American Mineralogist, Volume 68, pages 1174-1182,l9E3
Composition, orderdisorder and lattice parametersof olivines: determinative methodsfor Mg-Mn and Mg-Ca silicate olivines
Gnecony R. Luupxrxl Departmentof Physics Univ e rsity of California Berkeley, California 94720
Peul H. RrsnE, Departmentof GeologicalSciences Virginia Polytechnic Institute and State University B lacks b ur g, Virginia 2406I
eNo NnNcy E. Luuprrnr 524 45th Street Oakland, California 94609
Abstract
A methodhas beenderived to estimateboth the bulk compositionand the distributionof Mg and Mn and of Mg and Ca atoms betweenthe Ml and M2 octahedralsites in olivines of the forsterite-tephroite and forsterite-monticellite series, making use of the regression equations,a = 0.93216+ 0.236ry2+ 3.918,D:0.505rr,,rr + 3.Zllrvt2+7.535,determined by Lumpkin and Ribbe (1983).The strongdependence of a on ry1, the radiusof the Ml cation, and of D on ry2 is exploited on an a-b plot contoured for composition, 100Mg/[Mg + (Mn or Ca)1, and for the Mn (or Ca) content of the M2 site. Predictionsof bulk compositionfrom a-b are within -+l.sVoFo (on the average),and of site occupanciesare usuallybetter than +0.05 Mn or Ca. Natural olivinesof the forsterite-tephroiteseries and zincian varieties from Franklin, New Jersey are found to be highly ordered with nVo or more of the total Mn in M2 for sampleswith less than one Mn atom per formula unit and with >0.94 Mn in M2 for those specimenswith more than one Mn atom per formula unit. Synthetic Mg-Mn olivines are more highly disordered;synthetic Mg-Zn olivines are completely disordered.Single-phase Mg-Ca olivines synthesizedby Warner and Luth (1973)are highly ordered:in Fo55>EIVo of the Ca presentis in M2, in Mo55 >95Voof the Ca presentis in M2. The d-spacingsfor the 130and l3l peaksin X-ray powder patternsof olivinesare very sensitive to Mg-Mn and Mg-Ca order-disorder, but d112was found to be insensitive (to within one part in 2500) to cation distribution in Ml and M2. Regressionequations to estimatecompositions are 100Me/[Me + Mn + minor (Fe,Zn,Ca)]: 2484.87- 970.42dtn, and 100Fo/(Fo + Mo) = 19tt6.25- 752.l4drn; precisionis estimatedat better than tl.5 moleVoFo.
I Presentaddress: Department of Geology,University of New Mexico,Albuquerque, New MexicoE7l3l. 0003-004>u83llI l2-l 174$02.00 n74 LUMPKIN ET AL,: ORDER-DISORDER AND LATTICE PARAMETERS OF Me.(Mn,Ca) OLIVINE rl75
Introduction the importance of the efect of ordering in the M sites on latticeparameters, and in this paperwe will exploit these Despite many crystal stmcture refinements of silicate relationshipsto devisea methodof simultaneouslydeter- olivinestMll[M2]SiOa, showinga wide rangeof composi- mining the bulk composition and the ordering of octahe- tion (M2+ : Ni, Mg, Co,Zn, Fe, Mn, Ca) and a variety of dral cations in binary silicate olivines. We will emphasize orderingschemes (see Brown, 1982,Table 5 and Lump- the Mg-Mn olivines and others in the sameseries contain- kin and Ribbe, 1983,Table l), no method of estimating ing up to 0.25 Zn atoms, using the recent studies of both the bulk composition and ordering of the M2+ Francis (1980)as our primary data base.Data for the Mg- octahedralcations from physical properties has yet been Ca olivines are taken from Warner and Luth (1973)and devefoped(but see Smyth and Taftb 0982) for a descrip- others. Preliminary reports of this work were presented tion of cHExE-CHannelling EnhancedX-ray Emission by Ribbe and Lumpkin (1982),Lumpkin et al. (1982)and spectroscopy-used to obtain, directly and quantitative- in Figure ll of Lumpkin and Ribbe (1983). ly, Fe, Ni, Mn and Ca concentrationsin Ml and M2 sites.)Determinative methods for compositionin the Mg- Parameters for determining composition Fe olivinesare well known, beginningwith earliestopti- and cation ordering cal studiesand including the recent work of Laskowski Brown (1970)recognized significant negativedeparture and Scotford (1980) relating refractive indices ro Mg/ from linearityin plots ofa versusmean octahedral cation (Mg+Fe). Bloss (1952)established the nonlinearrelation- radius (ry) for the Mg-, Fe- and Mn-Ca olivines, and ship of density to Me/(Mg+Fe), and Yoder and Sahama Ganguli(1977) observed a positivedeviation from linear- (1957),Fisher and Medaris (1969),Schwab and Kustner ity in a plot of b versus(ry). (1977), and others (see Shinno, 1980) have produced Figure I is a compilation of silicate olivine data, determinativecurves basedon the d13espacing. showingessentially straightJine trends for specimensin To determine compositions of Mg-Fe-Mn olivines, which the occupanciesof the Ml and M2 sites are the Mossmanand Pawson(1976) used relationships between same. Lines arbitrarily drawn between Mg2SiO4(forster- the refractive index B and d13s.But Shinno (1980)and ite) and MgCaSiOr (fully ordered monticellite with all the Francis (1980)have recently demonstratedthat d13sis Cain M2), and betweenmonticellite and a-Ca2SiOashow stronglydependent on the degreeof M cation ordering, how a, b and V vary for the ordered compounds (large severelylimiting the utility of this parameter. cationsin M2). Equations or diagrams relating unit cell dimensions to Akimoto et al. (1976,their Fig. 3 reproducedas Fig. 15 composition have been produced for Mg-Fe olivines in Brown, 1982)also describedsignificant nonlinearity in (Louisnathanand Smith, 1968;Fisher and Medaris, 1969; plots of cell parametersversus composition in synthetic Schwaband Kustner, 1977),forFe-Mn olivines(Shinno, binary olivines containingMg with Mn, Co, Ni and Zn, 1980),for Mg-Mn olivines (Nishizawaand Matsui, 1972; and Francis(1980) found nonlineartrends for a, b, V, and Akimoto et al., 1976;Shinno, 1980;Francis, 1980),for d13sversus composition of orderedMg-Mn olivinesfrom Mg-Mn-Zn olivines(Francis, 1980), and for Mg-Zn, Mg- LEngban, Sweden and Madagascar (c/. Francis and Ni andMg-Co olivines(Akimoto et al., 1976).Fewer data Ribbe, l9E0).Although Francis (ms.) fitted second-order exist for olivines containingsubstantial amounts of cal- equationsto his data, eachofhis plots ofa, b and,dgsfor cium, but seeWarner and Luth (1973)for dataon Mg-Ca naturally occuring specimensappear to be equally if not olivines.Brown (1970,1982) attributed the nonlinearityin better fitted with two straight lines, one spanningthe plots of certainlattice parametersversus composition or compositionrange Mg2SiOa to MgMnSiOnand the other versus mean radii of the octahedral cations to M-cation MgMnSiOato Mn2SiOa.Data for syntheticMg-Mn speci- ordering. mens deviated toward the straight line presumed to In Part I of this work, Lumpkin and Ribbe (1983,see representdisordered olivines (see discussion below). also 1982)quantified the relationshipsamong unit cell As mentionedearlier, Lumpkin and Ribbe (1983)found parameters and the radii and formal charges of both that the lattice parameters of silicate olivines with diva- octahedral(M) and tetrahedral (T) cations in a wide range lent octahedral cations are highly correlated to the radii, of compounds that crystallize with the olivine structure ry1 and ry2, of thosecations. Their regressionequations (M = Li, Na, Mg, Al, Ca, Sc, Cr, Mn, Fe, Co, Ni, Zn, are given in Table l. Notice that in the equation for a the Ga, Y, Cd, Sm, Gd and Lu; f : Be, B, Si, P and Ge), regressioncoefficient of ry1 is -4 times as large as that using multiple linear regressiontechniques. They suc- for ry2, and in the equation for b the coefficient for ry2 is cessfully used cell volume to estimate the ordering -6 times as large as that for r1a1.Therefore it appearsthat schemesof a variety of synthetic compoundswith the a and b,, when consideredtogether, might be used to olivine structure.They also calculatedindividual sets of determine the degree of ordering of larger and smaller regressionequations for the phosphate,beryllate and divalentcations between the Ml and M2 sites,at leastin silicateolivines, correlatinga, b, c and volume V to the binary systemsin which ry1 and ry2 differ by -0.14 or mean radii of the Ml and M2 octahedralcations. These more. Of course, both a and D, as well as other lattice results unequivocallysupported Brown's suggestionof parameters,are also sensitiveto bulk composition. n76 LUMPKIN ET AL.: ORDER-DISORDER AND LATTICE PARAMETERS OF Me-(Mn,Ca) OLIVINE
Ribbe, 1980)and synthetic Mg-Mn olivines (Nishizawa o rs (ro),1 and Matsui, 1972;Ghose et al., 1975),(2) the composi- tions of Francis' natural specimens include less than 2 moleVo[Fe+Ca+Zn], and (3) site refinementsof crystal structures indicate significant disorder in synthetic sam- ples (Ghoseand Weidner,1974;Ghose et al., 1975),and nearly completeorder in natural Mg-Mn olivines (Francis b rs (re),1 and Ribbe, 1980),providing the means of testing the method. To construct the a-b plot shown in Figure 2, cell dimensions of four forsterites and four tephroites were averaged,giving the end-point^valuesof d : 43fi4, b = l0.l93A for Fo and a : 4.9044, b = 10.5984for Te (see c rs (rs),1 alsoTable 2). The linejoining thesevalues represents the locus of a and b for the disordered Mg-Mn olivines, and distance along it is presumed proportional to the Mg/ .lr"-o'c- (Mg+Mn) ratio. Given the broad rangeof data from which the equations in Table I were determined,it is not surprisingthat values V rs (rq)s,F for a and b for Fo and Te calculatedfrom these equations do not agree exactly with the observed values. Small correction factors, Aa and Ab, have been introduced to compensatefor these differences. They are applied in proportion to the bulk Mg-Mn content of all calculated reference points in this (or for that matter, any) binary system (see Table 2 footnote for a samplecalculation). . Ditord!.ad Having thus calculated corrected a and b dimensions o Ordcrad based on ordered MgMnSiOa, disordered (Mgos o40 060 080 l.oo Mns and antiorderedMnMgSiOa (with Mn in Ml, (t")t' F 5)2SiOa Mg in M2), thesevalues are then plotted in Figure2. The Fig. L Plots of a, b and c cell dimensions (in Angstroms) straight line joining these three points represents the versusthe meanradius of the octahedralcations (r") (in A) and of locus of all possible a and b values for Fo5eTe5s,and volume V versus (ro)3 (in A3) for a variety of binary silicate distance along it is proportional to x, the Mn content of olivines.The specimensknown to have chemicallyequivalent the M2 site (and thus to l-x, the Mg contentof M2). The Ml and M2 site occupancies are shown as solid dots and parallelogramcan be contoured with compositionaldeter- generallyfall along the linesjoining MgzSiOrand Ca2SiOa.Those parallel in with fully ordered arrangementsare plotted as open circles; lines minative lines to this diagonal,and labelled drawn connectingMgz-MgCa and MgCa-Ca2represent the locus of ordered olivines containing Ca in M2. Data are from Table I of Lumpkinand Ribbe(1983).
The a-b plot: its construction To illustrate this determinative method we have chosen the forsterite-tephroite (Fo-Te) series, because (l) a substantial number of lattice parameter refinements are '(!a available for both natural (Francis, 1980; Francis and o
Table l. The regressionequations relating unit cell parametersof silicate olivines to the radii of cations in the Ml and M2 and Ribbe(1983, Table 5): radii octahedralsites. From Lumpkin '-:l/z usedwere thoseof Shannon(1976). f N / \l/"- E Exonptc I soo rcrr } k/t\"*l-y i r,ririiriiiod Morlui{rs?zt
g '0.932 + + (R2 - = A) l/j';';' ; Fl$;.1,gBBi"'"'''a rMl 0.236 tM2 3.918 0.982; eed 0.010 Ms?sio.(Fo) x iloiiii Riti. ils6o) b = 0.505 r"a + 3.2!r Ev2 + 7.535 (R'z - 0.996; esd = 0.025 &) to4
g . 1.231 rMl + L,484 tU2 + 4.010 (R2 = 0.9933 eed - 0.019 A) b,l
V = 149.4 rMr + 187.5 rrr2 + 46.8 (R2 - 0.997; esd = 1.64 A3) Fig. 2. An a-b plot for the Mg-Mn silicate olivines. See text for detailsof its construction and use and Tables2 and 3 for data. LUMPKIN ET AL.: ORDER-DISORDER AND LATTICE PARAMETERS OF Me-(Mn,Ca) OLIVINE ll77
Table 2. Calculatedand observedcell parametersofcertain end-membersilicate olivines and calculatedand corrected cell parameters of intermediatecompositions. Calculated values of a and D were derived from equationsin Table I and the Shannon(1976) ionic radii. Observed values of end members are averagesof values taken from the referenceslisted in the right hand column (see footnote of Table).
Slte Calculated Correctlon colfected or conlents -i-----F-pararetera factorsi ---Z-lrobserved values )calc ET--frT- M 6- "rr2 RerE.
Ms Ms 4.759 10.210 -0.006 -0.017 4.753 r0. 193 2,456 t, 2, 3, 4 Mn Mn 4.887 10.619 1.0.017 -0.02r 4.903 r0.59E 2.559 1, 5 Mg l{n 4. 785 10. 564 +0.006 -0,019 4,791 r0.545 2,507 lln Mg 4.861 10,266 4.a67 70.247 2.506 Me.rl lug.. 4.823 ro.415 4.a29 t0.396 2.506 lm.s m.5l Ce ce 5.086 IL251 -c.008 -0.026 5.O78 tt,225 2,729 6 M8 ca 4.825 I1.Il0 -o.oo7 -o.022 4.915 11.088 2,586 Ca M8 5.020 10.352 5.013 10.330 2.585 ues| fles 4.s22 ro.73r 4.915 10.709 2.586 lua.5 ue.5l (zt zl)** 4.782 ].0.285 +0.008 r{.013 4.790 10.298 Ms zn 4,764 10.274 +0.001 -0.002 4.765 rO.272 zn Ms 4.778 lO,22O 4.779 LO.2ta Mn Zn 4.865 10. 330 r{.0r2 -0.003 4.878 10.327 Zn Mn 4.803 10.574 4.815 r0.571 Fe Fe 4.E29 10.433 -0.009 {{.041 4,820 rO.474 3,1,8,9
''values of Ae and db are deternlned fot end renbels by subtractlng a and b (as calculated fr@ lhe eqstlons in Table 1) fron the observed valuee. Correctlon to calculaled a for, say, MB!'1nSi04ls Aa = +0.0065 eEctly half way between Aa -0.006 **of for Mg2S1o4 and +0.017 for 1,1n2S104. Ilypothetlcal end renber. The vaLues of a and b (glven) and c - 6.019 A Predtcted fron equations in Table 1 sgree w€11 with those d€temlned by extraPolation (4 - 4.79 t,, b = 10.31 l,and c = 6.02 A) by Akinoto et al. (I97q their F18. 3 and Table 1). Our extrapolatlon (see !'18. 2) givee b ! 10.298 A.
References
I. Fujlno er al. (I98I) Acla Clyst, 837, 513. 2. Hezen (1976) AD. Ml.nera1. 61, 1280. 3. Schwab & KusEner (1977) N. Jhb, H1n. Mn., 205. 4. Takel 6 Kobayashl (1974) J. Cryst. crowth 23, 12I. 5. Nlshizawa & Mat€ui (1972) Phys. Earlh PIan. lnt. 6, 377. 6. czaya (1971) Acta cryst. 827, 848. 7. Akinoto et a1. (1976) Phys. Cheil. Min. & Rocks. John wl1ey' N.Y. 8. Snyth (1975) An. Mineral. 60, 1092, 9. Ilazen (1977) An. Mineral. 62, 286. termsof 100Mg/(Mg+Mn) or moIeVoFo. Lines parallelto The a-b plot: its use the Mn2SiO4-MgMnSiOaand Mg2SiO4-MnMgSiOasides Included on Figure 2 are the a-b values of natural and representloci of equalx, the Mn-contentin M2. The sum, synthetic Fo-Te specimensfrom Table 3. There is excel- )x, of the x valuesat the oppositeends of a compositional lent agreementbetween the reported compositions,ex- contour is equal to the total number of Mn atoms per pressedas 100Mg/(Mg*Mn), and those estimatedfrom formula unit. the contoured a-b plot: the mean deviation is tl.l An example will suffice to illustrate how to interpret mole%oFo, only slightly greater than that expectedon the dataon the a-b plot. Supposean unknown olivine in this basis of estimated errors in a and b. binary system_has dimensions4 = 4.828*0.0034, b : There are clearly two populations of samples.Natural 10.497-+0.007A(open rectanglein Fig. 2). The NW-SE specimensare highly ordered, with the M2 site containing compositionalcontour on which this value lies indicates %+ % of the total Mn for sampleswith less than one Mn 40 moleVoMg (= Foa6Te66)to be the bulk composition. atom per formula unit (x < 1), and >0.94 Mn for samples The endsof this line have x : 0.20and x : 1.00,thus )x with x > I (seeTable 3). The least-squaressite refine- = 1.20 Mn atoms. The chemical formula is ments of two of these, 9a from L&ngban, Sweden Mg6.sMn12SiOa. The Mn content of the M2 site is x : (Fosr.gTeas.z)and 15a from Madagascar(FogrTesos), 0.80, and the structural formula, in the order have structuralformulas [Mgs e2Mns.6B][Mg1lMns.se]SiOa tMlltM2lSiOa,is [Mg1-;*+*Mn>*-^][Mgr-xMn^]SiOaor and [Mgo17Fe6 e3Mns.ss][Cao.orMno.ge]SiOa, respectively, [Mg6.6Mns.a][Mg62Mns.s]SiOa. Estimated errors in x are which agreerather well with those predicted from the a-b -10.02 +0.03 Mn and in )x Mn or t2 moleVoMg, based plot: [Mg6.e2Mne.qE][Mgs.17Mno.sr]SiO+(predicted compo- on the given esd's of a and b. Systematic error in sition: Fo5aTeld and [Mgs.22Mnq.7s][Mgo.ooMnro0]SiO4 estimatingMg-Mn content and distributionwill result if (ForrTess). the Ca contentexceeds 0.1 atoms.See discussion below. Only two of the natural specimens-l5a (see above) I 178 LUMPKIN ET AL.: ORDER-DISORDERAND LATTICE PARAMETERSOF Ms4Mn,Ca) OLMNE
Table 3. Observeda and b and calculatedd112 values, observedand estimatedM-cation distributionsof natural and synthetic specimensin the systemsforsterite-tephroite and forsterite-monticellite.
Forete?ite-IepTvoite
Saup Ie Slte occupancy ffon a-b (xLO2, - JaIc number a (tr) b (i) froa a-b ttot M1 M2 4il" FSTS 4.753 10.190 2.456 r00 100 r00. 5 100 00 L20 00 TeK 4.753 10.191 2.457 100 100 101.5 100 00 100 00 F2 4.757 10.219 2,46r vJ. o 96.5 96.7 100 00 93 07 F3 4.760 I0,244 2,465 9L.6 92 92.8 98 02 86 L4 E4 4.761 LO.254 2.466 91.6 9t 91.8 99 01 83 L7 F5 4.775 r0.344 2.48r 77.4 77.3 94 06 58 42 4.773 10.351 2.482 77.2 76 76.2 96 04 56 44 N6M 4.782 r0.339 2,485 75.0 74.O 88 L2 60 40 F7 4.778 10.398 2.490 68.4 68.5 97 03 42 58 F8 4.782 10.406 2.492 67.8 67 66.5 94 06 40 60 GEW 4,811 10.421 2.505 53.0 54.0 69 3r 40 60 F9 4.799 LO.499 2.507 51.4 51.5 52.O 88 L2 15 85 FR9a 4.794 10,491 2.506 51.3 54 )J.4 92 08 L? 83 N&tt 4 .8r8 ro.447 2.5rO 50.0 49 49,L 65 35 33 67 F10 4.810 r0,540 2.5L6 45.8 43 43.3 81 19 05 95 Fl1 4.827 10.549 2,524 37.0 35.5 67 33 04 96 F12 4.830 10.553 2.527 30.7 33.5 32.6 63 37 04 96 N&M 4.855 10.536 2.537 25.0 26 ,t o 40 60 12 88 Fr3 4.850 10.568 2.537 23.3 24 22.9 s0 50 02 98 F14 4.860 10.580 2.544 18.6 19 t6.1 39 6r 00 100 F15 4.880 10.586 2.550 09.0 tt 10. 2 20 80 01 99 FRl5a 4.879 10.589 2.549 09.1 11 r0.8 22 78 00 r00 FSTS 4.902 10.596 2.559 00.0 01 01.6 00 100 01 99 TA(EI 4.906 10.598 2.559 00.0 <00 0r.6 00 r00 0r 99 M&R 4,091 10.598 2.559 00.0 0r. 5 01.6 03 97 00 100 F or s te" tte -Mmt t c eL Lit e I00 Fo/(Fo + Mo) Mg Ca Ug Ca s6H 4.822 1r, 100 2,586 00.5 100 0 00 100 L&1..1 4.825 11.111 2.589 -01 -r.2 99 0l 00 100 ONKEN 4.822 11. 108 2. 588 00.0 00 -0. 3 100 00 00 100 wL1 4.82L 11.091 2.545 01.0 01.5 2.O 100 00 01.5 98.5 rrL2 4.820 11,053 2.580 05.5 05 5.7 99 0r. 06 94 IJL3 4.420 11. 510 2,579 uo. f u).) 6.5 99 01 06.5 93.5 wL4 4.818 11.007 2.573 11.0 09.5 11.0 98.5 01.5 11 89 wL5 4.815 r0.960 2.565 ao.4 14.) L7.O 98 02 to. ) oJ. ) r.116 4 .814 10.913 2.560 2L.8 19 20.8 98 02 2t 79 wL7 4,769 10. 318 2.476 82.0 83.5 83.9 97 03 do.) rJ. ) wL8 4.766 ro.293 2.477 86.3 87 47.7 97.5 02.5 89.5 10.5 "wt 9,l0 4.760 ro,248 2.464 90. 9 92,5 93.0 98 02 v4.) u). ) *wltr-t3 4.75a ro.207 2,40L 95.5 96.5 95.2 99 01 *wt t4-t6 4.tss 10.198 2.457 100.0 99.5 98.2 100 00 99.5 00.s Average values of cell para@ters. See VJarner and Luth (1973' Table 3). Actual coupoaltlons glven." MB'OO.5F"O.O'OC.O.96ZSlo4for s&H and MBO.9:6F"O.OltC.l.00gSlO,99204fo. L&M trererences Derowr. REFERENCES(alphabetically ) F2-15 Francis (19E0) Ph.D. Dlssertation (see Refe?eneea) N&|1 Nlshlzasa & ltatsul (1972) Phys. Earth Plan. Int. 6' 37i FR9a,15a Francls & Ribbe (1980) An. Mlneral. 65, L263 oNKENOnken (1965) Tchero, Mln. Pet. Mttt. 10, 34 FSTS Fullno et al. (1981) Acta Cryst. B37' 513 s&H schwab& Kusrner (1977) N. Jhb. Mln. Mn., 205 G&I'I Ghose & weldner (1974) Geol. Soc. An. Abstr. 6, 751 TAKEI Takei (1976) J. Crystal GrowEh 34' 125 L&M Lager & Meagher (1978) AE. Mtneral. 63, 365 T&K Takel & Kobayashl (1974) J. Cryst. Growth 23' I2l MER Muller & Roy (1974) Major Ternary strucrl. Fauilles WLl.,.Warner e Luth (1973) Am. Mlneral. 58' 998 and 13-contain sufficientcalcium to affectthe valueof x. a-b datLtm(andthus the value of x = Mn in M2) is located The opencircles in Figure2 representa-b pointscorrect- 66 to 76% of the distance along the composition contour ed to accountfor 0.013and 0.024Ca, assumingthe Ca is from the antiordered side of the parallelogramtoward the in the M2 site. (See the discussionin the next section orderedside. Ghoseand Weidner's(1974) sample is the whereCa contentis of majorconcern in the interpretation only syntheticspecimen whose structurehas beendeter- of the zincian tephroitesfrom Franklin, New Jersey.) mined, and the observed structural formula, The four syntheticsare, in termsof the "order parame- [MgozzMno.zr]lMgo.sMno oo]SiOr, and bulk composition, ter" definedby Lumpkin and Ribbe (1983,Fig. ll), Fo53Tea7,agree reasonably well with calculatedvalues: between66 and 76Voordered. This simply meansthat the [Mg6.6eMne31][Mg6.asMnq 60]SiO4 and Fo5a.5Tea55. LUMPKIN ET AL.: ORDER_DISORDER AND LATTICE PARAMETERS OF MS4MN,CA) OLIVINE 1179 Zincian Fo-Te from Franklin, New Jersey. The a-b determinativediagram of Figure 2 is partially reproduced in Figure 3, but the zincian Fo-Te specimens(analyses and cell dimensionsfrom Francis, 1980)plotted here contain up to 0.045 Ca (average0.021), up to 0.104 Fe (average0.033), and up to 0.251Zn (average0.17). The most notable feature is that specimens4 through 8 plot off the Mg-Mn parallelogramaltogether. This is due neither c< to the minor Fe nor the more significantZn content, 0 becausethe Shannon(1976) radii of Fe (0.784) and Zn 4 8l (0.744)fall betweenthe Mg lO.72A)and Mn (0.83Atradii. The corrected,calculated data points for (hypothetical) orderedZnMnSiOa and end-memberZn2SiOa are shown in Figure3 (andinset), and indicatewhat the major effect (1983b) I Obsarvadvoluca from Froncis of Zn contenton Fo-Te specimenswould be on the actual 6 volu.s corrected for Co in M2 locationof the compositioncontours. I Zn-tcDhroilalrom Brovn (1970) + E3limdl.d crrors on d ond , 47 It is in fact Ca that displacesthe a-b points up to to3 to4 0.0254 highervalues of b and 0.002Ahigher values of a. b,i If one makessome assumptions about site occupanciesin Fig.3. A partiala-b diagram(c/. Fig.2) for theMg-Mn silicate thesesamples, it is possibleto adjusta and particularlyb olivineswith datafor zincianvarieties plotted on it. The open to correct for Ca content. The procedureis simple: first circlesrepresent a-D valuescorrected for Ca contentin M2. See assumean orderedlarge cation distribution, /.e., assignto text for discussion.The inset(upper left) is an a-b plot for the M2 all the Ca and either all the Mn (plus Mg, as needed) Mg-Znolivines synthesized at hightemperature.s and pressures or sufficientMn to fill the site. The remaining cations (upto 90kilobars) by Syonoet al. \1971).The Zn'SiO' point was (Mg, Fe, Zn and left-over Mn) are assignedto M1. Then determinedby extrapolation(see footnote in Table2 for details). calculatea' and b' using the equationsof Table l. These valuespresumably mimic the true distributionfairly well, sincewe know from structuralstudies that Ca is alwaysin tephroite", and to which he assignedthe [Ml][M2] site M2 (for Ca < 1.0atoms), Mn likewiseorders into M2 (see occupancy [Mno+rzMgo 3a5Zns lssFee q+:][Mno soaFeo oas above)andZn prefersMl (seeFrancis and Ribbe's(1980) Zno otsf. It is hard to defendthis assignment,based on X- reinterpretationof Brown's (1970)refinement), even in ray site refinementalone. Using mean Ml-O and M2-O synthetic Mg1 5TZnsa3SiOa(Ghose et al., 1976). (The bond lengths and data from other crystal structures, exactdetails of theseassumptions about site assignments Francisand Ribbe (1980)argued that 1.00Mn is ordered are not critical, becausethe Ca content, small though it into M2 in the specimen,with the remainingcations in be, controls the correction, and it is the dffirences in Ml. The a-b plot supports their analysis,predicting a calculateda andb that are of interest.)The secondstep is fully orderedstructure with 1.00Mn in M2. to remove Ca from considerationby normalizing the Earlier estimatesof cation ordering in two Franklin formulasto 2.000total cations,i.e., multiplyingall values olivinesequivalent to samples2 and4 (Fig. 3) were made by l2l(l-Ca content)1.Then fill M2 with Mn (or Mn+Mg) by Huggins(1973) using an infra-red spectroscopictech- andcalculate a" andb". The differences,6c' : a' - a" and nique.For sample4 (his #16), our estimateof 0.99Mn on 6b = b' - b", representcorrections to be subtractedfrom M2 is somewhathigher than Huggins'value of 0.91.The the observeda and b values to accountfor Ca content. discrepancyfor sample2 (his #17) is considerablygreat- These are shown as open circles connectedby lines to er, with our prediction of 0.92 Mn on M2 far exceeding their respectivedata points. In all cases(except specimen Huggins' estimateof 0.67. Readersare referred to the #8), the corrected datum is in or on the edge of the work of Francis (1980) for discussionconcerning the parallelogram,indicating, as expected,highly orderedMn generalutility of the IR method. distributionsin thesenatural zinciantephroites. The usefulness of Figure 3 for determining Mg/ Figure3 will be usefulonly if both compositionand cell (Mg+Mn) ratios is obviouslylimited due to the chemical dimensionsare known. To predict 6a and Dbfrom total Ca complexityof the zincian samples,but the coruecteda-b content,use theseequations: 6d : 0.04 x (Ca-content); points(open circles) give valuesof )x (= total Mn) fairly 6b : 0.54 x (Ca-content).They were derived from data close, although consistently higher than the observed we calculatedusing the Franklin suite of Francis (1980), valuesbecause of the Zn (plusminor Fe) for Mg substitu- but they could be determinedequally well from observed tion. The usefulnessof Figure3 is mainly in the prediction and correcteda and b valuesfor Mn2 and MnCa olivines of order-disorder. in Table 2. Significanceof ordering in Mg-Mn olivines. The ability The only test of this diagramcomes from the specimen to determine ordering in synthetic and natural Mg- that Brown (1970; 1982,p. 361-364)calls "zincian picro- Mn(Zn) olivines makesit possibleto analyzethe depen- I 180 LUMPKIN ET AL.: ORDER_DISORDER AND LATTICE PARAMETERS OF Me-(Mn,Ca) OLIVINE denceof cationdistribution on a sample'sthermal history It is of interest to note that Warner and Luth (1973) (c/. Francis and Ribbe, l9E0; Shinno, 1980).Nishizawa usedthe 20131values from CuKc powder patternsof the and Matsui (1972)synthesized their samplesby heating single-phasesamples (those plotted in Fig. 4) to derive mixturesof Mg2SiOaand Mn2SiOaat 13fi)'C for 12hours equationsfor predictingthe compositionsof the coexist- under controlled./C2, with H2/CO2: l/3. The olivine ing Fo55and Mo55 phasesin their experimentsdesigned describedby Ghoseand Weidner(1974) and Ghose er a/. to delineate the solvi in the Fo-Mo system at high (1976)was "heat treated at lfi)0'C" for an unspecified pressuresand temperatures.They were troubledby their duration. As previously discussed,these synthetic Mg- results(their Figs. 2a,b, p. 1002)which showeda widen- Mn olivines are only partially ordered. It would appear ing solvus above l2(X)'C at 10 kilobars. However, this likely that undercertain conditions even more disordered may well be an artifact of their using an Mg-Ca order- arrangementscould be quenched. dependentparameter to estimate composition!In fact, The highly ordered natural Mg-Mn olivines have equili- ds (andtherefore 20131) is the samefor all compositions brated at lower temperatures on a geologic time scale. betweenFo12Mo6s and Fo2Moe6if Fo12Mo6sis assumed Moore (1970)gave an estimate of at least 650"C for the to be ordered ([Mgr oo][Mgo12Caa.s]SiOa) and Fo2Moeg Mn orebodies and skarns at Lingban based on the -25% disordered ([Mgo.zrCaozo][Mgo.zeCao72]SiO4). presenceof manganositeand periclase. His estimate Lines representingequal valuesof calculatedd131-spac- correlates well with the occurrence of andalusite and ings are plotted in Figure 4 to illustrate this point. The sillimanitein the metavolcanicrocks (leptites)associated argument that higher pressuresincrease cation order with the skarns (Moore, 1970,Table l). Zincian Mg-Mn while decreasingmolar volumeis invalidfor theseMg-Ca olivines from the Franklin orebodies probably formed at olivines: the equationfor V in Table I predicts smaller similartemperatures. Frondel and Klein (1965)estimated volumesfor the more disorderedpolymorphs (c/. Fig. l). a minimum temperatureof 650-700"Cin regard to hetaer- Other binary silicate olivines. The Mg-Co, Mg-Ni, olite exsolution from franklinite, in general agreement Mg-Fe, Fe-Mn and Fe-Ca olivineshave also been stud- with the sillimanite grade of gneissiccountry rocks (Fron- ied successfullyusing a-b plots.However, somepractical del and Baum, 1974). difficulties arising from the similarities of the radii of Ni, The Mg-Ca olivines. Figure 4 is a partial a-b diagram Mg, Co, and Fe are under investigation.The data of constructed using forsterite (Fo) end-point data from Annersten et al. (1982) for ordered synthetic Ni-Fe Table 2, and a and b valuesfor monticellite(Mo) from olivinesprovide further confirmationof this method,with Onken (1965).The Fo and Mo solid solutions plotted the exceptionof their aberrantdatum at Fa52.The syn- there were synthesized hydrothermally by Warner and thetic Mg-Zn olivinesof Syonoet al. (1971.)appear to be Luth (1973,see p. 1007for techniques).The estimated completelydisordered (see inset to Fig. 3). compositions,100 Fo/(Fo+Mo), of Warner and Luth's specimenshave an averagedeviation of only 1.5 from The d-spacings of dffiaction peaks as their reported values, and they all appear to be very determinative methods highly, thoughnot completelyordered, with >80% of the The regressionequations (Table l) togetherwith the present Ca in Fo55in M2 and >95Voof the Ca presentin study of the dependenceof a and b on order-disorderof (see Mo55in M2 Table 3). cationsin olivine (above)lead to the following re-evalua- tion of d-spacingsof peakson powder diffraction patterns as compositionalindicators. In the orthorhombiccrystal system, This, together with our regressionequations, requires o that most of the peaks in an olivine powder diffraction pattern will have d-spacingsthat depend on order/disor- der as well as on bulk composition. In the Fe-Mn + LoE.r A M.o9h6r (1978) (Shinno,1980) and Mg-Mn olivines (Shinno, 1980;Fran- o wo.ner I Luih (1973) . onr.n (19651 cis, 1980;see Fig. 2) this fact was recognizedfor dr30, x Sohomo a Hylon.n {1958) which, of course,depends solely on a andb. Warner and ffo t2 U,A Luth (1973)used d131to determinecompositions in the Mg2-MgCasilicate olivines. Like dBs, this parameteris Fig. 4. A partral a-b plot for the Mg-Ca olivines constructed with data in Tables 2 and 3. The three parallel lines near the Mo extremely sensitiveto Mg-Ca order-disorder,as noted corner of the diagram are lines of constant d;31-spacings, above. calculated from values of a, b and c expected in that range of In a searchfor a diffraction peak in the powder pattern composition and order-disorder. which is relatively insensitiveto the distributionof large LUMPKIN ET AL.: ORDER-DISORDER AND LATTICE PARAMETERS OF Ms-(Mn,Ca) OLIVINE I lEl and small cationson Ml and M2, it was discoveredthat d112does not vary more than one part in 2500 from a singularvalue, regardlessof whether Mg is assignedto Ml and Mn to M2 (the ordered arrangement) or Mgs.5Mns.5to both sites(the disorderedarrangement) or €s Mn to Ml and Mg to M2 (the antiorderedarrangement). Eg- z eoti The d1p spacingswere determinedusing a, b andc values E&.24s487 -s7o 42diia' ( R2.oggo ) calculatedfrom the equationsin Table I and corrected as discussedabove (valuesfor a and b are in Table 2). O xoturol, F.ofrcl. (19830) O Synlh.lic, Gio.. A ,, ,l | 1976, It is fascinatingto note the sameinsensitivity of d1p tl.hltoro A Mol.ui {13?2) calculated for hypothetical ordered, disordered and an- 8070rcs40we lO0 Mg /( Mg + Mn +Zn + F. + Ca) tiorderedFeCaSiOa and MgCaSiO+(see Table 2), and to presume it holds for any pair of elements that form Fig. 5. A plot of d12-spacings calculated for natural and (Table versus 100Mg/ silicate olivines. This leads to the proposal that d112 synthetic Fo-Te specimens 3 and Fig. 2) (Mg+Mn+Fe+Zn+Ca), where (Fe+Zn+Ca) is lessthan 27aof replaced13s (which works for Mg-Fe olivines only be- total M cations. The light, curved line is the d13s curve (which causethey are all nearly disordered)and d131 did calculated for highly ordered natural specimens by Francis not work for Warner and Luth (1973))as the "composi- fi980). tion parameter" for all binary olivines. For the forsterite-tephroite series, the ll2 diffraction peak is fortunately very intense, and if dy2 is carefully of both composition and orderldisorder and should be measuredwith an internal standard(or calculatedfrom a, used in preference to d112. b and c) it shouldgive reasonableestimates of composi- Acknowledgments tion according to the following equation derived from data referencedin Figure 5: The authors are grateful for financial support of this work by N.S.F. grant EAR.77-23114to G. V. Gibbs and Paul H. Ribbe. (Harvard 100MgDM = 2484.87- 970.42Xtiti 1p12: 0.993) Mr. Mark Miller (VPI&SU) and Dr Carl A. Francis Museum) contributed significantly to the progressof this study, The compositionalparameter we haveused is the number and the latter is especiallyacknowledged for producing much of of Mg atoms in the formula divided by the total number of the data on which this work is based in advanceof publication. cationsin octahedralcoordination. In natural specimens small amounts of Fe, Zn, Ca and Ni will affect d112, References contributingto an estimatederror of -t-1.4moleVo Mg, Akimoto, S., Matsui, Y. and Syono, Y. (1976)High-pressure less than half of which should be attributable to measur- crystal chemistry of orthosilicates and the formation of the ing d12 or calculatingit from cell dimensions. mantletransition zone. In R. J. G. Strens,Ed., The Physics p.327-363. To test this equationthe cell parametersof two Mg-Mn and Chemistryof Mineralsand Rocks, JohnWiley York. olivinesrefined by Francisand Ribbe (1980)were usedto and Sons,New Annersten,H., Ericsson, T. and Filippidis, A. (1982)Cation calculatedly-and then the MgDM ratios. Observedand olivines. American Mineralogist, 67 l2l2- : ordering in Ni-Fe ' calculatedcompositions, respectively, are Mg/)M 51.3 1217. and 53.4 and 9.1 and 10.8. The agreementbetween Bloss, F. D. (1952)Relationship between density and composi- observedand calculatedcompositions is generallybetter tion in mole percent for some solid solution series. American than this-see Table 3. Mineralogist, 37, 966-981. The 112 peak in powder patterns of membersof the Brown, G. E. (1970)The Crystal Chemistry of the Olivines. forsterite-monticellite (Fo-Mo) series is also very in- Ph.D. dissertation. Virginia Polytechnic Institute and State tense,and thus d;12may be used to predict composition University,Blacksburg, Virginia. to aboutthe sameprecision (* l.3VoFo) as for the Fo-Te Brown, G. E. (1982) Olivines and silicate spinels. In P. H. Ed., Reviews in Mineralogy, Vol. 5, 2nd edition' series.The regressionequation, based on data in Table 3, Ribbe, Orthosilicates, p. 215-381.Mineralogical Society of America, IS Washington,D. C. Fisher, G. W. and Medaris, L. G., Jr. (1969)Cell dimensions 100Fo/(Fo+Mo) : 1946.25- 752.t4f,iti R,: 0.9993). and X-ray determinative curve for synthetic Mg-Fe olivines. Cation ordering may have a dramatic effect on the AmericanMineralogist, 54, 74l:7 53. (1980) Solid Solutionin intensitiesof diffraction peaks,and a study is underway Francis,C. A. Magnesium-Manganese the Olivine and Humite Groups. Ph.D' dissertation.Virginia to determinewhether ratios of certain peak intensities PolytechnicInstitute and State University, Blacksburg,Vir- practical might be of value in determining the distribution glnra. of cations of sufficiently different x-ray scatteringpowers Francis,C. A. and Ribbe, P. H. (19E0)The forsterite-tephroite betweenMl and M2. In the meantimethe a and b cell series. I. Crystal structure refinements. American Mineral- dimensions,determined by powder or single-crystaldif- ogist,65, 1263-1269. fractometry,have proven to be highly sensitiveindicators Frondel,C. and Baum, J. L. (1974)Structure and mineralogyof ll82 LUMPKIN ET AL.: ORDER-DISORDER AND LATTICE PARAMETERS OF Ms-(Mn,Ca) OLIVINE the Franklin zinc-iron-manganesedeposit, New Jersey. Eco- Nishizawa,O. and Matsui, Y. (1972)An experimentalstudy on nomic Geology,69, 157-180. partition of magnesiumand manganesebetween olivine and Frondel. C. and Klein. C. (1965) Exsolution in franklinite. orthopyroxene. Physics of the Earth and Planetary lnteriors, AmericanMineralogist, 50, 1670-1680. 6,377-384. Ganguli, D. (1977)Crystal chemical aspectsof olivine structures. Onken, H. (1965)Verfeinerung der Kristallstrukturvon Monti- Neues Jahrbuch ftir Mineralogie, Abhandlungen, 130, 303- cellite. TschermaksMineralogische und PetrographischeMit- 318. teilungen,10,34-44. Ghose,S., Wan, C., Okamura,F. P., Ohashi,H., and Weidner, Ribbe, P. H. and Lumpkin, G. R. (1982)Prediction of cation J. R. (1975)Site preferenceand crystalchemistry oftransition ordering in olivine-type compounds. (abstr.) l3th General '82, metal ions in pyroxenes and olivines. Acta Crystallographica, Meeting of the International Mineralogical Association A3l, Supplement576. Varna, Bulgaria,p. 139. Ghose, S. and Weidner, J. R. (1974)Site preferenceof transition Schwab, R. B. and Kustner, D. (1977)Prizisionsgitterkonstan- metal ions in olivine. (abstr.) Geological Society of America tenbestimmung zur festlegung r