Simplicity in melt densification in multicomponent magmatic reservoirs in Earth’s interior revealed by multinuclear magnetic resonance

Results and Discussion

The remarkable resolution among atomic configurations in the quaternary CNAS glasses quenched from melts at high pressure are shown in the multicomponent (Al-27, Na-23, O-17), two-dimensional 3QMAS NMR spectra (Fig. 1). The Al-27 NMR spectra for the CNAS melts (Fig. 1, Left) show ^[4]Al, ^[5]Al, and ^[6]Al at 8 GPa, whereas ^[4]Al is dominant (approximately 100%) at 1 atm (32). The fractions for ^[4]Al, ^[5]Al, and ^[6]Al are approximately 76.1%, 16.7%, and 7.1%, respectively (see SI Appendix). The peak width of the ^[4]Al for 8-GPa glasses in the MAS dimension is larger than that for 1 atm, suggesting an increase in the topological disorder due to the Al-O bond length distribution with pressure. The formation of highly coordinated Al leads to a change in the chemical connectivity (i.e., NBO and BO environments)

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Fig. 1.

Multinuclear (Al-27, O-17, and Na-23) 3QMAS NMR spectra for [(Na₂O_0.75CaO_0.25)₃Al₂Si₄O₁₁] (CNAS) glasses quenched at 1 atm and 8 GPa. Contour lines are drawn at 5% intervals from 13% to 93% of relative intensity, with added lines at the 4%, 6.5%, and 9% levels to better show low-intensity peaks. * denotes spinning side band.

O-17 3QMAS NMR shows two distinct groups of NBOs [Na-NBO(Na-O-^[4]Si) and a mixed cation NBO peak [{Ca,Na}-O-^[4]Si as labeled] and three BO clusters [^[4]Si-O-^[4]Al, ^[4]Si-O-^[4]Si, and ^[4]Al-O-^[4]Al] for CNAS glasses at 1 atm (Fig. 1, Center), consistent with the previous assignments (32). At 8 GPa, a feature due to ^[4]Si-O-^[5,6]Al (at approximately -40 ppm in the isotropic dimension) is evident. There is no evidence for the formation of ^[4]Si-O-^[5,6]Si that would be observed at approximately -60 ppm in the isotropic dimension (21), suggesting that Al tends to be highly coordinated, whereas Si remains 4-coordinated. The changes in the oxygen configuration in the CNAS melts with pressure thus stem mostly from the formation of ^[5,6]Al. Although the ^[4]Al-O-^[4]Al peak intensity apparently decreases with increasing pressure, the presence of the high energy cluster is evident at 8 GPa, implying that the higher-energy cluster at 1 atm can be stable in an elevated pressure regime. The pressure-induced change in the Na-O bond distance is also revealed in the Na-23 3QMAS NMR spectra for the CNAS glass (Fig. 1, Right). The position of the main Na peak changes slightly with increasing pressure, and the trend suggests that the Na-O distance decreases with increasing pressure and changes the role of Na⁺ from network modifying to charge balancing around ^[4]Si-O-^[5,6]Al (33).

An additional structural evolution with pressure in the silicate melts can be observed from the total isotropic projection (sum of data along the lines parallel to the y axis) of the 3QMAS spectra (Fig. 2). The X_NBO at 1 atm obtained from the fitting and subsequent calibration of each peak in the isotropic projection of O-17 3QMAS NMR spectrum is approximately 28.8%, consistent with the prediction from the composition (Fig. 2). The predicted fraction of NBO [Na-NBO + {Ca,Na}-NBO] at 8 GPa is approximately 24.3% (see SI Appendix). The Na-23 chemical shift for the main peak moves to a higher frequency (a positive peak shift in the isotropic dimension), confirming that the average Na-O distance decreases with pressure. Unlike Al, ^[5,6]Si species that would be observed at approximately −150 ppm for ^[5]Si and approximately −200 ppm for ^[6]Si are not detected in the Si-29 MAS NMR spectra of the glass at 8 GPa. The Si environment beyond its first coordination shell (i.e., Q species) in the glass may change with increasing pressure, but such a change is not detected (Si-29 MAS Inset, Fig. 2). Therefore, the pressure-induced Al coordination transformation is responsible for the total decrease in NBO [i.e., (∂X_NBO/∂P)_T = -∂^[5,6]Al/∂P)_T] in the CNAS melts. Because of the importance of multicomponent melts, their previous inaccessibility at high pressure, and our demonstration of the utility of multinuclear NMR for exploring their bonding nature at high pressure, the pressure-induced changes in multicomponent melts provide unique information about the densification mechanism for natural melts in the Earth’s interior.

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Fig. 2.

Total isotropic projection of multinuclear Al-27, O-17, Na-23 3QMAS NMR spectra for the CNAS glass quenched from melts at 1 and 8 GPa. Fitting results for CNAS glass using 4 Gaussians representing Na-NBO, Mixed-NBO, ^[4]Si-O-^[4]Si, and ^[5,6]Si-O-^[4]Si are shown as labeled (Top Right). The Si-29 MAS NMR spectrum for the glass is also shown (Bottom Right).

Pressure-induced changes in X_NBO for silicate melts are shown in Fig. 3A where X_NBO is scaled to be 100% at the reference pressure (P₀, 1 atm) [(X_NBO(P)/X_NBO(P₀)], which allows us to compare the available experimental data for silicate melts in a single plot. In general, X_NBO decreases slightly with increasing pressure at lower pressures but the magnitude of (∂X_NBO/∂P)_T increases with a further increase in pressure, which seems universal regardless of the melt composition. In detail, (∂X_NBO/∂P)_T exhibits a significant composition dependence. -(∂X_NBO/∂P)_T is larger for silicate melts with decreased alkali content (21, 34–37) (Fig. 3B) and is more significant for aluminosilicate with increasing degree of polymerization at 1 atm (38, 39) (Fig. 3C). The pressure-induced changes in X_NBO are also more significant with increasing cation field strength (e.g., charge/ionic radius) for the network-modifying cations at the constant degree of polymerization at 1 atm (27, 40) (Fig. 3D). Note that the pronounced pressure-induced changes in NBO fraction in the Al-free silicate melts results from the coordination changes in Si (e.g., CNS, NS2, NS3, and NS4 melts in Fig. 3). The current results thus show that the pressure-induced changes in NBO fraction can be explained with single exponential function regardless of type of network forming cations (Si or Al) in the melts {i.e.,(∂X_NBO/∂P)_T = -∂[(^[5,6]Al and/or ^[5,6]Si)/∂P]_T}. In general, a higher degree of polymerization of silicate melts at ambient pressure facilitate a further polymerization of silicate melts at high pressures of up to approximately 10 GPa.

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Fig. 3.

(A) Variation in the normalized nonbridging oxygen fraction with pressure in binary, ternary, and quaternary aluminosilicate glasses {alkali silicate glasses (black circle, Na₂O∶SiO₂ = 1∶2, NS2 (37); blue square, Na₂O∶SiO₂ = 1∶3, NS3 (21); red open circle, Na₂O∶SiO₂ = 1∶4, NS4 (35)], ternary mixed cation silicates, (black square, Na₂O∶CaO∶SiO₂ = 0.75∶0.25∶3, CNS) (40), depolymerized aluminosilicate glasses (black triangle, Na₂O∶Al₂O₃∶SiO₂ = 1.5∶0.5∶60, NAS4 (21); open triangle, Na₂O∶Al₂O₃∶SiO₂ = 1.5∶0.5∶20, NAS1 (39)], and CNAS glass (diamond)} as labeled. The fractions of NBO in the NAS melts were modified only on the basis of the Al-coordination environment and thus a little bit different from the trend shown in our previous report (21). The thick curves show the trend lines connecting experimental data, which are drawn for visual clarity. (B) Effect of the composition (Na/Si) on normalized NBO fraction in binary alkali silicate melts (37). (C) Effect of degree of polymerization at 1 atm on normalized NBO fraction in aluminosilicate melts. (D) Effect of cation field strength of network-modifying cation on normalized NBO fraction at a constant degree of polymerization at 1 atm. Simulation results of the normalized nonbridging oxygen fraction for diverse silicate melts at high pressure using Eq. 1 (the thin and dotted curves) with varying P_XNBO=0 from 10 to 19 as labeled [at constant α of 0.2 except that for NAS1 (α = 0.16) and NS2 (α = 0.18)]. Uncertainty of α is estimated to less than 0.05. (E) Normalized NBO fraction in silicate melts with pressure. (F) Variation in the normalized nonbridging oxygen cluster population with normalized pressure. Thick red line refers to a trend line based on Eq. 2 at α of 0.2.

Taking into consideration the observed compositional dependences of melts at high pressure, we have found that X_NBO can be expressed as follows: [1]where α is a dimensionless scaling constant relevant to the degree of rigidity of the network upon pressurization, describing the flexibility of melt network upon pressurization (41) (see SI Appendix). Pressure-induced structural changes become more abrupt (the network is more rigid) with decreasing α. The experimental data can be reproduced with α of approximately 0.2 without having much compositional dependence (Fig. 3 B–E). P_XNBO=0 depends on melt composition and is a fictive pressure where X_NBO in silicate melts is expected to be 0 if the trend in the NBO decay would follow an exponential function: Although Eq. 1 with an exponential decaying function is rather phenomenological, the trend in Eq. 1 is consistent with a recent model considering the distribution of local energy minima in the energy landscape for oxide glasses, particularly at lower pressure ranges where the conceptual meaning for P_XNBO=0 and α can be determined (see SI Appendix). Fig. 3 B–E also shows the fitting results with the above equation where P_XNBO=0, ranging from 10 to 19 at α of approximately 0.2. The α-value may deviate from the current value for the silicate melt composition that is significantly different from the melts studied here. Uncertainties in P_XNBO=0 for most melts are smaller than 0.5 GPa but increase with increasing P_XNBO=0 (e.g., approximately 1.5 GPa for NS3 melts and approximately 2.5 GPa for NS2 melts; see SI Appendix). P_XNBO=0 accounts for the observed trend in the effect of composition on (∂X_NBO/∂P)_T and thus decreases with an increase in the alkali/silica ratio and cation field strength in silicate glasses (27, 40). Ranges for P_XNBO=0 in melts is similar to the pressure ranges where melts are denser than solids, forming trapped melts in the early Earth (1).

Upon introducing normalized pressure P^′( = P/P_XNBO=0), normalized NBO fraction and its pressure dependence can be converged into a simple trend as follows: [2][3]The above trend with remarkable simplicity may be regarded as a universal behavior of the degree of polymerization in silicate melts (Fig. 3F). Whereas previous experimental studies have shown that X_NBO decreases with pressure, it has been suggested that simple X_NBO-P relations might be difficult to achieve (21, 40). The current results demonstrate that the complex effect of composition and pressure on melt structure can be greatly simplified. These structural changes play a role in the melt properties in the Earth’s interior. Below, the expected trends in the pressure dependence of the properties of CNAS melts are shown on the basis of (∂X_NBO/∂P)_T. These properties are also scaled by the value at 1 atm with respect to the normalized pressure (i.e., P^′) (Fig. 4). More detailed information of the predicted properties is given in SI Appendix.

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Fig. 4.

(A) Effect of normalized pressure on the viscosity, oxygen diffusivity, and configurational entropy due to oxygen cluster mixing in the silicate melts with X_NBO(1 atm) = 0.285 and P_XNBO=0 = 15 GPa (red curve). The plots for viscosity and diffusivity are also based on the relations for pressure-dependent and . Note that these modeling parameters are only for a semiquantitative analysis for the trend of O^2- diffusivity and viscosity. (B) The effect of the normalized pressure and the reduction of NBO on the solubility of elements (dashed curve) and the activity coefficient of silica in silicate melts (solid black curve). The former was calculated with varying value (kJ/mol·K) ranging from -20 to 50.

The X_NBO and its complex compositional dependence in (∂X_NBO/∂P^′)_T may account for the nonlinear variation of pressure-induced changes in viscosity and oxygen diffusivity (21). As the degree of polymerization for CNAS melts increases with pressure, the predicted viscosity tends to decrease, but it then increases with a substantial decrease in X_NBO with a further increase in pressure (Fig. 4A). Oxygen diffusivity and bulk viscosity are expected to be anticorrelated for the CNAS melts studied here assuming the Stokes–Einstein relationship, which is consistent with the experimental trend for partially depolymerized melts (8). Based on the Adam–Gibbs theory, the configurational entropy (S^config) of CNAS melts is expected to show a similar pressure dependence with diffusivity (42). A part of S^config in the melts at high pressure may be calculated independently by considering the mixing of oxygen clusters. The calculated S^config for the quaternary CNAS melts due to the oxygen cluster mixing increases with increasing pressure below 10 GPa and then decreases with a further increase in pressure, consistent with the suggestion from the pressure-induced changes in melt viscosity (Fig. 4A). The results indicate that a certain aspect of S^config in silicate melts increases with increasing pressure up to approximately 10 GPa, whereas the total entropy of the melts decreases with pressure.

The composition of the melts generated in multicomponent silicate magmas is affected by the activity coefficients of oxides therein as well as activity of mineral phases in equilibrium with melts. The fraction of S-O-Si (X_Si-O-Si) in the melts is roughly proportional to the square root of activity coefficient of SiO₂ () in simple silicate melts (43). With increasing pressure, X_NBO and X_Si-O-Si (among BO clusters) decrease because of an increase in Si-O-^[5,6]Al. due to Si/^[4,5,6]Al mixing should thus decrease with increasing pressure (Fig. 4B). The trend in with pressure suggests that the composition of melts tends to be more silica-rich at high pressure. Although earlier high-pressure melting experiments for peridotite (KLB-1) showed that the SiO₂ content of partial melts does not vary with pressure up to 18 GPa (12), the high-pressure melting experiment for MORB with X_NBO of at 1 atm of approximately 0.3 (which is within the X_NBO range of the current experiment including CNAS melts) reported that the SiO₂ content of partial melts gradually increases with increasing pressure from approximately 51 wt % at 3 GPa to approximately 56 wt % at 20 GPa (44). Although the result is partly due to the changes in equilibrium mineral assemblages and chemical compositions of minerals, the change in configurational thermodynamic properties of the melts due to pressure-induced changes in connectivity contribute to these changes.

The (∂X_NBO/∂P^′)_T can be useful for predicting the solubility () of elements and volatiles into silicate melts. Microscopically, is affected by the excess energy needed to incorporate specific elements into the melt at high pressure () that is a complex function of the atomic configurations around m and their mutual interactions as a function of composition, temperature, and pressure. Together with (∂X_NBO/∂P^′), the effect of composition, particularly X_NBO on [i.e., ] and terms should be known to predict with pressure (see SI Appendix). The variation in with pressure for positive and negative is also shown in Fig. 4B. is expected to increase with an increase in pressure for positive and vice versa. The situation with a negative value of may explain the solubility of CO₂ in silicate melts (): Previous experimental studies showed that increases with increasing X_NBO [i.e., ] (ref. 3, and references therein). Because (∂X_NBO/∂P^′) for silicate melts is negative, the sign of () is expected to be negative and thus tends to increase with increasing pressure. As the maximum Ar solubility increases with an increase in SiO₂ (a decrease in X_NBO) from less than 1% for MgSiO₃ melts up to 5% for pure SiO₂ melts at 1 atm, is positive. Taking into consideration of negative (∂X_NBO/∂P^′) for silicate melts, Ar solubility is expected to increase with a decrease in X_NBO and an increase in pressure (7) (see SI Appendix).

Although the (∂X_NBO/∂P^′)_T can play an essential role on the solubility, it should be noted that the densification of silicate melts stems from changes in short-range structures (SRS) [g_SRS(r), coordination number and/or X_NBO], the topological-medium-range order (bond angle and lengths), and intermediate range structures in the 1- to 2-nm range [g_MRS(r)]. Both g_SRS(r) and g_MRS(r) should be further investigated to fully describe the observed trend in melt properties including an abrupt drop in the solubility of Ar into melts at high pressure (7). For instance, a previous experimental study for MgSiO₃ melts suggested the formation of triply coordinated oxygen cluster at high pressure (45, 46). The formation of an oxygen tricluster and associated changes in g_MRS(r) in the silicate melt at high pressure above 20 GPa play a role in bringing about pressure-induced changes in element solubility (45, 46) (see SI Appendix).

We note that because the structure of glasses quenched from melts at varying pressures was explored, the structure of the glasses studied here represents the atomic configurations of supercooled liquids at high pressure and at the glass transition temperature, below which the melt structure is frozen. The effect of temperature on (∂X_NBO/∂P)_T at high pressure is necessary to have improved understanding of the nature of melt polymerization above the melting temperature. At 1 atm, the effect of a fictive temperature on the X_NBO for diverse aluminosilicate melts was reported to be apparently minor (47). The sloped (∂X_NBO/∂P)_T thus derived from these supercooled liquids is likely to be representative of that in the melts themselves. Although the composition of the melts studied here has a similar NBO fraction at 1 atm with slab-derived melts and MORB compositions, primordial mantle melts (e.g., magma-ocean peridotite liquid has NBO/T = 2.5) are highly depolymerized, and the study of this melt composition at high pressure remains to be tested. Future experimental studies on glasses and melts in a wider range of composition are necessary to constrain the pronounced simplicity in melt densification at high pressure.

The presence of dense melts trapped at a pressure range of approximately 10–18 GPa (melt feeding zone) in early Earth has been suggested to account for hidden magmatic reservoirs with a primordial chemical signature (1). The satisfactory application of this proposal depends on the pressure-induced changes in the melt structure and properties. Melt density, a factor that plays a major role in the fate of the partial melts in the feeding zone, varies almost linearly with varying pressure from 10–18 GPa (1). On the basis of the above simple trend, the changes in melt solubility and activity coefficients of oxides due to changes in pressure-induced changes in melt polymerization may vary drastically at a normalized pressure range of 0.5–0.9 (and thus, the pressure ranges around approximately 0.5–0.9 × P_XNBO=0). Although the pressure-induced changes in the degree of polymerization in melt compositions for MORB and peridotite are not yet available, P_XNBO=0 tends to increase with decreasing SiO₂ content. At a P_XNBO=0 value of approximately 20, the effect of the degree of polymerization on melt properties may be significant at approximately 10–18 GPa around the melt feeding zone. Though speculative, the presence of silica-rich melts at high pressure due to a decrease in the activity coefficient of silica and the subsequent segregation of the melts in the early Earth may have partly contributed to the missing Si in the primitive mantle in addition to mechanisms involving partitioning of Si into core. Indeed, those partial melts, particularly from MORB, are reported to be Si-rich when the pressure is up to 27 GPa and the density of the melts was reported to be larger than the surrounding mantle around 12–13 GPa (44), implying possible segregation of melts as suggested for peridotite melts (1). Modeling with universality with high-resolution solid-state NMR thus sheds light on a unique opportunity to account for the unresolved nature of atomic structure of melts and microscopic origins of diverse thermodynamic and transport properties in the Earth’s interior. The current predictions imply the necessity to create a microscopically consistent future framework that can ultimately be used to understand the chemical evolution of the early Earth.