High-Temperature Grystal Ghemistry of Acmite, Diopside, Hedenbergite

American Mineralogist, Volume 58,pages 594-618, 1973

High-TemperatureGrystal Ghemistry of Acmite,Diopside, Hedenbergite,Jadeite, Spodumene, and Ureyite

MlnvnrrnN ClrunnoN, Ssrcrno SuBNo, C. T. Pnnwrrr, AND J. J. Plpmn

Department ol Earth and Space Sciences, State Uniuersity ol New York, Stony Brook, New York 11790

Abstract

Crystal structure parameters have been determined for acmite, NaFes*SLOs(at -400'C, 600'C, 800"C), diopside,CaMgSi.Oo (at -400"C, 700"C, 850'C, l00O"C), hedenbergite, caFe"*Si,ou(at -24"C,400"C, 600"C, 800"C,900"C, 1000"c), jadeite,NaAlsLo" (at -24"c, 400"C, 500"C, 800'C), spodumene, LiAlSi,On (at -300'C, 460"C, 76O'C) and ureyite, NaCrSi,On (at -400"C, 600"C). Refinementsin space group C2/c using anisotropic temperature factors and over 640 reffectionsfor each set of data resulted in unweighted R-factors rangingfrom 0.022 to 0.078. The increasein mean Si-O bond lengths with increasingtemperature is not statistically significant. but the mean M-O distances for both the 6- and 8-coordinated sites in the six pyroxenesexhibit relatively large increases.The mean thermal expansion coefficientsfor the various bonds increase in the following order: Sil--O < Cr"*-O 4 Fe"*-O 4 Al"*-O < Fee*-O ( Na*-O ( Mg'*-O q Caa-O < Li--O. This series is essentially a function of decreasing bond strength, although the position of Mg3--O may indicate an exception to this trend. The pyroxene structures accommodatethe differential mean M-O expansionsthrough (1) extension of the silicate tetrahedral chains, (2) distortion of the silicate tetrahedra, and (3) an increasein out-of-plane tilting of silicate tetrahedra. In all six minerals thermal expansion is accomplishedprincipally by expansion of the non-tetrahedral polyhedra with concomitant expansionof the voids betweenthe cation polyhedra, and rotation of the fairly rigid tetrahedra about the bridging oxygen atoms. The rate of increase of the equivalent isotropic temperature factor for a cation is generally proportional to the coordination number of that cation.

Introduction mentioned above and, in addition, should provide valuable insight into the mechanismsof anisotropic Although the basic structure of clinopyroxenes thermal expansion.Published refinements of pyrox- was determinedalmost 45 years ago (Warren and ene structuresusing intensitydata collectedat high Bragg, 1,928),the structural details are still being temperaturesinclude thoseof Smyth (1971; protc. investigated.Within the last 10 yearsmany excellent enstatite),Smyth and Burnham (1972; clinohypers- refinementsof structuresusing intensity data col- Brown, Prewitt, Papike, and Sueno lected at room temperaturehave becomeavailable thene), and (1972; (e.g.,for end-membercompositions: Christensen and pigeonite). In this study we have examinedthe structuresof Hazell, 1967 ; Fr eedand Peacor,19 67 ; Clark, Apple- jadeite, man, and Papike, 1969), and the resultshave been six C2/c pyroxenes(spodumene,r LiAlSi2O6; extensivelyused by workersinterested in phenomena NaAlSizOe;acmite, NaFe3.SizOo ; ureyite, NaCrSizOe; such as phasetransitions, exsolution, solid solution diopside,CaMgSi2O6; and hedenbergite CaFe2-SirO6) and intracrystalline equilibria that take place above at a seriesof temperaturesranging from room tem- room temperature.Since the extrapolationof room- peratureup to 1000'C (TableA-1).' End-member temperaturestructural data to higher temperaturesis t uncertain, it is important to examine the structures fnfuy u.toully be C2. 2 numbers preceded by the letter "A" are located in pyroxenes Table of while the crystalsare held at high tem- the Appendix at the end of the paper. The absence of a peratures. This type of structural data provides prefix indicates that the table can be located in the text of information on the high-temperature phenomena the paper.

594 CRYSTAL CHEMISTRY OF SIX PYROXENES

pyroxeneswere selectedin order to study thermal temperatureuncertainty depends on the crystaltem- expansionof eachcation uniquelyand to avoid ef- peratureand is approximately!20oC (Brown et al, fects of mixed site populations.The upper tempera- r973). ture limits for the seriesof intensity collectionsfor X-Ray Difiraction Data individual mineralswere determinedby pyroxenesta- bilities and furnace capabilities.The new room-tem- Using data collectedon the Picker diffractometer, peraturerefinements presented herein for jadeiteand unit cell parameterswere determinedby measure- hedenbergiteare in close agreementwith those pre- ment of 2'0values of 15 to 20 reflections,principally viously publishedby Prewitt and Burnham (1966; of the type ftkl. Refinementof these2d valuesin the jadeite) and Veblen and Burnham (1969; heden- pooBx2 programwritten by A. W. Sleightsyielded bergite). Room-temperaturerefinements of spodu- the cell pararneterslisted in Table A-2. No correc- mene, acmite, ureyite, and diopside of Clark et al tions for systematicerrors were included in the re- (1969) were used for comparison with our high- finements. temperaturedata. We will specifically consider the Between800 and 950 independentintensities were variation with increasingtemperature of cell param- collectedat eachtemperature (Table A-1) using a eters,interatomic distances, polyhedral volumes, and ror 15/35-controlledPicker diffractometer.Diffrac- thermal parametersand then, on the basisof these tometersettings were calculatedusing the cser pro- results,attempt to explainsome mechanisms of ther- gramcoded by C. T. Prewitt.To maintainuniformity, mal expansionin pyroxenes. we attemptedto collect the sameset of reflections within 20 = 10"-65o for eachstructure. The Picker Experimental Data diffractometerwas operated in an t,.'- 2d modeusing a graphitemonochromater and MoK" radiation. The Chemicaland CrystallographicData scan range was varied from 2o to 2.5", being in- Except for hedenbergite,all of the crystals used creasedat highertemperature because of peakbroad- in the structuralstudies presented herein were ob- ening. Five-secondbackground counts were taken tained from samplespreviously used by Prewitt and on both sidesof each peak. A standardreflection Burnham (1966; jadeite) and Clark et al (1969; 060 was monitoredthroughout each data collection. spodumene,acmite, diopside, and ureyite) in their It wasrepeated every 20 reflectionsand its structure room-temperaturerefinements. Jadeite, spodumene, factor usuallyvaried by lessthan one standardde- acmite,and diopsideare naturalspecimens but they viation. No absorptioncorrections were made for closelyapproximate end-member pyroxene composi- any of the pyroxenesdue to their small size (<0.1 tions (for chemical data see Prewitt and Burnham, mm in crosssection) and smalllinear absorptionco- t966, and Clark et al, 1969). The ureyite was syn- efficientsfor Mo radiation.a thesizedby L. Fuchs from a melt of NaCrs-Si2O6 Both isotropic and anisotropicrefinements were plus 10 wt percentNazSiOs in air at 1000"C for 2 calculatedfor each set of intensity data in space days. The hedenbergitewas synthesizedby D. H. group C2/cu using neutral atom scatteringfactors4 Lindsley at approximately980'C and 20 kbars for (Doyle and Turner, 1968), unit weights4and the 8 hours. RFINEprogram written by L. W. Finger. Starting The pyroxenespecimens were oriented parallel to parametersfor hedenbergitewere thoseof diopside, c* on Suprasilquartz glass fibers with a high-temppra- whereaspreviously published room-temperature pa- ture cementcomposed of solid AlzOs combinedwith rameterswere used for the remainingfive pyroxenes. a liquid binder. To preventoxidation of the Fe2.in hedenbergite,the crystalwas placed in an evacuated C.nt.rf n searchDepartment, E. I. duPont de Nemours and Company, silica capillary following the proceduredescribed Wilmington, Delaware. by aOur experiencehas shown the Brown, that use of absorption Sueno,and Prewitt (1973). Except in the corrections and different weighting schemesand scattering initial stagesof our hightemperaturestudy (i.e., factor curvesfor theseminerals has very little effect on final during the diopsidedata collection),one crystalwas results of the refinements,providing that significant syste- used to collect the completeseries of intensitiesat matic errors resulting from improper experimental tech- niques present various temperaturesfor each pyroxene. are not in the data. In most 6No reflections violating C2/c group instances space symmetry data collectionbegan within 8 hours after were observed in precession photographs of any of the the desiredtemperatures had been obtained.The crystals,including spodumene. 596 CAMERON, SUENO, PREWITT, AND PAPIKE

T hermal E x pansion T ermtn olo gy i fn" mean thermal expansioncoefficient

._.___| .xr- x24 Xro T-24

is used throughoutthis study to characterizethermal expansionsof selectedparameters. The terms X2a and Xr are the values of the parameter at 24"C [room temperature]and at somehigher temperature 7. The quantity ax repres€Dtsa percentageincrease per degree (actually percent x lo-'z/degree)over the temperaturerange studied,and algebraicallyit is equivalent to the rate of increasewith temperature Frc. l. The C2/c pyroxene structure projected down a*. divided by the room temperaturevalue of the param- Nomenclature is consistent with that of Burnham el al eter. In actual practice each'd was calculatedby di- (1967) . viding the slopeobtained from least-squaresanalysis, Observed structure factors and the pal's from the X, - Xrn final cycle of each anisotropic refinement may be ' ordered as NAPS document #02720.n Final posi- T-24 tional and thermal parametersdetermined from the anisotropic refinementsare given in the Appendix by the value of the parameterat room temp€rature. (Table A-3). R-factorsfor theseanisotropic refine- We have occasionallyused rate of increaserather ments of the 22 new setsof data rangefrom 0.025 than a5, the mean thermal expansion coeffi.cient, to 0.078 (Table A-1). The high valuesof the R- when describingsome of the data displayssince the factors for ureyite are not the result of experimental difficultiesduring collectionof the intensity data, but are due to the relatively poor quality of the crystal used.Selected interatomic distances, angJes, thermal ellipsoidsand their associatederrors, calculated using 9 the ennon programof L. W. Finger,are listedin the Appendix (Table A-4: Si-O interatomicdistances; Table A-5: tetrahedralO-O distances;Table ,4-6: tetrahedralangles; Table A-7: M(l)-O interatomic O (Al g.1q distances;Table A-8: octahedralGO distances;Ta- ble A-9: octahedralangles; Table A-10: M(2)4 interatomicdistances; Table A-11: magnitudesand orientationsof thermalellipsoids). Although thermal correctionsfor interatomic distancesmay be advis- able,we havenot madesuch corrections because of uncertainty in selecting a model which adequately describesthe thermal motion effecton bond distances T in the pyroxenestructure. Except for plots involving B, the slopes of all lines in the figures were deter- 400 600 mined with a linear least-squarescomputer program. renpEaltunE t Frc. 2. Variation of a unit cell parameter with increasing 0 Microfiche Publications, 305 East 46th Street, New York, temperature for six clinopyroxenes.Abbreviations: HD = N.Y. 10017.Please remit in advance$1.50 for microfiche or hedenbergite, DI : diopside, AC = acmite, UR = ureyite, $40.10 for photocopies (264 pages). Please check the most JD - jadeite, SP - spodumene. Error bars represent -rl recentissue of this journal for the current addressand prices. standard deviation. CRYSTAL CHEMISTRY OF SIX PYROXENES s97

5 4o

5 36

5 32 ctit

528

524

5 20 4oo 600 tgupealtun€ "c Fro. 4. Variation of c unit cell parameter with increasing temperature for six clinopyroxenes. (Abbreviations are the -Fl b(ir same as those in Figure 2.) Error bars represent standard deviation.

non-bridging oxygens. The O(3 )-O(3 )-O(3 ) ' uR _---=- angle is used as a measureof the extensionof the silicate chain. For further details of the clinopyroxene structure, the reader is referred to the paper by Clark et al (1969). The nomenclatureused throughout this paper is consistentwith that pre posed by Burnham, Clark, Papike, and Prewitt (re67).

Unit Cell Paranreters I 381 o 600 800 The variations in unit cell parametersas a function of temperature (Figs. 2-6) are linear with the Fro.3. variation of D'"t,::liilH..", *nn increasingexception of the p angles in diopside and heden- temperature for six clinopyroxenes. (Abbreviations are the bergite. Examination of the mean thermal expan- same as those in Figure 2.) Error bars represent -+l sion coefficientsof the cell parameters(Table 1) standard deviation. reveals that ,at ) ,a6 ) o" for all pyroxenesexcept spodumene.Expansions along dlee (- a*) (Fig. 7) are of interest becausethis is the direction perpen- rate of increase(i.e., the slope) is directly observ- ableon theseplots.

The Pyroxem Strucfure

Figure 1.shows a projection of.the C2/c pyroxene r_r_r_ J0 to74 structurealong c*. Tll.e M(l) site, which is octa- :------r:i=iF---t-ac hedrally coordinated,is occupiedby Al (spodumene ' ro70 and jadeite), Fet* (acmite), Cr3- (ureyite), Mg (diopside)or Fe2*(hedenbergite). The largerM(2) tosI site is either 6- or 8-coordinated and is occupiedby tos4 Ca (diopsideand hedenbergite), Na (jadeite,acmite, and ureyite) or Li (spodumene).There is only one ro50 type of tetrahedralsite, and it is completelyoccupied ro46 by silicon in all six pyroxenesexamined. There are three crystallographically non-equivalent oxygen IEMPERATURE C atoms,O(1), O(2) andO(3). O(3) is referredto Ftc. 5. Variation of n0with increasing temperature for six as a bridging oxygen in that it is bonded ro two clinopyroxenes. (Abbreviations are the same as those in silicon atoms, whereasO(1) and O(2) are both Figure 2.) Error bars represent -+1 standard devation. 598 CAMERON, SUENO, PREWITT, AND PAPIKE

460 956

450 9.54

440 9.52

i 430 9./.0 vla )

420 9.38

4to 9.21

4 0o 9.22

9.20

380 916 400 600 aoo rooo €

TEMPERATUREt 3 9.12. t FIc. 6. Variation of unit cell volume with increasing tem- 9.02 perature for six clinopyroxenes. (Abbreviations are the same as those in Figure 2.) Error bars represent -+1 9.00 standard deviation. 8.98 dicular to the octahedrallayers and, as such, should 8.90 be a better parameter with which to compare the 8.80 expansions along b. The mean thermal expansion 0 200 400 600 800 1000 coefficientsin this direction are also less than those TEMPERATURE.C in the b directions and they are quite similar to c in Frc. 7. Variation of d'* with increasing temperature for both diopside and hedenbergite.Both the rate of six clinopyroxenes. (Abbreviations are the same as those in increaseand the mean thermal expansionfor the b Figure 2.) Error bars represent -+1 standard deviation. cell parametersare significantlygreater for the two

calcic pyroxenes (Figure 3 and Table 1). With in- Tesrn 1. Mean Thermal Expansion Coefficients ("C" X creasingtemperature, the angle in the sodic py- 105) of Unit Cell Parametersx ,B roxenesand spodumeneeither decreasesor remains approximatelyconstant whereas in the calcic pyrox- Spodumene Jadeite Acmite Ureyite Diopside Hedenbergite Qq-taooc)(zq-aoooc) (z+-eoooc) (zq-eoooc) (zc-tooooc) 1z+-tooooc) enesit increasesnon-linearly. Mean thermal expansion coefficients(Table 1) and plots of the change d 0.380 0.850 0 727 0.585 0.719 o.724 in unit cell volumes (Fig. 6) as a function of 0 , 0.600 0.8r7 0.804 0.691 0 .606 0.483 "too temperatureboth indicate that diopside and heden- o. 1 ll 1.00 r.20 0.946 2.05 1.76 bergite exhibit higher rates of thermal expansion c 0.47s 0.631 0.450 0.390 0.646 0.597 than either spodumeneor the sodic pyroxenes. a 2.22 2.47 2.47 2.04 3.33 2.98 *** d 2.03 2.07 2.30 r .61 2.91 2,46 Polyhedral Expansions d **** 2.83 3.09 2.78 2.79 3,97 3.45

'Mean Silicate Tetrahedra thermal expansioncoefficients o are computed Mean Si-O bond lengths do not increase sig- fron the equation = + . {}, - wherethe ", l'24 nificantly with temperaturein any of the six pyrox- slope of the regressionequation is usedfor the enes. All remain within two standard deviationsof term -+-;: Seetext of pdper. | -24 thoseat room temperature(Table A-4). The largest "*For 0.380, read 0.380, i0-5 c-l . increaseobserved was that in ureyite, 1.624 A at v-p is the volure of spacebetween the cation polyhedra. p is the polyhedralvolune deternined by suming the 24oC to 1.629 A at 600oC (an increaseof 0.3 voluresof all polyhedrawithin a unit cell. percent), whereasthere was essentiallyno change CRYSTAL CHEMISTRY OF SIX PYROXENES 599

Tesrp 2. Polyhedral Volumes of bondingwithin the tetrahedra.Brown and Gibbs (1970, Fig. 5, p. 595) have shown rhat in silicates Tenperature volume(E3) ot volume(83) or volune(83) ot which contain both bridging and non-bridging Itlineral (oC) tetrahedron M(I ) octahedronl'1(2)polyhedron oxygens,the mean Si-O(br) distancedepends in Spodunene 24 2. I 58 9.240 l0.750 300 2.162 9.320 I 0.846 part upon the Si-O-Si angle, the shortest bonds 460 2. I 63 9.372 10.909 760 2 165 9.457 I 1.023 usuallybeing associatedwith the widestangles. This Jadeite 24 2. 183 9.373 24.581 relation is valid for the room-temperaturepyroxene 400 2 183 9.467 24.900 600 2 186 9.528 25.088 structures [for the sodic pyroxenes, Si-O3-Si - 800 2. t88 9.561 25.301 139o and Si-O(br) - 1.64A and for the calcic Acmite 24 2 201 rc.869 26.295 400 pyroxenes 2.205 '|10.922 26.536 Si-O3-Si 136" and Si-O(br) - 600 2.209 .001 26.774 800 2.209 I I .047 26.984 1.68A1,but not for the individual mineralswithin ljreyite 24 2.188 10.508 25.36I the sodic or calcic groups, possibly because the 400 2 196 10.602 25.699 600 2 206 10.604 25.A71 Si-O-Si anglesin the group rnay not be statistically Diopside 24 2,221 1I .848 25.760 different (range is - 0.5o). With increasingtem- 400 12.047 26.193 700 2.228 12.206 26.576 perature,the Si-O-Si angleincreases (a maximum 850 2 229 ']2.35312.244 26 686 1000 2.237 26.870 of about 1.4o in both diopsideand hedenbergite), Hedenbergite 24 2.224 r 2.808 26.102 and based on the conclusion of Brown and Gibbs 400 2.224 12.946 26.468 600 2.227 12.993 26.702 (1970), we would expect the Si-O(br) bonds to 800 2.225 13.092 26.886 900 2.226 l3 132 27.056 decreaseslightly. Examination of Table A-4 shows 1000 2.226 13.172 27.221 that the Si-O(br) bondsdo not appearto decrease in any of the pyroxenes. M( I in hedenbergitefrom 24oC to 1000"C. Relativeto ) Octahedra bridging and non-bridging oxygens,a tendency may Mean M-O distances(Fig. 8) and volume of the exist for the mean Si-O (br) lengthsto increaseat M(l) octahedron(Fig. 9) both increaselinearly a slightly higher rate than the Si-O (nbr), but the changesare well within experimentalerrors. Tesle 3. Mean Thermal As expected frorn the small changes Expansion Coefficients ("C- X in mean 106)for Individual,t"11ff#rPistances and Polyhedral Si-O lengths,the volumesof the tetrahedraincrease little with temperaturefor the six pyroxenes (Table 2). Mean thermal expansion coefficients for the Spodumene*Jadeite Acmite Ureyite Diopside Hedenbergite o24-76ooc o24-tooooc mean Si-O distancesand the tetrahedral volumes "z4-eoooc "zq-8oooc "zq-ooooc "2q-looooc 5i i icon tetrahedra are listed in Table 3. The change in the shape of si-o(r) o.rzg** 0.074 0 279 I 3t 0.025 2.16 -0(2) -0 the tetrahedra with increasing temperature can be r80 0.142 I 14 -0 020 -0 158 -0(3cl) 0.157 0,064 0 447 -0 851 0 362 0.038 described by comparing the O*Si-O tetrahedral -0(3c2) 0 ti8 0.267 0.059 0.481 0 180 0.144 anglesand the O-O distancesof the roon-tempera- meanSi-o 0,160 0_1 56 0.182 0 529 0 099 0 026 tet. vol. 0.432 0.300 0 s09 | 37 0.057 0 098 ture structure with those of the higher temperature structures Itl(I ) octahedron for each mineral, In general, the tetra- H(l)-o(lAr),(l8l) 1.79 1 79 1.67 t.33 2 08 1 94 hedral angles O(1)-Si-O(3CZ) and O(1)-Si- -0(1A2),(ls2) 0.427 0.541 0.271 0 352 0.418 -0.298 -0(2cr),(201) 0 887 0 4ll 0 483 0.035 1 83 I 46 O(3Cl ) decreasein all six pyroxeneswith increasing meanM(l )-0 1.06 0 947 0.781 0.633 I 44 1.05 temperature,whereas O ( 1)-Si-O ( 2) andO( 3C1)- i4{l) vol. 3.21 2 65 2 16 I 69 4.25 2,91 Si-O(3C2) increasewith the exceptionof diopside M(2) polyhedron whereO(1)-Si-O(2) is identicalat room tempera- 14(2)-o(rAt),(rBr) 2.58 1.67 I 98 1.63 I 7i t.49 -0(2c21,(2D2) 0-457 r.35 r 19 0 791 0.795 0.878 ture and at 1000'C (Table 4-6). The two remain- -0{3cr),(3Dt) 2 81 0 854 1 t4 0.913 0 958 0.415 ing tetrahedral -0(3c2),(3D2) -1 74 1.32 0.793 I .66 3.00 3.47 angles, O(2)-Si-O(3C1) and ',l5l nean14(2)-0 1.97 1.28 128 126 t54 O(2)-Si-O(3C2), decreasein the sodic pyroxenes M(2)vol. 3.46 3-74 3 38 3 50 4 42 4.29 and increasein the calcic pyroxenes. lileanthemal expansioncoefficients e are computed . \--\"n Becauseindividual frm the equation aX - whe-re Si-O distancesremain statis- X; +?i: , the tically identical with increasing temperature, it is slope of the regression equation is used for the term See paper. important to examine the tetrahedral angles for +?i: text of *'For trends which may help in understandingthe nature 0.379, read 0.379r to-5c-1. 600 CAMERON, SUENO, PREWITT, AND PAPIKE

thermal expansion coemcients (Table 3) of mean 'fr-'-'-' M-O bond lengthsresults in the following sequence T] Mg-O ) Fe,"-O > Al-O ) Fe8*-O ) Cr8*-O. I If we examinethe changesin individualM(l)4 bond lengths (Table A-7) with increasingtempera- ,!)-r--1 ture,we find that the M(1)-O(1A1), (1Bl) bond 209 r-l has the highest mean thermal expansioncoefficient ?-----'-] 207 in all six pyroxenesand the M(1)-O(1A2),(lB2) : F.1ic bond, which lies in a plane alrnostperpendicular to o 2 03 ,rt = i' the b axis,has the lowestin four of the six pyroxenes. Cr,UR The changesin octahedral O-O distances (Table 2 0l --l- for the two calcic and three I r al,JD A-8) are very similar sodic pyroxenes.The main differenceobserved is a decreasein O(2Cl)-O(2Dl) in the sodic pyroxenes and an increaseof this same distance in the looo 2oo 4oo 600 800 calcic ones. The O-M(|)-O angles (Table A-9) TEMPERATUREI changeon thg order of a few degrees,usually less, Fro. 8. Variation of mean M(l)-O interatomic distances with increasingtemperature. with increasing temperature for six clinopyroxenes. (Abbre- viations are the same as thosd in Figure 2.) Error bars M(2) Polyhedra -+1 represent standard deviation. The M(2) sites in both the calcic and sodie pyroxenes are 8-coordinated, whereas the Li in with increasingtemperature. The increasein mean spodumeneis 6-coordinated.Mean M(2)-O intet- M(l)4 bonds is almost an order of magnitude atomic distances(Fig. 10) and polyhedral volumes larger than that of the mean Si-O bonds and appar- (Fig. 11) increaselinearly with increasingtempera- ently reflects the lower strength of the M-O bond ture. The magnitude of the changes in mean relative to the Si-O bonds. Ranking of the mean M(z)-O distances is approximately the same as that of the mean M(l)-O drstances,i.e., both are an order of magnitudeTarger than that of the silicate tetrahedra.The mean thermal expansioncoefficients r30

i,"" Co,HD T F No.Ac r, -l-"'-' z 122 o F o il8 o

lrrc 250 o G o 3 ro | 24E C.,UR o to6 U U- U . l roz T- o '---"""-t 9'A r---'/L I

reupEaltune'c TETPERATURE C FrG. 10. Variation of mean M(z)-O interatomic distances FIc. 9. Variation of octahedral volume with increasing with increasing temperature for six clinopyroxenes. (Abbre- temperature for six clinopyroxenes. (Abbreviations are the viations are the same as those in Figure 2.) Error bars same as those in Figure 2.) represent =l standard deviation. CRYSTAL CHEMISTRY OF SIX PYROXENES 601

O(3C2),(3D2) interatomicdistance decreases sig- nificantly at higher temperatures(3.144A at 24oC to 3.103A at 760'C) althoughthe O(3C2) and O(3D2) oxygensare still too distant to be con- sideredas coordinatingthe lithium. This sameinter- atomic distance increases considerably in both diopside (2.7174 to 2.797A) and hedenbergite (2.7204 to 2812A) over the 1000"C interval studied,thus indicatingthat the Ca in M(2) in both pyroxenesis becoming more nearly 6-coordinated. This result has important consequencesin solid solution of the calcium-rich 6 ^.- lr<"f t | | | | r I t l | | | I I i | | I and calcium-poorpyrox- >245l...... "J.4 o 200 aoo 600 aoo looo eneswhere M(2) is generally6-coordinated. The increasein the M(2)-O(3C2),(3D2) rempenlrune "c disrancesin the sodic pyroxenesis almost Frc. 11. Variation ot M(2) polyhedral volume with in- an order of magnitude creasing temperature for five clinopyroxenes. The volume smaller than that in the calcic pyroxenes.The large of. the M(2) polyhedron in spodumene is shown in Fig- increasein the M(2)-O(3C2),(3D2) bond in the ure 9. (Abbreviations are the same as those in Figure 2.)

for the meanM(2)-O bonds (Table 3) are nearly identical for Na in the three sodic pyroxenes and 2.9 for Ca in the two calcic pyroxenes. However, U 2.8 d.trr(z)yolure varies somewhat from mineral to mineral z within eachseries, probably as a result of the slightly 2,7 different distortions. It is of interest to note that cmearrM(2)-o for Na in acmite, jadeite, and ureyite is

less than that for Ca in diopside and hedenbergite. U MEAN Of the eight oxygenscoordinating the M(2) sites .t------l-----__---'t------l o M2-O2 in the sodic and calcic pyroxenes,four are shared ?- t-I with the M(l) octahedraand four with the silicate M M2-O3Cl tetrahedral chains. The coordination polyhedra of 23 0 thesetwo pyroxene groups have different configura- 400 600 800 looo TEMPERATURE'c tions at room temperature.The sodic pyroxene (Fig. l2a) havesix shortbonds (2.3-2.4A) and two considerably longer (2.7-2.8A), whereas the calcic '3 pyroxenes (Fig. l2b) have four short bonds (- 2.354) and four longer ones (2.55A-2.7A). z In spodumenewhere the Li inthe M(2) is 6-coordinated,all bondsare short (2.1-2.5A); the two next I closestoxygens lie at a distanceof.3.l44A and are T well beyond the first neighbor cordination sphere. F 0 25 The M(2)-O(3C2),(3D2) interatomicdistance is G o z always the largest in the pyroxenesand it is these 24 two oxygenswhich move in or out of M(2) coordination sphere when coordination number of the z3 o 200 400 600 M(2) site changes. 800 tooo Since the movementsof the O(3) oxygensare renpealtuaet intimately interconnectedwith the straighteningof FIc. 12. (a) Variation in individual M(z)-O interatomic distanceswith increasingtemperature in jadeite. (b) the tetrahedralchains, the changesthat occur Varia- in the tion in individual M(2)-O interatomic distanceswith M(2) coordinationpolyhedra in- with increasingtem- creasing temperature in hedenbergite. Error bars represent perature are complex. In spodumenethe M(2)_ t3 standarddeviations in both figures. CAMERON, S(/ENO, PREWITT, AND PAPIKE calcic proxenesresults from a higher rate of tetra- Thermal Parameters hedral chain straightening(Fig. 13) which in turn I sotropic Temperalure Factors is due, at leastin part, to the high rate of expansion of Fe'. and Mg in the M(1) sites.This effectis In general,equivalent isotropic temperaturefac- reflectedin the increasein p angle for the calcic tors,calculated using L. W. Finger'sERRoR program pyroxenes. and results from the anisotropicrefinements, in- The relativemovements of the M(2) cationswith creaseat the highestrate for 8-coordinatedcations increasingtemperature has been determinedfrom (Fig. 1a) but at the lowestfor 4-coordinatedcations the ratio of the M(z)-o(lAl),(1B1) distanceto (Fig. 15). An exceptionis 6-coordinatedLi in M(2) the M(2)-O(3C1),(3Dl) distance.With the ex- in spodumene,for which the rate of increasewas the ception of ureyite, the Ca and Na atoms move away highest observed.Because of the linear trend de- from the octahedralstrip. terminedfor B(A'z) for the Li atom, it does not

r90

0 U

t78 o

o 174

o z B(A"2 ) z e r7O E )

3 r oe

u F

AI,JD

600

TEMPgRATURE C TEMPERATURE t FIG. 13. Variation of the tetrahedralchain angle,O(3)- of the O(3)-O(3), with increasingtemperature for the six clino- Frc. 14. Variation with increasing temperature 8-coordi pyroxenesof this study and the A and B chains in pigeonite equivalent isotropic temperaturefactors of 6- and are the (Brown et al., 1972). (Abbreviations are the same as those nated cations in six clinopyroxenes.(Abbreviations in Figure 2.) Error bars represent -+1 standard deviation' sameas thosein Figure 2.) CRYSTAL CHEMISTRY OF SIX PYROXENES 603

the lowest rate of increasewith increasingtemperature when compared to all atoms. Differences in dB/dT for the same atoms-f61 glsrnple, Al in spodumeneand jadeite (Fig. l4)-may result in part from varying configurationsof the sites in different structures and in part from different atomic speciesin M(2)-for example,Li in spodumenebut Na in jadeite-with which M(l) sharesedges. The rates of increase of the oxygen isotropic temperaturefactors lie roughly betweenthose of the 6- and 8-coordinatedcations, and their rate of increase can also be correlated with coordination number. With the exceptionof spodumene,the rate Fra. 15. variation;']:il'"'J:g't"-p".utu." of th. of increasefor the 3-coordinatedO(2) oxygen is equivalent isotropic temperature factors of 4-coordinated greater than that for the 4-coordinatedO(1) and silicon atoms in six clinopyroxenes. (Abbreviations are the sameas thosein Figure 2,) O(3) oxygens.Although both O(1) and O(3) are coordinatedby four cationsin a very distortedtetra- hedral arrangement,the four cations coordinating seemthat a significantamount of Li couldhave been O(1) are closer (- 2.4A) than those cordinating lost during the heatingexperiments. In general,the O(3) (two > 2.58A). Consequently,B(A,) for the rate of increasein the isotropic temperaturefactors apical O(1) oxygen has a lower rate of increase of the cations increaseswith increasingcoordination with temperature. number (henceincreased M-O distances),decreasing chargeon the cation (less electrostaticattrac- tion), and increasingelectro-positivity. It is of interestto examinethe relationshipbe- tween mean bond length expansions and rate of increaseof the isotropictemperature factors, since bond length expansionscould reflectincreased ampli- Li tude of vibration of the atoms. We have plotted o dB/dT u.f o6qmna-e rather than an u,s a6,g2a,_o (Fig. to Ca 16) and our reasoningfor this follows.The majority I r.o of the room-temperaturestructures were done by o Mq other workers, and although the refinements are c Na quite good, we have o found in our wolk that the C t.z * isotropic temperature FeZ factors are extremely sensitive x Al' to data collection and refinement procedures.The -3+ positive re trend in Figure 16 suggeststhat, in general, 0.8 a positive correlation exists between bond length ci' expansionsand the increase in isotropic temperature factors, although in detail a direct correlation 0.4 doesnot appearto exist.This is consistentwith the observationthat the isotropic temperaturefactor of sJ silicon increasessignificantly with increasingtemperature whereasthe mean bond length appearsto 0 1.0 2.o 3.0 1.0 5.0 show little or no increase.This rate of increase, d-E y 16+3'- dB/dT, wasdetermined to be asfollows: Cr,0.769; dT " Si, 0.993;A1, 1.083;Fe3*, 1.L96; Fe2*, 1.535; Mg, Frc. 16. Relationship between the rate of increase of 1.619;Ca,2.301; Na, 2.982;L| 4.114 (all times equivalent isotropic temperature factors and mean thermal I0-342/oC). These figures reveal that (dB/dT)yr expansion coefficients of mean M-O interatomic distances. CAMERON, SUENO, PREWITT, AND PAPIKE

Thermal Ellipsoids soids appearsto be strongly controlled by configura- tion of the site. The orientation of the long axis of Sincethe M(1.) and M(2) cationsin the C2/c the vibration ellipsoids is very similar for all the pyroxeneslie on a two-fold rotation axis,the orienta- pyroxenes and changesvery little with increasing tions of their thermal ellipsoids are constrainedto temperature.To emphasizethe similarity in orienta- certain crystallographic directions. Symmetry re- tion, the angular relationshipsof the long axeswith quires that one of the three principal axes of the the crystallographicaxes as 400'C are listed below: ellipsoid must lie parallel to the 2-fold axis (which is parallel to the b crystallographicaxis) and the two remaining ellipsoid axes are therefore con- angle to a angleto b angleto c strained to a plane at right anglesto this direction. (jadeite) 160o 900 52" The pyroxenesincluded in this study are all highly Na (acmite) 159 90 52 ordered end membersand, with the possibleexcep- Na (ureyite) 154 90 47 tion of Li in spodumene,we haveassumed that posi- Na (diopside) 155 90 49 tional disorder is at a minimum and that the rms Ca Ca (hedenbergite) 158 90 53 displacementsobserved are mainly the result of thermal motion. The thermal ellipsoids of atoms occupying the The shortest axis of the ellipsoid is usually perpen- M( 1) site are not highly anisotropicand the orienta- dicular to the plane containing the long ellipsoid the longestellipsoid axesvaries considerably tion of axis and the b crystallographicaxis. The short axis from structure to structure. The Al atom in spodu- of the oblate spheroidof Li is oriented similarly. has an almost spherical vibration surface, mene The silicon and oxygenatoms occupy general posi- whereasthe Al in jadeite,Fes* in acmite,and Fe2* tions in the pyroxene structure and thus neither the atoms in hedenbergiteare slightly triaxial. With in- orientation nor the shapeof their vibration ellipsoids creasing temperature, these ellipsoids maintain are constrainedin any manner.?The silicon atoms roughly the same shapebut thefurms amplitudesof have triaxial vibration ellipsoidswhich are not mark- vibration increase in all directions. The thermal edly anisotropic and whose orientation varies from ellipsoid of the Cr atom in ureyite becomesmore structureto structure.In general,the oxygenthermal prolate at high temperaturesand that of the Mg atom ellipsoidsare triaxial with the longest axis lying ap- in diopside changesfrom prolate to oblate. The proximately perpendicular to the associatedSi-O atoms occupying the M(2) site have vibration el- bond. For example,the long axesof the O(1) and lipsoidswhich are highly anisotropic(Table A-11). O(2) vibration ellipsoidsare oriented at high angles The Na and Ca atoms can be describedas having to the Si-O(1) and Si-O(2) bonds,respectively, and prolatetriaxial ellipsoids;that is, the three axesare the O(3) oxygens,each of which are bondedto two two are similar in length and the third unequal,but silicon atoms, have vibration ellipsoids whose long longer. The vibration ellipsoid of the Li is much axis is also at high anglesto the Si-O-Siplane. atom in spodumene is almost spherical at room temperature,but becomesmore oblate at high tem- Discussion peratures. Ellipsoids characterizing pure thermal motion are prolate with the long axis perpendicular Dffirential PolyhedralExpansion positional to b, whereasstructures in which disorder One of the most important aspects of thermal is also a factor have oblate ellipsoids whose short expansionin pyroxenesis the concept of differential axis is perpendicularto b. The lengtheningof the polyhedral expansion, since it may be possible to ellipsoid axis parallel to b in the latter instance is correlatethe relative sequenceof rates of expansion the result of different cations occupyingslightly dif- or meanthermal expansioncoefficients (Table 4) with ferent positionsalong the b axis. This effecthas been t pointed out by Takeda (1972) and is discussedfor lt r^rtt t" emphasized that the shapes and orientations ellipsoids listed in Table A'11 were calcu- amphibolesby Suenoet al (1973). With increasing of the thermal lated for atoms occupying the positions listed in Table A'3. temperature,the lengths of the 3 ellipsoid axes in- Application of this data to atoms outside the asymmetric crease,the long axis at a slightly higher rate in most unit is correct only after the appropriate symmetry trans- of the minerals. The orientation of the M(2) elhp- formations have been applied. CRYSTAL CHEMISTRY OF SIX PYROXENES'

Tenrp 4. Mean Thermal Expansion (.C* Coefrcients X weakestbonds (Uris ov, 1967 ) . Experimentalstudies Itr) and Rate of Increase of Mean M-O Distances of Fe'z--Mg silicate systemsreveal that Fe-bearing (A/"C X ltr), silicates usually have lower thermal stabilities than theirMg-analogues, thus indicating that Fer.-O Coordinati on bonds Bond Number amean d(t4-O)/dl l,t-0 may be weaker.In this study, however,the mean

h Mg-O bond in diopside exhibits both a higher rate si -0 o.I 9za 0.312" of increaseand a higher mean thermal expansionco- Cr-0 0.533 1.?64 efficientthan the meanFe2*-O bond in hedenbergite. Fe" -0 0.781 L581 Our expansiondata for diopside (,or'- 3.33x10-5 oC-1) and hedenbergite(*, : oG1) Ar-0 1.002 l t'l'1 2.98x10-s are also consistentwith expansiondata in other Fe Fe' -0 I .048 2.23'l and Mg end membersilicates and oxides (B. Skinner,ln M9-o 1.442 2.995 Clark, 1966). For example, Na-0 t.?76 3.',I80 av : 2.64 X 10-uC-' for fayalite Ca-0 1.627 4.075 av : 3.86X lO-uc-' for forsteriteat l000oC Li -0 1.967 4.349 : aFor av 2.38X l0-5C-'for almandite(Fe'*Al) 0.192, read 0.192x l0-5 C-]. : bFor av 2.51X lO-uc-' for pyrope(Mg'9.Al) at 800oC 0.312, read 0.312x lo-5 R/oc. ay = 3.50X l0-5C-'for FeO av : 3.75X l0-uc-1for MgO at 600oC relativebond strengthsof the various M-O bonds. In general,the smaller values of both d_u,o14._eond Mechanismsol Therm,alExpansion d(M-O)/dT are associatedwith (l) decreasedco- An obvious problem that arisesas a result of the ordination number of the cations, (2) more highly differential meanM-O expansionsis how the silicate chargedcations, and (3) more electronegative cations. chains and octahedrallayers accommodatethese ex- The correlation with coordination number can be pansionswith increasingtemperature. Mechanisms understood in terms of the inverse relationship for accomplishingthis include: (1) extensionof the between bond strength and interatomic distance silicatetetrahedral chains, (2) distortionof the sili- (Badger, 1935).The type of bond is also important since mean thermal expansioncoefficients for compounds such as alkali haJidesare much higher than those for compounds such as diamond where the type of bonding is significantlydifferent. The relation with cation charge is consistentwith spectral data which show that the frequenciesfor the symmetric 320 modes of vibration decreasewith decreasingcharge on the cation. Spectrafor variouspolyhedra important J-'o zeo Fe-' in silicatestructures have been calculated by Alekhina ; and Akhmanova .lN (1971)using the structureof forsterite E 2Lo as a model. Frequenciesdetermined for the totally o symmetric stretch of groups with To(43m)symmetry c (SiO,) and on(4/m32/m)symmetry (Mg'tou, Fe,*ou, Fet*Ou, A13*06,Cr'*Ou) have been J substitutedin r60 i.z+ the equation k : 4v'r'trc', where z is frequency, Mg p is reducedmass, and c is the velocity of light. The resulting 120 force constants show an inverse relation- 0 20 10 60 80 loo t2o 110 150 ship with o,meanM-ovalues (Fig. l7). O."on y-6 X l0{5 It has been generallystated that thermal stability, Ftc. 17. Relationship between force constants and mean as characterized,bymelting temperatureor tempera- thermal expansion coeffcients of mean M-O interatomic ture of dissociation,will be controlled in part by the distances.See text of paper for explanation. 606 CAMERON, SUENO, PREWITT, AND PAPIKE cate tetrahedra,and (3) an increasein out-of-plane Tlnln 5. Tetrahedral Angle Variance for Silicate Tetrahedra in Six ClinoPYroxenes tilting, that is, tilting the tetrahedraas a result of movementof the O(2) atom farther from the bc 2* planewhich containsthe O(3) atoms.EExtension of Str ucture oo(tet) Structure oo(tet) the tetrahedralchains in the c direction (Fig. 13) involvesa rotationof 2-3 degrees;and overthe tem- Spodumene Jadei te peratureranges investigated, the increaseis linear. z+lc 18.21 z+o^c 22.89 300:c 18.34 400;c 24.24 which exhibit 600;c 24.09 The tetrahedralchains in spodumene, 460:c '118.58 S-rotations (Papike et al, L973), also straighten 760"C 8 .84 800'c 24,58 with increasingtemperature. The relatively small Ureyite anglesof the pyroxenes Acmite changesin the O3-O3-O3 z+o^c 15,79 z+o^c ,l5.3013.77 .|6.78 includedin this study contrastsstrongly with those 400;c 400;c 600:c 15.44 600-c 18.22 that occurin pigeoniteover comparabletemperature 8oo"c 16.38 intervals(Brown et al, 1.972).Structural accommG- dation is also aidedby smallincreases in the out-of- Diopside Hedenbergi te plane tilting (-0.5' for diopsideand ureyite) and z+o^c 28.44 zc2c 24.s7 400:c 27.93 4oo:c 24.63 by slight distortionsinvolving an increasein the 700:c zo .21 600:c 24.72 25.05 O(3C1 interatomicdistances. Change in '1000"c850:c 27.85 8oo:c )-O(3C2) 27.78 900:c 24.74 distortionof the silicatetetrahedra appears to be a '1000"c 24.56 relativelyminor mechanismin thermalexpansion in pyroxenesbecause the tetrahedralangle variance, = (.' - 1os.470)2/5. oo(t.t)2 .,!'' which gives a quantitativemeasure of distortion (Robinson,Gibbs, and Ribbe, l97l), varies con- siderablymore from one pyroxeneto anotherthan porting evidence that the bridging oxygens act as it doesfor eachpyroxene with increasingtempera- pivotal points during thermal expansion. ture (Table5). The volumeof the spacebetween the cationpoly- Cell Parameters hedra,determined by subtractingthe volumesof all polyhedrain a unit cell from the cell volume, in- With the exception of spodumene, mean thermal creaseslinearly with temperaturein all six pyroxenes expansion coefficients for the cell parameters (Table (Fig. 18). At room temperaturethe polyhedrain 1) decreasein the order a6 ) a6 ) a". The appar' the sodic and calcic pyroxenesaccount for 38-39 ently anomalous behavior of the a axis in spodumene percentof the cell volumebut with increasingtem- has been discussedin a previous section and its mean perature, expansionof the polyhedra account for thermal expansion coefficientis cornparablewith that 43-50 percent of the increasein cell volumes.In of the droo directions in the other five pyroxenes. spodumenethey occupy 25 percentof the cell vol- The low rate of increase for c may be related to a ume at room temperature,but at high temperatures "clamping" or "restraining" effect of the relatively they accountfor 32 percentof the increasein cell inert tetrahedral chains. The high rate of expansion volume.Thus, it appearsthat the polyhedraexpand for the b direction relative to the a can be explained partially at the expenseof the interpolyhedralspace by a consideration of "paths" through the structure (Table1). in these directions. Along the b direction a path In summary,the phenomenaof thermalexpansion through the structure can be defined which involves in pyroxenescan be attributedto expansionof the only 6- and S-coordinated sites which show a rela- cation-containingpolyhedra with concomitant ex- tively large thermal expansion rate. In the a direc- pansionof the voids betweenthe cation polyhedra tion, however, the "path" traverses both octahedral (Table 1), and rotationof the fairly rigid tetrahedra. and tetrahedral layers, and since expansion of the Isotropic temperaturefactors of the oxygen atoms silicate tetrahedra is negligible, a relatively lower and the increasein the Si-O-Si anglesprovide sup* thermal expansion is exhibited. Comparison of mean thermal expansion coefficients of individual bonds 8A study investigating the relative importance of these also shows that bonds in M(l) and M(2) polyhedra three mechanismsis in progress. increase at a higher rate in the b direction than in CRYSTAL CHEMISTRY OF SIX PYROXENES 607

thea or c directions.In all six pyroxenes,the M(l)- As has been noted in previous sections,the B O(1A2),(1B2) bondswhich have large bond-length angle of each of the six pyroxenesbehaves uniquely componentsin both the a and c directions and al- with increasingtemperature. fn the sodic pyroxenes, most none in the b direction, exhibit low mean ther- it decreasesor remains approximately the same, mal expansioncoefficients. whereasin the calcic pyroxenes,it increasesnon- Examination of the individual plots of each cell linearly. The calcic pyroxeneswith smaller B angles parametershows that the relativeexpansions in the and more kinked tetrahedral chains have shorter a, d11,oand c directions in the six pyroxenescannot M(2)-O(3C2),(3D2) distances(-2.74) than in be simply explainedby a considerationof the mean the sodic pyroxenes(-2.8A). As a result,with in- thermal expansioncoefficients given in Table 4, and creasingtemperature and concomitant straightening additional factors. such as distortion. must be taken of the tetrahedral chains, the calcic pyroxenescan into account. Mean thermal expansion coefficients accommodatean increase in the ,B angle and still for the b cell dimensiondo expandlargely as pre- maintain the S-fold coordination. The sodic pyrox- dicted from a considerationof dmean.rr-o.The larger eneswould not be able to maintain S-fold coordina- values of the mean thermal expansion coefficients tion, if both O(3)-O(3)-O(3) and p increased, for the b direction in the two calcic pyroxenesmay and thus the B angleseither decrease(acmite and be a result of the combinationof the relatively large ureyite) or remain constant(jadeite). The M(2)- dmean1r-o values of the Ca-O, Mg-O, and Fe,*-O O(3C2),(3D2) bond in jadeite is sigrrificantly bonds. shorter than that in either acmite or ureyite, but not as short as thosein diopsideand hedenbergite;therefore with increasing temperature ,[and increasing O(3)-O(3)-O(3) anglel the 8-fold coordination can be maintained with little changein the B angle. Mean thermal expansioncoefficients for the unit cell volumesincrease in the same sequenceas the dnean.&1-ovalues of. the M(I) andM(2) sites(Table 3 ). This is as expectedsince the a-e'n14-6 valueS merely representthe averageincrease in M-O dis- 276 tancesin all directionsin the pyroxenestructure. Implications with Respectto Solid So'IutionBetwee'n Pigeoniteand Augite 272 It is now known that significantdifferences exist 270 6 betweenthe M(2) sitesin high-calciumand low-cal- $ zse cium pyroxenesand betweenthe analogousM(4) U > 266 in high-calcium and low-calcium amphiboles. f sites J 9 ,"" It has also been concludedthat thesedifferences are largely responsiblefor the limited miscibility between the high-calcium and low-calcium varieties of these mineral groups (Papike, Ross, and Clark, 1969; Takeda, 1972). Takeda (1972) has discussedthe to 250 changesthat take place in quenchedsolid-solutions ,-t'-t 218 of low-calcium and high-calcium pyroxenes. He showed that when (Mg,Fe'z-)atoms are added to 0 r00 200 'oo 'oo 'ooo in- "'r.il1.;Irr:'J,lll calcium-richpyroxenes, the M(2)-O(3) bonds creasewhereas the M(2)-O(1),O(2) bonds de. Frc. 18. Variation, with increasing temperature, of the crease. In addition, he demonstrated that when volume of the space between the cation polyhedra in the calciumis addedto (Fe,Mg) pyroxenes,the M(2)- unit cells of six clinopyroxenes. The volume is determined by subtracting the volumes of all polyhedra in a unit cell O(1), M(2)-O(2) andM(2)-O(3) bondsall in- from the unit cell volume. (Abbreviations are the same crease.This increasein M(2)*O(3) bonds from as those in Figure 2.) either side of the solid-solution series leads to a CAMERON, SUENO, PREWITT, AND PAPIKE highly unsymmetricand unstabledistribution of oxy- T,rsrr 7. Comparison of Pigeonite, Diopside, and at Room and High gens around the M(2) cation. Thus, these observa- HedenbergiteM(2)4 Distances Temperature tions are consistentwith a large miscibility gap be- pyroxenes tween high-calcium and low-calcium at Bond oistance (R) 0istance (R) low temperatures.However, we do know that con- Pigeoni te gaooc siderable solid solution between these end-mem- ztoc lezr/"\ (cz/") high temperatures.It is therefore, M2-0lA 2.168 M2-01 2.176 ber types occursat t12-01B 2.140 n2-01 2.176 to the high-temperaturecalcic t42-024 2.071 M2-02 2.081 necessary compare M?-O2B 2.035 M2-02 2.081 (Fe2.,Mg)-pyroxenestructures. We now have r,r2-03A 2.460 r42-03 2.656 and r,,42-038 2.663 t42-03 3.173 the data to begin these comparisonswith the high- l',t2-03A' 3.407 t42-03 3.173 r42-038' 2.935 t42-03 2.656 (Brown temperaturepigeonite data et al,1972) and Diopside(c2lc) Hedenberqite (c?lc) (re- high-temperaturediopside and hedenbergitedata zqoc tooooc zqoc rooooo ported here). Tables6 and.7show a comparisonof r,t2-o(rA1 ), (l Br) 2.360 2.399 2.3s5 2.388 the M(2) sites of pigeonite,diopside, and heden- M2-0(2c2),(202) 2.353 2.370 2.341 2,363 r'r2-0(3cl ), (3Dl) 2,561 2.586 2.627 2.639 bergite at room, as well as high, temperature.These r42-o(3C2), (302) 2.712 2.797 2.720 2.812 tables show about equal difterences between the q!ql (1972). pigeoniteM(z)-O distancesand the averageddiop- Dataand norenclaturefrom Brown side, hedenberylteM(z)-O distancesat both room temperature and high temperature. Therefore, the increasedsolid solution betweenthese phases at high M(2) cation Thus, although essentiallysix-coordi- temperaturecannot be explainedby the fact that the nated in both room and high temperature,the nature sites become more similar through the increase of of this six-coordinatedM(2) site changes signifi- M-O distances,as has been previously suggested. cantly. Thesecomparisons are discussedin detail by What then is the reason for the significantincrease Brown et al (1972) and Papikeet al (1973). An in solid solution betweenpigeonite and augite with important aspectis that the M(2) site in the high- temperature?The answer appearsto be in the co- temperature pigeonite structure (when the tetra- ordination of the M(2) cationsin pigeonite at high hedral chainsare relatively extended) can be readily temperaturein space group C2/c comparedto that transformedinto an eight-coordinatedsite similar to at low temperature in space group P21/c. In the that of diopside and hedenbergiteby simple tetra- transition from low to high pigeonite (Brown et al, hedral chain displacement.When Ca replaces (Mg, 1972), the B tetrahedralchain undergoessignificant Fe2*) in pigeonite at high temperature, the tetra- extension and becomesequivalent to the A tetrahedral chains displacerelative to each other so that hedral chain at the transition temperature.This chain two additional oxygensare brought into the coordi- straighteningalso causesa significant changein the nation sphere.This is documentedbelow. primary coordination of the M(2) cation During Pigeonite(960"C) Hedenbergite,Diopside (1000"C) the transition,one O(3) atom movesout and a dif- 2.176(L) 23e4(L) ferent one movesinto the coordinationsphere of the M(2)4(1) M(2)-0(2)2.081 2.366 M(2H(3) 2.656 2.612 TlsrB 6. Comparisons ol M(2)-O Distances (A) in M(2)-0(3)3.173 2.804 Pigeonito and (Diopside * Hedenbergite) at Room and High Temperature Thus, with this tetrahedralchain displacementgoing from pigeonite to (diopside, hedenbergite) at high Averaqe. temperature,the M(2)-O(1) and M(2)-O(2) Pigeonite* diopside+heienbergite a (H) Hioh bonds becomelonger while the M(2)4(3) and ?4oc 9600c z4oc I ooooc 24oc remperature M(2)-O(3) bondsbecome shorter. This chain dis- M2-01 ?.154 2.176 2.358 ?.394 +0.204 +0.218 in the M?-0? 2.053 2.081 2.347 2.366 +0.294 +0.285 placementis reflectedin a rather large change -0.211 -0.206 M2-03 2.866 ?.914 2.655 2.708 B anglefrom 109.4oin pigeoniteto 105.6oin diop' side, hedenbergite.Therefore, it appearsthat as pi- Pigeonite data from Brtrn et al (1972). geoniteis raisedto highertemperatures, its M(2) site A is the difference betweenthe average diopside + hedenbergite M(2)-0 distances and comparab'ledistances and tetrahedralchain configurationchange in such a in pigeonite, manner that calcium can be acceptedmore readily CRYSTAL CHEMISTRY OF SIX PYROXENES into solid solution. In addition, it is interesting to creaselinearly over the temperatureintervals in- note that diopside and hedenbergiteare not passive vestigated. in this regardbut also changeso that (Fe2*,Mg) can 8. Mean thermal expansioncoefficients for the cell be acceptedinto solid solution. This is indicated in parametersgenerally decrease in the order ,a6) that their M(2) sitesare becomingmore six-coordi- a, ) a". The greater expansionin the b direc- nated, as discussedabove and indicated in Figure tion can be explainedby considerationof "paths" l2b. In conclusion,it is apparentthat to understand through the structure since a path parallel to a the true atomistic model for solid solution between must traverse the fairly inert tetrahedral layer pigeonite and augite, data for the high-temperature whereas a traverse parallel to b does not. Ex- structuresis an absolutenecessitv. pansion in the c direction may be restrainedby the relatively inert tetrahedralchains. Conclusions 9. Mean thermal expansioncoefficients are, in gen- 1. With increasingtemperature, the increasein mean eral, higher for the cell pararnetersof the calcic Si-O interatomic distancesof the six pyroxenes pyroxenes and are probably the result of the included in this study are not statistically sig- relatively high ,a-*uoff-o values of the Ca-O, nificant. The largest change observedwas that Mg-O and Fe2*-Obonds. in ureyite,I.6244 at24"Cto 1.6294at 600"C. 10. In general,the equivalentisotropic temperature 2. Mean M-O distances and polyhedral volumes factors of the 4-coordinatedcations increaseat of both M(1.) andM(2) sitesincrease regularly the lowest rate, whereasthose of the 8-coordi- with increasingtemperature. Rates of expansion nated cations increasethe fastest. The rate o,f for both sites are an order of magrritudegreater increasein B(A'), Cr < Si < Al < Fe8* ( than that of the tetrahedralsites. Fez* ( Mg < Ca < Na

Tenre A-1. Data Collection Information for Six Tegle A-2. Unit Cell Parametersof Six Clinopyroxenes Clinopyroxenes

TempRrature Itumber of l'4ineral ("C) r (ff) e(o) u(83) reflections Isotropic Ani sotropi c "(fi) "(ff) Tempera- used in - 14ineral tri:E-i6ct ."iin"r"nt Ra wtd.Rb wtd. R Spodumene 24 e.463(r)a8.392(r) 5 2r8(r)r1o.r5(r) 38e o(r) 300 9.468(r) 8.4r2(r) s.224(r)ro.05(r) 3eo 8(r) 460 e.473(2)8.430(r ) 5.22e(l)roe.ee(r) 3e2.4(r) Spodumene 300 656 0 042 0.045 0.023 0 029 760 e.489(r)8.460(r) 5.236(r)r09.88(r) 395.3(r ) 460 652 0.049 0 055 0.026 0 035 760 649 0.060 0.063 0.427 0 032 Jadeite 24 e.423(r) 8.s64(r) 5 223\1)107 56(r) 40r 8(r) 400 e.4so(2)8.5e4(r ) 5 233(r)r07 57(r) 405.2(r) Jadei te 24 647 0 036 0 036 0.030 0.032 600 9 45e(2)8.614(l) 5.240(r) r07.s7(r) 4a7 4(2) 400 661 0.057 0 057 0 034 0.036 800 e,483(r)8.630(r) 5.2490(4\r07.59(l ) 409.5(l ) 600 664 0 054 0.052 0.037 0.039 800 659 0.067 0.064 0 049 0.049 Acmite ?4b e.6s8(2)8.7e5(2 ) 5.2e4(1)107.42(2) 42e.1 (l ) 400 e.677(r)8.829(r) s.2e8(r)r07.33(r ) 432.1(l) Acni te 400 715 0.053 0 05t 0.030 0.032 600 9.699(r)8.8ss(1) 5 307(r)r07.32(r) 435.r(r) 600 724 0 060 0 057 0.032 0.034 800 e 71r(r)8 876(1)5.3r2(r)r07.2e(r) 437 2(1) 800 713 0.065 a 062 0.034 0.035 ljreyi te 24 9.57e(2)8.722(1) 5 267(1)107 37(r) 420 0(2) Ureyi te 400 667 0.100 0.095 o 472 0.074 400 e.597(r)8.75r(r) 5 274(r)r07 2s(1) 422 e(1\ 600 651 0.099 0 097 0.077 0.078 600 e.6r2(r) 8.770(r) 5.?79(1\ 107 2s(r) 425 0(l) Di ops i de h 400 733 0.075 0 072 0 038 0.042 Diopside 24" 9.746\4) 8.8ee(5) 5.25r(6) r0s.63(6)438.6(3) 700 721 0.082 0.075 0.039 0.039 400 9 .77611) 8.e7e(r)5.267(r) r05.e4(l)444.5(l) 850 696 0.089 0 082 0.031 0.03] 700 9.799(1 e.02e(r) 5.274(r) r06.00(t) 448.5(1) I 000 696 ) 0.122 0. I I 6 0.041 0.043 850 e.806(r) e.050(r)5.280(r) r06.00(l) 450.4(l) 1000 e.822(4)9.08r(r ) 5.285(3) r05.e8(3)453.2(5) Hedenbergite ?4 741 0.030 0.032 o 022 0.025 400 747 0.052 0.051 0 427 0.029 Hedenbergite 24 9 845(r e.024(r) 5.245(r) 104.74(l) 450.6(l) 600 725 ) 0.064 0 062 0.028 0.030 400 9.870(l) e.077(1)5.258(1) r05.01(l) 455.0(l) 800 734 0.078 0.074 0.032 0.033 600 9.884(r e.il0(r) 5.264(r)l05.rl(l) 4s7.6(l) 900 731 ) 0.085 0.079 0.034 0 035 800 9 897(l) 9.r38(r) 5.269(1)r05.r7(l) 459.9(2) 1000 709 0.092 0.088 0 042 0.044 900 9.906(r ) e.r64(l)5.273(l) 105.22(l) 461.e(l) I 000 9.916(r) 9.179(t) s.276(1) r05.28(l) 463.2(l ) an = rl lFol- lFcll/:lFol. aErrors jn bwtd. = - parentheses are I standard deviation R trw|rol 1r"l)21:wlrol2lt bcell pararet"rs from clark et al (1969).

Tnsr,r A-3. Final Pbsitional Parametersand Equivalent Isotropic TemperatureFactors (Az) for Six Clinopyroxenes

Spodumene Jadeite Acmite AtomParameter ?4oca 300oc 4600c 760oc z4oc 6000c - 4000c 8000c z40ca 4000c 6000c Boooc x 0.1099(zPo.tror(r)o.ll04(t) 0.il05(r) o.l09z(2)o.roe6(2) 0.r097(z) 0.r098(2) 0.il41(2)0.ll4l(2) 0.1142(2) 0.1146(2) 0(t) q 0.0823(z)0.0819(t) 0.0815(2) o.o8t0(z) 0.0760(2)0.0756(2) 0.0756(2) 0.0751(3) 0.0784(2)0.0778(2\ 0.0775(2) 0.0771(2) o.rqoz(ri0.1397(z) 0.13e4(3) 0.1383(3) 0.r285(3) 0.r279(3) 0.r278(3)',r.01(3) 0.1274(4) 0.r380(4)0.r368(3) 0.1364(4)',l.20(3) 0.1356(4) B" 0.24(2\'0.67(2) 0.83(2) 1.2112) 0.45(2) 0.80(2) r.23(4) 0.3s(2) 0.e3(3) 1.48(3) 0.3582(2)0.3586(2) 0.3587(2) 0.3s88(2) 0(2) 0.2s58(2)0.2545(2) 0.2537 (2) 0.2532(2) 2 0.300l(4) 0.2e8e(4)0.2s75(4t 0.2s67(s) B 0.53(3) 1.32(3) r.7r(3) 2.03(4) 0.3565(2)0.3565(r) 0.3s65(2) 0.3562(2) 0.35',r8(2)0.35r4(2) 0.35r(2) 0.3507(2) 0(3) v 0.987r(2)0.9886(2) 0.9896(2) 0.eell(2) 0.007e(2)0.0076(2) 0.0074(2) 0.0070(3) z 0.0578(3)0.0546(2) 0.0526(3) 0.0495(3) 0.0il8(4)0.0il2(4) 0.00e8(4) 0.00e3(4) B 0.4'r(2) r.05(2) r.33(2) 1.86(3) 0.s2(3) r .r5(3) r.50(3) r .82(3) 0.2e4r('r)0.2943(0) 0.2s43(l) 0.2e43(r) 0.?905(r)0.2e04('r) 0.2902(r) 0.2902(r) si I 0.0s35('1)0.0932(0) 0.0e3'r(l) 0.0e28(l) 0.0894(1)0.08er(r) 0.088e(r) 0.0888(r) 0.2560(r)0.2547(r) 0.2537(r) 0.2522(1') 0.235r(r)0.2338(r) 0.2332(l) 0.2327(1)'r.r2('r) B 0.r5(r) 0.53(r) 0.63(r) 0.e5(r) 0.2e(r)0.6s(r) 0.er(r) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 [()) 0.ec66(1)0.905e(1) 0.9054(r) 0.9044(l) 0.9058(t)0.s050(r) 0.9043(r) 0.9039(2) 0.8e89(r)0.8e79(r) 0.8974(r) 0.896e(r) 0.2500 0.2500 0.2500 0.2500 0.2s00 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.r7(r) 0.57(r) 0.7r(r) r.07(r) 0.37(r) o.70(2) o.eo(2) 1.12(2) 0.3i(r) 0.78(r) r.04(r) r.30(r) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 M(2) 0.2752(e)0.2758(7) 0.27s0(e) 0.2769(r0) 0.3005(2)0.3006(2) 0.3007(2) 0.3008(3) 0.zsse(?\0.3000(2) 0.300'l (3) 0.3002(3) 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0. 2500 0.2500 0.2500 0. 2500 r.1(1) 2.re(8) 2.83(il) 4.r3(r4) l.oo(2) l.e3(3) 2.48(4) 3.06(5) 0.e8(3) 2.24(3) 2.s9(4\ 3.s8(s)

ooata from c'lark et al (1969). bErrors in Darenthesesare one standard deviation. CRYSTAL CHEMISTRY OF SIX PYROXENES 6tr

TasrB A-3. Continued

Ureyite Diopside Hedenbergite Atm Parareter 24oca 4oooc 6oooc 240ca 4oooc Toooc 85ooc tooooc 240c 4oooc soooc Soooc goooc r ooooc 0.il40(3)0.il39(4) 0.1 t40(4) 0.1156(r)0.il60(2) 0.1164(2) 0.il61(2) O.ll64(2) 0.il97(r) 0.il95(2)c.ile4(r) 0.ile5(2)0.lre3(2) 0.il96(3) o(l) s 0.079r(3) 0.0794(4)0.0782(4) 0.0873(r) 0.0868(2)0.0864(2) 0.0853(2) 0.0864(2) 0.0e04(2)0.0898(2) 0.0894(2) 0.08e2(2) 0.088e(3) 0.0890(3) 0.r374(5)0.t369(8) 0.1362(7) 0.1422(2) 0.1424(4\ 0. 1423(4) 0. l4t 8(3) 0.1423(4) 0.rs25(3)0.r51e(3) 0.rsr4(3) 0.rsr7(4) 0 r506(4)0.r502(5) B 0.42(4) r.04(6) 0.94(6) 0.33(2) r.0s(3) r.s2(3) 1.65(2) t.e5(3) 0.58(2) r.08(2) r.3e(3) r.5e(3) r.er(3) 2.02(4)

0.35e9(3)0.3607(4) 0.36| (5) 0.36r (r ) 0.3611(2) 0.3604(z)0.3607(2) 0.3607(3) 0.3627(2\0.3619(2) 0.3620(2) 0.36r8(3) 0.3617(3) 0.36r7(3) o(2) s 0.2583(3)0.257r(s) 0.2573(5) 0.2s00(r ) 0.2486(2\0.2477 (2) 0.2468(2)0.2464(3) 0.2461(2) 0.2449(2)0.2444(2) 0.2436(2) 0.2429(3) 0.2428(31 0.3037(6)0.30r2(9) 0.3025(9) 0.3i80(3)0.3r63(4) 0.3149(4) 0.3144(3) 0.3143(5) 0.3228(3)0.32r1(4) 0.3200(4) 0.3193(5) 0.3r88(s) 0.3r73(6) B 0.s5(4) 1.32(7) 1.44(7) 0.46(2) r.3e(3) r.96(4) 2.23(3) 2.62(4\ 0.77(2) r.46(3) r.84(3) 2.30(4) 2.4e(4') 2.76(6)

0.353r(3)0.3s2r(4) 0.3s19(4) 0.3505(l) 0.3s0r(2) 0.3495(2)0.3492121 0.3487(2) 0.3502(r) 0.34e7(2)0.3494(2) 0.3490(2) 0.3486(2) 0.3484(3) 0(3) s 0.010s(3)o.o0e9(5) 0.0094(5) 0.0r76(r)0.0r65(2) 0.01s7(2) 0.0tst(2) 0.0145(3) 0.0r98(2)0.0r80(2) 0.0172(2) 0.0r64(3) 0.0r62(2) 0.0r60(3) 0.0066(6)0.0062(9) 0.0074(8) (4) (4) 0.9953(2)0.ee6]'t.22(3) 0.9971 0.9e75(3)-0.0024(4)0.9e32(3) 0.9949( 3) 0.ee6e(3)0.997 6(4) 0.e973(4) 0. 9976(5) B 0.53(3) r .26(6) r.29(6) 0.39(2) r.7r(3) 1.86(3) 2.14(4) 0.65(2) r.20(3) r.s2(3) r.86(3) 2.03(4) 2.?2(5) (l 0.2921 ) 0.2920(1) 0.2921(2\ 0.2852(r) 0.2862(r ) 0.2861(t ) 0.2861(1 ) 0.2859(t) 0.2878(l) 0.287s(r) 0.2875(r)0.2812(1) 0.2872(r) 0.287r(t ) slv 0.0918(l ) 0.0e18(2)0.0912(2) 0.0933(r) 0.0929(l ) 0.092s(l) 0.0e2s(1) 0.0924(t ) 0.0924(r)0.092r(r) 0.oer8(r) 0.0916(l) 0.915(r) 0.091s(l) 0.2333(2)0.2328(3) 0.2324(3) o. 2293(1) 0.2294(1 ) 0.2294(1 \ 0.22e3 (I ) 0.2292(1 \ 0.2326(1\ 0.2329(t) 0.2329(1) 0.2324(1) 0.2327(r ) 0.2327(2) B 0.35(2) 0.77(3) 0.83(3) 0.228(7)0.80(r) 1.1212\ l.t8(i) 1.37(t) 0.3e(r) 0.75(r) 0.e6(r) r.r7(r) 1.29(2) r.4l(2)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Mll ) 0.9076(1) 0.e072(t ) 0.e066(l) 0.9082(l) 0.9072(l) 0.906e(2) 0.9066(l ) 0.9063(2)0.907s(0)0.s064(r) 0.e0s7(r) 0.9054(r) 0.90sr(r) 0.e049(r) 0.2500 0.2500 0.2500 0.2500 0.2s00 0.2s00 0.2s00 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 B 0.42(r) 0.81(3) 0.84(3) 0.26(r) 0.e6(2) 1.40(2) 1.s7(2) t.89(2) 0.44(l) 0.e3(r) 1.25(r) r.s4(]) 1.74(2\ l.e6(2) 0.0 0.0 0.0 0.0 0.0 0.0 (2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 r,4 ) c 0.3008(3)0.3001 (4) 0.3010(4) 0.30r5(1) 0. 3008(l ) 0.3005(t) 0.3003(t) 0.3ool(l ) 0.3003(r)0.2e93(r) 0.2990(r) 0.2989(r) 0.2987(l) 0.2e84(t) 0.2500 0.2500 0.2500 0.2500 0.2s00 0.2s00 0.2500 0.2500 0.2s00 0.2500 0.2500 0.2500 0.2500 0.2500 B 0.77141 L9l (7) Z.44(8\ 0.s14(7) t.4l (2) 2.14(2\ 2.37(2\ 2.83(2) 0.66(r) r.40(r) r.85(l) 2.3112\ 2.63(21 2.87(3)

TasLr A-4. Si-O Interatomic Distances(A; in Six Clinopyroxenes

Spodumene Jadeite Acmite

Atoms z4oca 3oooc 46ooc 7600C 24oc 4oooc ooooc Soooc z4oca 4oooc 6oooc 80ooc si-0(r) r.638(2)br.64',r(1) 1.640(l) 1.643(l ) r.637(2)r.636(2) r.637(2) r.638(2) r.62s(211.63r (2) 1.633(2) 1.632(2) 'r.5e4(2) 'r.5e8(2) -0(2) r.s86(2)',r.585(r)1.s84(2) r.584(r) r .5e3(2)r.5e4(2) r.5e6(3) r.598(2)r.598(2) r.5s8(2) 't.62e(2) -o(3cl) 1.622(2',)1.624(1) 1.624(2) 1.624(1) 1.62e(211.62e(21 1.630(2) r.637(2)r.535(2) r .64r(2)1.642(21 ',t -0(3c2) t.bzblz) r.626(r) t.627\211.628(1) 1.539(2).642(21 1.643(21 1.64?(2) r.645(2)r.64e(2) r .647(?)1.647(2)

mean 1.618 1.619 1.619 1.620 l .52s r.625 1.626 1.627 | .628 1.628 1.630 1.630

Ljreyi te Diopside Hedenbergi te

Atoms 24oca 4oooc 6oooc z4oca 4oooc Toooc B5ooc I O0ooc z4oc 4oooc 6oooc Boooc aoooc I OOOoC ',r.603(2) si-0(r) r.625(4)r .635(4) r.638(4) r.602(2)r.601 (2) r.600(2)1.603(2) 1.602(2) l .60r(l ) r .602(2\1.603(2) r.605(2)I .603(3) -0(2) r .586(3)l .s86(4)1. se8(4) r.58s(r) r.s86(2)1.s86(2) 1.583(2) 1.586(2) 1.s8s(2)r.582(2) r.584(2) r.583(2) 1.582(2) r.582(3) ',l 'r.666(2) -0(3cr) r.640(4)1.53s(4) I.631 (5) r .654(2 ) .671(2) 1.570(21 1 .670(2) 1 .671 (2) r.67r(2) r.566(2)r.66s(2) 1.658(2) r.66e(3) -0(3c2) r .545(4)r.646(s) r.6s0(s) r.687(2)1 .687(2) 1.688(2) 1.68e(2) 1.6e0(2) r .585(2)r.684(2) r .688(2)r.689(2) r .687(2)1.687(3) '1.635 mean 1.624 1.627 1.629 1.635 i .636 1.636 l 536 1.637 1.635 I .635 1.636 1.635

'oata from Clark et a] (1969). oErrors in parenthesesare one standard deviation. 612 CAMERON, SUENO, PREWITT, AND PAPIKE

Tr,nlr A-5. G-O InteratomicDistances (A) in SilicateTetrahedra of SixClinopyroxenes

Spodumene Jadei te Acmite

Atoms z4oca 3oooc 46ooc Toooc z40c 4oooc 6oooc 8000c 24oca 4oooc- 6oooc Soooc o(r )-o(2) 2.742Q\b2.747(?) 2.747(2)2.752(2) 2.778(2\ 2.780(2) 2.782(3) 2.786(3\ 2.742(3\2.750(2) z,l)J\5l a.tao\Jl -0(3cr) 2.635(2)2.640(2) 2.63e(2)2.640(21 2.637(2) 2.634(2\ 2.635(2')2.634(2\ 2.650(3\2.647(2) 2.652(3')2.647(3\ -0(3c2) z.ocr(J,z.ocrlzl 2.650(212.651(21 2.639(2)2.638(2\ 2.639(2')2.635(3) 2.654(3\2.657(2) 2.6s7(3)2.655(3) o(2)-o(3cr) 2.658(2) 2.655(2\ 2.653(2)2.650(2) 2.646(2)2.644(2\ 2.642(2) 2.645(3) 2.65r(3) 2.649(3)z.o?ttJ, z.o3J(J/

-0(3c2) t.aJa\z I z,aJa\z l z.]JO\Z I Z.aJt \Z l 2.57e12) 2.sgr (2t 2.582(3) 2.582(3) 2.58s(3)2.583(3) 2.583(3)2.s82(3)

U(JLI ]-U\JLZ' 2.6r6(r) 2.6re(r ) 2.620(11 2.622(1) 2.614(l) 2.619(1)2.622(1) 2.627(1) 2.65r(r)2.652(1) 2.657(r)2.65e(r) mean 2.640 2.641 2.641 2.642 2.649 2.649 2.650 2.652 2.656 2.656 2.659 2.659

Ureyi te Diopside Hedenbergite

Atoms z4ocu 4oooc 6oooc z4oca 4oooc Toooc 85ooc looooc 24oc 4000c 6oooc Soooc 90ooc I0000c

0(r)-o(2) 2.736(5)2.74e(5) 2.764(6) z.tJl\z) z.tJo\Jl 2.732(3)2.737 (2) 2.738(5)2 72)12\ ) 72t12\ ? 72a(1\ 2.723(3)2.726(3) 2.723(4) -0(3c1) 2.644(5)2.647(5) 2.64r (6) 2.678(2)2.683(3) 2.679(3)2.680(2) 2.679(5) 2.687(2) 2.6e2(2)2.588(2) 2.689(3\2.687 (3) 2.685(4) -0(3C2) 2.636(7) 2.642(6,)2.646(5) 2.6e5(3)2.68e(3) 2.686(3)2.68s(2) 2.686(5) 2.696(2)2.693(2\ 2.695(2) 2.6e2(3)2.6s2(3\ 2.6s2(4) 0(2)-0(3ct)2.657(4) 2.652(6)2.660(6) 2.658(212.664(2) 2.667(3) 2.666(2)2.672(5) 2.658(2)2.663(2) 2.66r (3) 2.663(3)2.663(3) 2.661 (4)

-0(3c2) 2.s83(4)2.586(6) 2.590(6) 2.570(2\2.57s(2) a.)t6\Jl a,atllz ) z.tta\a l 2.574(2) 2.570(3)2.574(3, 2.570(3)2.570(3) 2.s75(4) 0(3ci)-0(3c2) 2.643(5)2.643(1 ) 2.645(l) 2.644(3)2.650(r ) 2.65?(11 2.654(1 ) 2.656(1) 2.647(r')2.649(r) 2.65r (l ) 2.65r(r ) 2.653(',r) 2.6s4(r ) mean 2.650 2.653 ?.658 2.663 2.666 2.666 2.667 2.668 2.664 2.665 2.666 2.665 2.665 2.565

llata trom Clark et al (r e6e). b- LrrorS tn thesesare one standard deviation

TrsI.B A-6. Interatomic Angles (') in Tetrahedral Chains of Six Clinopyroxenes

Spodumene Jadei te Acnite ^"0^a Angles 3oooc 46ooc 76ooc z4oc 4oooc 6oooc Soooc 24oca 4oooc eoooc Soooc 'r18.9(r) 0(r)-si-0(2) il6 s(r)D il6.7(r ) il6.8(r) il7.0(l) il8.6(r)il8.e(r) il9.0(r) il6.4(r)r'16.8(r) 1r6.9(r) il7.1(r ) o(r)-s'j-o(3cr ) 107.e(r)r07.e(r) r07 s(r) r07.8(r) i07.7(l)r07.6(r) r07.6( r) r07.4(r) r08.5(r)108.3(r) r08.2(r)r07.e(r) 0(r)-si-0(3c2) r086(1) r08.5(6)r08.4(t) 108.3(r) 107.4(r) r07.2(1 ) r07.2(r ) r06.e(r ) r08.3(l)r08.2(r) r08.2(r)r08.r(r) 0(2)-si-0(3cr ) rr.9(r) ilr.7(r)1'n.6(r) ilr.4(1) il0.4(8)r10.3(r ) ri0.2(r) r10.2(r) il0.r(r) il0.r(r)r0e.e(r)r10.0(1) 'r04.3(r 0(2)-si -0(3c2) r042(r ) r043(r ) ) r04.4(r) r05.9(r) r05.8(r ) r05.8(r) r05.8(r) 105.6(l)r05.4(r) r05.5(r)'105.4(1) 0(3cr)-si-0(3c2) 1073(r ) r07-4(r) r07.4(r ) r07.5(r ) r06.3 (r ) r06.4( r ) r06.5( r ) r06.8 (r ) r07.7(r)r07.8(r) r07.8(1)r07.e(r) mean I09.4 r09.4 I 09.4 109.4 I09,4 109.4 I09.4 I09.4 I09.4 I09.4 I09.4 I09.4 'r74.6(r) 03c2-03c1-03c2 r70.5(2)r7r.6(1) 172.3(2) 173.4(2) r74.8(2)r7( t/r\ t7q ?/?\ 174.0(2\174.2(2\ 114.4(2\174.7(2) si-03-si 13e.0(r)r3e 3(r) r3e.5(l) 13e.7(l) r39.r(r)r39.4(r) r39.5(r) 13e.8(2) 13e.4(2)r3e.5(1 ) r39.6(r ) r3e.8(r )

Ureyite Diopside Hedenbergi te Angles 24oca 4oooc oooot 24ocu 4oooc Toooc 8sooc r ooooc z4oc 4oooc 6oooc Soooc goooc I ooooc 0(r)-si-0(2) 116.8(2)117 .2(2) 117.4(21 r8.3(r)r8.3(r ) il8.r(r)r8.4(r) il8.3(l) il7.4(r)il7.3(r) il7.4(r) il7.4(r)il7.s(r) ili.6(2) 'r'r0.0(r 0(r)-sj-0(3cr) r08.r(2)r07 s(2) r07.8(2) r0.r(r) |0.1(l) ) r0e.e(r) r0e.e(1) ilo 6(r) ro.6(r) il0.6(r) il0.7(r)il0.3(r) il0.3(2) '109.7 'roe.5(1) 0(r)-si-0(3c2) r07.4(2)r07.3(2) r07.1(2) rr o. o( r ) (r ) roe.5(r)ros.4(r ) r't0.2(r)rr0.0(r) r0e.e(r) r0e.7(l) r0e.7(r ) r0e.7(2) 'r0.0(r 0(2)-sj-0(3cr) ilo.s(2) il0.6(2) 1r0.9(2) 10e.8(r)r09 8(r) ) il0.0(r) il0.2(r) r09.7(r)r0s.e(r) tnq ort\ ilo.r(r) ilo.r(1)loe.e(2) o(2)-si-0(3c2) r06.r(2)r06 3(2) r05.8(2) r03.5(r)r03.7(r) r03.e(i)103.7(r) r03 6(r) r03.7(1)r03.7(r) r03.7(l) r03.5(r) r03.7(r) r03.9(2) o(3cr)-si-o(3c2) r07.1(2)r07 r(2)'t07.4(2) 104.2(r)r04.2(1) r04.3(r) r04.4(1) r04.4(r) r04.3(r)r04.3(r) |04.4( r ) r04.5(r)r04.5(r) r04.5(r) ',109 't09.3 nean 109.4 1094 1094 1093 1093 109.3 109.3 3 I09.3 r09.3 I 09.3 109.4 109.3

03c2-03c1-03c2 1121(2J 172.5(4J172.8(4) 166.4(r) r67.r (2) 167.7(2) 168.2(2\168.5(2) r64.5(r) r65.8(2) r66 4(2) 167.1(2) 167.2(21167.3(3) 'r36.0(r si-03-si r3e.7(2)r40 2(3) r40.3(3) r35.93(e)r36.30 ) r36.8(1)r37 0(r) r37.3(1) ) r364(r ) r36.8(r) r37.r(r) r37.3(2)137.4(2) uDutu fro. clarl, et al (1969). bErrors in parenthesesare I standarddeviation CRYSTAL CHEMISTRY OF SIX PYROXENES 613

Tnsln A-7. M(IFO InteratomicDistances (A) in SixClinopyroxenes

Spodurene Jadeite Acmite -. M(l) = a1 It1(l)= n1 M(l) = FeJ'

Atoms 24oca 3oooc 46ooc 76ooc z4oc 4oooc 6oooc goooc z4oca 4oooc 6oooc Soooc r,r(l)-0(rAr),(rB1) r.997(2)b2.005(r) 2.0r2(r) 2.023(r) f .e95(2)2.008(2) 2.017 (2\ 2.022(2) z.ros(z)2.\20(21 2.'tzs(2) 2.136(2\ -0(rA2),(182) 1.s43(2)1.e46(r) r.s48(r) r.s4e(r) r.940(r)r.943(2) r.e46(2) 1.948(2) 2.02e(2) 2.02s(2)2.032(2\ ?.033(2) -o(2cl), (2Dr) r.8'r8(2)r.823(r) 1.825(2) r.830(2) r.8s2(2)r.8s7(2) r.8s7(2) 1.858(3) r.936(2)r 937(2) r.94r(2) 1.943(2)

mean 1.919 1.925 t.928 1.934 1,929 L936 I.940 L943 2.025 2.029 2.034 2.037

Ureyite Diopside Hedenbergi te = t'l(l) = s' r'l(l) = I'is fit(l) Fezr 24oca 4oooc 6oooc z4oca 4oooc Toooc 85ooc looooc 24oc 4o0oc 6oooc Soooc aoooc looooc M(r)-0(rAr),(rBr)2.039(3)2.052(4) 2.054(4) 2.1r5(r)2.r3s(2) 2.147(2\ 2.150(2) 2.160(2\ 2.163(l)2.178(2) 2.187(2) 2.193(21 2.te8(21 2.206(3) -0(rA2),(r82)2.00e(6)2.0r2(4) 2.0r3(4) 2.065(3)2.067(2\ 2.070(21 ?.o6s(2) 2.015(2\ 2.140(r)2.r37(2) 2.r35(2) 2.138(2) 2.133(2) 2.133(3) -o(2cr),(2Dr)r.e47(3)1.e4e(4) r.e47(4) 2.0s0(r)2.063(2) 2.076(2) 2.08r(2) 2.086(3) 2.087(l)2.100(2) 2.102(21 2.110(2) 2.116(2) 2.116(3)

rean 1.998 2.004 2.005 2.077 2.088 2.098 2.100 2.107 2.130 2.138 2.141 2.14'1 2.149 2,152

aD"ta f.o. clark et al (1969). "Errors in Darenthesesare one standarddeviation.

T,lsr,BA-8. G-O InteratomicDistances (A) in the M(1) Octahedraof Six Clinopyroxenes

Spodurene Jadei te Acnite

z4oca 3oooc 46ooc 76ooc z4oc 4oooc 6oooc Soooc z4oca 4oooc 6oooc Soooc 0lAt-01 81 2.694(4)2.705(2')2.714(3) ?.727 (3t 2.724(3')2.742(3') 2.751(3)2.760(4) 2.798(4)2.809(3) 2.82r(4)2.83s(4) 02cl-020] 2.787(4) 2.78612')2.787(3) 2.791 (3) 2.787(3')2.788(4) ?.782(412.782(5) 2.s41(4)2.s32(4) 2.931(4)2.929(5\ (2)0rA1-C2Cr 2.661 (21 2.675(2)2.683(2) 2.6e8(2) 2.710(2')2.727(?\ 2.741(3)2.746(3\ 2.860i3)2.877(3) 2.89',r(3)2.899(3) (2)olAr-0rA2 2.e51(2) 2.953(r)2.954(l) 2.ess(r) 2.er8(r) 2.e2r(r)2.926(2')2.928(21 ?.98s(2\2.984(2) 2.988(?')2.988(2) (2)0rA2-02Cr 2.705(2)2.714(212.71s(2) 2.727 (2) 2.682(212.685(?\ 2.684(3)2.587(3) 2.8re(3)2.820(3) 2.822(3)2.822(3) (2)orA2-02Dr 2.697 (2) 2.708(2')2.716(2) 2.72s(2) 2.820(2\2.838(2\ 2.84e(3)2.858(3) 2.s64(3)2.s7e(3) 2.992(3)3.004(3) (2)o1At-0r82 2.504(3 ) 2.50i(2)2.5r0(3) 2.5r2(2) 2.462(3')2.46e(3) 2.476(3)2.475(4\ 2.63e(4)2.638(3) 2.642(4\2.644(4) nean 2.710 2.717 2.722 ?.730 2.725 2.734 2.740 2.744 2.856 2.861 2.869 2.873

Ureyite : Diopside Hedenbergite

Atoms 24oca 4oooc Goooc 24oca 4oooc Toooc gsooc looooc z4oc 4oooc 6oooc Soooc goooc tooooc 0tAl -0r Bl 2.775(6)2.785(8) 2.795(7 \ 2.781(3)2.799(4) 2.8r4(4) 2.8rs(3) 2.82r(4) 2.7e8(3)2.808(3) 2.8r6(3) 2.81e(4) 2.826(41 2 .837(5) 02cl-0201 2.8e7(7 | 2.880(8)2.883(e) 2.e81(3) 2.e84(4)2.ee8(4) 2.9s2(4\ 2.ee6(s) 2.e90(3)3.008(4) 3.005(4) 3.011(s) 3.0r2(5)3.ooe(7) (2)0rAr-02c'l 2.815(5)2.84r (6) 2.835(6) 3.0r3(2)3.04s(3) 3.0i0(3) 3.08s(2) 3.099(3) 3.r13(2)3.137(2) 3.150(3) 3.165(3) 3.r78(3)3.r86(4) (2)0rAr-0rA22.e75(5\2.e81 (4) 2.e75(4) 3.05r(3)3.060(2) 3.064(2) 3.068(2) 3.074(2) 3.088(2)3.0e3(2) 3.0e5(2) 3.0e8(2) 3.oee(2)3.r03(3) (2)or42-ozcl?.7e7(5\ 2.78s(6)2.7e8(6) 2.878(3\2.892(3) 2.900(3) 2.90s(2) 2.912(3) 2.s40(2)2.e51(2) 2.e53(3) 2.e61 (3) 2.963(3)2.9s7(4) (2)01A2-0201 2.e04(6\2.921 (6) 2.92s(5) 2.e7e(3)2.eee(3) 3.02r(3) 3.026(2) 3.035(3) 3.o57(2)3.074(2) 3.otll (3) 3.093(3)3.099(3)3.',I0s(4) (2 )0r Ar -0r 82 2.617l7 t 2.631(8\ 2.624(7| 2.8r3(3)2.821(4) 2.829(4) 2.826(3) 2.839(4) 2.976(3\2.s7 0(31 2.s68(41 2.971 (4) ?.965(4')?.971(5) mean 2.824 2.833 2.833 2.936 2.952 2.965 2.969 2.978 3.012 3.022 3.026 3.034 3.037 3.041

aData from clarki et a'l (1969). DErrors in theses are one standarddevlation. 6t4 CAMERON, SUENO, PREWITT, AND PAPIKE

TAsLEA-9. InteratomicAngles (") in M(1) Octahedrain SixClinopyroxenes

Spodumene Jadeite Asite

Atms z4oca 3oooc 46ooc 76ooc 240c 4oooc 6oooc 24oca 4oooc 6oooc 0tA2,0182 r74.s(r)or74.0(l) r73.5(r) r72.8(t ) r70.8(r) r70.r(r) r69.8(r) 169.3(2) r68.7(1) 157.s(r ) 167.5(r) r67.0(r) (2)0rAr,02Dr r67.8(r)r68.0(l) r68.0(r) r68.0(r ) r66.2(r)166.1(r) r56.0(r) r65.e(r) r67.3(',r) r6i.3(r ) 167.2(t)167.2(1') 0lAt,01 Bl 848(l) 84.e(r)84.8(r)84.8(r) 86.r(r)86.r(r) 86.0(1) 86.1(r) 83.r(1)83.0(r) 83.0(l)83.r(r) 'r00.0(r) 02ct,0201 9e.7(r)ee.6(r) ee.4(r) e7.6(r)e7.3(r) e7.0(l) e6.e(2) e8.s(1)s8.4(r) e8.r(r)e7.9(r) (2)0rAr,02c1 88.3(r) 88.5(t)88.6(1) 88.7(t) 8e.5(r)8s.7(r) 8e.e(r) 90.0(1) 8e.e(r)s0.2(l) e0.4('r)e0.4(r) (2)0rAr,0rA2 s7.0(r) e6.7(r)e6.s(r)e6.r(r) e5.7(r)e5.4(r) es.2(r) s5.0(r) e2.3(r) er.e(r) sr.8(r)el.5(l) (2)0rAr,0r82 78.e(t) 78.8(1)78.7(r)78.5(t) 77.s(r)77.3(l) 77.3(r) 77.r(',r) 7e.2(r)78.s(r) 78.8(r)78.7(r) (2)0rA2,02C1 e2.o(l) e2.l(t) 92.2(1)92.3(1) e0.o(r)8e.s('l) 8e.8( r) 8e.8(r) eo.6(r)so.6(r) 90.5(r) 90.s(r ) (2],01A2,0201 e1.6(r) er.8(r)e2.0(t)e2.4(t) e6.r(1)e6.6(r) e7.0(r) e7.3(1) e6.i(1)e7.3(r) 97.7(r)98.r(r)

Ureyite Diopside Hedenbergite z4oca 4oooc g5ooc 6oooc 24oca 4oooc Toooc z4oc 4oooc 6oooc Soooc aoooc 10oooc 't73.4(2) 'r77.8(r) 01A2,0182 173.3(2)172.4(?\ r77.1(1)176.7(l) 176.5(l) t76.4(l) r79.0(r)r78.r(r) r77.6(r)ri7.4(r) li7.r(r) r77.0(r) (2)0tAl,02Dl r6e.2(1)l6e.I(2) l6s.2(2) r7r.3(r)r7r.3(t) 171.3(t) 171.3(l) lil.3(l) 173.0(11172.7 172.6(1)172.6(t) r72.5( r) r72.s(r) 0tAl,0rBt 85.8(2)85.5(2) 85.8(2) 82.2(r)8r.e(r) 8r.e(1)8r.8(1) 8r.6(r) 80.6(r)80.3(r) 80.2(l)80.0(r) 80.0(r) 80.0(r) 02cl,0201 e6.r(2) e5.3(3)e5.s(3) e3.3(r)e2.6(r) e2.4(r) er.e(t) e].8(2) e1.5(r) e'l.5(r ) er.3(r)er.0(r) 90.8(2) e0.5(2) (2)0lAt,02c18e.8(2)e0.5(2) eo.2(2 ) e2.6(r)e3.l(l) e3.3(l)e3.6(l) 93.8(1) e4.r(r)e4.3(r) e4.5(l)94.7(1) 94.e(r) e4.e(r) (2)01A1,01A2e4.6(r) e44(2) e4.0(2) e3.8(l)e3.5(r) e3.2(r) e3.i(t) e3.l(1) er.7(r)er.6(r) er.5(r)91.4('r) er.4('r) e'r.3('r ) (2)0rAt,018280.6(r) 80.7(2)80.4(2) 84.6(l) 84.3(t) 84.3(i) 84.1(l) 84.2(l) 87.5(t)87.0(l) 86.7(l) 86.6(t) 86.4(l) 86,4(l) (2)01A2,02C1 8e.8(2 8e.5( ) 2) 8e.e(2 ) e8.8(r) 88.e(t) 88.s(l) 88.8(t) 88.8(t) 88.r(l)88.3(l) 88.4(r) 88.4(l) 88.4(l) 88.2(l) (2)0rA2,0201 e4.4(21ss.0(2) e5.2(2) e2.8(r)e3.t(t) e3.6(l)e3.6(l) e3.7(l) 92.6(r)93.0(t) e3.3(r)s3.s(r) e3.6(l) e3.e(l) aData f"om Clark et a't (']969). "Errors in parenthesesare one standard deviation.

Tnsr.r A-ll. Magnitudesand Orientations of the Principal Axes of Thermal Ellipsoids in Six Clinopyroxenes

r'4(r ) r,4(2)

rms ^ rns rms ElIipsoid amplltude Angle (") of ri wjth amplltude Ang]e (") of ri with amplitude Angle (o) of ri with Pyroxene oC axrs, ri t,x A a b t ti a b c r ab "i u l Spodumene 244 0 034(3)" 36(8) s5(6) ee(r4) 0.04r(4) 80(221 e0 30(22\ 0.11(r) 17(27) 90 s3(27| 0.042(2) 77(14) e6(r2)r7r(r4) 0.048(3) 10(?2\ e0 120(22) 0.12(r) 90 180 90 0.05r(2) 57(7\ 144(6\ 8e(il) 0.05r(3) e0 0 e0 o.r3(1) 107127 ) 90 3 0.074(r) 7e(12)7e(6) 33(13) o.08r(2) 88(r6) 90 22(16) o.I 5e(7) 77(20r, e0 33(20) 0.077(l) 27(6) 68(4)r22(r3) 0.08s(2) r78( r6) 90 68(r6) 0.',r66(8) 90 180 90 o.oe3(1)66(3) r55(3) e3(2) 0.038(2) 90 0 90 o.175(7 ) 16i(2r) 90 57(21) 460 0.082(r) r43(r2)ror (6) 37(r4) 0.092(2) r42(34) 90 32(34) 0.r82(e) 75(35) 90 0.08s(r)lre(r3) r'r0(4) r26(r4) o.oe4( 2) r30( 34) 90 120(34) o.re2(9) 90 180 90 o.roo(r) 6e(3)r57(3) 87(3) 0.097(2) 90 0 90 0 194(9) r63(34) 90 53(34) o.roo(r) 55(5) 67(2) 62(6) 0.r12(r)63(ro) 90 46(ro) 0.206(e) 7o(9) eo 4o(9) 0.'r06(r) 46(5) 77(3) r5r(6) 0.118(1) 26(r0) 90 135(10)0.222(1ol 90 180 90 0.r22(r) 65(2) r53(2) eo(2) 0.il9(r) 90 0 90 0.2s5(r0)r6o(e) eo 5o(s) 0.04e(2) 88( 3 ) 86( 4) 20(3) 0.055(3) eo(4) 90 r8(4) 0.08e(3) 75(2) e0 32(2) 0.068(2) 75(7) r6(7) ee(5) 0.068(3) 90 180 90 0.097(3) 'r90 180 90 0.078(2) r6(17)r06(7) r08(3) 0.080(2) 0(s) 90 r08(4) 0.r44(2) 65(2) e0 58(2) 0.078(2) 7e(4) 73(5) 33(5) o.o8r(2) 8o(4) 90 28(4) o.r 25(3 ) 70(r) 90 38(r) 0.08e(2) 5e(6) 3e(6) lre(6) 0.096(2) eo r80 90 0.r 30( 3) 'r60(r)90 180 90 o.oee(r) 34(5) 124(5) r04(4) 0.r04(2) r70(4) 90 62(4) 0.202(2) 90 s2(r)

I o.o8e(2) 73(4) 7r(4) 40(4) 0.0e5(2) 72(4) 't8090 36(4) o 133(3) 70(r) 90 37(r) 2 o.r02( r ) 49(e) s2(e) 128(5) 0.'108(2) 90 90 o.]5o(3) 90 lB0 90 3 0.r08( r) 46(e) r36(8) ee(6) 0.r 16(2) r62(4) 90 54(4) 0.232(3)r60('l) 90 53(',l ) I o.oe3(2) 87(3) 8r(4) 23(4) 0.r00(3) 82(3) 90 26(3\ 0.r 48( 4) 7s(r) 90 33(r) 2 0.112(21 58(7) 34(7) loe(4) 0.r20(3) 90 180 90 0.165(4) 90 180 m 3 o.r2r (2) 33(7) r23(7) r02(3) 0.134(2) 172(3) 90 64(3) 0.25e(4) r6s(r) 90 57(l) CRYSTAL CHEMISTRY OF SIX PYROXENES 615

Tner.BA-10. M(2)-Olnteratomic Distances(A) in Six Clinopyroxenes

Spodumene Jadeite Acmite tl(z) = ri !(2) = Na 14(2)= Na u z|ocu 3oooc 46ooc 76ooc z4oc 4oooc 6oooc Soooc 24oc qoooc 6oooc Soooc q2)-0(tAr),(tBl) 2.r05(6) 2..t1e(5)2.12216\ 2 146(7\ 2.3s6(2\2.370(2) ?.377 (2\ 2.387(3) 2.398(3)2.413(2) ?.424(3\ 2.435(3\ -il)r)\ Itnt\ 2.278(2)2.281(2)2.281 (2) 2.286(2\ 2.412(2)2.421 (2\ 2.430(2)2.437 (3\ 2.415(2\2.42212) 2.431 (2\ 2.437(2) -0(3cr ), (30r) 2.2s116)2.268(5)2.286(6\ 2.296(7\ 2.366(2)2.37 4(2) 2.377 (2) 2.382(3\ 2 430(3)2.438(2) 2.446(3) 2.45't(3\ -UIJLZ', IJUZ' 3.144(5)3.r29(4)3.124(5) 3.t03(6) 2.740(2)2.753(2) 2.761(2) 2.768(3\ 2 83r(3) 2.838(2)2.842(2\ 2.84e(3) mean of 6 2.211 2.223 2.230 2.243 rean of 8 2.469 ?.480 2.486 2.494 2.518 2.528 2.536 2.543

Ureyite Diopside Hedenberoite lil(2) = xq M(2)= 63 Itl(2)= ca

Atoms 24oca 4oooc 6oooc zloca 4oooc Toooc gsooc looooc 24oc 4000c 6oooc 8oo0c aoooc I 0o0oc 14(2)-0(rAr),(lBt)2.378(4)2.381 (s) 2.403(s)2.360(1)2.377(2) 2.3s1(2) 2.3s4(2) 2.3es(2) 2.35s(1)2.364(2) 2.373(2) 2.379(2) 2.386(2) 2.388(3) -0(2c2),(2D2)2.38s(7)2.400(s) 2.3ee(4) 2.353(3)?.357(2) 2.366(2) 2.368(2) 2.370(3) 2.34r(l)2.348(2) 2.352(2) 2.35s(2) 2.357(3) 2.363(3) -0(3cr ), (3Dr) 2.424(4)2.440(5\ 2.43s(s) 2.56't(2) 2.571(2) 2.s78(2) 2. s80(2 ) 2. 586(3) 2.627(2\2.628(21 2.628(2) 2.62s(2) 2.636(3) 2.63e(3) -o(3c2),(3D2) 2.764(4)2.783(5\ 2.790(s) 2.717('t)2 74e(212.773(2) 2,784(2\ 2.7e7(2) 2.720('t)2.7s6(2) 2.778(2) 2.7s4(2) 2.803(2) 2.8t2(3) nean of 6 nean of 8 2.489 2.501 2.507 2.498 2.514 2 527 2.532 2.538 2.524 2.533 ?.539 2.546 2.551

*Data from Clark et al (1969). "Errors in parenthesesare one standarddeviation

TnsrB A-ll, Continued

0(l) 0(2) 0(3) rms rms rms ElI ipsoid nng'le(o) (o) ampl Angle (o) of ri with -C^ amplitude of ri with amplAtude Angle of ri with itude axis. r. A .' t l a b ai a b c abc "i . " I Spodumene 244 0.042(5)" 6l(14) 86(r2) 4e(r5) 0.045(5) r32(6) r38(6) 75(5) 0.043(6) e6(r2) 58(s) 26(5) 0.05i(5) 't15(25)40(23)64(29) r34(r8) 0.07e(8) 52(8) r25(8) r36(12) 0.061(s) r5r (6) 76(6) 83(r2) 0.064(4) ?7(?el 73(22) 0.0e2(3) 66(e) rlr(8) 50(12) o.tot(3) r08(4) l 53(4) 66(3)

o.oie(3) 38(r'r)87(5) i2(il ) 0.083(3) s6(3) 35(2) e6(3) o 084(3) roo(8) 66(2) 25(2\ 0.08e(2) 55(il) i2(6) r55(ro) o.r 20(2) 5r(4) l ro(4) r50( 5) o.oee(2) r65(6) 84(4) 84(7) 0.105(2)r03(5) r8(6) 74(6) 0.138(2) s8(4) il7(3) 6r(5) 0.152(2) ror(2) r55(2) 65(r) 0.086(3) r8(7) 8r(4) es(8) o.o8e(3) 52(2\ 38(2) ee(3) o.oeo(3) r12(5) 65(r) 25(2) 0.r0l(3) 77(8) 77(8)r66(8) o.r 34(3) 54(4) l l4(3) r4e(5) 0.1r4(3) r55(5) 8e(3) e5(5) 0.Il7(3) 102(4) r6(7) 76(8) 0.156(2) 58(4) rl8(3) 6l(5) 0.172(?)r02(2) r55(r) 65(r) 760 0.1o0( 3) 28(4) 85(3) 82(4) 0.r0e(3) 56(2) 35(2) s4(2) o.]]o(3) 104(5) 6s(1) 25(1) 0.r23(2) 65(5) 7r(4) r60(4) 0.r 64(2) 4e(4) rro(3) r48(5) 0.12e(2) 161(4) 85(3) 88(5) 0.r45(2) r03(3) 2o(4) 7r (4) 0.r80(2) se(s) il7(3) 5ei6) o.204(2)r02(r) rs4(r) 6s(r) Jadeite ?4 0.053(4) 68( il ) e3(s) 40(il) 0.073(4) 73(5) 32(13)70(ls) 0.058(5) e2(5) 78(s) 20(5) (4 0.078 ) 22(12)9t(32)130(r'r) 0.084(4) 83(8) 64(r5)r53(r3) 0 0er(3) r50(34)',r4e(3r6r(33) 82(n) 0.083(4) 88(30) 3(r ) 88(22) o.r04(3) r62(5) 72(6) 72(7) o.oe5(3) r20(34) ) 72(7) 0.088(4) 52(12\ 87(e) 56(r 3) 0.086(4) 66(3) 3r( 4) 80(5) oosr(4) e6(s) 65(3) 2B(3) 0.099(3) 48(13)60(r0)r36(13) 0.il7(3) e5(6) 68(5) t4e(6) 0.il3(3) ',rr68(6) 83(5) 82(5) 0.1r3(3) il5(e) 3r(ro) 67(9) o.r40(3) r56(3) 6e(4) 6r(6) o.r 37(3) o0(6) r54(3) 64(3)

0.0e4(4) 33(6) d6( 5,, / 5t b, 0.r0r(4) 64(3) 28(3) 88(4) 0.0e4(4) e7( 5) 64(3 ) 27(3) 0.r r6(3) 64(8) 57(14)r4s(r3) 0.138(3) er(7) 7e(5) 15e(i) o.'r24(3) r66(5) 8r(4) 84(5) 0.r26(3) r08(8) 33(r4) 5s(l4) o.r 57(3) r54(3) 64(3) 6e(8) 0.r56(3) r03(4) r53(3) 63(2) o.r oi (4) 68(e) e6(5) 40(e) 0.il2(5) 68(3) 2s(4) 86(5) o.roo(5) 104(4) 68(3) 23(3) 0.rzs(4) 30(I 0) 67(r0)124(r0) 0.r46(4) er(6) 78(5) r58(6) o.r4r(4) r56(6) 77(6) e3(5) 0.r4r(4) 109(10)24(10\71(7) 0.r75(4) r58(3) 6e(3) 68(6) 0.r57(4) rce(7) r54(4) 68(3)

dData frm Clark et al (1969). DErrors in parenthesesare one standard deviation. 6r6 CAMERON, SUENO, PREWITT, AND PAPIKE

T,rnlr A-11, Continued

si M(2) rms rms rm5 Ellipsoid (o) (") Pyroxene oC amplitude Angle of ri with amplitude Anqle(") of ri with amplitude Angle of ri with axts, ri I ri ' bc bc r. a b 1 I Acmite ?qa I o.o4o(3) 35(3) 77(r0) i3(3) 0.0s4(2) 38(2) 90 69(2') 0.086(5) 90 o 90 2 0.0s4(3) ee(8) r3(r0) e7(5) 0.0s8(2) s0 180 90 0.086(5) il8(3) eo r34(3) 3 0.08r(2) r25(3) 87(4) r8(3) 0.088 128(21 eo 21(2) o.149(3) Is2(3) 90 44(3) 400 I 0.082(2) 23(6) 75(21 8e(7) o.oer(r) 3s(s) e0 73(s) 0.r33(3) 6e(?) eo 38(2) 2 0.oer(I) 7?(7) 8e(4) r78(5) o.lor(l) ss(s) on tA?lq\ 0.r 5l (3) 90 r80 90 3 0.r07(r) 76(3)r65(2) el(4) 0.106(r)eo 090 0.212(3) r5e(2) eo 52(2) 0.0e8(r) s5(21)75(3) 55(22\ 0.r07(r)ss(7) e0 52(7) 0.148(3) 70(r) 90 38(r) 0.10](r) 37(21\85(6) 144(22) 0.il4(r) 35(7) 90 142(7\ 0.174(3) 90 r80 90 0.122(r) 77(3\164(2\ 85(3) 0.r22(l) 90 090 0.248(3) 160(r) eo 52(r)

0.'r05(r ) 29(5) 73(2) 84(5) 0.r'r8('r) 43(3) 90 6s(3) 0.r5e(3) 7o(r) 90 37(l) 0.il6(l) 67(5) er(3) ri4(s) o.r3r(l) 47(31 90 155(3) 0.185(3) 90 180 90 0.134(r) 74(?) r63(2) 88(3) o.r3s(r) 90 090 o.2i1(3) 160(r) e0 53(l) Ureyi te 244 0.043(s) 8e(4) 83(6) 20(4) 0.054(3) 9r(3) 90 16(3) 0.057(8) 7s(3) eo ??f1\ 0.07r(3) 78(r 3) r4(12)100(7) 0.075(2) e0 180 90 0.080(5) 90 r80 90 0.08r(3) r2(r3)r02(r3)r07(5) 0.086(2) I (3) 90 r06(3) 0.140(5) 165(3) 90 57(3) 0.078(4) 40(17) 50(t7)103(s) 0.087(3) 90 090 0.r r4(7) 90 0 90 0.087(4) 50(r7) r40(r7)'r03(5) 0.087(3) r80(3) 90 72(3\ 0.r 39(6) r r5(4) 90 r37(4) 0.125(3) 8e(3) e2(3) r8(3) 0.1?6(21 so(3) eo r8(3) o.2or(5) r54(4) eo 47(4') 0.087(4) r58(11)rr(r2) 57(6) 0.oer(3) 90 090 0.129(7) 90 0 90 0.l0r (4) 71(12\rs7(r2)t08(9) 0.098(3) r80(6) 90 73(5) 0.r 52(6) il4(3) e0 I ?Ol?l 0.r'li(3) i9(5) es(8) 30(7) o.il e(3) eo(5) 90 r7(s) o.230(6) r56(3 ) eo 4e(3) Diopside 244 0.04s(2) 2t(t7l 72(20) 85(sl 0.0s2(3) s6(ro) eo 4e(r 0) 0.066(r) 66(r) 90 3e(t) 0.0s3(2) '105(8)67(2olrs5(r7)r06(1r) 0.0s5(3) eo 180 90 0.068(l) 'r56(r)90 r80 90 0.05e(r) 107(il) r7(r'r) 0.055(2) r46(r0) 90 41(10) 0.l03(r) eo 50(l) 0.08e(2) 45(i) s4(8) 77(3\ o.r03(3) 63(5) 90 43(6) o.]0e(2) so o 90 0.0e7(2) 123(7\ 35(8) e4(4) 0.105(3) 90 r80 90 o.ils(2) ils(r) eo 139(l) 0.1r3(r) ll8(3) s4(4) r3(3) o.r2r ( 2) 153(6) e0 47(61 0.r6e(1) r55('l) so 4e(r)

Tlsr.B A-11, Continued

)l M(t) M(2) rms rms rms El'li psoid ampl nngte(o) of ri with amplAtudeAngle (o) of ri with amplitude Angle(") of ri with -C,. itude x axis, ri ri rabc tt a b b I " Diopside 700 o.r04(r)2?(31 6e(3) e8(2) o.r 28( 2) 42(13) 90 64(r3) 0.r39(l) 90 0 90 114(r) 90 l40(l) 0.r2r(r)68(3) r55(4) r08(6)',r9(s) 0.135(2) 49(r3) 90 r5s(13) 0.r43(r) o.r3r(r)e2(3) i04(5) 0.r37(2) 90 0 90 0.203(r) 156(1) eo 50(1)

0.r1i('l) 22(2r) 6e(lo) ee(37) 0.t28(2) 8l(4) '18090 25(4) 0.r43(1) 72(1') e0 34(r) 0.rr8(r) 75(2e)r03(r2) r56(r5) 0.147(2) 90 90 0.r47( r ) eo ]80 90 0.'l3r(r) 72(3) 154(3) 78(3) 0.147(2t r73(r0) 90 67(lo) 0.2r8(r) 162(r) e0 s6(l) 1000 0.r22(r ) 22(5\ 74(3) er( 5) o.r 4l ( 2) 7/(5) 90 20fq\ 0.r54(r) 7r(r) eo 35(l) 0.r32(r ) 7r(5) r08(6) r62(6) 0.160(2) 90 180 90 0.r 62('r ) 90 r8o 90 0.14r(r) 8o(3) r56(5) 72(6) 0.r5r(2) 168(s) 90 0.240(r) 16r(1) eo s5(r) Hedenbergite24 0.05s(2 ) r02(ll) 5o(8) 4o(8) 0.070(l) 90 0 'r90 o.o7e(r) 6s(2') e0 3s(2) o.07r (2) r68(r5)r0r(2r) 80(21) 0.075(l) 12o(12) 90 3s(r2) 0.084(r) 90 180 90 0.073(2)84(33)r3i(r3) 52(l',l) 0.078(l) r50(12) 90 4s(r2) o.ro8(r) r5e(2) eo 55(2) 0.0e3(r) 85(24) 68(r3) 2s(2s) o.r03(l) 90 42(3\ o.'r10(l) 68(r) 90 37(l) r80 90 0.oes(r) r 52(e) ',r45(7)r r4(r 3) 63(27) o.lo8( I ) 90 180 90 0.rr9(l) 90 0.r02( l ) 52(8) 80(7) o.ils(r) t53(3) 90 48(3) 0.164(r) 158(r) e0 s3(r) ',r2(e) 0.'r04(1) e8(10)80(5) o.lr7(r) 75(?l 90 0.r25(r) 7r(r) eo 34(l) r80 90 0.109('l) r57(7) r'r2(5) 80(ro) 0.r27(l) 'r6s(2)90 180 90 0.136(l) 90 o.'r17('r)6e(6) r55(6) 83(4) 0.r33(r ) 90 60(2) o.r90(r) r6'r(8) so s6(r) 0.rr3(r) 4e(7) 54(3) 6s(8) o.r2e(1) 71(2t 90 a^l )\ o.l4o('r) 7o(r) so 3s(l) ',r55(8) 90 180 90 0.r2r (1 ) sr(7) ',r53(3)83(6) o.r40('l) 90 180 90 0.150(r) 0.r30(r) 66(4) 8s(s) 0.r4e( l ) r6r (2) 90 ro( z, 0.2r3(r) 160(r) 90 55(l)

0.r2r(r) 83(ro) 78(5) 26(',il) 0.r34(l) 72(2) '18090 ??f2l o.r5o(r) 70(r) eo 3s(l) 0.r26(r) 23(6) 70(6) lls(ll) 0.152(l) 90 90 o.]s8 (r ) 90 l8o 90 0.t37(1)58(s) r55(s) 87(4) 0.rs8(l) 162(2) 90 57(2) 0.228(r) r60(r) eo s5(l) 0.124(2) se(e) 74(4) l8(5) o.]4s(l) 73(2) 90 3?(2) 0.153(2) 7o(r) eo 3s(l) 180 90 o.r32(2) r5e(7) e9(5) 8r(8) 0.',r60(l) 'r53(2)90 180 90 o.r 68( 2) 90 0.r44(?) 84(6) rdl(4) 75(4) 0.157(l) 90 58(2) 0.240(2) 160(r) eo 5s(l) CRYSTAL CHEMISTRY OF SIX PYROXENES 6r7

Tenu A-11, Continued

o(t) 0(2) 0(3) rms rms rms ElI i psoid ampl (o) (") (") 0C itude Angle of r- with amplitude Angle of ri with amplitude Angle of ri with Pyroxene A axls, ri A -rabcA tr bc ti . b c l Acmite 24u 0.04r(8) 37(5) 82(lr) 71(5) o.o4s(8) 6r(6) 30(7) 8e(4) 0.054(6) 41(r6) 87(re) 67(rs) 0.069(5) eo(ro) 12(r0)r02(e) 0.081(5) 132(7) 6r(7) roe(8) 0.074{5) 63(20)r40(8) r25(r3) 0.092(4) 127(5) 80(9) ??(6\ o.r07(4) 124(7\ 8r(s) re(8) o.l0r (4) r r8(6) r30(7) 44(7)

0.084(4) 24(7| 82(4) 85(e) o.oe7(4) 4e(3) 4r(3) e5(3) o.ror (4) 5(243)e2( r40)102(305) 0.r03(3) 72(e) 70(5) r60(5) 0.r4r(3) 5e(36)roe(33) r56(53) 0.r 02(4) 83(251)1r5(5)154(e2) 0.r 32( 3) r0s(4) 22(5) 70(5) 0.r44(3) 56(34)r25(22) 66(54) 0.r52(3) e4(3) r55(3) 66(3) 0.r02(4) 25(r0)88(4) 83(to) 0.r0(4) 55(3) 36(3) e4(3) o.ilo(4) 88(r3) 7r(3) 27(e) 0.il 7(3) 66(ro) 77(s) 155(7) 0.r5e(3) 73(r4) e5(r0)r75(e) 0.122(3) r70(3) 8r(3) 7416) 0.r48(3) e8(4) r3(5) 77(5) 0.r67(3) 40(8) r2s(3) 88(r8) 0.r73(3) ee(3) r5e(2) 6e(2) 800 0.r08(4) 23(5) 83(3) 85(5) 0.il7(4) s4(2) 37(2) e2(3) o.r 26(4) e5(r8) 68(3) 25(8) 0.r35(3) 7r(6) 71(5) l6l(5) 0.r77(3) 59(40)r03(3r) r60(54) 0.r35(3) r73(r3)87(7) 80(r6) 0.r63(3) r03(3) 20(5) 7t( 5) 0.r7e(3) 51(37)r24(r5) 70(55) 0.r87(3) e5(3) r58(2) 68(2)

Ureyi te 24 0.047(r0) e2(r0)t0l(lt) le(8) 0.062(e) 72(10) 48(22) 57(24\ 0.047(ro) e2(8) 7ol7) 2617) o.o7e(7) r33(32)135(31) 87(15) 0.076(7) 7s(r3) 5l(22)141(23) 0.088(6) r64(22)76(20) 80(r3) 0.088(6) r37(32)47(31) 7l(s) o.r06(6) r56(8) 56(8) 73(e) 0.r02(6) r06(22)r55(r3) 67(7)

0.087(e) r6r(t4)r08(r4)70(6) 0.07'r(rr ) 65(6) 2e(6) 84(4) o.ro5(B) r43(r6) s4(rs)67(8) 0.1r2(7) 72(14)r62(r4)e7(12) o.r30(7) 25(6) il5(6) 107(8) o.126(1) r27(r6)l3e(r7) 93(tb, 0.r40(7) 86(7) eo(n ) 22(7) 0.r68(7) e4(7) r03(5) re(8) o.r 44(7 ) er(r2)r07(r4) 23(e) 600 0.072(lr) 162(9)r02(8 ) 60(7) o.o8o(n) 62(6) 28(6) e4(s) 0.r08(9) il6(8r) 47(31)47(r0) 0.1r8(7) r08(e) 56(2e)r30(23) 0.144(8) 3r(8) il6(7) r2r(r5) 0.il3(8) r54(80)106(58)e4(s7) 0.r28(7) e2(12)37(28) 55(24) o.r6s(7) 78(r3)ror(8) 3l(r5) 0.1s7(7) e4(8) 132(6) 43(6) a 0iopside 24 0.osr(4) 30(s) e8(e) 77(8) 0.050(4) 62(3) 30(4) 87(s) 0.058(4) il3(27) qqaA\ ??/a\ 0.06e(3) 65(r4)45(35)r32(34) o.o7e(3) r03(7) 72(6) r46(8) 0.064(3) 156( 26) e6(r 5) e8(23) 0.073(3) r05(17)46(35) 44(34) o.oe4(3) r4e(5) 67(4) 56(8) 0.085(3) e7(6\ r48(5) se(s) 0.0e6(4) 23(6) e2(7) 83(6) o 0ee(4) 68(3) 28(4) Br(4) o.r 0(4) r47(45)63(2e) 58(25) 0.ile(4) 80(e) 2r(r6)il0(r6) 0.r37(4) 8e(8) 73(5) r57(8) 0.il3(4) r23(45)r24(2s)rr8(28) 0.r29(3) ilr(6) 59(r5) 22(',t5) 0.r55(3) r58(3) 6e(4) 6e(8) 0.146(3) e6(4) 134(5) 45(5)

TesLEA-11. Continued

0(2) 0(3) rms rms rms (") ElI i psoid amplitude Angle (o) of ri with amplitude Anqle (") of ri with amplitude engle of ri with Pyroxene axls, ri A l r, bc abc abc I Diopside I 0.]l2(3) 7(4\ 88(4) ee(4) o.ile(4) 63(2) 2e(2) 87(3) 0.r2r(3) r38(e) 67(5) 43{s) 2 0.149(3) 84(4) 76(40)r63(33) 0.r65(3) 88(7) 79(s) 162(8) o.r3e(3) 132(e)r'r5(5) il3(7) 3 0.r 52(3) e3(6) r4(4r ) 76(4r) 0.r82(3) rs3(2) 63(3) 73(8) 0.r76(3) eo(3) r4s(3) s6(3) 850 r 0.12',r(3) 1s(4) eo(3) e1(4) 0.r27(3) 64(21 2e(2) 85(3) 0.120(3) |ro(s) 64(2) 27(2) 2 0.146(2) 75(5) 7e(6) r6e(6) 0.r66(3) 85(3) 7e(3) 164(3) 0.r45(3) r5e(4) e4(3) e5(4) 3 o.164(2) e3(3) n(6) 7s(6) 0.203(2) 154(2) 64(2) 75(4) 0.r88(2) 96(2) ls3(2) 63(2) I 000 0.132(3)re(s) 8e(3) 87(5) n r?ql?\ 6qlt\ 33(2) 78(3) o.r2e(3) ile(5) 63(2) 32(3) o.r60(3) 7r(5) 84(8) r73(8) o.'186(3) 83(s) 72(4) r60(5) 0.l s6(3) r50( s) e7(4) r03(s) 0.r76(3) 93(4) 6(8) 84(8) 0.2r3(3) r54(2) 54(3) 74(5) o.2oo(3) e8(3) r52(2) 62(2)

Hedenbergite 24 o.073(4) 25(r0)100(7) 82(r2) 0.080(4) 64(4) 32(5) 7e(8) 0.076(4) r2(r6) 62(6) 30(s) 0.086(3) 70(r2)r02(r3) r67(r3) 0.09e(3) 80(8) 75(8) r65(8) 0.086(4) rs8(r6) r05(r0)e2(14) 0.097(3)r04(7)r64(il ) 7e(r3) 0.r1s(3) 28(5) il8(5) r0r(8) 0.r08(3) 86(6) r48(5) 60(5) 400 o.roo(3) 21(6) roo(s)86(7) n ln?/1\ 67f?\ 27(3) 83(4) o.oe8(4) r08(8) 6r(3) 30(3) 0.12r(3) 71(7) er(rB)r76(7) o.r4'r (3) 8i(8) 80(s) r68(7) 0.115(3) r60(8) e2(5) e5(7) 0.r28(3) 8r(7) r0(5) e0(r6) 0.r 57(3 ) 25(4) il5(3) roo(8) o.rso(3) e7(4) rsr(3) 6r(3) 0.l14(3) 24(7) e3(4) 8r(7) o.r r 6(3) 66(2) 2e(3\ 80(4) o.r08(3) r07(5) 64(2) 26(2) o.r 32(3) 66(7) 76(8) r63(8) 0.r5s(3) 8r(s) 76(4) r65(4) 0.r36(3) r63(s) e6(4) er(s) o.i 4e(3) 94(s) r4(7) 76(8) o.r8r(3) 2s(3) r'r5(2)ror(5) 0.r67(3) e2(4) t53(2) 64(2) o.r re(3) 20(5) e7(3) 86(5) o.l30(4) 64(2) 2e(2) 8s(3) 0.r'l8(4) r02(6) 64(2) 26(2) 0.r46(3) 7r(5) 85(6) r73(6) o.r77(3) 85(6) 78(4) r64(7) 0.144(3) r67(5) eo(4) 88(5) 0.16e(3) 86(3) 8(4) 84(6) 0.r98(3) rs3(3) 63(3) 75(8) 0.r90(s) e6(3) r54(2) 64(21

0.131(3) l3(5) aq/i\ 01/a\ 0.t4r(4) 66(2) ?7(3) 85(4) o.ll8(4) ilo(4) se(2) 32(2\ 0.157 (3) 78(6) 87(8) r76(7) 0.r77(3) er(5) 77(4) r5e(5) 0.15s(3) r59(4) e7(3) e5(4) 0.r7s(3) 95(4) s(5) 87(8) 0.20e(3) 156(2) 67(2) 70(5) 0.198(3) 95(3) r48(2) 58(2)

0.r 33(4) 29(8) 8e(3) 76(8) 0.r46(5) 63(3) 33(3) 8r(5) o.r 30( 5) e8(6) 62(2) 2e(3) 0.r54(4) 6t(8) 88(5) r66(8) 0.r88(4) 86(6) 73(s) r60(6) 0.l58(4) 112(6) 9l(4) 83(6) 0.'l88(4) 92(41 2(s) 88(5) 0.2re(4) rs3(3) 63(3) 72(6\ 0.206(4) e3(4) r52(2) 62(2) 618 CAMERON, SUENO, PREWITT, AND PAPIKE

References Perrre, J. J,, Mercoru Ross, eNo Joen R. Crmx (1969) ALEKHTNA,L. G., eNn M. V. ArnueNove (1971) The Crystal-chemical characterization of clinoamphiboles vibrational spectra of structural groups in orthosilicates. based on five new structure refinements. Mineral. Soc. Geochem. Int. E, 504-510. Amer. Spec,Pap.2, 117-136, T. BADcER,R. M. (1935) The relationship between the inter- C. Pnewrrr, S. SurNo, lNo M. Cerrarnow (1973) nuclear distances and force constants of molecules and Pyroxenes: Comparisonsof real and ideal struc- its application to polyatomic molecules, I. Chem. Phys. tural topologies. Z. Kristallogr. 69, 254-273, 3,710-7t4. PREwrrr, C. T., eNo CnenrEs W. BunNneu (1956) The jadeite, BnowN, G. E., euo G. V. Grsss ( 1970) Stereochemistry crystal structure of NaAlSLOe. Amer. Mineral. and ordering in the tetrahedral portion of silicates. Amer. 51,956-975. (1971) Mineral. 55, 1587-1607. RortNsoN, K., G. V. Gmrs, eNo P. H. RrssB quantitative C. T. Pnewrrr, J. J. Perrrn, eNo S. SueNo (1972) Quadratic elongation: a measure of distortion polyhedra. 172, A comparison of the structures of low and high pigeonite. in coordination Science, 567-570. (1966) l. Geophys. Res.77, 5778-5789. SrrNNEn, B. J. Handbook of Physical Constants. Soc. pp.76-96. S. SurNo, lNo C. T. Pnr.wrrr (1973) A new Geol. Amer., ( single-crystal heater for the precession camera and four- Suvrn, J. R. 1971) Protoenstatite: a crystal-structure circle diffractometer. Amer. Mineral. 58, 698-7M. refinement at 1100"C. Z. Kristallogr. 134, 262-274. -, (1972) BunNrHu, Cnenrrs W., Joer* R. Clem, J. J. Plrxr, eNo ero Csenres W. BunNneu The crystal low Earth C. T. Pnpwrrr (1967) A proposed crystallographic no- structures of high and clinohyperstheae. menclature for clinopyroxene structures. Z. Kristallogr. Planet. Sci. Lett. 14, 183-189. 125, 109-119. SusNo, S., M. Cetrenou, I. J. PAprKE,eNo C. T. Pnnwm (1973) High-temperature crystal chemistry of BusINc, W.R., eNp H. A. Levy (t964) The effect of tremolite. thermal motion on the estimation of bond lengths from Amer. Mineral. 58,649 664. H. (1972) diffraction measurements. Aaa Crystallogr. 17, 142-146, Trrnoe, Crystallographic studies of coexisting high pressure CnnrstrNseN, A. N., lNo R. G. HlzBr.r, (1967) The crystal aluminan orthopyroxenes and augite of 77, 1. structure of NaIn(SiOe)". Acta Charn. Scand. 21, 1425- origin. .I. Geophys. Res. 5798-581 (JRUsov, 1429. V. S. (1967) Chemical bonding in silica and Int. Clmx, JoeN R., D. E. ApprsDrAN,AND J. I. Plprr_e (1969) silicates. Geochem. 4, 350-362. BURNHAM(1959) Crystal-chemical characterization of clinopyroxenes based VEBLEN,D. R., eNo Cs.mrrs W. The (abstr.) on eight new structure refinements. Mineral. Soc. Amer. crystal structures of hedenbergite and ferrosilite Spec.Pap.2, 3l-5O. Can. Mineral, lO, 147. (1928) Doyln, P. A., eNo P, A. TunNBn (1968) Relativistic WemnN, B,, lNo W. L. BRAGc The structure of Hartree-Fock X-ray and electron scattering factors. Acta diopside CaMg(SiOs)a. Z. Kristallogr. 59, 168-193. Crystallogr. L24, 39U397. Fneeo, R. L., eNo D. R. Pancon (1967) Refinementof the crystal structure of johannsenite. Amer. Mineral. 52, Manuscript receiued,Nooember 6, 1972; 709-720. accepted lor publication, lanuary 30, 19'73,