American Mineralogist, Volume 76, pages 1761-1764, 1991
LETTER
Coordination changesand the vibrational spectrumof SiO, glass at high pressure
Llns SrrxRUDEr*
Ana OsnacANr**M.S.T. Buxowrxsxr
Department of Geology and Geophysics,University of California at Berkeley, Berkeley,California 94720, U.S.A.
Arsrru.cr
We investigated the persistenceof tetrahedral coordination in SiO, glass under high
pressuresby comparing experimental infrared spectrawith the calculatedspectraof Monte
Carlo simulations of SiO, glass. The calculations are self-consistent:we used the same
potential model, which prevents bonded Si-O coordinations higher than four, to generate
the simulated structuresand to calculate the eigenfrequenciesand eigenvectors.The simulated, tetrahedrally coordinated structures agreewell with available structure and equation-of-state data and, at higher pressures,are expectedto differ from the real glassonly
if the latter undergoescoordination changes.The calculated vibrational density of states
and infrared spectrum atzero pressureagreewell with the data. The calculationsreproduce
most of the important featuresof the observedhigh-pressureinfrared spectrum,including
the features thought to be indicative of the onset of octahedrally coordinated Si at high
pressures.We therefore suggestthat the infrared spectrado not yield a unique structural
interpretation and leave open the possibility that SiO, glass preservesits tetrahedral coordination to at least 40 GPa.
the glasslessdenseat high pressure,despite the competing effectsof thermal expansion (Stixrude and Bukowinski, I 99 I ). Further, although SiO, crystalsreadily convert
to octahedral coordination near l0 GPa if the temperature is greaterthan severalhundred kelvins, at room temperature four-coordinated quartz and coesite survive
compressionto roughly three times the equilibrium transition pressure to octahedral stishovite (Hemley et al.,
1988). Thus, the structure of SiO, glass compressedat
room temperature may be very different from the liquid
at the same pressure.
Vibrational spectroscopyprovides the only in situ highpressure constraints on glass structure (Hemley et al.,
1986; Williams and Jeanloz, 1988; Wolf et al., 1990).
Becausethe atomic structure and the form of the vibrational eigenmodesin glassesare complex, quantitative
interpretation of these data demands comparison with
precise theoretical calculations, based on realistic structural models. At zero pressure,this approach is well established, beginning with the pioneeringwork of Bell and
Dean (see Bell, 1976), who used a continuous random
network and a force constant model to predict zero pressure spectra.It is difficult to extend such work to higher
pressures because of the lack of independent structural
information from, for instance,X-ray diflraction. Murray
and Ching (1989) treated pressureas a perturbation by
* Present address:Geophysical Laboratory, 525 I Broad Branch
assuming that the bonding topology of their continuous
Road NW, Washington,DC 20015-1305,U.S.A.
** Presentaddress:SpaceComputer Corporation, 2800 Olym- random network was independent of volume. They used
pic Boulevard, Suite 104, SantaMonica, California 90404-4119, a force constant model to predict the responseof bond
lengths and the Raman spectrum to compression. The
U.S.A.
INrnooucrroN
Igneousprocessesin the Earth's interior are ultimately
controlled by the physical properties and the atomic
structure of silicate liquids. To the extent that glassesare
faithful analoguesof their molten counterparts, investigation of their high-pressurestructure can provide important constraints on magma genesis and transport.
Characterizingthe gradual changein coordination ofSi-O
from four to six as a result of increasedpressurein amorphous silicates is of central importance since this structural changewill substantially increasemagma densities,
perhaps beyond those of coexisting solids, thereby preventing the magma's ascent.
Analogies with SiO, crystalsand NMR experimentson
a variety of quenched,high-pressuresilicate liquids (Xue
et al., l99l) indicate that SiO, liquid may become octahedrally coordinated by approximately 20 GPa. However, kinetic hindrances are likely to play a significant
role in the compression of SiO, glassand may delay the
four- to sixfold coordination changeto much higher pressures. Monte Carlo simulations show that kinetic hindrances cause SiO, glass at room temperature to compress less efficiently than SiO, liquid at 2000 K, making
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1762
STIXRUDE ET AL.: SiO, GLASS AT HIGH PRESSURE
THEORY
vl
o
o
tions (Stixrude and Bukowinski, l99l). These structures
are quenched to the local energy minimum at zero temperature to eliminate residual forces on the atoms.
Vibrational frequenciesand modes at the Brillouin zone
center are determined by solving the eigenvalueproblem:
Wa : Ils, where a and tr are the eigenvectorsand eigenvalues, respectively,and the elementsof W are given by
^ l a ' u\
EXPERIMENT
o
o
o
.tv
ota
J'.r
500
t00o
F R E Q U E N C Y( c m - r )
W , . . i u :( m , m ) - '' [ r _ ^ _ |
.'
i,i:
{ 1 ,. . . , N } ;
\o^rdo^rp/o
a,B: {1,2,3}
(l)
where U is the total energy, m, is lhe mass of atom i, the
x- are its Cartesian coordinates, the subscript 0 indicates
equilibrium, and N is the total number of atoms in the
unit cell of the simulated structure (N : 192). The IR
intensity of eigenmode{ is given by
(o* >(4or:ff)'
Fig. 1. Comparison
(Galeener
ofcalculated
andexperimental
(2)
et al., 1983)vibrationaldensityof statesat zeropressure.
The
dashedline is the estimatedtwo-phononcontribution(Galeener
et al.,1983).
whereA^: mi-t/zctioandrr. is the a Cartesiancomponent
of the dipole moment, calculated by assuming effective
charges, Q,, equal to formal ionic charges(Bell, 1976).
resulting structures are probably inaccurate above ap- Vibrational mode assignments,rocking, bending, stretchproximately 8 GPa, where network rearrangementbegins ing, and cation contributions to an eigenmode,are based
to contribute substantiallyto compression(Hemley et al., on the Bell and Dean decomposition method (Bell, 1976).
1986; Stixrude and Bukowinski, l99l). Although comRnsur-rs
puter simulations can overcome these limitations by simultaneously predicting high-pressure structure and
Figure I shows the calculated and experimental vibraspectra,their accuracydependscritically on the assumed tional density of states.The three main peaks of the exform of the interatomic forces. The simple ionic models perimentally determined profile are reproduced, as well
used so far have not reachedthe level ofagreement typ- as the smaller peak near 600 cm-' and the broad lowical of the Bell and Dean approach (Garofalini, 1982; frequency shoulder on the 400 cm-' peak. The experiRustad eI al., l99l and referencestherein).
mental high-frequency peak may be divided by LO-TO
To investigate the persistenceoftetrahedral coordina- splitting, although the neutron diffraction data do not
tion in SiO, glassunder compression,we compare results demonstrate this conclusively. Becausethe model conof Monte Carlo simulations with measured,high-pressure tains no long-range coulomb forces, this effect is absent
vibrational spectra.Simulated structuresand vibrational in the calculations. Our calculations match the data sigspectra are based on an empirical covalent model of nificantly better than ionic molecular dynamics simulabonding in four-coordinate SiOr, which prevents bonded tions (Garofalini, 1982;Rustadet al., l99l) or the results
Si-O coordinations greaterthan four. Within this context, of Bell and Dean (Bell, 1976).Murray and Ching (1989)
the model has proved successfulin matching a wide va- achieve comparable agreement by optimizing potential
riety of data and is the first to reproduce the structure parametersto minimize disagreementwith experiment.
and equations of state of tetrahedral crystalline, liquid,
Calculated and experimental IR spectraare compared
and vitreous SiOr, including irreversible compaction of in Figure 2. At zero pressurethe locations and relative
the latter above l0 GPa (Stixrude and Bukowinski, 1989, heights of the four main peaks agreewell with the meal99l). We therefore expect the simulations and spectral sured spectrum. Although discrepanciesmust be caused
calculationsto mimic closely the real glassand to deviate in part by the simple point-chargemodel usedto calculate
substantially only ifthe latter developsa significant pop- intensities,certain differencesare attributable to deficienulation ofSi-O coordinations that exceedfour.
cies in the simulated structuresand the potential model.
Analysis of compression mechanisms in SiO, crystals
MnrHooor,ocy
suggeststhat the Si-O stretching force constant predicted
These are the first self-consistentcalculations of the by our interatomic force model is too large (Stixrude and
vibrational density ofstates and infrared spectraofSiO,
Bukowinski, 1988), probably accounting for the overesglass:we use the samemodel to generatesimulated struc- timated frequency of the peak at 1080 cm '. An undertures and to solve the vibrational eigenvalue problem. estimated intertetrahedral Si-O-Si angle in the simulated
Glass structures are taken from the final configurations structures(Stixrude and Bukowinski, l99l) probably exof equilibrated room-temperature Monte Carlo simula- plains the overestimated frequency of the experimental
STIXRUDE ET AL.: SiO, GLASS AT HIGH PRESSURE
1763
ts
a
-u
=
F
z
o
IE
.lO0
600
tOO l00O
lllo0l.o0 600 too t@or2oQraoo
I
FREQUENCY(cm-')
Fig. 2. Comparisonof calculatedand experimental(WilIiams and Jeanloz,1988)infraredabsorbance.
The calculated
spectraare labeledby the appropriatepressurein GPa. From
top to bottom,the experimental
spectraweretakenat 2.2, 17.2,
27.5,and,38.9GPa.By comparingwith our calculatedspectra,
we assignthe four measuredpeaks,in order of increasingfrequency,to rocking(R), bending(B), cation(C), and stretching
(S)motions(seeFig. 3). The bendingandcationpeaksconverge
at high pressures
in both calculatedand experimentalspectra.
The straightlinesareguidesto the eye.
of predictednorFig. 3. Bell and Deantypedecomposition
mal modesof SiO,glass,showingthe totalcontributionof rockpeak at 600 cm-'. This band is due mostly to bending ing,bending,stretching,
andcationmotions(3) at eacheigenfremotion of bridging oxygens, which involves increasing quency.
amounts of Si-O bond length variation as the Si-O-Si
angle closes.Although the model was constrained independently of structural or vibrational data on glass,our pressures(Fig. 3). At low pressuresthe four IR peaks
calculations match the IR data somewhatbetter than the coincide with maxima in rocking, bending, cation, and
results of Bell and Dean (Bell, 1976) and at least as well stretching motion in order of increasingfrequency. This
as those of Murray and Ching (1989), who used an op- pattern agreeswell with the resultsof Bell and Dean (Bell,
timized potential function.
1976). No new types of atomic motion are needed to
At higher pressures,though the agreementis not fully explain the high-pressurespectrum. Rocking and stretchquantitative, the calculations reproduce most of the im- ing still account for the relatively isolated lowest and
portant pressure-inducedtrends in the experimental IR highest frequency peaks, respectively, whereas maxima
spectra(Fig. 2). In calculations and experiments,the po- in bending and cation motions merge with increasing
sitions ofthe lowest and highest frequency bands change pressure,accountingfor the single,greatly amplified midlittle with pressure,whereas at midfrequencies the two frequency peak.
peakspresentat low pressuremergeto form a singlehighThe effect of pressureon the basic bitetrahedral unit
pressurepeak. The increasein midfrequency intensity and readily explains the frequency shifts of the various modes.
the insensitivity of low-frequency intensity to pressure Bending is most strongly affectedsince closing the Si-Oare also reproducedby the calculations.The calculations' Si angle increasesthe participation of Si-O bond length
inability to reproduce the observeddecreasein intensity variation in this motion. A competition between Si-O
of the high-frequencypeak may be due to underestimated bond compression, which raises stretching frequencies,
distortion of the SiOo tetrahedra at high pressure as a and Si-O-Si angle bending, which lowers them through
result of an overly strong Si-O bond (Stixrude and Bu- decreasedparticipation of Si-O bond length variation,
kowinski, 1988). The necessarydistortion need not be probably accountsfor the small effect ofpressure on the
large enough to compromise tetrahedral coordination: high-frequencypeak. Rocking and cation motions are less
elimination of the O-Si-O force constant yields almost directly affected by angle bending or bond compression
vanishing intensities of this peak at pressuresabove 30 and change little with pressure.
Basedon a comparison with our results,we have idenGPa while retaining well-defined fourfold Si-O coordination with an O-Si-O angular variance of 22" from the tified rocking, bending, cation, and stretching peaks in
ideal tetrahedral value (Oshagan, 1990). Significantly the high-pressureexperimental spectra(Fig. 2). The preslarger distortions are needed to produce pseudo-octahe- sure shifts of the experimental modes share important
featureswith the calculatedones.The strongestmeasured
dral coordinations.
Analysis of the eigenvectorsshows that four types of pressureshift, that of the bending mode, agreesvery well
atomic motion readily account for the IR peaks at all with the calculatedvalue, as doesthe pressureshift ofthe
1764
STIXRUDE ET AL.: SiO, GLASS AT HIGH PRESSURE
cation mode. Measured rocking and stretching modes,
like the calculatedones,are relatively insensitive to pressure.
AcxNowr,rocMENTs
We thank J. Rustad and an anonymous referee for their conscientious
reviews and C. Lithgow-Bertelloni for helpful comments on the manuscript. Supportedby NSF grant EAR-88 16819.
DrscussroN
The calculated vibrational spectrum of a tetrahedrally
coordinated glassaccountsfor most ofthe featuresofthe
observed IR spectrum. In particular, the dramatic pressure-induced increase in midfrequency absorption, previously attributed by analogywith crystalsto the appearance of SiOu octahedra (Williams and Jeanloz, 1988), is
readily explained by the combination and intensification
of tetrahedral bending and cation modes. A four-coordinated high-pressurestructure also readily accountsfor
the tetrahedral rocking mode (500 cm '). Its nearly constant shape and intensity in both experimental and calculated spectraare difrcult to reconcilewith the pressureinduced disappearanceof SiOo tetrahedra proposed by
Williams and Jeanloz.We suggestthat comparatively minor structural changes,tetrahedral distortions somewhat
greater than those predicted by our model, may account
for the observed pressure-induceddecreasein intensity
of the tetrahedral stretching mode.
The sursival of fourfold coordination in SiO, glass to
at least 40 GPa is also consistent with Raman spectroscopy of SiO, and GeO, glasses.Raman spectra of SiO,
glassshow significant broadeningand weakeningofbands
at high pressurebut no evidence of new bands up to 40
GPa (Hemley et al., 1986).In contrast,GeO, glass,for
which there is independent evidenceofa four- to sixfold
coordination changefrom 8 to l3 GPa (Itie et al., 1989),
develops a new low-frequency Raman band over the same
pressureinterval, which has been attributed to GeOuoctahedralmodes(Durben and Wolf, l99l).
I-argerpopulations of nonbridging O atoms or the presenceof AI in more complex silicatesmay alleviate kinetic
hindrances somewhat and allow glassesto undergo coordination changesat lower pressuresmore typical of the
liquid (sodium tetrasilicate may be an example, Wolf et
al., 1990). However, experiments on anorthite and diopside glasses(Williams and Jeanloz, 1988), like measurementsof SiO, glass,show low-frequency (500 cm-r)
peaks whose shapeand intensity are virtually unaffected
by pressure,and neither glass,showsdistinct high-pressure bands that would require the appearanceof new
structural units such as AlO. or SiOu octahedra. Thus,
these glasses may also be tetrahedrally coordinated
throughout the experimental pressurerange. Our results
emphasizethe importance, for geophysicalapplications,
of studying liquids directly or liquids quenchedin situ at
high pressure.
RnrnnnNcBscrrED
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MeNuscmp'r REcETVED
Jurv 8, l99l
M,truscnrm AccEprEDAucusr 8, l99l