American Mineralogist, Volume 73, pages1235-1254, 1988
Electrical conductivity of diopside: Evidence for oxygen vacancies
J. SrnpnBN Hunnxnn, DoNnn E. Vorcr* U.S. Geological Survey, Reston, Virginia 22092,V-5.4.
Arsrn-rcr Impedance spectra for two natural single crystals of diopside were obtained at 800 to 1300'C and l-bar pressureover the frequencyrange 0.001 Hz to 100 kHz in a system closed to all components but oxygen. For the near
INtnonucttow neededto model pyroxenesthat exist under different con- When Huebner et al. (1979) measured the electrical ditions. Huebner et al. went on to stressthat differences conductivity oforthopyroxene as a function oftempera- in the states of aggregation might bring about uncertain- single crys- ture, composition, orientation, andfr, the resulting mea- ties in applying laboratory measurementson Point surements were not sufficiently systematic to be inter- tals to real rocks.The 1982Chapman Conference on importance of preted in terms of the activation energiesand mechanisms Defects (Schock, 1985) emphasized the consideringpoint defectswhen trying to interpret electri- cal and mechanical properties measured in the labora- tory. Recently,we have encounteredsimilar uncertainties * Present address: Department of Geosciences,204 D{ike Building, PennsylvaniaState University, University Park, Pefin- when applying laboratory measurementsof chemical dif- sylvania 16802,U.S.A. fusion rates to natural assemblages.To addressthese un- 0003-o04x/88 / | | | 2-r 235$02.00 r236 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE certainties,we choseto return to electrical measurement Duba et al. (1976)subsequently measured orthopyrox- techniquesbecause they are a fast, yet accurate,method ene from Bamble, Norway; we identified talc in this sam- for deducingdefect structures(Tuller, 1985).We chose ple and determinedthe bulk compositionto be remark- initially to focus on relatively pure diopside for three rea- ably devoid of Al and Cr, NarCa,,Mn,Mg,urrFerrrTir- sons. (l) Augite is an important mineral in mafic rocks Alosi20roo6000.At 1000 "C and log.for: -9.5 U"rin bars), and the mantle, where it contributes to observedelectro- initial valueswere again anomalouslyconductive and un- magnetic sounding profiles and has undergonetransfor- stable, presumably becauseof dehydration of the talc. mations involving chemical diffusion. (2) Diopside, the Subsequentmeasurements were stable. At 1000 "C and principal end memberof most augites,is chemicallysim- logfo,of - I to -l6,thesloped(logo)/0(logf",)was-\f6. ple, thereby reducing the number of compositional vari- At s-kbar pressureand log ,fo, approximately - 12, the ables. (3) There is no unambiguous set of electrical con- results were complicated by (presumably) dehydration and ductivity measurementsfor this phase or for any other melting. The apparent activation eneryieswere 1.0 eV at pyroxene. In this first report we limit ourselvesto mea- <1250 oCand 1.8eV at >1250 'C. The conductivitywas surementson the diopside singlecrystals that will be used greater at 5 kbar than at I bar. to synthesizeaggregates for future studies. In future re- Dvorak and Schloessin(1973), in an investigationde- ports, we expect to discuss how changesin the state of signed to reveal conduction mechanisms,also measured aggregationand the cation ratios will change the mea- an orthopyroxene from Bamble, Norway. We have found sured conductivities, enabling us to compare data on sin- two compositions(Mg:Fe : 96:3 and 86:13) of ortho- gle crystals and polycrystalline aggregatesand to extract pyroxene from this locality, each with included talc (and bulk conductivity data from aggregatesprepared to de- one with magnetite).Unfortunately, Dvorak and Schloes- sired compositions. This long-rangeintention influenced sin failed to identify the composition of their pyroxene, our choice of measurementtechnique. worked at a difficult experimental range of pressure(24- 56 kbar) and low temperature,and neither measurednor defined the redox state (/or) of the orthopyroxene. Mea- Pnrvrous wonx sured values ofthe activation energyranged from 0.45 to Reports in the literature present an ambiguous "pic- 0.65 eV, distinctly lower than most other values.On the ture" of pyroxeneelectrical-conductivity values (data that basis of the variation with pressureand temperature,the can be used to quantify geophysicalmodels that use nat- activation energycould be resolved into two terms. The ural compositions, temperatures, pressures,and redox dominant energyterm was associatedwith increasingthe states).A review of previous measurementssuggests that number of chargecarriers; only 0.06-O.08eV was attrib- the conductivity measurementsthemselves are precise; uted to misration. rather, the ambiguity is probably causedby subtlechanges Will et al. (1979) measured the conductivity of syn- in composition or by differencesin the state of aggrega- thetic Fe-free orthoenstatite (MgrSirOu)aggregates at l0 tion within the sample cell. The following summary will kbar and 1600 Hz, using quartz to buffer the silica activ- illustrate some of the uncertainties in past efforts and ity or forsterite to buffer the MgO activity. No attempt thereby provide a rationale for the design of our experi- was made to distinguish the bulk component from any menls. grain-boundary component of the measuredconductivi- Much early work dealt with crystalsthat contained in- ty. On the assumption that the conductivity would be clusionsof a secondphase (commonly talc). For instance, independent of/or, they made no attempt to control or Duba et al. (1973) measuredthree orthopyroxene single measure/or.At 600 "C the measuredconductivity of en- 'C, crystals at 525 to 1009 controlled oxygen fugacity, statite in equilibrium with quartz was slightly greaterthan l-bar pressure,artd 1592 Hz. Two of the samplescon- for enstatite in equilibrium with forsterite. With increas- tained talc (A. Duba, pers. comm.), which should have ing temperature, the differencesin conductivity declined dehydratedin this temperaturerange and probably caused until, at 1000'C, the conductivitieswere equal. The mea- the anomalously large and unstable conductivity values sured activation energieswere l.l I eV for enstatitein observed when the samples were first heated. Gem-quality equilibrium with quartz and 1.25 eV for enstatitein equi- orthopyroxene[NarCarrMnrMg,rruFe, ruNi,Cr.TioAIroSi,rrr- librium with forsterite. The usefulnessof these conduc- Ouooo],the third sample, had no talc inclusions and be- tivity valuesmust be regardedas uncertain becauseof the haved stably. Although it had an intermediate value of uncertaintyin prevailingf,. Fel(Mg + Fe) and higher concentrationsof minor com- In a similar study,Voigt etal. (1979)searched for sys- ponents,the gem-quality orthopyroxenewas lessconduc- tematic variation between the conductivity of synthetic tive than the two otherpyroxenes,Na2Ca3Mn3Mgr873Fers0- orthopyroxene aggregatesand pressureor Fe/(Mg + Fe). CroTi,AlrSi,nrrOuoooand Ca,rMg,rorFerrsNirAlTSiree5O6ooo.Conductivity regularly increasedwith increasingFe/(Mg Measured activation energiesat constant values of /o, * Fe) over the completerange of solid solution.Over the were in the range 1.2-1.9 eV with a slight tendency for range Fel(Mg + Fe) : 0.0 to 0.2, an increasein pressure higher valuesat temperaturesgreater than 900 .C. At 1000 from l0 to 20 kbar decreasedthe conductivity and in- the slope of d(log o)/0(log varied from -/,r, : "C, "f"r) lrrto creasedthe activation energy. At Fe/(Mg + Fe) 0.5, where o is electrical conductivity. the efect of pressurewas small. A surprising feature of HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t237 these results is that conductivities of the Fe-rich pyrox- (1981,p. 250)attributed the enhancedconductivityto the enesat temperaturesof 900'C, below that of the pyrol- Fe content of natural diopside; we would have attributed ene solidus,exceed the conductivities expectedofbasaltlc a significant role to the trivalent elementsAl and Cr. The melts, whereaswe would have expectedthe silicate melts activation energiesare distincil 0.4 eV for the natural and to be more conductive than the crystalline silicates.The 1.3 eV for the synthetic diopside. The value of 0.4 eV is decreasein conductivity of polycrystallineaggregates witrh matched only by the values of Dvorak and Schloessin pressures pressurecontrasts in behavior to the increase found in (1973) for Bamble orthopyroxene at high and singlecrystals by Duba et al. (1976).Perhaps, in the cape low temperaturesand by the values of Voigt eI al. (1979) ofthe aggregate,the decreasein conductivity is due to a for synthetic FeSiO. at 20 kbar. closingofgrain boundarieswith pressure,rather than being Most recently,Parkhomenko (1982) reviewed conduc- a bulk property ofthe pyroxene.Leakage paths acrossthe tivities obtained from six contrastingcompositions of py- oC, high-pressureassemble and the inability of controlling roxene. At 300 a temperature at which she expected oxygen fugacity are additional factors to be considered. that extrinsic conductivity caused by impurities would Huebner et al. (1979) questionedthe use of composi- predominate, diopside and enstatite were poor conduc- tionally pure natural and synthetic pyroxenes as ana- tors (10-?to l0-8 S/m) but hedenbergiteand acmitewere logues of pyroxenes that contain significant concentra- relatively good conductors(10-3 S/m). Activation ener- tions of trivalent elements,as is the casein many natural gies,calculated from plotted data, rangedfrom 0.2 to 0.7 assemblages.By comparing measurementsof three gem- eV. Without chemical analysesor knowledgeof the struc- quality orthopyroxene crystals having similar Fe/(Mg + tural state, it is probably unwarranted to conclude that Fe), the least pure with composition NarCa'MnuMg,urr- increasedconductivity is causedby alkalis or Fe. At 1000 oC, 4 'zS/m NirFe.,,Cr, rAlrrsi,er2o6ooo(reanalyzed by us), they dem- conductivitiesranged from l0 to l0 (ensta- onstrated that increasedAl3* and Cr3* content was asso- tite, diopside, spodumene)to I to l0 S/m (adeite, hed- ciated with increased conductivity. They observed no enbergite,acmite). Activation energiesof 2.7, 0'7, and dependenceofconductivity onforor frequency(50 Hz to 4.4 eY, respectively, are reported for this latter group. l0 kHz). Despite use of gem-quality crystals that con- The highest conductivity values may be due to decom- tained no inclusions, the results were unsystematicwith position or melting, making uncertain the significanceof respectto crystallographicorientation. The authors chose the reported activation energies. This systematic ap- not to tabulate activation energiesthat might be used for proach was extended to measurementsat I to 20 kbar, unwarranted extrapolations. Approximate values of 1.3 showing that conductivity increasedwith the sum of al- eV at > 1000"C and 1.0eV at < 1000'C canbe estimated kalis, FeO, and FerO, and with pressure.In no case,how- from their Figure 7, suggestinga change in conduction ever, is enough information given about a sample, the mechanismat about 1000.C. Duba et al. ( I 979) measured measurement technique, or the conditions of measure- very aluminous orthopyroxene (NarCauoMnrMg,.ruFelo+n-ment to compare the magnitude of a measurementwith Felf Cr,AIrroTi,oSi,8,806000)and confirmed the trend of in- that determined in another laboratory. creasing conductivity with increasing trivalent-element Despite much effort usingorthopyroxene and two stud- content. They also noted a break in the slope ofconduc- ies using Ca-rich clinopyroxenes, it is difficult to place tivity at about 900'C; from their Figure I we estimate a the conductivity measurementsinto a systematicframe- high-temperatureactivation energyof 1.2 eV and a low- work. Conductivity does not changesimply with crystal- temperaturevalue of 0.8 eV, similar to energiesestimated lographic orientation, Fe/(Mg + Fe), trivalent-element from Huebner et al. (1979). In contrast, the pure poly- content, pressure,or state of aggregation(Fig. l). There crystalline orthoenstatite of Will et al. (1979) at 1000'C appearto be two families ofactivation energies,<0.8 and and l0 kbar was more canducting than these impure py- > 1.0 eV, with the lesservalues occurring at low temper- roxenesand at 700'C had conductivity equal to the most ature. Some conductivities appear to depend upon the conducting impure pyroxenes. furnacefo, but others do not. It is clear that resolution Hinze et al. (1981) also found that natural aluminous of these ambiguities will require, at a minimum, knowl- enstatite aW egate (Na, rCaurMnoMgr.rrFe,r, Crr rTiuAlrr.- edgeof the chemistry and structural stateof the substance Si,8r8o6oo0)was /essconducting than synthetic aggregate being measured, characleization of a sufficient quantity with comparable Fe/(Mg + Fe) but no additional com- of material that measurementscan be made on different ponents.Again, no attempt was made to distinguish bulk statesofaggregation at different physical conditions, the and grain-boundary componentsof the conductivity. The ability to vary cation/cation and cation/anion ratios, and activation energy was 1.0-l.l eV, but the temperature the control and measurementof oxygen fugacity during range (<850 "C) was not sufficient to reveal a changein the measurements.In this paper we only begin to address slope. Clinopyroxene aggregatebehaved differently. Nat- these issues,limiting ourselvesto (1) single crystals, (2) ural augiteof compositionNarCarroMnuMgro,rFe,r, Cr,, - minimal composition variation, and (3) l-bar pressure Ti2oA.l566si,r,,O.o*, thermodynamically bufered by the ol- with the intent ofdefining how conductivity and conduc- ivine-orthopyroxeneassemblage in which it occurred,was tivity mechanismsvary with temperature,crystallograph- an order of magnitude more conducting than synthetic ic orientation, andfo,. In future work, we will study an CaMgSirOuat l0 kbar (and unknown fo). Hinze et al. isotropic aggregateof identical bulk composition, using 1238 HUEBNER AND VOIGT: ELECTRICAL CONDUCTMTY OF DIOPSIDE
E --o\l o (, o
Fig. l. Summary of electrical conductivity measurementsof pyroxenes discussed in text. Solid lines represent synthetic pyroxenes that contain no impurities such as trivalent elements; dashed lines representnatural, impure samples. Compositions are indicated as atomic propor- tions of Ca:Mg:Fe.Total pressureis I bar unless indicated. (A) Orthopyroxene; (B) clinopyrox- ene. Sourcesof data: D73 (Duba et al., 1973), D76 (Duba et al., 1976),V79 (Voigtet al.,1979), w'79 (Will et al., 1979), H'79 (Huebner er al.. 1979), D79 (Duba et al., 1979), H8l (Hinze et al., l98l), P82 (Parkhomenko,1982). DK7 and MAL represent conductivity ranges of the two diopsides reported in this study. The results of Dvorak and Schloessin(1973) were collected at low temperatures(293-507 K) and are not shown.
changesin the frequency,temperature, and/o" responses one of us (J.S.H.)by the U.S. National Museum of Nat- of conductivity to distinguish the componentl of grain- ural History, Washington, D.C. We initially selectedsix boundary and volume conduction. In this manner, we crystals (DKI-DK6); the USNMNH subsequently as- will explore the relationship betweenmeasurements made signedacquisition numbers R18682-R18684 to the lot. on single crystals and on aggregates.Finally, we will in- We later obtained three more crystals (DK7-DK9) from vestigatethe effectsof varying the cation ratios (both pro- split RI8682. Thesecrystals are very pale green;0.7- to portions of elemental constituents and deviations from 1.5-mm-thick platesare colorless.White, clayJike ma- stoichiometry) of synthetic aggregateshaving composi- terial (talc) adheres to some surfaces;cracks and fluid tions that cannot be obtained in natural single crystals. inclusions make some parts of the crystals cloudy. For this first report, we used only the clear, gem-quality por- tions of crystal DK7. CH,c,RAcrrnIzATIoN oF DropsrDE We also usedgreen diopside from Malacacheta,Brazil, Crystal DK7 is one of severalhundred l- to 3-cm-sized removed from a lot that was subsequently assigned diopside crystalscollected from a vug near De Kalb, New USNMNH acquisition numbers 125990 and 127104. York for Wards, Inc.,' and acquired at the suggestionof Diopside from Malacachetais intensegreen, even in l-mm plates,and shows "oscillatory" zoning in color and slight heterogeneityin Fe/Mg ratio. The I Use of trade namesand namesof suppliersof materials and cracksappear unfilled, equipment is for descriptive purposesonly and does not imply yet thin plates of the material remain intact. endorsementby the U.S. Geological Survey. Microprobe analysesof the crystalswere performed by HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t239
TABLE1A. Chemicalanalyses of diopside
Avg DK1-9 PXKA*- MAL Unheated Heat. Heat'- Unheated Found Expected Unheated Heatedt Microprobe(wtc/o) sio, 55.64(2s) 55.67(3s) 56.06 55.58(31) 50.61(53) 50.73 54.59(28) s4.60(22}. Prot 0.01(02) 0.00(00) 0.00 0.01(02) 0.01(01) n.a. 0.00(00) 0.00(00) Alros 0.54(04) 0.56(19) 0.58 0.52(07) 8.78(21) 8.73 0.66(18) 1.03(03) Tio, 0.02(01) 0.02(00) 0.01 0.01(01) o.77(O2l 0.74 0.01(00) 0.01(00) CrrOB 0.00(00) 0.00(00) 0.00 0.00(00) 0.15(01) 0.17(04) 0.15(03) Mgo 17.90(14) 17.84(12) 18.01 17.99(14) 16.6109) 16.65 15.92(14) 16.18(28) Fett 0.88(04) 0.88(02) 0.92 0.81(07) 6.3600) 6.34 4.14(121 3.74(07) 0.06(01) Nio 0.01(01) 0.01(01) 0.00 0.01(02) 0.03(01) 0.04(02) MnO 0.0s(00) 0.06(01) 0.06 0.06(01) 0.13(01) 0.13 0.13(01) 0.12(00) CaO 24.83(16) 24.72('t0l 24.91 24.8604) 15.41(26) 15.82 24.48\11) 24.50('t4l ZnO 0.01(01) 0.02(02) 0.02 0.02(01) o.o2(02) 0.02(02) 0.01(01) Naro 0.40(02) 0.40(01) 0.43 0.38(04) 1.31(03) 1.27 0.21(021 0.27(01) Subtotal 100.30(44) 100.1 8(40) 100.98 100.26(38) 100.20(90) 100.41 100.37(66) 100.66(32) Analyses o 4 2 25 18 44 Points 46 32 16 186 67 32 32 Semiquantitatiye emission spectlographic analyses (pPm)ttt ZtO2 24 9J9 14 Tio, 300 160-380 230 CeO, <43 <43 66 P,O" <1550 <1550 <1550 Vro. 4'l 41-59 oo ScrO3 3 3-5 15 B,O. 110 64-1 10* n.a. Cr,O3 3 2-14 1200 1750 DY,o" <25 <25 25 Er"O" <,| <5 18 La,O" <12 <12-16 <12 Yro. 4 J-O Nio 8 7-13 460 600 CoO <2 <2-13 38 MnO 340 340-1 550 2700 CuO I 3-16 b GeO standardanalytical procedures using the reduction scheme analyses.We report the mean of pyroxene analysesmade of Benceand Albee (1968). Primary standardswere sili- on two or more operating shifts (Table lA), thereby catesand an oxide, evaluated by Huebner and Woodruff "averagjng out" the shift-to-shift scatter that was most (1985) and used as follows: AMKH (Al, Ti); FSBO (P); evident in values for Si. For comparison, the mean of OLNI (Ni);OXTB (Cr); PXBK(Zn);PXEN (Mg); PXHD replicate analyses of working standard PXKA and the (Fe, Mn); PXKA (Na); and PXPS (Si, Ca). Backgrounds expectedvalue (classicalmineral analysis)are given. The were obtained by interpolation, basedon the mean atom- agreementis good for all major elementsexecpt Ca' Long- ic number of the unknown, between the count rates ob- term monitoring of the CaO contents of a suite of work- tainedon OXQZoTOXPE atlow Zand OXNC oTOXVA ing standards and use of a substitute primary standard at high Z. We used a focused l5-kV electron beam, a (PXPI) for Ca (and Si) suggeststhat the assumedCa val- nominal l5-nA sample current, and a count time of 30 ue of the working standard is too low. Thus, no adjust- to 90 s for peak measurements and 120 s for back- ment to the cao value of the De Kalb diopsides was grounds. A pyroxene analysiswas calculatedfrom X-ray applied before calculating nominal formula units (Table count data obtained from four to eight consecutivespot lB) from the chemicalanalyses (Table lA). 1240 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE TABLE18. Nominalformula units per 40000 cations,analyzed diopside DK7 DK1-9 Heated Heated Heated Cation Unheated (001) plate- (100)platet. Unheated Unheated (010) platet Si 20020 20056 19989 19989 19911 19803 Ps* 3'| 3 3 3 1 '| I 2 2 B 7 7 5 AI 2 87 195 )T 20031 20067 20000 20000 20000 20000 M(1) Ti4- 7 5 5 4 4 AI 229 238 99 218 197 244 Cr3t 50 47 Ni 0 16 15 17 Co,* 1 1 Fe2* 162 173 219 117 1263 1136 Mg 9600 9580 9677 9644 8470 8551 >M(1) 10000 10000 10000 10000 10000 10000 M(2) Fe,* 103 92 127 127 187 192 Mnr* 13 16 24 24 62 60 Ce4* 1 1 Sr 1 1 1 'I Zn J 4 J J 4 4 9572 9542 9579 9579 9567 9520 NA 279 279 26s 265 146 190 Li 32 31 >M(2) 9970 9933 9997 9999 10000 oooo Oxygens 60010 60050 s9830 59980 60000 59940 /Vote;Footnotes are in Table 1a. Each crystal was also analyzed by semiquantitative 0.027. The fact that the chemistry of DK7 cannot be emission spectrographic(DC arc) techniques;the results distinguished from the averageof the nine DK diopside are also summarized in Table lA. As a rule-of-thumb, crystalssuggests that the inherently inaccurateminor- and these results have an uncertainty of +500/oand give us trace-element analysesare at least precise (i.e., consis- confidencein microprobe determinations at the level of tent). Within limits of analytical error, the nominal site <0.10lo(1000 ppm). occupanciessuggest that tetrahedral(T), octahedral(Ml), Chemical analyseswere converted to nominal site oc- and 6- to 8-fold coordinated M(2) sitesare fully occupied cupanciesbased on 40000 cations (Table lB), and charge with cations ofappropriate size. In particular, there is no balance was assumedto be maintained by oxygen ions evidencefor small interstitials such as Si. If the M(2) site (divalent anions). The cation to oxygen ratios are very of the De Kalb diopsides is fully occupied with Ca, Na, close to that ofideal pyroxene (4:6) and suggestthat Fe3* Zn, ar.d Sr [which are too large to fit into the M(l) or T is not present. However, without a direct determination positionsl, De lklb diopsidescontain no significant con- ofthe anionsor ofthe oxidation statesofthe polyvalent centrations ofoctahedral vacancies.The chemistry ofthe elements, we cannot conclude that these pyroxenes are Malacheta diopside is similar except for its greater Fe/ perfectly stoichiometric. Crystal DK7 has almost end- (Mg + Fe) valueof 0.127. member CaMgSirOucomposition with Fe/(Mg + Fe) : Unit-cell dimensions (Table 2) were determined by Trale 2. Unit-celldimensions and densitiesof diopsides DK1-9 MAL Unheated DK7(001)-2 DK7(010)-3 DK7(100)-2 Average MAL(100) a (A) s.738(2) 9.743(1) 9.744(11 s.742(31 b (A) 8.e21(2) 8.920(1) 8.922(1) 8.920(2) c (A) 5.249(1) 5.248(1 5 2s2(1) 5 252(3) pf) ) 105.84(21 105.8s(2) 105.8s(1 ) 105.85(2) t4A.) 439.7(1) 438.7(1) 439.2(1) 4391(2) 3.275 3.296 3.280 3.279 rfc) unheated 1001 1200 1200 unheated unheated log fo, (lo. in bars) -17.47 -12.00 /.oo 3.270(9) 3.271(41 3.27s(2) 3 290(9) 3 263(17) 3.315(3) No of p observations 17 R I I 4 -0.004 -0.025 .) +0.008 -0.016 Condition reduced reduced oxidized 7 7 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t24l X-ray powder diffractometry using BaF, internal stan- heated plates suggestthat systematicloss of Fe to the electrodes dard fao: 6.197l(l) A] and an automatedmethod sim- was not a problem. ilar to that describedby Huebner and Papike(1970) ex- Our furnace configuration is vertical with an alumina muffie The temperature and oxygen cept for the use of magnetic tape-recording medium tube of 44-rnm inner diameter. were maintained constant and measuredusing the non- instead of punched paper tape. Densities of regularly fugacity automated techniquesdescribed by Huebner (1987). Pt-PtroRhro shaped pyroxene fragments, each approximately 25 rng thermocouple wire was calibrated against the melting points of in weight, were determined by immersion in carbon tet- diopside and gold; the entire measurementcircuit wascalibrated rachloride, using a microbalance. Densities determined against the ice point and the gold melting point. The oxygen- by immersion are inherently imprecise; nevertheless, fugacity sensorwas placed beside the sample cell; the tempera- measureddensities of unheated DK and MAL diopsides ture gradient acrossthe sample cell and sensorwas less than 2 'C. are within 0.7o/oof the values calculated from the com- 'C. Measured temperatures are believed accurate to +1.5 position and unit-cell dimensions,assuming l6 cations The gas flow rate entering the furnace was 1.67 cm3/s to give (cold) and 24 oxygens(40 atoms) per unit cell (Table 2). Because liner flow rates of 1.2 mm/s at the bottom of the furnace (estimated)past the cell and sensorat 1200'C' the substitution for oxygenof anions with different atom- and 6.7 mm/s flow rates are much slower than is generallyrecommend- ic weights would change the density, the agreementin- These ed. At high temperatures,measured /o, agreedwith that calcu- dicatesthat an oxygen-basedformula unit is appropriate. lated (Deines et al., 1974)from the mixing ratio of CO and CO' greater Natural diopside crystals such as thesedeserve to within 0.10 log unit; at lower temperatures,the measuredf, attention from geophysicists.We suspectthat the De Laib was less than calculated,although not by as much as might be crystals are more homogeneousand stoichiometric than expectedat higher rates of flow (Huebner, 1975). Over a wide could be achieved by laboratory growth from a silicate rangeof fo, values,we saw no evidencethat the oxygen-fugacity melt of even pure diopside bulk composition. This is be- sensor(type SIRO, from Ceramic Oxide Fabricators)developed cause diopside melts incongruently (and nonstoichio- a component of electronic conduction. potenio- metrically) to a melt enriched in SiO, and CaSiO, com- Impedance spectrawere obtained with a model 273 lock-in amplifier, manufac- ponentsand a residual pyroxeneenriched in MgrSiOoand stat and model 5208 two-channel by EG&G Princeton Applied Research,and the manufac- MgrSirOucomponents (Kushiro, 1972).Pyroxene crystals tured turer's "turn-key" software that uses the composite-waveform grown from a flux will, in addition, most likely contain (FFT) method at TABLE3. Measuredconductivities (d in siemensper meter),lock- TABLEs.-Continued in technique Dura- Dura- tion T Resid- tion T Resid- Date Time (h) fC) log fo" log o ual* Date Time (h) ('c) loS f., Iog o ual' Measurements ot DK7(Ol0)-2 conductivity resumed -7.15 -4.33 36.3-MO resistor, expected log o : -7.556 to -2.564 4124 6:45 13.1 1300 4lo1 -7.56 11 :30 17.9 1300 -7 .'15 -4.36 15:43 22.1 1300 -7.15 -4.39 1o-k0 resistor,expected log o: -3.996 to -4.0(X -7.15 -4.41 -4.00 4125 10:36 42.O 1300 4107 16:00 4127 15:09 4.4 1300 -5.66 -4.50 -6.92 -5.03 DK7(100)-2,GF : 9.68m ,, 4 : 0.068cm, 4 : 0.068cm 15:47 13.3 1202 3/30 06:55 87.3 1200 -8.82 -4.40 -0.032 4128 16:43 38.3 1201 -6.94 -5.04 1O:21 90.7 1200 -8.50 -4.43 -0.006 4129 15:48 7.0 1100 -8.41 -5.5 13:23 0.7 1300 -7.22 -4.13 0.053 4130 8:58 1.5 1000 -10.11 -5.92 -0.0779 15:39 2.9 1300 -7.22 -4.15 0.033 13:46 11 900 -12.09 -6.30 0.0173 3131 9:45 1.8 1200 -8.48 -4.45 -0.022 15:39 I0 1300 -3.36 -4.51 11:27 0.9 1300 -8.48 -3.95 0.009 5/01 10:16 2.O 12OO -3.40 -5.02 13:29 1.1 1100 -8.50 -5.0 -0.040 12:01 1.0 1002 -3.36 -5.95 15:35 1.2 1000 -8.47 -5.68 -0.093 15:42 10.8 800 -3.22 -6.70 4101 12:55 3.7 1300 -6.99 -4.17 0.054 5104 13:27 3.3 1300 -8.93 -4.30 15:41 1.9 1200 -7.00 -4.63 0.060 15:51 11.7 1300 -8.92 -4.30 0.1474 4102 9:30 170 1100 -7.05 -5.30 -0.082 5/05 10:11 2.0 1200 -9.02 -4.8 0.0740 11:52 1.2 1000 -7.58 -5.80 -0.055 13:15 2.0 1300 -9.90 -4.24 15:44 3.0 1300 -6.00 -4.30 0.100 16:05 10.0 1300 -9.90 -4.23 0.1'172 4103 8:54 1.5 1200 -6.02 -4.86 0.004 5/06 15:17 3.0 1200 -9.98 -4.77 10:17 0.7 1100 -6.02 -5.43 -0.029 5107 12:O0 21.3 1200 -9.98 -4.79 -0.0142 13:21 1.8 1300 -5.04 -4.36 16:25 10.7 1100 -10.08 -5.32 -0.0539 15:43 1.6 1202 -5.01 -4.91 0.124 5/08 15:45 10.0 1200 - 13.85 -4.54 4lO4 17:05 6.0 1298 -3.91 -4.43 5/11 8:10 7O.7 1200 -13.84 -4.50 4l0s 16:02 6.1 1300 -3.23 -4.41 -6.332 -3.47 -5.0 2.15-MOresistor, expecled log o: 4106 9:42 2.2 1200 5/11 -6.334 13:33 2.7 1100 -3.45 -5.45 15:13 07 1000 -3.42 -5.9 Measurements of DK7(010)-2 resumed 4107 8:10 160 1300 -10.93 -3.6 -0.076 5118 9:00 70.0 1100 -15.10 -4.92 12:00 2.6 1300 -11.92 -3.5 12:4O 1.8 1000 -16.79 -5.36 14:56 6.8 12OO -11.89 -3.86 -0.038 14:57 1.4 900 -16.91 -5.89 4108 8:30 18.8 1200 - 11 .90 -3.89 -0.075 : -6.384 -11.97 -4.30 2.42-Mfl resistor, expected log o 11:06 1.5 1100 0.044 5121 -6.38s 13:01 1.1 1000 -12j0 -4.78 0.162 15:07 0.7 1300 -12.79 -3.53 Measuremenis of DK7(010)-2 resumed 16:10 5.9 1201 -12.94 -3.83 5121 15:45 72.O 12OO - 12.66 -4.53 -0.0284 4109 10:07 1.6 1100 -12.98 -4.20 -0.035 5122 16:30 32.3 1300 -12.81 -4.10 -0.0506 13:46 2.0 1000 - 13.04 -4.67 0.105 5123 19:33 8.3 1206 -12.57 -4.57 -0.0871 15:55 6.8 1200 - 14.06 -3.83 5125 17:08 8.4 1000 -13.00 -5.52 0.0264 4110 11:01 2.9 1100 -13.98 -4.16 5126 9:58 2.0 900 -13.09 -6.10 0.1150 14:15 2.1 1000 -13.98 -4.59 0.018 15:50 5.0 1200 - 14.08 -4.52 16:02 6.1 1198 -14.63 -3.92 5127 8:29 21 3 12OO -14.25 -4.54 4111 14:39 >2.7 1000 -17.78 -4.57 13:03 33 1100 -13.91 -4.96 4113 8:40 16.0 1200 -7.65 -4 66 -0.085 14:42 0.4 1000 -13.97 -5.46 12:13 19.9 1200 -7.66 -4.67 -0.097 16:16 9.0 902 - 13.96 -6.07 0.0413 5128 12:00 3.3 1100 -12.40 -5.00 0.0287 DK7(010)-1,GF: 12.59m-1, 4:0.075, ,,:0.075 -9.42 -4.34 9l't2 1200 - 8.46 -4.93 0.0013 16:13 11.3 1300 0.0563 -7.32 -4.51 5129 9:38 1.1 1200 -9.49 -4.88 -0.0540 9/15 1300 -9.58 -5.3 o/l A -9.80 -5.34 -0.0560 12:33 2.0 1102 0.0065 1102 -9.51 -5.31 1002 -11.33 -5.75 -0.0452 14:54 4.2 1101 0.0090 -10.56 16:10 8.7 1003 -9.21 -5.85 1100 -4.45 -6.3 atl-7 -11.10 -4.23 -0.0056 5/30 15:18 8.4 900 1300 -4.45 -6.3 1197 -12.42 -4.57 -0.0298 6/01 8:55 29.8 900 -13.72 -4.85 1108 DK7(010)-3,GF : 55.53m-1, 1 :0.109 cm, {: 0.109cm 9/18 1100 -13.86 -4.90 7lO2 15:45 75.1 1200 -7.7O -5.24 7106 15:40 18.0 1200 -9.08 -5.15 -0.0493 DK7(010)-2,cF: 18.42m-', 1: 0.106cm, 4: 0.102cm -8.46 -4.20 7107 16:15 19.0 1200 -11.74 -4.78 -0.0577 4114 14:38 2.0 1200 -9.07 -5.14 -0.0379 15:46 6.0 1200 -8.46 -4.70 TlOg 13:13 4.3 1200 -8.46 -4.96 16:00 13.0 1000 -9.03 -5.99 4116 8:22 55.0 1200 - -5.94 4117 16:17 85.0 1200 -8.46 -4.96 -0.0287 7109 12:00 3.5 1000 10.00 -9.15 -5.47 -0.1088 7110 9:20 20.6 1000 -13.46 -5.63 -0.0634 4120 16:05 6.1 1100 -10.82 -4.88 -0.0268 412'1 11:54 2.2 1000 -9.00 -5.92 12:45 2.6 1200 -g -6.32 16:30 10.8 1200 -9.97 -5.02 -0.0459 16:03 2.4 900 13 -12.26 -5.75 -0.0127 4122 12:45 3.0 1300 -7 83 -3.89 7111 11:20 16.3 1000 -7.83 -3.91 7112 16:00 8.5 1000 -11.34 -5.84 O.O282 14:51 5.0 1300 -12.32 -4.72 -0.0802 16:19 10.0 1299 -7.84 -4.08 7l'13 15:10 7.5 1200 -7.81 -4.12 16:17 8.6 1200 - 12.88 -4.7O 4123 9:02 23.0 1299 -13.33 -4.67 14:55 31.0 1299 -7 .81 -4.17 7114 15:40 7.4 1200 16:31 9.6 1200 -13.98 -4.67 2.42-Mg resistor, expected log o : -6.384 7116 9:24 24.9 1000 - 13.95 -5.51 4t24 -6.35 14:40 30.1 1000 -13.95 -5 52 -0.0231 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t243 T^BLE3.-Continued Trcte 3.-Continued Dura- Dura- tion f Resid- tion I Resid- Date Time (h) (rc) bg fo. log o ual' Date Time (h) fc) log fo" log o ual- -13.63 -3.63 -0.0313 7117 14:58 21 1000 - 13.46 -5.58 -0.0234 8112 8:32 16.5 1200 -15.01 -4.67 11:37 1.6 1000 -17.01 -4.65 7 118 14:40 16.4 1197 -17.07 -4.67 7l2O 11:42 24.2 1000 -14.95 -5.40 -0.0454 14:55 4.9 1000 - -4.71 16:50 8.6 1000 -15.2 -4.38 7l2'l 8:18 19.3 1200 15.05 -4.44 -15.72 -5.33 8/13 8:25 16.2 1000 -15.32 16:15 7.2 1002 -16.19 -4.59 7122 7:57 22.9 1002 -15.75 -5.35 12:23 1.3 1000 -17.29 -5.33 16:04 5.0 1000 -16.18 -4.75 7 123 8:15 23.6 1000 - -4.45 18:32 9.6 1200 -8.48 -5.15 8114 8:22 15.5 1000 11.38 -8.48 -5.17 1.0 1100 -11.38 -3.96 7124 6:45 21.8 1200 0.0161 11 :08 -0.0503 -8.50 -5.18 15:12 5.1 1101 -11.36 -3.95 12:35 3.2 1200 -3.70 - -4.65 0.0339 16:50 8.7 1200 -11.28 7127 8:54 68.0 1200 12.01 -11.27 -3.67 15:21 24.0 1175 - 12.00 -4.75 0.0550 8117 8:26 64.7 1200 0.0055 -12.01 -4.86 1O:44 1.2 1200 -12.20 -3.60 7128 14:10 2.5 1150 0.0674 -12.20 -3.63 14:40 9.6 1't26 -12.00 -5.03 0.0219 14:24 4'9 1200 0.0152 -13.02 -3.59 0.0282 7 129 14:00 5.5 1150 - 12.00 -4.88 0.0489 8/18 9:00 17'4 1200 -12.O -5.16 1.6 1175 - 13.02 -3.69 -0.0170 15:36 8.7 1100 0.0301 11 :30 -0.0107 -12.01 -5.29 15:09 1.0 1150 -13.02 -3.74 7130 11:45 3.6 1075 0.0366 -3.76 -11.99 -5.43 0.0426 16:05 8.2 1't25 -13.02 15:33 2.9 1050 - -3.79 -0-0203 7 131 7:10 15.4 1025 -11.98 -5.61 0.0126 8/19 8:15 16.3 1125 13-02 -12.00 -5.75 1.0 1100 - 13.02 - 3.83 0.0181 12:28 4.0 1000 0.0243 9:52 -0.0095 -11.96 -5.87 14:O2 2.0 1075 -13.02 -3.92 16:02 19.1 975 -0.0467 -11.96 -6.01 15:45 8.75 1051 -13.02 -4.02 8/01 15:24 9.1 950 -13.03 -4.17 8lO2 6:50 16.5 950 -12.06 -5.96 8l2O 10:00 1.7 1025 -12.00 -6.11 '13:00 2.7 1000 - 13.03 -4.30 8/03 14:00 5.3 925 -13.00 -4.48 16:09 15.3 900 -12.00 -6.21 15:10 1.2 975 -11.99 -6.30 16:16 2.3 975 -13.02 -4.49 8lO4 13:03 5.0 875 -4.65 -12.03 -6.44 8121 9:55 2.1 950 -13.03 16:00 16.0 850 -13.03 -4.84 8/05 11:00 2.0 900 -11.99 -6.22 13:26 3.7 925 - -5.78 -0.0057 15:50 8.4 900 -13.02 -5.14 14:37 3.3 1000 12.00 -5.52 -12.01 -5.20 -0.0113 8124 12:15 3.2 850 -13.02 18:51 3.9 1100 - - 8/06 7:45 12.5 1200 - 12.00 -4.63 0.0553 8126 12:21 46.6 800 13.03 6.1 16:00 5.5 900 -13.01 -5.12 8127 13:52 5.0 1000 - 13.03 -4.33 ', -3.83 DK7(001)-2;GF:8.70 m 4:0.96 cm, 4: 0'095cm 8128 7:30 16.7 1100 -13.02 0.0181 -8.43 -4'658 3111 15:50 59.0 1200 0.0529 9:57 1.0 1200 - 13.00 - 3.60 0.0192 -7.31 -4.30 3t12 14:55 5.2 1300 0'0959 11:00 24'4 1200 -9.03 -3.74 -8.42 -4.753 -0.0413 -3.75 3/13 12:45 0.7 1200 8131 9:45 71.3 1200 -9.03 -9 -5'14 -0.0801 -0.0015 14:45 0.8 1101 76 14:15 75.3 1200 -9.03 -3.75 -9.77 -5.14 -0.0763 15:25 7.0 1100 17:06 12.0 1102 -8.96 -3.97 -11.25 -5.54 -0.0581 -3.97 3114 10:43 6.0 1000 9/01 8:27 17.3 1100 -8.98 0.0097 - -5'96 3/15 13:03 6.0 900 12.90 0.0236 16:39 16.6 1000 -8.97 -4.48 -15.05 -6.51 -5.15 3/16 12:45 4.2 800 0.0407 9lO2 15:35 16.0 900 -9.10 -15.00 -6.50 -5.10 16:15 16.0 800 0.0580 9/03 10:29 24'9 900 -9.O2 -8.45 -4'72 -0.0120 3117 11:00 2.4 1200 16:22 18.4 850 -9.05 -4.73 -7 -4.34 -5.01 13:00 1.0 1300 '32 0.0544 9lO4 9:38 20.0 850 -9.2 -7.87 -4.53 16:20 9.2 1250 0.0156 11:08 215 850 -9.4 -5.15 -9.10 -4.93 -0.0524 3/18 8:46 0.6 1150 14:27 24.0 850 -9.6 -5.19 -11.89 -4.16 3/19 15:10 27.0 1200 0-0473 15:46 0.3 1100 -8.97 -3.97 -12.43 -4'12 3t20 15:15 3.0 1200 0.0087 16:13 0.8 1100 -8.96 -3.97 -12.44 -4-11 -3.98 -0.0009 22:16 10.0 1200 0!142 9/05 15:55 24.5 1100 -9.00 -10.15 -4.45 -3.80 3121 16:45 6.4 1200 0.0106 9/08 12:00 O.2 1100 -12.94 -8.02 -4'86 -0.0898 3123 13:55 19.6 1200 12:15 0.5 1100 -12.95 -3.795 -3.33 -5.20 3124 8:15 17.6 1200 13:00 1.2 1100 -12.95 -3.80 -5.47 -5.08 11:30 2.0 1200 0.0618 13:45 2.0 1100 - 12.95 -3.79 -5.57 -5.08 -3.79 12:25 2.8 1200 0'0472 9/09 7:45 20.0 1100 -'12.97 0.0598 -8.79 -5.90 -0.0600 -3.93 13:55 0.8 1000 9/10 9:00 23.5 1100 -9.28 0.0400 -7.59 -6.00 15:45 1.3 1001 0.0079 -6.388 -7.55 -6.03 -0.0231 2.42-M{, resistor, expected logo : -6'380 to 3124 16:12 10.1 1002 '1'4:40 -6.39 3125 9:15 0 4 1000 -3.13 -6.19 9/15 -3.26 -6.13 -7.564 9:55 1.1 1000 36.3-MO resistor, expected log o : -7.556 to -12.45 -4.18 -0.0542 13:12 3.0 1200 15:45 -7.54 14:19 0.9 1000 -15.67 -4.83 0.0086 : m 1, 0.144cm' 0.145cm 17:00 2.O 1200 -14.37 -4.15 Mal(010)-1,GF 8.68 1: {': 1225 -9.54 -3.59 0.0051 17:17 8.0 1199 - 14.39 -4.10 4t2g 1125 -10.87 -3.80 0.0223 3t26 9:00 1.2 1001 -17 .47 -4.75 1025 -12.37 -4.06 0'0252 1225 -7.58 -3.67 -0.0388 : 35.38 m ', : 0.'142cm, : 0.142 cm 5/01 Maf(100)-1,GF I 4 1125 -8.87 -3.82 0.0391 8107 10:23 18.4 1200 -9'93 -3'74 -4.11 -9.93 -3.73 1025 - 10.37 0-0120 16:09 32.1 1200 -11.57 -3.56 -0.0023 -9.93 -3.76 5to2 1225 8/10 9:05 89.1 1200 -12.88 -3-74 0.0453 1200 -g 93 -3-76 -0.0408 1125 13:05 93.1 1025 -14.41 -4.01 0.0376 16:35 10.8 1200 -8.15 -3.78 -0.0029 8/11 16:38 8.s 1200 -13.61 -3.63 @ntinued 1244 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE TABLE3.-Continued N o Dura- o tion Resid- J Date Time (h) log fo. log o ual- o fc) u s/08 1223 -1 1.59 3.56 0.0020 5112 1125 -12.86 -3.82 -0.0343 Ell Q 1025 14.40 -4.11 -0.0622 975 -15 22 -4.22 0.0246 5114 -9.54 -3.61 -0 N 1225 0149 o c/ tc 1225 -9.54 -3.64 -0.0449 o J 5t20 1225 -1257 -3.53 0.0093 -12.57 (5 1225 3.53 0.0093 U 1125 -13.87 -3.72 o o.0471 s 1025 - 15.39 -4.03 -0.0005 975 16.22 -4.22 -0.0430 900 17.61 -4 41 0.0114 N /Vofe;Where a resistoris designated,a precisionresistorwas substituted o for the sample o and electrodes.Where a pyroxene plate is designated,GF J is its geometricfactor, and /,are its initialand final thicknesses(see . 1 text). o Residualis the observedlog o minusthe calculatedlog o; for u calculated o log d, see least-squaresfitting parametersin Table 5. G FREOUENCY(HZ) therms in log/",-log o space.Conductivity measurementsin the Fig. 3. Representativeimpedance spectra ofdiopside, show- central part ofthe investigarcdfo2rangeappear to have a linear ing plots of impedance(Z) and,phase angle (0). The transition dependenceon/o, and were fit to the expression from low-frequencyFFT to high-frequencylock-in measure- loga: Ao + B/T + N(Iog/",) mentsat l0 Hz causesa slightdiscontinuity. The decreasein Z at high frequencyis due to the capacitanceeffects of the elec- by using oRcrs2, the generalnonlinear least-squaresprogram of trodes,leads, and measurement circuit. (A andB) For DK7, the Busingand l-evy (1962),where ?"is temperaturein kelvins. Each impedanceis flat over mostofthe frequencyrange and specifi- data set was fit to 0.03-0.07 a unit (one standard error of an cally does not increasewith decreasingfrequency. (C) The observation).Because the possiblesystematic errors in the mea- impedanceof the Fe-bearingdiopside from Malacachetain- surement technique are of the same magnitude, we did not try creaseswith decreasingfrequency. This effect,which we have to improve the fit by using higher-order terms to, for instance, alsoobserved in olivine,might be causedby polarizationat the identifu a possible temperature .C, dependenceof B, which is pro- blockingelectrodes. (A) PlateDK7(001)-2, 1200 bE fo.: ponional to the thermalaclivation energy. -14.39.(B) PlateDK7(100)-2, 1000'C, logfo,: -7.58. (C) PlateMAL(010)-1, 1225'C, log/", : -9.60. Rnsur,rs Impedance spectra at a variety of temperatures and oxygen-fugacity values were obtained perpendicular to spectra are shown in Figure 3. For DK7, impedance is (100), (010), and (001) platesof crystatDK7 and (100) usually independent of frequency below about 500 Hz, and (010) platesof MAL, all at l-bar pressure.Typical and the phaseangle d is close to 0" (dispersion is small). However, for the more-Fe-rich MAL diopside and, to a slight extent,some spectraof the (010) orientation of DK7 N atlow values, there appear to be high-frequency-low- o fo, o J impedance and low-frequency-high-impedanceregimes distinguishedby the decreaseof impedancewith frequen- N cy and separatedby frequency intervals in which d is o negative. The use of metallic electrodeswas intended to 9 block the passageofall pyroxenecomponents except elec- trons. In practice the electrodesconducted electrons,al- N lowed oxygento pass,probably leakage a by along the elec- J trode-sample interface, and provided no mechanism for ' supplying or removing the cationic LOG FREOUENCY(HZ) speciesin diopside. The fact that most diopside spectra show no increaseof Fig. 2. Impedance spectraused to verifu conductivity mea- impedance at very low frequency suggeststhat ions are surementsand demonstrateinsignificant leakagepaths at room not accumulating at the crystal-electrodeinterfaces, even temperature.In each casea Teflon plate, 0.86 mm thick and 16 at 0.0001 Hz. Thus polarization does not mm in diameter, was positioned between the electrodesin the appearto be position normally occupied by diopside plates and a represen- significant for most DK7 plates but does appear to be tative value ofthe geometric factor is incorporated in the dafa. significant for MAL diopside at low frequencies.The ex- (A) l0-kO resistor in parallel with electrodes.(B) 20-MO resistor act causeis not yet understood, but possibitities will be in parallel with electrodes.(C) No resistor (oo O) in parallel with discussedin a subsequentpaper that deals with the sig- electrodes. natures of the components that contribute to an imped- HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE r245 TABLE 4. Sample numbers and conditions for curves in Figure4 Curve Sample I fC) loS(f..), li fC) log(fo,) -40 -8.4 1 DK7(001)-2 zc -0.7 1200 - DK7(010)-2 ZJ 1200 8.5 DK7(010)-3 25 -o.7 1200 -7.7 25 -0.7 1200 -9.9 E 4 MAq100)-1 o DK7(010)-3 1000 - 10.0 1000 - 13.5 - 5 -ns o DK7(010)-3 1000 - 13.5 1200 10.8 -9.1 -11 o -____{L_____d,_ 7 DK7(010)-3 1200 1200 7 I 8 DK7(010)-3 1200 -11.2 1200 -9.1 9 DK7(010)-3 1200 ,7.7 1000 -9.1 10 DK7(010)-3 1200 -9.1 1000 -9.1 ]-.--*--- --o------€)- 2 '11 DK7(001)-2 1000 -J-l 1200 -12.4 12 DK7(001)-2 1000 -'15.7 1200 -14.4 13 MAL(100)-1 850 -9.6 1100 -9.0 14 MAL(100)-1 1100 -9.0 1100 -13.0 15 DK7(010)-3 1100 -17.3 1200 -8.5 -17 60 to DK7(001)-2 1200 -14.4 1000 .5 TIME, HOURS ance spectrum. For most spectra, the phase angle was f-" approximately0'in the frequencyrange 0.01 to I kHz. Above I kH4 the impedance falls in all the spectra,in- cluding those of Teflon, alumina, silica glass, and net- works of standard components. Simple calculations based on the geometry of the electrodeassembly and leads pre- dict a similar response.Thus, we attribute this high-fre- quency behavior as due simply to the capacitanceof the metal electrodes,leads, and the measuringcircuit (com- o{ pare Figs. 2 and 3). Some other measuring techniques (, compensatefor these components during the measuring J processso that theseeffects are not readily seen.It is clear that had we relied on measurementsmade at a single frequencyin the commonly usedfrequency range 1.0-1.7 kHz, the conductivity would have been sensitive to fre- quency and perhaps reflect compon€nts of conductivity that are not associatedwith the interior of the sample. The polarization of MAL diopside did interfere with the impedancedetermination, but only at 800'C- At this low temperature,the changesin impedance(decrease with in- polarization to the capac- TIME,HOURS creasingfrequency) due to and itance ofthe electrodesand leads were indistinguishable' The maximum value of the phased was only - 10'(at l3 Hz), causinga small error in the reported impedancefor that measurement.Critical conductivity values for each spectrum are tabulated in Table 3. o The immediately preceding temperature-/or-timehis- 6 manner in which a sample o tory of a sample affects the o J respondsto changesin the furnace environment. When (- rapid. The responseto temperaturechanges used in this work is faster than the responseto changesin oxygen fugacity. (C) The C TIME,HOURS responsesof conductivity to temperature arrdfo, are opposite in sense,and the responseto temperaturechange is faster than the Fig. 4. Response,as a function of time, of conductivity to responseto changein /or. Thus, when the temperature and /o, changesin temperature and oxygen fugacity. (A) On the initial both decrease(or both increase),the conductivity of DK7 diop- heating,the conductivity of DK7 platesdecreases relatively slowly side passesthrough a maximum (minimum). The sample num- as if they previously had been more reducing.(B) When furnace bers and conditions representedby eachcurve are shown in Ta- conditions change, re-equilibration is reversible and relatively ble 4. 1246 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE TABLE5. Fit parameters of conductivity, diopside No.of measure- log ,4o Ao O (ev) menls rfc) DK7(100)-2 1.434 + 0.202 27.16 2.154+ 0.016 -0.1776 + 0.0065 26 1000-1 300 DK7(010)-1,2 1.075+ 0.148 11.89 2.009+ 0.045 -O.1O23 + 0.0093 25 900-1300 DK7(010)-3 0.540+ 0.163 346 2.026+ 0.048 -0j423 + 0.0078 26 >1000 DK7(010) avg. 0.885 7.68 2.O18 -0.1223 DK7(001)-2 1.583+ 0.101 38.28 2.198+ 0.033 -0.1456 + 0.0048 800-1300 DK7 avg. 1.39 24.4 2.12 -0.15 -0.890 MAL(100)-1 + 0.184 0.129 0.922+ 0 052 -0.0326 + 0.0037 17 1050-1 200 -0.252 MAL(010)-1 + 0.111 0.56 1.046+ 0.040 -0.0184 + 0.0044 21 900-122s MAL avg. -0.46 0.34 0.98 -0.026 _ Nole.'logo:log4 +tAlRTl + A,{logfo),wheredisconductivityinsiemenspermeter,Oisinelectronvolts, fisinkelvins,Nisaconstant,and fo. is in bars. first placed in the furnace, plates were allowed to equili- 5, and residuals(observed minus calculated value of log brate with the furnace atmosphereaI 1200 oC for several o) are included in Table 3. days. The conductivity of DK7 diopside decreased The MAL diopside behavesdifferently (Fig. 6) but not monotonically with time, falling as much as one log o entirely as anticipated. We expectedthat its conductivity unit and requiring as much as 45 h to stabilize (Fig. 44, would be greater than in DK7 becauseCr3*, which is Table 4). In contrast, when first heated, MAL diopside present in MAL diopside, has been associatedwith in- equilibrated rapidly. For subsequentchanges in temper- creasedconductivity in orthopyroxene [compare the re- ature at constant/o, steady-statevalues ofconductivity sults for crystals #173 (Duba et al., 1973) and MF#l-3 were usually achievedwithin 5 h (Fig. 4B). Equilibration (Huebner et al., 1979)l and becausean increase in Fe/ of DK7 diopside was slowestin a very reducing environ- (Mg + Fe) is associatedwith increasedconductivity in ment. MAL diopside equilibrated within minutes. In sev- syntheticolivine (Hinze et al., l98l) and orthopyroxene eral casesinvolving DK7 diopside,the conductivity passed (Voigt et al., 1979) aggregates.This expectation was re- through a maximum or minimum (Fig. aC), suggestive alized. We also expectedthat the significant Fe content of competingprocesses with different rate constants.With of the MAL diopside might have causedthe conductivity the exception of the first heating (for which the initial to increasewith oxygen fugacity as it does with olivine stateof the sample is unknown), measuredconductivities (Cemic et al., 1980; Schock and Duba, 1985), but we were reversible with respect to changesin both temper- observed a slight decrease.Within measurementuncer- ature and fo, a fact that can readily be gleaned from tainties, this observation is consistent with the observa- Table 3 becausethe measurementsfor each sample are tions of Huebneret al. (1979,their Fig. 2) who found no reported in the sequencein which they were obtained. To dependenceof log o on logf, in impure Fe-bearing or- reduce the time needed for equilibration, we adopted a thopyroxenes.At <900'C, the behavior pattern of MAL strategy of following oxygen isobars, rather than iso- changes,suggesting a positive slope of d(log o)/6(lo9f"r). oC therms, whenever possible, and of changing-fo, at high At 1000 and logfo, <-15, the measurementswere temperature (1200-1300 "C) to hasten equilibration with unstable.Schock and Duba (1985) associatedunstable the furnace atmosphere. readingswith reduction and loss of Fe from olivine. Be- Our initial approach was to explore log o-logf, space causewe could subsequentlyreproduce earlier measure, for DK7 diopside at various temperatures.Isotherms are ments at I 100-1200'C and found no evidenceofreduc- plotted in Figure 5. At constant temperature,conductiv- tion when the sample was removed from the furnace,we ity decreaseswith increasing/o, throughout much of the do not think that our experiments were troubled by re- range that is easily obtained with CO + CO, furnace-gas duction of Fe. mixtures. The log ,6r-temperature relationships of the Oxygen isobars in conductivity-temperature space(Fig. oxygen-bufferassemblages iron + wi.istite + vapor (IW) 7) were carefully determined for one orientation each of and quartz + fayalite + magnetite + vapor (QFM) are DK7 (at logfo,: -12.0) and MAL (logfo,: -13.0). indicated becausethese reactions define a volume (in Z, The data are reversiblewith respectto temperature,each P,,6, space)that encompassesmany igneous and meta- isobar can be describedby two straight line segments,and morphic processesin the crust. (The buffer reactions are the transition between segmentsoccurs over a narrow shown for convenienceonly. They are not meart to imply temperaturerange. The slope [d(log o)/0(l/T), where Zis that equilibrium among Fe speciescontrols the conduc- in kelvins] decreaseswith decreasingtemperature for DK7 tivity!) Conductivity decreaseswith increasing/", [d(log but increaseswith decreasingtemperature in the caseof -'lrl o)/6(logf"r) = throughout this6, range.kast-squares MAL diopside. DK7 behaveslike other pyroxenes(Duba fitting parametersfor data in this rangeare given in Table et al., 1973;Huebner et al., 1979;Duba et a1.,1979) and HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE 1247 DK7(100)-2 DK?(010)-3 @ E f 6 o o_. -u J- o t-s t1@- -- 0t012 .LOG [to2, barl 81012 -LOG lto2, barl DK7(001F2 E ah g (, o{ o J o o 24601012141618 D B -Loc for, ba4 -LoG lfo2, bad Fig. 5. Electrical conductivity values for three orientations buffer assemblagesiron-wi.istite-vapor (IW) and fayalite-mag- of diopside DK7 (nearly end-member CaMgSi'Ou).Conductiv- netite-quartz-vapor(FMQ) indicate the rangewithin which most ities are measuredperpendicular to each plate and projected from igneous and metamorphic rocks will fall, but are not meant to temperatureonto the log o-log/o, plane at l-bar pressure.Solid imply that equilibrium among Fe speciescontrols the conduc- symbols representsome of the data (Table 3) usedin the regres- tivity. Results for first and second (010) plates (B) are similar, sions (Table 5); regresseddata are those with an entry in the but the third (010) plate (C) appearsto be lessconductive. This right-hand column ofTable 3. Vertical bar representsone stan- differencemay be due to differencesin the nature of the sample- dard error in log o for each data set. Projections ofthe oxygen- electrodecontact. 'C) olivines (Duba and Nichols, 1973;Cemic et al., 1980)in isobar at - ll20 suggeststhat reduction of the sample that the slope invariably decreasesat lower temperature, is not an explanation. if it changesat all. The behavior of the MAL diopside is The observed variation in density with fo, is pro- without precedent,yet these data atlo9.for: - 13.0 are nounced and systematic (Table 2). The density of oxi- reversible and otherwise internally consistent.The facts dized DK7 is 0.017 g/cm3(0.50/o) greater than reduced that the slope steepensand that the measuredimpedances DK7. Similarly, oxidized MAL is 0.027 g/cm3 (0.80/0) (beforeapplication of the geometricfactor) of MAt(100)-l greaterthan reducedMAL. The cell volumes, determined are lessthan those of the single-crystalalumina both sug- on splits of the chips used for the density measurements, gestthat an unanticipatedelectrical path around the sam- change by only marginally significant amounts, *0.10/o ple (leakage)is not an explanation for the strangebehav- and -0.2o/o,respectively. Thus, the unit-cell contents of ior of MAL. Further, the fact that the change in slope DK7 and MAL diopside must increasein massas furnace occursat anfo, value that is above that of the iron-wiistite /o, is increased.Finally, the thicknessesof the pyroxene -13 assemblage(the IW buffer intersects the log fo, : plates did not changeas a result of the temperature pro- t248 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE 1100 MAL(r00)-l ]l=--511ifi"oo"" c 1000 goo De5o O O -4.5 Bo Ee@ o E { o 850 D -s.o o o s J -6.0 o o J -5.5 r225.C lrlArrzs t t--..{_{F-to2s--a---e75 {5 900 610121416 -LOG fo2, barl 6.5 7.O 7.5 8.0 8.5 9.0 9.5 Fig. 6. Isothermsofelectrical conductivity measuredperpen- 104/T(K) dicular to (100) and (010) plates of MAL diopside and plotted as a function of oxygen fugacity. As in Fig. 5, solid symbols Frg. 7. Oxygen isobars of conductivity versus temperature. - representdata used to obtain the regressionsand the positions Squaresare measured values for MAL(100)-l atlogfor: 13.0 - of the iron-wtistite (IW) and quartz-fayalite-magnetite(QFM) (6, in bars);circles are values for DK7(010)-3at logf ,: 12.0. assemblagesare shown for convenience.At 1000-1225 .C, the Open symbols signify that temperaturewas decreasedbefore the conductivity of MAL diopside is greaterthan that of DK7 diop- measurementwas taken; closed symbols indicate that tempera- side and is alrnost independent of/o,, but at the lower temper- ture was increased.The straight-line relationship was drawn to atures,the behavior changes,suggesting a changein conduction passthrough the measurementsthat were bracketedwith respect mechanism. to direction of temperature change.Activation eneryies(Q, see text) are shown. The break in slope for DK7(010) can be ex- plained by the presenceof two mechanisms,the mechanismwith cess(Table 3). This admittedly imprecise determination Q : -2.12 eV being dominant at high temperature and the -1.27 of plate thickness,when combined with the constancyof mechanism with O : eY being dominant at low temper- cell dimensions (Table 2), suggeststhat the number of ature. The break in slope for MAL (100) cannot be explained by unit cells in a diopside plate was not changeddrastically the coexistanceof only two mechanisms,one of which is dom- by exposureto furnace conditions. inant at high temperature and the other dominant at low tem- perature. DrscussroN The conductivity rangesofhypothetical isotropic (ran- of augite (in planetary mantles) than it would be to use domly oriented) aggregatesof DK7 and MAL diopsides, the data for pure forsterite to model mantle olivine. The calculatedby averagingour results for the different crys- green MAL diopside is a much more appropriate model tallographic orientations, overlap the range for mantle for the conductivity of mantle augite. Its use as an ana- olivines (compositionFo,oo to For,) but are lessconduct- logue is simplified by the absence of a strong log /o, de- ing than orthopyroxenesand plagioclase(Fig. 8). By anal- pendence. ogy with end-memberFo,oo (Pluschkell and Engell,1968; The principal goal of this investigation is to identify Schockand Duba, 1985),which is less conductingthan point defects that might enhance electrical conductivity olivines Fonuand For, (Duba eI al., 1974; Schock and and other transport properties such as chemical diffusion. Duba, 1985),it is not surprisingthat DK7 diopside is This process of identification proceeds from relationships more insulating than Fe-rich pyroxenes.But it is surpris- between conductivity and composition and from mea- ing that the -t/t dependenceof log o on log/or-which is sured activation energies. The work of Stocker (1978a) observed in synthetic forsterite, Fo,oo,but not in either provides an excellent framework. He tabulated point-de- Fon,, (T. Parkin, 1972, cited,in Schock and Duba, I 985) fect reactions that might occur in enstatite, (Mg,Fe)rSiOu, or any previously measured pyroxene-is present in a and distinguished reactions that can occur in a closed natural diopside. Apparently the small amounts of Fe system, a system open only to Or, and a system allowed [Fe/(Mg + Fe) : 0.027] and perhapsAl and Na in DK7 to exchange all of its components with other phases. Our are not sufficient to modify its behavior from what we measurement technique is that of a system presumably presume to be the behavior pattern of pure end-member open only to Or. The nominal diopside bulk composition CaMgSirOu.Thus, it would be no more appropriate to differs from that of enstatite in having the M2 site filled usethe DK7 diopside to model the electricalconductivity largely with Ca, rather than Mg and Fe. Because Ca ions HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t249 "c -3 E tt 5-c o o J -5 -6 Fig. 8. Rangesofconductivity at I -bar total pressureofsingle- similar to olivine For,, with Fe/(Mg + Fe) : 0.095, distinctly crystalanalogues ofphases related to thosethat occur in the lower lessthan impure orthopyroxenesand plagioclase.Sources ofdata: crust and mantle at higher pressures.DK7 and MAL diopside DK7 and M-l clinopyroxenes, this study; Alp-8 orthopyroxene, conductivities are shown as enclosed regions bounded by the Duba et al. ( I 979); MF I -3 orthopyroxenes,Huebner et al. (1979); and oxygen isobars QFM (at low conductivity) and IW (high con- Pc plagioclase,Maury (1968); For', Foru,and Fo'ooolivines ductivity). Like pure forsterite, Fo,*, almost pure diopside DK7 forsterite, Duba et al. (1974). M-l is MAL elsewherein text. conductspoorly. The Fe-bearingdiopside, M- l, hasconductivity are large and cannot easily be oxidized, they are highly Sinceeach oxygen interstitial causesthe formation of two unlikely to form paired vacanciesand interstitials (the Ca holes, Frenkel reaction). Becauseour measurement system is th'l : 2loil closedto all componentsbut Or, Ca cannot exchangewith external phases.We concludethat Ca will be lessa defect- K(u",): [h']216'1+ former than the Mg and Fe it replacesin the enstatite and model. Thus the enstatite defect structure is a suitable model for that of diopside, and Stocker's analysis pro- [h.] c ffi,),/6. vides a suitable framework for interpreting our measure- ments of initially stoichiometric or nearly stoichiometric According to this reaction, the defect concentration in- crystals. creaseswith oxygen fugacity, an effect that is opposite to The electricalconductivity ofa speciesi is proportional the relationship that we observed. In addition, some to its concentration c and its mechanicalmobility B, (see workers regard oxygen interstitials as being too large to (see Rickert, 1982,p. 84-86): be accommodatedin the pyroxene structure Stocker, 1978a).In olivine, oxygen interstitials and electron holes o,: c,BVzeF probably are energeticallyunfavorable defects (Stocker, where z, e, afid F are valence, charge,and Faraday con- l 978b). stant. (Mechanical mobility is related to electrical mobil- Reaction 2 results in the formation of Si vacancies: ity p through the expression trr,: zeB,.) To understand + 2v'{i" + 605 + lzh' (2) the conduction mechanism in diopside DK7, we must 3Or:2Y'fr" (c') identify a reaction in which the concentration of a K rfor)' : lv'in"l'Iv'J,"1'z[od]6[h' ]''?' charge-carryingspecies varies according to c, o (fo)', whereN : -l/(7 + l) (seeTable 5) and all other aspects Since the concentration ofoxygen on oxygen lattice sites = of the bulk composition remain constant. We consider is close to the standard-stateconcentration, [O6]u t. four reactions. Using the defect-speciesnotation of Kr6- Further, each Mg and Si vacancy create two and four ger(1974, p. 14),Reaction I involves the incorporation holes, respectively,leading to the expression of oxygen to form oxygen interstitials (I) and to leave : electron holes ft) in the valenceband: K,u;)' [h.],[h.],[h']', o:-:20( + 4h' (l) and K,(.f",): [o/]'[h'].. lh'l * Uo)'''u. t250 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE This expression also predicts an /o, dependenceof the relation is linear over an interval of severallogf, units conductivity that is opposite to that observed. We con- suggeststhat a single reaction, or a combination ofreac- sider Si vacancies[V("] to be energeticallyunfavorable in tions whose proportionate contribution to conduction is the pyroxene structure, which is based on tightly bound constant over the range ofinterest, is operative. (Had the SiOounits. Stockerand Smyth (1978) reacheda similar observed/o, dependencebeen causedby a combination conclusion when considering possibledefects in olivine. of two or morefr-dependent mechanismswith different Reaction 3 involves cation interstitials: ranges,one would have expecteda break in slope with a narrow transition range betweentwo different/or-depen- 2M9il"+2sid+605 dent regimes,a highly coincidental situation not revealed :30, + 2Mg;'+ 2Si;"' + 12e' (3) by the data.) Additional considerationsled us to favor Reaction 4, K, : (",)'lMg;'1,[Si;"'],[e']',. by which oxygenvacancies are formed, as the mechanism Since Mg and Si interstitials create 2 and 4 electrons, that is responsiblefor the observed dependenceof log o respectively, on lo9,6r. Most important is the observation that the mass of a diopside unit cell increaseswith increasingf, tz K, : (.f"r)'Ie'lr[s']z[s'] (and vice versa), whereas the number of diopside unit and cells remains constant.The changein massindicates that oxygen moves into (or out of) diopside in responseto q c, le'l: Ki(fo,)-"'u' changesin fo* in accord with either Reactions 3 or 4. But Reaction 3 requiresthat four interstitial cationsbe formed This oxygen-fugacitydependence is slightly larger than for each six oxygen atoms that leave the diopside plate, that measuredfor DK7(100)-2 and significantlylarger than correspondingto the destruction ofa unit cell. Thus, the found for all other DK plates (Table 5). Continuing the constancyof the number of unit cells is incompatible with analogywith olivine (Stockerand Smyth, 1978), Mg and Reaction 3. Less compelling considerationsare that Re- Si interstitials have lower defect energies,and are thus action 4 is likely to operate in olivine (seediscussion by more likely to form, than the oxygen interstitials and Si Smyth and Stocker, 1978, p. 188) and is simpler than vacanciesofthe first two reactions. Reaction3. Reaction 4 involves oxygen vacancies,which are esti- The fact that a defect-forming reaction can explain the mated to have intermediate formation energiesin olivine observed log o-logfo, relationship does not prove that (Stocker,1978b): the corresponding defects are the dominant defects in diopside DK7, but the fact that the conductivity increases 4O5 :20, + 4V5 + 8e' (4) by almost an order of magnitude with change in fi does indicate that the defect reaction is principally responsible Ko : (f",),N5la[e']E/[Oj ]a. for the observed conductivity, at least at low for. The As before, if the oxygen-vacancyconcentration is small, charge carriers are not positively identified by these re- the activity of oxygen ions on normally occupied oxygen actions, but if the mobilities are independent off, the lattice sites is close to unity, and chargecarrier concentration must vary inversely with log The possiblecarriers are electrons,cation interstitials, KoUo)-": [V6.][e,],. .for. or oxygen vacancies.An argument in favor of small mo- To preserve charge neutrality, each vacancy createstwo bile chargecarriers (electrons)is the observation that the electrons: conductivity is relatively isotropic. An argument against is le'l:2[v;] cations the observation that conductivity does not de- creasewith frequency, as would be expected if cations so that accumulatedat the interface with the blocking electrodes. The relatively high conductivity of MAL diopside, the K o(fo)-" : (le'lle' 12)/ 2 lack of a strong dependenceof conductivity on f' and le'l: IeQ[o)-ve the smaller activation energy clearly indicate that the and conductivity is controlled by a mechanism that is differ- o : lK(f",)-'/618,*eF. ent from the mechanism responsiblefor the behavior of DK7. The fact that the slight/", dependenceis uniform over a range of 5 logf, units again suggeststhat a single This/", dependenceis close to the observeddependence fr-dependent mechanismcontrols the/o, dependenceover for DK7 diopside. Thus, the observed changesin con- this entire range.As in the caseof DK7 diopside, two or ductivity with f, are better accountedfor by the simple more mechanisms could operate if their proportionate formation or destruction of oxygen vacancies(Reaction contribution remained constant, but this would again be 4) than by the elimination of diopside unit cells, leaving a highly coincidental situation. The enhancedconductiv- cation interstitials in the residual diopside and forming ity of MAL diopside is probably associatedwith the sub- oxygen vapor (Reaction 3). The fact that the log o-logfo, stitution of Fe for Mg. One possible reaction that does HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE t25r not depend upon /o, (and is not likely to have a limited rangewith respectto/"r) is the thermal ionization of Fe2* 1200=C lrt - to form Fe3*plus electronsin the conduction band: Fq! ':F!4ii;; Feilr: Fei,rs+ e' The activation energy (1.04 eV, Table 5) derived from v_ I our measurementsof MAL diopside is relatively small (5 o and consistentwith this suggestion. J -4.5 The fact that MAL diopside is more conducting than tl E DK7 does not signify that a reaction to form oxygen va- o not operate in MAL diopside, but it does canciesdoes 9. -5.0 indicate that the electronsassociated with oxygenvacan- 0 o cies are no longer the dominant defectsfor electrical con- J duction. It is likely that the concentration ofoxygen va- cancies in MAL still varies with /o, but is obscured by much greater concentrations of another defect. Indeed, the smallestlo, dependenceanticipated by Stocker(1978a) is d(log o)/0(logf",) : - 0.07 I , a much larger dependence than the value we observedfor MAL diopside. Thus we suggestthat the conductivity of MAL diopside can be 8101214 -LOG[to2, barl explained by a combination of two mechanisms.The ef- fect can be shown in a simplified diagram of defect-con- Fig.9. Simplifieddiagram showing selected relationships be- centration isotherms in log q - logfo, space(Fig. 9). The tweenconductivity and/o, ofdiopside. Conductivity is theprod- (K) incorporatesmo- contribution due to conduction by the /o,-independent uct of concentrationand a constant that (1000 lines defect is much greater than the contribution due to oxy- bility (seetext). Light solid(1200'C) and dashed "C) (lowertwo lines)and the gen vacancies.The total charge-carrierconcentration, the representcomponents of conductivity sums (uppermostline) of the components.The observedcon- sum of the two contributions,has a slightly negativeslope, ductivity of MAL diopsidewith Fe/(Mg+ Fe) : 0.127canbP- By measuringadditional diop- similar to that observed. brokeninto two components:the/or-dependent conductivity ob- sides with different Fe/(Mg + Fe) values but otherwise servedfor diopsideDK7 [Fe/(Mg+ Fe) : 0.0271and an f",- similar chemistries, it should be possible to confirm the independentcomponent. Point-defect reactions that might de- suggestionthat ionization ofFe2t is the sourceofthe en- termineeach component of conductivity are suggested. hanced conductivity. Ideally, activation energy refers to a process that is thermally activated. We calculated/or-independentacti- 'C vation energiesthat range from 2.01 to 2.20 eY (and av- DK7 at f > 1000 and compare this result with cal- erage2.12 eD in the DK diopside. (We calculated the culated activation energiesof 1.4 eV along the fayalite- gas energy at constant fo, rather than along art for-T path magnetite-quartzbuffer and of 1.3 eV at a CO/CO' defined by an oxygen buffer, as might be done if there mixed in the proportions 10/90. Detailed measurements were evidence that the defect-forming reaction were de- revealed a transition at 1000 "C and a smaller activation pendent upon an Fe2+-Fe3+equilibrium with a positive energy (1.3 eV, Fig. 7) at lower temperatures' Because value of d(log o)/d(logfo,), or along a path defined by a DK7 diopside is such a poor conductor at these lower constant gas-mixingratio.) However, we suspectthat this temperatures,we were not able to invetigate whether or energy does not solely reflect a thermally activated pro- not this activation energy is also associatedwith the strong cess. The temperature dependenceof the equilibrium ,fo, dependenceof conductivity that is observedat higher constant K in the oxygen-defect-forming reaction will temperatures. causethe bulk composition (stoichiometry) of the diop- The activation energy for MAL diopside at f > 1050 side to slightly vary with temperature,yet we know nei- 'C is 1.0 eV, distinctly lessthan that of the more magne- ther the diopside composition nor the activities of the sian DK7 diopside. In veiw of the different conduction speciesin the equilibrium. Thus the activation energy mechanisms,we had anticipated a different activation en- calculated from our measurementsmay have two com- ergy. The increasein activation energy to 2.4 eV in the ponents: a major component due to pure thermal acti- temperaturerange 1050 to 800 "c (and perhapseven low- vation and a minor apparentcomponent due to the slight er temperatures)is disturbing becausethis increasecan- changein bulk composition as oxygenpasses between the not be simply explainedby two mechanisms,one of which sample and furnace atmosphere.Comparison of our re- is dominant at high temperature, the other dominant at sult with other reported activation eneryiesmay be am- low temperature.The obvious explanation is a structural biguous, especially if the thermally activated processes transition, but we are not awarethat diopside-hedenberg- are dependenton for. To illustrate this ambiguity, we re- ite has any transition in this temperature range.The na- port an /o,-independent activation energy of 2.1 eV for ture of the transition in MAL diopside remains unknown. 1252 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE The diopside plates respondedsystematically and rap- 1978;Smyth, 1980;Gasparik, 1984), we commonlyas- idly to changesin the furnace/or.Ifthe transportofoxy- sume that at low pressure,pyroxenes have cation : anion gen through the diopside is by chemical diffusion across ratios exactly equal to 4:6. Our results suggestthat this the surfacesofthe plates,and ifthe changein conductiv- assumption is incorrect. If the observedchange in density ity is linearly proportional to the changein oxygen con- with/o, is due solely to changein oxygen content, which tent of the diopside, the changein conductivity with time appearsto be likely, the measureddensity changes of 0.50/o (Fig. a) is a measureof the transport progressvariable. It and 0.9olocorrespond to gain or loss of I . l0loand 2.0o/oof is possible to calculate a rate constant for this process, the oxygenatoms present,or 0.13 and 0.24 charges,re- using Figure4.6 ofCrank (1975),and ifthat rate rs con- spectively, per six-oxygen formula unit. Changesof this trolled by bulk diffusion (rather than some processat the magnitude will invalidate Fe2*/Fe3*ratios calculated as- interface),the rate constant is a diffusion coefficient.This suming perfect four-cation to six-oxygen stoichiometry. method does not require knowledgeof the absolute con- For instance, a change of +0.20 chargeswill affect the centration of the diffusing species.The rates calculated calculatedvalence of 50o/oof the Fe atoms of a pyroxene from curves 5 and 7 ofFigure 4b are surprisingly fast: 9 of nominal compositionCao rMg rFeo4SirO6! 8 x l0 cm2/sat1000 "C and 3 x l0 ? cm2lsat 1200"C. The DK7 diopside equilibrated rapidly and reversibly The curves are not linear when plotted as o and t-%, sug- with respect to changesin the /o, of the furnace atmo- gesting that the rates are not controlled solely by ditru- sphere.Because Reactions 3 and 4 each require the pas- sion. Thus the actual diffusion rates would be somewhat sageofoxygen or oxygen vacanciesthrough pyroxene, it fasterthan the ratescalculated from the equationofCrank appearsthat migration ofoxygen or oxygen vacanciesin (1975).These rates seem unreasonably fast. For compar- DK7 diopside is a relatively rapid process,observable on ison, the oxygen self-diffusion rate in synthetic forsterite, a time scale of hours. If the migration path is by bulk Fo,oo,ranges from l0-t6 cm2/sat 1200'C to l0-t8 cm2ls diffusion, it contrastswith the much slowerbulk diffusion (extrapolated)at 1000"C (Jaoulet al., 1983).For natural of Ca, Mg, Fe, Sr, and Sm cations in diopside (Huebner olivine, Forn,oxygen self-diffusion is faster than in Fo,oo and Voigt, 1984; Sneeringeret a1., 1984)and calls into by a factor of 100 to 1000 (Houlier et al., 1985).The questionthe common assumptionthat the oxygenions direct measurementsof the oxygen self-diffusion rates in or SiOo groups form a rigid and immobile framework. olivine are so much slower than our indirectly deter- Conversely, some oxygen migration might occur along mined rates in diopside that we conclude that our rates dislocations. Nevertheless,our proposed oxygen vacan- are not oxygen-diffusioncoefficients. cies provide a possiblechemical diffusion mechanism for Ifthe oxygen vacanciesare assumedto be the charge- pyroxenes. The large Ca cation is a principal diffusing carrying species,it is possibleto calculatea diffusion coef- speciesduring exsolution in pyroxenes,yet without large ficientfrom the conductivity vacancies,it is difficult to imagine Ca diffusion through the pyroxene lattice. The proposed vacancies D,: oRT/c,z2F2 oxygen would form a possiblemigration path for Ca, Mg, and Fe (Tuller, 1985,Eq. 4) using representativevalues ofcon- cations. Finally, our results provide some insight for ductivity u0-5 S/m or s3.A2l(m3.kg)1,temperature (1373 choosing values of experimental parameters when at- K), concentration(5.4 x 103mol/m3), and valence(2) tempting to measurediffusion rates. Surprisingly, use of and expressingthe gasand Faradayconstants in baseunits relatively low/o, values may enhancecation diffusion in [8.314m').kg/(s,.K.mol) and 96485A.s/mol, respecrive- Fe-bearing pyroxenes. We did not observe the positive lyl. The resultingvalue of D is 2.3 x l0-r' cm2ls,larger dependenceofelectrical conductivity on oxygen fugacity than the oxygendiffusion rate in olivine and, surprisingly, that would occur if Fefi, was oxidized to Fe;,{sthrough a larger than the Ca-(Mg,Fe) diffusion rate in pyroxenes processthat changedthe bulk composition, and we would (Huebnerand Voigt, 1984).Ifour oxygen-vacancycon- not expect this reaction to causethe large vacanciesthat centration is overestimated,the calculateddiffusion coef- Mg, Fe, and particularly Ca ions must require for diffu- ficient would be even larger. Thus, the relatively large sion. Instead, diffusion may best be promoted by the rel- calculateddiffusion coefficientleads us to suspectthat the atively reducing conditions that produce oxygen vacan- initial assumption is incorrect and to suggestthat elec- cies. To hasten slow-diffusion reactions, experimental trons, not oxygen vacancies, are the charge-carrying studiesof diffusion should be attempted atlow forvalues, specres. even in Fe-bearingsystems. These results have important implications for under- Our resultsare surprisingly complicated but are rncom- standing crystal chemistry and chemical diffusion in py- plete and indicate directions for future research.The be- roxenes. One might have anticipated that the SiOo unit havior of MAL diopside, with a small activation energy rn pyroxene would be so tightly bonded that oxygen va- at high temperatureand a larger activation energyat low cancies would be energetically unfavorable defects and temperature, indicates the presenceof a reversible tran- that changesin the oxygen content would be exceedingly sition that will introducea new mechanismat 1050"C. slow becauseof slow diffusion rates. Further, although High-temperature (900-1200 "C) unit-cell and calorimet- there is convincing evidence for cation vacanciesin cli- ric measurementsmight reveal the presenceof a transi- nopyroxenes at high pressures(Wood and Henderson, tion in MAL and other diopsides.Extrapolation of trends HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE r253 observed at high temperature is necessaryif our results Busing,W.R., and Levy, H.A (1962)ORGLS: A generalleast squares National lab- are to be used as models of behavior in the metamorphic program. U.S Atomic EnergyCommission, Oak Ridge oratory, ORNL-TM-27 l, 39 pages.[An updated version is reproduced temperaturerange, yet we have no confidencethat these in Baes,C F., Jr., and Mesmer, R.E (1976) The hydrolysis of cations, extrapolations are justified. In particular, we cannot be p.443458. Wiley, New York l confident that the,6, dependenceof conductivity, and Cemic, L., Will, G., and Hinze, E (1980) Electrical conductivity mea- thus the oxygen-vacancymodel ofdiffusion, is appropri- surementson olivines MgrSiOaFerSiOounder definedthermodynamic Physicsand Chemistry of Minerals, 6,95-lO7 ' ate at T < 1000 'C. One wonders whether or not other conditions. Crank, J ( I 975) The mathematicsof diffusion. ClarendonPress, Oxford. silicateswill have as many conductivity regimesas does Deines, Peter, Nafriger, R.H., Ljlmer, G.C., and Woerman, Eugene.(1974) diopside. We know very little about the absoluteconcen- Temperature-oxygenfugacity tables for selectedgas mixtures in the trations of any point defects in silicates and how these system C-H-O at one atmospheretotal pressure.Pennsylvania State Experiment Sta- concentrationschange in responseto/or. Were their con- Universiry Bulletin ofthe Earth and Mineral Sciences tion,88, 129p. centrations to be determined, thermogravimetrically and Duba, A., and Nicholls, I.A. (1973) The influence of oxidation state on as a function of time, one could extract diffusion rates the electricalconductivity of olivine. Earth and PlanetaryScience Let- (from the rate of changein mass)and mobilities of charge ters, 18, 59-64. carriers from the data. Duba, A., Boland, J.N., and Ringwood, A.E. (1973) The electrical con- pyroxene. of Geology, I l, 727 -7 34. Our results will provide a basis for validating the use ductivity of Journal Duba, A., Heard, H.C., and Schock,R.N. (1974) Electrical conductivity of aggregatesto determine bulk or single-crystalproper- ofolivine at high pressureunder controlled oxygenfugacity. Journal of ties. Unlike the limited selectionof composition provid- GeophysicalResearch, 7 9, 1667-167 3 ed by natural samples,synthetic aggregatesmake it pos- - ,1976\ Electricalconductivity oforthopyroxene to 1400'C and the sible to vary a single cation ratio (useful in identifying resulting selenotherm.Proceedings of the 7th Lunar ScienceConfer- ence,3l73-3181. defectmechanisms), to definethe activity or activity ratio Duba, A., Dennison, M., Irving, A.J., Thomber, C.R., and Huebner, J'S. of components by means of additional phasesthat are ( I 979) Electricalconductivity of aluminous orthopFoxene' Lunar and dispersedto promote rapid achievement of equilibrium, PlanetaryScience X, p. 3 I 8-3 I 9. Lunar and PlanetaryInstitute, Hous- and to study the grain-boundary component ofconduc- ton. Texas. H.H. (1973) On the anisotropic electrical tion. The biggestuncertainty in the use of pyroxene ag- Dvorak, 2., and Schloessin, conductivity of enstatite as a function of pressureand temperature. gregateshas concerned possible conduction along grain Geophysics,38,25-36 boundaries.By comparing measurementsmade on aggre- Gasparik, Tibor. (1984) Experimentalstudy ofsubsolidus phaserelations gatesof DK diopside under different conditions with the and mixing propertiesof pyroxenein the systemCaO-AlrOr-SiOr. Geo- -2545' "isotropic" conductivity obtained by averagingthe con- chimica et CosmochimicaActa, 48, 2537 Hinze, E., Will, W., and Cemic, L. (1981) Electrical conductivity mea- ductivity in three orientations of DK7 (Table 5), it should surementson synthetic olivines and on olivine, enstatiteand diopside be possible to distinguish the components of bulk and from Dreiser Weiher, Eifel (Germany) under defined thermodynamic grain-boundaryconduction and to test the hypothesisthat activities as a function of temperature and pressure.Physics of the "isotropic" bulk conductivity measurementscan be ob- Earth and PlanetaryInteriors, 25,245-254. B, O., and Lieberman, R.C. (1985) Oxygen and silicon tained from aggregates. Houlier, Jaoul, self-diffusion in natural olivine: First dat^ ^t T: 1300'C. EOS, 66, AcxNowr-tlcMENTS Huebner, J.S. (1975) Oxygen fugacity values of furnace gas mixtures. American Mineralogist, 60, 8 I 5-823 people Through generouscooperation, numerous made contributions -(1987) Use of gasmixtures at low pressureto speciS oxygen and to this study. Vandall King of Ward's GeoscienceEstablishment arranged other fugacitiesof furnace atmospheres.In Ulmer, G.C and Barnes, for the collection of the diopsidecrystals from De Kalb, New York. Daniel H L., Eds., Hydrothermal experimental techniques,p. 20-60. Wiley, Appleman of the Mineral SciencesDepartment, U.S. National Museum New York. of Natural History, agreedin principle to acquire largequantities of crys- Huebner, J.S., and Papike, J.J. (1970) Synthesisand crystal chemistry of tals that could be shared by the mineralogical and geophysicalresearch sodium-potassium richterite, (Na,K)NaCaMg'SLOz(OH'Dr: A model community and, in the caseof the De Kalb crystals,did so. Al Duba of for amphiboles American Mineralogist, 55, 1973-1992. the LawrenceLivermore Laboratory kindled the first author's interest in Huebner, J.S., and Voigt, D.E. (1984) Chemical difusion in Ca-Mg-Fe electrical conductivity. Rosemary Ifuight of Stanford University first drew pyroxenes:Measured rates ofcation exchangeand interfacemovement. his attention to impedance spectroscopytechniques, and Ian Raistrick, GeologicalSociety of America Abstracts with Programs, 16, 546. also of Stanford, provided early advice about the necessaryequipment. M.E. (1985) Chernical compositions and Brian Seegmilerof the Coors PorcelainCompany made it possiblefor us Huebner, J. S., and Woodruff, microprobe standards available in the Reston to acquire the insulating Vistal rods used to support the sample cell in critical evaluation of GeologicalSurvey Open File Report 85-718. the furnace. F. L. Harmon of the USGS manufactured the complicated microprobe facility. U.S furnace fittings. Randall Cygan of the University of Illinois acted as a Huebner, J.S.,Duba, A., and Wiegins, L.B (1979) Electricalconductivity measurements sounding board for our interpretations of the spectralsignatures; Cygan, of pyroxene which contains triYalent ions: Laboratory profile. of Geophysical Research, Gordon L. Nord, Jr., ofthe U.S. GeologicalSurvey, Robrt N. Schockand and the lunar temperature Journal Al Duba of the lawrence Livermore Laboratory, and an anonymous re- 84,46524656. viewer for the journal all reviewed the manuscript and provided helpful Jaoul, Olivier, Houlier, Bernard, and Abel, Francois.(1983) Study of'8O suggestrons. diffusion in magnesiumorthosilicate by nuclearmicroanalysis. Journal of GeophysicalResearch, 88, 613424. Kushiro, Ikuo. (1972) Determination of liquidus relations in synthetic RrrnnnNcps crrED silicate systems with electron probe analysis: The system forsterite- Bence,A.E., and Albee, A.L. (1968) Empirical conection factors for the diopside-silicaat I atmosphere.American Mineralogist,57, 1260-127l. electron microanalysisof silicatesand oxides. Joumal of Geology, 76 Krdger, F.A. (1974) Chemistry of imperfect crystals,vol. 2' North Hol- 382403. land, Amsterdam. t254 HUEBNER AND VOIGT: ELECTRICAL CONDUCTIVITY OF DIOPSIDE Maury, R. (1968) Conductibilit6 6lecrriquedes tectosilicatesI. M6thode partial pressure: Comparison of observed and predicted behavior. et resultatsexperimentaux. Bulletin de la Soci6t6Frangaise Min6ralogie Physicsofthe Earth and PlanetaryInteriors, 17, P34-P40. et Cristallographie,9 l 267-27 8. -(1978b) Point defectformation parametersin olivine Physicsof Parkhomenko,E.L (1982)Electrical resistivity ofminerals and rocks at the Earth and PlanetaryInteriors, 17, 108-117. high temperature and pressure. Reviews of Geophysics and Space Stocker, R.L., and Smyth, D.M. (1978) Effect of ensratite activity and Physics,20,193-218. oxygenpartial pressureon the point-defect chemistry ofolivine. Phys- Pluschkell,W., and Engell,H.J. (1968)Ionen- Und Elekrronenleitungim ics ofthe Earth and PlanetaryInteriors, 16, 145-156. Magnesiumorthosilikat.Berichte der Deutschen KeramischenGesell- Tuller, H L (1985) Electrical conducion in ceramics:Toward improved schaft.45. 388-394. defect interpretation. American Geophysical Union Geophysical Rickert Hans. (1982) Electrochemistryof solids. Springer-Verlag,New Monograph3l,p 47-68 York. Voigt, R , Seifert, K F-, and Will, G. (1979) Die elektrischeIritfahigkeit Schock,R.N, Ed. (1985)Point defectsin minerals.American Geophys- von Pyroxenen der Reihe MgSiO.-FeSiO. bei l0 und 20 kbar unter ical Union GeophysicalMonograph 3l definiertenthermodynamiscben Bedingungen. Neues Jahrbuch fiir Mi- Schock,R N., and Duba, A.G. (1985)Point defeclsand rhe mechanisms neralogieMonatshefte, 29 6-308. of conduction in olivine. American Geophysical Union Geophysical Will, G., Cemic, L., Hinze, E., Seifert, K.-F., and Voigt, R. (1979) Elec- Monograph31,88-96. trical conductivity measurementson olivines and pyroxenesunder de- Smyth, J R. (1980) Cation vacanciesand crystal chemistry ofbreakdown lined thermodynamic activities as a function of temperatureand pres- reactionsin kimberlitic omphacites American Mineralogist,65, I185- sure.Physics and ChemistryofMinerals, 4,189-197. I 19l Wood B J., and Henderson,C M.B. (1978)Compositions and unit cell Smyth, D.M., and Stocker,R.L. (1978) Point defectsand non-stoichi- parametersof synthetic non-stoichiometric tschermakitic clinopyrox- ometry in forsterite. Physicsofthe Earth and Planetary Interiors, 10, ene American Mineralogist, 63, 66-72 t83-192. Sneeringer,Mark, Hart, S.R.,and Shimizu,Nobumichi. (1984) Strontium and samariumdiffitsion in diopside.Geochimica et CosmochimicaActa, 48,1589-1608. MnNuscnrrr RECEIvEDNowMssn 20, l98l Stocker, R.L (1978a)Variation ofconductivity in enstatitewith oxygen MeNuscnrm AccEPTEDJur-v 12. 1988