American Mineralogist, Volume 70, pages 332-343, 1985

High-resolution 2esi NMR study of silicate and aluminosilicate glasses:the effect of network-modifying cations

Jm,res B. Mr;noocn.t JoNlrneN F. SrsssrNs

Earth Sciences DiuisionLawrence Berkeley Laboratory, Berkeley, Califurnia 94720

,lNo Ltrr S. E. Canmcrnrr,2

Department of Geology and GeophysicsUniuersity of Califurnia, Berkeley, California 94720

Abotract

The effect of network-modifflng alkali and alkaline-earth cations on the degree of poly-merization in silicate glasses is investigated using 2eSi magic-angle spining NMR. The NMRlinewidth is found to increase (reflecting a broader range of silicate environments) as thepolarizing power of the cation increases. A similar effect occurs in three-dimensional frame-work aluminosilicate glasses: smaller, more highly charged cations create greater variety inthe distribution of silicate and aluminate tetrahedra. Linewidths as a function of the silicon-to-aluminum ratio suggest, however, that Loewenstein's aluminum avoidance principle islargely obeyed. Spectra of three natural silicic glasses are analyzed in terms of the Si/Al ratioand the concentration of paramagnetic species.

Introduction

The structure of silicate glasses is of interest not onlywith regard to their commercial applications but also inthat they are frozen approximations of silicate melts, forwhich a detailed knowledge of silicate speciation is neededto better understand magmatic processes. As such, silicateglasses have been studied using a variety of techniques,notably SiKp X-ray absorption (de Jong et al., 1981), X-rayradial distribution functions (RDF's) (Konnert and Karle,1973;Taylor and Brown, l97la,1979b), laser Raman spec-troscopy (e.g., Brawer and White, 1975; Mysen et al., 1982;McMillan, 1984a; Matson et al., 1983), and nuclear mag-netic resonance (NMR) spectroscopy (Holzman et al., 1956;Mosel et al., 1974; Harris and Bray, 1980; de Jong andSchramm, 1981; Lippmaa et al., 1982; Kirkpatrick et al.,1982;de Jong et al., 1983).

In nuclear magnetic resonance spectroscopy, a nucleuswith non-zero spin is used as a sensitive probe of its localelectronic environment. The most useful parameter ob-tained is the chemical shift (or shielding) whichcharacterizes the degree to which nearby electrons shieldthe probe nucleus from a large external magnetic field.Nuclei in different bonding sites or environments areshielded differently and hence absorb energy at differentfrequencies.

In a polycrystalline solid, however, spectral features arebroadened by the orientational anisotropy of chemicalshielding and by interactions between nuclei. By rapidly

I Present address: Technicare Corporation, P.O. Box 5130,Cleveland, Ohio,f4101.

2 Reprint requests should be addressed to I.S.E. Carmichael.0003-o04x/85/0d++$zsoz.oo 332

spinning a powdered sample at the magic ang)e, 54.7", rela-tive to the external magnetic field, the broadened lineshapebreaks up into a center peak located at the isotropic chemi-cal shift plus a series of spinning sidebands spaced at therotational frequency, typically l-4 kHz (Andrew, l97l;Maricq and Waugh, 1979). For crystalline samples, side-band intensities can be analyzed to obtain the principalvalues of the chemical shielding tensor (Maricq andWaugh, 1979; Herzfeld and Berger, 1980; Smith et al.,1983), but are often made negligible by spinning rapidlycompared to the static linewidth expressed in Hz. One canobtain wellresolved spectra of isotropic chemical shifts,similar to NMR spectra commonly obtained from liquids.

At least four magnetically active nuclei have been used instudying silicate minerals with magic-angle spinning (MAS)NMR: silicon-29, aluminum-27, sodium-23, and oxygen-l7.Of these, 2"Si has the advantage that its spectra are intrin-sically better resolved. Unlike 2esi, the other three nucleiwith spin | > U2 have a quadrupolar charge distributionand hence are affected by local electric field gradients(Abragam, 1961, Chap. 6). In a polycrystalline sample, thisnuclear quadrupole interaction gives rise to a broadeningof the center MAS peak that cannot be removed by magic-angle spining. The broadening can be so severe for nuclei(such as 21 All in distorted sites that no measurable NMRsignal is obtained (de Jong et al., 1983). In contrast, thewidth of a 2esi MAS NMR peak for a non-paramagneticglassy sample reflects merely the range of isotropic shiltstherein, and the spectrum can provide a quantitative mea-sure of relative site populations if the delay betwcen suc-cesive rf pulses is long enough to allow all relevant nucleito fully equilibrate.

MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GLASSES 333

A second virtue of 2esi NMR spectroscopy is that iso-tropic chemical shifts vary systematically as a function ofsilicate structure. Lippmaa et al. (1980) first observed dis-tinct 2esi chemical shift ranges for different types of silicatestructural units in crystalline materials, specifically, that asilicon nucleus is deshielded (and its chemical shift d mea-sured relative to a tetramethylsilane standard becomes lessnegative) as the number of attached Si-O-Si bridging oxy-gens decreases. Later measurements (Smith et al., 1983;Grimmer et al., 1983b, 1983c; Miigi et al., 1984) on a largerand more varied collection of silicates indicated an appreci-able overlap of the isotropic chemical shift ranges associ-ated with different Q" species, where Qn is short for anS(O-Si), (O-M)o-" unit (Engelhardt et al., 1975). (Here nis the number of bridging oxygens; 4 - n is the number ofnon-bridging oxygens, which serve to coordinate anetwork-modifying cation M.)

The silicon chemical shift is also affected by the numberof adjacent aluminate tetrahedra. In tectosilicates (Qaunits), for example, silicon nuclei are deshielded and 6 be-comes less negative as the number of neighboring alu-minum atoms increases from zero to four (changing typi-cally by - 5 ppm per Si-O-Al linkage). Table 1 lists theexperimentally determined chemical shift ranges associatedwith each of these species, as compiled by Thomas et al.(1983b). The reasonably good separation in these shiftranges has greatly facilitated the study of silicon-aluminumordering in zeolites (Lippmaa et al., 1981., Klinowski et al.,1982; Thomas et al., 1983b).

Additionally, isotropic silicon chemical shifts have beencorrelated with a number of more general crystalline struc-tural parameters. The value of 6 becomes more negativewith a decrease in the average Si-O bond length (Higginsand Woessner, 1982), an increase in the total cation-oxygen bond strengths for all the oxygens in the silicatetetrahedron (Smith et al., 1983), and for tectosilicates, anincrease in the average Si-O-Si bond angle (Smith andBalckwell, 1983; Thomas et al., 1983a); (Ramdas and Klin-owski, 1984). A similar dependence on the Si-O-Si bondangle has been found for the 2eSi chemical shift in a seriesof sorosilicates with distinct Si2O9- anions (Grimmer etal.. 1983b).

In this paper, isotropic 2eSi chemical shifts from MAS

Table 1 lsotropic 2eSi chemical shift ranges (relative to TMS) for

Qa units in crystalline aluminosilicates*

S i l i c a t e s p e c i e s Range of d values (ppm)

spectra will be used to investigate the range of silicon envi-ronments in glasses, specifically the degree of poly-merization in disilicate and metasilicate glasses, the vari-ation in Si-O-Si bond angles in silica glass, and the distri-bution of silicate and aluminate tetrahedra in three-dimensional framework aluminosilicate glasses.

Experimental

Sample preparation

Glasses were prepared from reagent grade alkali and alkalineearth carbonates and dehydrated silicic acid, and were fused andground several times to insure homogeneity. Wet chemical andelectron microprobe analyses indicate that the desired compo-sitions were obtained with the following exceptions, (which weconsider to be inconsequential to the results reported here): theBaSirO, sample contains approximately I wt."/. SrO, and theMgSiO, glass contains approximately 0.5 wt.% AlrOr.

To prevent crystallization, NaAlSiOn, CaSiOr, and MgSiO.glasses were quenched in water; liquid nitrogen was used for lith-ium and sodium disilicate glasses to prevent crystallization andpossible unmixing. Strontium disilicate glass was quenched bypouring the melt onto a graphite slab. The thick pieces that re-sulted in this composition were opalescent due to metastablephase separation during cooling. Smaller, more rapidly quenchedpieces were clear, and these were selected for NMR use. Otherglasses were quenched in air. The hygroscopic alkali silicateglasses were crushed for NMR work in an Nr-filled glove box andwere subsequently handled for only brief periods of time in air. Allsamples were stored in vacuum dessicators.

Samples of the alkali and alkaline earth disilicate glasses werecrystallized at 700'C for roughly 24 hours. MgSiO, glass wascrystallized at about 12100'C for several days. The crystalline ma-terial was therefore originally protoenstatite that transformed toclino- or possibly a mixture of clino- and ortho-enstatite onquench.

SpectroscopyAll spectra were recorded on a home-built Fourier transform

NMR spectrometer operating at 8.5 Telsa. Powdered sampleswere packed in alumina rotors and spun at roughly 3 kHz in amagic-angle spinning probe from Doty Scientific. (The angle wasadjusted by maximizing 127I rotational echoes from a sample ofNaI). From 190 to lo4() free induction decays were averaged to-gether for each glass; the rf pulse flip angle was approximately 32"and the delay between pulses was 120 sec unless noted otherwise.Silicon chemical shifts were measured relative to an externalsample of tetramethylsilane (TMS) and are reported to the nearest0.5 ppm.

Results and discussion

Alkali and alkaline earth silicote glasses

We first will consider the effects of alkali and alkalineearth cations on the network structure of disilicate andmetasilicate glasses. To interpret their MAS NMR spectra,we turn to the 2esi chemical shifts of related crystallinecompounds, listed in Table 2.In this restricted but relevantassemblage of silicates, chemical shift ranges are fairly wellseparated for different Qo species, changing by roughly tenppm with the conversion of each non-bridging oxygen(NBO) to a bridging one. Caution is of course required in

si (-0A1 ) 4si ( -oA1 ) 3

(-os i) 1

s i ( - o A l ) 2 ( - o s i ) 2

s i ( -oA1 ) 1 ( -os i )

3s i ( - 0 s i ) 4

- 8 0 t o - 9 0 . 5

-88 ro -97

- 9 3 r o - 1 0 2

- 9 7 . 5 t o - 1 0 7

- 1 0 1 . 5 r o - 1 1 6 . 5

* f r o m T h o n a s e t a l . ( 1 9 8 3 b )

334 MURDOCH ET AL: SILICATE AND ALUMINOSILICATE GLI4SSES

Table 2. Isotropic 2eSi chemical shifts for crystalline alkali andalkaline earth silicates and SiO, polymorphs

where SirO!-, SiO3-, and SiO2 refer to structural unitswith sheetlike, chainJike, and three-dimensional frame-work environments respectively.

More generally one can write

2e3=Q2 + e4, (2)

where only the relative number of bridging and non-bridging oxygens rather than an extended silicate geometryis specified (Matson et al., 1983). For metasilicate glasseslike MgSiOr, equilibria such as

2Q'z+Ql+ Q3

2Q2+Qo + Q4

can be envisaged.Different network-modifying cations are expected to shift

these glass equilibria to the left or to the right. To the leftimplies the same type of silicate polymerization as theyfound in the corresponding crystal, with a more-or-lessevenly spaced distribution of cations. To the right implies abunching of cations near those silicate units with extranon-bridging oxygens and a paucity of cations near thosewith fewer NBO's.

The 2esi MAS NMR spectra of potassium, sodium, andlithium disilicate glasses are displayed in Figure 2, those ofbarium and strontium disilicate glass in Figure 3, and thoseof the metasilicate glasses CaSiO., CaMgSi2Ou, andMgSiO3 in Figure 4. Each center peak is flanked by a pairor two of spinning sidebands, but the intensities of thesewill not be analyzed here. The Li2Si2O5 glass spectrum ismuch narrower than the one reported by de Jong andSchramm (1981) and more nearly resembles their partiallydevitrified Li2Si2O5 spectra. We have no indication, how-ever, that our glass has devitrified.

Three observations regarding the center peaks in Figures24 are immediately apparent. First, most of the peaks are

-2o -4o -""

u"'ttot"-'

-loo -izo -14o

Fig. 1. 2esi MAS NMR spectra of glassy and crysrallineMgSiOr. The full widths at half maximum are 22.7 and 0.8 ppmrespectively. The two peaks in the lower spectrum correspond totwo crystallographically distinct positions for silicon in clinoensta-tite (Ohashi and Finger, 1976).

S i 1 i c a ! e 6 (ppm fron Tl.tS) Reference** Polyrcrph

QO

Q3

Qo

q1

Q2

Mg2sio4

CaltCSiO4

L i . s 1 ^ 0 -

Na6S1207

c"3si2o7

Ca2MgS1207

MgSiO3

CaMgSi2O6

CaSiO3

Sr S iO3

BaSiO3

sio2

s i02

sio2

- 6 2

- 6 6

- 6 8 . 4

- 7 4 , 5 , - 7 6 . O

- 7 3

rank in i re

c l inoensEat i te

wo11a s ton i te

3

3

3

2(3)

(4)

L i 2 S i 2 o 5 - 9 2 . 5 1

N a 2 S i 2 O 5 - 9 4 . 5 I

K 2 S 1 2 O 5 - 9 1 . 5 ' - 9 3 ' - 9 4 . 5 1

B a S i 2 O 5 - 9 3 . 5 1

- 8 1 , - 8 3 . 5 r

-84 2

- 8 8 . 5 I

- 8 5 2

-80 2

- 1 0 7 . 1 4-108.5 4

- 1 0 8 . 1 , - 1 1 3 . 9 4

_ +

c r i s t o b a l i t e

al l synthet ic except CaSiO. ( from wl l1sboro, NY) aod thesi l ice oolvmorohs

I = r h i s w o r k ; 2 = S n i t h 4 a I . , 1 9 8 3 ; 3 = c r i m e r 4 a L , 1 9 8 3 b ;4 = Smith and Blackwel l . 1983

iassrned poly.orph based on devitr i f icat lon condlt ions

assigning specific Q" units on the basis of 2eSi chemicalshifts since the value of d can change by as much as 25ppm depending on Si-G-Si bond angles (Grimmer et al.,1983b). Nonetheless. if it is assumed that no radical differ-ence in bond angle distribution exists between glass andcrystal, the variation of silicate polymerization in glasses asa function of network-modifying cations can be estimatedfrom the crystalline chemical shift differences in Table 2.

There is a much broader range of silicate environmentsin a glass than in the corresponding crystalline material, asreflected in the MAS NMR spectra of enstatite (MgSiO., apyroxene with single chains of Q2 tetrahedra) and enstatiteglass in Figure 1. The width of the glass peak is due in partto variatioqs in Si-G-Si bond angles and Si-O bondlengths, these being a natural consequence of the lack oflong-range order. In addition, there is the possibility ofvariation in the number of non-bridging oxygens per sili-cate tetrahedron. Indeed, the MgSiO. glass peak en-compasses the entire chemcial shift range from Qo to Qaunits.

For disilicate glasses like NarSirOr, the following equi-librium has been proposed to describe the nature ofsilicatepolymerization (Virgo et al., 1980):

siro3-+sio3- + sio2, (1)

MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GL,4SSES 335

Fis. 2. 2esi r^, -r-";fi ";;'

o],,,,"",, grasses. rhedip in the left spinning sideband of KrSirO, is an artifact. Peakheights are normalized in this and subsequent figures.

featureless, with no distinct "bump" for each Q" species.This lack of structure results from the fact noted earlierthat the silicon chemical shift is sensitive to variations inbond lengths and angles as well as the degree of poly-merization. Only the spectra of sodium and lithium disili-cate glasses have noticeable shoulders. (Indeed, the onlyglass for which we have seen distinct Qn species isNarSirO", which contains an average of 3.5 bridging oxy-gens per Si. Its 2esi MAS spectrum contains two centralpeaks of roughly equal intensity at -92.5 and - 104.5ppm, the former with a sideband intensity pattern muchlike that of NarSirO, glass, the latter without sidebands.These peaks reflect the presence of well-defined Q3 and Qaunits. The sample, which is rapidly quenched and opticallyclear, is currently being examined for sub-microscopicphase separation).

Second, in each case the position of the peak maximumindicates that the dominant silicate species present in the

Fig. 3.glasses.

-20 -4 -60 -60 -ioo _r20 _r40Es (ccm)

2esi MAS NMR spectra of alkaline earth disilicate

-20 -@ -60 -60

6q tmm)

Fig. 4. 2eSi MAS NMR spectra of alkaline earth metasilicateglasses.

glass is the one found in the corresponding crystalline ma-terial, namely Q3 units in disilicates and Q2 units in metas-ilicates. This finding is consistent with previous MASNMR results (Kirkpatrick et al., 1982), with Raman work(Brawer and White, 1975; Mysen et al., 1983; Matson etal., 1983), with an RDF measurement on NarSirO, glass(Imaoka et al., 1983), and in general with the results of deJong et al. (1981) from SiKB spectroscopy (although we seeno evidence for bimodal Q" distributions).

Third, in each of Figures 24, the chemical shift rangeencompassed by the glass peak increases as the size of thecation decreases. These trends suggest the greater thepolarizing power of a network-modifying cation, the moreit will disrupt a silicate structure, shifting the equilibriadiscussed earlier to the right, localizing the negative chargeassociated with NBO's, and creating a broader range ofsilicate species. Again, the result agrees with Raman find-ings (Brawer and White, 1975; Mysen et al., L982; Matsonet al., 1983; McMillan, 1984b). This interpretation of sili-cate liquid speciation is also consistent with, and was ulti-mately inspired by, work on the effect of cation substitu-tion on the chemical activity of SiO, in binary melts (e.g.,Charles, 1967).

A complementary description, in accord with CNDO/2molecular orbital calculations (de Jong et al., 1981), is thatsmaller cations prefer to cluster together: as an example,the creation of silicate units with multiple O-M linkagestends to be energetically favorable for M: Li but not sofor M: K.

Table 3 lists the integrated linewidths for each of theMAS glass spectra. Calculated as the area under a centerpeak divided by its height. (This measure is more sensitivethan the full width at half maximum to variations in peakshape, particularly to the occurrence of small shoulders).These linewidths are plotted in Figure 5 as a function ofthe polarizing power (or ionic potential) of the network-

336 MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GL,4SSES

Table 3. Isotropic peak positions and linewidths in the 2eSi MASNMR spectra of disilicate and metasilicate glasses

C I a s s

The NarSirOs glass spectrum was also deconvolutedinto three Gaussian peaks at -77, -88.5 and -99.5 ppm(Q', Qt, and Qa units) with relative intensities of 8:84:8.Furthermore, the signal-to-noise ratio of the full spectrumis high enough that we believe the small bump at -62.5

ppm is probably a real feature, one we ascribe to isolatedSiOl- tetrahedra (Qo units). Its intensity is 0.4% of themain peak and may be present in the LirSirOs spectrum aswell.

In most of the spectra presented here, the maximum ofthe glass peak is within a few ppm of the correspondingcrystalline peak(s). One exception is CaSiO3, for which theglass maximum appears at -81.5 ppm, whereas the spec-trum of crystalline CaSiO3 features one fairly broad peakat -88.5 ppm. In comparison, peak maxima for crystallineand glassy samples of both CaMgSi2O6 and MgSiO3 liebetween -81 and -84 ppm. This difference suggests thatcrystalline CaSiOr, with its peculiar silicate chain repeatlength of three tetrahedral units (Deer et al., 1966), relaxesin a glass to a chain structure more like that of the pyrox-enes CaMgSirOu and MgSiO..

Silica glass

Before the effect of network-modifying cations on thestructure of aluminum-bearing framework silicates is ana-lyzed, an examination of SiOt glass itself is warranted. Onthe basis of RDF analysis (Konnert and Karle, 1973) andRaman spectroscopy (Seifert et al., 1982), silica glass is be-lieved to consist for the most part of interconnected six-membered rings of silicate tetrahedra, similar to a distortedtridymite. Additionally, there is Raman evidence for four-membered rings (Sharma et al., 1981). Although every sili-con is expected to be in a Q* tetrahedron, the distributionof Si-O-Si bond angles in this structure can give rise to abroadening of the MAS linewidth.

Our sample was a crushed piece of fused quartz glasstubing with a small amount of crystalline MgrSiOo added

Cotionic polenl iol Z/r (nm ')

Fig. 5. Integrated linewidths (peak area/height) ofdisilicate andmetasilicate glasses as a function of the ionic potential(charge/radius) of the network-modifying cation. Ionic radii arethose of Shannon and Prewitt (1969). For CaMgSirOu, the cat-ionic potential was assumed to be the average of the values for Caand Mg.

Peak posit ion(ppn from TMs)

Integratedl ioewidth (ppn)

13.2

i : . o1 8 . 7

l 7 . 6

2 L . 3

modifying cation, simply the ionic charge divided by anappropriate ionic radius in nm. [A number of other cationproperties-ionization potentials, field strengths, molecularorbital mixing coefficients (de Jong et al., 1981), etc,--couldbe used as well with the same qualitative result.l For bothdisilicates and metasilicates, the trend towards a wider Qndistribution in glasses with smaller, more highly chargedcations is apparent.

It is curious, however, that the two lines in Figure 5 aredisplaced, or to be specific, that the linewidth of CaSiO.glass is noticeably less than that of SrSirO, glass. Thisdifference in width can be partially attributed to the factthat the separation between Qa and Q3 chemical shiftranges in Table 2 is larger than that between Q3 and Q2,Q2 and Qt, or Qt and Qo. Because of the higher overalllevel of polymerization, there are in general more Qa tetra-hedra in disilicate glasses than in metasilicate glasses, andthe higher concentration of these Qa silicons gives rise toextra broadening of the disilicate MAS peaks. (The nonlin-earity in the relationship between chemical shift and degreeof polymerization is also the likely cause of the peak asym-metries in Figures 3 and 4.) The difference in disilicate andmetasilicate glass linewidths may in addition reflect alarger equilibrium constant for reaction (2) than for rea-tions (3) and (4).

The pronounced shoulders in the lithium disilicate glassspectrum, implying more clearly defined Qo units than inthe other glass samples, are probably related to its propen-sity to separate into reigons of higher and lower lithiumcontent (Tomozawa, L972). L deconvolution of the line-shape into three Gaussians yielded peaks at -78.5, -90.5,and -105 ppm with relative intensities of roughly8 :81 : 11. These we assign to Q', Qt, and Qa silicate unitsrespectively. To determine whether the silicon nuclei givingrise to these peaks have different spinJattice (Tr) relaxationtimes, lree induction decays were accumulated with rf pulsespacings of 15, 120, and 600 seconds. A difference in relax-ation times would be a possible indication of distinctlithium-rich and lithium-poor regions, but no appreciablechange in lineshape as a function of pulse cycle time wasobserved.

K2Si205

N"2 s i2o5

Li2si2o5

BaSi2O5

SrSi2O5

CaSiO3

CaMsS i^o,

MCSi03

- 9 0 . 5

- 8 8 . 5- 9 0 . 5

- 9 2 , 5

- 9 2 , 5

- 8 r . 5

- 8 2 . 0

- 8 1 . 5

1 5 . 3

1 8 . 0

2 2 . O

E

t

MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GL,4SSES 337

-60 -so -too -r20 -t4o -t60

Esr (pp.)

Fig. 6. 2esi MAS NMR spectrum of silica glass, obtained byaveraging 433 free-induction decays.

as an internal shift reference; its 2esi MAS spectrum ap-pears in Figure 6. The signal-to-noise ratio is relativelypoor because a long silicon spin-lattice (Tr) relaxation timelimited the rate at which successive free induction decayscould be collected. (Radiofrequency pulses with a flip angleof - 15' were spaced at 6 minute intervals). SiO2 glasscontaining a small amount of dissolved paramagneticFe2O3 (-0.1%) would have a shorter relaxation time(Mosel et al., 1974), but we were unable to prepare such asample with available apparatus.

In Figure 6, the SiO, peak maximum lies at -110.9ppm, and the full width at half maximum (FWHM) is 13.2ppm, from -103.8 to -117.0 ppm. These chemical shiftscan be converted to a range of average Si-O-Si bondangles using the empirical formulas of Smith and Blackwell(1983) or Thomas et al. (1983a). One obtains a correspond-ing range of angles from roughly 135' to 160', a result inqualitative agreement with the molecular dynamics (MD)calculations of Mitra (1982) and of Gaskell and Tarrant(1980). (It should be noted, however, that these authorspresent distributions for individual Si-O-Si angles,whereas the NMR linewidth reflects a range of values forthe average over four Si-O-Si angles). The angle corre-sponding to the NMR peak maximum is 148', which com-pares well with the average Si-O-Si angle derived fromRDF work (150') (Konnert and Karle, 1973\, as well asMD values [e.g., 153" (Mitra 1982)].

Dupree and Pettifer (1984) have recently presented amore detailed anlysis of the Si-O-Si bond angle distri-bution associated with a 2esi MAS NMR spectrum of vit-reous silica" but their peak maximum appears to lie at- l(D ppm, corresponding to an average angle of 145.5'.

Alumino silic at e g I as se s

Our focus n6w turns to aluminum-bearing glasses,specifically tectosilicate glasses in which aluminum is be-lieved to act as a network-forming cation, substituting forQa silicons in tetrahedral units rather than changing thedegree of polymerfation in the role of an octahedrally

coordinated network modifier (see Mysen et d., 1982, orSharma et al., 1983). The type of equilibrium that can beaffected by the identity of an alkali or alkaline earth cationnow involves silicon-aluminum distributions instead ofvariations in Qn populations. If we let Qa(kAl) stand for a3-D framework silicate tetrahedron linked via oxygen to kaluminate tetrahedra (0 < k < 4), we can imagine the fol-lowing type of equilibrium condition (McMillan et al.,1982):

2Q4(kAl)+Q4[(k + 1)Al] + Qn(k - 1)All. (5)

By analogy to the results obtained for metasilicate anddisilicate glasses, we expect strongly polarizing cations toshift this equilibrium to the right, clustering cations nearthe aluminate tetrahedra linked to the Q4(k + 1)All sili-cate species and giving rise to more variety in the numberof aluminate neighbors around different silicons. Ramanspectra reported by McMillan et al. (1982) support thismechanism.

This trend is indeed apparent in Figure 7, which displaysthe 2esi MAS spectra of glasses with a 3: 1 Si/Al ratio:KAlSi3Os (K-feldspar), NaAlSi.O, (albite), andCao.rAlSi.Or. (This latter composition is equivalent toCaAlrSirO, '4SiO2 and thus will be referred to asanorthite4-euartz or AnaQ.) Peak positions and integrat-ed linewidths are given in Table 4 along with the chemicalshifts of the corresponding crystalline alkali feldspars.[These contain only Q4(lAl) and Qa(2Al) silicons (Smith,1974).f The glass peaks grow broader as the cation polar-izing power increases from K+ to Na+ to Ca2+, reflectinga widening distribution of Qa(kAl) species and probably awidening distribution of Qa Si-O-T angles as well (T:Si,Al). As evidence for this latter statement, we note thatRDF measurements on NaAlSirO, and KAlSi.O, glassessuggest the presence of six-membered tridymite ringsstuffed with alkali cations (Taylor and Brown, 1979a),

Coo.rAlSi.Oa

NoAISiJOB

KAtSi3Os

-40 -60 -80 -too 120 -t40

Esi (PPm)

Fig. 7. 2eSi MAS NMR spectra of tectosilicate glasses withSi/Al : 3. The wiggle to the left of the albite spectnrm is an arti-fact.

338 MURDOCH ET AL.: SILICA'(E AND ALUMINOSILICATE GL,4SSES

KAISi^0^

NaAlSi30B

NaA1Si2O6

NaA1Si04*

cdt2tt12o28

C a A l ^ S i - O , .

CaAl2S14012

CaAl2S 1208

CaAI2Sio6

s 1 0 2

- o q n - o c n - 1 n 1 n

- o 1 n - o t n - 1 n < n

8 5 . 0 * *

+- 8 2 . 5 , - 8 4 . 5 , - 8 9 . s

++- 1 0 8 . 5

Table 4. Isotropic peak positions and linewidths in the 2esi MASNMR spectra of crystalline and glassy tectosilicates

FormulaCrystal l ine Peakposit lon lntegrated

s1/A1 chemical in glass l insidth ofshl f t (s) (ppn) (ppm) glass peak (ppn)

CoAl2Si2Os

NoAl S tOa

E5; (ppm)

Fig. 8. 2eSi MAS NMR spectra of tectosilicate glasses with

si/Al : 1.

(Taylor and Brown, 1979a, 1979b) have indicated that thetwo glasses have markedly diflerent structures: six-membered, "stuffed tridymite" rings in nepheline glass,four-membered feldspar-like rings in anorthite glass. Thesmaller rings may well entail more variety in bond angles.What is more, on the basis of Raman data, Seifert et al.(1982) have postulated the existence of a small quantity ofsix-membered rings in addition to the four-membered ringsin CaAlrSirO* glass. This variation in structure would beexpected to create a wider range of bond angles.

Another possibility is that the gr€ater polarizing powerof calcium inspires a breakdown in aluminum avoidance.Indeed, Sharma et al. (1983) have seen evidence in theirRaman spectra of Si-Al disorder in anorthite glass. Thatthe increase in width of the anorthite peak versus the neph-eline peak in Figure 8 is mainly an expansion into morenegative chemical shifts is also an indication that Q4(3Al)silicate tetrahedra may well be present in anorthite glass.

It should be noted, however, than when examined as afunction of the Si/Al ratio, the linewidths of Figure 7 and 8

Coiionic potentiol Z/r (nm-t\

Fig. 9. Integrated linewidths of tectosilicate glasses as a func-tion of cationic potential for different silicon-to-aluminum ratios.Linewidths increase with increasing cation polarizing power.

3

3

2

1

6

3

2

I

0 . 5

- 9 9 . 0

- 9 7 . 9

- 9 2 , 4

- 8 6 . 0

- r07 . 1- 1 0 1 . 0

- 9 5 . 6

- 8 2 . 3

-110.9

r 7 . 3

1 8 . 0

1 8 . 3

1 3 . 3

1 9 . 3

21.3

1 7 . r

1 3 . 9

1 3 . 6

*El. .a.oo nicroprobe analysls of the natural ctystal l ine smpfe

v i e l d e d t h e a p p r o x l m a t e f o * * 1 " " " 3 . 0 3 K 0 . 2 0 s 1 4 . 2 2 4 1 3 . 7 8 ( t u o . o z

C"O.Ot)0t6 (Si/A1=1.12). The glass was prepared synthet lcal ly

as NaA1St04.

Addlt lonal snal l peaks occur at -88.5 and -92.5 ppm which we

essign to Q4(3lt) ana Q4(2AI) " i t t "or"

respecEively. These appear

because Si/Al > 1.

-Mrl t ip l . peaks ref lect crysral lographical- ly dlst lnct q4(4AI)

si l icon si tes.

t iatr .aob. lra. , smith and Brackwel l , 1983.

whereas the Raman spectrum of An4Q glass has been in-terpreted in terms of both six-membered SiO, rings andfour-membered Al2Si2O3- rings (Seifert et al., 1982). Theexistence of two ring sizes would be expected to result in awider range of inter-tetrahedral angles.

Figure 8 compares the 2eSi spectra of two tec-toaluminosilicate glasses with a Si/Al ratio of unity:NaAlSiOn (nepheline) and CaAlrSirO, (anorthite). In thecorresponding crystals (see Table 4), silicon and aluminumcations are generally assumed to strictly alternate in thetetrahedral framework---+ach silicon is surrounded by fouraluminums and uice-uersa. fHowever, Sharma et al. (1983)have recently detected weak bands in the Raman spectrumof crystalline CaAlrSirO, that imply some imperfection inthe ordering.] The alternating arrangement of Al and Si isa manifestation of Loewenstein's aluminum-avoidance rule(Loewenstein, 1954), which states that Al-O-Al linkagesbetween aluminate tgtrahedra are energetically un-favorable. If this principle holds in glasses as well, thenequilibria such as (5) are not important since every silicatetetrahedron must be a Q"(4Al) unit.

Integrated linewidths for both sets of glasses are plottedas a function of cation polarizing power in Figure 9. In-spection of Figure 8 or Figure 9 reveals that the width ofthe anorthite glass peak exceeds that of nepheline glass.One cause for this difference might again be a greater rangeof bond angles in the anorthite glass. RDF measurements

Eo

o=

A S i / A l = 3r Si/Al = !

- L

,/ '

MURDOCH ET AL; SILICATE AND ALUMINOSILICATE GLISSES

are consistent with substantial adherence to Loewenstein'srule. Specifically, the width of the albite glass peak is 4.9ppm greater than that of nepheline glass, and the width ofthe An4Q glass peak is 5.2 ppm greater than that of anor-thite glass. In short, glasses for which substantial re- €arrangement of Si and Al cations is possible without creat- Eing Al-O-Al linkages have broader linewidths than those Efor which compliance with the aluminum-avoidance prin- fciple imposes a rigid ordering scheme.

339

This argument can be generalized somewhat by con-sidering a statistical model for silicon-aluminum ordering,with and without the aluminum-avoidance constraint. LetR be the Si/Al ratio in a 3-D framework glass. Without therestrictions of aluminum avoidance, the relative occurrenc€of a Qa(kAl) silicate tetrahedron is given simply by theprobability of choosing k aluminum neighhols and (4 - k)silicon neighbors:

PG):11)+-,=\r/R-ry' (6)where the binomial coeffrcient is defined as

/4\ 4tI r : _ ( 7 )\k / k ! (4 _ k) ! '

With this probability distribution, the average number ofaluminum neighbors (which governs the location of the2esi peak maximum) is given by

(k) : --l-. (8)' (R+ 1 ) '(Strictly speaking, the peak maximum will correspond tothe average value of k only for a symmetric lineshape, butthe diflerence between (k) and its most probable value isnot important.) The variance in the number of aluminumneighbors (which contributes to thc NMR lindwidth) isgiven by

ot : (k t ) 4R- (k)" :

iR + l)t (e)

The variance is a maximum (o2 : tl when R : 1 ; i.e., for acomposition like that of anorthite or nepheline. For R : 3as in albite glass, o2 : 0.75.

In contrast, the imposition of aluminum avoidance re-quires four Si-O-Al linkages for each aluminum atompresent. The relative occurrence of each eo(kAl) silicatetetrahedron is given by

pG): f1) (R -r)t+-rt

(10)\k/ Ra

(Klinowski et al.,1982). Now (k) : 4/R and

o2 = (kz)- (k) , : \ f (11)

In this case the variance is zero (no disorder) for R: 1.achieves its maximum value of 1.00 for R:2. and falls to0 . 8 9 f o r R : 3 .

Fig. 10. Integrated linewidths of tectosilicate glasses as a func-tion of R : Si/Al for different charge-balancing cations.

As noted above, the variance of k contributes at least inpart to the NMR linewidth of aluminosilicate glasses. Toexplore this effect, we have collected 2eSi spectra forjadeite(NaAlSi2OJ glass and a series of glasses of the formulaCaAlrOo'nSiO2 (n : 1, 2,4,6, l2). Results are included inTable 4 and Figure 10, and are clearly more consistentwith an aluminum avoidance effect than with its absence.However, linewidth maxima for both Na and Ca glassesoccur near to R : 3, not R : 2. This perhaps indicates thatother contributions to linewidth, such as variance inSi-O-T bond angles, also increase with the Si/Al ratio.Such a conclusion is supported by the molecular orbitalcalculations of Geisinger et al. (1984), which suggest that asthe Si-O-T angle varies from its most stable value, energiesincrease more rapidly for Si-O-Al than for Si-O-Si.

In comparison, a 2esi MAS NMR study of three gallosil-icate glasses (G. S. Henderson and J. B. Murdoch, unpub-lished data) has shown that isotropic linewidths increase inaccord with a statistical model of "gallium avoidance":

NaGaSiOo < NaGaSi.O, J NaGaSirOu. (2)

fl.ike aluminum, gallium has a deshielding eflect on neigh-boring 2eSi nuclei (Vaughan et al., 1983).1

N atural composition glasses

To investigate the usefulness of 2eSi MAS NMR in theanalysis of magmas, we turn finally to three glasses madeexperimentally from Fe-poor silicic lavas collected atMono Craters (A), Mt. Lassen (B), and Mt. Shasta (C). Allthree were remelted under reducing conditions in graphitecrucibles; calculations using the results of Kilinc et al.(1983) indicate that >99o/o of the iron present is Fe2+.Table 5 gives the chemical analysis and CIPW norm ofeach, plus the Si/Al ratio and the number of non-bridgingoxygens per tetrahedral cation (NBO/T). Rhyolitic glass Acan be represeoted an approximately one third silica glass,one third albite glass, and one thlrd K-feldspar glass. Ingoing to glasses B and C, the K-feldspar component ispartially replaced by anorthite and the number of non-bridging oxygens increases, indicating a drop in the

,i 1,---Jn"l i t K

1 , ,- t

{c "

s'o. f*

340 MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GL,4SSES

Table 5. Analysis ofnatural composition glassesaverage degree of polymerization. Nevertheless, all threeglasses are expected to have predominantly three-dimensional framework structures, i.e., a predominance ofQa tetrahedra.

The 2esi NMR spectra of the natural compositionglasses are displayed in Figure 11. The first trend to strikethe eye is the increase in spinning sideband intensity ingoing from A to B to C. This change is not related to amassive increase in chemical shielding anisotropy butrather to an increase in concentration of paramagneticFe2* ions. Magnetic dipole-dipole coupling between therapidly relaxing unpaired electrons on the iron and nearbysilicon-29 nuclei induces a paramagnetic shift in the NMRspectra of these nuclei. The form of this largely inhomoge-neous shift is similar to that of a chemical shift, but themagnitude can be much greater (Sanz and Stone, 1977). Asthe concentration of iron increases. the number of siliconnuclei affected by paramagnetic shifts in turn rises; as aresult, spinning sidebands cover a wider range of fre-quencies and become more intense. Oldfield et al. (1983)have reported a similar effect in minerals caused by ferro-magnetic inclusions, but such inclusions were not observedmicroscopically in these glasses.

The ovirall spectral intensity (including sidebands) alsodrops in going from A to B to C; the relative values are1.00:0.70:0.37. This drop too is a. function of increasingparamagnetic content. Those silicon nuclei that are locatedvery near unpaired electrons not only experienc€ a largeshift but also relax rapidly (Abragam, 1961, Chap. 9). Botheffects can cause such severe broadening that these per-turbed silicons are not seen at all in the spectrum.

The linewidths and chemical shifts of the three centerpeaks are collected in Table 6. An unambiguous analysis isdifficult because in going from A to B to C, two factors-the decrease in the Si/Al ratio R anil the increase in thenumber of non-bridging oxygens-would be expected to

851 (oom)

Fig. 11. 2esi MAS NMR spectra of glasses made from lavacollected at Mono Craters (A), Mt. Lassen (B), and Mt. Shasta (C),

California. All three are drawn to the same height, but the numberof observable silicons and hence the measured signal intensitydecrease in going from A to B to C.

GlassA

Glass ClassB C

chemical *c o n s t i t u e n E s

(vE 7")

CIPI{ norn(ilE 7")

NBO/T

S1/A1 rat io

s102

Tio2

Ar2o3

Fe0

Mn0

Mgo

Cao

Na2O

Kzo

s102

KAISi ̂ 0^J O

NaAlSi308

caAl2Si208

Ce (Mg, re) Si20d

( M B , F e ) S 1 0 3

FeT103

74.98 69 .L6 6r ,17

0 . 0 7 0 , 3 8 0 . 6 9

1 2 . 3 0 1 4 . 8 1 1 6 . 5 8

1 . 0 1 2 , 4 2 4 . 4 r

0 . 0 5 0 . 0 6 0 . 0 8

0 . 0 4 1 . 4 r 4 . 0 3

0 . 6 0 3 . 0 0 6 . 7 3

4 . 0 1 4 . 3 0 4 . 2 r

4 . 6 6 2 . 7 3 1 , 0 5

3 1 . 9 0 2 3 . 7 8 1 1 . 1 9

2 7 . 5 4 1 6 . 1 3 6 . 2 0

33.93 36 .39 35 .62

r . 8 0 1 3 . 0 5 2 3 . 2 4

1 . 0 4 1 . 5 3 8 . 3 0

1 . 3 8 6 . 6 8 1 3 . 0 8

0 . 1 3 0 . 7 2 1 . 3 1

0.027 0 .105 0 ,294

3 . 9 6

*Pro . lg .o . "d and a l l i l on assuned to be Fe2*

**c l l iu t " t .d accord ing to Mysen e t a l . (1982)

broaden the peak and shift its maximum to less negativevalues of d. Moreover, additional broadening is caused bythe paramagnetic ions present, as found by Grimmer et al.(1983a) in a study of Fe,Mg substitution in synthetic oli-vlnes.

The location of the peak maximum, however, is largelydependent on the Si/Al ratio. From Table 4, the averagechemical shift for alkali feldspar glasses is roughly -98.5

ppm; the average number of aluminum neighbors per sili-cate tetrahedron is 4/3 : 1.33. In comparison, the silicaglass NMR peak lies at -lll ppm and (k) :0. Fromthese two data pairs, we get the following simple relation-ship:

6 (ppm) : - 111 + 9.4 (k)

: - l l 1 +37.51rR. (13)

Using values for R in Table 5, one can predict that thepeak maxima should lie at -103.5, -101.5, and -99.0

ppm for samples A, B, and C. These numbers are indeedclose to the experimental results in Table 6.

Conclusions

For the disilicate and metasilicate glasses investigatedhere, 2eSi MAS NMR spectra indicate that the predomi-nant Q" silicate unit in the glass is the one found in the

MURDOCH ET AL.: SILICATE AND ALUMINOSILICATE GLASS_ES 341

Table 6. Isotropic peak positions and linewidths in the 2esi MASNMR spectra of natural composition glasses

preparing several of the glasses, and D. F. Weill (University ofOregon) for supplying the KAlSirO, and An4Q glass samples.

This work was supported by the Director, OIfice of BasicEnergy Sciences, Division of Engineering Mathematics, and Geo-sciences, of the U.S. Department of Energy under contract DE-AC03-765F00098.

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corresponding crystalline material, and that the range ofsilicate species present increases with smaller, more highlycharged network-modifying cations. Similarly, such cationsprobably induce greater variety in the distribution of Siand Al in tectosilicate glasses. The dependence of linewidthon the Si/Al ratio indicates, however, than an aluminumavoidance effect is present. In silica glass itself, the MASlinewidth reflects a range of average bond angles from-135" to -160o, a result in good agreement with RDFand MD findings.

Because our one measurable parameter, the isotropicchemical shift, is sensitive to a variety of structural featuresaffecting a silicon-29 nucleus-the number of non-bridgingoxygens, the identity of neighboring tetrahedral cations,bond angle values, and the presence of nearby paramagne-tic ions-the spectra of multicomponent glasses cannot bereadily interpreted. Nonetheless, the location of peakmaxima for the three natural composition glasses we exam-ined can be correlated with the Si/Al ratio.

Note adileil in proof:

Recently, Schramm et al. (1984) have published spectrafor a series of lithium silicate glasses and crystals, and havedeconvoluted glass spectra to estimate distributions of Q.species, a range of which was apparent in all compositions.Their reported fractions of Q2 and Q4 in Li2Si2O5 glassare somewhat higher than those given here. They showpartially resolved double peaks in high silica glasses, as wesaw in NarSinO, glass, but many of their samples wereapparently phase separated. Grimmer et al. (1984) havereported spectra on both sodium and lithium silicateglasses which are generally similar to ours and those ofSchramm et al. (1984). These authors have chosen a mark-edly different interpretation, however, by assuming thatsingle Q" species are present unless separate peaks areclearly resolved. We feel the widths of observed NMRpeaks, the results of Raman spectroscopy mentioned above,and thermodynamic considerations, all make a distributionof species more likely to be correct.

AcknowledgmentsWe are grateful to Professor A. Pines (Univeristy of California)

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t42 MURDOCH ET AL: SILICATE AND ALUMINOSILICATE GLz4SSES

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Manuscript receioed, March 15, 1.984:accepted for publicatiog N ouember I 9, 1984.