American Mineralogist, Volume 82, pages 245-258, 1997

Single-crystalcompression and crystalstructure of clinopyroxeneup to 10 GPa

Lr Znanc, HlNs Ansnlns, Srnr,q.NrS. HarNnn, lNn Ar-r Kurocr,u

Scientific Center of Materials Sciencesand Institute of Mineralogy, University of Marburg, 35032 Marburg, Germany

Ansrnacr The hydrostatic compressionof synthetic single crystals of diopside, CaMgSirOu,and hedenbergite,CaFeSi,Ou, was studied at 33 pressuresup to 10 GPa by X-ray diffraction. In addition, intensity data for hedenbergitewere collected at 12 pressuresup to l0 GPa. For determination of the elasticity two crystals were loaded together in a diamond cell. The axial compressibilitiesB", Br, and B.of diopsideand hedenbergiteare 2.36(4),3.17(4), and2.50(4)x 10 3 GPa 1,and 1.93(5),3.38(6),and2.42(8) x 10-3GPa-r, respectively. The bulk moduli (K..) and their pressurederivatives (Ki) were determinedsimultaneously from a weighted linear fit of a third order Birch-Murnaghan equation of stateto the volume data at elevatedpressures. K.n and Kl," are 104.1(9) GPa and 6.2(3) for diopside and 117(1) GPa and 4.3(4) tor hedenbergite,respectively. The unit-cell parametersdecrease continuously with pressure.The larger polyhedra show more compression than the smaller ones. Between 0.1 MPa and 10 GPa the polyhedral volumes of CaO*,FeOu, and SiO" decreaseby 8.4, 6.6, and 2.9Vo,rcspectively. The longest bonds of CaO. and FeOu show most compression. Significant compression in the two shortest Si-Ol and Si-O2 bond lengths of the SiO, tetrahedrawas observed at relatively low pressures,resulting in a tetrahedral volume compressionof 1.6Vobetween 0.1 GPa and 4 GPa and I.3Vo between 4 and 10 GPa. The compression of the unit cell can be described by the volume compression of the individual CaO* and FeOu polyhedra, with the SiOotetrahedron playing a minor role. Diopside is more compressiblethan hedenbergite as shown by their axial and volume compressibilities because the FeOu octahedron is significantly more rigid than MgOo at high pressures.This observation implies that octa- hedrally coordinated Fe'z*behaves differently from Mg at high pressures,in conffast to their behavior at ambient conditions.

fNrnonucrroN fraction at high pressures (Levien and Prewitt 1981; et al' 1995)' Because those experiments were Ca-rich clinopyroxenesare regardedas major minerals 9oTo9i. of the mantle models and they have been thl subject of limited to.pressuresup to about 5 GPa' it is necessaryto pressures, several recent studies (Levien et al. l9l9; Levien and measure da-taat higher considering the rela- prewitt lggl; Kandelin and weidner lggg; zhang et al. tively small compressibility and relatively high structural 1989; Zhang and Hafner 1992; Comodi et al. 199i;. For freedom of clinopyroxene. Extended extrapolation of example, significant amounts of Ca-rich clinopyroxenes elasticity data, measured at relatively low pressures,to properties pressures yield are accountedfor in both the pyrolite GingwooA 1SZS1 at high in this case may large and piclogite (Anderson and Biss 1984) models, with a errors (Zeug et al. 1993). volume fraction ranging from about l0-407o in the upper Another interesting question is how cations such as mantle. One way td cJnstrain these models tightly is to Fe2* and Mg influence the elasticity of Ca-rich clinopy- compare seismic velocities directly with sound veiocities roxenes at high pressures.Although such information is measured on mantle minerals in the laboratory under highly desirable in mantle modeling as well as for un- mantle pressures(Zhang and Chopelas 1994). To accom- derstanding the structure and dynamics of the Eafth's plish this, data are needed for precise determination of mantle, it is not yet available, mainly for the following equationsof state at high pressures. reasons: (1) difficulties in precise measurementof unit- Ca-rich clinopyroxenes have monoclinic symmetry cell parameters,(2) comparatively small compressibilities (spacegroup C2/c). Becatse of their low symmetry, it is associatedwith comparatively large errors in the pressure not easy to obtain precise crystal structure data using determination (> 0.5Voup to l0 GPa), and (3) complex high-pressuretechniques on polycrystalline samples be- substitution of cations in natural samples.To circumvent cause of coincidence of equilvalent reflections and acci- theseproblems in the presentstudy, high-pressuresingle- dental overlap of nonequivalent reflections. Data now crystal diffraction techniqueswere used to obtain precise available were obtained mainly from single crystal dif- unit-cell data. Synthetic end-member crystals of the bi- 0003-004x/97l0304-0245$05.00 245 246 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE nary system Ca(Mg,Fe)Si,Ouwith well-defined cation oc- ed simultaneouslyin the same cell together with a ruby cupancieswere loaded together in one diamond cell as- chip for pressurecalibration. A 4:1 mixture of methanol sembly to compare distinct compressions between to ethanol was used as the hydrostatic pressure-transmit- individual crystals without superpositionof the additional ting medium. Pressure was measured before and after error associated with independent pressure determina- each X-ray diffraction experiment using the pressure-in- tions. In this paper, we present single-crystal compress- duced shift of the Rl fluorescenceline of ruby at hydro- ibility results for synthetic diopside,CaMgSi,Ou, and hed- static pressure(Munro et al. 1985). The error of the pres- enbergite, CaFeSirOu,up to l0 GPa. We also present sure measurementwas estimatedto be 0.05 GPa. Typical crystal structure data of hedenbergiteup to 10 GPa. The halfwidths of reflections from hedenbergiteas well as di- equations of state of these minerals as well as the com- opside were about 0.2" in o. The measurementswere pression mechanisms of the crystal structures will be completed with two consecutive mounts. For the first described. mount a broadening of the hedenbergitereflections from Zhang and Hafner (1992) reported changes in the Fe2* 0.2" to about 0.4' at 10 GPa was observed, while the electronic state of Ca-rich clinopyroxenes shown by .tFe reflections of diopside remained unbroadened,i.e., they ^yresonance experiments at high pressures.It is interest- remained the same as at ambient pressure.This suggests ing to study the pressuredependence of these statesand possible squeezing of the crystal between the two dia- compare it with that of the Fe2* polyhedral geomeffy, mond anvils. This broadening disappearedby releasing which determinesthe Fe-O bonding. Furthermore,Zhang pressureto about 1 GPa.This implies that the crystal was and Hafner (1992) interpreteda discontinuity in 57Fehy- not crushed, consistent with optical observations under perfine parametersof hedenbergiteat 4 GPa as a phase polarized ffansmitted light. This slight squeezinghas little transition. The data on Fe-O bond lengths at high pres- effect on the unit-cell parametersof hedenbergitemea- sures will allow correlated studies such as theoretical ab sured at 10 GPa as demonsffatedin Figure 1. The unit- initio calculation to describein detail the changesof Fe2* cell parametersof each crystal were measuredat 33 pres- electronic stlucture at high pressures, which are con- sures on increasing as well as decreasingpressure. strainedby experimental data (Zhang and Hafner 1992). Diffraction measurementswere performed with a Stoe automatedfour circle diffractometer using MoKct radia- ExpnnrNrnNrAt, DETATLS tion (0.7107 A) monochromatedby a giaphite crystal. Samples The diffractometer was operated at 55 kV and 35 mA. Single crystals of hedenbergite,CaFeSirOu, were syn- The unit-cell parameterswere determined from up to 2l thesizedin a belt apparatusat about 1150'C and 4 GPa reflections with 20 ranging from 13" to 39'. Each reflec- with an experimenttime of 5.5 h. The crystals were trans- tion was centered in eight positions (King and Finger parent and yellowish- to brownish-green in color. Their 1919) to reduce zero and crystal-centering errors. The chemical compositions were confirmed by electron mi- unit-cell parameterswere calculated using the procedure croprobe analysis. Fe3* in the samples could not be de- of Ralph and Finger (1982). There was not any significant tected in 57FeMrissbauer spectra. Single crystals of di- deviation between the unit-cell parametersconstrained or opside, CaMgSirOu, were grown with the Czochralski not consffainedto monoclinic symmeffy in all the refine- method at about 1400 'C. The crystals were colorless. ments. The results presentedin this paper are constrained For the measurementof the unit-cell parametersa hed- values. enbergitecrystal with dimensionsof about 80 x 64 x 48 Intensity measurement at high pressure. For inten- pm and a diopside crystal of about 96 x 50 x 25 pm sity measurementson hedenbergiteat high pressures,the were used. For X-ray diffraction intensity measurements same technique was employed as for unit-cell parameter on hedenbergite,two polished crystals with dimensions measurements.A hemisphereof integrated intensities in of about 80 x 128 x 50 pm and 130 x 130 x 50 pm reciprocal space6" < 20 < 60" at l1 different pressures were used. up to 10 GPa was collected below the limiting value of (sin 0)/f : 0.7560 A ', whereasthe integratedintensities High-pressureX-ray diffraction technique at 4.2 GPa were collected below (sin 0)/\ : 0.9044 A ' Unit-cell parameters at high pressure. A modified in reciprocal space6'< 20 < 80". The to-scanwidth was Merrill-Bassett four-screw diamond anvil cell was used. 1.2' with a step size of 0.02". The diameter of the diamond culet was 600 pm. A gasket A specially designedcollimator placed on the diffract- was machined from Thyrodur 2709 steeland preindented ed beam side of the diamond cell was used to reduce the to about 80 pm with a 330 pm hole. After preindention background produced mainly by the beryllium backing and sample hole drilling, the gasket was hardenedin an plates of the diamond cell (Ahsbahs 1987). A reduction inert atmosphereor immersed in iron powder in a closed of the background up to a factor of 4 could be achieved vessel at 500'C without changing its surface character- in this way. For measuringthe absorptionthat results pri- istics and dimensions thereafter. This material allowed marily from the diamond anvils and the beryllium plates, significantly larger sample thickness and larger sample a collimator with a diameter of 0.15 mm was used. The hole at high pressuresthan the routinely used Inconel diameter of this beam was similar to that of the beamsin alloys. The hedenbergiteand diopside crystals were load- the intensity collection procedure defined by the size of ZHANG ET AL.: COMPRESSIONOF CLINOPYROXENE 247

Frcunn 1. Unircell parametersof diopside and hedenbergite o CaFeSi206 at 33 pressures.The standard deviations are generally smaller CalvlgSi2O6 than data symbols. <-

430

-tr the crystal. For absorption measurementthis small-sized 420 ^Alal E incident beam was adjusted to the center of the diamond a ^^ 410 ^ culets of an empty cell without a gasket. The absorption A curve, which dependson the tilting angle of the cell, was Y.Y expressedanalytically for the correction of the measured u*. intensity. measuredintensity of a reflection "E===* a(A) It is known that the .:eu varies becauseof simultaneousreflection of the dia- a^ - tl^^r^ ==E%3= monds (Lovedayet al. 1990).For our hedenbergitecrys- tal the variation was as much as 25Vo.The width of the ^t\ =o was about 1.5". It was not easy to detect heden- * = dips bergite reflections,the intensity of which is weakened ^ela^A by simultaneousreflection of the diamonds.Because of AAet the low crystal symmetry and the pressure cell geome- try, most of the reflectionscan be measuredonly twice. We therefore adopted a procedure that helps to detect () ER reflections weakened by simultaneous reflection: In a +t 9.0 o B routine high pressure intensity measurement,the fixed- tr g mode is usually used. For a reflection with its reflec- 0v -96o, (t' tion position at 1 : 199" or 1 : a rotation around (U $ is a rotation around the reflection vector (r! scan) and o- 88 this should not change the reflection intensity (Rennin- ^4r B ger effect ignored). If we make a seriesof intensity mea- -al B O 8.7 E surements on a reflection at different rotating angles (,f /l. around the reflection vector in a distance of more than I A 1.5' (typical width of a dip), it is possibleto distinguish c o.o the intensitiesweakened by simultaneousreflections and f approach statistically the real intensity. This, however, 524 will not work for reflectionswith positionsfleilr x : Qo or x : 1800.To circumventthis problem and to measure c(A) all accessiblereflections at different rJiangles, we adopt- 2.ZU ed the following procedure: First, the reflections in re- -135" A*- ciprocalspace between *45' < X < +135" and 6Sr -45' < X < were measured at five different fixed-S E E angleswith stepsof 1.8". This resultedin four stepsof tr - 512 tra 1.8'for reflectionswith x 90'and of 1.3" for those with x - 45'. Subsequently,the pressurecell was man- ually rotated relative to its fixing mount by 90" around 106.0 the axis of the x circle and the other half of the reflec- tions were measuredin the same way. This worked rea- 1055 sonably well for detecting affected intensities, especially attt thoseof strongreflections. By using the sameweighting 1050 scheme, l/o2,, in the least squares refinement, the weighted R values were reduced significantly compared 104.5 E- 6E- L]fu to the measurementswithout using the above procedure ruoE EE (Table 1). The detectionof damagedintensities for re- 104.0 E@- " EE flections with relatively weak intensities remained, how- ever, difficult even by using this procedure.This is dem- 1035 0123456 onstrated by the deteriorated goodness-of-fit values for measurements,in which the above procedure was ap- P (GPa) plied. This can be attributed to the different data quality 248 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

Taele 1. Intensitymeasurement parameters for hedenbergiteat variouspressures

Weights Retlections 1/ol 1/(oi + cP). P After Usedfor (GPa) & R, Total averagrng refinement />3o 0.0 181 302 2.O7 3.20 294 1 13 840 377 334 275 't 1.1 78 3.29 z tc 3.20 317 1.12 913 422 372 288 2.1 213 400 2.41 4.33 383 123 916 418 370 297 2.8 176 317 2.68 295 306 171 1356 410 373 309 3.6 213 357 2.49 3.66 343 1.29 906 404 364 301 193 387 252 3.44 370 128 912 349 408 324 4.6 2.06 3.43 2.62 3.21 333 1.22 918 354 318 258 5 3-', 1.33 330 3.26 2.73 290 106 4444 349 324 269 o.J 133 J tc 318 297 2.89 1 15 4275 346 313 261 7.6* 134 3.06 327 2.74 108 4177 347 322 269 I 7.. 135 247 2.98 253 104 4187 343 311 265 9 9.. 1.38 265 332 2.51 230 100 4138 342 319 268 - Refinedby SHELXTo .. Intensitydata collectedusing the procedureof measuringevery reflectionat different'.1, angles

of strong and weak reflections. Further work is needed the program package CRYMIS (Kutoglu 1995). The ob- to circumvent this problem. served integratedintensities were calculatedaccording to All data for the hedenbergitewere collected with the Lehmann and Larsen (1974), and were corrected for ab- crystal in the diamond cell. For data collection from 0- sorption by the diamonds and beryllium backing plates. 4.6 GPa the constant-precisionmode was used with a The intensitiesof the symmetrically equivalentreflections maximum counting time per step of 8 s for llo, > 20 (0, were averagedin Laue group Zlm, yielding between 311 1.0,and 2.1 GPa) andI/o, > 40 (2.8,3.6, 4.2, 4.4, arrd and 408 reflectionsfor the data setsat different pressures. 4.6 GPa). Above 5.3 GPa the procedure of rotating In the data sets above 5.3 GPa. reflections.the intensities around the reflection vector was used for data collections of which deviated more than 35o, from their averaged with counting times of I s per step. No significant drift values, were excluded in the averaging procedure. The could be detectedby monitoring the intensity of standard intensities were conected for Lorenz and polarization ef- reflections every 2 h. Profiles of several reflections were fects. No correction for absorptionby the crystal was ap- scannedat each pressureto confirm hydrostatic pressure plied to the intensities. Neutral atomic scatteringfactors and crystal perfection. Further experimentswere stopped of the International Tablesfor X-ray Crystallography (Ib- becauseraising the pressureto I 1.4 GPa causeda signif- ers and Hamilton 1974) were used in the structurerefine- icant broadening of reflections that suggesteda nonhy- ments. The initial atomic position parameterswere ob- drostatic pressure. tained from Cameron et al. (1973\. The refined For data reduction and structural refinementswe used parametersincluded a linear scaling factor, an isoffopic

Tnele 2. Positionaland isotropicdisplacement parameters of hedenbergiteat high pressures

P (GPa) ll 2.1 28 4.2

v 0 29953(19) 0 30040(19) 0 3011 8(24) 0 3011 4(1 8) 0.30210(1 9) 0.30236(11) tr 0 68(3) 0 68(2) 0 66(3) 0 5s(2) 0 56(3) 0 55(2) Fe v o.9o720(14) 0 90764(13) 0 90829(16) 0.90831(1 3) 0.90860(14) 0.90902(8) B o 44(2) o.47(21 o 44(2) o 45(2) 0.45(2) 0 40(2) si X o 287 84\14) o.28782(13) 0 28800(17) o 28797(14) 0.28768(15) o 28771(2) v 0 092495(1 8) 0 0930s(17) 0 09319(22) 0 09355(17) 0.09394(18) o 09362(10) z 0 23270(15) 0.23216(1 8) 0 23188(2) 0 23180(17) 0.23127(20] 0 2311 6(1 9) B o 44(2) o 43(2) 0 43(3) 0 43(2) 0.41(2',) o 42(2) o1 x 0 11965(37) 0 11951(35) 0 12013(45) 0 12006(36) 0.11 987(41 ) 0 12010(54) v 0 089 95(44) 0 09068(44) 0 09058(53) 0 09073(45) 0.09107(44) 0 0911 2(25) z 0.152 06(s1) o 15267(47) 0.15349(61 ) 0 15283(45) 0.1s330(53) 0.15252(48) B 0 56(s) 0.57(5) 0 58(6) 0 65(4) 0.6e(5) 0 65(4) x 0 362 90(36) 0 36247(35) o 36220(44) o 36200(37) 0.36200(41) o 36106(4e) v 0 245 96(4s) o 24747(44) o 2479't(54) o 24830(44) 0.24843(51) o 24851(28) z 0 32346(50) 0 32409(51) 0 32470(65) o 32479(49) 0.32509(58) 0 32682(48) B 0 81(6) 0.88(6) 0 88(7) 0.84(6) 0.e1(6) 0 70(5) x o 35022(37) 0.35052(36) 0 35093(44) 0 35139(37) 0.35217(42) 0 35240(52) v 0 01994(40) 0.02100(42) 0 0211 4(51 ) 0 02186(39) 0.02278(44) o 02332(26) z 0 99292(53) 0 99087(52) 0 98950(66) 0.98851(49) 0.98826(58) 0.98737(sl) B 0 66(5) 0 70(5) o 63(6) 0 55(5) 0.60(5) 0 68(4) . Equivalentisotropic displacement parameter (A,) ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE 249 secondary extinction factor, and positional and isotropic Taele 4. Unit-cellparameters of diopsidebetween 0.1 MPa displacementparameters for each atom. The structurefac- and 10 GPa tors, F, were weighted according to ll(ol + cF2), where P o/ was calculated from counting statistics and c was re- (GPa) a (A) b (A) c(A) Bf) v (4.) fined from SHELX76. The reflections that obviously 0.0 e.74s(2\ 8.922(1) 5 2480(8) 106 04(1) 438 82(11 ) overlappedwith diamond reflections were rejected in the 0.36 e.736(2) 8.e0s(1) 52420(9) 10596(1) 437 22(11\ refinements. The refinement conditions and the refined 038 e.7330(6) 8 e07(1) 52402(5\ 105 961(5) 436.82(6) 073 e.71s(2) 8 892(1) s 2360(4) 105.902(9) 435 20(10) parametersare included in Tables I and 2. The observed 0.81 e.7200(e) 8 8e20(8) 52370(4) 105 910(7) 435 37(6) and calculated structure factors are listed in Table 3.' 1 19 e.70e0(7) I 882(1) 52271(6\ 10s 833(6) 43370(7) t.cu 97042(4) 8 8749(8) 5.2242(4) 1O5771(4) 432 99(5) tcJ e.704(2) 8 873(1) 52240(9\ 105 80(1) 432 88(11) Rnsur-rs 1.78 I 6907(8) 8 8s6(1) 5.2158(7) 105.739(7) 430 85(8) Our presentstudy includes data on the unit-cell param- 215 e 6s1(2) 8.852(2) 5.215(1) 105.73(2) 430.70(12) 238 s.6758(s) 8 841(1) s.2o87(7) 105.667(7) 429.07(8) eters of diopside and hedenbergiteat pressuresup to l0 275 I 6688(e) 8 833(2) 52042(7) 105.630(7) 428.06(8) GPa as well as data on the crystal structure of heden- 295 e 6638(9) 8.824\1) 5.2013(6) 105.s97(6) 427.23(71 bergite at 12 pressuresbetween 0.1 MPa and l0 GPa. J tc 9.6586(7) 8 82(1) 5.1e88(6) 105.573(6) 426.65(6) 3.33 e 659(2) 8.817(21 5.198(1) 10558(2) 426.54(13) Unit-cell parametersof diopside up to 5.3 GPa and of e 651(2) 8.808(2) 5.194(1) 105.54(2) 425.44(121 hedenbergiteup to 5.0 GPa were reported by Levien and 3.88 I 640(1) 8.799(2) 5 1889(8) 105 501(8) 424.18(el (1981) (1989), 4.44 e.628(1) e.784(2) 5.1814(8) 105.446(8) 42244(91 Prewitt andZhanget al. respectively.Lev- 4.83 9.620(1) 8.775(2) 5 1767(9) 105416(9) 42130(10) ien and Prewitt (1981) also determined the crystal struc- 3.4U 9.60s9(6) 8.756(1) 5 1681(5) 105353(5) 419.20(6) ture of diopside at pressuresup to 5.3 GPa, whereaspre- 5.74 e.5e6(4) 8,754(4) 5 166(2) 10525(3) 41872(25) 595 e.5e4(4) I 748(3) 5.165(2) 105.24(3) 418 33(22) vious sffucture determinations of hedenbergite at high 600 s.5947(e) 8 74s(1) 5.1623(7) 105314(8) 41777(81 pressuresare not known to us. 604 9.592(2) 8748(2) 5 162(1) 1O527(2) 417.95(14) 645 e.586(2) 8732(1) 5 1580(e) 10s.26(1) 41665(10) Axial compressibilitiesof diopside and hedenbergite 6.47 s 588(2) 8732(1) 5.1570(9) 10526(1) 41665(10) 695 s.s76(2) 8718(21 5 151(1 ) 10s.22(2) 415.03(11) Unit-cell parametersof diopside and hedenbergitede- 708 s 577(2) 8714(21 5.150(1) 105.21(2) 414.84(13) 763 e 562(2) 86e7(2\ 5.143(1) 105.17(2) 41287(11) tetmined at 33 pressuresbetween 0.1MPa to 10 GPa are 835 e 551(2) 8 682(1) 5.1359(9) 105.14(1) 411.13(10) presentedin Tables4 and 5 and Figure 1. The data mea- 875 s 543(2) 8 669(1) 5.130(1) 105.0s(1) 409.79(10) sured in the diamond cell at ambient conditions are com- 934 e 529(2) 8 65s(1) 5.1240(9) 105.06(1) 408.15(10) 997 I s20(1) 8 640(1) 5.1180(7) 105.03(1) 406.62(8) parable with data published previously by Cameron et al. (1973). At high pressuresthe parametersdecrease contin- Note: Standarddeviations in the last decimaldigit are given in paren- theses uously with increasing pressure.No discontinuity could be detected within the experimental error. Our diopside

1A copy of Table 3 may be orderedas DocumentAM-97-634 from the BusinessOff ice, MineralogicalSociety of America,101 5 Eighteenth Street, NW, Suite 601, Washington, DC 20036, U.S.A.Please remit $5.00 in advancefor the microfiche.

Taate 2-Continued

P (GPa) CJ LO 4.7

v 0 s0279(14) 0 30307(11 ) 0 30336(12) 0.30423(11) 0.30447(10) o 30506(10) g 0 53(2) 0 s0(2) 0 55(2) 0 50(2) 0.52(21 0.53(2) Fe v 0 9091 8(1 0) 0 e0937(8) o sog72(8) 0 90987(7) 0.91001(7) o 91031 (7) B 0.38(2) 0 39(2) 0 41(2) 0 39(2) 0.41\2) o 42(1) X o 28780(24) o 28772(20) o 287 56(21) o 28779(20) 0.28793(19) o 28757(17) v 0.09364(1 2) 0.09392(10) 0.094256(11) 0 09454(10) 0.09474(9) 0 09506(9) z o.23offi(22) 0.23071(1 8) 0.23086(21) o 23074(19) 0.23087(18) 0.23088(17) E o.42(2) o.37(21 0.44(2) 0 38(2) 0.3e(2) 0.3s(2) x 0.120 64(59) 0.12070(51 ) 0.119 43(51) 0 11919(50) o 12003(47) 0 11951(43) v 0 09106(30) 0.09143(24) 0.09205(25) o 09226(23) 0.09248(23) 0.09289(21) z 0 15289(53) 0.1s1 40(47) 0 15201 (52) 0.15276(471 o 15227(45) 0.15248(42) B 0 se(s) 0.64(4) 0 58(5) 0.63(4) 0 62(4) 0 61(4) X 0.36107(56) 0 36140(s1) 0 36140(49) 0.36074(47) 0 3s991(45) 0.35991(40) v 0.24928(36) 0 2500s(28) 0 2s068(30) 0.25155(271 o.2s2o3(27) o 25266(24) z 0 32680(57) 0 32681(52) 0.32834(53) 0.32893(47) 0 32914(48) 0.33002(43) B 0.72(61 0 71(4) 0 82(5) 0 78(5) o 77(4) o 74(4) x 0 3s193(61 ) 0 35300(52) o 35246(54) 0 35303(50) 0 3s338(47) 0 35335(44) v 0 02338(31 ) o 02373(24) 0.02412\26) 0 02516\24) o.02592(241 o.o2s93(22) z 0 9871 6(60) 0 98570(50) 0.e8553(s9) 0 98s11 (53) 0.98464(51) o.98444(48) B 0.6s(5) 0.59(4) 0 67(5) 0 63(4) 0.63(4) 0 62(4) 250 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

Taele 5. Unit-cellparameters of hedenbergitebetween 0.1 MPaand 10 GPa I Thisstudy

lO Zhanget al 1989 P ta (GPa) a (A) b(A) c(A) tso v (41 tbt 0 0 e 8389(8) 9.0214(7) 5 2424(7) 104.797(8) 449.90(7) 0 0 e 838(2) s.o22(2) 5 241(2\ 104.76(2\ 449.88(15) a^ i- 0.36 I 831(1) e.014(1) 5237(1\ 10469(1) 44e.o1(12\ I 0 38 98277(8\ 9.0074(7) 5 2352(71 1O4717(8\ 448.23(71 *'r 073 I 8193(7) 8 9955(7) 52297(71 104 650(7) 446 92(6) . 1.19 I 8086(7) 8 9832(7) 52233(71 1O4579(7\ 44542(61 1 50 9797(1) 89742(8) 52201(7\ 104 53(1) 444.31(8\ 094 1 53 I 802(1) 8 97s(1) 5 219(1) 10450(1) 44459(9) 1.78 I 7910(9) 8.9590(8) 52120(81 104481(9) 44268(81 CaFeSi^O^ 215 I 789(1) 8955(1) s211(1) 1O442(1) 44248(9) zb 238 9.7793(9) 8 e413(8) 5 203s(8) 104400(9) 44073(8\ 092 275 97722(9\ 8 9307(8) 5 1989(8) 104354(9) 439 56(8) 100 A 295 9 7684(9) 89240(8) 5 1963(8) 104332(9) 43888(7) I r Thisstudy 3.1s 9.7639(9) 8 9185(8) 5 1943(8) 10431 1(9) 43828(8) , o toa Levien,Prewitt 1981 3.33 9762(1) 8 e18(1) 5 1s3(1) 1o427(1) 43828(e) a McCormicket al 1989 3.65 I 756(1) 8 907(1) 5 18s(1) 1O424(1) 437 16(10) 098 r.$ lo 3.88 I 7498(9) 8 8e81(8) 5 183s(8) 104 220(9) 435 es(8) ...A

4.44 I7378(9) 8 8806(8) 5 1767(8) 104 166(9) 434.06(7) I 4 83 I 731(1) 8 870(1) 5172(1) 10414(1) 43301(s) t^ s 30 9.722(1) 8.858(1) 5 167(1) 10407(1) 4316e(e) 096 a6 5 40 I 7194(8) 8 8s18(7) 5,1642(7) 104069(8) 43O97(7) t'i 574 I 716(1) 8 847(1) 5 1620(9) 10403(1) 43054(9) 5 95 9715(21 8 843(1) 5 161(1) 104.02(2) 43O24(13) 6 00 I 709(1) 8.8358(8) 5.1572(8) 104.01(1) 42s.26(8) 094 6 04 I 710(1) 8.840(1) 5 1se(1) 104 01(1) 42e74(e\ CaMgSirO. 6 4s 9 704(1) 8 827(1) 5 1s3(1) 103.98(1) 42844(9) 6 47 I 704(2\ 8.825(2) 5.153(2) 103.e7(2) 428.35(1s) 6 95 e 6s2(1) 8.8110(s) 5 147(1\ 103.e2(1) 42670(9\ 7 08 9 693(1) 8.809(1) s 146(1) 103.e3(1) 426.52(s\ 7 63 I 680(1) e.78s(1) 5 138(1) 103.87(1) 424.49(10\ P (GPa) 8 35 I 672(21 8.774(2) 5 132(2\ 103 83(2) 42290(121 875 I 663(1) 8 7580(9) s 1250(9) 103.80(1) 421.31(8) Frcunr 2. Pressuredependence of the unitcell volumesfor I 34 9 653(1) 8.742(1) 5 119(1) 10376(1) 419.64(10) I 97- I 649(3) 8717(3) 5 116(3) 103 76(3) 418.02(27\ diopsideand hedenbergite

Note. Standarddeviations in the last decimaldigit are given in paren- theses . Slighlsqueezing observed. a significant deviation from the present single-crystal data. This appearsto result from nonhydrostaticpressure applied to the polycrystalline sample in the previous data between0.1 MPa and 5.3 GPa agreewith those of study. Levien and Prewitt (1981) as shown in Figure 2. They The technique of loading several crystals together in deviate, however, from the data of McCormick et al. the samediamond cell assembly(Hazen 1993) allows de- (1989).McCormick et al. (1989) attributedthis deviation tection of very small differences of compressionamong to error in the pressuredetermination. The presentsingle- crystals. This is especially useful for mantle minerals crystal hedenbergitedata agreewell with those measured with comparably small compressibilities. Our data ob- on a polycrystalline sample between 0.1 MPa and 3.7 tained by this technique show that both diopside and hed- GPa (Zhang et al. 1989). The data at 4.4 and 5.0 GPa enbergiteexhibit anisoffopic compression.The axial com- obtained from the polycrystalline sample,however, show pressibilities,9", 9,, and p., are 2.36(4), 3.17(4), and

Teale 6. Bulk moduli(K,") and their pressurederivatives (K") of diopsideand hedenbergite

Sample K," (GPa) K'r" P,",- (GPa) Method Reference

Diopside,SC"" 112 0 Brillouin Aleksandrovand Rythova(1961) Diopside,SC 113 0 Brillouin Levienet al (1979) Diopside,SC 11 4(41 4 5(18) 5.3 X-ray Levienand Preweitt(1981) Diopside,SC 122(21 401 6.0 X-ray McCormicket al (1989) Diopside,SC 1041(9) 6 2(3) 10 X-ray This study Diopside 105 6.2 5 Simulation Matsuiand Busing(1984) Hedenbergite,SC 120 0 Brillouin Kandelinand Weidner(1988) Hedenbergite,PC 119(2) 4.01 X-ray zhang er al (1989) Hedenbergite,SC 117(11 4.3(4) 10 X-ray This study Note:Standard deviations in the last decimaldigit are given in parentheses " P.* : maximumpressure ." SC : singlecrystal; PC - polycrystallinesample I K,.tixed at 4 ZHANG ET AL.: COMPRESSIONOF CLINOPYROXENE 251

z.t3

o Ca-O(1Al,1B1) 2.70 r I t Ca-O(2C2 -- Ca-O(3Ct,3D1) z-oa l" rr -- r I r Ca-O(3C2'3D2) *:r 2.60 E 120 TfIfr

f o) I I (U o o- 2.50 o 100 LL o 2.45 o) TD =ou a 2.40 o o b- 1so z.Jc c - * o *t+s* N Z -JU * + ,- *

- tou

L 01234567E910 z P (GPa) 140 FrcunB 4. Pressuredependence of Ca-O interatomicdistances in the CaO, polyhedra

I z to I r Fe-O(1,A1,181) T I o Fe-O(1A2,182) T- o Fe-A(2C1,2D1) 2.14 T -- +; iUIT- -91 ' iIr rT 0 000 0 005 0 010 0 015 0 025 T +A o) _ad -f -# EulerianStrain f o 2.10 l_L J it Frcuru 3. Eulerianstrain (/) versusthe Birch normalized E t- stress(F). Solid linesare the weightedlinear regressions to F-f rI o "nn datapoints m T t --.l+- T -l --'f 3 ' 206 r 2.50(4) x l0 GPa for diopside,and 1.93(5),3.38(6), T- and 2.42(8) x l0 3 GPa ' for hedenbergite.The b axis is I? the most compressibledirection. The compressionsalong 204 TI the three crystallographic axes in both minerals follow T the same trend. The difference in the compressionof the 01234567E910 a axis between diopside and hedenbergite,however, is (GPa) abottt 20Vo. P FIcunn 5. Pressuredependence of Fe-O interatomicdistances Equations of state of diopside and hedenbergite in the FeOuoctahedra The isothermal bulk moduli K, at zero pressure,Kz", and their first pressurederivatives K'r,,may be derived by Tnele 7. Reussand Voigt averagesof diopsideand a third-order Birch-Murnaghan equation of state (Birch hedenbergite 1978) expressedin terms of the Eulerian strain, f, and Average CaMgSi,O6- CaMgSi,Ou"" CaFeSi,Out the Birch normalized pressure,F, Fleuss(GPa) 108(1 ) 105(4) 116.1 o : K,oll + t.sf(K;"- 4)l (l) Voigt (GPa) 117(-. 118(4) 1239 Notej Standard deviations in the last decimal digit are given in where parentheses . Datatrom Levienand Prewilt(1979) f:l(vtv")"-rltz (2) -- Datafrom Aleksandrovet al. (1964) t Datafrom Kandelinand Weidner(1988). and 252 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

Teele 8. Selectedbond lengths(A) and angles('), polyhedralvolume (43), and distorlionparameters for the polyhedrain hedenbergiteat high pressures

P(GPa) 000 11 2.1 2.8 36 42 CaO! polyhedron Ca-O(1A1,81)x2 2 3518(36) 2 3403(35) 2.3407(43) 2 3342\35) 2.32e3(38) 2.3308(36) Ca-O(2C2,D2)x 2 2 3329(36) 2.3315(35) 2 3284(441 2 3270(35) 2.3239(40) 23192(35) Ca-O(3C1,D1)x 2 2 6316(35) 2.6270(351 2.6176(43) 2 6181 (34) 2.6086(38) 2.6092(36) Ca-O(3C2,D2)x 2 2 7199(3s) 2 68e3(3s) 2.6676(43) 2 6510(34) 2.6266(38) 2 6149(36) Volume 26.02(5) 2s.71(51 25.46(5) 25 29(5) 25.00(5) 24.92\6) FeO6octahedron Fe-O(1A1,81)x 2 2 1619(35) 2 1524(34) 2 1421(42) 2.1385(34) 2 1299(s8) 2 1278(361 Fe-O(142,82)x 2 2.1348(35) 2.1333(34) 2 1355(42) 2.1303(34) 2 1283(38) 2.1244\36) Fe-O(2C1,D1)x 2 2 0e48(35) 2 0737(35) 2 0712(43) 2.06s4(35) 2 0606(40) 2 0698(35) Fe-Fe 3 1089(10) 3 0e26(10) 3 0767(12) 3 0701(1 0) 3 0584(10) 3 0514(6) o(1A1)-O(181) 2757(5) 2781(5) 2.778(4) 2.773(4) 2 759(5) 2764(5) o(2c1)-o(2D1) 2.s87(5) 2.s88(5) 2 987(6) 2 985(5) 2 978(5) 3 001(5) o(1A1)-O(2C1)x2 3 10s(5) 2 926(s) 3.066(6) 3 061(5) 3 053(s) 3 053(5) o(1A1)-O(1A2)x 2 3.082(5) 3 077(4) 3 071(6) 3 061(5) 3.055(5) 3.0s3(5) o(1A2)-O(2C1)x2 2.e40(5) 2 s26(5) 2.920(6) 2 910(5) 2 e03(5) 2.e06(5) o(1A2)-O(2D1)x2 3.052(5) 3.038(5) 3 038(6) 3 037(5) 3 024(5) 3 014(5) o(1A1)-O(182)x 2 2.966(5) 2.967(s) 2.e72(6) 2 e66(5) 2 963(5) 2 962(5) O(1A1)-Fe-O(1 B1 ) 80 6(1) 80 5(1) 80.8(2) 80.9(1) 80 7(1) 810(1) O(1A1)-Fe-O(lA2)x 2 e1 6(1) el 8(1) e1.6(2) 91.6(1) 91 7(1) e1 8(1) O(1A1)-Fe-O(2C1)x 2 e4.1(1 ) 93 8(1) e3 6(2) 93.5(1) e3.5(1) e3.2(1) O(1A1)-Fe-O(l82)x 2 87.3(1) 87.6(1) 88.0(2) 88.0(1) 88 2(1) 88 3(1) O(1A2)-Fe-O(2C1)x 2 88.3(1) 88 1(1) 87.9(2) 87 8(1) 87.7{1) 87.7(1) O(1A2)-Fe-O(2D1)x 2 s2.6(1) e2.4(11 e2.5(2) 92 5(1) 92 4(1\ 92.3(1) O(2C1)-Fe-O(2D1) e1 5(1) e2.2(1) s2.3(2) 92 s(1) 92 5(2) 92.s(1) Volume 12 75\2) 12.62(2) 12.56(3) 12 48(2) 12 39\2) 12.41(31 (\) 1.0045(23) 1 0045(23) 1 0041(28) 1 OO42(27) 1.0042(20) 1 0040(14) 02 1487 1468 1353 1359 13.71 13.24 SiOntetrahedron sio(1c1) 1 5992(37) 1 5978(36) 1 5902(45) 1.5889(1 6) 1 58s3(39) 1 5819(38) sio(2c1) 1.5839(37) 1 5846(36) 1 5818(45) 1.5780(36) 1 5733(41) 1 5733(37) si-o(3c1) 1.6661(36) 1.6657(36) 1 6658(44) 1.6668(35) 1.6643(40) 1 6639(38) si-o(3c2) 1 6844(36) 1 6828(36) 1 6768(44) 1.6773(35) 1 6833(40) 1 6808(38) Si-Si 3 1060(19) 3 0993(18) 3 0909(23) 3 0878(18) 3 0826(20) 3.0765(20) o(1c1)-o(2cl) 27226(491 2 7176(48) 2.7076(59) 2 7O4O(48) 2 6991(s4) 2 689s(50) o(1c1)-o(sc1) 2.6830(48) 2 6843(471 2 6787(58) 2.677O(47) 2.6790\52) 2 6747(511 o(1c1)-o(3c2) 2.6e19(48) 2.6906(47) 2.6807(58) 2 6836(47) 2 6886(52) 2.6887(51) o(2c1)-o(3c1) 2.6575(48) 2 6591(48) 2.6602(59) 2 6564(47) 2 6456(54) 2 6503(50) o(2c1)-o(3c2) 2.5721(48) 2.5751(48) z.5b/u(59, 2 5671(47) 2.5653(54) 2 5620(50) o(3c1)-o(3c2) 2.6441(48) 2.6376(47) 2.6299(58) 2 6266(46) 2 6220(52) 2.6209(50) o(1c1)-si-o(2c1 ) 1176(2) 1173(2) 117.2(21 117.3(2) 117 4(2) 116 9(2) o(1c1)-si-o(3c1 ) 110.s(2) 1107(2) 11o.7(2) 110.6(2) 1110(2) 1110(2) o(1c1)-si-o(3c2) 110.1(2) 11O2(2\ 110.212) 110s(2) 1107(2) 111.0(2) o(2c1)-si-o(3c1) 109.7(2) 109.8(2) 1100(2) 109.9(2) 1096(2) 1099(2) o(2c1)-si-o(3c2) 103 8(2) 104O\2) 103.s(2) 104.1(2) 103.e(2) 103 8(2) o(3c1)-si-o(3c2) 104.2(21 103.9(2) 103.8(2) 1035(2) 1031 (2) 103.2(21 si-o3-si 135.s(2) 135.5(2) 135.2(3) 134 8(2) 134 1(2) 133.8(2) o3-o3-o3 1644(21 163.6(2) 163.5(2) 162 e(2) 1622(2) 161.8(2) Volume 2 218\7) 2 216(71 2 1eg(s) 2 196(7) 2.189(8) 2184(7) t^l 1 0061(23) 1 0059(22) 1 0060(28) 1 0061(29) 1.0062(26) 1 0062(30) o2 25 58 24.83 25 18 25 59 Zb UJ 25.44 Tiltingangle (')" 3 07(s) 2 88(9) 2.71(11) 2.55(10) 2.36(10) 2 08(10) ivote. Standard deviationsare given in parentheses. - Angle betweenbasal plane of a tetrahedronand the (100)plane

F : Pl[3f(r+ 2f)"1. (3) from 4. The data in Figure 3 demonstratea positive slope for diopside and a nearly zero slope for hedenbergite, In Equations l-3 P is the pressure,and V and Vo are the correspondingto values of K!," = 6.2(3) for diopside and molar volumes at high pressureand at ambient pressure, : respectively. K'r" 4.3(4) for hedenbergite.The K,o and Ki" values The K." and K^ values were determinedby a weighted obtained from this procedure are presentedin Table 6. linear least-squaresfit to the f and F terms of Equations Comparison of K,o determined in this study with the ad- l-3, using the unit-cell parametersof Tables4 and 5. As iabatic bulk modulus K, derived from Voigt-Reuss-Hill is clear from Equation I the intercept of this fit at P : 0 averagesby use of measurementsat ambient conditions is K,", whereas the slope indicates the deviation of Kn (Aleksandrov and Rythova 1961; Levien et al. 1979; ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE 253

Ttete FContinued

P(GPa) 4.6 53 76 87 9.9 CaOspolyhedron Ca-O(141,B1)x 2 2.3331(41) 2 3288(35) 2 3138(35) 2 3057(34) 2 3061(32) 2.2969(29) Ca-O(2C2,D2\x 2 2 s199(41) 2 3171 (36) 2 3oe8(36) 2 3077(33) 2 3078(32) 2.3025(29) Ca-O(3C1,D1)x 2 2 6060(421 2 5992(35) 2 5982(38) 2 5888(35) 2 5864(33) 2.5763(31) Ca-O(3C2,D2)x 2 2 6114(421 2.5896(35) 2.5835(38) 2 5577(35) 2 5442(33\ 2 5333(31) Volume 24.92\61 24.65(5) 24 45(5\ 24 16\5) 24.08(41 23 84(4) Fe060ctahedron Fe-O(1A1,B1)x2 2 1258(40) 2.1245(34\ 2 11 33(3s) 2.101 8(33) 2 1037(32) 2 0945(291 Fe-O(142,82\ x 2 2.1263(40) 2 11 69(34) 2 1132(35) 2 1112(33) 2.1O87(32) 2 1044(291 Fe-O(2C1,D1)x 2 2.0634(41) 2.0524\36) 2.0495(35) 2 0422(331 2.0426(32) 2 0365(29) Fe-Fe 3.0462(7) 3.0368(5) 3.0274(6) 3.0148(5) 3 0073(5) 2 es60(5) o(1A1)-O(181) 2770(6) 2773(5) 2.75e(5) 2.723(51 273e(5) 2721(4\ o(2c1)-o(2D1) 2 998(6) 2 98s(5) 3 009(5) 2 993(5) 3.006(5) 3.004(4) o(1A1)-o(2c1)x 2 3 036(6) 3.024(5) 3.018(5) 2 997(5) 2 987(5) 2.974(4) o(1A1)-O(1A2)x 2 3.04e(6) 3 044(5) 3 042(s) 3 03s(5) 3.030(5) 3.026(4) o(1A2)-O(2C1)x 2 2 899(6) 2 879(s) 2 888(5) 2 e74(5) 2 864(5) 2.858(4) o(1A2)-O(2D1)x 2 3 023(6) 3.010(5) 3 014(5) 2.982(5) 2 986(5) 2 972(4) o(1A1)-O(182)x 2 2 e67(6) 2 961(s) 2 964(5) 2 943(5) 2 e50(5) 2 s42(4) O(1A1)-Fe-O(181) 81.3(2) 81 5(1) 81 3(1) 80 7(1) 81.2(1) 81.0(1) O(141)-Fe-O(1A2)x 2 e1.6(2) 91.7(1) 91 7(1) e22(11 92.0(1) 92.2(1) O(1A1)-Fe-O(2C1)x 2 e2.s(21 92.7(1) e2.5(1) e2 6(1) 921(1) e2 1(1) O(1A1)-Fe-O(182)x 2 88.5(2) 88 6(1) 88 7(1) 88 6(1) 88.s(1) 88.9(1) O(1A2)-Fe-O(2C1)x 2 87 6(21 e7 3(1) 874(1) 87 5(1) 872(11 87.3(1) O(1A2)-Fe-O(2D1)x 2 92 4(2) s2 4(11 92 3(1) 918(1) 92 0(1) e1.7(1) O(2C1)-Fe-o(2D1) 93 2(2) e3.3(1) 93,9(1) 94.2(1) 94 8(1) 95.1(1 ) Volume 1237(3\ 1225(21 12 14(2) 12.02(2) 12o2(2) 11.s0(2) (\) 1 0037(14) 1.0037(1 4) 1.0040(14) 1 oo41(13) 1 0039(13) 1 0041(1 2) o2 1230 1319 1354 13.O2 1342 SiO4tetrahedron sio(1c1) 1 5769(43) 1 5734(371 1 5824(37) 1.5827(36) 1 s751(34) 1 5744(31) sio(2c1) 1 5768(43) 1 5781(38) 1 5795(38) 1 5751(35) 1 5701(34) 1.s698(31 ) si-o(3c1) 1 6582(45) 1 66s7(37) 1 6612(40) 1.6552(37) 1 6543(35) 1 6532(33) si-o(3c2) 1 6788(45) 1 67s9(37) 1 6752(40t 1.6766(37) 1 6768(35) 1 6741(33) Si.Si 3.0730(23) 3 0679(19) 3 0648(20) 3 0561(1 9) 3.0516(1 8) 3 0459(17) o(1c1)-o(2c1) 2 6868(s7) 2 6870(49) 2 6942\49) 2 6858(47) 2 6715(45) 2 6716(41\ o(1c1)-o(3c1) 2.6646(s8) 2.6676(49) 2 6722\51) 2 6708(481 2.6624(45) 2 6625(42) o(1c1)-o(3c2) 2.6790(58) 2.6846(49) 2 6886(51) 2 6893(48) 2.6843(45) 2 68s7(42) o(2c1)-o(3c1) 2.6512(58) 2.6528(50) 2 6539(51) 2 6469(48) 2.6426(451 2.6419(42) o(2c1)-o(3c2) 2.5648(58) 2.5631(50) 2 5637(51) 2 5647(481 2 5657(45) 2.5602(42\ o(3c1)-o(3c2) 2.6185(59) 2 6134(49) 2 6094(s3) 2 6037\49) 2.6014(46) 2.5947(43) o(1c1)-si-o(2c1) 116 9(2) 117O(2) 116 9(2) 1165(2) 116 3(2) 1164(2\ o(1c1)-si-o(3c1) 110 9(2) 110 e(2) 110 e(2) 11 1 .1(2) 1110(2) 1111(2) o(1c1)-si-o(3c2) 11O.7(2) 1114(2\ 1112(2\ 111.2(21 1114(2) 1115(2) o(2c1)-si-o(3c1) 1101(2) 109 7(2) 1099(2) 110.0(2) 1101(2) 1101(2) o(2c1)-si-o(3c2) 103.9(2) 103s(2) 103e(2) 1041 (2) 104.4(2) 104 2(2) o(3c1)-si-o(3c2) 103.4(2) 1029(2) 1O29(2) 1028(21 102.7\21 102 5(2) si-o3-si 134.1(3) 133.3(2) 133 4(2) 1331 (2) 132.7(2) 1325(2) 03-o3-o3 1618(2) 161.5(2) 161 2(2) 1605(2) 159 9(2) 161.5(1 ) Volume 2.175(8) 2.177\7) 2 182(8) 2 174(7) 2 161(7) 2 155(6) t\l 1 0061(34) 1.0065(30) 1.0064(30) 1 0063(29) 1 0061(27) 1 0064(25) o2 25 28 27 27 26 91 zf, v3 25.O1 26 33 Tiltingangle ('). 2 19(11) 2 01(10) 2,14(10) 1 84(10) 1 56(9) 1.57(8)

Kandelin and Weidner 1988) shows that our values are mogeneousstress, which should apply also to our exper- up to 8Vosmaller (Table 6). Considering imental conditions (Watt et al. 1976).Thus, our K,. values for both diopside and hedenbergiteare in agreementwith K, : + aryO (4) &(1 the Reuss averageswithin 2-3qo after appropriate con- where ct is the thermal expansioncoefficient, 1 the Grii- version using Equation 4 as shown in Table 7. Taking the neisen parameter,and Z the temperature,the difference anisotropic compression of the clinopyroxenes into ac- between K, and K. is about 2-3Vo for Ca-rich clinopy- count, it is not surprising that the difference between the roxenes. At 298 K the K," value of hedenbergiteagrees Reuss and Voigt averagesare indeed significant. From well with the Ks value obtained from Brillouin experi- this point of view the K.o and K\ values of diopside and ments. Strictly speaking,our Krnvalues should be directly hedenbergitedetermined in this study should be consid- comparableto K, derived by the Reussaverages because ered as more reliable than previously published data. It the latter values were obtained under conditions of ho- is remarkablethat our K.n and Ki" values for diopside are 254 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

| -bY (x100%) T-T- i! 1.68 I T- | -T-r al llT II 098 lf, T -t I o/ q) n T ddYa 096 !rl I t!r+ I E I ^ 1.66 -T- = 094 gdT- 6 092 c 1.65 090 (U '1 P r.oa L 00 o o I J ,^^ o I r.. Vr" rO l 'bJ -c 098 o:.f d r-r o 1.62 o 096 - l. 't U (L .. E 094 t.ol o \/lr-Mo N 092 1.60 6 I 100 t.3Y E L .o. T I o ?.o o 158 I -L z 098 ll I a1a 4 1'7 -f f 0 1 2 3 4 5 6 7 8 9 10 P (cPa) P (cPa) Froune6. Pressuredependence of Si-Ointeratomic distanc- FTGURE7. Comparisonof polyhedralcompression in diopside es in the SiOotetrahedra. and hedenbergiteup to 5.3 GPa.The MgOuoctahedra in diop- sideare about 1% more compressible than the FeOuoctahedra in hedenbergite.The CaO" polyhedra and SiOu tetrahedra exhibit practically identical with the values obtained from a the- about the same compressionin diopsideas well as in oretical calculation for simulated pressuresup to 5 GPa hedenbergite. (Matsui and Busing 1984).

Polyhedral compressionin hedenbergite respectto the shortestpolyhedral bond, the ratio l:1.8: The positional parametersof hedenbergiteat 12 pres- 1.6:5.3 is obtained in the sequencefor increasing bond sures are listed in Table 2. The interatomic distances length. Between 0.1 MPa and 5.3 GPa our data of hed- (bond lengths) and bond anglesas well as polyhedral vol- enbergite can be comparedwith those for diopside (Lev- umes are presentedin Table 8 and Figures 4, 5, and 6. ien and Prewitt 1981). The respectiveratios for that range The compressions among the bond lengths within the are 1:1.4:1.8:7.0and 1:0.6:0.6:3.2.In both suucturesthe three polyhedra, CaO' FeOu,and SiOo, show significant longest bond pair shows the highest compression,where- anisotropy. To describepolyhedral geometry the nomen- as the values for the second and third longest pairs are clature of Burnham et al. /196'7\is used with M : Fe for quite similar. However, the shortestbond pair in heden- Ml (point symmetry 2) and M : Ca for M2 (point sym- bergite is obviously compressedthe least; this is not the metry 2). case in diopside. Over this pressurerange CaO, in hed- CaO" polyhedron. There are four unique pairs of bond enbergite has a volume compression of 5.3Vo,which is lengths. Between 0.1 MPa and 10 GPa, the longest bond comparable to that of diopside: 57o. paiA Ca-O(3C2,3D2),exhibits the highest compressionof FeOu octahedron. The three bond pairs of the FeOu 6.9(2)Vo.The secondlongest bond pair, Ca-O(3C1,3D1), octahedrondisplay anisotropic compression.Between 0.1 with a value 2.1(2)Vo,however, is not that with the second MPa and l0 GPa,the longestbond pair, Fe-O(1A1,1B1), highest compression. The third longest bond pair, compressesby 3.1(3)7o, the second longest pair, Ca-O(1A1,181),reveals a somewhathigher compression Fe-O(1A2,1B2), by 1.4(3)Vo,and the shortestpair, value of 2.3(3)Vo.The shortest bonds, Ca-O(2C2,2D2), Fe-O(2Cl,2Dl),by 2.3(3)Vo.The volume compressionis are compressedthe least: 1.3(3)Eo.The volume compres- 6.6(3)7o.Comparing bond compressionin our hedenberg- sion is 8.4Vo.This highly anisotropic behavior results in ite and that in diopside between 0.1 MPa and 5.3 GPa, a crossover of the longest and the second longest bonds slightly smaller values are observed for all three bond at about 4.5 GPa, where the lengths of two bond pairs pairs in hedenbergite.The respective values are 1.7(3), apparentlybecome the same.At about 10 GPa, the short- 0.8(3), and 1.6(3)Voin the former and 2.1, 1.2 and 2.0Vo est and second shortest bond pairs merge together, be- in the latter. The respective volume compressions are coming indistinguishablein length within the experimen- 4.0(4)Vo and 5Vo (Fig. 7). Thus, the MgOu octahedronis tal error. more compressiblethan FeOu.As in CaO* a crossoverof If the relative compressions of the individual bond the longest and secondlongest bond pairs is observed at lengthsbetween 0.1 MPa and 10 GPa are normalized with about 4.5 GPa. At pressureshigher than 4.5 GPa, the ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE 255

Fe-O(1A1,1B1) pair is significantly shorter than the Drscussrou Fe-O(|A2, lB2) pair (Fig. 5). Compressionmechanism SiOn tetrahedron. Significant anisotropiccompression between0.1 MPa and 10 GPa was also found in SiOo The anisotropic unit-cell compression of Ca-rich cli- tetrahedrafor all four bond lengths (Fig. 6). Unlike CaO, nopyroxenes may be generally accounted for by their polyhedral the bond- and FeOu,the longest,Si-O(3C2), is not the most com- constituentpolyhedra, linkages, and atoms. The CaO, and (Fe,Mg)Oupolyhedra build pressibleone. The longest,Si-O(3C2), and secondlon- ing of up a two-dimensional sheet in the b-c plane sandwiched gest, Si-O(3C1) bonds compressonly by 0.6(4)7o and by tetrahedral chains. This sheet actually possessesno 0.8(4)Vo,respectively, whereas the values for the shortest, rotational freedom. In fact the unit-cell compression is Si-O(2C|), and second shortest,Si-O(lCl), bonds are due mainly to the reduction of polyhedral volume. The 0.9(4)7oand |.6(4)Vo,respectively. It is interestingto note sandwich sheet of CaO' FeOu, and the SiOo chains are that compression of the latter two bonds occurs mainly expectedto be essentiallyresistant to compressionalong between 0.1 MPa and 4.5 At pressures GPa. higher the the a axis. Along the c axis, the tetrahedralchain has a lengths of these two bonds are virtually the same within relatively large rotational freedom through the corner- the experimentalerror. Moreover they becomeapparently sharing tetrahedrathat is describedby the O3-O3-O3 an- insensitiveto pressure.The volume compressionbetween gle. This rotational freedom of SiO, facilitates the com- 0.1 MPa and l0 GPa is 2.9(6\7o. pression in the c axis direction although the volume Several previous studies,especially that of orthoensta- compressionof tetrahedrais small. In addition, the com- tite up to 2.1 GPa (Ralph and Ghose 1980), orthoenstatite pression of (Mg,Fe)Ou and CaO* also contribute to the up to 8 GPa (Hugh-Jonesand Angel 1994), fassaite up axial compressionalong the c axis. It is obvious that the to 5.2 GPa (Hazen and Finger 1977), and diopside up to relatively long Ca-O bonds projectedinto the b axis could 5.3 GPa (Levien and Prewitt 1981),implied that the Si-O account above all for the large compression in that bonds are quite incompressible below 4 GPa, but they direction. indicated considerable shortening above 4 GPa (Hugh- The longitudinal elastic moduli, cr, czz,c.., for diop- Jonesand Angel 1994). Our results demonstrateremark- side(223, l'71, and235 GPa)and hedenbergite(222, 176, able compressionsof the Si-Ol and Si-O2 bonds even at and 249 GPa), determined by Brillouin specffoscopyat relatively low pressures. The respective values are ambient conditions (Levien et al. 1979; Kandelin and l.l(S)Vo and0.1(5)Vobetween 0.1 MPa and4.2 GPa.This Weidner 1988), are closely related to the compressibilities can be visualized by looking at the volume data. For ex- along the a, b, and c axes. Consistent with the above ample, there is a volume compressionof l.6%ofrom 0.1 analysis, c, is smallest for both diopside and hedenberg- MPa to 4.2 GPa that can be attributedmainly to the short- ite. It should, however,be noted that c,, and c.. are about ening of the two shortestSi-O bond, whereasthere is only equal, with c.. being the largest. This disagreeswith our along a reductionof 1.37oin SiOovolume from 4.2 to 9.9 GPa, high-pressureresults, which show that compression results of X-ray dif- resulting primarily from shortening of the two longest the a axis is the smallest. From the fraction c,, should be the largest among the three longi- bonds. The volume compressibilitiesof SiOoin the lower tudinal elastic moduli c,,, c22,c... Furthermore,the similar and the higher pressureranges are comparable:3.7(8) x magnitudes of c,, for diopside and hedenbergitecontrast l0 ' GPa ' and 2.3(5) x l0 3 GPa ,, respectively.These with their distinct a-axis compressibilities found in this new results indicate that at high pressure SiOo behaves study. like other polyhedra such as CaO. and FeOuin the sffuc- The CaO, polyhedra, FeOuoctahedra, and SiO. tetrahedra ture. This was not observed in diopside (Levien and constituteabout 387o of the unit-cell volume. Compression Prewitt 1981). Comparing the few high-pressurestructure of the cation polyhedra is 7.3Voand that of voids 6.1%. data measuredwell above 5 GPa, the averageSiO. com- Thus the unit-cell compression can be accounted for, to a pressibility x 3 of 2.9(3) 10 GPa-, in hedenbergitebe- large extent, by the compressionof the constituent polyhe- tween 0.1 MPa and 10 GPa is obviously smaller than, dra. Based on the fact that the elastic coefficients c, mea- 3 3 e.9.,6.2(l) x l0 in orthoenstatite,'l.l(3)x l0 in for- sured for diopside and hedenbergiteare practically identical, 1 sterite and 5.0(4) x 10-. GPa in andradite(Hugh-Jones and theseparameters are different in orthoferrosilite and or- and Angel 1994, and referencestherein). thoenstatite,it was concluded (Kandelin and Weidner 1988; The kinking angle of tetrahedralchains in silicatesmay Bhagat and Bass 1992) that CaO. polyhedra determine the be described by the O3-O3-O3 angle. The tilting angle sffuctural srength of Ca-rich clinopyroxenes. From our of tetrahedra can be defined by the angle between the present results the compressibilities along the a axes of di- basal plane of a tetrahedronand the (100) plane. We ob- opside and hedenbergitediffer by as much as 20qo over a served a continuous kinking of this angle by 4.4' wide pressure range. At pressureslower than 3 GPa this [2.7(2)Eolas well as a continuous decreaseof tetrahedral difference can be more than 50Vo (Fig. 8). Up to 10 GPa tilting with increasing pressure.This change is accom- the CaO, polyhedronhas an averagebulk modulusof 118(3) panied by a rotation of the SiO. tetrahedron around the GPa, FeO" octahedron 149(4) GPa, and SiO. tetrahedron normal to the tetrahedralbasal plane. 341(36) GPa, whereasthe bulk modulus of all cation poly- 256 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

10 e e es ee 46*c axial compressibilitiesin dependenceofpressure (Fig. 8). ,****** It is immediately clear that diopside shows significantly gB at pressures 7 V higher compressibilitiesin all axial directions 6 below 3 GPa. Parallel to the b and c axes the compress- ibilities of both minerals approacheach other with rising

0 r pressure.In the ax direction diopside is about 20Vomorc rr rrlll 'r' ,rflir compressiblethan hedenbergiteup to 10 GPa. This fea- rr ture can be unambiguously attributed to the substitution c of Mg for Fe'* in the octahedra.The difference in the compression of these two minerals at high pressuresis ci- -r- characterizedby this feature. Because the high pressure 1 data for diopside include a few data points only and are . a a..aAS-a-a-a---a-4---4 at" *a.'- limited ro 5.3 GPa (Levien and Prewitt l98l), it is diffi- "^ cult to explain this difference in terms of the individual 7 bond lengths. From the results of 5?Fe"y resonance on a Ca-rich cli- 5 0 nopyroxene solid solution, Zhatg and Hafner (1992) I concluded that even at ambient conditions the Fe'z"and ^^ a aa a a rarrellrr A /lar Mg cations in crystallographically equivalent octahedra 7 must assume somewhat different geometric configura- 6 aSinB tions. This may becomemore pronouncedat high pres- sures. It implies that in solid solutions with similar cat- ion compositions,Fe2* and Mg occupanciescould show P (GPa) increasing instability at mantle pressures. Our present results confirm that. In fact significant Mg-Fez* ordering Frcune8. Comparisonof axialand volume compressibilities was observed in high pressure mantle minerals such as betweenhedenbergite and diopside. The ratios of thecompress- olivine and wadsleyite(Aikawa et al. 1985;Finger et al. plotted. ibilitiesare 1993). The preferential participation of Fe2* in oxide and Mg in perovskite in the lower mantle, following transformation from spinel (Mg,Fe)rSiOo at about 670 hedra is 136 GPa, which is just about the average of the km depth, could be explained by the distinct crystal bulk moduli of CaO, and FeOu.Thus, from these two ob- chemical behavior of Fe2* and Mg at high pressuresas servations,we conclude that the compressionof Ca-rich cli- observedin this study. nopyroxenes is determined mainly by both the CaO, and FeOu polyhedra. It is the distortion of these polyhedr4 Polyhedral distortion in hedenbergite through their anisofropic compressionsin bond lengths, that From the anisotrospiccompression of bond lengths and contributes mainly to the unit-cell compression. The com- bond anglesin hedenbergiteit is expectedthat the degree pression of the SiOo tefrahedraplays a marginal role. of polyhedral distortion changeswith increasingpressure. For testing this, distorrion parameters defined by Baur Influence of Fe,Mg substitution on elasticity and (1974)and Robinsonetal. (1971)were used:bond length structural compression distortion (BLD), angle distortion (AD), edge-lengthdis- The dependenceof bulk modulus on Fe and Mg in tortion (ELD), quadraticelongation, <\>, and angle vari- mantle minerals is interesting for modeling the mineral- ance, o2. The BLD, AD, and ELD values are plotted in ogical composition of the mantle as well as for high- Figure 9. The <\> and o2 values are given in Table 8. pressure crystal chemistry. Our experimental results on Within the error there is no significant change in <\> Ca-rich clinopyroxenes show clearly that K'r" of diopside and o2 values for FeOu and SiOo for pressuresup to 10 is larger than that of hedenbergite,i.e., in the pressure GPa. By examining the distortion parametersBLD, AD, range between 0.1 MPa and 10 GPa, diopside is about and ELD for CaO., FeOu,and SiO". it is evident that the ll%o more compressiblethan hedenbergite.This result is distortion for CaO, decreasessignificantly with increasing inconsistent with the predictions of the bulk modulus- pressure,whereas the other polyhedral distortion param- volume systematics and provides another example for eters show only marginal changes. Zhang atd Hafner compressionanomalies in silicate minerals. Such behav- (1992) concluded that the geomeffy of FeOu becomes ior was also observed in silicate garnets and olivine more regular with increasingpressure up to about 4 GPa (Zhang et al., unpublisheddata) as well as in Fe-Mg spi- on the basis of the 57Fedata up to l0 GPa and by assum- nel solid solution (Hazen 1993). ing a pseudoaxialsymmetry at Fe'?*in hedenbergite.This The effect of the Fe/IVIg ratio on the compressional ffend seemsto be confirmed by angle and edge distortion behavior of diopside and hedenbergitecan be further vi- parametersof the FeOu,which decreaseslightly with in- sualized by comparing the pressuredependence of their creasingpressure. The cation off-center shifts in the CaO,. ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE 257

-tr Phasetransition in hedenbergite 030 ttl I I I o25 I I Recent studies of the sTFe"y (Mdssbauer)resonance in 020 three Ca-rich clinopyroxenes up to l0 GPa revealed a 't discontinuity in the electronic configuration of the Fe,* U) L 0'10 o o o ooo o o o o o ion at about 4 GPa, which may suggesta phasetransition o A (Zhang and Hafner 1992).As demonstratedby the present

(J v u/u results, neither any significant discontinuity in the unit- A ts A cell parametersnor any abrupt changein bond lengths or O ooos AA angles was observedwithin the experimentalerror in our X-ray diffraction study. The relatively large scatterof our data for the bond lengths and bond angles in FeOudoes not allow detection of any such small discontinuity re-

o 60 E quired for a changein Fe2" electronic state.Although the E Ir_*tT 5'Fe hyperfine parametersare critically dependenton the O aa lIi .9. Ea local geomeffy of the FeOu octahedrait is not yet clear Ooo how these parametersrelate to that state. However, it is

ou interesting to note that the discontinuity in hyperfine pa- cD od y _ - r r t T r d I'r- I I { rameters of Fe2* coincides with the crossoverof the two J longest bond lengths in both the CaO, and FeOupolyhe- E20 dra at about 4 GPa. Furthermore,there is a changein 15 the o r I I f-rA r a (D i! { r compressibilitiesof the two shortestbond lengths in the 10 SiOotetrahedron at about 4 GPa. No reflections violating 175 t_- I f I tltt spacegroup CZlc were detectedabove 4 GPa. tt Diopside and hedenbergiteundergo twining at nonhy- c l7o drostatic pressureseven in a pressuretransmitting medi- E um of solid argon. This behavior was tested by using a ,"" methanol-ethanol, solid argon, and teflon oil as O 36 oooo pressure-ffansmittingmedia. No twinning could be ob- q) served in the methanol-ethanolmedium up to 10 o) 34 ooo GPa. aao Twinning was observedin the crystals in the argon pres- ooa ^' AA sure medium beginning at about 3 GPa and persisting up ^ A A to at least 15 GPa. The twining disappeared,however, 30 after releasingpressure. In teflon oil the twinning started at much lower pressuresand was retained after releasing 15 T-r'f T - rILI pressure.Twinning of both diopside and hedenbergiteis, r|++lI T +| I| rJ rI I -a as demonstrated here, clearly induced by deviatoric E L stresses.Although the high pressure Mcissbauerexperi- Oii ments on Ca-rich clinopyroxeneswere not conductedun- a u25 T- der hydrostatic conditions, twinning due to nonhydrostat- o IT tl+-l ic pressure would not change the hyperfine parameters !'" ii+++ i + + measuredfrom polycrystalline samples.Furthermore, the uJ '15 pressure of the hyperfine parameter discontinuity was IIJ +tTt _LI { r _L4 II -r1..I t? | I I 10 I found to be much higher than that neededfor twinning, 46810 even if comparedwith the pressurein the argon medium. P (GPa) Considering that the Mcissbauerexperiment probes the Fe'?*elecffonic state in the FeOu octahedron with much FrcuRE9. Distortionparameters and cationotf-center shifts more sensitivity than X-ray diffraction, it seemsinevita- forCaOr, FeOu, and SiOo. For a regularpolyhedron the distortion ble that more precise structure on parametersBLD, AD, and ELDare equal to zero. data diopside and hed- enbergite will be neededto clarify this question.

AcrNowr-nncMENTs and FeOopolyhedra, defined by the deviation of the av- erage mass center of the ligands from the mass center of We thank U Sdffler, Max Planck Institut fiir Chemie, Mainz, and A. Bakhshandeh,Institute of Mineralogy, University of Marburg, for donat- the cation in a polyhedron, decreasewith increasingpres- ing diopside and hedenbergitecrystals D Hugh-Jonesand M.D. McGuinn sure, whereas the off-center shift for SiOn is unchanged are acknowledgedfor their critical reviews. This work was financially with pressure. supportedby DeutscheForschungsgemeinschaft grant Ha828132. 258 ZHANG ET AL.: COMPRESSION OF CLINOPYROXENE

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