A thermodynamic assessment of silica phase diagram

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VOL. 99, NO. B6, PAGES 11,787-11,794, JUNE 10, 1994

A thermodynamic assessmentof silica phase diagram V. Swamy and SurendraK. Saxena Theoretical Geochemistry, Instituteof EarthSciences, UppsalaUniversity,Uppsala,Sweden Bo Sundman

Divisionof PhysicalMetallurgy,RoyalInstituteof Technology, Stockholm, Sweden

J. Zhang Centerfor High Pressure Research, Depamnent of EarthandSpaceSciences, StateUniversityof New York at StonyBrook

Abstract. An internallyconsistent dataset9n the thermodynamic pro•rties of the silica polym0rphs stableup to 15 GPa (a-quartz,•_•--quartz, tridymite,cristobalite, coesite,and

stishovite) andtheliquidphase ispresented. Thedatasetwasproduced through a computer-based

assessment of thepr0pert•es in whichtheavailablethermochemical (calorimetric), pliysical(bulk modulusandthermalexpansion), andsolid-state andmeltingtransitiondata(includingsome newl determineddataon the h?•h-"ressure--•-l-'mor-'hs cc,esiteand sfishovite)were considered. •, 1-' l-n:? •. 1-'

The •taset can beused tocalculate phase relauons atpressures of0.1MPa to15GPa and

temperatures of 300 to 3200K. The chlculated phasediagramusingthesedataagreesquitewell

witlithephase equilibrium determinations exceptforthehigh-temperature partof thecoesite-

stishovite boundary.The properties of theliqmdphaseobtfiinedarealsoin goodagreement with

the available data.

Introduction

Polymorphism and Melting of Silica Phases

The phaserelationsof silica (SiO2) havebeenthe subjectof intense researchbecauseof the multiplicity of polymorphic transitions,including lambda transitions,and becauseof the geophysical and geochemical importance of these polymorphs. The high-pressuretransformations of crystalline silica are often used as calibrationstandardsin high-pressure piston-cylinderand diamond anvil experiments. Although there are numerous experimental studies of the solid-state phase transitions at low pressures, the high-pressure transformations and the melting curve of the silica phases have not been determinedsatisfactorily. The experimental difficultiesof studyinghigh-pressure transitionsas well as the inherent kinetic problems at low temperatureshave made the available high-pressure experimental data contradictory. Thermodynamicstudyof the SiO2 phasediagraminvolvingthe high-pressurepolymorphsand the liquid phasehas also been limited. Thermochemical and elastic properties of the crystallinesilica phasesare rather well known throughdirect measurements and indirectdeterminations, but suchproperties of the liquid phaseare not knownpreciselyenoughto calculate crystal-liquidequilibiumat high pressures.We presentin this paperan evaluationof the thermodynamic propertiesof all the crystalline phases of silica stable up to 15 GPa (quartz, tridymite, cristobalite,coesite, and stishovite) and the liquid from a studyof the availablecalorimetric,experimentalphase equilibrium,and physicalpropertydata.

Copyright1994by the AmericanGeophysical Union. Papernumber93JB02968. 0148-0227/94/93JB-02968505.00

Several polymorphs of silica are known, and their temperature-pressure stabilityhasbeendiscussed andreviewed by a numberof authors[e.g.,Sosman,1965;Deer et al., 1966; Liu and Basseft, 1986; Taylor, 1984]. The principal polymorphsstable at pressuresless than about 3 GPa are quartz,tridymite,and cristobalite,eachwith a low-temperature (or) and a high-temperature(fl) form. The a-fl quartz transformation occurs at 846.45+1.50 K at atmospheric pressure[Tuttle, 1949]. At ambientpressure,t-quartz is metastableabove 1140 K, where tridymite is the stableform. The phasetransformationbehaviorof tridymite is complicated and is not clearly understood. Several modifications of tridymite,especiallyat low temperatures, have beenreported. Fenner [1913] identified three major forms: low-temperature (up to 388 K), intermediate-temperature (388-433 K), and high-temperature (above433 K) forms. Minor thermaleffects corresponding to possiblestructuralmodificationshave been observed at 337 K, 483-708 K, and 748 K. Synthetic tridymite shows transformationat 653 K and 693 K [see Taylor, 1984]. fl-Cristobalite,the one-atmosphere liquidus mineralof SiO2, is stablefrom 1743 K up to themeltingpoint at 1999+5K [seeRicheret al., 1982]. The a-fl transformation ßin cristobalitetakesplace at about533 K, with the transition temperature typicallyfalling in the rangebetween493 and 543 K [Hill and Roy, 1958]. From the available experimental phaseequilibriumdata [Fenner, 1913; Kennedyet al., 1962; Ostrovsky,1966;Grattan-Bellew,1978], the/]-quartz- hightridymite-/•-cristobalitetriplepointis placedat about1460 K and 0.15 GPa. Tridymite is not a stable polymorph above 0.15 GPa, cristobalitemay be stableup to 0.6 GPa [Jackson,

11,787

11,788

$WAMY EF AL.: THERMODYNAMIC ASSESSMENT OF SILICA PHASE DIAGRAM

to 1500 K and compared these data with the available experimentaldata [Holm et al., 1967; Akaogi and Navrotsky, 1984] and the internally consistentthermodynamicdata sets of Kuskovand Fabrichnaya[1987], Berman [1988], andFei et Bassett, 1986]. The a-quartz - fi-quartz and quartz-coesite al. [1990]. Kuskov et al. [1992] examined the standard transitionshave been extensively investigated(reviewed by thermodynamicproperties of coesite and stishovite in the Weaver et al. [1979]; later investigationsby Mirwald and light of their newly determined calorimetric values for the enthalpy of quartz-coesitetransition. The CODATA Task Massonne [1980], Bohlen and Boettcher [1982], and Kanzaki [1990]). Experimental studies of the coesite-stishovite Group on GeothermodynamicData has recently compiled the transformationinclude those by Ostrovsky [1965], Akimoto calorimetrically determined thermodynamicpropertiesof the and Syono [1969], Yagi and Akimoto [1976], Suito [1977], crystallineand liquid forms of silica [I. L. Khodakovsky,E. F. Pacalo and Gasparik [ 1990], andZhang [ 1992]. The agreement Westrum, Jr., and B. S. Hemingway, personalcommunication, of the various determinations is reasonably good in the 1993]. temperature range of 800-1700 K. However, the phase boundaryat higher temperatures(2273 to 3073 K) determined Thermodynamic Relations by Zhang [1992] is at variancewith the availabledata at lower temperatures,unless the coesite-stishovitephase bounday is The Gibbs free energy of formation of a phase from the stronglycurved. Zhang's [1992] data above2273 K definesa phase boundary with a dP/dT slope two-and-a-half times as elementsat temperatureT (K) and 1 atm pressureis givenby large as that defined by the in situ X-ray data of Yagi and Akimoto [1976] below 1375 K and Pacalo and Gasparik's (1) [1990] reversaldata at 1473 K and 1673 K. Kinetic problems at lower temperaturesand different startingmaterials,a curved phaseboundary,or a secondorder and nonquenchablephase whereAHT andAST are transformation in coesite may account for the discrepancy [Zhang, 1992]. AC•,(T)dT

1976], and the quartz polymorphsare stableat pressuresup to 3.5+1.0 GPa [Mirwald and Massonne, 1980; Kanzaki, 1990]. At pressuresabove 3.5+1.0 GPa, first coesite and then stishovite become the stable modifications of silica [Liu and

o

o

o

o

o

In addition to these modifications, silica is known to exist

in metastableforms (e.g., keatite and moganite) and at very high pressureexperimentalconditions,with the ot-PbO2-type [German et al., 1973], modified Fe2N-type [Liu et al., 1978], and CaC12-type structures as well as with some unknown structures[Tsuchida and Yagi, 1989, 1990]. None of these very high pressureforms, however, has been confirmedas a stable phase. Three experimentaldeterminations of the anhydrousmelting curve of silica polymorphs at pressuresup to 14 GPa are available. Jackson [1976] determinedthe melting curve of cristobaliteandthatof fi-quartzin thepressure range0.6 to 2.5 GPa and locatedthe triple point of cristobalite,fl-quartz, and liquid at approximately 1973 K at 0.6 GPa. Jackson [1976]

(2)

AST =

AC•,(T) dT.

1,298.15

T 98

(3)

Thermochemicaldata are usually listed in terms of the enthalpyof formationof the compoundat 1 atm and 298.15 K

(AH•1.298.15)), theentropy of thecompound at 1 attoand ASø 1.298.15), and the heat capacity at constant pressure of the compound from 298.15 K expressedas a

298.15 K

(

polynomial on temperature C•,(T). We usethefollowingform

[Saxena et al., 1993]: noticedthe steepinitial slopeof the ]•-quartzmelting curve. of C•,(T)expression Kanzaki [1990] studiedthe melting curvesof fi-quartz and coesite at pressuresof 3 to 7 GPa and located the quartzcoesite-liquid triple point at 4.5 GPa and 2723 K. Zhang [1992] determinedthe melting curvesof coesiteand stishovite in the temperature andpressurerangesof 1273 to 3125 K and9 to 14 GPa, respectively, and bracketedthe coesite-stishoviteliquid triple point between13.5 and 13.8 GPa at 3073 K. A linear extrapolationof the coesite-stishovitephase boundary throughthe data of Yagi and Akimoto [1976] and Pacalo and Gasparik [1990] would place this triple point at a much lower pressure(about2.5 GPa below Zhang'sdetermination). Thermochemical properties of the quartz polymorphs are more accurately known [e.g., Hosieni et al., 1985; Hemingway, 1987] thanthoseof the otherforms. Holm et al. [1967] first studied the thermochemicalpropertiesof coesite and stishovite calorimetrically. By comparing the data of Holm et al. [1967] with the available phase stability and elastic data for quartz-coesite and coesite-stishovite transformations,Weaver et al. [1979] found inconsistencyin the former. Akaogi and Navrotsky[1984] measuredenthalpies of transition among quartz, coesite, and stishovite by hightemperature solution calorimetry and calculated the phase boundarycurves among quartz, coesite,and stishovite. Gillet et al. [1990], using vibrational modeling of room pressureand high-temperatureRaman spectroscopicdata, derived a set of specific heat and entropy values for coesite and stishoviteup

Cs,(T) = a+ bT+ cT'2+ dT2+ eT'3+ fT'• + gT'•.

(4)

At pressures above1 atm, a volumecontributionGVp hasto be

added toAG•,Tj togetthetotal Gibbs free energy. Gvpis given by

GVp =I•V(t'.r• dP,

(5)

where V(•,.r) isthemolar volume asa function ofpressure and temperatureand can be calculated using the well known Murnaghanequation

=

(1.fKr;P)

(6)

In the aboveequation,Kr is the isothermalbulk modulus, expressedhere as [Saxena, 1989]:

Kz= 1/([3o + [51T + 1•2T 2+ I•zT3)

SWAMY ET AL.: THERMODYNAMIC

ASSESSMENT OF SILICA PHASE DIAGRAM

! 1,789

andK'ris thepressure derivative of bulkmodulus whichin

minimization program called ChemSage[Erikssonand Hack,

somecaseshas a temperature dependence expressed as'

1991].

We usedthe thermodynamicand volumetricpropertiesof the

K• = K•rr+K•r(T-Tr) In(TiTr).

(8)

quartz polymorphs; zlHø•.298.•5) value,ASø•.29•.•5 value,andthe C•,(T)coefficients for coesite;andthe C•,(T) coefficients and

Tr is the referencetemperature(298.15 K for solidsand 1673

K fortheliquid).NotethatK'vandK•r arethesamewhen thereis no temperature dependence.The molar volumeat T(K) and 1 atm in (6), is given by

volumetric propertiesfor stishovitefrom Saxenaet al. [1993]. The data summarizedby Saxena eta/. [1993] are from earlier evaluationsby Saxena and coworkers [e.g., Fei et al., 1990; Saxena and Shen, 1992] that considerthe internal consistency among phase equilibrium data, calorimetric data, constant

pressure heatcapacityCp, constant volumeheatcapacityC•, Vo.r• = Vi•.r0 exp

ot(T) dT

thermalexpansivity,and compressibility. The Cv(T)

,

coefficients for tridymite and cristobalite were obtained by

(9)

where Vi•.rO isthemolar volume atreference temperature and1

refittingthe CODATA C•, data[I. L. Khodakovsky, E. F. Westrum, Jr., and B. S. Hemingway,personalcommunication, 1993] to (4). The liquid heat capacity and the enthalpy and

arm,anda (T) is thecoefficient of thermal expansion defined entropy of fusion of cristobalite(8.92+1.00 kJ mol'• and as a function of T [Saxena, 1989]:

4.46+0.50 J mol '• K'•, respectively)are from Richet et al. [1982].

ct(T)= • + a•T + a2T4 + ct3T'2.

(10)

Note that in our thermodynamictreatment,we specifically model the temperature dependence of bulk modulus (or compressibility)as discussed by Saxenaand Shen[1992]. The Murnaghanequationis thereforeused to generatea seriesof isothermsat differenttemperatures [seeSaxenaet al., 1993]. If the pressureand temperaturedependencesare correctly modeled,the isothermsshouldshow the effect of a decreasing ct with increasingpressure,as seen in Figure 1. The total

Gibbsfree energyat any temperature andpressureAGøP,Tis

We consideredthe following volumetricdata on cristobalite, tridymite, coesite,and the liquid. Thermal expansiondata for the crystalline phases are given by Taylor [1984]. The available volume thermal expansiondata on liquid silica have a large spread. From density data at temperaturesof 22082438 K, Bacon et al. [1960] obtained a coefficient of volume

thermalexpansivity of 108 x 10'6 K'l for liquidsilica. Lange and Carmichael [1987] obtained a value of almost zero for the partial molar expansivity of silica in multicomponentliquids.

Herzberg[1987]andBottinga[1991]useda valueof 1.0x 10'5 K4 in theirthermodynamic analyses [seeHerzberg,1987,for a

thesumof AGø(1,T)andGVp. In thepressure rangeof this compilationof estimatedthermalexpansivitydata]of/t-quartz study(0.1 MPa to 15 GPa), thereis no significantdifferencein

the calculatedAGøp,T if one uses the Birch-Murnaghan

melting. Dingwell et al. [1993] gavea rangeof 12-123x 10'6 K4 for the thermalexpansivityof liquidsilica.

The available data on zero-pressure bulk modulus of cristobaliterange between15 and 20 GPa (18+1 GPa by X-ray diffraction data of Tsuchida and Yagi [1990], 17.2 GPa by molecular dynamics calculationsof Tsuneyukiet al. [1988], Method of Optimization and Data Used and-16.0 GPa by Brillouin spectroscopicdeterminationby The optimization was carried out by using the computer Yeganeh-Haeri et al. [1992]). Except for indirect estimates 1988], we have not come across an program Parrot, available in the Thermo-Calc data bank [e.g., Berman, package [Sundrnanet al., 1985] and the Gibbs free energy experimental determination of compressibility of tridymite. We thereforerelied solely on phaseequilibriumconstraintsin obtaining the compressibility coefficient for tridymite. Levien and Prewitt [1981], using available experimentaldata, Stishovite concludedthat the true zero-pressurebulk modulusof coesite

equationinsteadof the Murnaghanequation.

should lie in therange of 89-109GPa,witha K'rof ~8.0.

15.0

Unlike the thermal expansivity data, the experimentally determinedand estimateddata on bulk modulusof liquid silica available in the literature agree very well. These include the experimentalvaluesof 11.8 GPa given by Bucaro and Dardy [1976] and 12.95 GPa given by Krol et al. [1986] and the estimated values with a mean of 13.0+1.3 GPa [Herzberg, 1987]. The data for the liquid phaseare discussedin the next

14.5

section.

14.0

13.5

13.0

0

5

10

15

20

Pressure, GPa

25

30

The phaseequlibfiumdata includedin our assessment are the following: (1) equilibria among the quartz polymorphs, tridymite, and cristobalite[Cohen and Klement, 1967; Fenner, 1913; Kennedy et al., 1962; Grattan-Bellew, 1978; Ostrovsky, 1966; Jackson, 1976]; (2) quartz-coesite transition [Mirwald and Massone, 1980; Bohlen and Boettcher, 1982; Kanzaki, 1990]; (3) coesite-stishovite transition [Yagi and Akimoto, 1976; Suito, 1977; Pacalo and Gasparik, 1990; Zhang, 1992]; and (4) melting of cristobalite, /t-quartz, coesite,and stishovite [Jackson, 1976; Kanzaki, 1990; Zhang, 1992].

Figure 1. Isothermsfor stishovitcillustratingthe effects of thermal Statistical error estimates of fits to individual reactions can expansivityandcompressibility on thevolumeas a functionof pressure. data. The curveslabeleda, b, c, d, e, andf representisothermsat 300, 900, be evaluatedanddependon the scatterof theexperimental Such estimatesfor the thermodynamicdata such as enthalpy 1500,2100,2700, and3200 K, respectively.

11,790

SWAMYET AL.:THERMODYNAMICASSESSMENT OFSILICAPHASEDIAGRAM

and entropy cannot be exclusively assigned because the

presentedin Figure5. The o•-11quartzand the quartz-coesite

optimization proceduresinvolve AG ø for severalreactions simultaneously.A sensitivitytest would reveal that errorsof the order of 100 J mol-• in enthalpyof a phasemay lead to considerablemisfit of the calculatedcurvesto the experimental

transitions are very well reproduced by our data except at temperatures roughlybetween975 and 1400 K, wherea slight overestimation of pressure is seen in relation to the experimental data of Mirwald and Massonne [1980] and

data [see Fei eta/., 1990].

Results

and

Discussion

The thermodynamic propertiesat 298.15 K and0.1 MPa, the heat capacitycoefficients,and the volumetricpropertiesof the phasesare listed in Tables 1, 2, and 3, respectively.It should be noted that the volumetricpropertiesof liquid silica given in Table 3 areour preferredvalues(seebelow). The calculatedand experimental volume thermal expansion of cristobalite, tridymite, and coesiteare shown in Figure 2 [see Taylor, 1984, for the experimental data]. In Figure 3, V/V ø of tridymite,cristobalite,coesite,and liquid silica are shownas a functionof pressure.The experimentalcompressibility dataof Yeganeh-Haeriet al. [1990] andPalmer and Downs[1991] on cristobalite and of Levien and Prewitt [1981] on coesite are

alsoplottedin Figure3. A bulk modulusof 19.5 GPa (with a pressurederivativeof 6) for cristobaliteis consistent with the experimental data at lower pressures,where this phase is stable. A bulk modulusof 25 GPa for tridymite derived from phase equilibrium constraintis in keeping with its density being intermediatebetweenthat of cristobaliteand quartz (the latterhas a Kr between28 and44 GPa). In Figure 4, the calculated phase diagram showing the

Bohlen and Boettcher [1982].

In sharp contrast to all the other phase boundaries,the misfit betweencalculatedand experimentaldata in the case of coesite-stishovitetransition is most striking. The existing experimental data on coesite-stishovite transition are controversial,as mentionedearlier. Zhang [1992] arguedthat in all likelihood, all the phase equilibrium experiments performed to date below 1673 K did not position the phase boundary correctly becauseof the inherent kinetic problems under these conditions and that precise determinationof the coesite-stishovite boundaryis favored at higher temperatures. While the marked disagreementin dP/dT slopesbetween the determinationsat low temperaturesand high temperatures needs to be resolved, the exact nature of the coesite-stishovite

transition (the possibility of a curved phase boundary or a second-ordernonquenchabletransitionin coesite[see Zhang, 1992]) is also unclear. Given these circumstances, our approachwas not to bias our assessmentto any particulardata set but instead

to obtain

an evaluation

that satisfies both the

low-temperatureand the high-temperaturedata. Our calculated coesite-stishoviteboundary matches reasonably well with most of the availableexperimentalphaseequilibriumdata over the temperaturerange of 500 to 2000 K. The calculated boundarydoes not agree well with Zhang's [1992] data at higher temperatures,notwithstandingthe considerationsthat the errorsof pressureestimationcouldbe asmuch as 1 GPa and that in the worstcase,the error in temperaturecouldbe +75 K

stability relations among o•-quartz, ]l-quartz, tridymite, cristobalite, and liquid is presented along with the experimentaldata. The calculatedcristobalite-tridymite phase under these conditions. boundarydoesnot agreewell with the experimentalreversals. The factors that contribute to the relative high-temperature It is possibleto get a better fit to experimentaldata by using different thermal expansivitiesfor tridymite and cristobalite stabilitiesof coesiteand stishoviteare C•, and the elastic properties.The availableheatcapacitydataare preciseenough than the measured values, for instance, as done by Berman only in the low-temperaturerange (up to about500 K). The [1988]. The SiO2 phasediagramwith all the polymorphsstableup to 15 GPa and the liquid phase calculated using our data is Table la. Thermodynamic Propertiesof the Silica Phasesat 298.15

K and 0.1 MPa

extrapolation of C•, to highertemperatures mayleadto some

errors. Our heat capacitydata are similar to the CODATA values [I. L. Khodakovsky, E. F. Westrum, Jr., and B. S.

Hemingway,personalcommunication,1993] up to 1800 K.

TheCt, of coesite isverycloseto thevalues obtained byGillet et al. [1990] with anharmonic correction for C,,. In the

ASo,JI• •

o JK-I C•,

-910,700.00 -910,497.00 -906,913.00

41.460 41.700 45.116

44.589 44.589 44.254

Cristobalite Coesite Stishovite

-906,034.00 -906,900.00 -864,000.00

46.060 40.500 29.500

44.299 42.794 42.159

Liquid

-901,013.00

49.033

44.217

Phase

AHø,j

a-Quartz ]•-Quartz Tridymite

temperature rangeof 1000-1500K, our C•, for stishovite is slightlysmallerthanthe dataof Gillet et al. [1990] corrected for artharmoniceffects (at 1500 K, the difference is about 3%).

Our C•, extrapolation has the expected correctbehaviorat highertemperatures, thatis, theCt, valuesapproach constant valuesand are not overestimatedin comparisonwith the liquid

C•,. The elasticproperties of bothstishovite andcoesiteat high temperaturesare also not known. Our heat capacityand elasticparameters(Tables 2 and 3) were obtainedthroughan optimizationprocedurewhich seeks an internal consistency

The datafor quartzare the sameas thoseof Robieet al. [1978]. The datafor tridymite,cristobalite,stishovite,andliquid silicaare from this C•,, C,,, thermalexpansivity, andcompressibility, as study.See Saxenaet al. [1993] for the dataon coesite.The enthalpies among detailed in Saxena and Shen [1992]. Additionally, for and entropiesof transitionamongthe variousphasesare comparedin

stishovite, the data systematization also considered several

Table lb.

Table lb. Comparisonof Enthalpyand EntropyChangeof PhaseTransitionat 298.15 K

AS,Gibbsmol-1

AH, kJmol-1 Reaction

This Akaogi and Study Navrotsky[ 1984] Quartz=coesite Coesite=stishovite

3.80 42.90

2.93+0.30 48.95+1.72

Holm et al. [1967] 5.06+0.63 44.27+1.42

This

Study -0.96 -11.00

Holm Akaogi and Navrotsky[ 1984] et al. [1967]

-2.92+0.83 -4.184+1.70

-0'962 -12.594

SWAMY ET AL.: THERMODYNAMIC

ASSESSMENT OF SILICA PHASE DIAGRAM

11,791

Table2. Coefficients forHeatCapacity Cp(T)

C•,(T) =a+bT+cT'2+dT2+eT '3+tT'•a+gT '• Jmol_ 1K-1 Phase

•-Quartz 298.15-848 K 848 -4000 K

298.15-848 K 848 - 4000 K Tridymite 298.15-4000 K

a

b,103

c,10-4

d,108

e,10-8

f

81.1447 78.8120

18.2800 1.2050

-18.0986 173.1000

540.5800 0.0000

0.000 1.202

-698.458 0.000

0.0000 -1.2130

0.84

81.1447 78.8120

18.2800 1.2050

-18.0986 173.1000

540.5800 0.0000

0.000 1.202

-698.458 0.000

0.0000 - 1.2130

0.84

66.6993

5.2779

-213.2338

-35.4783

0.000

0.000

0.0000

907.7209

-3,083.8590

-1,971.8167

31,256.5000

0.000

0.000

0.0000

74.9325

-1.6202

-440.5322

99.4385

0.000

0.000

0.0000

78.0000

0.0000

0.0000

5.858

0.000

-0.6689

58.1200

7.0020

-1268.9000

0.0000

17.928

0.000

1.7010

73.7932 81.3700

1.6786 0.0000

-620.6124 0.0000

0.0000 0.0000

10.532 0.000

0.000 0.000

0.0000 0.0000

g,10-4

H*

Cristobalite

298.15-523 K 523-4000 K Coesite

298.15-4000 K

-310.0000

Stishovite

298.15-4000 K Liquid 298.15-1480 K 1480-4000 K

Heatcapacity coefficients wereobtained bya leastsquares computer fit of datafromthefollowing sources to (4): c•- and quartz,Robieet al. [1978];tridymiteandcristobalite, CODATA (I. L. Khodakovsky et al., personal communication, 1993); liquidsilica,Richetet al. [1982]. Theheatcapacity coefficients for coesite andstishovite arefrom Saxenaet al. [1993][see Saxena and Shen, 1992].

* Enthalpy of transition, kJmo1-1. phase boundariesinvolving stishovite in the MgO-SiO2

choiceof the AS (-11.0J mol '• K'• at 298 K) is dictatedby

Zhang's[1992] data. Gillet et al. [1990] did arguein favorof a The enthalpy and entropy data on coesite-stishovite smallerentropyof transitionthan that determinedby Akaogi transition presented in Table lb indicate that our data are and Navrotsky [1984] [see Richet, 1990]. From our

system.

closer to those of Holm et al. [1967] than to the values of

calculations we obtain AS values of-8.72

Akaogi and Navrotsky [1984]. Kuskov et al's [1992] calculations demonstrated the possibility of obtaining transitionenthalpiesand entropiesthat are close to either of the two calorimetric determinationsdepending on the experimentaldata set chosenfor the phase transition. Our

for coesite-stishovite transitions at 1000 K and 1500 K, respectively,which are close to the data of Gillet et al. [1990].

and -7.76 J mol '• K 4

Thusour entropyandheatcapacitydataseemto be reasonably well constrainedat least up to 1500 K. With these data, an

optimizationdone by excludingZhang's [1992] data to get a

Table 3. VolumetricPropertiesof the $iO2 Phases

Phase Vø,cm 3 (Xo, 105

107

a-Quartz

22.688

2.7513

0.29868

]•-Quartz Tridymite

22.865 26.530

2.0604 23.4923

0.34694 -2.40434

27.51'

2.!797

-0.15300

Cristobalite 25.739

4.5445

0.81508

27.40*

0.5000

0.00000

20.641

0.5430

0.07600

Coesite

Stishovite•14.014 0.2300 0.12000 Liquid 27.20 • -774.1104 9.66613

10 • 5.5722

130.7500 -10,750.0000

0.0000

102 [5 o,10 • 9.1181

[5•, 10 •ø

2.55600

0.11557

-163.7600 12.7930

1.39699 4.00000

24.11910 0.00000

[52, 10•4 [53, 10•7K•, 0.01013

-215.18000 0.0(X}(O

0.0889

6.4

64.5430 5.3 0.0000 6.0

0.0000

4.00000

0.00000

0.0(X}(O

0.0000

5.13000

0.00000

0.00000

0.0000

0.0000

0.{KD0

5.13000

0.00000

0.00000

0.0000 6.0

0.0000

0.0000

0.00000

0.0000

4,461.9600

6,200.0000 -113.0000 20.2E-6 -167.6800

1.05000

1.50000

0.29540 7.44500

0.89610 0.09492

176.2630a

1,740.16200

-3.29000 0.00000 5,713.22800

0.0000 6.0 6.0 8.4

2.3310 6.0 0.0000 4.0 -587.3007

4.0

Vø is themolarvolume at 298.15K and0.1MPafromRobieetal. [1978]unless notedotherwise. Thermal expansion (K'l) is expressed as

ct(T) = Cto +ctlT+ctzT 4+ct3 T'2., and isothermal bulk modulus (in10 '5Pa 'l) isexpressed asKi= 1/(13o + [•lT+•2T2+[•3 T3). K3isthe pressure derivative ofbulk modulus. *Molar volumeat 623.15 K. *Molar volumeat 533.15 K.

•Here,K•,•,= 0.001 • Molarvolume at 1673.15 K (seetext). a Bulk modulusabove 2700 K.

11,792

SWAMY ET AL.: THERMODYNAMIC

1.08

•

•

1.07-

•

•

ASSESSMENT OF SILICA PHASE DIAGRAM 2200

•

Uquid

Cristobalite

1.06 -

2000

•

-

1.05 -

Cdstobalite

1800

-

1600

Tridymite

1.04-

•

x

X Cohen & Klement [1967] [] Fenner [1913] A Grattan-Bellew [1978]

1400

0 Kennedy et al. [1962] 00strovsky [1966]

1 .o3 -

.o2 -

Beta-quartzV Jackson [1976] 1ooo

1.Ol

1.oo I 200

0 Jackson [1976]

1200

I

400

I

600

800

I

I

1000

1200

1400

800 I

I

I

I

I

i

0

1

2

3

4

5

Temperature, K

E8

6

7

8

9

10

Pressure, Pa

Figure 2. Comparisonof calculatedand experimentaldata for volume thermalexpansionof cristobalite,tridymite, and coesite. See Taylor [1984] for the experimentaldata.

coesite-stishoviteboundary that is consistentwith the data of Yagi and Akimoto[1976] andPacalo and Gasparik [1990] gave

a transitionenthalpyof 41 kJ mol'1. From Figure 5 it can be seen that the experimentaldata on melting are also reasonably well describedby our data set except near the triple point with coesite and stishovite. The volumetric properties of liquid silica (molar volume and thermal expansivity) are among the less well determined parametersthat influence liquidus phase relations shown in Figure 5. The spreadin the available data on referencestate (1673 K and 0.1 MPa) molar volume of liquid silica could lead to an error of up to 2% of the volume (Herzberg's [1987]

Figure 4. Calculated phaseequilibrium relations amongg-quartz,•uartz,tridymite, cristobalite, andliquidsilica.Theexperimental dataof ohenand Klement[1967] representct-quartz=I•-quartz.Data from Jackson [1976] are on silica glass(open circles),•-quartz (solid circles),and cristobalite(solid triangles). The openand solidsymbols from the othersourcesrepresenthalf-brackets on oppositesidesof each equilibrium.

I

3300

I

I

I

I

I

I

I

I

Liquid

3000 -

ß

2700 -

compilationgavea rangefrom 26.75 to 27.20 cm3;Langeand Carmichael [1987] derived a partial molar volume of 26.90-z0.06cm3; Krol et al. [1986] useda valueof 27.30 cm3).

2400Coesite

Stishovite

21001.00 •-

i

i

I

i

i

1800 -

X Jackson [1976]

1500-

O Mirwald& Massonne[1980J

Cohen & Klement [1967]

0.96

^

-J- Bohlen & Boettcher (1982]

[] Kanzaki [1990]

1200 -

0.92

A&

900 -

• 0.88

B c

O.84

I• Pacalo & C.•sparik [1990] 0 Zhang [1992]

600 0

i

i

i

i

i

i

i

i

i

2

4

6

8

10

12

14

16

18

20

Pressure, GPa

0.80

D- Liquid 0.76

A Suito[1977] 0 Yagi & Akirnoto [1976]

o

1

•

D

3

4

5

6

Pressure, GPa

Figure 5. Calculated phaserelationsof SiO2 up to 15 GPa. Tr andCr standfor tridymiteandcristobalite,respectively. The experimental data represented are as follows:uncorrected pressure-temperature data fo;' •-quartz=liquidequilibriumfromJackson[1976];a-/• quartztransition (selecteddata from Cohen and Klement [1967]); quartz=coesite equilibrium [Mirwald and Massonne,1980; Bohlen and Boettcher, 1982]; quartz=coesiteand melting transitionsof quartz and coesite [Kanzaki, 1990] (the solid, open, and open-with-diagonalboxes

represent liquid,coesite,and•-quartz, respectively); coesite=stishovite Figure 3. Calculatedisothermalvolumecompressibility of coesite, tridymite,cristobalite, andliquidsilica. Experimental dataof Levienand Prewitt [1981]on coesite(opencircles)andthedataof Yeganeh-Haeri et al. [1990] (opensquares)andPalmer and Downs[1991] (plussigns) on cristobaliteare represented.

transitionfrom Suito[1977] andYagi and Akimoto[1976] (eoesite,open symbols;stishovite,solid symbols)and reversaldata from Pacalo and Gasparik [1990]; coesite=stishoviteand melting transitionsof eoesite and stishovite[Zhang, 1992] (the solid,open,and hatchedpentagons indicateliquid, toesite,andstishovite,respectively).

SWAMY ET AL.: THERMODYNAMIC

ASSESSMENT OF SILICA PHASE DIAGRAM

However, this error in molar volume does not affect the results

significantly. Our preferredvalue for liquid molar volume is 27.20 cm 3 and we use two sets of coefficients for bulk modulus.

Beginning witha valueof 13.4GPaat 1673.15 K anda K•,'of 4.0, the bulk modulushas a slight temperaturedependenceup to 2700 K. The temperaturedependenceis stronger in the secondrange (above 2700 K) (see Table 3). The thermal expansioncoefficientswere assessedon the basis of liquidcrystal phaseequilibria. Acknowledgments. The Swedishteam thanks the SwedishNatural ScienceResearchCouncil (NFR) and NUTEK (throughCAMPADA)

for financialsupport.We thankthereviewersM. AkaogiandB. Mysen for their criticalcomments, whichimprovedthe qualityandaccuracyof our presentation.

11,793

Kanzaki, M., Melting of silicaup to 7 GPa, J. Am. Ceram.Soc., 73, 3706-3707, 1990.

Kennedy,G. C., G. J. Wasserburg,H. C. Heard, and R. C. Newton, The upperthreephaseregionin the systemSiO2-H20, Am.J. Sci.,260, 501-521, 1962.

Krol, D. M., K. B. Lyons, S. A. Brawer, and C. R. Kurkjian, Hightemperature light scatteringandthe glasstransitionin vitreoussilica, Phys.Rev. B, 33, 4196-4202, 1986. Kuskov,O. L., and O. B. Fabrichnaya, The SiO2 polymorphs:The equations of state and thermodynamic properties of phase transformations, Phys.Chem.Miner., 14, 58-66, 1987. Kuskov, O.L., A. P. Zhidikova, Y. V. Semenov,Y. V. Babich, and O.

B. Fabrichnaya, Thermodynamics of silicapolymorphism, Geochem. lnt., 29(3), 93-102, 1992.

Lange, R.L., and I. S. E. Carmichael,Densitiesof Na20-K20-CaOMgO-FeO-Fe203-A1203-TiO2-SiO 2 liquids:New measurements and derivedpartial molar properties,Geochim.Cosmochim.Acta, 51, 2931-2946, 1987.

Levien, L., and C. T. Prewitt, High-pressurecrystal structure and compressibility of coesite,Am. Mineral., 66, 324-333, 1981. References Liu, L., and W. A. Basseu, Elements, Oxides,Silicates,High-Pressure With Implicationsfor the Earth's Interior, 250 pp., Oxford Akaogi, M., and A. Navrotsky, The quartz-coesite-stishovite Phases UniversityPress,New York, 1986. transformations: New calorimetric measurements and calculation of Liu, L., W. A. Basserr,and J. Sharry, New high-pressure modifications phasediagrams,Phys.EarthPlanet.Inter.,36, 124-134,1984. of GeO2 andSiO2, J. Geophys.Res.,83, 2,301-2,305,1978. Akimoto,S., and Y. Syono, Coesite-stishovite transition,J. Geophys. Mirwald, P.W., and H.-J. Massonne, The low-high quartz and Res., 74, 1653-1659, 1969. quartz-coesite transitionto 40 kbar between600ø and 1600øCand Bacon.J. F., A. A. Hasapis,andJ. W. WhoHey,Jr.,Viscosityanddensity somereconnaissance dataon the effect of NaA102 componenton the of moltensilicaandhighsilicacontentglasses,Phys.Chem.Glass,1, low quartz-coesite transition,J. Geophys.Res.,85, 6983-6990,1980. 90-98, 1960. Ostrovsky,I. A., Experimentalfixation of the positionof coesiteBennan,R.G., Intemally consistent thermodynamic datafor mineralsin stishoviteequilibrium curve, Izv. Acad. Sci. USSR Geol. Ser., the systemNa20-K20-CaO-MgO-FeO-Fe203-A1203-SiO2-TiO2 1965(10), 132-135, 1965. H20-CO2, J. Petrol.,29, 445-522,1988. Bohlen,S. R., and A. L. Boettcher,The quartz-coesite transformation: Ostrovsky,I. A., PT-diagramof the systemSiO2-H20, Geol.J., 5, 127134, 1966. A precisedeterminationand the effects of other components,J. Pacalo, R. E.G., and T. Gasparik, Reversalsof the orthoenstatiteGeophys.Res.,87, 7073-7078, 1982. clinoenstatite transitionat high pressures and high temperatures,J. Bottinga,Y., Thermodynamicpropertiesof silicate liquids at high Geophys.Res.,95, 15,853-15,858,1990. pressureand their bearing on igneous petrology, Adv. Phys. Palmer,D.C., andR. T. Downs, High pressurebehaviorof cristobalite Geochem., 9, 213-232, 1991. revealed by single crystal X-ray diffraction, Eos Trans. AGU, Bucaro,J. A., and H. D. Dardy, Equilibriumcompressibility of glassy 72(44), Fall MeetingSuppl.,478, 1991. SiO2 betweenthe transformation and meltingtemperature, J. Non Richer, P., GeO2 vs SiO2: Glass transitions and thermodynamic Cryst.Solids,20, 149-151,1976. properties of polymorphs, Phys.Chem.Miner., 17, 79-88, 1990. Cohen, L. H., and W. Klement, Jr., High-low quartz inversion: Richer, P., Y. Bottinga,L. Denielou, J.P. Petitet, and C. Tequi, Determination to 35 kilobars,J. Geophys.Res.,72, 4245-4251, 1967. Thermodynamicpropertiesof quartz, cristobaliteand amorphous Deer, W. A., R. A. Howie, and J. Zussman, An Introduction to the SiO2: Drop-calorimetry measurements between1000and 1800K and Rock-FormingMinerals,528 pp., Longman,Essex,U.K., 1966. a review from 0 to 2000 K, Geochim. Cosmochim. Acta, 46, 2639Dingwell, D. B., R. Knoche,and S. L. Webb, A volume-temperature 2658, 1982. relationship for liquidGeO2 andsomegeophysically relevantderived parameters for networkliquids,Phys.Chem.Miner., 19, 445-453, Robie, R. A., B. S. Hemingway, and J. R. Fisher, Thermodynamic 1993.

Eriksson,G., and K. Hack, Handbook for ChemSage, GTT mbH, Aachen,Germany, 1991. Fei, Y., S.K. Saxena, and A. Navrotsky, Intemally consistent thermodynamic dataandequilibrium phase relations for compoundsin the system MgO-SiO2 at high pressureand high temperature, J. Geophys. Res.,95, 6915-6928,1990. Fenner,C. L., The stabilityrelationsof the silica minerals, Am. J. Sci., 36, 331-384, 1913.

German,V. N., M. A. Produrets,andR. G. Trunin, Synthesisof a high-

densityphaseof silicondioxidein shockwaves,Soy.Phys.JETP,37, 107-108, 1973.

Gillet, P., A. Le Cleat'h, and M. Madon, High-temperatureRaman spectroscopy of SiO2 nd GeO2 polymorphs:Anharmonicityand thermodynamicpropertiesat high-temperatures.J. Geophys.Res., 95, 21,635-21,655, 1990.

Grattan-Bellew,P. E., Quartz-tridymitetransitionunder hydrothermal conditions,Expl. Miner, 11, 128-139, 1978. Hemingway,B. S., Quartz: Heat capacitiesfrom 340 to 1000 K and revisedvaluesfor the thermodynamic properties,Am. Mineral., 72, 273-279, 1987.

Herzberg, C.T., Magma densityat highpressure,1, The effect of composition on the elasticproperties of silicateliquids,in Magmatic Processes:PhysicochemicalPrinciples, edited by B. O. Mysen, Geochem.Soc.Spec.Publ. 1, 25-46, Pennsylvania, 1987. Hill, V. G., and R. Roy, Silica structurestudies, V, The variable inversionin cristobalite,J. Am. Ceram. Soc.,41,532-537, 1958. Holm, J.L., O.J. Kleppa, and E. F. Westrum,Jr., Thermodynamics

of polymorphic transformations in silica:Thermalproperties from5 to 1070øK and pressure-temperature stability fields for coesiteand

prol•erties ofminerals andrelated substances at298.15 K and1 bar

(10ø pascals)pressureand at highertemperatures,U.S. Geol. Surv. Bull., 1452,456 pp., 1978. Saxena,S.K., Assessment of bulkmodulus,thermalexpansionandheat capacityof minerals,Geochim.Cosmochim. Acta,53, 785-789, 1989. Saxena,S.K., and G. Shen, Assessed dataon heatcapacity,thermal expansionand compressibilityfor some oxides and silicates, J. Geophys.Res., 97, 19,813-19,825, 1992. Saxena, S.K., N. Chatterice, Y. Fei, and G. Shen, Thermodynamic Data on Oxidesand Silicates,428pp., Springer-Verlag,New York, 1993.

Sosman,R. B., ThePhasesof Silica,389 pp., RutgersUniversityPress, New Brunswick,N.J., 1965.

Suito,K., Phaserelations of pureMg2SiO4 upto 200kilobars,in HighPressure Research: Applications in Geophysics,edited by M. H. Manghnaniand S. Akimoto, pp. 255-266, Academic,San Diego, Calff_omia,1977. Sundman, B., B. Jansson, and J.-O. Andersson, The Thermo-Calc

databanksystem,Cornput.CouplingPhaseDiagramsThermochem., 9, 153-190, 1985.

Taylor, D., Thermal expansion,IV, Binary oxideswith the silica structures,Br. Ceram. Trans. J., 83, 129-134, 1984.

Tsuchida, Y., and T. Yagi, A new, post-stishovite high-pressure polymorph of silica,Nature,340, 217-220,1989. Tsuchida,Y., and T. Yagi, New pressure-induced transformations of silicaat roomtemperature, Nature,347, 267-269,1990. Tsuneyuki,S., M. Tsukada, H. Aoki, and Y. Matsui, First-principles

interatomic potentialof silicaappliedto moleculardynamics, Phys. Rev. Lett., 61,869-872, 1988.

Tuttle,O. F., The variableinversiontemperature of quartzas a possible geologicthermometer, Am.Mineral.,34, 723-730,1949. stishovite,Geochim.Cosmochim.Acta, 31, 2289-2307, 1967. Weaver, J.S., D. W. Chipman, and T. Takahashi,Comparison Hosieni,K. R., R. A. Howald, and M. W. Scanlon, Thermodynamics betweenthermochemicaland phase stability data for the quartzof the lambdatransitionand the equationof stateof quartz, Am. coesite-stishovite transformations,Am. Mineral., 64, 604-614, 1979. Mineral., 70, 782-793, 1985. Yagi, T., and S. Akimoto, Directdetermination of coesite-stishovite Jackson,I., Melting of the silica isotypesSiO2, BeF2 and GeO2 at transitionby in-situX-ray measurements, Tectonophysics, 35, 259elevatedpressures, Phys.EarthPlanet.Inter., 13, 218-231, 1976. 270, 1976.

11,794

SWAMY ET AL.: THERMODYNAMIC ASSESSMENTOF SILICA PHASEDIAGRAM

S. K. Saxenaand V. Swamy, TheoreticalGeochemistryProgram, Yeganeh-Haeri, A., D. J. Weidner,LB. Parise,J. Ko., M. T. Vaughan, X. IAu,Y. Zhao,Y. Wang,andR. Pacalo,A newpolymorph of SiO2, Institute of Earth Sciences,UppsalaUniversity, Uppsala,S-75236, Eos Trans.AGUo 710167l, 1990.

Sweden.

B. Sundman,Division of PhysicalMetallurgy, Royal Institute of cristoballte: A silicondioxidewith a negativePoisson's ratio,Science, Technology,Stockholm,S - 100 44, Sweden. $. Zhang,Centerfor High Pressure Research,Departmentof Earth 257ø650-652, 1992. and SpaceSciences,State Universityof New York at StonyBrook, Zhang, $., Meltingof mantlemineralsat highpressures: Experimental StonyBrook, NY 11794-2100. studyandthermodynamic evaluation, Ph.D.thesis,114pp.,City Univ. of New York, New York, 1992. (ReceivedSeptember 7, 1993;accepted October20, 1993.)

Yeganeh-Haeri, A., D. $. Weidner,and$. B. Parise,Elasticityof •z-