Amorphous boron oxide at megabar pressures via inelastic X-ray scattering

• amorphous boron oxide
• extreme compression
• megabar pressures
• inelastic X-ray scattering

When under extreme compression, amorphous oxides undergo structural transitions into more densely packed glassy networks that are significantly different from those at ambient pressure (e.g., refs. 1⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–16). The detailed structures of the glasses at high pressure are among the remaining fundamental mysteries in modern physical sciences. Particularly, information about the structure of oxide glasses under megabar pressure conditions is important to identify the inherent yet unknown densification mechanisms upon extreme compression and to clarify the evolution of Earth’s lower mantle up to the boundary between the core and the mantle at ∼134 GPa, where formation of dense oxide melts has been suggested (17, 18). Despite the fundamental importance and geophysical implications, the in situ probing of bonding environments in glasses beyond megabar pressure conditions has not been successful, primarily because of the lack of suitable experimental probes.

While elastic X-ray scattering can be used to study oxide glasses at high pressure, the direct coordination environments of framework cations including B in low-z glasses above 100 GPa are unknown because of the small atomic scattering factors of the low-z elements and the extensive overlap among multiple pair correlation functions that accompany the formation of multiple coordination states (e.g., ^[4,5,6,7]Si and ^[3,4]B) (3, 19). The limited scattering vector range under high-pressure conditions adds ambiguity in the pair distribution function of the first coordination environments. Although NMR spectroscopy has revealed novel structural transitions in low-z glasses under extreme environments, its application has been limited to the maximum quench pressure of ∼12 GPa because of the necessity of a large amount of glass sample (∼3–10 mg) and the lack of in situ high-pressure solid-state NMR techniques (1, 4, 8, 20⇓⇓–23). Similar pressure limits of ∼17 GPa have been documented for neutron scattering (9, 11, 16, 24).

Nonresonant inelastic X-ray scattering (NIXS, or X-ray Raman scattering), which can probe core electron excitation from glasses in a diamond anvil cell (DAC), has enabled exploration of the pressure-induced changes in atomic configurations around boron and oxygen in oxide glasses under extreme compression (25⇓⇓⇓⇓⇓–31). For example, boron K-edge NIXS showed the transition from ^[3]B to ^[4]B in diverse borate glasses up to ∼30 GPa (e.g., refs. 5, 25, 32, and 33). The evolution of oxygen configurations (oxygen K-edge) in SiO₂, GeO₂, and B₂O₃ glasses (v-B₂O₃) as well as other more complex glasses up to ∼40 GPa has been reported (25, 29, 34⇓–36). Furthermore, a silicon L-edge spectrum was obtained for v-SiO₂ up to ∼74 GPa (37). Nevertheless, NIXS has not been performed beyond 100 GPa because of the inherent challenges of inelastic X-ray techniques (with a signal intensity several orders of magnitude smaller than that of elastic X-rays). The collection of a high-quality single-oxygen K-edge NIXS spectrum of oxide glasses at high pressure can take 1–2 d of beam time in the third-generation synchrotron sources (25). With increasing pressure, the gap between the diamond anvils decreases, increasing the background signals from the gaskets and anvils. These inherent difficulties pose a major challenge for probing structural changes in glasses with NIXS above 100 GPa. While the signal reduction of incident and scattered photons is inevitable, a polycapillary postsample collimator with improved X-ray optics provides a new opportunity to collect the signal primarily from the sample, with significantly reduced background signals (see Materials and Methods and SI Appendix, section S1 and Fig. S1 for comparison of NIXS spectrum with and without the polycapillary postsample collimator). This provides the potential to explore details of structural transitions in glasses at megabar pressure conditions (38, 39).

Like GeO₂, and SiO₂ glasses, B₂O₃ is an archetypal glass former with a peculiar metastability toward crystallization (19, 40, 41). The addition of boron into oxide melts reduces the viscosity and melting temperatures (42). The pressure-induced bonding changes in framework cations, including boron, account for the anomalous pressure dependence of its viscosity and elastic properties (20, 43, 44). While pioneering experimental efforts have been devoted to studying the structure of v-B₂O₃ at high pressure up to ∼30 GPa (5, 9, 33), the post-^[4]B transition into ^[5]B has not been experimentally identified. Ab initio calculations suggested the prevalence of only ^[3]B and ^[4]B in v-B₂O₃ up to ∼1.5 megabars (45, 46). This is in contrast to Si and Ge in SiO₂ and GeO₂ glasses, respectively, where successive coordination transformation into multiple coordination states (e.g., ^[4,5,6]Si and ^[4,5,6,7]Ge) is expected at relatively low pressure up to ∼5–30 GPa (e.g., refs. 10, 13⇓–15, and 47⇓⇓⇓–51). Although this difference indicates the effects of the nature of the cations and their electronic structures on the transition pressures of the corresponding cations, a systematic relationship between the types of cations and the transition pressure in the glasses has not been established. Experimentally verifying the bonding environments around boron in v-B₂O₃ at pressures above 100 GPa has thus been anticipated. Along with the cation environments, changes in oxygen coordination beyond megabar pressures may reveal the densification mechanisms of boron coordination transformation. The formation of ^[4]B in v-B₂O₃ accompanies the formation of ^[3]O. Most of the suggested densification mechanisms in oxide glasses involve oxygen coordination transformation from ^[1]O (i.e., nonbridging oxygen) to ^[2]O (i.e., bridging oxygen) at a relatively low pressure and the subsequent transition to ^[3]O (4, 8, 20, 22, 52). However, the densification involving ^[3]O itself and its effect on the densification in glasses under extreme compression remain unexplored. In this study, we report boron and oxygen K-edge NIXS spectra for v-B₂O₃ in the megabar pressure range close to that at the Earth’s core–mantle boundary.

The boron K-edge NIXS spectra for v-B₂O₃ up to 119.4 GPa [with a beam size of ∼8 × 5 μm² (h × v)] unveil the evolution of boron coordination states upon extreme compression (Fig. 1). The spectra for v-B₂O₃ at 1 atm and 15.0 GPa have been reported previously, where a much larger beam (80 × 20 μm²) with a culet size of 500 μm was used (5). These spectra are consistent with the current measurements at 1 atm and 16.7 GPa, respectively. The features at 194 eV and 203 eV stem from the transition of a 1s electron to an unoccupied B–O π* antibonding orbital and to an σ* antibonding orbital, respectively. These features are characteristic of ^[3]B. The additional feature at 198–200 eV is due to ^[4]B, corresponding to a transition to its 2p/2s σ* antibonding orbital (53). The intensity of the ^[4]B peak increases with pressure, confirming the coordination transformation from ^[3]B to ^[4]B. Most boron is ^[4]B above ∼30 GPa, as evidenced by the disappearance of the π* peak. With a further increase in pressure up to megabar levels, the gradual shift in the main ^[4]B peak is observed, indicating densification within amorphous tetrahedral borate networks. The observed peak shift is not significant, suggesting the extended stability of ^[4]B in v-B₂O₃ up to ∼120 GPa. The NIXS data do not show any signs of coordination transformation to ^[5]B, which is consistent with ab initio calculations (45, 54). The minor features at ∼201 eV and ∼205 eV and an emergence of the pre-edge feature (at 194 eV) are identified at high pressure (e.g., 119.4 GPa), reflecting the possibility of structural changes. While these features cannot be fully disregarded based solely on the statistical variation in the spectrum, consideration of the current signal-to-noise ratio and the statistical uncertainty of the B K-edge spectra at high pressure suggests that these minor features are likely to be spectral noises (SI Appendix, section S2 and Fig. S2).

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Fig. 1.

Boron K-edge NIXS spectra for B₂O₃ glass at pressures up to ∼119.4 GPa, as labeled. The spectra are plotted as normalized scattered intensity vs. energy loss (incident energy – elastic energy). Those for 1 atm and 15 GPa have been previously reported (5). The spectra in black were collected with a 0.7-eV scan. See SI Appendix, Fig. S2 for the NIXS spectra without smoothing with spectral uncertainty.

Fig. 2 shows the oxygen K-edge NIXS spectra for v-B₂O₃ at low pressure range (5) and at 101.6 GPa (SI Appendix, section S2 and Fig. S3). The spectrum at 1 atm shows a sharp peak at 536 eV and a broad feature at 544 eV, both stemming from the bridging ^[3]B–^[2]O–^[3]B (5). The major portion (∼75%) of ^[3]B in bridging oxygen constitutes a trimembered planar ring (i.e., boroxol ring) (41, 55, 56). Only a broad σ* feature at 543 eV is observed at 8.4 GPa and 22.5 GPa, while the peak at 536 eV decreases, suggesting a collapse of the boroxol ring. The oxygen K-edge NIXS spectrum for v-B₂O₃ at 101.6 GPa shows a shift in the main σ* feature and an increase in the intensity of feature at ∼547 eV (Fig. 2). The observed changes can stem from multiple structural changes upon extreme compression and are similar to those observed for MgSiO₃ and SiO₂ glasses at high pressure (29, 36, 57). Recent ab initio calculations of oxygen K-edge NIXS spectra for crystalline MgSiO₃ and SiO₂ phases up to ∼120 GPa indicated that the shift can be primarily correlated with a decrease in the average O–O distance (34, 36, 58). The main oxygen K-edge feature is further broadened at 101.6 GPa, indicating a much wider O–O distribution and, thus, an enhanced topological disorder that is due to an increase in bond angle (^[2]O–^[4]B–^[2]O and ^[3]O–^[4]B–^[3]O) and B–O length distribution.

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Fig. 2.

Oxygen K-edge NIXS spectra for B₂O₃ glass at pressures ranging from 1 bar to 100 GPa, as labeled. Those for 1 atm and 8 GPa were previously reported (5) but are shown here for comparison. The shaded box shows the shift in the feature and peak broadening with increasing pressure (only to the guide for eyes). See SI Appendix, Fig. S3 for the NIXS spectra without smoothing with spectral uncertainty.

With increasing pressure, formation of 3^[4]B–^[3]O is expected at the expense of ^[2]O and ^[3]B (i.e., ^[3]B–^[2]O–^[3]B + ^[3]B → 3^[4]B–^[3]O). Because the boron coordination number in v-B₂O₃ is 4 above ∼30 GPa and up to ∼120 GPa, the fraction of ^[3]O for this pressure range is invariant and is two-thirds of all oxygen in the glass (SI Appendix, section S3). Therefore, the oxygen K-edge feature of ^[3]O at megabar pressures consists of contributions from the two-thirds of ^[3]O (i.e., 3^[4]B–^[3]O) and one-third of ^[2]O that are linked to ^[4]B (i.e., ^[4]B–^[2]O–^[4]B). The observed shift in the edge feature at 101.6 GPa is due to the topological contraction of networks mainly around ^[3]O. More extensive NIXS studies of model compounds above 100 GPa are required to establish the quantitative effect of pressure on their local structures and NIXS features. Nonetheless, our results confirm that the reduction in the O–O distance in ^[3]O is the major densification mechanism in v-B₂O₃ above ∼30 GPa.

Theoretical calculations of the NIXS spectrum can provide useful constraints on the atomistic origin of the pressure-induced NIXS feature changes (Figs. 1 and 2) (36, 58). Fig. 3, Left shows the calculated boron K-edge NIXS spectra for crystalline B₂O₃–I and B₂O₃–II with increasing pressure. Detailed calculation conditions and information about crystal structures are presented in SI Appendix, section S4, Fig. S4, and Table S1. The stability of B₂O₃–II at high pressure has been explored up to ∼46 GPa (59, 60), but the post-B₂O₃–II phase transition at higher pressure has not been observed. Therefore, we extended the existing equation of state (EOS) of B₂O₃–II to 120 GPa to explore the evolution of the edge features with a variation in the B–O bond length [d(B-O)] up to the megabar pressure range (SI Appendix, section S4). The d(B-O) in the extrapolated EOS can also be underestimated if distortion of ^[4]B polyhedra is not considered. Therefore, we calculated the metastable EOS for the B₂O₃–II beyond megabar by relaxing the atomic positions in the unit cell with a fixed space-group symmetry (SI Appendix, section S4). Note that the current ab initio simulations do not allow us identify the new, high-pressure B₂O₃–II above 46 GPa, which is beyond the scope of the current study. Further experimental and theoretical studies are necessary to confirm the stability of B₂O₃–II beyond 46 GPa. Therefore, the current theoretical calculation provides a qualitative guide to the effect of pressure on the σ* peak shift. The edge features shift to higher energy with increasing pressure: While the change in the NIXS peak maxima (Peak_max) for the optimized cell (red dotted curve) is smaller than that obtained from the extrapolated EOS (gray dotted curve), the calculated Peak_max for both cases shifts with increasing pressure mainly because of a reduction in d(B-O) (Fig. 3, Right and SI Appendix, section S4). Based on the calculated trends, an observed minor shift in the σ* peak in v-B₂O₃ (Fig. 1) corresponds to a decrease in d(B-O) of ∼0.05–0.08 Å upon compression up to 120 GPa. This change is somewhat smaller than that estimated from the compression of B₂O₃–II to 120 GPa [∼0.08 (estimated from the red curve)–0.2 Å (from the extended EOS)] (Fig. 3). These results indicate that densification of v-B₂O₃ is mostly due to the reduction in the average O–O distance without the formation of highly coordinated boron (e.g., ^[5]B), at least up to ∼120 GPa, confirming the stability of sp³-bonded ^[4]B in v-B₂O₃. Once the fraction of ^[3]O reaches a threshold value of two-thirds, the flexibility of the network is expected to decrease. However, the current observation shows that the reduction in the average O–O distance is prevalent without involving further coordination transformation in ^[4]B. Therefore, the structural densification in v-B₂O₃ is largely topological (without forming ^[5]B). A decrease in O–O distance at a given coordination number has been known for the other covalent oxide glasses, such as v-GeO₂ below the threshold pressure at which the coordination transformation does not occur (e.g., ref. 61 and references therein). This decrease in B₂O₃ is also likely to be associated with the increase in packing density that stems from a decrease in ^[2]O–^[4]B–^[2]O and ^[3]O–^[4]B–^[3]O bond angle and formation of smaller ring networks (i.e., puckering of the networks). While ab initio simulations of the NIXS feature for v-B₂O₃ at high pressure remain to be calculated, the current simulations of crystalline polymorphs provide a systematic relationship between bond length and its effect on edge features (SI Appendix, section S4). Further experimental exploration of the glasses above several megabars is required to observe evidence of post-^[4]B transition (SI Appendix, section S5).

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Fig. 3.

(Left) Calculated boron K-edge NIXS spectra for crystalline B₂O₃–I and B₂O₃–II, with varying unit cell volumes and pressures, as labeled. The gray and red dotted curves show the calculated peak maximum (Peak_max) for σ* based on extended EOS and optimized metastable EOS. See SI Appendix, section S4 for the detailed calculation methods and crystal structures of B₂O₃–I and B₂O₃–II with varying pressures. The calculated NIXS spectra for B₂O₃–I with varying unit cell volumes with respect to that at 1 atm, as labeled, are added to demonstrate the effect of pressure on the position of the π* peak (^[3]B). While the exact pressure value may not be fully known, the estimated pressures of the contracted cell of B₂O₃–I are ∼4.5 (with a normalized unit cell volume of 0.94) and 10.3 GPa (with a normalized volume of 0.88). See SI Appendix, section S4 for additional details. (Right) Calculated peak maximum [Peak_max, red rhomboids (with geometry optimization) and black rhomboids (based on extended EOS)] of ^[4]B in B₂O₃–II with varying pressures (Top) and B-O bond lengths [d(B-O), Bottom]. The latter can be roughly described by the following linear equation: Peak_max = −15.8 × d(B-O) + 220.

The current results provide a prospect for the study of densifications in archetypal oxide glasses, including v-B₂O₃, v-SiO₂, and v-GeO₂. For v-SiO₂ and v-GeO₂, successive transformation of ^[4]Si (and ^[4]Ge) into highly coordinated ^[5,6,7]Si (and ^[5,6,7]Ge) contributes to the overall densification of the glasses (SI Appendix, section S6). The transition pressure for these highly coordinated Ge in v-GeO₂ (∼12 GPa for ^[5]Ge) is much lower than that in v-SiO₂ (∼25 GPa for ^[5]Si) obtained from in situ high-pressure experiments (10, 11, 47, 48, 50, 51, 61), which is due to the significantly more contracted electron distribution in the latter [Si (with an atomic radius of 1.1 Å at ambient pressure): [Ne] 3s² 3p²] than that in the former [Ge (1.25 Å): [Ar] 3d¹⁰ 4s² 4p²]. While a similar trend was predicted by the theoretical simulations of v-Al₂O₃ under compression (62), experimental results at high pressure are not available because of difficulty in synthesis of Al₂O₃ glass. Rather, direct Al [1.25 Å: [Ne] 3s² 3p¹] coordination states for aluminosilicate glasses are well-documented experimentally: ^[5,6]Al is observed at 3–10 GPa, depending on the glass composition, similar to the threshold pressure for ^[5,6]Ge (1, 8, 20, 63⇓⇓–66). The systematics suggest that the atomic radii of framework cations play a major role in the nature of the pressure-induced coordination transformation.

In borate glasses, ^[3]B begins to transform to ^[4]B under low-pressure conditions (3–5 GPa), reaching the average coordination number of ∼3.5 at ∼8–15 GPa (5, 9) (SI Appendix, section S6). However, in contrast to the successive coordination transformation in Al (and Si and Ge) in glasses, once the sp³ bond in ^[4]B forms [B (0.85 Å): 1s² 2s² 2p¹] (Figs. 1 and 3), the boron coordination transformation into ^[5]B is hindered at least up to ∼120 GPa. With the new ^[4]B results, the predominance diagram of distinct coordination states (labeled with Roman numerals) of framework cations (B, Si, and Ge) in archetypal covalent oxide glasses can be constructed as functions of the pressures and atomic radii of the framework cations (Fig. 4). Because the diagram is the predominance diagram, not a stability field diagram, it labels the most abundant species among the diverse and mixed coordination states in a given pressure and atomic radius. The dotted lines represent the hypothetical boundaries where the fractions of two coordination numbers of the cations are expected to be similar (SI Appendix, section S6). For example, along the line crossing III and IV, the average coordination number of the cation is 3.5, and the fractions of ^[3]B and ^[4]B are close to identical. The shaded areas between the boundaries show the most dominant coordination state (III, IV, V, and VI) of these cations. For instance, in the region marked with VI, the 6-coordinated species are expected to be dominant, although multiple coordination environments (e.g., 4, 5, 7, and other coordinated species) are possible (SI Appendix, section S6). Considering the predicted (and/or confirmed) coordination transformation in other framework cations in oxide glasses (SI Appendix, section S6), the current results account for the effect of the chemical nature of framework cations on the transition pressure. Note again that the boundaries and areas are to visually distinguish the states and are based on a limited number of data points. Therefore, the figure is a conceptual model because the atomic radii at high pressure and the quantitative transition pressures for these oxide glasses are not fully known. More experimental data to quantify the boundaries and additional theoretical confirmations of the proposed predominance are needed. An earlier empirical approach based on the hard-sphere model used the concept of pressure-dependent oxygen-packing density for revealing quantitative coordination number of cations and the threshold packing fraction for coordination transformation (67). In contrast, the current model uses the atomic radii obtained at 1 atm as a controlling indicator independent of pressure to provide a guideline for predicting the transition pressure. Because an increase in cation–oxygen bond length (that is partly dependent on the cation radius) is one of the important controls of oxygen radius in the earlier packing-density model, from which the packing density is estimated, the current model provides a complementary view of the model on oxygen packing fraction.

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Fig. 4.

Predominance diagram, where the most dominant coordination states (labeled with Roman numerals) of framework cations (B, Si, and Ge) in B₂O₃, SiO₂, and GeO₂ glasses with varying pressure and atomic radius of the framework cations are shown. While single coordination states are labeled, cations with multiple coordination environments coexist. The effect of pressure on the atomic radius of the cations in these glasses is not taken into consideration. Further exploration of this effect remains to be done. The red, black, dark blue, green, and light blue squares denote the average coordination numbers of the cations of 3.5, 4, 4.5, 5.5, and 6.5, respectively (SI Appendix, section S6). The dotted lines indicate the hypothetical boundaries among the dominant coordination states.

The structural information provided in the current study is qualitative because of the insufficient number of IXS pressure scans (particularly the O K-edge data) and uncertainty in the spectra at high pressure. In addition, the lack of structural information about crystalline B₂O₃ phases beyond the megabar pressure range makes it difficult to establish the robust relationships between the internal structural variables, including the B–O length and edge feature at the extended pressure condition (SI Appendix, section S4). We, thus, use the ab initio calculations only to provide a guide to the observed transition. The need for extensive effort remains before the nature of structural transformation in oxide glasses is fully explained. Furthermore, whether the ^[4]B is quenchable is of central importance. ^[4]B is not quenchable to 1 atm upon decompression from ∼22.5 GPa (5). As the NIXS spectrum for the decompressed glass from ∼120 GPa is not currently available, a B K-edge NIXS experiment for the decompressed glass above megabar remains to be performed.

The current study highlights the utility of in situ NIXS as a unique probe for the electronic structures of soft and/or condensed matter (both crystalline and amorphous) under extreme compression above megabar pressure conditions. The in situ NIXS for prototypical v-B₂O₃ revealed the novel densification paths characterized with the extended stability of sp³-bonded ^[4]B beyond 100 GPa. Major densification is associated with the contraction of ^[3]O and the average O–O distance reduction. The results allow us to conclude the effect of the atomic radius (and/or the nature of electron distribution) on the threshold pressure in the highly coordinated states, confirming that the framework cation with a smaller atomic radius will undergo coordination transformation at higher pressure. While the effect of atomic radius of cation on the pressure for coordination transformation in crystalline materials has been demonstrated, development of a similar proposal for noncrystalline oxides has not been available. The current result confirms that a similar conceptual framework can be used to reveal the nature of noncrystalline materials under extreme compression. This simple relationship may provide a useful guide to study the structural transformation in complex, multicomponent glasses where the structural transformation can be more complicated by the presence of diverse nonnetwork forming cations. The densification model can be applied to account for the stability, oxygen configurations, and solubility of elements and isotopes into the dense melts at the core–mantle boundary. Particularly, dense oxide melts with predominant ^[3]O can result in enhanced contraction at the basement of the lower mantle, increasing melt density, which suggests the stable presence of the dense melts in contact with crystalline Mg-silicate polymorphs. Potential prevalence of ^[4]B in the compressed melts and magmas may account for the enrichment of ¹⁰B (instead of ¹¹B) in Earth’s mantle, as the lighter B can be preferentially partitioned into the highly coordinated boron in oxides.