to the behaviour of Si–O and Al–O bond distances in SiO2 glass (Sato and Funamori, 2010
Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
) and CaAl2Si2O8 glass (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
) with 6-fold coordinated structure, respectively. The Si–O bond distance shows a linear compression slope of drSi–O(6CN)/dP = −8.77 × 10−4 Å/GPa at 35–102 GPa (Fig. 2a). Similarly, the Al–O bond distance shows a slope of drAl–O(6CN)/dP of −8.30 × 10−4 Å/GPa (Fig. 2a), which is almost identical to the slope of Si–O. We therefore consider that the slope of the T–O bond distance (T = Si, Al) with T–O CN of 6 in the A40S glass can be expressed by the same dr1/dP as those of Si–O and Al–O bond distances. Indeed, when the r1 values are plotted with slopes of dr1/dP being −8.77 × 10−4 Å/GPa and −8.30 × 10−4 Å/GPa at 34.5–101.7 GPa for SiO2 and CaAl2Si2O8 glasses, respectively, it appears that the behaviour of r1 in the A40S glass below 110 GPa can be well explained by the dr1/dP slopes of the 6-fold coordinated structure. Above 110 GPa, however, r1 values deviate from the linear trends (Fig. 2a). Even if the linear range is selected at different pressure ranges (for example, at 35–131 GPa) or used for individual runs in experiment 1 and 2, the deviation of r1 from linear trends above 110 GPa can still be clearly identified (Fig. S-1). These results suggest a structural change at short range scale at ultrahigh pressures above ~110 GPa.The kink in r1 of the A40S glass at 110 GPa in this study is consistent with the behaviour of Al–O distance in CaAl2Si2O8 glass reported by Ghosh and Karki (2018)
Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
. Ghosh and Karki (2018)Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
showed a decrease of Al–O distance between ~10 and ~110 GPa, while it becomes constant or slightly increases above ~110 GPa in CaAl2Si2O8 glass. The average Al–O CN of CaAl2Si2O8 glass is constant at around 6 in a pressure range between 41 and 105 GPa, while it starts to increase to >6 above ~110 GPa (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
). Thus, the kink in the pressure dependence of Al–O distance in CaAl2Si2O8 glass at ~110 GPa is considered to represent the average Al–O CN increase from 6 to >6 (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
). Although it is difficult for us to determine the average T–O CN in our A40S glass because of the lack of available density data for the A40S glass, the similarity between the Al–O distance change in Ghosh and Karki (2018)Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
and the change in r1 in this study suggests an ultrahigh pressure structural change in the A40S glass to a more than 6-fold coordinated Al–O structure above 110 GPa. While r1 is nearly constant at 110–121 GPa, there is a decrease in r1 at 121–131 GPa. This decrease of r1 may imply that the change of Al–O CN may be completed at 131 GPa, in contrast to the theoretical prediction of a continuous Al–O CN increase to at least 155 GPa (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
). However, data points are still limited, and further structural measurements at higher pressures are required to understand this question better. In addition, our observed decrease in r1 may be influenced by Si–O bond of the A40S glass, since the evolution of Si–O CN is still controversial in literature (for example, a gradual increase of Si–O CN to more than 6 above 50 GPa in Prescher et al., 2017Prescher, C., Prakapenka, V.B., Stefanski, J., Jahn, S., Skinner, L.B., Wang, Y. (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proceedings of the National Academy of Sciences of the United States of America 114, 10041–10046.
, while Si–O CN of less than 6 up to 155 GPa in Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
).The pressure condition of the ultrahigh pressure structural change in the A40S glass observed in this study (110 GPa) is similar to the pressure condition where a kink in dvS/dP is observed for Al2O3–SiO2 glasses (116 GPa for 20.5 mol. % Al2O3–79.5 mol. % SiO2 glass, Ohira et al., 2016
Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
). The data suggest that the kink in the dvS/dP is attributable to the increase of average Al–O CN to >6. Ohira et al. (2016)Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
argued that incorporation of Al decreases the pressure of the sound velocity change of Al2O3–SiO2 glasses. Therefore, the ultrahigh pressure structural change to more than 6-fold coordinated structure in Al2O3–SiO2 system may also depend on the ratio of Si and Al.The pressure condition of the Al–O CN change at 110 GPa is shallower than that of the CMB. Considering the similarity in the pressure-induced structural changes between aluminosilicate glass and melt at very high pressure conditions of the Earth’s lower mantle (Sanloup, 2016
Sanloup, C. (2016) Density of magmas at depth. Chemical Geology 429, 51–59.
), the Al–O CN change may occur in aluminosilicate melt in the CMB region and may have a significant influence on the behaviour of Al-rich aluminosilicate magmas generated by partial melting of MORB (Pradhan et al., 2015Pradhan, G.K., Fiquet, G., Siebert, J., Auzende, A.-L., Morard, G., Antonangeli, D., Garbarino, G. (2015) Melting of MORB at core–mantle boundary. Earth and Planetary Science Letters 431, 247–255.
). It is interesting to note that Al-rich glasses show different behaviour in density from those of Al-free silicate glasses. Petitgirard et al. (2015Petitgirard, S., Malfait, W.J., Sinmyo, R., Kupenko, I., Hennet, L., Harries, D., Dane, T., Burghammer, M., Rubie, D.C. (2015) Fate of MgSiO3 melts at core–mantle boundary conditions. Proceedings of the National Academy of Sciences of the United States of America 112, 14186–14190.
, 2017Petitgirard, S., Malfait, W.J., Journaux, B., Collings, I.E., Jennings, E.S., Blanchard, I., Kantor, I., Kurnosov, A., Cotte, M., Dane, T., Burghammer, M., Rubie, D.C. (2017) SiO2 glass density to lower-mantle pressures. Physical Review Letters 119, 215701.
) showed a similarity in density of SiO2 and MgSiO3 glasses at the pressure conditions of the Earth’s lowermost mantle, which indicates a minor effect of SiO2 content on the density of silicate glasses (Fig. S-2). On the other hand, we note that the density of CaAl2Si2O8 glass (Ghosh and Karki, 2018Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
) becomes higher than those of SiO2 and MgSiO3 glasses above 82 and 64 GPa, respectively (Fig. S-2), likely due to an average Al–O CN change to >6 while the average Si–O CN remains at 6. It has been known that densities of SiO2 and MgSiO3 glasses are lower than that of the Preliminary reference Earth model (PREM) (Dziewonski and Anderson, 1981Dziewonski, A.M., Anderson, D.L. (1981) Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 25, 297–356.
) at the pressures of the CMB (Petitgirard et al., 2017Petitgirard, S., Malfait, W.J., Journaux, B., Collings, I.E., Jennings, E.S., Blanchard, I., Kantor, I., Kurnosov, A., Cotte, M., Dane, T., Burghammer, M., Rubie, D.C. (2017) SiO2 glass density to lower-mantle pressures. Physical Review Letters 119, 215701.
). The important role of Fe in the formation of silicate magma with density higher than PREM has been discussed in previous studies (e.g., Petitgirard et al., 2015Petitgirard, S., Malfait, W.J., Sinmyo, R., Kupenko, I., Hennet, L., Harries, D., Dane, T., Burghammer, M., Rubie, D.C. (2015) Fate of MgSiO3 melts at core–mantle boundary conditions. Proceedings of the National Academy of Sciences of the United States of America 112, 14186–14190.
, 2017Petitgirard, S., Malfait, W.J., Journaux, B., Collings, I.E., Jennings, E.S., Blanchard, I., Kantor, I., Kurnosov, A., Cotte, M., Dane, T., Burghammer, M., Rubie, D.C. (2017) SiO2 glass density to lower-mantle pressures. Physical Review Letters 119, 215701.
; Karki et al., 2018Karki, B.B., Ghosh, D.B., Maharjan, C., Karato, S.-I., Park, J. (2018) Density-pressure profiles of Fe-bearing MgSiO3 liquid: effects of valence and spin states, and implications for the chemical evolution of the lower mantle. Geophysical Research Letters 45, 3959–3966.
). A recent study showed that only highly Fe-rich melts (e.g., ~0.35 of Fe/(Mg+Fe)) could be denser than the surrounding mantle (Karki et al., 2018Karki, B.B., Ghosh, D.B., Maharjan, C., Karato, S.-I., Park, J. (2018) Density-pressure profiles of Fe-bearing MgSiO3 liquid: effects of valence and spin states, and implications for the chemical evolution of the lower mantle. Geophysical Research Letters 45, 3959–3966.
). However, to generate such a Fe-rich melt, very low partition coefficients (DFemineral/melt) and low degree of partial melting are required (e.g., Andrault et al. 2017Andrault, D., Bolfan-Casanova, N., Bouhifd, M.A., Boujibar, A., Garbarino, G., Manthilake, G., Mezouar, M., Monteux, J., Parisiades, P., Pesce, G. (2017) Toward a coherent model for the melting behavior of the deep Earth’s mantle. Physics of the Earth and Planetary Interiors 265, 67–81.
), while these parameters at ultrahigh pressure and high temperature conditions of the deep lower mantle are still under debate (e.g., Andrault et al. 2017Andrault, D., Bolfan-Casanova, N., Bouhifd, M.A., Boujibar, A., Garbarino, G., Manthilake, G., Mezouar, M., Monteux, J., Parisiades, P., Pesce, G. (2017) Toward a coherent model for the melting behavior of the deep Earth’s mantle. Physics of the Earth and Planetary Interiors 265, 67–81.
). On the other hand, Fe-free CaAl2Si2O8 glass has markedly higher density than SiO2 and MgSiO3 glasses above 100 GPa (Fig. S-2), which suggests an important densification role of average Al–O CN to more than 6 in the formation of dense magma at pressures near the CMB.top
Acknowledgements
We are grateful to the three anonymous reviewers for their comments that helped to improve the manuscript. High pressure experiments were performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT operation is supported by DOE-NNSA under Award No. DE-NA0001974. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02- 06CH11357. This research is supported by JSPS overseas fellowships to IO and the National Science Foundation under Award No. EAR-1722495 to YK. GS acknowledges the support of DOE-BES/ DMSE under Award DE-FG02-99ER45775. YS acknowledges the support of JSPS KAKENHI Grant Number 15K17784.
Editor: Wendy Mao
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References
Andrault, D., Bolfan-Casanova, N., Bouhifd, M.A., Boujibar, A., Garbarino, G., Manthilake, G., Mezouar, M., Monteux, J., Parisiades, P., Pesce, G. (2017) Toward a coherent model for the melting behavior of the deep Earth’s mantle. Physics of the Earth and Planetary Interiors 265, 67–81.
Show in context
However, to generate such a Fe-rich melt, very low partition coefficients (DFemineral/melt) and low degree of partial melting are required (e.g., Andrault et al. 2017), while these parameters at ultrahigh pressure and high temperature conditions of the deep lower mantle are still under debate (e.g., Andrault et al. 2017).
View in article
Drewitt, J.W.E., Jahn, S., Sanloup, C., de Grouchy, C., Garbarino, G., Hennet, L. (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. Journal of Physics: Condensed Matter 27, 105103.
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However, direct structure measurements on aluminosilicate glasses have been limited to <30 GPa (e.g., Drewitt et al., 2015), and pressure-induced structural changes of Al–O at the pressure condition in the deep lower mantle have not been experimentally studied.
View in article
Drewitt et al. (2015) showed an increase in Al–O distance in CaAl2O4 glass with increasing pressure below 15 GPa, and then it displayed a slight decrease above 15 GPa.
View in article
Along with the increase in Al–O distance, the average Al–O CN of CaAl2O4 glass increases from 4 at ambient pressure to 6 at ~23.5 GPa (Drewitt et al., 2015).
View in article
The behaviour of the Al–O distance experimentally determined by Drewitt et al. (2015) and calculated by Ghosh and Karki (2018) is consistent with the change in r1 of the A40S glass obtained in this study (Fig. 2a).
View in article
Dziewonski, A.M., Anderson, D.L. (1981) Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 25, 297–356.
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It has been known that densities of SiO2 and MgSiO3 glasses are lower than that of the Preliminary reference Earth model (PREM) (Dziewonski and Anderson, 1981) at the pressures of the CMB (Petitgirard et al., 2017).
View in article
Garnero, E.J., Revenaugh, J., Williams, Q., Lay, T., Kellogg, L.H. (1998) Ultralow velocity zone at the core-mantle boundary. In: Gurnis, M., Wysession, M.E., Knittle, E., Buffett, B.A. (Eds.) The core-mantle boundary region. The American Geophysical Union, Washington, D.C., 319–334.
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Pressure-induced structural change of silicate melts is one of the key factors in understanding the behaviour of silicate melts in the deep lower mantle to the core-mantle boundary (CMB), where the presence of silicate melt has been suggested by seismological studies as a cause of ultralow velocity zones (e.g., Garnero et al., 1998).
View in article
Ghosh, D.B., Karki, B.B. (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Physics and Chemistry of Minerals 45, 575–587.
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The slope change may imply a structural change in the A40S glass around 110 GPa, and may be explained by the change in Al–O distance associated with the Al–O CN increase from 6 to >6 as predicted by molecular dynamics simulations (Ghosh and Karki, 2018).
View in article
Since Si–O and Al–O bond distances are very close (for example, 1.64 Å and 1.81 Å, respectively, in CaAl2Si2O8 glass calculated by Ghosh and Karki, 2018), these bond distances are not resolvable even in the measurements at ambient pressure (e.g., Okuno et al., 2005; Ohira et al., 2016).
View in article
The slope of r1 changes with pressure at 25–102 GPa is similar to those of the Si–O bond distance in SiO2 glass with Si–O CN of ~6 at 35–102 GPa (Sato and Funamori, 2010) and Al–O bond distance in CaAl2Si2O8 glass with Al–O CN of ~6 at 41–105 GPa (Ghosh and Karki, 2018) (Fig. 2a).
View in article
Figure 2 [...] Open diamonds and squares indicate the Si–O and Al–O bond distance in CaAl2Si2O8 glass, respectively, simulated with 416 (black) and 208 (gray) atom simulation cells (Ghosh and Karki, 2018).
View in article
In addition, a recent simulation study for CaAl2Si2O8 glass found that the Al–O distance increases with increasing pressure below ~20 GPa together with an increase of average Al–O CN (Ghosh and Karki, 2018) (Fig. 2a).
View in article
The behaviour of the Al–O distance experimentally determined by Drewitt et al. (2015) and calculated by Ghosh and Karki (2018) is consistent with the change in r1 of the A40S glass obtained in this study (Fig. 2a).
View in article
Contrary to the behaviour of Al–O distance, Si–O distance decreases with increasing pressure up to ~10–20 GPa and then increases at ~20–35 GPa (Sato and Funamori, 2010; Ghosh and Karki, 2018) (Fig. 2a), which is markedly different from our observed r1.
View in article
We find that the slope of the r1 changes in the A40S glass at 25–102 GPa shows a trend similar to the behaviour of Si–O and Al–O bond distances in SiO2 glass (Sato and Funamori, 2010) and CaAl2Si2O8 glass (Ghosh and Karki, 2018) with 6-fold coordinated structure, respectively.
View in article
The kink in r1 of the A40S glass at 110 GPa in this study is consistent with the behaviour of Al–O distance in CaAl2Si2O8 glass reported by Ghosh and Karki (2018).
View in article
Ghosh and Karki (2018) showed a decrease of Al–O distance between ~10 and ~110 GPa, while it becomes constant or slightly increases above ~110 GPa in CaAl2Si2O8 glass.
View in article
The average Al–O CN of CaAl2Si2O8 glass is constant at around 6 in a pressure range between 41 and 105 GPa, while it starts to increase to >6 above ~110 GPa (Ghosh and Karki, 2018).
View in article
Thus, the kink in the pressure dependence of Al–O distance in CaAl2Si2O8 glass at ~110 GPa is considered to represent the average Al–O CN increase from 6 to >6 (Ghosh and Karki, 2018).
View in article
Although it is difficult for us to determine the average T–O CN in our A40S glass because of the lack of available density data for the A40S glass, the similarity between the Al–O distance change in Ghosh and Karki (2018) and the change in r1 in this study suggests an ultrahigh pressure structural change in the A40S glass to a more than 6-fold coordinated Al–O structure above 110 GPa.
View in article
This decrease of r1 may imply that the change of Al–O CN may be completed at 131 GPa, in contrast to the theoretical prediction of a continuous Al–O CN increase to at least 155 GPa (Ghosh and Karki, 2018).
View in article
In addition, our observed decrease in r1 may be influenced by Si–O bond of the A40S glass, since the evolution of Si–O CN is still controversial in literature (for example, a gradual increase of Si–O CN to more than 6 above 50 GPa in Prescher et al., 2017, while Si–O CN of less than 6 up to 155 GPa in Ghosh and Karki, 2018).
View in article
On the other hand, we note that the density of CaAl2Si2O8 glass (Ghosh and Karki, 2018) becomes higher than those of SiO2 and MgSiO3 glasses above 82 and 64 GPa, respectively (Fig. S-2), likely due to an average Al–O CN change to >6 while the average Si–O CN remains at 6.
View in article
Karki, B.B., Ghosh, D.B., Maharjan, C., Karato, S.-I., Park, J. (2018) Density-pressure profiles of Fe-bearing MgSiO3 liquid: effects of valence and spin states, and implications for the chemical evolution of the lower mantle. Geophysical Research Letters 45, 3959–3966.
Show in context
The important role of Fe in the formation of silicate magma with density higher than PREM has been discussed in previous studies (e.g., Petitgirard et al., 2015, 2017; Karki et al., 2018).
View in article
A recent study showed that only highly Fe-rich melts (e.g., ~0.35 of Fe/(Mg+Fe)) could be denser than the surrounding mantle (Karki et al. 2018).
View in article
Murakami, M., Bass, J.D. (2010) Spectroscopic evidence for ultrahigh-pressure polymorphism in SiO2 glass. Physical Review Letters 104, 025504.
Show in context
Murakami and Bass (2010) found a kink in the pressure dependence of the shear wave velocity (dvS/dP) of a SiO2 glass at 140 GPa, and proposed a possible ultrahigh pressure structural change with an increase of the average Si–O coordination number (CN) to >6.
View in article
On the other hand, a recent structure measurement on SiO2 glass up to 172 GPa showed a gradual increase of the average Si–O CN from 6 to higher than 6 above 50 GPa (Prescher et al., 2017), while the trend of the gradual increase of Si–O CN is different from a sharp structural change as the kink observed in the dvS/dP (Murakami and Bass, 2010).
View in article
Ohira, I., Murakami, M., Kohara, S., Ohara, K., Ohtani, E. (2016) Ultrahigh-pressure acoustic wave velocities of SiO2–Al2O3 glasses up to 200 GPa. Progress in Earth and Planetary Science 3, 18.
Show in context
Kinks in dvS/dP have also been observed in Al2O3–SiO2 glasses at 130 GPa (3.9 mol. % Al2O3–96.1 mol. % SiO2 glass) and at 116 GPa (20.5 mol. % Al2O3–79.5 mol. % SiO2 glass) (Ohira et al., 2016).
View in article
Ohira et al. (2016) suggested that incorporation of Al lowers the pressure condition of the ultrahigh pressure structural change, and indicated the role of aluminum in the structural change of aluminosilicate melts in the deep lower mantle.
View in article
Since Si–O and Al–O bond distances are very close (for example, 1.64 Å and 1.81 Å, respectively, in CaAl2Si2O8 glass calculated by Ghosh and Karki, 2018), these bond distances are not resolvable even in the measurements at ambient pressure (e.g., Okuno et al., 2005; Ohira et al., 2016).
View in article
The pressure condition of the ultrahigh pressure structural change in the A40S glass observed in this study (110 GPa) is similar to the pressure condition where a kink in dvS/dP is observed for Al2O3–SiO2 glasses (116 GPa for 20.5 mol. % Al2O3–79.5 mol. % SiO2 glass, Ohira et al., 2016).
View in article
Ohira et al. (2016) argued that incorporation of Al decreases the pressure of the sound velocity change of Al2O3–SiO2 glasses.
View in article
Okuno, M., Zotov, N., Schmücker, M., Schneider, H. (2005) Structure of SiO2–Al2O3 glasses: combined X-ray diffraction, IR and Raman studies. Journal of Non-Crystalline Solids 351, 1032–1038.
Show in context
Since Si–O and Al–O bond distances are very close (for example, 1.64 Å and 1.81 Å, respectively, in CaAl2Si2O8 glass calculated by Ghosh and Karki, 2018), these bond distances are not resolvable even in the measurements at ambient pressure (e.g., Okuno et al., 2005; Ohira et al., 2016).
View in article
Our observed r1 at ambient pressure (1.753 ± 0.004 Å) is consistent with that reported in a previous ambient pressure study (1.76 ± 0.01 Å with T–O CN of 4.3 ± 0.1; Okuno et al., 2005).
View in article
Petitgirard, S., Malfait, W.J., Sinmyo, R., Kupenko, I., Hennet, L., Harries, D., Dane, T., Burghammer, M., Rubie, D.C. (2015) Fate of MgSiO3 melts at core–mantle boundary conditions. Proceedings of the National Academy of Sciences of the United States of America 112, 14186–14190.
Show in context
Petitgirard et al. (2015, 2017) showed a similarity in density of SiO2 and MgSiO3 glasses at the pressure conditions of the Earth’s lowermost mantle, which indicates a minor effect of SiO2 content on the density of silicate glasses (Fig. S-2).
View in article
The important role of Fe in the formation of silicate magma with density higher than PREM has been discussed in previous studies (e.g., Petitgirard et al., 2015, 2017; Karki et al., 2018).
View in article
Petitgirard, S., Malfait, W.J., Journaux, B., Collings, I.E., Jennings, E.S., Blanchard, I., Kantor, I., Kurnosov, A., Cotte, M., Dane, T., Burghammer, M., Rubie, D.C. (2017) SiO2 glass density to lower-mantle pressures. Physical Review Letters 119, 215701.
Show in context
Petitgirard et al. (2015, 2017) showed a similarity in density of SiO2 and MgSiO3 glasses at the pressure conditions of the Earth’s lowermost mantle, which indicates a minor effect of SiO2 content on the density of silicate glasses (Fig. S-2).
View in article
It has been known that densities of SiO2 and MgSiO3 glasses are lower than that of the Preliminary reference Earth model (PREM) (Dziewonski and Anderson, 1981) at the pressures of the CMB (Petitgirard et al., 2017).
View in article
The important role of Fe in the formation of silicate magma with density higher than PREM has been discussed in previous studies (e.g., Petitgirard et al., 2015, 2017; Karki et al., 2018).
View in article
Pradhan, G.K., Fiquet, G., Siebert, J., Auzende, A.-L., Morard, G., Antonangeli, D., Garbarino, G. (2015) Melting of MORB at core–mantle boundary. Earth and Planetary Science Letters 431, 247–255.
Show in context
In fact, the composition of the melt generated by partial melting of a mid-ocean ridge basalt (MORB) at around 100 GPa contains a significant amount of Al2O3 (~20 wt. % or ~13 mol. %) (Pradhan et al., 2015)
View in article
Considering the similarity in the pressure-induced structural changes between aluminosilicate glass and melt at very high pressure conditions of the Earth’s lower mantle (Sanloup, 2016), the Al–O CN change may occur in aluminosilicate melt in the CMB region and may have a significant influence on the behaviour of Al-rich aluminosilicate magmas generated by partial melting of MORB (Pradhan et al., 2015).
View in article
Prescher, C., Prakapenka, V.B., Stefanski, J., Jahn, S., Skinner, L.B., Wang, Y. (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proceedings of the National Academy of Sciences of the United States of America 114, 10041–10046.
Show in context
On the other hand, a recent structure measurement on SiO2 glass up to 172 GPa showed a gradual increase of the average Si–O CN from 6 to higher than 6 above 50 GPa (Prescher et al., 2017), while the trend of the gradual increase of Si–O CN is different from a sharp structural change as the kink observed in the dvS/dP (Murakami and Bass, 2010).
View in article
The basic feature of g(r) in the A40S glass above 16 GPa is similar to that of SiO2 glass with 6-fold coordinated structure at high pressures (Sato and Funamori, 2010; Prescher et al., 2017), while the peak positions are different due to the difference between the Al–O and Si–O distances.
View in article
The pressure condition where the Al–O CN reaches 6 is markedly lower than the pressure where the Si–O CN in SiO2 glass reaches 6 (at ~35–50 GPa: Sato and Funamori, 2010; Prescher et al., 2017).
View in article
In addition, our observed decrease in r1 may be influenced by Si–O bond of the A40S glass, since the evolution of Si–O CN is still controversial in literature (for example, a gradual increase of Si–O CN to more than 6 above 50 GPa in Prescher et al., 2017, while Si–O CN of less than 6 up to 155 GPa in Ghosh and Karki, 2018).
View in article
Sanloup, C. (2016) Density of magmas at depth. Chemical Geology 429, 51–59.
Show in context
Considering the similarity in the pressure-induced structural changes between aluminosilicate glass and melt at very high pressure conditions of the Earth’s lower mantle (Sanloup, 2016), the Al–O CN change may occur in aluminosilicate melt in the CMB region and may have a significant influence on the behaviour of Al-rich aluminosilicate magmas generated by partial melting of MORB (Pradhan et al., 2015).
View in article
Sato, T., Funamori, N. (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Physical Review B 82, 184102.
Show in context
Sato and Funamori (2010) investigated the structure of SiO2 glass and reported a constant Si–O CN of 6 from 35 GPa to 102 GPa.
View in article
The basic feature of g(r) in the A40S glass above 16 GPa is similar to that of SiO2 glass with 6-fold coordinated structure at high pressures (Sato and Funamori, 2010; Prescher et al., 2017), while the peak positions are different due to the difference between the Al–O and Si–O distances.
View in article
The slope of r1 changes with pressure at 25–102 GPa is similar to those of the Si–O bond distance in SiO2 glass with Si–O CN of ~6 at 35–102 GPa (Sato and Funamori, 2010) and Al–O bond distance in CaAl2Si2O8 glass with Al–O CN of ~6 at 41–105 GPa (Ghosh and Karki, 2018) (Fig. 2a).
View in article
Figure 2 [...] Triangles indicate the Si–O bond distance in SiO2 glass (Sato and Funamori, 2010).
View in article
The pressure condition where the Al–O CN reaches 6 is markedly lower than the pressure where the Si–O CN in SiO2 glass reaches 6 (at ~35–50 GPa: Sato and Funamori, 2010; Prescher et al., 2017).
View in article
Contrary to the behaviour of Al–O distance, Si–O distance decreases with increasing pressure up to ~10–20 GPa and then increases at ~20–35 GPa (Sato and Funamori, 2010; Ghosh and Karki, 2018) (Fig. 2a), which is markedly different from our observed r1.
View in article
We find that the slope of the r1 changes in the A40S glass at 25–102 GPa shows a trend similar to the behaviour of Si–O and Al–O bond distances in SiO2 glass (Sato and Funamori, 2010) and CaAl2Si2O8 glass (Ghosh and Karki, 2018) with 6-fold coordinated structure, respectively.
View in article
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Supplementary Information
The Supplementary Information includes:
- Material
- Method
- Figures S-1 to S-5
- Supplementary Information References
Download the Supplementary Information (PDF)
Figures and Tables
Table 1 Experimental pressure conditions and the first (r1), second (r2), and third (r3) peak positions of g(r).
Pressure | r1 | r2 | r3 |
(GPa) | (Å) | (Å) | (Å) |
Ambient | |||
0.0001 | 1.753 ± 0.004 | ||
Experiment 1 | |||
10.8 ± 0.7 | 1.805 ± 0.006 | ||
21.1 ± 1.1 | 1.809 ± 0.006 | 2.604 ± 0.040 | 3.213 ± 0.040 |
24.9 ± 1.2 | 1.811 ± 0.006 | 2.582 ± 0.040 | 3.206 ± 0.040 |
34.5 ± 1.7 | 1.806 ± 0.007 | 2.560 ± 0.040 | 3.182 ± 0.042 |
40.2 ± 1.7 | 1.801 ± 0.007 | 2.561 ± 0.040 | 3.208 ± 0.040 |
47.3 ± 2.9 | 1.793 ± 0.007 | 2.545 ± 0.041 | 3.184 ± 0.043 |
53.7 ± 3.3 | 1.790 ± 0.007 | 2.544 ± 0.041 | 3.186 ± 0.043 |
62.2 ± 2.3 | 1.787 ± 0.007 | 2.534 ± 0.040 | 3.184 ± 0.041 |
69.4 ± 2.5 | 1.775 ± 0.007 | 2.533 ± 0.040 | 3.165 ± 0.041 |
74.1 ± 3.2 | 1.775 ± 0.006 | 2.532 ± 0.040 | 3.175 ± 0.040 |
81.9 ± 3.1 | 1.771 ± 0.006 | 2.537 ± 0.040 | 3.192 ± 0.040 |
88.7 ± 2.8 | 1.767 ± 0.006 | 2.524 ± 0.040 | 3.172 ± 0.040 |
96.6 ± 2.7 | 1.760 ± 0.006 | 2.522 ± 0.040 | 3.154 ± 0.040 |
101.7 ± 3.3 | 1.754 ± 0.006 | 2.548 ± 0.040 | 3.185 ± 0.040 |
110.3 ± 4.3 | 1.752 ± 0.006 | 2.540 ± 0.040 | 3.175 ± 0.040 |
Experiment 2 | |||
3.7 ± 0.3 | 1.773 ± 0.006 | ||
15.5 ± 0.6 | 1.810 ± 0.006 | 2.601 ± 0.041 | 3.206 ± 0.041 |
37.4 ± 2.1 | 1.793 ± 0.007 | 2.510 ± 0.040 | 3.131 ± 0.040 |
45.8 ± 1.6 | 1.782 ± 0.006 | 2.515 ± 0.040 | 3.125 ± 0.040 |
57.8 ± 4.4 | 1.778 ± 0.007 | 2.502 ± 0.040 | 3.109 ± 0.040 |
65.6 ± 1.5 | 1.776 ± 0.007 | 2.480 ± 0.040 | 3.084 ± 0.040 |
86.3 ± 4.9 | 1.756 ± 0.007 | 2.486 ± 0.040 | 3.110 ± 0.041 |
91.4 ± 3.4 | 1.760 ± 0.007 | 2.485 ± 0.040 | 3.101 ± 0.040 |
108.1 ± 3.3 | 1.750 ± 0.006 | 2.474 ± 0.040 | 3.109 ± 0.040 |
113.9 ± 5.3 | 1.750 ± 0.007 | 2.492 ± 0.040 | 3.144 ± 0.040 |
120.9 ± 4.3 | 1.753 ± 0.006 | 2.481 ± 0.040 | 3.107 ± 0.040 |
130.8 ± 4.5 | 1.736 ± 0.006 | 2.473 ± 0.040 | 3.136 ± 0.040 |