Effects of Compositional Variation on the Crystal Structures Of

American Mineralogist, Volume 73, pages 798-808, 1988

Effects of compositionalvariation on the crystal structuresof pyroxmangite and rhodonite

LrNoa R. hncxxny Corning GlassWorks, SullivanPark FR-51, Coming, New York 14831,U.S.A. Cn.q.RLrs W. BunNrr.qlr Department of Earth and Planetary Sciences,Harvard University, Cambridge,Massachusetts 02138, U.S.A.

Ansrnlcr As adjacent members of the pyroxene-pyroxenoid polysomatic series, constructed of fragments of the wollastonite (W) and pyroxene (P) structures,pyroxmangite (WPP) and rhodonite (WP) possessvery similar structureswith comparablesite distortions and cation ordering patterns. The two structuresrespond quite similarly to cation substitutions. Oc- tahedral and tetrahedral distortions generally lessenand the silicate chains straighten as larger cations substitute for smaller. Both structures exhibit limited stepwiseordering of cations over the octahedral sites,with large cations preferentially entering the sites on the edgesof the octahedralbands. Detailed structural responsesto cation substitution generally parallel those observedin pyroxenes. The characteristics of the inner octahedral sites strongly influence several structural parameters,including the sizesand configurations ofthe outer polyhedra. There is, however, no well-defined mean cation size limit that differentiatesrhodonite from pyroxmangite from pyroxene. Structural parametersfor both rhodonite and pyroxmangite structures changesmoothly with composition and produce only minor structural adjustments.These adjustments,however, produce localized higher-energystructural configurationsthat cluster at the boundariesbetween the W and P modules of the structures.Such configurations include a strongly kinked tetrahedral chain, short Si-Si distances,and a highly distorted octahedron. In contrast, the P-P boundary in pyroxmangite is virtually distortion-free. Concentrationsof strain energyat W-P boundaries likely play a major role in controlling phasetransformations in this system.

INrnooucrroN structed by appropriately stackingthese wollastonite (W) Pyroxenesand anhydrous pyroxenoids have the gen- and pyroxene (P) modules, thereby deriving wollastonite eral chemical formula MSiO3, where M most commonly (W), rhodonite (WP), pyroxmangite (WPP), ferrosilite III is Ca, Mg, Fe, and Mn. Their structuresconsist of single (WPPP), and pyroxene (P). The structures of rhodonite chains of silicate tetrahedra arrangedin layers parallel to (n: 5) and pyroxmangite (n : 7) areillustrated in Figure (100) that alternate with layers containing bands of di- l. Bustamite, another three-repeatpyroxenoid, is based valent cation octahedra;oxygen atoms are approximately on a different linkage ofoctahedral and tetrahedral layers closest packed (Prewitt and Peacor, 1964). The various and thereforeis not a member of this series.This concept structuresdiffer in the periodicity of the tetrahedralchain is discussed more fully by Koto et al. (1976) and by and in the correspondingarrangement of the octahedrally Thompson (1978). coordinated cations. In this manner they constitute a A number of workers have addressedthe observed structural seriesthat has been classifiedaccording to the temperature,pressure, and compositional stability limits number n of tetrahedrabetween ofsets that intemrpt py- that exist for each pyroxenoid structure (e.g., Akimoto roxene-likechain configurations(Liebau, 1962).Pyrox- andSyono, 19721'Ito,l972;MareschandMottana, l9T6; ene representsone end member of this structuralseries: Ohashi and Finger, 1978;Brown et al., 1980).Akimoto a pyroxenoid with no offsets(n: oo). and Syono (1972) determined that a pyroxenoid of When the entire structural configuration of octahedral MnSiO. composition undergoessuccessive polymorphic bands and tetrahedral chains is considered, these struc- transformations from rhodonite to pyroxmangite to cli- tures are seento constitute a polysomatic series,which is nopyroxene and ultimately to garnet-type structures as defined as a group of distinct structures constructed of pressureincreases at constanttemperature. A similar trend different numbers of slablike portions of end-member is observedwith respectto composition: As mean cation structures-in this case,of wollastonite and clinopyrox- size decreases,structures with increasing n predominate. ene. All members of the pyroxenoid seriesmay be con- These observations raise an intriguing question: Can 0003-004x/88/0708-0798$02.00 798 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE 799

TreLe 1. Crystal-structurerefinements of pyroxmangiteand rhodonite

Symbol Composition Samole source Reference Pyroxmangites CWB-P (Feo&Cao,3Mno@Mgoor)Sioo Apollo11 site. Burnham(1971) Roth-P (MnolsMgo6s)SiOg Synthetic-- D. Rothbard(unpub.) FH-P (Mno51Mgo€)Siog Synthetic" Fingerand Hazen(1978) ntro (Mno@FeooTMgo @Cao@)SiO3 Japant Ohashiand Finger(1975) AJ-P (Mnor?Mgoozoaool)SiOg Japantf Pinckneyand Burnham(1988) Nar-P MnSiO. Synthetic+ Naritaet al. (1977) Rhodonites FH-R (Mno6rMgo ss)SiO3 Synthetic.- Fingerand Hazen(1978) MT-R (Mno665Mgo 315)Si03 Synthetic.- Murakamiand Tak6uchi(1979) Peac-R (Mno75Mgo rscao 1o)SrO3 Balmat,NY$ Peacoret al. (1978) OF-R (Mnosr Feo oTMgo o6Cao ou)Siog Japanf Ohashiand Finger(1975) Nar-R MnSiO3 Syntheticf Naritaet al. (1977) ' Lunarmicrogabbro. " Synthesizedby J. lto. t Taguchimine: regionally metamorphosed manganese ore deposit. tt Aiiro mine:mineralized manganese ore lens in chert. + Synthesizedby Akimotoand Syono(1972). $ Metamorphosedsedimentary evaporite sequence.

the phaserelationships be readily understood in terms of though this correlation was briefly examined by Mura- structural attributes identifiable in each phase?The sta- kami and Tak6uchi (1979), the exact nature ofthe rela- bility of micas, for example, is related to the geometric tionship has not been defined. Nor has there been any fit of the octahedral and tetrahedral sheets(Hazen and systematic study, similar to the plT oxene studies of Ohashi Wones, 1972, 1978); if the octahedral layer becomesso et al. (1975) and Ribbe and Prunier (1971), regardingthe large that normal tetrahedral rotations and polyhedral specific efects of compositional variation, temperature, distortions can no longer compensatefor it, then the sheet or pressureon these crystal structures. silicate will be renderedless stable relative to alternative This paper examinesthe effectsof compositional vari- structures.We might anticipate that there could be sim- ation on the crystal structuresof pyroxmangite and rho- ilar constraints inherent in the linkages ofthe octahedral donite, concentratingprimarily on Mn-Mg substitutions. bands and tetrahedral chains ofpyroxenoids. Becausethere is substantial compositional overlap between the Mn-Mg pyroxmangite and rhodonite stability Pntvrous woRK fields along the MgSiOr-MnSiO, join, thesecompositions Although the chemical and structural relations among are particularly suitable for examining any developing the pyroxeneshave been studied intensively (e.g., Cam- structural instabilities. Accordingly, data from previous eron and Papike, l98l), analogousstudies for the pyrox- crystal-structure refinements of pyroxmangite and rho- enoids are relatively scarce. Ohashi and Finger (1975) compared the structures of pyroxmangite and rhodonite and noted the close topologic and configurational corre- spondencebetween certain cation polyhedra in the two structures.Ohashi and Finger (1978) studied the role of the octahedral cations in the crystal chemistry of the three- tetrahedral repeat hydrous and anhydrous pyroxenoids and demonstrated that the different stacking configurations oftetrahedral and octahedral layers determine the resulting cation-ordering patterns and limit the extent of solid solution. Very little has been written, however, concerning the relationship between bulk composition and structural stability of the intermediate pyroxenoids. Liebau (1962) noted that the chain configuration in pyroxenoids is apparently a function ofthe averagesize ofthe octahedrally coordinated cations. More specifically,based on the observation (e.g., Freed and Peacor, 1967) that pyroxene stability dependson the relative size of the Ml octahe- Rhodonite Pyroxmongite dron, Tak6uchi (1977) suggestedthat the sizesof the cat- Fig. l. Projections ofthe rhodonite and pyroxmangite struc- ions in the inner Ml-like octahedra of pyroxenoids are tures onto (100). Octahedral(M) sitesin both structuresare iden- primarily responsible for their relative stabilities. Al- tified by number. After Ohashi and Finger (1975). 800 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE donite (listed in Table l) have been assessedalong with Site those from a new refinement of a nearly pure MnSiO, Occupancy' pyroxmangite. Data for pyroxferroite (Burnham, l97l) are also included in the analysis. We employ the CI setting for the pyrxoxenoids; data Ml(3,4) taken from previous refinementsbased on the PI setting have beenconverted into their CI equivalents.The series ofAppendix TablesAl through A,5compiles selecteddata for pyroxmangite and rhodonite taken or calculatedfrom the crystal-structurerefinements listed in Table l.

Srnucrunq.L vARIATToNS M6(2) Cell expansion

For the most part, the pyroxmangite and rhodonite Mg structures respond very similarly to compositional vari- Mn ation. Cell parameters of both structures, for example, increasefairly smoothly with the substitution of Mn for Mg, although small amounts of Ca presentin natural rho- M5.M7 donites cause marked increasesin the a and D cell di- mensrons. A completedescription of lattice strain due to chemical Mg MgSiO3 MnSiO3 substitution of a larger cation (Ca or Mn) for a smaller one (Mg) requires that a strain ellipsoid be calculated Bulk Composition (Ohashi and Burnham, 1973). Using the cell parameters Fig.2. Cationsite occupancy, Mn/(Mn + Mg),as a function given in Appendix Table Al and the computer program of bulk compositionfor pyroxmangitesalong the join MgSiOr- srRArN,written by Y. Ohashi, the magnitudes and ori- MnSiOr.Points represent ayerage site occupancies over the two entations of strain ellipsoids for several compositional or threesites indicated. increments of pyroxmangite and rhodonite were calculated. Becauseof the relative complexity and lower sym- tation of the averagestrain ellipsoid for Ca-free rhodo- metry of these structures, their ellipsoids are somewhat nites, which are all relatively Mn-rich, strongly resembles more difficult to interpret than are those of pyroxenes. that of the high-Mn pyroxmangites. Nevertheless, several clear trends emerge. The pyrox- The reason for this changein ellipsoid magnitude and mangites,whose compositions rangefrom (Mno ,rMgorr)- orientation becomesclear if we examine cation ordering SiO. to MnSiOr, exhibit two distinct strain-ellipsoid ori- patterns. Figure 2 plots M-site occupanciesin pyroxman- entations depending on Mn content. These are summa- gite as a function of bulk composition (Mn,Mg)SiOr; three rized in Table 2 as averagelow- and high-Mn ellipsoids, ordering patternsare apparent.Although cation occupan- with the breaking point at about MnroMgro. The orien- cies of the Ml, M3, and M4 sitesvary linearly with bulk composition, the other sites display a limited stepwise ordering pattern, with the M2 and M6 sites showing a TneLe2. Principalstrain components of expansiondue to chem- marked preferencefor small cations and the large, seven- icalsubstitution coordinated M5 and M7 polyhedra taking up Mn early Principalstrain in the series. components Addition of Mn to a low-Mn pyroxmangite producesa Orientation:Angle with x 10_3 per strain ellipsoid in which the greatestexpansions lie close 1%Mg-Mn to the b-c plane, with the largestexpansion about halfway Averagelow-Mn pyroxmangite(Mn1s - Mnsl) between the b and c axes. This reflects a marked expan- q 26(2) 131(6) 60(s) 68(s) sion of the structure along directions in which the density e2 20(1) 109(9) 146(9) 3s(e) e 13(2) 47(61 75(8) 64(8) of M5-O and M74 bonds is highest.The relatively small Volume 59(3) volume expansion, compared with that of the equiva- Averagehigh-Mn pyroxmangite (Mns1 , Mnr?) lent composition increment (Mno'Mgor)SiOr-(Mnon, e1 42(11 87(41 25(2) 88(2) "Mg"oo,)SiOr,is due to the ability of the M5 and M7 e" 32(11 25(2') 76(4) 127(2) polyhedra, located at the edgesofthe octahedralband, e 16(1) 65(2) 110(2) 37(2) to Volume 90(2) expand into the adjacent void spacewithout unduly dis- torting Rhodonite(CaJree, Mn62 - Mnloo) the structure. 37(2) 47(15) 37(21) 119(21) As Mn content increases,expansion of the small and 34(3) 117(18) 60(27\ 54(20) inner octahedrabegins to contribute most to the overall 18(3) 55(3) 110(8) 49(3) expansion. The resulting strain ellipsoid suggestsa less PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE 801 distorted expansionor "swelling" ofthe octahedralband more kinked in pyroxmangite than in rhodonite of iden- due to the more isotropic expansion of the inner octa- tical composition. This suggeststhat the W-P boundary- hedra, with the greatestexpansions perpendicular to the and, as will be demonstrated, the W module itself-be- band and the least expansionparallel to the band because comes less favorable energetically in pyroxenoids with of the constraints imposed by the tetrahedral chain. At smaller mean cation size. this stage,the direction ofgreatest expansionlies parallel The Si-Si distanceswithin the chains range ftom 2.94 to the "dense zone" ofcations, first describedfor pyrox- to 3.11 A. tne longer Si-Si distancesare those associated enesby Morimoto et al. (1966) and defined for pyrox- with the P modules. The shorter ones are the Si6-Si7 mangites and rhodonites by Aikawa (1979). In pyrox- distancesin pyroxmangite and the equivalent Si4-Si5 dis- mangite,the densezone is parallelto [031].1,which for tances in rhodonite, as well as the Sil-Si2 distances in the Ajiro sample is oriented 90", 30o,and 79" from the a, both structures.Both of thesedistances are located at the b, and c axes, respectively. The direction of largest ex- W-P module interface.The former is a result of the highly pansion is thus parallel to the zone having densestcon- kinked chain angle mentioned above. The latter is the centration ofM and Si cations. shortest Si-Si distance in each of these pyroxenoids and is a manifestation of the inherent peculiarity of the py- Silicate chain roxenoid tetrahedral chain as it jogs sidewaysto follow Chemical substitutions in the octahedral sites neces- the octahedralband, causingtwo tetrahedra (Sil and Si2) sarily influence the silicate chains as well since they link to point in the same direction. Oxygens OBI and OB2 the octahedral bands. The chains respond to their new thus lie on the same side of the "backbone" of the chain environment with expansionand distortion of individual formed by the bridging oxygens.This is the natural con- tetrahedra and by rotation oftetrahedra with respect to sequenceof connectinga W and a P module. each other. Becausethe number of crystallographically band distinct tetrahedra is fairly large, there are many degrees Octahedral of freedom in the chains; thus substantialstructural com- The octahedralbands in chain silicatescontain two ba- pensationscan be achieved with only small adjustments sically different kinds of sites, those on the inside of the in each parameter. bands and those on their edges.The inner octahedrapos- Individual tetrahedra. Mean Si-O bond lengths do not sessedges defined by the apical oxygensofthe tetrahedral changeappreciably (<0.006 A) witfr the substitution of chain. Except for the Ml octahedrain pyroxenoids,these Mn for Me (App. Table A2). As in almost all single-chain octahedra are situated in the P modules, have environ- pyroxene, like silicates, the Si-OC Oridging oxygen) bonds are longer ments very similar to that of Ml in and, than the nonbridging bonds, and of the latter, the Si-OA the pyroxene Ml octahedron, are relatively undistorted. (apical oxygen)bonds are longer than the Si-OB bonds. The Ml octahedraof pyroxmangite and rhodonite, which In both pyroxmangite and rhodonite, tetrahedral dis- possessthree such "apical edges" becauseof the lateral tortions decreaseas mean octahedralcation sizeincreases jog ofthe tetrahedral chains acrossthem, are the basis of (App. Table A4). This effect is seen also in pyroxenes the W module and as suchhave no pyroxeneequivalents. (Cameronand Papike, l98l) and is due to the dispro- The sites on the edgesof the bands are distorted poly- portionate lengthening of the OC-OC edge of the tet- hedra that shareedges with tetrahedra and correspondto rahedron, which opens up the OC-Si-OC angle and the M2 polyhedra in pyroxenes. thereby lessensthe distortion. This is a simple yet effec- In light ofthese correspondences,Tak6uchi (l 977) pro- tive means of stretchingthe chain without increasingthe posedthe designationof Mli for the inner octahedra(in- : averageSi-O distance.Tetrahedral distortions are rough- cluding Ml) and M2i fot the outer polyhedra, where i ' ' '. ly the same for pyroxmangite and rhodonite of similar 0, 1,2,' ' ' andT: 1,2, The Mli sitesin pyroxman- compositions (App. Table A4); they increase along the gite, for example, comprise Ml through M3. Although chain from Sil to Si7, primarily becausethe Si4 through we retain the original nomenclature for each individual Si7 tetrahedra share edgeswith octahedra. The distor- site in this paper, the concept of basically different Mli tions of the non-cdge-sharingtetrahedra are comparable and M2j polyhedra is useful since both the geometries to thosein clinopyroxene(e.g., Ohashi, et al., 1975). and the resulting cation occupanciesof the two groups Tetrahedral chain angles.As the mean octahedral-cat- are quite distinct. The concept of Mllike and M2-like ion radius increases,the tetrahedral chain undergoesan sites also facilitates comparison with pyroxenes. overall gradual straighteningby about 2'(see App. Table Inner octahedra.The changesin mean M-O distance A5). Not unexpectedly,the "straightest" chain angles(OC- (NI5) as a function of site occupancyfor the inner oc- OC-OC closest to 180") are those associatedwith the P tahedra in pyroxmangite and rhodonite are plotted in modules.The most highly kinked angleis OC5-OC6-OC7 Figure 3. M4e.-" and M3.n.o are included in the figure in pyroxmangite, and its rhodonite equivalent is OC3- although they are not true Mli octahedra.Several inter- OC4-OC5. This angle is associatedwith the tetrahedral esting features are apparent in these plots. Whereas the "triplet" of the W module and is located at the boundary NFO of severalof the octahedra,such as M I and M4 of between the W and P modules. Although the angle wid- pyroxmangite, exhibit a linear relationship with cation ensby up to 6oas Mn replacesMg, it remains significantly substitution, the curves for M2 and M3 exhibit a slight 802 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE

(A) ary. This effect is observed also in the WPPP structure, ferrosiliteIII (Weber, 1983). Outer octahedra. A plot of NFO for the outer sites shows considerablescatter becauseof the varying coor- 219 dinations of thesepolyhedra. WhereasM4o"-n and M3,n"o xAA-l'\ lvl- v 217 are fairly regular octahedra, the M5o--",.1.dand M7p*.n 215 siteshave effectiveoxygen coordinations describedbetter as seventhan as six, with distortion from ideal increasing in the order M7e--" ( M5,noo< M5o*-n. This distortion difference is due to a combination of polyhedral angles 220 and to the slightly different coordination characteristics M3-O zB of the three polyhedra:M5o*-, and M5.n- are coordinated by four short and three medium-toJong bonds, whereas M7e--, has four short, two medium, and one very long 2.14 bond. By virtue of this one very long bond, M7o,-, is the closestto six-coordinated;in fact, its distortion parameters calculatedusing the six shortestbonds are similar to those of M2 in clinoferrosilite[(I) : 1.06, osz: 164 2.19 (Ohashi et al, 1975)1. M 2-O 217 Substitution of Mn for Mg does not cause significant polyhedra 215 distortion of the large M5 and M7 in pyroxmangite. Addition of Ca to these sites, however, causes 213 a considerable increase in distortion and a closer ap- proach to seven-coordinationas short M-O bonds lengthendisproportionately relative to long bonds, which undergo little or no change.The rhodonite M5 polyhe- )10 M1-O dron respondsto Ca occupancyin the samemanner. IJn- 217 like in pyroxmangite, however, the rhodonite M5 poly- 2.15 hedron responds also to Mg substitution, causing the oxygen configuration to shift to four short, one medium, o 20 40 60 ao 100 and two long bonds. This polyhedron, therefore, tends Mg Occuponcy Mn toward seven-coordinationin Mg-rich as well as in Ca- rich rhodonites, although the geometry of the polyhedra Fig. 3. Mean M-O bond distances(NF-O) of the regularoc- is quite different. tahedraof pyroxmangiteand rhodonite as a functionof siteoc- The small irregular M6".-" and M4.hodoctahedra cupancyMn/(Mn + Mg). undergosignificant changes in configuration as cation size increases,resulting in a coordination closer to five than bend, which suggeststhat the oxygen framework of these to six in Mn-rich compositions. Five-coordination is par- polyhedra may be held open by the nature of the structure ticularly pronouncedwhen Ca is present.Such seemingly to a minimum M-O- of about 2.B A. Moreover, for any anomalousbehavior, in which effective coordination de- given cation occupancy, the mean bond lengths of the creasesas cation size increases,is readily understood in rhodonite octahedraare almost always longer than those light of the fact that, although large cations (except Ca) ofthe equivalent pyroxmangite octahedra. This effect is do enter this site, they are filling neighboring cation po- particularly pronounced for M2. sitions at a much faster rate (recall Fig. 2). In pyroxman- Distortion parametersfor the inner octahedra of both gite, this causesthe tetrahedral chain angle OC5-OC6- pyroxmangite and rhodonite (App. Table A.4) indicate OC7 to straighten by up to 6", which in turn pulls the that, although distortions generallyare slightly greaterfor OA7 oxygenatom sharply away from the M6 cation (Fig. Mg-rich compositions, the presenceof Ca in the outer 4). Charge repulsion also increasesthe distance between polyhedra does not causesignificant distortion ofthe in- the now-larger M6 cation and the Si7 cation with which ner octahedra.Distortion is comparablefor topologically the M6 cation sharesa polyhedral edge. An important equivalent octahedraof the two structuresexcept that the result of these relative movements is that, as Mn or Ca distortion of M2.noois greaterthan that of M2o*-n,partic- fills the M5 and M7 sites, the OA7 oxygen moves away ularly in angle variance. The M2 octahedraare discussed from the M6 cation faster than the cation itself moves further in the next section. away from Si7. Eventually the OA7 oxygenis farther from Finally, it should be noted that the M3 octahedron in the M6 cation than is the Si7 atom; in Ca-rich pyroxfer- pyroxmangite, located at the boundary betweenadjacent roite, thesedistances are 2.9A2 and 2.873 A, respectively P modules, is consistently less distorted than the other- (Burnham,l97l). wise similar M2 octahedron, located at the W-P bound- The M6 octahedron is a component of the W module PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE 803

(A) a Pxmn o Rhod 222

214 M1i

216

214

)1)

oorr"r.uo 80 Mg sio=,20 MnSio,

Fig. 5. Variationof grandmean Mll-O bond length,Mli, as a functionof bulk compositionfor Mg-Mn pyroxmangites and rhodonites.

seenby correlatingtheir sizewith other structural param- oc5 etersand comparing the correlationswith those observed Fig. 4. Configurationchanges ofthe M6 polyhedronin py- in pyroxenes.It is convenient to define Mfi for pyrox- roxmangiteas Mn/(Mn + Mg)increases. Double arrows indicate enoidsas the grandmean Mll-O bond length,where Mli relativemovements of atoms.As the tetrahedralchain angle octahedrainclude Ml througlr M3 in pyroxmangite and OC5-OC6-OC7straightens, the OA7 oxygenatom moves away M I and M2 in rhodonite (Murakami and Tak6uchi, 1979). from the M6 cation.The distancebetween the M6 cationand A plot of Mfi as a function of bulk composition along or the Si7 atom alsoincreases because of increasedcharge repul- near the join MgSiO.-MnSiO, for pyroxmangites and sion,but at a slowerrate. Eventually, the M6 cationis closerto rhodonites is given in Figure 5. it is resulting M6 Si7than to OA7, in becomingfive-coordinat- Unlike pyroxenes, the cell parameters of natural py- ed. roxmangite and rhodonite follow MTI only approximately, becausemoderate amounts of Ca in the outer M27 and as such is best suited geometrically for larger cations sitesexert little influence on the Mli ocatahedrabut have (Ohasi and Finger, 1978).Presence of small cations in the a marked effect on the cell edges.In most respects,how- site causesthe extreme kinking of the OC5-OC6-OC7 ever, the relationship ofMll'- with other structural param- tetrahedral chain angle (discussedabove) and contributes eters parallels those observedin pyroxenes. to the "unfavorableness" of W modules in structureswith More unexpectedis the influence of the Mli octahedra small mean cation size. on the M2l polyhedra. One significant observation that has emerged from pyroxene studies is that the sizes of Significanceof the Mli octahedra polyhedra are frequently constrainedby the nature ofthe The pyroxene Ml octahedrondoes not vary drastically structure itself and that an important control is the Ml among the different structure tlpes (ortho, clino, and pro- octahedron.Ghose and Wan (1975), for example, ob- to); it is appropriate to consider it the major building served that in MCaSirOu clinopyroxenes(i.e., with con- block of the pyroxene structure (Cameron and Papike, stant M2 cation occupancy),the averageM2-O distance 1981).Various workers (e.g.,Ribbe and Prunier, 1977; increaseslinearly with increasing mean Ml-O distance, Cameron and Papike, 1981) have demonstratedthat the which implies that the size of the outer octahedra may Ml octahedron determines to a large extent the unit-cell be ultimately controlled by the size of the inner octahe- dimensions,the relative displacementand kinking of the dra. Figure 6 indicates that a similar relationship exists tetrahedral chain, and the size and configuration of the for pyroxmangite and rhodonite as well. Taking the term M2 polyhedron. We therefore might anticipate that the @ to representthe grand mean M274 bond length for topologically equivalent Mli octahedra would play an each particular structure, two curves of M2j versus Mli equally central role in the pyroxenoids, and indeed this have been plotted for each structure, reflecting two dif- is the case. ferent assignmentsof coordination numbers to the M27 The significanceof the Mli octahedra is most easily polyhedra. Although the plots for pyroxmangite are very 804 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE

Pynoxmangjte 2.40

230 t Bust

Pxmn 4JY Rhoo zzv ..X, a7 M1i a jt' . iT: /i\ 2.1o t'! "

2.OO 'Px

oo 1.90

2 90 3.OO 3r O 3.20 3.30 3 40 3.50 216 218 22a 2.22 224 (A) L (A) M1i Fig. 7. Variation of grandmean bond lengthMTi with Z parameter(see text) for pyroxmangitesand rhodonites.

of the M27 polyhedra are linked to and constrained by the sizesofthe inner octahedra. As this correlation seemsto hold true for chain silicates u2) in general,it may be one way in which the Mli octahedra ultimately control the relative stability of the pyroxenoid structures(including pyroxenes),as suggestedby Tak6u- chi(1977). The relationship betweenthe Mll cations and pyroxenoid stability, however, is by no means a simple one. For example, the large degree of overlap in Mli valuesbetween pyroxmangites and rhodonites (Fig. 5), as indeed in Fig.6. Variationof grandmean bond lengths M| with Mll-. the bulk composition itself, indicates that al- (a) Pyroxmangites:the lowercurve (filled circles) considers all though a trend does exist, there certainly is no cut-off M sitesas six-coordinatedexcept M6 in CWB-Ppyroxferroite, point in Mli size that controls the relative stability of which is takenas five-coordinated.The uppercurve (open cir- pyroxmangite and rhodonite. cles)considers M5 and M7 as seven-coordinated. In an attempt to definethe correlation betweenthe Mli (b) Rhodonites:filled trianglestake all M sitesas six-coordi- cations and pyroxenoid stability, Murakami and Tak6u- nated,whereas open trianglestake M5 as seven-coordinated.chi (1979) examined the relationship between MTI and Significanceof the dashedcomposite curve is explainedin the the average distance between apical oxygens along the text. tetrahedral chain, which is a qualitative measureof chain extension. They defined a quantity

well defined, the rhodonite data produce breaks in both /, \ curves. These breaks are a result of the previously dis- L: l> ti+ tol/@+ t), / cussedchange in M5.noocoordination with increasingMg \rl content. Becausethe sixth and seventhoxygen atoms are where n is the periodicity ofthe tetrahedral chain and Z then approximately equidistant from the M5 cation, con- is essentiallythe averagedistance between apical oxygens sidering M5.n* as six-coordinated produces artificially low including the apical-apical distance /o acrossthe triplet. data points for the relatively Mg-rich rhodonites MT-R They then plotted I versus Mli for a number of pyrox- and FH-R. When M5 is taken as seven-coordinatedin enoid and pyroxene structures; their plot is reproduced these Mg-rich phases,however, their distances plot on in Figure 7. The set of data points for each structure type the lower curve defined by the points of the Mn-rich rho- defines an approximately straight line, with very little donites (in which M5 is more nearly six-coordinated). overlap in Z values between structures. Murakami and This composite curve is given as the dashedline in Figure Tak6uchi therefore concluded that there is a critical limit 6b. of I for eachstructure type. They suggestedthat this limit The strong correlation apparent in thesecurves is even in Z might be related to /obecause of the systematic change more remarkable given that it encompassesnot only in /0 with Mfi. tne lerm lo, however, merely reflects the Mn + Mg substitution but also Ca-bearingcompositions distanceacross the relatively undistorted Ml octahedron, such as the Ca-rich pyroxferroite CWB-P. It is clear, and there is considerableoverlap in /o values for pyrox- therefore, that regardlessof bulk composition, the sizes mangite and rhodonite (seeTable 3). PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE 805

We suggestinstead that the lack of overlap in Z values, TneLe3. Additionalparameters for pyroxmangiteand rhodonite at least betweenpyroxmangite and rhodonite, is due pri- Ml-O- M]l* M2-4.. I zit lof L4 marily to the significantly different sizes and distortions Pyroxmangites of the M2 octahedron. Although the M2 octahedron in Nar-R 2.223 2.222 2 272 2.318 2.635 3.263 rhodonite is topologically equivalent to that of pyrox- AJ-P 2.220 2 214 2.264 2.309 3.609 3.260 mangite, i.e., located in the P module adjacent to the OF-P 2 207 2.199 2.252 2.297 3.599 3.252 t-H-t- 2.174 2.164 2 213 2.256 3.515 3.218 W-P boundary, it is much larger and more distorted in Roth-P 2.139 2.137 2.177 2.223 3.457 3.194 rhodonite than in pyroxmangite. The difference is inde- CWB-P 2.185 2.169 2.2265 2.265$ 3.646 3.216 pendent of bulk composition and apparently is an inher- Rhodonites ent, structurally controlled phenomenon. The high dis- Nar-R 2.219 2.231 2.272 2.296 3.626 3.301 OF-R 2.213 2.221 2.265 2.287 3.599 3.292 tortion of this octahedronsuggests that the P module may Peac-R 2.219 2.220 2.269 2.284 3.569 3.293 be less stablein rhodonite than in pyroxmangite of iden- MT.R 2.200 2.210 2.236 2.258 3.537 3.283 tical composition. FH-R 2.186 2.197 2.223 2.244 3.511 3.271 . Mllcomprises M1-M3e,M1-M2'. lvrlr--: mean M-O bond distance CoNcr,usroNs of these octahedra. -- M2l comprisesM4-M7", M3-M5F. All polyhedraare consideredto be Rhodonite (WP) and pyroxmangite (WPP) are adjacent six-coordinated. members of the pyroxenoid-pyroxenepolysomatic series; f M2l sites are the same, only M5", M7p, and M5" are consideredto they possessvery similar structures with octahedral and be seven-coordinated. f lo and L are defined in the text. tetrahedral sitesthat are topologically equivalent and ex- $ M6 is consideredto be five-coordinated. hibit comparable distortions and cation ordering patterns. As a result, the two structuresrespond in much the same way to compositional variation. significant that in pyroxmangite, the P modules remarn As larger cations replace smaller ones in these struc- relatively undistorted regardlessof composition; nearly tures, octahedral and tetrahedral distortions generally all of the distortion occurs at the W-P boundaries. lessen,and the silicate chains straighten.Both structures Becausedecreasing cation size in rhodonite leads to exhibit limited stepwiseordering of cations, with larger distortions that causehigher-energy configurations to de- cations preferentially entering the large sites on the edges velop at W-P boundaries, W modules are destabilized of the octahedral bands. Very large cations, such as Ca, relative to P modules, and P-P boundary stability is appear restricted to these sites and so place limitations thereby enhanced.This tends to favor nucleation ofad- on bulk composition. Mean Si-O distanceschange very ditional P modules within the mineral. A mechanism for little. These structural responsesto cation substitution such a nucleation processconsistent with this notion has mirror those observedin pyroxenes. been formulated by Angel et al. (1984) and by Veblen Also as in pyroxenes,the nature of the octahedra on (1985) to explain phasereactions in the pyroxene-p)'rox- the inside of the band (Mli octahedra)strongly influences enoid system.Conversely, as cation size increasesin py- the entire structure, including the ultimate size and con- roxmangite, the W module is stabilized and W-P bound- figuration ofthe outer polyhedra. Although there is a gen- aries become more favorable. eral correlation between cation size and structure type, Accumulation of higher-energystrained configurations with the number of P modules per unit cell increasing at W-P boundaries as cation substitution proceeds sug- with decreasingmean cation size,there is no critical cut- geststhat a yet-unidentified maximum strain limit may off in mean size that differentiates pyroxmangite from contribute energeticallyto phasetransformations in this rhodonite or, for that matter, from pyroxene. Structural system.Indeed, suchbuildup of distortion-induced strain parameters for both pyroxenoid structures change energyat W-P interfacescan explain the common obser- smoothly with composition and produce only minor vation in transmission electron microscopy (Ried and structural adjustments. Korekawa, 1980; Czank and Liebau, 1980;Alario Franco Theseadjustments, however, produce localized higher- et al., 1980;Czank and Simons,1983) that excessP mod- energystructural configurationsthat cluster at the bound- ules, and hence excessP-P boundaries, are much more aries between the W and P modules, leaving the P-P common in pyroxenoids than are excessW modules. boundaries virtually strain-free. Decreasingmean cation size in a pyroxenoid, for example, results in smaller P AcrNowr,nocMENTS modules. The configurations and minimum sizes of W This researchwas supported by National ScienceFoundation Srant EAR- modules, however, are constrained by the tetrahedral 7920095to C.W B. We thank D. R. Peacorand R. J. Reederfor helpful chains; the chains develop strong kinks at the W-P reviews,through which the manuscript was substantiallyimproved. boundaries, forcing pairs of Si cations close together to RrrnnrNcns crrno Si-Si distancessignificantly shorter than the 3.0 A pro- pyroxmangite posed by Hill and Gibbs (1979) as the lower limit of Aikawa, N. (1979) Oriented intergrowth ofrhodonite and and their transformation mechanism. Mineralogical Joumal, 9, 255- nonbonded Si-Si contacts. Both the W modules and the 269. W-P boundaries therefore become energeticallyless sta- Akimoto, S., and Syono, Y (1972) High pressure transformations in ble in compositions with smaller mean cation size. It is MnSiOr. American Mineralogist, 57, 76-84. 806 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE

Alario Franco,MA, Jefferson,DA., Pugh,NJ., Thomas,J.M., and Pinckney,L.R., and Burnham, CW (1988) High-temperaturecrystal Bishop, A C (1980) Lattice imaging of structural defects in a chain structure of pyroxmangite.American Mineralogist, 73, 809-817. silicate:The pyroxenoidmineral rhodonite.Materials Research Bulle- Prewitt,C.T , and Peacor,D.R. (l 964)Crystal chemistry ofthe pyroxenes tin, 15,73-19 and pyroxenoidsAmerican Mineralogist, 49, 1527-1542. Angel,R J, Price,G.D., and Putnis,A (1984)A mechanismfor pyrox- Ribbe,P H , and Prunier,A R, Jr. (1977)Stereochemical systematics of ene-pyroxenoidand pyroxenoid-pyroxenoidtransformations Physics ordered C2lc silicate pyroxenes.American Mineralogist, 62, 7 lO-720. and Chemistryof Minerals,10,236-243. Ried,H , and Korekawa,M. (1980)Transmission electron microscopy of Brown, P E, Essene,E J., and Peacor,D R (1980)Phase relations in- synthetic and natural fiinferketten and siebenerkettenpyroxenoids. ferred from field data for Mn pyroxenesand pyroxenoids. Contribu- Physicsand Chemistryof Minerals,5, 351-365. tions to Mineralogyand Petrology,74.417425. Robinson,K , Gibbs,G.V , and Ribbe,P H ( 1971) Quadratic elongation: Bumham, C W (1971) The crystal structure of pyroxferroite from Mare A quantitative measureof distortion in coordination polyhedra. Sci- Tranquillitatis. Proceedingsof the SecondLunar ScienceConference, ence,172,567-570. |, 47-57. Tak6uchi,Y. (197'7)Designation of cation sitesin pyroxenoids.Miner- Cameron,M , and Papike,J.J (1981)Structural and chemicalvariations alogicalJournal, 8, 431-438, in pyroxenesAmerican Mineralogist, 66, l-50. Thompson,J.B., Jr (1978)Biopynboles and polysomaticseries. Ameri- Czank,M, and Liebau,F. (1980)Periodicity faults in chain silicates:A can Mineralogist,63, 239-249 new type of planar lattice fault observedwith high resolution electron Veblen,D R (1985)TEM study of a pyroxene-to-pyroxenoidreaction microscopy.Physics and Chemistryof Minerals,6, 85-94 AmericanMineralogist, 70, 885-901. Czank,M, and Simons,B (1983)High resolutionelectron microscopic Weber,H.-P. (1983)Ferrosilite III, the high-temperaturepolymorph of studieson ferrosiliteIII Physicsand Chemislryof Minerals,9, 229- FeSiO,. Acta Crystallographica,C39, l-3

Finger,L W, and Hazen,R M (1978)Refined occupancy factors for syn- Me.NuscnrprRECETvED Jurv 15, 1986 thetic Mn-Mg pyroxmangiteand rhodonite CamegieInstilution of MeNuscnrm ACCEPTEDMancH 4. 1988 WashingtonYear Book 77, 850-853 Freed,R.L., and Peacor,D.R. (1967)Refinement of the crystalstructure of johannsenite.American Mineralogist, 52, 7O9-i 20 Ghose,S., and Wan, C (1975) Crystal structuresof CaCoSirOuand CaNiSirOu:Crystal chemical relations in C2lc pyroxenes(abs ). EOS, TSle Al, hit-cel] &b for Wroffigite atd rhad@ite 56. tO76 Hazen,R.M, and Wones,D.R. (1972)The effectof cation substitutions on the physical properties of trioctahedral micas. American Mineral- ogist,57, lO3-129 -(1978) Predictedand observedcompositional limits of trioctahe- a (A) 9-71013) 9-112(2t 9.69012t 9.585(1) 9.519(5) 9.63s(1) b (A) 10 495(4) 10.535(2) 10.50s{3) 10.359(r) 10.280(5) 10.431(l) micas dral AmericanMineralogist, 63, 885-892. c (A) 1?.455(6) 17 43S(3) l? 391(3) 11 24112t 17.125(9) 17.3Sr(2) Hill, RJ., and Gibbs, GV. (1979)Variation in d(T-O), d(T T) and d (deg) tII 8(1) 112.15(1) 112.1?(2)112.335(3) 112.35(5) 112-23121

Mno.rrMgo,,rSiOr,and compositionaltransformations in pyroxenoids. NA T-P OF_P Fg-P ROIh_P 4B_P MineralogicalJoumal, 9, 186-304 Narita, H, (1977) I. Pyroxnangite M-o distanceE (I) Koto, K, and Morimoto, N The crystalstructures of trt-oAr 2 141 2 rS5 2.749 2.128 2.083 2.121 MnSiO, polymorphs (rhodonite- and pyroxmangite-type).Mineralog- -oAl 2 336 2 321 2.312 2 290 2.259 2,305 -oA2 2 271 2,623 2 241 2 202 2.L81 2.233 ical Journal,8, 329-342. -oA5 2 262 2.215 2 253 2.227 2.782 2.214 -oA7 2.161 2.t42 2 L36 2.098 2,069 2,014 Ohashi,Y., and Bumham, CW (1973)Clinopyroxene lattice deforma- -oA8 2.163 2-164 2.141 2.t00 2 062 2.09S 2 221\9) 2.22011) 2 20114) 2.174t3) 2.t39 2.r85(2) tions: The roles of chemical substitution and temperature.American MZ-OA2 2,!15 2.110 2.158 2,1t9 2.091 2.L45 Mineralogist,58, 843-849. -oA6 2 320 2 283 2.216 2 238 2.225 2.212 -oA3 2 342 2.330 2 3I3 2 260 2.220 2.220 Ohashi,Y., and Finger,LW (1975)Pyroxenoids: A comparisonofre- -oA5 2.209 22\6 2L95 2.t57 2.158 2-209 2,154 2-140 2,123 2.011 2 07r 2-093 fined structuresofrhodonite and pyroxmangite CarnegieInstitution of -oB4 2.118 2 L07 2.089 2.035 2 009 2.078 WashingtonYear Book 74, 564-569. 2-220(9) 2.208|.1) 2.192i'4) 2.1{8({) 2 130 2.159t2t -(1978) The role of octahedralcations in pyroxenoidcrystal chem- il3-OA3 2.190 2.199 2 I71 2.152 t29 2,r7 4 -oA{ 2 191 2-182 2.183 2,L48 111 2 , r11 istry. I. Bustamite,wollastonite, and the pectolite-schizolite-serandite -oA4 2 384 2.300 2-351 2 -339 359 2-269 -oA5 2-258 2,255 2 240 2.209 r14 2.L56 series American Mineralogist, 63, 274-288 -oB2 2.190 2113 2L66 2 1r9 080 2 -L43 -oB5 2.118 2.089 2.044 2.045 004 2.055 Ohashi,Y., Bumham, C W., and Finger,L W (1975)The effectof Ca- 2-222(9t 2-211t1) 2.20014) 2.159(I ) 143 2.162(2) Fe substitution on the clinopyroxenecrystal structure American Min- x4-oA3 2 254 2.242 2.234 2.210 2.165 2.224 -oA5 2 t52 2.rsr 2.724 2 081 2.058 2. 093 eralogist,60,423434 -oA8 2 334 2.322 2.318 2 298 2 245 2-315 (1978) -oB1 2 245 2,216 2 209 2-165 2-140 2-112 Peacor,D.R , Essene,E.J., Brown, P.E, and Winter, G A The -oB2 2.019 2-067 2 068 2.032 2.007 2.055 crystalchemistry and petrogenesisofa magnesianrhodonite. American -oc6 2.251 2-255 2,230 2.189 2.151 2 rgL 2.223191 2-209(Ll 2.20t14) 2.164(3) 2.t28 2.180(2) Mineralogist,63, | 13'7-l | 42. PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE 807

rable A2 (ContinuGd) rrbl. A2 (Conttnu.d)

OF-P 8H_P Roth-P CWB-P oa-R ils-OAs 2.206 2 189 .187 2 116 123 2 2t1 rv Rhodonit€ si-o distanc!6 {R) -oA4 2 125 2.r31 r31 1,118 080 2 161 -oB4 2 \09 2.100 103 2 .099 081 2 r41 s I 1-OAr r -621 L.629 1.629 t.627 -oB5 2 122 2.t14 . 141 2.151 r30 2.19I r 588 r. 582 l. 590 1,590 1.587 .-oc3 2.174 2.545 559 2 -683 I 619 7,542 1.54? -oc4 2 S2A 2.426 351 2-492 -oc5 L 642 1.543 r.642 1.649 1.5t{ --oc2 2.921 2.90! 2.900 2.881 850 2,839 L 623(1| 1.625{4) 1.530(3) 1.628(3 ) r 525(3) xean(l) 2.399(9) 2.392|.L ) 2.181| 4) 2.3s5(4) 325 2 300(2) xean(6) 2.11119) 2 1011r) 2 300(1) 2.269| 4) 239 2.315(2) st 2-Aoz L 623 r 514 1.5r8 |,622 -oB2 r 500 L -591 1.598 1,591 1.594 M6-OA1 2 r15 12! 2.096 2.059 2.011 2.058 -oc2 L 621 r 537 I 638 !.624 -oA8 2 248 214 2.201 2 L5S 2.r40 2 -2r7 -oc1 r.65? 1 5{9 1.54r -oa1 2,0{r 053 2.027 1,989 r.979 2.0!2 trGtn L-521t7 | r 624(4) r 626t3t 1.521(3) 1.519(3) -oB5 2.006 987 1 958 r,922 r.905 -oc7 2.396 3S4 2 371 2.268 2.221 2.342 s i 3-oA3 1.523 1.510 1513 1.514 1.51{ -oA? 2.795 807 2.161 2.620 2.902 -oE3 1. 595 1.595 1,591 1. 590 uean(5) 2.27219) 261(I) 2-231/.4't 2.170({) 2.1{3 2.2 49/.21 -oc3 1.517 L.626 r.621 1.521 1.624 Meanl5) 2.16719) 152(r) 2-13214t 2.081(4) 2.059 2.r18{3) 1.545 r.645 1-651 1.6{5 1.5{1 1.520(?) 1.519(4) r.622131 1.518(4) 1.618{{) M7-OA2 2,234 2-237 2 226 2.188 2.149 2.231 2 158 2.L34 2 141 2.142 2.088 2.113 si4-oA4 t.6rl r.603 1.617 1.606 1.512 -oB3 2 071 2 079 2,084 2.0?0 2. 031 2.160 -oB4 I.596 1.602 1.587 1.597 t . 592 2.101 2-tt6 2.122 2.124 2,090 2 182 -oc4 1.539 1.548 r.644 r 5{l r.5{4 -ocl 2,519 2.581 2 -369 2.586 2 524 -oc3 r.515 1 -624 1.532 L 627 l-625 -oc5 2.549 2-529 2-490 2.374 2 311 2.466 1 517(?) 1.519({) 1.520(3) 1,518(3) 1,518(3) 2.960 2.957 2 920 2-444 2 463 2.864 trean( 7 ) 2 380(9) 2.375(1) 2.365(4) 2.333(4) 2.294 2-31rl2| si5-oA5 r 592 1.587 I.597 1.595 r. 594 tean( 6 ) 2 28419) 2.280(l) 2,21214) 2.248(4) 2,L99 2 -2891 2) -oA6 I .509 1,508 1.510 -oc5 L -649 I .548 I .559 1,551 1.650 -0c 4 1.638 1 641 1.553 r.652 II. Pyroanangi!e Si-O dis!ances (I) L.62311) 1 523(3) I 532(3) 1.527{3J 1.62113) Si I-OAI 1.5{1 1.621 1.535 -oBt I S90 1 585 1 S92 1.588 1.515 -oct 1.542 r 637 1 559 L 652 1.661 | .649 r For estinated standard d€viation individua] bond distances, 1.544 | 652 1.5{3 I .649 the reader is referred to the original PaperE. Er1016 on Rolhbard r.529(9) 1 524(1) 1 531(4) r 528(4) r 515(3) dislances are not known. si 2-oA2 r -625 1 613 1.619 1.525 1,611 -oB2 1.605 r 589 1.590 r 588 1.59{ 1.509 -oc2 1.525 1.643 | 532 1.525 I 635 -oc1 L 551 1.677 1.558 1.658 1 554 ilean 1.531(9) 1.630(1) t.621| 4) 1.526({) 1.530(3) si 3-oA3 1.613 t.536 1.515 -oB3 1 598 1.596 I 598 1.594 r.587 1.585 -oc3 r 644 1.630 r 629 I .521 1.607 1.530 ! 613 1.551 1 651 r.550 r 650 1.533(9) r.520(r) 1.625({) r.520({) I 520 1.523(3) Table B. Gtid ocdpancies in WrMgite td rhodmitea 3i4-OA4 \,629 1,513 1.508 507 1.613 1.501 -oB4 1.614 r 594 1.601 595 I 594 1.594 -oc4 1638 1543 1551 644 1 6{4 1.631 --oc3 1633 1538 r631 617 I 638 r-642 !VroMgites Mean 1.629{9) I 622(I) I 625(4) 62r(4t r 622 1.619(3) Mr-e Aj-P OF-P N.P fuU-P si 5-oa5 ! -622 1 508 1 .513 506 SilehMghx9 highxg -oB5 r 580 1.595 1.597 1.593 1.592 -oc5 I 549 1.640 r.650 539 r -637 t.524 -oc4 7 652 r.652 1.639 1 -646 1.539 n 1.0 0.0 0.9?3 0.027(7) 0.97 0.03(r) 0.516 0.484(5) 0.0{ 0.95(1 ) ffean I 62519) I.5241!) r.625(4) 520({) r 5r6(3) fr 1.0 0.0 0.952 0.048(7) 0.81 0.19(r) 0.351 0.5{9(5) 0.00 1.00(I ) si5-0A6 6L1 1.502 1.518 1.508 1 508 0.0 0.962 0.038(7) 0.93 0.17(1) 0.45r 0.549(5) 0.05 0.95(1 ) -oB5 596 !.585 1.595 1.588 1.589 1 598 B 1.0 -oc6 624 !.642 1.549 r.639 1.643 1.651 x4 1,0 0.0 0.96? 0.033(?) 0.89 0.11(1) 0.452 0.s48(5) 0.03 0.97(r ) -oc5 530 1.529 l -621 1.638 1.641 1 632 0-12(1) 0.?SS 0.212(5) 0.30 0.70{1 ) 517(9) 1 515(1) | 62214) 1.518{4) r 622 I 622(3) tr5 1.0 0.0 0.999 0.00r(7 ) 0.88 x6 r.0 0,0 0.921 0.079(7) 0.s1 0.19(1) 0.253 0,?47(5) r.02(1) si 7-oA7 602 1.585 1 598 l. 591 1.500 1 559 0 -27 073 -oA8 598 1.507 r 608 1.503 I 5r2 n t0 0.0 1.00 0,00 0.91 0 09 0,111 0-223 -oc 7 664 1.590 1,660 !.549 1 645 -oc5 661 1 543 1,551 1.658 1.554 1.654 632(9) r62r(rt r62914) 1.625({) 1.628 1.620{3 ) lhodonites

Nar-R OF-R Peac-R m-R tr-R silehflghtrghn9htrghig

E 1.0 0.0 0.93 0.07(1 ) 089 0.11(1) 0.596 0.304(6) 0,6150.383(5) P€ac-B w I.0 0.0 0.93 0.07(r) 0.85 0.14(1) 0.?46 0,254(6) 0.6S?0.313(5) r3 L0 0.0 0.9r 0.09( 1) 0.85 0,1{{1) 0 634 0.355(5) 0.5720.{28(s) Rhodoniie ff-O distlnces (X) x{ 1.0 0.0 0.78 0.22(1 ) 0.4?(1) 0.{81 0.519(5) 0.3500,650(5) M1-OA1 2.170 2 r10 2.152 trs 1.0 0.0 0.83 0.r? 0.40 0.50(ca) 0.858 0.132 0.8760.12{ 2.331 2.321 2,302 2.258 2.257 2,243 -oA{ 2.253 2.230 2 2t4 -oA roblaind fr@ least- squres refiren! using a llrear cdimtl@ of iMg. h d 5 2.I 55 2.134 2.139 2.130 2 113 increae6 thc afF.r6nl xg ocdgancy. -oA5 2.139 2. r29 2.L31 2.109 2.093 8e Ere grdped tqEtJ|er, dile G eflectiwly in ced refin@nt. 2.2L9(7t 2.27314J 2.219(3) 2.200(3) 2.186( 3) tubl @6ition ms coEtrained t2-oaz 2.229 2.2r3 2 200 2 IE? -oA4 2.313 -oA3 2 236 2 242 2 224 2 216 -oA3 2 280 2 2AA 2.213 2.150 2,135 2.119 2.140 2 .089 2.105 2.085 2 24217\ 2.22L(4) 2.22O13) 2.201| 3l tr3-OA3 246 2 249 2.246 2.231 102 2 099 2 r04 2.068 2.060 -oA{ 13? 2 t22 2.1r8 2-102 2.083 -oA5 365 2 214 2 342 2.328 -OBI 2t6 2.217 2,198 2.200 2.189 271 2 -243 2.234 2.220 2.204 223(1) 2.211(4) 2.2I71 3) 2,195(3) 2.184{3) u4-oA1 140 2.108 2.090 2.08{ 2 -069 -oA6 246 2.224 2 200 069 2.042 2.026 2.013 2.002 -oB4 004 I.912 I .954 r.950 I 943 -oc5 2.344 2.334 2.291 2.213 -oA5 118 2.193 2.110 2.612 2 627 xean(6) 251(1 | 2-248|4| 2.22813 | 2.201\ 3) 2.185(3) nean{5) r65(7 ) 2.140({ ) 2.201t3l 2.114{3) 2.099{3} M5-OA2 2.r92 2.222 2 210 2 r12 2 161 -oA5 2.150 2.180 2,224 2.r48 2.!49 -oB3 2.099 2.l5{ 2.109 -oB{ 2.113 2.159 2.239 2.r25 2.128 -oc1 2.710 2.775 -oc3 2.775 2.5r9 -oc2 2.424 2 742 2 108 2.739 uern( ? ) 2.39711 ) 2 39s({) 2.{05(4) 2,112\ 3 ) 2.36213 ) Xean{5 ) 2.325(7| 2.33ri{) 2.356| 4') 2.305(3) 2.299(3 | Appendixescontinued on the next page 808 PINCKNEY AND BURNHAM: PYROXMANGITE AND RHODONITE

TibIE A{ Table A{ (continued)

NAT-P OF-P CWB-P oa-R

I. Pyrox[rnglte: Tetrahedral volun.6 83 and dlEtor!lon6 Ill Rhodonite: Te t rahed ra I and dl6!0r!lonE 2.18 2.20 2 27 2,20 2,19 sll v 2 21 2.19 2.2I 2,20 2.r9 2.23 I 0018 1 0037 1 0038 1.00{5 1.0048 1.0037 1.0040 r.0041 1.0058 1.005s 1,0041 1{.51 13 95 L4.14 17.{8 18.88 o2 13.39 14,50 15.40 22.L4 24,49 220 219 s12 V 2.2r 2.22 2.20 2.r9 2.L9 1.0044 1.0044 1.0048 1.004{ 1.00{5 \ 1.0040 1 0037 1.0039 1.0047 1.0050 1.00{2 19 05 19 l5 20.81 19.05 19.59 2 15.49 19.59 21.16 2.L1 2,71 2.15 2,!5 sil v 2.22 2 -19 2.16 2,L6 1 0049 r.0051 L-O012 1 0055 I .0058 1,0040 1.00{0 I 0040 r .0056 1 .0055 1 .0045 20.48 28.50 30.39 28.05 2e 3r 2 17.03 l?,09 17.06 23.49 21.95 L9.29 2.14 2.L4 214 si4 v 2.20 2.L1 1 0092 1.0105 1.0100 1.0113 1,0120 3? 30 42.73 40.03 4S.58 {8.01 I 1.0046 1.005r 1.0056 1.0056 1.0079 1.0065 2 r9.18 28.l1 2.16 I . 0115 r.0122 I.013r 1.0125 1.0135 si5 v 2.1S 219 2.LA 2.1S 2.!6 2.t4 5{.84 58.99 56 35 61.19 1,0087 1.0079 1.0083 1,009{ 1,0102 1.0085 2 34.8S 39,19 {l .60 XI 14 14 14,05 74,17 13.80 si5 v 2.73 2.r2 2.!5 2.13 2.r4 2.15 1.021 1.020 1.019 r 020 1,020 1.0116 r.0122 I.0121 l.0l{3 1.0154 1 , 0113 o2 55.l4 60.8r 57.{5 50.55 60.21 2 47,08 49.66 51.05 {4.91 14 48 14.28 14.18 14.05 13 ?9 I 026 t.024 L.O2Z | ,021 1.028 si7 v 2.20 2.t5 2.18 2 -15 2. L5 2,14 z 88.80 89 32 92,25 1.0110 1.0121 1.0110 1.0131 1.0156 1. 0132 2 49.16 54.88 49.09 58.98 59.{{ 59.78 M3 13.57 13 45 13.4{ l3.lI I 05{ 1 054 t .0s3 I .053 oZ 183 56 IA2.A7 185,30 !16.42 175. 89

14.25 L4.2L l3 .94 12.79 13.48 v{5) 13.84 13.06 12.18 1.020 1.020 1 ,020 1.019 1.019 1.023 2 1 09a 1.092 t .084 I .075 1.070 50,88 55.50 oZ 246.52 215 61 2tt.22 r99,95 l8{.82 x2 14.21 14.03 13.72 !2.9r 12.60 13.18 v(5) 7.3{ ?.19 5.99 1.015 1.015 r .010 1.017 1.020 1.013 o2 53,53 53.79 64.90 {1.85 H5 v(5) 15.02 15.58 1{,70 14.55 1.090 1.084 I .083 1.085 1.085 x3 14.34 T4 14 t3.92 13.30 12.81 o2 234 06 240.38 235,13 240.21 1.014 1.015 I .015 1.01? 1.020 1.013 2 44.68 {5.58 46.41 s2 11 50,18 12.2L v(7) 18.57 l8 5{ 19.01 18.07 1? 87 ff4 13 57 13.41 13.24 12,61 12.05 12.82 Polyhedral voluae6 and dl6tortions we!e calculated using the corput€r r.049 1.049 1.050 1,0{8 1.044 1.053 progran VOLCAI, writlen by L. c. 8lnger. The dlalortlon frarar€lelE of 2 nean quadratic elongation and angle v!rirnce.re defined by Bobin8on 163 83 16S,20 170.26 153 45 150.80 170.81 et aI (1971).

v( 5) !2,23 12.22 12.10 11,80 11,43 11,99 \ 1.213 r.22A 1.231 1.213 1,208 L,249 o2 qss,oz Asi zB 4G6.9s {59,04 4{5.49 519.05

v(7) 1S.51 18.38 18.28 17.58 17.00 Table A5. letrehedral chain lngles in pyroxrangite anal rhodonite

v(5) 13 88 !2.72 13.33 12.51 12.10 L3.23 x 1.098 1,097 1.094 1,0?1 1.065 1.119 Pyrox[anai te5:

o2 256.g1 z4a,i2 24g.5i 18 5 ,9 2 L12.11 289.23 Angler Nar-P FH-P ROIh-P CWB-P

v(5) 1.52 1,37 1.20 5,68 5.46 7.06 ocl-2-3 r47.8 1{8.I 148,9 150 5 147.9 150.7 oc2-l-4 !64,4 168.5 157.9 165.4 x? v(6) 1{.53 1{.40 14.38 13.90 13.1S L4.62 oc3-4-5 171.4 111,6 r76.2 r74.1 I11.1 \ 1.055 1 055 1.066 1.066 1.060 1.066 oc4- 5-6 167.7 153.I 160 I 167.1 o2 tls,B3 185.5g r9o.1g 196.12 r?9.03 207.16 oc5-5-7 145.6 144.9 143.7 1{1.7 139.6 14{.1 oc5-?-1 151.4 r52.2 t6t.1 r52 9 162.0 158.0 v(7) 18.15 18,00 1?,81 17.1? L6.31 18.01 157.8 r56.4

Angle Nar-F O8-R Peac-R

ocl-2- 3 154.5 150.{ t11 .6 17{.5 175.8 r75.4 150,1 t41.3 t45.0 145.3 L45.2 oc4- 5-1 160 0 150.5 161,1 150.3 160,{ oc5-l-2 154.1

I Angles forDed by brldging orygen.toi6i 9.9. rcad OCI-2-3 as the anglc fortr€d by oxygens OC1-OC2-OC3