JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. B5, PAGES 6967-6978, MAY 10, 1990 ElectricalConductivity of Olivine, a Dunite, and the Mantle STEVEN (•ONSTABLE ScrippsInstitution of Oceanography,La Jolla, California AL DUBA LawrenceLivermore National Laboratory,Livermore, California Laboratorystudies of the electricalconductivity of rocksand minerals are vital to the interpretation of electromagneticsoundings of theEarth's mantle. To date,the most reliable data have been collected from singlecrystals. We haveextended these studies with electricalconductivity measurements on a dunitefrom North Carolina,in the temperaturerange of 600ø-1200øC and undercontrolled oxygen fugacity.Observations of conductivityas a functionof oxygenfugacity and temperature demonstrate that conductionin the duniteis indistinguishablefrom conductionin singleolivine crystals.Thus the commonpractice of exaggeratingthe single-crystalconductivities to accountfor conductionby grain boundaryphases in the mantleis unnecessary.Because the duniteconductivity is consistentwith that publishedfor singlecrystals under similar conditions, we havemade a combinedanalysis of these data. Conductivityas a functionof temperaturebetween 600 ø and 1450øCdisplays three conduction mechanismswhose activation energies may be recoveredby nonlinearleast squaresfitting, yielding activationenergies of 0.21 4- 2.56x 10-19 J (0.134- 1.60eV) below 720øC, 2.56 4- 0.02x 10-19 J (1.604- 0.01eV) between720øC and 1500øC and 11.46 4- 0.90 x 10-19 J (7.164- 0.56eV) above 1500øC.The behaviorof conductivityas a functionof oxygenfugacity is well explainedby a model in whichan fo2-independentpopulation of chargecarriers is supplementedat high oxygen fugacities witha populationthat is proportional to fo20'3. This parametrization produces a clear correlation of the fo2 dependentterm with iron content, which is otherwiseobscured by variationsin conductivityamong olivines. INTRODUCTION mantle mineralogy using information such as density, seis- Estimates of the electrical conductivity of Earth form mic velocity, and composition of volcanic nodules, then an important part of our understandingof our planer's laboratory conductivity-temperaturemeasurements may be combined with observational conductivity-depth estimates interion Observations of the response of Earth to an [obtainedfrom geomagneticand electrical sounding]to give applied electromagneticfield, either of natural or man- made origin, give us a direct measurementof bulk mantle a temperature-depthrelationship; an electrogeotherm[Duba, conductivity, in situ, although the deconvolution of the 1976]. electromagneticresponse to obtain conductivity is by no A second,less well developed,use of the laboratorymea- means a trivial operation. While we might use Earth surementsis to constrainthe interpretationof observational conductivity estimatesto infer structure, as delineated by conductivity-depthdata. If laboratorydata can provide lower domains of differing conductivity, the use of laboratory and upper limits on the conductivityof mantle material as a measurementsof conductivityfor rocks and minerals allows functionof temperatureand if one has an idea, a priori, of the us to go further and to estimate temperature,phase state, geotherm, then mantle conductivity may be predicted. One fluid content, and even mineralogy. To do this, we must approachmight then be to ask whetherthe observationaldata replicate as many of the in situ conditionsof the mantle as are consistentwith this prediction. Agreementreinforces the possible.The focus of this paperis a laboratorystudy of the assumptionsmade; disagreementdirects attention to the need conductivityof a rock composedprimarily of olivine, under for more work. Note that this approachdoes not necessarily conditionswhich might representthose of the upper mantle requirethe generationof a model to fit the observationaldata, to the depthof the 400-km seismicdiscontinuity. and so the problem of nonuniquenessin the interpretation of geomagneticdata does not arise. Another approachis to Importance of Laboratory ConductivityMeasurements combinethe laboratorypredictions with the observationaldata to improve one's model of Earth conductivity.For example, Perhaps the most important use of laboratory conduc- the controlled source experiment of Cox et al. [1986] was tivity data is the estimation of temperature within Earth. sensitiveto mantle structuredeeper than about 15 km, but this In the absence of volatiles or conductive grain bound- deep structurewas highly correlatedwith shallowerstructure. ary phases, the electrical conductivity of a silicate rock By constrainingthe deep structureto follow upper and lower is strongly dependent on temperature. If one can infer bounds of conductivity inferred from the laboratory studies, the shallow structurewas better resolved. However, the upper bound used by Cox et al. was derived from a rather ad hoc extrapolationof single crystal olivine conductivity. Further- Copyright 1990 by the American GeophysicalUnion. more, there were no olivine conductivitydata applicableto Paper number89JB03514. the cooler temperatureregime associatedwith the uppermost 0148-0227/90/89JB-03514505.00 oceanic mantle. 6967 6968 CONSTABLEAND DUBA: CONDUCTIVITY OF OLIVINE Olivine as a Mantle Analogue [1982] and Cox et al. [1986] both used RSPx 10 as limits on The uppermantle is thoughtto be composedprimarily mantle conductivity. of the mineralsolivine and pyroxene,olivine being the Electrical Conduction in Olivine dominant mineral both in terms of its volume fraction and its electricalconductivity [Duba, Boland and Ringwood,1973]. Many years of researchand speculationhave failed to Thisdominance has led to the extrapolationof theproperties provide a definitiveexplanation for the electricalconduction of the mineralolivine to the propertiesof the rockperidotite, mechanismin olivineat geophysicallyinteresting tempera- whichis a constituentof the uppermantle. From the point tures,although recent data [Schocket al., 1989] havemade the of view of many laboratorystudies, including those used educatedguesswork more reliable. One critical observationis to measureconductivity, there is great advantagein using that forsterite[Mg2SiO4, or Fo•00] has a differentconduction single crystalsof mineralsover using whole rocks. The mechanismthan naturally occurring olivine [approximately sample size can be small and still representativeof the Mg•.sFe0.2SiO4,or Fo90], basedon differingmagnitudes largermaterial, the problemsof maintaininggrain to grain of conductivity,thermoelectric effects, dependence on fo, cohesionat temperatureare avoided,the possiblephases and anddependence on crystallographicdirection. This suggests phasetransitions are greatlysimplified (a giventemperature that the iron in natural olivine is involved in the conduction pathin a multiphasesystem will usuallycross several phase process.The positivefo, dependenceof olivineconductivity boundaries),the grain boundary phases due to weatheringnear requiresthat incorporationof oxygengas into the crystal Earth'ssurface can be avoided,and the physical interpretation lattice generates an appropriatelylarger population of charge of the datais lessambiguous. The complexitiesof studying carriers.The curvaturein the conductivity-temperaturedata wholerocks may be betterappreciated if one recallsthat the at 1200ø-1500øC[Duba et al., 1974; Schocket al., 1989] conductionmechanism in olivineis still a matterof study indicatesthat there is a changein conductionmechanism [Schock,Duba and Shankland,1989]. On the other hand, aroundthese temperatures. This is supportedby the observa- Earthis madeof rock,and extrapolation from singlecrystal tion of Schocket al. [1989]of an associatedchange in sign datato the mantleenvironment must be madeat somepoint. in thethermoelectric coefficient, from positive to negative,at We addressone aspectof this extrapolationin this paper, 1390øCand hence a changefrom positive charge carriers to takingthe stepfrom a singlemineral crystal to a nearly negativecarriers at this temperature. monomineralic,polycrystalline rock. The mechanismpresented by Schocket al. for conduction Goodsingle-crystal conductivity data for olivineare already below13900 is thegeneration of electronholes in thevalence available,at leastat relativelyhigh temperatures.One data bandand cationvacancies by incorporationof oxygeninto set that we consider reliable and which will be used later the lattice: in this paper is that of Duba, Heard and Schock[1974]. tt tttt Thesedata are for a singlecrystal of Red Seaperidot (RSP) 202 • 2VMg+ Vsi + 40•9+ 8h' (1) in the [010] crystallographicdirection, measuredbetween Theseholes are thenaccepted by the iron substitutingat the about 9000 and 1600øC. Pressure was varied but shown magnesiumsites: to have little effect, less than that of a 5 CO change in temperature.More importantly, oxygen fugacity (fo2), + -- (2) equivalentto partialpressure for an idealgas at the conditions Thus the holes are not free to move in the valence band but of the experiment,was controlled.The log of the electrical conductivityof olivine has been observed tovary as fo2 •/7 are trappedby the iron. For sufficientiron concentrationsthe at the temperaturesunder discussion[Schock and Duba, holescan "hop" from one iron ion to another,with a mobility more characteristicof ionic conductionthan band conduction, 1985], that is, the moreoxidizing the atmosphere,the more a hoppingmechanism first suggested by Bradleyet al. [1964]. conductivethe olivine. Furthermore,leaving the stability