American Mineralogist, Volume 78, pages 27 l-284, 1993

Brucite [Mg(OH)rl dehydration and the molar yolume of HrO to 15 GPa

Manrn C. JonNsoNo D.l,vIo War-rnnlamont-Doherty Earth Observatory and Department of Geological Sciences, Columbia University,

Palisades, New York 10964, U.S.A.

Ansrn-q.cr

The dehydration of brucite to produce periclase and HrO [Mg(OH)' - MgO + HrO]was experimentally investigated from I to 15 GPa in order to study the compressibilityof HrO at very high pressures. Low-pressure experiments were performed in a piston-cylinder apparatus and high-pressure experiments in a multianvil. The dehydration bound-ary was identified using both differential thermal analysis and quenching experiments.Thermal gradients present in the multianvil assemblies promoted thermal diffusion andallowed thermally compacted periclase to quench as periclase in quenching experimentsperformed at conditions outside the brucite stability field. Many experimental difficultieswere encountered, including obtaining pure brucite starting material, preventing contam-ination by the pressure medium, and assuring that HrO leakage did not occur during theexperiment. This dehydration equilibrium is especially vulnerable to these types of prob-lems, and special care was required to reduce these sources oferror. The resulting exper-imental data indicate that the reaction boundary has a positive dP/dT slope to 15 GPaand is nearly vertical above 6 GPa (- 1200 'C). These new data are combined with ther-modynamic and PVT properties of brucite and periclase in order to calculate the molarvolume of HrO along the dehydration curve. These calculations suggest that the molarvolume of HrO decreases from 21 cm3 at I GPa and 845 "C to 10 cm3 at 15 GPa and1280 "C. These volumes are very similar to the molar volumes predicted using empiricalmodifl ed Redlich-Kwong P tr/T models.

INrRooucrroN

Accurate thermodynamic data must be combined withreliable physical property data to understand and predictthe behavior of materials at high pressures and temper-atures in the Earth's mantle. The development of veryhigh-pressure experimental techniques (multianvil, dia-mond-anvil) allows these kinds of data to be obtainedunder static conditions and bridges the gap between datacollected using standard piston-cylinder techniques anddata generated under the transient but super high-pres-sure conditions of shock waves. Most recent experimentaldata collected using these very high-pressure techniquesconcern the physical properties and phase equilibria ofthe principal anhydrous minerals found in the Earth'smantle. The physical properties (thermal expansion, bulkmodulus) of hydrous minerals are largely unknown. Thebehavior of fluids (H2O, CO2, etc.) at very high pressureshas not been widely investigated experimentally either,although a few shock wave studies exist (e.g., Rice andWalsh, 1957).

Knowledge of the pressure-volume-temperature rela-tionship, or equation of state, of HrO is crucially impor-tant because HrO controls many physical properties, in-cluding melting temperature, extent of melting, viscosity,phase stability, and mineral relations. In addition, deep-focus earthquakes have been attributed to hydrous min-

0003-004x/93 / 0304427 l$o2.oo

eral dehydration in downgoing slabs (Meade and Jeanloz,199 l). A PVT relationship for H,O would allow phaseequilibria constraints on the stabilities and compositionsof mantle hydrous phases to be calculated. Although sev-eral models of the PW properties of HrO at high pressureexist (e.g., Halbach and Chatterjee, 19821, Belonoshko andSaxena, I 99 I ), these models could be further constrainedby new experimental data at high pressures.

At pressures below I GPa, formidable experimentaldifficulties have been overcome, and the volume of HrOhas been measured directly as a function ofpressure andtemperature (Burnham et al., 1969). Although concep-tually simple, this method has not been successfully ap-plied at pressures ereater than I GPa. At these high pres-sures, one of three approaches may be adopted. First, atheoretical PVT relalionship can be derived using molec-ular dynamics (Belonoshko and Saxena, l99l; Brodholtand Wood, 1990). Second, an empirical Ptr?relationshipcan be deduced on the basis of a modified Redlich-Kwong(MRK) model (e.g., Kerrick and Jacobs, l98l; Holloway,1981; Halbach and Chatterjee, 1982). Because these MRKmodels are purely empirical, they generally fit the dataon which they are based extremely well but cannot beextrapolated with confidence to pressures and tempera-

tures beyond this range. A few of these MRK models

incorporate existing shock wave data for HrO (Lyzenga

271

272 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

et al., 1982' Rice and Walsh, 1957) in order to calculatevolumes at very high pressure. These shock wave dataare limited, however, because temperature cannot bemeasured independently of pressure; it must be calculat-ed using Hugoniot expressions.

A third option based on phase equilibria is adoptedhere. The slope of a univariant curve in pressure-tem-perature space is a function of the differences in volumesand entropies of the products and the reactants. For asimple dehydration equilibrium (H * A + nH,O), theslope of the curve depends on the thermodynamic andphysical properties of HrO, as well as the solid phases. Ifthe volumes and entropies of the solid phases, H and A,and the entropy of HrO are well known as functions ofpressure and temperature, then lhe PW relationship ofthe fluid can be calculated from the location ofthe equi-librium boundary.

Several restrictions must be met for this phase equilib-ria approach to yield useful data. For example, the heatcapaqities and bulk moduli of the solid phases must bewell-known functions of temperature and pressure. Thehydrous phase must break down by dehydration ratherthan by melting over a wide P-T range. Finally, the solidphases must not undergo pressure-induced polymorphicphase transitions, which cause discontinuities in the P-Zslope. An ideal reaction that meets all three requirementsis the dehydration of brucite to form periclase and H.O[Mg(OH), - MgO + H,O]. In addition, this reaction de-serves special interest because the dehydration curve hasbeen predicted to change from a positive to a negativeslope at about 8 GPa (S. Saxena, personal communica-tion). This predicted change in slope reflects the highcompressibility of the fluid phase relative to the solidphases.

The brucite dehydration reaction has been the subjectof much experimental effort at low pressures (<3 GPa)(i.e., Roy and Roy, 1957; Ball and Taylor, 1961; Barnesand Ernst, 1963; Weber and Roy, 1965; Yamaoka et al.,1970; Irving et al., 1977; Schramke et al., 1982). Manyofthese experimental studies produced contradictory re-sults. For example, Yamaoka et al. (1970) reported thatthe slope of the dehydration curve changes from positiveto negative at 3.2 GPa and 1000 oC. In a later investi-gation, these results were disproved, and a positive slopewas recorded to 3.3 GPa (Irving eI al., 1977). The dis-crepancy in results among different investigations may belargely attributed to difficulties in quenching this reac-tion; the kinetics of dehydration and rehydration are sorapid that periclase and HrO tend to reform to bruciteupon quench from high temperature and pressure. Thistendency causes the brucite stability field to be overesti-mated. Furthermore, this reaction is vulnerable to theexperimental environmental controls. Any cryptic leaksthat allow H.O to escape give P".o < P,.,, and an artifi-cially enhanced periclase stability field.

This difficulty with quenching is well recognized, andseveral in situ techniques have been developed to avoidquenching problems. For example, at pressures below 0.8

GPa, the volume of the sample was measured directly atpressure and temperature using a specially fitted inter-nally heated pressure vessel (Schramke et al., 1982). Re-cent attempts to determine this reaction boundary at highpressures have used either in situ X-rays (Leinenweber etal., l99l) or differential thermal analysis [DTA] (Kan-zaki, 1990, I99l).

This paper reports an experimental effort to determineaccurately the brucite dehydration equilibrium from I tol5 GPa. The approach adopted here is a combination ofDTA and quenching experiments. The quenching exper-iments are more reliably interpreted than in previousstudies because thermal gradients cause diffusive migra-tion of periclase and HrO to different regions of the ex-perimental charge. This separation facilitates quenchingof periclase in experiments outside the brucite stabilityf,eld. These new data are then used to calculate the vol-ume of HrO at pressures and temperatures along the re-action boundary. These calculated volumes are comparedwith volumes calculated using MRK PW modell

ExpnnrrvrsNTAr, TECHNTeUES

Reconnaissance experiments were done using reagent-grade brucite obtained from Johnson Matthey. Thisbrucite was found to contain 3 wto/o impurities (mostlyCaCO,). Impurities will alter the brucite dehydrationtemperature. To avoid introducing this uncertainty, purebrucite had to be obtained. Therefore, brucite was syn-thesized hydrothermally from starting materials consist-ing of ultra-high purity 99.80/o MgO (Ozark Tech.) anddeionized, distilled HrO. These starting materials wereweighed, loaded into a Teflon vessel, placed in a large-capacity oven, and held at 225'C for 48 h. The synthesiswas terminated by shutting off power to the oven andletting the Teflon vessel cool down gradually. After cool-ing, the solid product was weighed; the weight gain in-dicated a 98.80/o yield. Standard X-ray diffraction analysisrevealed that the product was brucite, and no other phaseswere present. This new, pure starting material was usedfor all the quenching experiments reported here.

Experiments were performed from I to 15 GPa in twoapparati using two techniques. The low-pressure experi-ments (<4 GPa) were performed in standard piston cyl-inders of the type designed by Boyd and England usingYz-in. furnace assemblies. All these experiments em-ployed in situ DTA to detect the reaction boundary. Ap-proximately 40 mg of brucite was loaded into a Pt capsulewelded on both ends. MgO was used as filler rods, andS-type (1000/o Pt-Pt/100/0 Rh) thermocouples were used tomonitor temperature. In order to produce a differentialsignal, two thermocouples were introduced into the sam-ple region using a double junction thermocouple. The hotthermocouple was embedded directly in contact with thePt capsule, while the cold thermocouple junction was - 5mm above this junction. Graphite tubes served as heat-ers, and the pressure medium was BaCO..

The high-pressure experiments were performed in amultianvil device using a 600-ton press. The pressure

JOHNSON AND WALKER: MOLAR VOLUME OF H,O 273

A) DTA assmbly B) cook md quench

HFig. l. Schematic diagram showing the two multianvil ex-

perimental assemblies. Scale bar is 2 mm in both cases. (A)Assembly for DTA experiments. (B) Assembly for quenchingexpenments.

medium consisted of a fired castable MgO-AlrOr-SiOr-based ceramic [compound 584 made to old Fl00 batchspecifications (CaCOr-free, sieved MgO), Aremco Co.lwith integral gaskets. Initially, a hole with an outside di-ameter of 3. I 75 mm was drilled from face to face throughthe octahedron and lined with Re foil, which served as aheater. Brucite (-20 mg) was loaded either into a hardalumina annulus (2 mm long), or directly in contact withthe heater on top of an MgO filler rod (2.5 mm long).This initial setup proved highly unsatisfactory, however,because the brucite reacted with the alumina annulus andformed Mg-Al spinel. Even in the experiments withoutthe alumina, SiO, and AlrO. from the octahedron werefound to difiirse through small slits in the Re foil andcontaminate the sample. To preserve sample purity a dif-ferent strategy was needed.

The experimental setup was modified so that a holewith a 4.690-mm o.d. was drilled in the octahedron andlined with a tube 1.520 mm thick of high-purity MgO,which was then lined with Re foil. The alumina annuluswas discarded. The MgO liner prevented the pressure me-dium from contaminating the sample. For quenching ex-periments, one thermocouple was introduced into thesample region. This thermocouple was inserted into thecenter of the furnace by drilling a small hole from oneequatorial fin to the opposite equatorial fin. This setuphad the advantage that the thermocouple bead was burieddirectly in brucite. For DTA experiments, a second ther-mocouple was added by slitting the Re foil at the top ofthe heater and inserting the thermocouple there. All ther-mocouple leads were electrically insulated from the heat-er by MgO ceramic sleeves. No correction was made forthe effect of pressure on the emf generated. The two mul-tianvil configurations are shown in Figure l.

After loading the pressure medium, the gasketing finswere wrapped with Teflon tape, and then the octahedronwas surrounded by eight tungsten carbide cubes (2.54 cm)with either 6- or 8-mm truncated edge lengths (TEL). Thestack of cubes was held together by gluing GlO plasticsheets to the backs of the cubes. Cu strips were insertedinto the plastic to serve as electrodes to the cubes in con-

,z/ forstetite'coesite- ,.t Bspinelstishovite

Bi III-V

6 mm TBL

Bi II-IIIBi I-II

0 100 200 300 400 500

Tons forceFig.2. Calibration curves for 6-mm truncated edge length

tungsten carbide cubes. The calibrations were performed at roomtemperature (-25'C) using the three Bi transitions and at 1200'C using the transitions coesite to stishovite and forsterite toB-spinel transitions. Tons of force was calculated from the oilpressure on a 16-in. ram.

tact with the Re foil. This setup was loaded into the mul-tianvil device and pressurized. Many of the experimentaldetails are described more fully in Walker et al. (1990)and Walker (1991).

Experiments below 12 GPa were slowly pumped topressure (-8 h to reach 12 GPa), and then heated totemperature. Experiments above 12 GPa were pumpedto 9 GPa, heated to 500 "C, pumped to the desired pres-sure, and then raised to the desired temperature. Thistwo-step pumping procedure greatly reduced carbide lossresulting from blowouts. The 6-mm TEL octahedra werecalibrated at room temperature using the Bi I-II, Bi II-III, and Bi III-V transitions. At 1200 {, calibrations wereperformed at 9.3 GPa using the coesite to stishovite tran-sition, and at 14.3 GPa using the forsterite to B-spineltransition. The 8-mm TEL octahedra were calibratedsimilarly up to the coesite-stishovite transition. Thesefixed points yield the force (tons) vs. sample pressure(GPa) curves in Figure 2. The most critical high-pressurecalibration experiments were performed using the exper-imental setup shown in Figure lB.

In DTA experiments, the differential signal was record-ed on an analogue chart recorder and interfaced to a per-sonal computer. Considerable care was required to con-dition the signal and filter electrical noise. In the DTAexperiments, temperature was raised and lowered in 25-30' steps either by controlling the cold thermocouple orby increasing and decreasing furnace power. In thequenching experiments, samples were brought to the de-sired pressure and temperature, held there for 30 min,and then quenched by shutting off furnace power. De-compression for both types of experiments was accom-plished over the course of about 12-24 h depending onthe pressure achieved.

After quench, the entire octahedron was mounted in

15

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274

TABLE 1. Summary of experiments

JOHNSON AND WALKER: MOLAR VOLUME OF H,O

DTA experimenls Cook and quench experiments

Comments (min)T E L P T

Expt. Type (nm) (GPa) ("C) Comments Heating/cooling rateT E L P T

Expt. Type (nm) (GPa) fC)

P C 4P C 4P C sY V I

P C 7168121123162

223 MA 6218 MA 6217 MA 6215 MA 6219 MA 6206 MA 6205 MA 6204 MA 6174 MA 6198 MA 6179 MA 6184 MA 6196 MA 6190 MA 6197 MA 6203 MA 6210 MA 6208 MA 6214 MA 6224 MA 6

P C 1 0P C 1 5PC 2.0P C 3 0PC 4.OMA 8 6.0MA I 8.0MA 8 10.0M A 6 1 1 . 5

782 +5'930 +5.984 +7'

1076 +5"'1120 +10'1 1 6 9 + 1 2 " ( 1 1 5 7 - 1 1 8 1 )1191 +19 " ( 1172 -1210 )1186 +12 . ( 1174 -1198 . )1120 +19 ' ( 1101 -1138 . )

100-300'C/min100-300'C/min100-300 "C/min100-300'C/min100-300'C/min100_300 "C/min100-300 ec/min100J00 qC/min100-300 rc/min

brucite (Pt capsule) 30periclase 30periclase 30periclase 20brucite 30brucite/periclase 30periclase 30periclase 30brucite 20periclase 30periclase 30brucite 30brucite/periclase 30periclase 10brucite 30brucite 30periclase 20periclase 30brucite 30periclase 30

4.0 10504.O 10204 0 1 0 5 04 . 0 1 1 0 06.0 ' t120

6 0 1 1 4 06 0 1 1 6 06.0 12008 0 11708 0 12008.0 1225

1 1 . 5 1 1 7 0'| 1 .5 120011.5 122513.0 1 20013.0 122513.0 125013.0 127515 0 125015 0 1280

Nofe; PC : piston cylinder; MA: multianvil

epoxy, cut in half longitudinally to expose the sample,and polished. The polished sections were examined inreflected light and with backscattered electron imagingusing an electron microprobe. Qualitative analyses weresufficient to reveal if the sample remained uncontami-nated, and to distinguish brucite from periclase; peak MgOcounts are lower for brucite than for oericlase.

RESULTS

The results of both DTA and quenching experimentsare summarized in Table l. The dehydration of bruciteto periclase and HrO is an endothermic reaction, and thusa small negative dip was observed in the differential traceas the phase boundary was crossed with increasing tem-perature in DTA experiments. An example of this typeof signal is shown (Fig. 3). As the temperature was in-creased in successive small increments, the differentialtemperature normally had a slight positive slope (Fig. 3a);this behavior is contrasted with the pronounced negativeslope that occurs when the reaction boundary is passed(Fig. 3b). DTA experiments were carried out to 11.5 GPa,and the results are shown (Fig. a). The theoretical phaseboundary calculated using available thermodynamic dataand molecular dynamics to constrain the PZlpropertiesof HrO is also plotted in Figure 4 (S. Saxena, personalcommunication; Johnson et al., l99l).

The brucite dehydration curve is controversial at lowpressures, and many different sets of experiments haveresulted in many different curves. Therefore, the DTAresults needed to be confrrmed by a second independentmethod. Several different approaches were tried. For ex-ample, another in situ method based on a resistancechange was tried. The mixture of periclase and HrO wasreasoned to be more conductive than brucite, and there-fore, if the resistance across the charge could be moni-

tored, it might be possible to detect that phase change bya sudden change in resistance. Unfortunately, the ther-mocouple ceramics become semiconductors at high pres-sures and temperatures, and reliable resistance measure-ments were not obtained.

After further in situ attempts were abandoned, a non-standard type of quenching experiment was tried. Giventhe rapid kinetics of the periclase hydration reaction (bothat high temperature, facilitating DTA experiments, andat low temperature, facilitating brucite synthesis) inter-preting the appearance of quenched experiments may bedifficult because of possible quench modifications. Thus,an experiment designed to produce textural features thatmight ineradicably record the state of the charge at P and?n rather than during the subsequent quench became apriority. Therefore, a homogeneous 5:l mix of brucite tozirconia was prepared. Inert zirconia should not affect thebrucite dehydration temperature, and it should not par-ticipate in any quench reactions. Initially, the zirconiaand brucite were well mixed. When the phase transitionoccurred, the zirconia grains would no longer be sup-ported in a solid matrix; gravity would then cause themto settle to the bottom of the charge. After an experimentwas held at pressure and temperature, optical examina-tion would reveal either a marker layer of zirconia at thebottom of the charge, indicating periclase and HrO hadbeen stable, or the zirconia would still be homogeneouslydistributed, indicating brucite had remained stable. Inpractice, although the fluid makes up 50 molo/o of thecharge after breakdown, the zirconia grains did not settleout of suspension. Evidently, the periclase still formed aself-supporting network, or the fluid was too viscous forsettling to occur, or the zirconia crystal distribution wascontrolled by factors in addition to gravity.

Figure 5,A. is a backscattered electron image ofa section

a(a) o

0.6 0 .8 1 .0 1 .2 t .4 1 .6 1 .8

Time (minutes)

JOHNSON AND WALKER: MOLAR VOLUME OF H,O

1033

1025

1018

1011

1003

1t43

I 140

r 136

r t 3 2

I r 3 0

1t26

600 700 800 900 1000 1100 1200 1300Temperature (oC)

Fig. 4. Experimentally determined phase diagram for the de-hydration of brucite to periclase and HrO. Circles represent thedata determined using DTA. Squares represent the data deter-mined using quenching experiments; open squares indicate bruc-ite was stable, stippled squares indicate periclase was stable, andhalf-stippled squares represent temperatures at which both bruc-ite and periclase were stable. The plus signs are a theoreticalphase boundary calculated using molecular dynamics.

concentration in the unreacted brucite preserved at thecold ends ofthe heater beyond these compacted periclasemasses. Clearly, the zirconia crystal distribution appearsto be controlled more strongly by the thermal structureofthe charge than by gravity.

The brucite and periclase distributions, with or withoutzirconia crystal concentrations, are also related to thethermal structure of the charge. Mass diffusion caused bysolubility variation within this temperature gradient mostreasonably explains the compaction of periclase withinits complementary fluid once brucite broke down. Thethermal compaction process in a solubility gradient hasbeen described in detail for silicate systems by Walker etal. (1988) and Lesher and Walker (1988). Buchwald et al.(1985) coined the name thermal migration from obser-vations of the process in metal alloy systems. Within thefluid + periclase aggregate initially produced by brucitedehydration, HrO diffuses toward the hottest parts of thecharge, while MgO diffuses along the periclase solubilitygradient toward the coldest regions that are still abovethe brucite stability temperature. This tendency causesfluid to accumulate along the furnace walls and periclaseto compact along an interface, with stable brucite at bothends ofthe charge. (This process occurs independently ofthe Soret effect, if it exists, within the fluid. The Soreteffect can be an additional agent of mass transport andmay either reinforce or inhibit the solubility-induced massflux.) The periclase that fully compacts by thermal mi-gration expels vapor to the hotter parts of the charge andquenches as periclase; since this periclase is no longer incontact with vapor, it does not fully rehydrate to bruciteupon quench. The narrow channels betwe€n periclase

275

9.95

9.86

9.78

9.69

9.60

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I 1 . 1 3

11.09

11.050.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Time (minutes)

Fig. 3. Trace of the DTA signal recorded at Il.5 GPa. (a)This trace shows the normal slightly positive slope of the hotthermocouple as the power is increased in small steps. (b) Thistrace shows a negative slope and signals that the dehydrationboundary has been crossed.

ofa mixed brucite and zirconia charge quenched after 30min at I 1.5 GPa and 1225 "C (at the thermocouple junc-tion). The sample is much larger than in the DTA exper-iments and was in a substantial temperature gradient.Theoretically, the isotherms should display an hourglassconfiguration about the charge's center of thermal sym-metry. From the saddle point at the center of the hour-glass, isotherms of increasing temperature should ap-proach the inner walls of the Re heater, and isotherms ofdecreasing temperature should recede along the heateraxis. An hourglass pattern is obvious in the zirconia crys-tal distribution (light speckles), which are slightly concen-trated beyond their initial abundance in an X-shaped re-gion. The hot equatorial fields between the arms of theX near the heater walls are occupied by aggregates ofzirconia-free brucite platelets with a material of low atomicnumber (presumably HrO-rich) in the interstices. The po-lar fields along the heater axis between the arms of the Xare occupied by rather densely compacted periclase (andzirconia), with some interstitial brucite. The thermocou-ple junction is visible in the upper of these regions. Theinitial zirconia crystal abundance may be judged from its

+.*+,-+

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(b)

2'.16 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

Fig. 5. Backscatteredelectronimage ofan experimentalchargeheated to 1225 "C at I 1.5 GPa for 30 min. (A) View of the enrirecharge showingzirconia liner (ZR) between Re-foil heater (Re)and ceramic octahedron, thermocouple junction (TC), quenchedbrucite platelets (Q), compacted periclase (P), and stable brucite(B). White grains are zirconia crystais. The symmetrical hour-glass shape of the labeled fields is controlled by the thermalstructure of the charge. Scale bar is 1 mm. (B) Close up of boxin A clearly showing a triple junction among stable brucite (B),compacted periclase (P), and quenched brucite platelets (e). Notethe lens of periclase at upper left of picture. This triple junctionrepresents a thermal erosion front produced during quenching.Scale bar is 200 pm.

grains are filled with finegrained brucite and are inter-preted as the entry points for rehydrating the compactedpericlase along grain boundaries upon quench. Also uponquench, the fluid pocket reverts to slender brucite plate-lets with very different morphologies from the equantbrucite crystals observed in the cold ends of the charge.This morphological difference is partly related to quenchgrowth from a fluid, in contrast to solid-state recrystalli-zation of the unreacted brucite. But the morphologicaldifference of the area labeled Q (quench brucite) is alsotied to the HrO-rich interstitial material. Because not all

the periclase rehydrates, these regions must contain moreHrO than the brucite composition to preserve mass bal-ance.

Thus, although the zirconia-brucite experiments did notwork as expected, they demonstrated that the process ofthermal compaction creates textural markers that are notfully eradicated upon quench. Thus, the aspect of thethermal gradient that leads to periclase preservation isadvantageous, but it also emphasizes that it is importantto observe whether compacted periclase or brucite is incontact with the thermocouple bead. This region is theonly one where the temperature is well known. The pres-ence ofbrucite or periclase in other regions ofthe chargeis ambiguous because the temperature at other regions ispoorly known. Exploiting the thermal gradient in thisfashion greatly simplifies the task of interpreting whetherpericlase and HrO or brucite had been stable at peaktemperature and pressure.

The inference that vapor and periclase can react to pro-duce brucite on quench is reinforced by an additionaltextural aspect of this experiment. The thermocouple beadis clearly in a field of compacted periclase (Fig. 5A). Theinteresting feature ofthis texture, however, is that a triplejunction exists among equant brucite crystals, compactedpericlase, and brucite platelets (Fig. 5B). This geometrycannot be an equilibrium phenomenon because it impliescrossing isotherms. Equant brucite, compacted periclase,and brucite platelets are features that form at increasinglyhigher temperatures, and no temperature exists where allthree can be stable.

Since this geometry cannot be an equilibrium feature,it must have formed on the quench. We infer that a layerof compacted periclase existed at equilibrium along theinterface with the stable brucite crystals; this layer is pres-ent in the three other corners of the charge (Fig. 5A).Indeed, a small lens of compacted periclase is still presentat the upper left corner of this interface (Fig. 5B). Duringquench, this periclase layer was thermally eroded by re-acting with the adjacent vapor and rehydrating to bruciteplatelets. The inference that rapid brucite regrowth is pos-sible during quench is strengthened by the observationthat brucite was synthesized very easily from periclaseand HrO at only 225 "C. Although the temperature fallsquickly (- 5 s) from peak temperature to 100 'C, the ther-mal inertia of the wedges and cubes keeps the tempera-ture at - 100 "C for 3 or 4 min. We suspect that some ofthe thermal erosion may occur at these low temperaturesrather than strictly during the high-temperature quench.

Figure 6A and 68 illustrates the symmetrical distri-bution of unrecrystallized brucite, compacted periclase,and quenched fluid (now brucite platelets and interstitialHrO-rich material) without the additional complicationsof the zirconia crystal distribution. Clearly, the compact-ed periclase has suffered substantial rehydration, as shownin the detail of Figure 68. Because the thermocouplejunction is not in the unrecrystallized brucite field, weinterpret this experiment's pressure and thermocoupletemperature as being in the periclase + fluid field. We

JOHNSON AND WALKER: MOLAR VOLUME OF H'O 277

address below the issue of whether this fluid is a vaporor a melt.

The results of the quenching experiments interpretedusing the above guidelines are shown in Figure 4. TheDTA and quenching curves agree fairly well to 10 GPabut diverge quite rapidly at higher pressures. Most im-portantly, the unique change from positive to negativeslope predicted by molecular dynamics and corroboratedby the DTA experiments (Johnson et al., 1991) was notconfirmed.

DrscussroN

Experimental difficulties

The discrepancy in the DTA and quenching results atI1.5 GPa requires an explanation. After the experiment,careful analysis of the DTA charges using backscatteredelectron imaging revealed that these samples suffered fromfluid phase contamination. Specifically, SiO, and Al,O,peaks, as well as MgO peaks, were observed by energy-dispersive X-ray analysis in the fluid-rich regions of thesecharges. The source of the SiO, and AlrO, is the sur-rounding octahedral pressure medium. Evidently, theseoxides could invade the sample region through micro-scopic slits in the Re foil heaters, possibly by leachingwhen HrO was formed from brucite dehydration.

The contamination of these experiments by the pres-sure medium makes the DTA results suspect. Since SiO,and AlrO. dissolve in the fluid phase, they lower the Gibbsfree energy ofthe fluid and artificially increase its stabilityfield; fluid phase contamination, therefore, will causebrucite to dehydrate at a lower temperature than in theuncontaminated case. Because the DTA and quenchingresults agree very nearly to about 10 GPa, the contami-nation problems appear to become severe at pressuresgreater than l0 GPa. This observation could mean thatthe fluid phase solubility of SiO, and AlrO, increases atl0 GPa. The piston-cylinder experiments were conductedin sealed Pt capsules and thus did not suffer from con-tamination problems. The quenching experiments did notsuffer from contamination because the MgO liner isolatedthe pressure medium from the charge. The quenchingresults above l0 GPa are believed to be more accuratethan the DTA results because they are uncontaminatedand thermal migration allowed the results to be inter-preted reliably. These quenching experiments are as-sumed to define the brucite breakdown curve at highpressures most accurately.

We infer that brucite breaks down by dehydrating atall pressures studied. If a melting curve was intersectedat some pressure, then the reaction would change (e.g.,Ellis and Wyllie, 1979). By analogy with other hydrousminerals, the most likely melting reaction to intersectwould be Mg(OH). - MeO + melt. One possible expla-nation of the slope change initially signaled by the DTAresults was that an invariant point was reached, and thebreakdown changed from a dehydration reaction to amelting reaction. The quenching results, however, show

Fig. 6. Backscattered electron image ofan experimental chargepressurized to 13 GPa and heated to 1250'C for 20 min. (A)View of the entire charge showing Re-foil furnace (Re), ther-mocouple junction (TC), quenched brucite platelets (Q), com-pacted periclase (P), and stable brucite (B). The TC junction isentirely outside the field ofstable brucite crystals. The horizontalgray stripe of material in the middle of the charge directly belowthe TC junction is partly MgO thermocouple insulation. Scalebar is I mm. (B) A close up of the interface between compactingpericlase and stable brucite (box in A). Contrast the featheryquench brucite crystals between the lenses of periclase to theequant brucite crystals in the fields labeled B. Scale bar is 200 pm.

278 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

Temp

Per Bru Vap per Bru Vap

Fig. 7. Four possible topologies representing how brucite canbreak down at high temperatures and pressures. (a) Brucite meltscongruently. (b) Brucite melts to an MgO-rich liquid. (c) Brucitemelts to an MgO-poor liquid. (d) Brucite dehydrates to periclaseand vapor, which melt at a higher temperature. The experimen-tal results suggest that topologies a, b, and c are incorrect.

no discontinuity in slope at these pressures, making thisexplanation less likely. Indeed, one smooth curve can befitted to both the low-pressure DTA data points and thehigh-pressure quenching results, implying that the reac-tion is continuous from I to 15 GPa. The possibility ofa melting reaction was investigated experimentally, how-ever.

Theoretically, brucite must break down in one of fourways (Fig. 7). If brucite melts congruently (Fig. 7a) or ifbrucite breaks down to produce a very MgO-rich tiquid(Fig. 7b), then a brucite bulk composition cannot producepericlase as an end product of the initial decomposition.Since periclase is observed as an end product in manyexperiments, these two constructions must be topologi-cally incorrect. Two possibilities remain; either brucitebreaks down by melting to form an MgO-poor liquid (Fig.7c), or it breaks down by dehydrating (Fig. 7d). A brucitebulk composition produces periclase plus fluid in eithercase, and these two topologies are texturally indistin-guishable.

To differentiate between these two possible topologies,a more HrO-rich composition than brucite (38 mg ofbrucite and72 mg of distilled, deionized HrO) was loadedinto a Pt capsule, which was sealed on both ends. Thecapsule was held in a large Cu heat sink during weldingin order to keep most of the capsule at a temperaturebelow the boiling point of HrO. Some Pt was observedto spall off during welding, so the molo/o HrO remainingin the capsule after welding was calculated in two ways.For the best case, the weight difference measured beforeand after welding was all attributed to Pt loss. For theworst case, the weight difference was all attributed to HrOIoss. The two calculations yield 82 and 68 molo/o HrO,respectively. This capsule was then brought to I1.5 GPaand 1225 oC, a pressure at which the DTA curve shows

a change in slope at lower temperature, and held at theseconditions for 30 min.

If brucite breaks down by melting at this pressure andtemperature and our bulk composition lies to the right ofthe liquid composition, then an MgO-poor liquid and aHrO-rich fluid will be generated (Fig. 7c). If brucite breaksdown by melting and our bulk composition is to the leftof the Mgo-poor liquid composition (but more HrO-richthan a brucite bulk composition alone), we will be eitherin the brucite + liquid stability field or in the periclase+ liquid stability field. Since we are at a temperature only25 'C above the stable brucite field at this pressure, wesuggest that we are most likely to encounter the brucite+ liquid stability field. In either of these cases, uponquench the fluid + liquid or brucite + liquid will revertto brucite. Periclase will not be observed as an end prod-uct. On the other hand, if brucite breaks down at thispressure and temperature by dehydrating, then a brucite+ HrO bulk composition will generate a HrO-rich fluidand periclase (Fig. 7d). The periclase will compact to-wards the cold end ofthe charge, and, although the fluidwill revert to brucite upon quench, some of the com-pacted periclase will quench as periclase. This scenario isthe only one in which periclase will be observed as anend product. The experimental charge was sectioned andpolished after being held at P and T, and periclase andquenched brucite were observed. This experiment cou-pled with the continuous nature of the reaction curvesuggests that, to at least these pressures and temperatures,brucite breaks down by dehydrating; a melting reactiondoes not appear to intersect the dehydration curve. Thisinterpretation is in contrast to the recent study of Gas-parik and Zhang (1992), who state that brucite appearsto melt incongruently between 12 and 22 GPa aI 1250 "C.

Comparison with previous results

Previous experimental results on brucite stability atpressures above 1 GPa are compared with the presentresults (Fig. 8). The low pressure results agree well withIrving et al. (1977) and do not reproduce the change inslope observed by Yamaoka et al. (1970) at - 3 GPa and1000 'C. The new results indicate that the brucite dehy-dration curve is at a higher temperature than that re-ported by Kanzaki (1991) and do not confirm the changein slope at about 6-7 GPa observed by Leinenweber etal. (1991) using in situ X-rays. One difference betweenthis study and the two recent studies is the thermocoupletype used. Pt-Pt/Rh thermocouples were used in thisstudy, whereas Kanzaki (1990, l99l) and kinenweberet al. (1991) used W-Re thermocouples. All the reportedtemperatures are uncorrected for a pressure efect on thethermal emf. The pressure effect correction is differentfor each thermocouple type because the Seebeck coeffi-cients vary uniquely with high pressure. Although abso-lute pressure corrections have not been determined, rel-ative pressure corrections for W-Re and Pt-Pt/Rhthermocouples have been observed (Williams and Ken-nedy, 1969; Ohtani, 1979). These corrections indicate that

vap

JOHNSON AND WALKER: MOLAR VOLUME OF H,O 2',19

both thermocouples record lower temperatures than am-bient at high pressure, but that the pressure effect on W-Rethermocouples is less severe. Therefore, qualitatively cor-recting for an emf pressure effect would raise all the re-ported temperatures but would raise the Pt-Pt/Rh tem-peratures more than the W-Re temperatures at thetemperatures considered here (<1300 "C). This correc-tion would increase rather than decrease the difference inresults.

Experimental studies can be plagued by many differentproblems. Two problems that were experienced duringthis study are fluid phase contamination and loss of HrOleading to P"ro less than P,",. Fluid phase contaminationwas avoided in later experiments by using an MgO linerand pure MgO thermocouple insulators. HrO leakage wasavoided in the piston-cylinder experiments by using sealedPt capsules. At pressures greater than 6 GPa, we inferthat HrO-vapor did not completely leak from the exper-imental assemblies because periclase easily rehydrated tobrucite upon quench in the hottest regions of the charge.For this reaction to occur, HrO must have been presentat the end of the experiment. As argued above, this HrOwas present as a vapor rather than dissolved in a meltphase. The presence of an HrO-vapor at the experiment'sconclusion guarantees that P"ro remained equal to P,., atpressure and temperature, even if slight Hr-diffusion oc-curred during the experiment. This observation suggeststhat at these very high pressures, no cracks or voids existthat allow HrO to escape from the charge. H.O may onlyleak from the experiment by diffusing through the Re foilheater and the MgO liner. The short experimental times(30 min) prevented this process from proceeding to com-pletion. Thus, the Re foil and MgO end pieces served asphysically sealed capsules for these experiments, althoughit is unlikely that H, diffusion through these materialswas entirely inhibited.

Our results at 6 GPa and higher pressures are contrast-ed with our quenching results at 4 GPa. Experiments con-ducted at 4 GPa using identical procedures as in the high-pressure experiments consistently yielded periclase evenat temperatures well within the brucite stability field, asinferred from our 4-GPa DTA experiment. A notable dif-ference between these 4-GPa quenching experiments andthe 6-GPa quenching experiments is that no vapor fleld(quench brucite field) was observed in any of the 4-GPaexperiments. Secondly, a small portion of the MgO linerhydrated to brucite in some of the 4-GPa experiments.These two observations imply that HrO had leaked fromthe sample region, but it had not traveled far. It merelyreacted with the MgO liner, which was at a slightly lowertemperature, to form brucite. Therefore, the presence ofpericlase at experiments well within the predicted brucitefield must be attributed to a loss of H'O, which allowedPrro to become less than P,",. This condition causes bruc-ite to dehydrate at lower temperatures than when P"ro :

P,",. This suggestion was tested by conducting an experi-ment at similar conditions but loading the brucite into asealed Pt capsule. This experiment yielded stable brucite

Me(OH)' 2

Leinenweberi

xanzax;/,Yamaoka

Irving -4 MgO + HrO

15

A: 10

sl(ta )s?

0600 700 800 900 1000 1100 1200 1300

Temperature (oC)

Fig. 8. Comparison of the new data with previous experi-mental studies of brucite stability conducted at pressures aboveI GPa. The new data are shown by the thick unlabeled curve'Previous data are from Yamaoka et al. (1970), Irving et al. (1977),Kanzaki (1991), and Leinenweber et al. (1991). The new datashow the highest thermal stability for brucite and are believedto be the least subject to experimental error.

consistent with our explanation and the high pressure ex-periments. The difference in HrO leakage rates between4 and 6 GPa implies that a void in the octahedral pres-sure medium is not completely sealed off at the low ton-nage required to reach 4 GPa but is sealed off by 6 GPa.

The differing results in our quenching experiments at4 and 6 GPa combined with the recognition of fluid phasecontamination clearly demonstrate that the periclase andfluid stability field can be markedly overestimated. Thislesson may apply to the experiments of others as well.An additional problem in multianvil experiments is theoffset between the sample and the thermocouple bead. Ifthe sample is located in the hot spot, but the thermocou-ple is displaced from the sample, the thermocouple willrecord a temperature lower than the sample temperature.We avoided this problem by surrounding the thermocou-ple bead with brucite and then observing whether bruciteor compacted periclase was present immediately adjacentto this junction. Experiments conducted at identical pres-sures but above the breakdown temperatures reported byKanzaki ( I 990, I 99 I ) and kinenweber et al. ( I 99 l) yieldeuhedral brucite crystals, indicating that brucite is stableat these temperatures. These new results are inconsistentwith the previous findings. The only problem that couldcause brucite stability to be overestimated in our exper-iments is lack of recognition of brucite formed on quenchfrom rehydrated periclase. Rehydrated periclase was eas-ily recognized in this study because ofthe action ofther-mal migration. All of the difficulties discussed abovewould lead to underestimation of the brucite stability field.Because our data show the highest temperature brucitestability field for any given pressure, we argue that our

280 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

experimental data are the least subject to the types oferrorsjust described. These new data most accurately re-cord brucite dehydration temperatures.

Thermodynamic calculations

The objective of this work was to determine the brucitedehydration curve to 15 GPa and then use these newphase equilibria data to calculate the volume (density) ofHrO at mantle pressures. Brucite dehydration appearedto be a particularly appropriate reaction to study becausethe P-Z slope was predicted to change from positive tonegative. This slope change would allow the molar vol-ume of HrO to be calculated very accurately at the tem-perature maximum. The Clausius-Clapeyron equationrequires that for some special univariant equilibria, theP-Zcurve is a function of the differences in entropies andvolumes of the solids and reactants:

dP _ A,Sdr av . ( l )

If the P- f curve shows a maximum temperature, thenthe slope is infinite, and AV:0 at this maximum. There-fore, the molar volume of HrO at this pressure and tem-perature is exactly equal to the difference in volumes ofpericlase and brucite; the entropies at pressure and tem-perature of brucite, periclase, and HrO are irrelevant. Be-cause only molar volumes need to be calculated, errorsassociated with the thermochemical data are not intro-duced.

The experimental data, however, indicate that the sloperemains positive to l5 GPa. Since the entropies of bruc-ite, periclase, and HrO are not well-known functions oftemperature and pressure, the molar volume of HrO alongthe dehydration curve was calculated using the equation

L G ( P , 7 ) : 0

rP: A,Hot - fA.S? + | LV,(P, T) dP

r+ | v,(P, T) dP (2)

J r n a r

where A11} and AS} are the enthalpy and entropy changesfor the reaction at I bar and temperature Z, AZ. equalsthe volume change in the solid phases, and Z' is the fluidvolume. Note that Equation 2 has been written so thatthe only unknown quantity is the last term on the RHS.

In Equation 2, AS? and A,Hu, are defined as

a,s.,: a,sge8 + I,,o* * (3)

FAHo,: A119"s +

JrnrOr, Or. (4)

The volume integrals for the solids were solved using theMurnaghan equation

where Z(l bar, T) follows directly from the definition ofthermal expansion as

V(l bar,7)

f a , (T ' ) o . f l ': %e*p l a "T + 2 l * a , l n f - ; l lL L l l l z g z

In Equations 5 and 6, ko is the bulk modulus, ( is thepressure derivative of the bulk modulus, Zo is the molarvolume at I bar, 298 K, and a(T) is the thermal expan-sion. The constants es, e17 e21 a. are determined by re-gressing experimental data. Evaluating this integral for,say, periclase gives

rI v*,(P. T) dP

/ t \ l / t r ' p \ " ' ^ 6 ' I: v ( t bar . n( r r=) l ( ' . Ta) - r l . e)\Ko

- r / L \ Ko / I

The bulk modulus (or compressibility) was treated as anexplicit function of temperature following Saxena (1989).Thermodynamic constants and the sources where theseconstants were obtained are listed in Table 2. The volumederivatives a and p in Table 2 are corrected for misprintsin the published versions (S. Saxena, 1992 personal com-munication) and are based upon optimized fits of a va-riety of low-pressure phase equilibria data involving thesephases.

Equation 2 is valid only along the univariant curve.Therefore, the new experimental data were fit with asmooth curve determined by minimizing the residuals ina least-squares sense. To facilitate constraining the curveaccurately at low pressures, the experimental data ofBarnes and Ernst (1963), Schramke et al. (1982), and Ir-ving et al. (1977) were included, along with the new dataof this study in the fitting procedure. The form of thisfitted curve is not intended to have thermodynamic sig-niflcance; it merely allows the dehydration curve to bemanipulated mathematically. The equation for the fittedcurve (P in GPa, I in 'C) is

7 - : 1307 + t . t 54P - = ! t ? '== . ( r , : 0 .992 ) . ( 8 )P + t . 5 7 6

Since little consistent phase equilibrium data exist forthis dehydration reaction at pressures below I kbar (e.g.,compare Barnes and Ernst, 1963, vs. Weber and Roy,1965, vs. Bowen and Tuttle, 1949), the volume integralof HrO (or R?"ln/rro) from I bar to I kbar was computedusing the modified Redlich-Kwong model of Kerrick andJacobs (1981). This modification was incorporated intoEquation 2 by making the following changes:

Ve. n: lz( l bar. n[ *ry|-"rt (5)^o -i

: voexp [ '"*1r1u,

(6)

JOHNSON AND WALKER: MOLAR VOLUME OF H,O

Tlele 2. Thermodynamic properties

281

vo(cm3/mol)

AFl3.u(kJ/mol)

AS8.,(kJ/moUK) Ref -

BrucitePericlaseHrO

24.630 -925.50011.250 601.490

-241.814

64 4026.94

1 88.83

4 7124.170

R , H , SR , JR

a ( r ) ( K l ) : a + b T + c l T + d J T ' ?a ( x 1 0 s ) b ( x 1 0 3 ) c ( , 1 0 2 l d ( . 1 0 1 )

BrucitePericlase

8.7s4 1 8093.754 0.791

P(ba rs ' ) : a + bT + cT2 + dTxa ( x 1 0 6 ) b ( x 1 0 " ) c ( x 1 0 1 3 )

-2.218 5.8430 000 -7 836

SSZ

J

SZ

d ( x 1 0 1 6 )

BrucitePericlase

1 . 751000.59506

-0.54898.2334

b ( x 1 0 ' ? )

2 044500.32639

1 105000 0 1 0 1 8

C"(J/K): a + bT + c lT2 + dT2 + elTi + f lTos + glTc ( x 1 0 6 ) d ( x 1 0 8 ) e( ' 10 t ) 91 x 10,)

BrucitePericlaseHrO

103.01 043.57046.461

1.6s330.54800.5966

b(P l :

0.00-6.31

- 1 .3650.000

-1.14133.390

- 1 66.300

-2.7462-1.6779

6.3200 0.00 -7957000

Halbach and Chatteriee ( 1 982) coefficients

a(D: 1.616 x 108 - 4.989 x 104f 7.358 x 10'g/ f

| + 3.4505 x 10 aP + 3.8980 x 10 eP2 - 2.7756 x 10 15P3

KRR

0.000.000.00

6 3944 x 10-2 + 2.O776 x 10 5p + 4 5717 x 10 1oP2

Notej f is measured in degrees Kelvin; P is measured in bars.* References: R: Robie et a l (1979); H: Hol land and Powel l (1990); D: Duffy et a l . (1991); J: Jackson and Niesler (1982); SZ: Saxena and

Zhang (1989); S : Saxena (1989); K: King et a l . (1975).

rLGg, D: 0 : AG(l kbar. T) *

J, no- AV,(P, 7) dP

+ f' vr(P, T) dP (e)' f .r I kbar

where

f r k b a r

AG(l kbar, T): AHo, - rAS9 + | AV,(P, T) d.P

f r k M r*

J,.,, VIP' N dP

the volume as a function of pressure curve. Since volumeis a function of Z as well as P, a series of isothermalcurves exist on this plot. Therefore, the integral of thevolume of HrO at a particular P and I along the dehy-dration curve (Pr, I') is the area under the Z(P) curvefor the particular isotherm (T') at which P, is the equi-librium brucite dehydration pressure. The integral can beformed agatn at some new Pr, T, along the dehydrationcurve, and a new area under the second curve is identi-fied. If both integrals had been formed at the same I,,Ihen V(Tr) at the average pressure between Pt and P.canbe computed from

r , l P , + P , - \v n o \ 2

, t r l

(10)

The practical effect of computing L,G(P, T) from abaseline of I kbar rather than the standard I bar is thatthe uncertain and contradictory phase equilibria data thatexist below I kbar are no longer of interest in computingV".o at high pressure on the basis of the phase equilib-rium curve. Inasmuch as YH2o is well known by directmeasurement at I kbar, we sacrifice little new knowledgeby using Vn,o to I kbar as input, rather than seeking itsrecovery as output. Furthermore, the direct measure-ments of Zrro from I to 10 kbar can still be used to checkthe calculated volumes in a region where the lowest pres-sure noise in phase equilibrium determinations has sub-sided.

The last term on the RHS of Equation 9 can be eval-uated as a function ofpressure every 200 bars along theP, T of the dehydration curve using Equation 8 and thedata in Table 2. Figure 9a illustrates the graphical mean-ing of this term. Physically, this term is the area under

( 1 1 )

In other words, the volume we seek is equal to the dif-ference in the integrals of the volume of HrO at P2 ardP, divided by the difference between P, and P,. Figure 9ashows, however, that the integrals computed from Equa-tion 9 do not bear the required isothermal relationshipfor V^ro computation, as a result of the shaded wedgeintroduced by the covariant change of ?'with P variationalong the dehydration curve. This shaded wedge makesthe molar volumes calculated using this approach tooIarge.

Figure 9b presents volume integrals (: RZ ln /) of theinformation in Figure 9a as a function of P. The phase

( a ). Points on BruciteDehydration Curve

282 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

a.)

fis

F

t l

16) RT, ln f(Pr) T\

TRT, ln f(P,)

\

RT,ln f(Pr) =

Bru .." I Rr, ln f(Pr)J'(T,/Tr)P+W

P, P,

PressureFig. 9. (a) Schematic illustration of molar volume vs. pres-

sure for two isotherms. The volume integral of the fluid in Eq.9 is physically represented as the area under the curve for someP and T. The shaded region represents the extra volume that iscalculated when two successive integrals at different pressuresand temperatures are subtracted. (b) Schematic illustration ofrelationship between RT ln f and, pressure. To correct for theextra volume of a, the rerm RTrln /(Pr) must be reduced bymultiplying by T,/Tr. See text for details.

equilibria allow R?",In f(P,) ar'd RT,ln f(P,) to be cal-culated from Equation 9. However, to use Equation I Ito compute Vnro al l(Pt + Pr)/2, ?n,], one needs RI,ln

/(Pr). This term is found by multiplying the term weknow [namely RZrln f(Pr)]bV a correction factor, T,/Tr:

V(P2, T,) dP : RT,h f(P,)

T: [Rr,ln f(P,)|,, n.i. Q2)

With this substitution, Equation I I has been used tocompute Vrro at 200-bar intervals along the brucite de-hydration curve to 15 GPa. These results are shown inFigure l0 from I to 15 GPa. The calculations give a Zrroat I GPa and 845 'C of 21.3 cm3 compared with theaccepted value of 20.8 cm3 from Burnham et al. (1969).

This residual error could probably be removed by furtherparameter optimization. These calculations were repeat-ed using the thermodynamic and volumetric propertiesof Holland and Powell (1990), which are applicable to 4GPa. No difference exists in the calculated volume ofHrO to this pressure, and thus further attempts at inputparameter selection were deemed unjustified.

Very recently, new physical property data on brucitehave become available as experiments have been con-ducted in a diamond-anvil cell using synchrotron X-raydiffraction to 35 GPa at 300 K and to 80 GPa at 600 K(Yingwei Fei, 1992 personal communication). These ex-periments are one of the first attempts to measure thethermal expansion coefficient of brucite at I bar, the pres-sure dependence of the thermal expansion, and the tem-perature derivative of the bulk modulus. These new datawere used to define a more accurate equation of state forbrucite than was previously possible (Yingwei Fei, 1992personal communication). The thermodynamic calcula-tions performed above were repeated using these newbrucite PVT properties. The calculated molar volume ofHrO changed by less than 10/o at I GPa and by less than0.lo/o at l5 GPa. Although the calculated results changednegligrbly, these new volumetric data greatly reduce apossible source of error in our input parameters.

The molar volume of HrO was also calculated at thesame pressures and temperatures using two MRK models(Halbach and Chatterjee, 1982; Kerrick and Jacobs, l98l).The original Redlich Kwong equation is

P :R T a ( l 3)v -b V(V + b )7o ' '

The two terms on the RHS correct for the repulsive andattractive intermolecular interactions, respectively. Red-lich and Kwong (1949) modeled a and b as constants forindividual gas species. Modifications of this originalequation have involved attempts to parameterize a andb as functions of pressure and temperature. For example,Kerrick and Jacobs (1981) assumed that a is a functionofP and Z, although b was still treated as a constant (b: 29 for H,O). However, they modified the repulsiveterm ofEquation 13 to incorporate Carnahan and Star-ling's (1972) hard sphere model. In contrast, Halbach andChatterjee described a(7) and b(P) only. A second im-portant difference between these two models is that Ker-rick and Jacobs used only the low-pressure PVT data ofBurnham et al. (1969) to constrain their parameteiza-tions, whereas Halbach and Chatterjee used low-pressuredata in conjunction with super high-pressure shock wavedata (i.e., Rice and Walsh, 1957). The Kerrick and Jacobsmodel is claimed to be accurate to only 2 GPa, whereasHalbach and Chatterjee considered their model to be ro-bust to 1000 'C and 20 GPa. The molar volumes of HrOcalculated using these two MRK equations and the newdata calculated from brucite dehydration are comparedin Figure 10. The agreement at high pressures betweenthe new calculations and Halbach and Chatterjee's MRKis impressive. In this range of P and T, the molecular

283

dynamic model of Belonoshko and Saxena (1991) pre-dicts virtually the same volumes as Halbach and Chat-terjee's model.

Although the volume of HrO would appear then to bequite well constrained at high pressure along the dehy-dration curve, we should point out that this constraintdoes not imply that the slope of the dehydration curvecan be computed with great accuracy. Even though therelative importance of the heat capacity terms is smallerthan the volume terms as a consequence of the steep dPldZ slope, the steepness of the slope dictates thal. A'V ofthe reaction is very small. Therefore, small errors in Zr,ocan lead to large errors in predicted dehydration curveslope.

Sources of error

Errors associated with the experimentally determinedpressures and temperatures were evaluated by fitting de-hydration curves with slopes as different as possible, butstill consistent with the experimental data. These fittedcurves were then used to calculate high-pressure volumes,and the calculated volumes differ by less than lo/o at 15GPa. Therefore, this source of error was considered triv-ial. Three other major sources of error, however, need tobe considered. None of these errors can as yet be evalu-ated quantitatively.

1. The P-?" coordinates determined from the experi-mental data are subject to error because a correction forthe effect of pressure on the thermal emf of S-type ther-mocouples has not been imposed. An attempt to estimatethe magnitude of this correction was made by using thecorrection factors of Getting and Kennedy (1970). Thesecorrection factors are based on experimental data up to1000 'C and 3.5 GPa. Using the reported polynomialequation and a pressure seal temperature of I 50 'C resultsin a correction factor of -14 "C ar 4 GPa, -21 "C at 8GPa, and only l7 "C at 15 GPa. This result does not makephysical sense because the magnitude ofthe pressure cor-rection should increase with increasing pressure. Thesepreliminary calculations confirm that the reported equa-tion cannot be extrapolated with accuracy beyond the5-GPa limit implied by the authors. Instead, the correc-tions above 5 GPa were estimated graphically, and theyamounted to +60 'C at 15 GPa and 1280 'C. A newsmoothed dehydration curve was fitted to these temper-ature-corrected data. Recalculating molar volumes usingthis new curve resulted in no change in volume to 6 GPa,and then slightly smaller volumes with increasing pres-sure (e.g., 10.5 vs. 10.2 cm3 at 15 GPa). These calcula-tions indicate the size ofthe error associated with ignor-ing the pressure effect on emf but cannot be performedquantitatively until more accurate data on this effect athigh pressure are available.

2. The molar volumes calculated above assume thatthe fluid phase is pure H2O. At these high pressures, how-ever, it is likely that some MgO is dissolved in the fluid.The quantity of MgO dissolved in the fluid is unknown.This dissolved MgO will result in an activity of HrO less

24

22

, 2 0

18

r6

t4

72

-this study- - -emfcor r- - -H&C------ K&J

0 2 4 6 8 1 0 1 2 1 4 1 6

Pressure (GPa)Fig. 10. The molar volume of H.O calculated using the new

phase equilibrium data from I to 15 GPa at temperatures alongthe brucite dehydration curve. These calculated volumes arecompared with the volumes calculated using the MRK modelsof Halbach and Chatterjee ( I 982; H&C) and Kerrick and Jacobs(1981; K&J). Also shown are the molar volumes calculated by

::rJ;;.",-t the pressure correction on thermal emf at high pres-

than one, will change the stoichiometry of the equilibri-um, and will modify the entropy and enthalpy of the flu-id. From the agreement between the calculations pre-sented here for high-pressure H2O volumes determinedfrom the slope of the dehydration curve vs. the volumesmeasured from shock waves, the MgO solubility appearsto have little effect on fluid volume.

3. Equation 2 calculates the difference in Gibbs freeenergy by raising the products and reactants first to tem-perature and then to pressure. This method of calculatingAG is only correct if the GPT surface is not curved irreg-ularly; ifthis surface has curvature, then Equation 2 willresult in an erroneous AG. The volume integrals are prob-ably the least affected by this assumption because thepressure derivative of the bulk modulus is incorporatedinto the expressions. This term, (, accounts for the cur-vature of the volume as a function of pressure. The ex-pressions used to evaluate the enthalpy and entropy athigh temperature, Equations 3 and 4, however, rely onusing the heat capacity at constant pressure. Since thecoefficients in Table 2 are derived empirically by linearlyregressing l-bar data, it is possible that the true heat ca-pacity coefficients at 15 GPa are different. It is difficultto estimate how much of a change may occur. However,since the P-Zcurve is nearly vertical in the range from 6to 15 GPa, the AZterm must dominate the AS term (Eq.1). Thus, the significance of errors in the heat capacitycoefficients is reduced.

Acxilowr,nocMENTS

We thank Surendra Saxena for initially suggesting this project, for gen-

erously allowing us the use of his as yet unpublished optimized thermo-dynamic and volumetric data, and for advice at various stages. We thank

l 0

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JOHNSON AND WALKER: MOLAR VOLUME OF H,O

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284 JOHNSON AND WALKER: MOLAR VOLUME OF H,O

Yrngwei Fei for providing us with his recently acquired brucite volumetricdata, and for kindly agreeing to allow us to cite them in this work. Wethank Peter McNutt and Teddy Koczynski for technical help and exper-tise. We thank John Longhi, Dean Presnall, and an anonymous revlewerfor thoughtful suggestions, which helped to improve this manuscript. Thiswork is supported in part by grants from NSF and DOE. Lamont-Dohertvcontribution no. 5029

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MrNuscnrrr REcETvED Apxrr 16,1992MeNuscr.rm AccEmED Nover*,rssn 25. 1992