Simplicity in melt densification in multicomponentmagmatic reservoirs in Earth’s interior revealedby multinuclear magnetic resonanceSung Keun Lee1

School of Earth and Environmental Sciences, Seoul National University, Seoul, 151-742 Korea

Edited* by Ho-Kwang Mao, Carnegie Institution of Washington, Washington, DC, and approved March 14, 2011 (received for review January 4, 2011)

Pressure-induced changes in properties of multicomponent silicatemelts in magma oceans controlled chemical differentiation of thesilicate earth and the composition of partial melts that might haveformed hidden reservoirs. Although melt properties show complexpressure dependences, the melt structures at high pressure and theatomistic origins of these changes are largely unknown because oftheir complex pressure–composition dependence, intrinsic tomulti-component magmatic melts. Chemical constraints such as the non-bridging oxygen (NBO) content at 1 atm, rather than the structuralparameters formelt polymerization, are commonly used to accountfor pressure-induced changes in the melt properties. Here, weshow that the pressure-induced NBO fraction in diverse silicatemelts show a simple and general trend where all the reported ex-perimental NBO fractions at high pressure converge into a singledecaying function. The pressure-induced changes in the NBO frac-tion account for and predict the silica content, nonlinear variationsin entropy, and the transport properties of silicate melts in Earth’smantle. The melt properties at high pressure are largely differentfromwhat can be predicted for silicate melts with a fixed NBO frac-tion at 1 atm. The current results with simplicity in melt polymer-ization at high pressure provide a molecular link to the chemicaldifferentiation, possibly missing Si content in primary mantlethrough formation of hidden Si-rich mantle reservoirs.

Early in Earth history, during the magma-ocean phase, the che-mical differentiation of the silicate earth, formation of core,

and evolution of atmosphere were controlled by the properties ofsilicate melts at high pressure (1–6). Pioneering experimentalstudies show that these thermodynamic and transport propertiesrelevant to the chemical evolution of the Earth vary nonlinearlywith changes in pressure (7–9). For instance, the solubility of Arinto melts increases with increasing pressure and then decreasesdrastically with a further increase in pressure, with data suggest-ing a strong composition dependence (7, 10, 11). Similarly, com-plex behaviors were reported for the diffusivity and viscosity ofsilicate melts at high pressure (8). Although the trend in the silicaactivity in the melts at high pressure is not known, phase relationsof mantle melts and minerals imply varying activity coefficients ofthe oxide in silicate melts with changes in pressure (12–14).Changes of up to two orders of magnitude in the element parti-tioning coefficient between melts and crystal/coexisting phaseshave been reported stemming mostly from the effect of the meltcomposition, constraining the fate of radioactive nuclides in theEarth’s interior (15–18).

The key to understanding these nonlinear changes in meltproperties with pressure is the melt structure at high-pressurein a short- (e.g., coordination number) to medium-range scale(19–21).While recent progress inmineral physics provides the linkbetween the macroscopic properties and the structures of thecrystals, the nature of changes in the melt structure at high pres-sures, such as those deep within the magma-ocean, remain poorlyconstrained as detailed knowledge about the structure of meltscannot be determined based on their compositions alone. Evenmore challenging is to unveil the structure of “multicomponent,”

and hence, natural silicate melts in the earth’s interior (22). Mostof the previous studies focused on the pressure-induced bondingtransition in simple model melts (e.g., from single component, toternary) (e.g., refs. 3, 23–26) and references therein). NMRspectra of simple melt compositions are subjected to less inhomo-geneous broadening due to a relatively small number of meltstructural components: For the quaternary oxide glasses, theexpected number of binary correlations is up to 16; inhomoge-neous broadening associated with such complexity obscures theotherwise useful structural information such as coordinationnumber and degree of melt polymerizations.

Although the degree of polymerization in melts originally de-scribes melt structures, the mole fraction of nonbridging oxygen[XNBO, NBO∕ðNBOþ bridging oxygen;BOÞ] at 1 atm can becalculated from the chemical composition of melts. Therefore,XNBO is often regarded as a chemical constraint from which otherproperties of melt structure are predicted. However, the XNBO athigh pressure varies with pressure with composition dependence(the Si∕Al ratio, fractions of alkali content, and types of network-modifying cations). The systematic relation between XNBO at highpressure and melt composition has not been available, limitingits usefulness in modeling the melt properties at high pressure.The simple predictive NBO fraction in the melt, if available, couldbe useful to yield the microscopic origins of melt properties.The advent of high-resolution, element-specific, multinuclearNMR techniques such as triple quantum magic angle spinning(3QMAS) NMR allows us to obtain previously unknown detailsof the pressure-induced structural changes in multicomponentmelts at high pressure (23, 27–29). Quaternary Ca-Na alumino-silicate (CNAS) melts is a model system for slab-driven magmaticmelts and midocean ridge basalts (MORBs) composition melts inthe Earth’s interior (30, 31) and provides insights into the struc-ture of complex primordial melts and magmatic reservoirs.

Results and DiscussionThe remarkable resolution among atomic configurations in thequaternary CNAS glasses quenched from melts at high pressureare shown in the multicomponent (Al-27, Na-23, O-17), two-dimensional 3QMASNMRspectra (Fig. 1). TheAl-27NMRspec-tra for the CNAS melts (Fig. 1, Left) show ½4�Al, ½5�Al, and ½6�Al at8 GPa, whereas ½4�Al is dominant (approximately 100%) at 1 atm(32). The fractions for ½4�Al, ½5�Al, and ½6�Al are approximately76.1%, 16.7%, and 7.1%, respectively (see SI Appendix). The peakwidth of the ½4�Al for 8-GPa glasses in theMAS dimension is largerthan that for 1 atm, suggesting an increase in the topologicaldisorder due to the Al-O bond length distribution with pressure.

Author contributions: S.K.L. designed research, performed research, contributed newreagents/analytic tools, analyzed data, and wrote the paper.

The author declares no conflict of interest.

*This Direct Submission article had a prearranged editor.1E-mail: sungklee@snu.ac.kr.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1019634108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1019634108 PNAS ∣ April 26, 2011 ∣ vol. 108 ∣ no. 17 ∣ 6847–6852

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The formation of highly coordinated Al leads to a change in thechemical connectivity (i.e., NBO and BO environments)

O-17 3QMAS NMR shows two distinct groups of NBOs[Na-NBOðNa-O-½4�SiÞ and a mixed cation NBO peak [fCa;Nag-O-½4�Si as labeled] and three BO clusters [½4�Si-O-½4�Al,½4�Si-O-½4�Si, and ½4�Al-O-½4�Al] for CNAS glasses at 1 atm (Fig. 1,Center), consistent with the previous assignments (32). At 8 GPa,a feature due to ½4�Si-O-½5;6�Al (at approximately −40 ppm in theisotropic dimension) is evident. There is no evidence for the for-mation of ½4�Si-O-½5;6�Si that would be observed at approximately−60 ppm in the isotropic dimension (21), suggesting that Al tendsto be highly coordinated, whereas Si remains 4-coordinated. Thechanges in the oxygen configuration in the CNASmelts with pres-sure thus stem mostly from the formation of ½5;6�Al. Although the½4�Al-O-½4�Al peak intensity apparently decreases with increasingpressure, the presence of the high energy cluster is evident at8 GPa, implying that the higher-energy cluster at 1 atm can bestable in an elevated pressure regime. The pressure-inducedchange in the Na-O bond distance is also revealed in the Na-233QMAS NMR spectra for the CNAS glass (Fig. 1, Right). Theposition of the main Na peak changes slightly with increasingpressure, and the trend suggests that the Na-O distance decreaseswith increasing pressure and changes the role of Naþ from net-work modifying to charge balancing around ½4�Si-O-½5;6�Al (33).

An additional structural evolution with pressure in the silicatemelts can be observed from the total isotropic projection (sum ofdata along the lines parallel to the y axis) of the 3QMAS spectra(Fig. 2). The XNBO at 1 atm obtained from the fitting and sub-sequent calibration of each peak in the isotropic projection ofO-17 3QMASNMR spectrum is approximately 28.8%, consistentwith the prediction from the composition (Fig. 2). The predictedfraction of NBO [Na-NBOþ fCa;Nag-NBO] at 8 GPa is approxi-mately 24.3% (see SI Appendix). The Na-23 chemical shift for themain peak moves to a higher frequency (a positive peak shift inthe isotropic dimension), confirming that the average Na-O dis-tance decreases with pressure. Unlike Al, ½5;6�Si species that wouldbe observed at approximately −150 ppm for ½5�Si and approxi-mately −200 ppm for ½6�Si are not detected in the Si-29 MASNMR spectra of the glass at 8 GPa. The Si environment beyondits first coordination shell (i.e., Q species) in the glass may changewith increasing pressure, but such a change is not detected (Si-29MAS Inset, Fig. 2). Therefore, the pressure-induced Al coordina-tion transformation is responsible for the total decrease in NBO[i.e., ð∂XNBO∕∂PÞT ¼ −∂½5;6�Al∕∂PÞT ] in the CNAS melts. Be-cause of the importance of multicomponent melts, their previousinaccessibility at high pressure, and our demonstration of the

utility of multinuclear NMR for exploring their bonding natureat high pressure, the pressure-induced changes in multicompo-nent melts provide unique information about the densificationmechanism for natural melts in the Earth’s interior.

Pressure-induced changes in XNBO for silicate melts are shownin Fig. 3A where XNBO is scaled to be 100% at the reference pres-sure (P0, 1 atm) [ðXNBOðPÞ∕XNBOðP0Þ], which allows us to com-pare the available experimental data for silicate melts in a singleplot. In general, XNBO decreases slightly with increasing pressureat lower pressures but the magnitude of ð∂XNBO∕∂PÞT increaseswith a further increase in pressure, which seems universal regard-less of the melt composition. In detail, ð∂XNBO∕∂PÞT exhibits asignificant composition dependence. −ð∂XNBO∕∂PÞT is larger forsilicate melts with decreased alkali content (21, 34–37) (Fig. 3B)and is more significant for aluminosilicate with increasing degreeof polymerization at 1 atm (38, 39) (Fig. 3C). The pressure-in-duced changes in XNBO are also more significant with increasingcation field strength (e.g., charge∕ionic radius) for the network-modifying cations at the constant degree of polymerization at1 atm (27, 40) (Fig. 3D). Note that the pronounced pressure-induced changes in NBO fraction in the Al-free silicate melts re-sults from the coordination changes in Si (e.g., CNS, NS2, NS3,and NS4 melts in Fig. 3). The current results thus show thatthe pressure-induced changes in NBO fraction can be explainedwith single exponential function regardless of type of networkforming cations (Si or Al) in the melts fi:e:;ð∂XNBO∕∂PÞT ¼−∂½ð½5;6�Al and∕or ½5;6�SiÞ∕∂P�Tg. In general, a higher degree ofpolymerization of silicate melts at ambient pressure facilitate afurther polymerization of silicate melts at high pressures of upto approximately 10 GPa.

Taking into consideration the observed compositional depen-dences of melts at high pressure, we have found that XNBO can beexpressed as follows:

XNBOðPÞ ¼ XNBOðP0Þ�1 − exp

�P − PXNBO¼0

αPXNBO¼0

��; [1]

where α is a dimensionless scaling constant relevant to the degreeof rigidity of the network upon pressurization, describing the flex-ibility of melt network upon pressurization (41) (see SI Appendix).Pressure-induced structural changes become more abrupt (thenetwork is more rigid) with decreasing α. The experimental datacan be reproduced with α of approximately 0.2 without havingmuch compositional dependence (Fig. 3 B–E). PXNBO¼0 dependson melt composition and is a fictive pressure where XNBO insilicate melts is expected to be 0 if the trend in the NBO decaywould follow an exponential function: Although Eq. 1 with an

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Fig. 1. Multinuclear (Al-27, O-17, andNa-23)3QMAS NMR spectra for [ðNa2O0.75CaO0.25Þ3Al2Si4O11] (CNAS) glasses quenched at 1 atmand 8 GPa. Contour lines are drawn at 5% in-tervals 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.

6848 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019634108 Lee

exponential decaying function is rather phenomenological, thetrend in Eq. 1 is consistent with a recent model consideringthe distribution of local energy minima in the energy landscapefor oxide glasses, particularly at lower pressure ranges where theconceptual meaning for PXNBO¼0 and α can be determined (see SIAppendix). Fig. 3 B–E also shows the fitting results with the aboveequation where PXNBO¼0, ranging from 10 to 19 at α of approxi-mately 0.2. The α-value may deviate from the current value forthe silicate melt composition that is significantly different fromthe melts studied here. Uncertainties in PXNBO¼0 for most meltsare smaller than 0.5 GPa but increase with increasing PXNBO¼0

(e.g., approximately 1.5 GPa for NS3 melts and approximately2.5 GPa for NS2 melts; see SI Appendix). PXNBO¼0 accounts forthe observed trend in the effect of composition on ð∂XNBO∕∂PÞTand thus decreases with an increase in the alkali∕silica ratio andcation field strength in silicate glasses (27, 40). Ranges for PXNBO¼0

in melts is similar to the pressure ranges where melts are denserthan solids, forming trapped melts in the early Earth (1).

Upon introducing normalized pressure P0ð¼ P∕PXNBO¼0Þ,normalized NBO fractionX̄NBOðP0Þ½¼ XNBOðP0Þ∕XNBOðP0Þ� andits pressure dependence can be converged into a simple trendas follows:

X̄NBOðP0Þ ¼ 1 − exp�P0 − 1

α

�: [2]

ð∂X̄NBO∕∂P0ÞT ¼ − exp½ðP0 − 1Þ∕α�∕α: [3]

The above trend with remarkable simplicity may be regarded as auniversal behavior of the degree of polymerization in silicatemelts (Fig. 3F). Whereas previous experimental studies have

shown that XNBO decreases with pressure, it has been suggestedthat simple XNBO-P relations might be difficult to achieve (21,40). The current results demonstrate that the complex effectof composition and pressure on melt structure can be greatly sim-plified. These structural changes play a role in the melt propertiesin the Earth’s interior. Below, the expected trends in the pressuredependence of the properties of CNAS melts are shown on thebasis of (∂XNBO∕∂PÞT . These properties are also scaled by thevalue at 1 atm with respect to the normalized pressure (i.e., P0)(Fig. 4). More detailed information of the predicted properties isgiven in SI Appendix.

The XNBO and its complex compositional dependence inð∂XNBO∕∂P0ÞT may account for the nonlinear variation of pres-sure-induced changes in viscosity and oxygen diffusivity (21).As the degree of polymerization for CNAS melts increases withpressure, the predicted viscosity tends to decrease, but it then in-creases with a substantial decrease inXNBO with a further increasein pressure (Fig. 4A). Oxygen diffusivity and bulk viscosity areexpected to be anticorrelated for the CNAS melts studied hereassuming the Stokes–Einstein relationship, which is consistentwith the experimental trend for partially depolymerized melts(8). Basedon theAdam–Gibbs theory, the configurational entropy(Sconfig) of CNAS melts is expected to show a similar pressuredependence with diffusivity (42). A part of Sconfig in the meltsat high pressure may be calculated independently by consideringthe mixing of oxygen clusters. The calculated Sconfig for the qua-ternary CNAS melts due to the oxygen cluster mixing increaseswith increasing pressure below 10 GPa and then decreases witha further increase in pressure, consistent with the suggestion from

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Na-23 Si-29

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Fig. 2. Total isotropic projection ofmultinuclear Al-27, O-17, Na-233QMAS NMR spectra for the CNASglass quenched from melts at 1and 8 GPa. Fitting results for CNASglass using 4 Gaussians representingNa-NBO, Mixed-NBO, ½4�Si-O-½4�Si,and ½5;6�Si-O-½4�Si are shown as la-beled (Top Right). The Si-29 MASNMR spectrum for the glass is alsoshown (Bottom Right).

Lee PNAS ∣ April 26, 2011 ∣ vol. 108 ∣ no. 17 ∣ 6849

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the pressure-induced changes in melt viscosity (Fig. 4A). Theresults indicate that a certain aspect of Sconfig in silicate meltsincreases 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 multicomponentsilicate magmas is affected by the activity coefficients of oxidestherein as well as activity of mineral phases in equilibrium withmelts. The fraction of S-O-Si (XSi-O-Si) in the melts is roughly pro-portional to the square root of activity coefficient of SiO2 (γmelt

SiO2)

in simple silicate melts (43). With increasing pressure, XNBO andXSi-O-Si (among BO clusters) decrease because of an increase inSi-O-½5;6�Al. γmelt

SiO2due to Si∕½4;5;6�Al mixing should thus decrease

with increasing pressure (Fig. 4B). The trend in γmeltSiO2

with pressuresuggests that the composition of melts tends to be more silica-richat high pressure. Although earlier high-pressure melting experi-ments for peridotite (KLB-1) showed that the SiO2 content ofpartial melts does not vary with pressure up to 18 GPa (12),the high-pressure melting experiment for MORB with XNBO of

at 1 atm of approximately 0.3 (which is within the XNBO rangeof the current experiment including CNAS melts) reported thatthe SiO2 content of partial melts gradually increases with increas-ing pressure from approximately 51 wt % at 3 GPa to approxi-mately 56 wt % at 20 GPa (44). Although the result is partlydue to the changes in equilibrium mineral assemblages and che-mical compositions of minerals, the change in configurationalthermodynamic properties of the melts due to pressure-inducedchanges in connectivity contribute to these changes.

The ð∂XNBO∕∂P0ÞT can be useful for predicting the solubility(θmmelt) of elements and volatiles into silicate melts. Microscopi-cally, θmmelt is affected by the excess energy needed to incorpo-rate specific elements into the melt at high pressure (Gxs;melt

m ) thatis a complex function of the atomic configurations around m andtheir mutual interactions as a function of composition, tempera-ture, and pressure. Together with (∂XNBO∕∂P0), the effect of com-position, particularly XNBO on Gxs;melt

m [i.e., ð∂Gxs;meltm ∕∂XNBOÞT ]

and ½∂Gxs;meltm ∕∂X ½5;6�ðAl;or SiÞ�T terms should be known to predict

Fig. 3. (A) Variation in the normalized nonbridgingoxygen fraction with pressure in binary, ternary, andquaternary aluminosilicate glasses {alkali silicateglasses (black circle, Na2O∶SiO2 ¼ 1∶2, NS2 (37); bluesquare, Na2O∶SiO2 ¼ 1∶3, NS3 (21); red open circle,Na2O∶SiO2 ¼ 1∶4, NS4 (35)], ternary mixed cation si-licates, (black square, Na2O∶CaO∶SiO2 ¼ 0.75∶0.25∶3, CNS) (40), depolymerized aluminosilicateglasses (black triangle, Na2O∶Al2O3∶SiO2 ¼ 1.5∶0.5∶60, NAS4 (21); open triangle, Na2O∶Al2O3∶SiO2 ¼ 1.5∶0.5∶20, NAS1 (39)], and CNAS glass (dia-mond)} as labeled. The fractions of NBO in theNAS melts were modified only on the basis ofthe Al-coordination environment and thus a littlebit different from the trend shown in our previousreport (21). The thick curves show the trend lines con-necting experimental data, which are drawn forvisual clarity. (B) Effect of the composition (Na∕Si)on normalized NBO fraction in binary alkali silicatemelts (37). (C) Effect of degree of polymerizationat 1 atm on normalized NBO fraction in aluminosili-cate melts. (D) Effect of cation field strength of net-work-modifying cation on normalized NBO fractionat a constant degree of polymerization at 1 atm.Simulation results of the normalized nonbridgingoxygen fraction for diverse silicate melts at high pres-sure using Eq. 1 (the thin and dotted curves) withvarying PXNBO¼0 from 10 to 19 as labeled [at constantα of 0.2 except that for NAS1 (α ¼ 0.16) and NS2(α ¼ 0.18)]. Uncertainty of α is estimated to less than0.05. (E) Normalized NBO fraction in silicate meltswith pressure. (F) Variation in the normalized non-bridging oxygen cluster population with normalizedpressure. Thick red line refers to a trend line based onEq. 2 at α of 0.2.

6850 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019634108 Lee

θmmelt with pressure (see SI Appendix). The variation in θm

melt

with pressure for positive and negative ð∂Gxs;meltm ∕∂XNBOÞT is also

shown in Fig. 4B. θmmelt is expected to increase with an increase inpressure for positive ð∂Gxs;melt

m ∕∂XNBOÞT and vice versa. The si-tuation with a negative value of ð∂Gxs;melt

CO2∕∂XNBOÞT may explain

the solubility of CO2 in silicate melts (θCO2

melt): Previous experi-mental studies showed that θCO2

melt increases with increasingXNBO [i.e., ð∂Gxs;melt

CO2∕∂XNBOÞT < 0] (ref. 3, and references there-

in). Because (∂XNBO∕∂P0) for silicate melts is negative, the sign of(∂θCO2

melt∕∂P0) is expected to be negative and thus θCO2

melt tendsto increase with increasing pressure. As the maximum Ar solubi-lity increases with an increase in SiO2 (a decrease in XNBO) fromless than 1% for MgSiO3 melts up to 5% for pure SiO2 melts at1 atm, ð∂Gxs;melt

Ar ∕∂XNBOÞT is positive. Taking into consideration ofnegative (∂XNBO∕∂P0) for silicate melts, Ar solubility is expectedto increase with a decrease in XNBO and an increase in pressure(7) (see SI Appendix).

Although the ð∂XNBO∕∂P0ÞT can play an essential role on thesolubility, it should be noted that the densification of silicatemelts stems from changes in short-range structures (SRS)[gSRSðrÞ, coordination number and/or XNBO], the topological-medium-range order (bond angle and lengths), and intermediaterange structures in the 1- to 2-nm range [gMRSðrÞ]. Both gSRSðrÞand gMRSðrÞ should be further investigated to fully describe theobserved trend in melt properties including an abrupt drop inthe solubility of Ar into melts at high pressure (7). For instance,

a previous experimental study for MgSiO3 melts suggested theformation of triply coordinated oxygen cluster at high pressure(45, 46). The formation of an oxygen tricluster and associatedchanges in gMRSðrÞ in the silicate melt at high pressure above20 GPa play a role in bringing about pressure-induced changesin element solubility (45, 46) (see SI Appendix).

We note that because the structure of glasses quenched frommelts at varying pressures was explored, the structure of theglasses studied here represents the atomic configurations ofsupercooled liquids at high pressure and at the glass transitiontemperature, below which the melt structure is frozen. The effectof temperature on ð∂XNBO∕∂PÞT at high pressure is necessary tohave improved understanding of the nature of melt polymeriza-tion above the melting temperature. At 1 atm, the effect of afictive temperature on the XNBO for diverse aluminosilicatemelts was reported to be apparently minor (47). The slopedð∂XNBO∕∂PÞT thus derived from these supercooled liquids islikely to be representative of that in the melts themselves.Although the composition of the melts studied here has a similarNBO fraction at 1 atm with slab-derived melts and MORB com-positions, primordial mantle melts (e.g., magma-ocean peridotiteliquid has NBO∕T ¼ 2.5) are highly depolymerized, and thestudy of this melt composition at high pressure remains to betested. Future experimental studies on glasses and melts in awider range of composition are necessary to constrain the pro-nounced simplicity in melt densification at high pressure.

The presence of dense melts trapped at a pressure range ofapproximately 10–18 GPa (melt feeding zone) in early Earthhas been suggested to account for hidden magmatic reservoirswith a primordial chemical signature (1). The satisfactory appli-cation of this proposal depends on the pressure-induced changesin the melt structure and properties. Melt density, a factor thatplays a major role in the fate of the partial melts in the feedingzone, varies almost linearly with varying pressure from 10–18 GPa(1). On the basis of the above simple trend, the changes in meltsolubility and activity coefficients of oxides due to changes inpressure-induced changes in melt polymerization may vary dras-tically at a normalized pressure range of 0.5–0.9 (and thus,the pressure ranges around approximately 0.5–0.9 × PXNBO¼0).Although the pressure-induced changes in the degree of polymer-ization in melt compositions for MORB and peridotite are not yetavailable, PXNBO¼0 tends to increase with decreasing SiO2 con-tent. At a PXNBO¼0 value of approximately 20, the effect of thedegree of polymerization on melt properties may be significantat approximately 10–18 GPa around the melt feeding zone.Though speculative, the presence of silica-rich melts at high pres-sure due to a decrease in the activity coefficient of silica and thesubsequent segregation of the melts in the early Earth may havepartly contributed to the missing Si in the primitive mantle in ad-dition to mechanisms involving partitioning of Si into core.Indeed, those partial melts, particularly from MORB, are re-ported to be Si-rich when the pressure is up to 27 GPa and thedensity of the melts was reported to be larger than the surround-ing mantle around 12–13 GPa (44), implying possible segregationof melts as suggested for peridotite melts (1). Modeling withuniversality with high-resolution solid-state NMR thus sheds lighton a unique opportunity to account for the unresolved natureof atomic structure of melts and microscopic origins of diversethermodynamic and transport properties in the Earth’s interior.The current predictions imply the necessity to create a microsco-pically consistent future framework that can ultimately be used tounderstand the chemical evolution of the early Earth.

Materials and MethodsO-17 enriched Ca-Na aluminosilicate glasses (CNAS, ½ðNa2OÞ0.75ðCaOÞ0.25�3Al2Si4O11, Na2O∶CaO∶Al2O3∶SiO2 ¼ 26.2∶8.2∶19.3∶46.3 wt %) were synthe-sized from carbonates (CaCO3 and Na2CO3) and oxides (Al2O3- and 17O-en-riched SiO2 obtained from the hydrolysis of 40% 17Owater with SiCl4). 0.2 wt% of Co oxide was added to reduce the spin-lattice relaxation time. The mix-

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mmelt

E0/T=-20

Fig. 4. (A) Effect of normalized pressure on the viscosity, oxygen diffusivity,and configurational entropy due to oxygen cluster mixing in the silicate meltswith XNBOð1 atmÞ ¼ 0.285 and PXNBO¼0 ¼ 15 GPa (red curve). The plots forviscosity and diffusivity are also based on the relations for pressure-depen-dent E0

NBO½¼ 150∕PXNBO¼0 þ 1.4P0 � and E0BO½¼ 300∕PXNBO¼0 − 2.8P0 �. Note that

these modeling parameters are only for a semiquantitative analysis for thetrend of O2− diffusivity and viscosity. (B) The effect of the normalized pres-sure and the reduction of NBO on the solubility of elements (dashed curve)and the activity coefficient of silica in silicate melts (solid black curve). Theformer was calculated with varying E0½¼ ð∂Gxs;melt

m ∕∂XNBOÞT �∕T value(kJ∕mol·K) ranging from −20 to 50.

Lee PNAS ∣ April 26, 2011 ∣ vol. 108 ∣ no. 17 ∣ 6851

GEO

LOGY

ture was decarbonated and heated at 1,673 K and then quenched. A negli-gible weight loss was measured. The resulting CNAS glass was loaded in amultianvil apparatus with an 18∕11 (octahedron edge length∕truncatededge length of the anvils) assembly at the Geophysical Laboratory. The CNASglass was then fused at 2,100 K for approximately 10 min, and the melt wasquenched to glasses at 8 GPa. The cooling rate was estimated to be approxi-mately 500 °C∕s in the first 1–2 s. The decompression rate in the experimentwas typically approximately 2.78 × 10−4 GPa∕s, or approximately 1 GPa∕h.Note that the time scale of melt quenching into glasses was much faster thanthe relaxations in the macroscopic high-pressure cell, indicating isobaricquench condition. The CNAS glass composition was studied previously at1 atm, yielding a good resolution among the peaks in the 17O 3QMASNMR spectra (32). The NBO∕T (nonbridging oxygen/tetrahedral cation) valueis approximately 0.67, similar to the degree of polymerization of tholeiiticmelts and MORB.

Multinuclear NMR spectra were collected on a Varian 400 solid-state NMRspectrometer at 9.4 Twith a 3.2-mm ZrO2 rotor in a Varian double-resonanceMAS probe at Seoul National University. O-17 3QMAS NMR were collected ata Larmor frequency of 54.23 MHz using an fast amplitude modulation-basedshifted-echo pulse sequence [3.3 μs-τ (delay)-0.7 μs-τ(delay)-15 μs] with therelaxation delay of 1 s and a magic-angle sample spinning speed of15 kHz. All spectra were referenced to tap water. Al-27 3QMAS NMR were

collected at a Larmor frequency of 104.3 MHz using a similar pulse sequence[3.3 μs-τ (delay)-0.7 μs-τ(delay)-15 μs] with the relaxation delay of 1 s and amagic-angle sample spinning speed of 15 kHz and were referenced to 0.3 MAlCl3 solution. The Na-23 3QMAS NMR spectra were collected at a Larmorfrequency of 105.3 MHz using shifted-echo pulse sequences [4 μs—delay—3 μs—echo delay (approximately 0.5–0.8 ms)—15 μs] with a phase table with96 cycles, which is suitable for the selection of the entire echo for spin-3/2nuclides. The spinning speed was 15 kHz with a recycle delay of 1 s withan external reference of 0.3 M NaCl solution. One-dimensional Si-29 MASNMR spectra for the CNAS glasses were collected at a Larmor frequencyof 79.4 MHz with a single 30° pulse of 0.6 μs and the relaxation delay of30 s and a magic-angle sample spinning speed of 11 kHz. All spectra werereferenced to tetramethylsilane solution.

ACKNOWLEDGMENTS.We thank Y. Fei, G. D. Cody, and J. Lin for discussionsand help with high-pressure synthesis and two anonymous reviewers forconstructive suggestions. Part of the cited NMR experiments was per-formed at the W. M. Keck Solid State NMR facility, which received supportfrom the W. M. Keck Foundation and the National Science Foundation(Cody). This study was supported by Grant 2007-000-20120 from theNational Research Foundation, Korea (to S.K.L.).

1. Lee CTA, et al. (2010) Upside-down differentiation and generation of a ‘primordial’lower mantle. Nature 463:930–U102.

2. Mookherjee M, Stixrude L, Karki B (2008) Hydrous silicate melt at high pressure.Nature 452:983–986.

3. Mysen BO, Richet P (2005) Silicate Glasses andMelts: Properties and Structure (Elsevier,Amsterdam) p 560.

4. Sakamaki T, Suzuki A, Ohtani E (2006) Stability of hydrous melt at the base of theEarth’s upper mantle. Nature 439:192–194.

5. Stixrude L, Karki B (2005) Structure and freezing of MgSiO3 liquid in Earth’s lowermantle. Science 310:297–299.

6. Tonks WB, Melosh HJ (1993) Magma ocean formation due to giant impacts. J GeophysRes-Planet 98:5319–5333.

7. Bouhifd MA, Jephcoat AP (2006) Aluminum control of argon solubility in silicate meltsunder pressure. Nature 439:961–964.

8. Poe BT, et al. (1997) Silicon and oxygen self-diffusivities in silicate liquids measured to15 Gigapascals and 2800 Kelvin. Science 276:1245–1248.

9. Wolf GH, McMillan PF (1995) Pressure effects on silicate melt structure and properties.Structure, Dynamics, and Properties of SilicateMelts, eds JF Stebbins, PF McMillan, andDB Dingwell (Mineralogical Society of America, Washington, DC), Vol 32, pp 505–562.

10. Carroll MR, Stolper EM (1993) Noble-gas solubilities in silicate melts and glasses—Newexperimental results for argon and the relationship between solubility and ionicporosity. Geochim Cosmochim Acta 57:5039–5051.

11. Chamorro-Perez E, Gillet P, Jambon A, Badro J, McMillan P (1998) Low argon solubilityin silicate melts at high pressure. Nature 393:352–355.

12. Herzberg C, Zhang JZ (1996) Melting experiments on anhydrous peridotite KLB-1:Compositions of magmas in the upper mantle and transition zone. J GeophysRes-Sol Ea 101:8271–8295.

13. Baker MB, Hirschmann MM, Ghiorso MS, Stolper EM (1995) Compositions of near-solidus peridotite melts from experiments and thermodynamic calculations. Nature375:308–311.

14. Ohtani E, Kato T, Sawamoto H (1986) Melting of a model chondritic mantle. Nature322:352–353.

15. Kohn SC, Schofield PF (1994) The importance of melt composition in controllingtrace-element behavior—an experimental-study of Mn and Zn partitioning betweenforsterite and silicate melts. Chem Geol 117:73–87.

16. Mysen BO (2004) Element partitioning between minerals and melt, melt composition,and melt structure. Chem Geol 213:1–16.

17. Murthy VR, van Westrenen W, Fei Y (2003) Experimental evidence that potassium is asubstantial radioactive heat source in planetary cores. Nature 423:163–165.

18. Walter MJ (1995) Partitioning of tungsten and molybdenum between metallic liquidand silicate melt. Science 68:1186–1189.

19. Spera FJ, Nevins D, Ghiorso M, Cutler I (2009) Structure, thermodynamic and transportproperties of CaAl2Si2O8 liquid. Part I: Molecular dynamics simulations. GeochimCosmochim Acta 73:6918–6936.

20. Allwardt JR, et al. (2007) Effect of structural transitions on properties of high-pressure silicate melts: Al-27 NMR, glass densities, and melt viscosities. Am Mineral92:1093–1104.

21. Lee SK, Cody GD, Fei Y, Mysen BO (2004) The nature of polymerization and propertiesof silicate glasses and melts at high pressure. Geochim Cosmochim Acta 68:4189–4200.

22. Guillot B, Sator N (2007) A computer simulation study of natural silicate melts. Part II:High pressure properties. Geochim Cosmochim Acta 71:4538–4556.

23. Stebbins JF, Xu Z (1997) NMR evidence for excess non-bridging oxygen in aluminosi-licate glass. Nature 390:60–62.

24. Lin JF, et al. (2007) Electronic bonding transition in compressed SiO2 glass. Phys Rev B75:012201.

25. MurakamiM, Bass JD (2010) Spectroscopic evidence for ultrahigh-pressure polymorph-ism in SiO2 glass. Phys Rev Lett 104:025504.

26. Lee SK, et al. (2005) Probing of bonding changes in B2O3 glasses at high pressure withinelastic x-ray scattering. Nat Mater 4:851–854.

27. Kelsey KE, et al. (2009) Cation field strength effects on high pressure aluminosilicateglass structure: Multinuclear NMR and La XAFS results. Geochim Cosmochim Acta73:3914–3933.

28. Lee SK, Mibe K, Fei Y, Cody GD, Mysen BO (2005) Structure of B2O3 glass at high pres-sure: B-11 solid-state NMR study. Phys Rev Lett 94:165507.

29. Lee SK (2010) Effect of pressure on structure of oxide glasses at high pressure: Insightsfrom solid-state NMR of quadrupolar nuclides. Solid State Nucl Mag 38:45–57.

30. Coltorti M, Beccaluva L, Bonadiman C, Salvini L, Siena F (2002) Glasses in mantlexenoliths as geochemical indicators of metasomatic agents. Earth Planet Sci Lett183:303–320.

31. Robinson JAC, Wood BJ, Blundy JD (1998) The beginning of melting of fertile anddepleted peridotite at 1.5 GPa. Earth Planet Sci Lett 155:97–111.

32. Lee SK, Cody GD, Mysen BO (2005) Structure and the extent of disorder in quaternary(Ca-Mg and Ca-Na) aluminosilicate glasses and melts. Am Miner 90:1393–1401.

33. Xue X, Stebbins JF (1993) 23Na NMR chemical shifts and the local Na coordinationenvironments in silicate crystals, melts, and glasses. Phys Chem Miner 20:297–307.

34. Allwardt JR, Schmidt BC, Stebbins JF (2004) Structural mechanisms of compression anddecompression in high pressure K2Si4O9 glasses: An investigation utilizing Raman andNMR spectroscopy of high-pressure glasses and crystals. Chem Geol 213:137–151.

35. Lee SK, Cody GD, Fei Y, Mysen BO (2006) The effect of Na∕Si on the structure of sodiumsilicate and aluminosilicate glasses quenched from melts at high pressure: A multi-nuclear (Al-27, Na-23, O-17) 1- and 2D solid-state NMR study. Chem Geol 229:162–172.

36. Lee SK, Fei Y, Cody GD, Mysen BO (2003) Order and disorder of sodium silicate glassesand melts at 10 GPa. Geophys Res Lett 30:1845.

37. Xue X, Stebbins JF, Kanzaki M (1994) Correlations between O-17 NMR parameters andlocal structure around oxygen in high-pressure silicates and the structure of silicatemelts at high pressure. Am Miner 79:31–42.

38. Yarger JL, et al. (1995) Al coordination changes in high-pressure aluminosilicateliquids. Science 270:1964–1967.

39. Yi YS, Lee SK (2010) The pressure-induced structural changes in silicate glasses at highpressure: Insights from solid-state NMR and first-principle calculations. GeochimCosmochim Acta 74(12):A1185.

40. Lee SK, Cody GD, Fei YW, Mysen BO (2008) Oxygen-17 nuclear magnetic resonancestudy of the structure of mixed cation calcium-sodium silicate glasses at high pressure:Implications for molecular link to element partitioning between silicate liquids andcrystals. J Phys Chem B 112:11756–11761.

41. Lee SK, Eng P, Mao HK, Shu JF (2008) Probing and modeling of pressure-inducedcoordination transformation in borate glasses: Inelastic x-ray scattering study at highpressure. Phys Rev B 78:214203.

42. Richet P (1984) Viscosity and configurational entropy of silicate melts. GeochimCosmochim Acta 48:471–483.

43. Lee SK (2005) Microscopic origins of macroscopic properties of silicate melts: Implica-tions for melt generation and dynamics. Geochim Cosmochim Acta 69:3695–3710.

44. Yasuda A, Fujii T, Kurita K (1994) Melting phase-relations of an anhydrous mid-oceanridge basalt from 3 to 20 GPa—implications for the behavior of subducted oceanic-crust in the mantle. J Geophys Res-Sol Ea 99:9401–9414.

45. Karki BB, Bhattarai D, Mookherjee M, Stixrude L (2010) Visualization-based analysis ofstructural and dynamical properties of simulated hydrous silicate melt. Phys ChemMiner 37:103–117.

46. Lee SK, et al. (2008) X-ray Raman scattering study of MgSiO3 glass at high pressure:Implication for triclustered MgSiO3 melt in Earth’s mantle. Proc Natl Acad Sci USA105:7925–7929.

47. Stebbins JF, Dubinsky EV, Kanehashi K, Kelsey KE (2008) Temperature effects onnon-bridging oxygen and aluminum coordination number in calcium aluminosilicateglasses and melts. Geochim Cosmochim Acta 72:910–925.

6852 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019634108 Lee