American Mineralogist, Volume 65, pages 1263-1269, 1980
The forsterite-tephroite series:I. Crystal structure refinements
Cenr A. FReNcIs Mineralogical Museum,Hamard University Cambridge,M assachusetts02 I 38
AND PAUL H. RIBBE
Department of Geological Sciences Virginia Polytechnic Institute and State University B lac ksbur g, Virginia 2 4 06 I
Abstract
The crystal structures of the following metamorphic olivines, M;*[SiO4], in the forsterite- tephroite (Fo-Te) serieswere refned in space group Pbnm: Cation compositionM Cell parameters(A) Mg Mn Ca Fe a b c Rfactor Fol 1.028 0964 0.006 0.002 4.794 10.491 6.t23 0.029 Ten, 0.181 1.780 0.013 0.026 4.879 10.589 6.234 0.039 Treating minql ps and Ca as though they were Mn, the refined cation distributions (esds < 0.01) and mean bond lengths are: M(1) site M(2) site Mg Mn (M(lFo) Mg Mn (M(2)-o) (si-o) For, 0.92 0.08 2.116I^ 0.1I 0.89 2.185A r.6374 Te", O.l7 0.83 2.0294 0.00 1.00 2.2274 l.6,t0A By comparison, a previously refned synthetic ForrT€o, specimen "heat-treated at l(X)0oC" is significantlymore disordered(KD : 0.196)than the naturally occurring For' (Ko: 0.011). As expected,mean M(l)-O and M(2)-O distancescorrelate linearly with Mgl(Mg+Mn) oc- cupancy.
Introduction However, the crystal structures of only two Mg- With the widespread availability of automated X- Mn olivines have previously been refined. One of ray di-ffractometeruand least-squaresrefinement pro- them contains I I mole percent of Zn SiOo, thereby grams, order-disorder has become a principal theme complicating the octahedral site refinement (Brown, of contemporary crystal chemical investigations 1970). The other is synthetic ForrTeo, which was (Burnham, 1973).Both natural and synthetic com- "heat treatedat l000oc" (Ghoseand Weidneg 1974; pounds with the olivine structure have been in- Ghoseet al., 1976)and thus doesnot representa nat- tensivelystudied (for a review,see Ganguli,1977). At urally equilibrated Mg/Mn distribution. The present least 25 different room-temperature refinements of refinementswere undertakento examineMg/Mn or- the geologically-importantMg-Fe olivineshave been dering in natural olivines uncomplicated by addi- carried out and 13 additional refinements extend the tional substituents. observationalconditions to temperaturesof - l000oC Experimental proceduresand structure refinenent and pressuresof -50 kbar @assoet al., 1979;Birle er al., 1968; Brown and Prewitt, 1973; Finger, 1970; The crystals used for refinement were selected Finger and Virgo, l97l; Hazen, 1976;Smyth, 1975; from the suite of specimensdescribed in Part II of Smyth and Hazen, 1973;Wenk and Raymond,1973). this study (in preparation). The manganoan forsterite w03-.004X/80/l I 12-1263$02.00 t264 FRANCIS AND KIBBE: FORSTERITE-TEPHROITE S.ERIES from Lingban, Sweden (Harvard University Te' were carried out using the program RFINE 4 #116463) has the compositioo Mg,orrMno"u4 (Finger and Prince, 1975).Scattering factors for neu- Ca"*uFeooouSio4.It occurs with fine-grained haus- tral atoms with corrections for anomalous dispersion mannite in a calcite skarn. In hausmannite-free were taken frort the International Tablesfor Crystal- bands anhedralforsterite crystalsrange from 0.1-1.0 lography(1974, p.99, 149).The refinementswere ini- cm in size.The tephroite, from an unspecifiedloca- tiated using the positional parametersof forsterite tion in Madagascar(Harvard University #108206) (Hazen, 1976),fully orderedcation distributions [Mg hasthe compositionMn, rroMgo,r,Feoo""Ca.o,rsiO4.It concentrated on M(l)], and reasonableisotropic tem- occurs as discrete rounded crystals l-2 mm in diame- perature factors. After several cycles varying the ter associatedwith rhodonite, yellow spinel, and blue scale factor and positional parameters, the conven- apatite in a calcite marble. For the purposesof site tional R factor dropped to -0.10. Site occupancyre- occupancy refinement these compositionswere ap- finements were undertaken by varying the Mg con- proximated as Fo'Teon and Te",Fonand are denoted tent of M(l) while constraining the total cation below as Fo' and Ter,. chemistriesto agreewith the observedcompositions. Refinements were carried out in the conventional Site occupancies were refined alternately with iso- but nonstandard spacegroup Pbnm. Unit-c.ell dinen- tropic temperature factors, and the R factors de- sions (Table l) were calculatedfrom the orientation creasedto R : 0.038for Fo' and R : 0.056for Ten,; matrices and are identical to within three estimated all positional parameters were identical within thlee standard deviations of those obtained by least- estimated standard deviations to those of the final squaresrefinement of powder data as reported in anisotropic model. Anisotropic thermal parameters Part II. The crystalsused for data collectionare tabu- and an isotropic extinction correction were applied in lar with dimensions0.24 x 0.24 x 0.07 mm for Fo' the final rycles of both refinements, leading to un- and 0.30 x 0.30 x 0.20 mm for Ter,. Intensity data weighted R factors for all data of 0.029for Fo' and were collectedin two octants(20 < 70") at l SoCon a 0.038for Ten,. Picker FAcs-l four-circle di-ffractometer,using Nb- Structure factors for which F"o"< 2oF"* were con- filtered MoKc radiation (I : 0.70926A)and ttLeo:-20 sidered unobserved and were excluded from the re- scanning technique at a rate of l" 20 per rrinute. finement. These are indicated in the structure factor Twenty-second background measurementswere tables(Tables 2a,b)' by asterisks.Atomic coordinates made at either end of dispersion-corrected scan are listed in Table 3, anisotropic temperature factors, ranges. Two standard diffractions were monitored equivalent isotropic temperature factors, and their during data collection and used to calibrate the in- root-mean-squareequivalents are listed in Table 4, tensities by interpolation. The data were corrected and interatomic distanc.esand interbond angles are for background, Lorentz, and polarization effects. recordedin Table 5. Crystal shapeswere approximatedby polyhedral en- velopesin the absorption correction. Linear absorp- The olivine structure tion coefficients(p) for MoKa are 47.7 cm-' for Fo' The olivine structure is so well-known that only a and 77.2 cm-' for Ten,.Finally, the data were aver- brief description is given here. [For structure dia- aged to yield sets of 731 and 773 unique structure grams the reader is referred to Birle et al. (1968) and factors for For, and Ten,respectively. Hazen (1976).1It consistsof a slightly distorted hex- Full-matrix least-squaresrefinements of Fo' and agonal closest-packedarray of oxygen anions with one-half of the octahedral sites filled with divalent Table L Crystal data cations and one-eighth of the tetrahedral sites occu- pied by silicon. The key structural feature is the ser-
to5, rated chain, parallel to c, of two symmetrically-inde- YI Langban, Sweden Madagascar pendent, edge-sharing octahedra. The M(l) 4.7 94(2)*A 4.879(2) A octahedron is at the interior of the chain and the b 10.491(4) 10.s89 (4 ) M(2) octahedron forms the "elbows" of the chain. c 6.r23(2) 6.234(3) -aa 'zar .3 Vol 3oa.z(z) n3 )zz. L\z) A Density (ca1c. ) 3.67 glcc 4.UO g/cc I To obtain a copy of Table 2, order Document AM-80-141 from the BusinessOffice, Mineralogical Society of America, 2000 ^Numbers ln parentheses represent es!imated standard Florida Avenue, NW, Washington" DC 20009. Pleaserenit $1.00 deviation (14) and refer to the last decimal olace. in advance for ttre microfiche. FRANCIS AND RIBBE: FORS TERI TE-TEP H ROI TE SERI'S 1265
Table 3. Atomic coordinates mentsby Brown (1970)failed to detectMglFe order. Subsequentrefinements by Finger (1970),Finger and t", )l t- Virgo (1971),Brown and Prewitt (1972),Wenk and Raymond (1973),Ghose et aI. (1976),and Basseer a/. Atom x v (1979) have shown small but signfficant degreesof M(1) ordering of Fe onto M(l) rather than M(2). This un- M(2) 0.9870(1) o.27 90 (r) , t4 b1 o. 4226(2) 0.0910(1) expected result, termed anti-ordering by Brown and 0(1) 0.7s8s (s) 0.0867(2) , Prewitt (1973), has generally been attributed to the 0(2) 0.2301 (s ) 0.4489 (2) ,4 0(3) 0.27 82 (3) 0.1590(2) o.037 4 (2) greater distortion from ideal Oo symmetry of the [M(l)O6] octahedron which results in a slightly Atom v z greater crystal field stabilization energy for Fe2* on M(1) M(l) (Walsh et al.,1974) [althoughfor someMg-rich M(2) 0.9877(2) 0.2801(1) ,4 t4 olivines, Fe'* may show a slight preferencefor M(2) 5a o . 4265(4) 0.0951(2) 0(1) o .7s7 4 (LO) 0.0914(5) ,4 (Wenk and Rayrrond, 1973). In general,site prefer- 0(2) 0.2162(rr) o. 452s(5) \ ence of divalent transition-metal cations relative to 0(3) 0.28s7 (8) 0.1625(3) 0.0401 (s) Mg in olivine is determined by two competing fac- tors: cation sizeand crystal field etrects(Rajamani et al., 1975). The [SiO.] tetrahedron sharesits basal edgeswith Divalent manganesetras t high spin d' 6snfigura- two M(l) and one M(2) octahedra.Its apex links to tion which is unaffected by crystal field effects.Thus the adjacentchain, which is related to the first by D- cation ordering in Mg-Mn olivines is predicted glide planes. (Brown, 1970;Burns, 1970,p.118) to be governedby the size criterion with Mg (r : 0.72L) preferring Cation ordering M(l) and Mn (r : 0.834) preferring M(2). The cat- Consideration of cation ordering in non-calcium ion distributions determined in the present refine- olivines began with the prediction of Ghose (1962) ments and an earlier refinement of a synthetic man- that becausethe effective ionic radius of Fe (r : ganoanforsterite (ForrTen ) "heat treatedat 1000"C" 0.78A) is larger than that of Mg (r : 0.72A) it should by Ghose and Weidner (1974)genfirm the predicted be preferentially ordered into the larger M(2) site. preferences(Table 6). Another refinement, that of Refinementsof four compositionsacross the forste- Mn, r*MgororZnorrrFeo..r"SiOofrom Franklin, New rite-fayalite seriesby Birle et al. (1968) and refine- Jersey(Brown, 1970)is consistentwith but is not a
Table 4. Anisotropic temperaturefactors (Bi;), equivalent isotropic temperature factors (Beq) and their root-mean-squareequivalents (p)
R*-11 -22R R -23R s (e') u(A) -33 Btz Brg eq
to5r
M(1) 3.r(4) r.35(8) 2.s(z) -o.r(2) -0.s ( 2) -0.34(9) 0.42 0.073 M(2) 6.L(2) 1.16(4) 3.66 (9) 0.24(8) 0.0 0.0 0.54 0. 083 Si 3.1(3) 0.96 (6) 2.s(2) 0.0(r) 0.0 0.0 0.36 0. 058 o(r) 2,2(7) L.7(2) 3.1(4) -0.2(3) 0.0 0.0 0.50 0.079 o(2) 4.o (8) r.r(2) 3.8(4) -0.5(3) o.o 0.0 0.48 0.078 o(3) 3.e (6) 1.3(r) 3.6 (3) 0.0(2) 0.0(3) 0.4(2) 0.50 0.079 T"91 M(1) 5.8(4) 2.2(L) 4.8(2) 0.0(2) -0.7(3) -0.7(1) 0.76 0.098 M(2) 6.7 (4) r.37(7) s.0(2) 0.1(2) 0.0 0.0 0.68 0.093 5a s.4(7) 1.4 (1) 4.s (3) 0.1(3) 0.0 0.0 0.61 0.089 o(1) 2.9(18) 2.s(4) 5.7(10) o.r(8) 0.0 0.0 0.81 0. r01 o(2) 5. 7(18) 1.4 (4) s.6(e) -o.2(7) 0.0 0.0 0.59 0.094 o(3) 7.s (13) 1.9(3) 4.9(6) 0.2(s) 0.0(8) 0.4(3) O.77 0.099
*8.. ls in the expression exp-(Brrt.2+3rr<2+9r/'2+gL|2hK+g]2h!+g1x2K9.) and values are quoted x103 1266 FRANCIS AND RIBBE: FORSTERITE-TEPHROITE S,ERIES
Table 5A. Interatomic distances(A) and angles (o) of Fo' Table 5B. Interatomic distances (A) and angles (o) of Tecr
Isioo1 tetrahedron Isiool tetrahedron
si-o(1)[1] 1.611(3)* sr-o(1) [1] 1.613(5)* o(2)[1] 1.651(2) o(2)[1] 1.663(6) o(3)[2] 1.638(2) o(3)[2] r.641(4) Mea 1.637 Mean1.640
O...O dlstaces Angles at Sl 0...O distmces Anglesat Sl
o(1)-o(2)[r] z.zss(:) 114.6 (1) o(1)-o(2)[r] 2.737(7) 1r.3.3 ( 3) o(1)-o(3)lzl -2.t sz(z) 115.8(1) o(1)-o(3)[2]^2.7 50 (6) LLs.4(2) o(2)-o(3)[2 ]?.550(3) 101.8(1) o(2)-o(3) 580(6) L02.7(2) [2] :2.'2.617 o(3)-o(3)[r l'2. oo+(g) r.os.3(1) o(3)-o(3)[1] (6) 105.8(3) llean 2.664 1o9.2 Mean 2.669 tog.2
[M(1)06 ] ocrahedron Iu(1) ouJoctahedron
M(1)-o(1)l2l 2.L24(2) M(1)-o(1)[2] 2.183(4) o(2)l2l 2.o7s(2) o(2)12) 2.L44(4) 0(3)t2l 2.L48(2) o(3)12) 2.228<4) Mean2.1L6 Mean2.185
O.,.O distances Angles at M(1) o...o distances Ang1esat M(1) bz,ttt(t) o(1)-o(2)[ 2]b 2.753(3) 8s.35(7) o(1)-o(2)[2] s6.26(1s) -o(2) o(1) [ 2] 3.087 ( 1) 94.65(7) o(1)-o(2)[2] 13,158(2) 93.74(L5) o(1)-o(3)[2] 2.752(3) 8s.93 ( 8) o(1)-o(3)[2]"2.7s0(6',) 85.20(16) o(1)-o(3)[2] 3. r.26(3) 94.07 (8) o(r)-o(3) 94.80(16) [2] J.247(5)-2.580(6) o(2)-o(3)[2] 2.s50 (3) ros.38(8) o(2)-o(3)[2] 107.59(16) o(2)-o(3) 2 3.3s9 ( 3) 74.62(8) o(2)-o(3)[2] 3.530(6) 72.3L(L6) I'Iean 2.940 90.0 Mean 3.000 Mean90.0
IM(2)06 octahedron] [M(2)06] octahedron M(2)-o(1)ltl z.zgo(z) u(2)-o(r)l1l 2.2s2(s) o(2)[1]2.rze(2) o(2)[1] 2.r39 ( s) 0(3)[2 ] 2.287(2) 0(3)[2] 2.318(4) o3)lzl 2.L26(2) 0(3)t2l 2.r47(3) l4ean 2.209 l.lean 2.227
0,..O disteces Angles at M(2) 0.,.O disteces Angles at M(2)
o(1)-o(3)lzlb z.tsz(t) 7s.so(1) o(1)-0(3)t2l "z.tso(o) 80.72(14) o(1)-o(3)[ 2] 3.1e7(3) e2.53(7\ o(1)-o(3)[2] 3,17s(s) 91.26(r2) o(2)-0(3)[2] 3.315(3) e7.28(8) o(2)-o(3)[2] 3.3ss(b) 97.59(rs) o(2)-o(3)[2]^3.3se(3) o(2)-o(3)[2] 89.84(12) eo.oe(7) '2.617^3.350(5) o(3)-o(3)[1]' 2.604(3' 69.40(8) o(3)-o(3)lrl (6) 68.73(17) o(3)-0(3)[2] 3.010(3) 89.r.2(6) o(3)-o(3)[2] 3.102(4) 87.e4(8) o(3)-o(3)[1] 3.s20(3) r11.70(e) o(3)-0(3)[1] 3.617(6) !L4.77(20) Mean 3.L16 Uean 89,75 Mean3.172 Mean89'85
*Number in Darentheses reDresents one estimated standard devlation i6) refers to last decimal place. *Nunber ln parentheses represents one estinated stmdard ""a deviation (d) and refers to the last decinal place. a, Edge shared between tetrahedron and octahedron.
a. Edges shared between tetrahedron and octahedron, b. Edge shared between octahedra, b. Edge shared between octahedra. valid test of the prediction, becauseMg had to be as- distribution Ko : 0, for a completely random distri- signedto M(l) in order to simplify the computation. bution Ko : l, and for an anti-ordered distribution The degreeof order for the three pure Mg-Mn oli- KD : @. These define the top and right edges,the vines is illustrated in Figure l, with data for Mg-Fe long diagonal, and the left and bottom edgesof the olivines included for comparison. Order is frequently parallelogramin Figure l. quantified by the use of a distribution coefficient Ko The Mg-Mn olivines are strongly ordered by com- lMe/(Me+Mn)M(2)l [Mn/(Ms+ Mn)M (r)l / IMe/ parison with Mg-Fe olivines. The contrast between 'the (Mg+Mn)M(1)l[Mn/(Mg+Mn)M(2)] written for heat-treatedsynthetic crystal (Ko : 0.196) and the ion exchange reaction Mg'z*M(l) f Mn2* the metamorphiccrystals (Ko : 0.000,0.01l) demon- M(2)SMg3*M(2) + Mn'z*M(l). For a fully ordered stratesthat the degreeof Mg/Mn order is dependent FRANCI S A N D RI BB E: FORSTERITE-TEPH RO ITE SER/ES 1267
Table 6. Refined site occupanciesof Mg-Mn olivines radii (Brown,1970).This relationshipis illustrated in Figure 2 for (Mg-Mn)-containing octahedra. The M(1) data (Table 7) fall into two distinct populations de- ConDoslEion l4n Mg Mn K-** 4C scribedby the following regressionequations: Fo53Tt47 * o.124 O.276(4) 0.339 0.661 0.196 :2.200 - : Fo51Tt49 0.921(5) 0.079 0.110 0.890 0.011 (M(l)-0) 0.096VoMg; R 0.997 roo9Tt91 o.172(9) 0.828 1.000 0.000 (M(2) -0) :2.223 - 0.097VoMs; R:0.998
*chose reflecting the inherent size differencebetween M(l) & weidner (1974). due to the difference in number **K-= [ Ms/ (Mg+lrn)M(2) ] [Mn/ (Ms+Mn)M(I ) ] and M(2) octahedra lMs/ (Ms+Mn)M(1) I IMn/ (Ms+un)M(2) ] of sharededges.
_t elongation, a measureof distortion of- Estimated standard deviations are in square brackets and refer to Quadratic the last decimal place. ten used in the analysis of finite homogenous strain, correlates linearly with bond angle variance for a large number of coordination polyhedra in minerals on a specimen'sthermal history. However, the rarity which show variations in both bond length and bond of Mg-Mn olivines seemsto preclude their wide use angle (Robinson et al., l97l). as petrogeneticindicators. Using the bond anglevariance parameter as a con- venient measureof polyhedral distortion, Robinson Stereochemistry et al. (1971) have shown that distortions of olivine The steric details of non-calcium olivine structures. [SiO.] tetrahedra decreasewith the weighted mean which arise from cation-cation repulsions across M-O distance.whereas distortions of olivine octa- shared polyhedral edges,have been thoroughly dis- cussedby Birle et al. (1968)and Brown (1970). One ( 1976 surprisingresult of the latter study is the constancyof Effectivelonic Rodius Shonnon, ) Si-O distancesirrespective of octahedral cation 2.24 chemistry.The Si-O distancesobserved in this study (Table 5) are typical, being statistically indistin- guishablefrom the correspondingvalues for ten oli- 2.22 vines studiedby Brown. In contrast,mean M-O dis- tancesare a linear function ofthe calculated effective o42
E -ordered (Kn=OOO)r- c|) \ \Fo51,K9=9.611 r*\ "" t'ii. .iuay) 6z.te \a.. !, c --synthetic oo V.-i .-^\. Foo3 KD=O 199 2.r6 t ( GhoseI Wei I Fo - Te series - o Fo Fo series 2.to roo 50 o Rr^ to0 Mole % Forsterite Mole 7" Forslerile Fig. l. Plot of percent magnesiumon M(l) as a function of Fig. 2. Plot of mean M(l)-O (dots) and M(2FO (squares) mole percent forsterite component, which illustrates the degree of distances as a function of refined site occupancy in percent cation order-disorder in the forsterite-tephroite series (squares) magnesium (lower abscissa) and effective ionic radius (upper and the forsterite-fayalite series (dots). Data from Table 7. abscissa).Lines represent regressionequations given in the text. 1268 FRANC I S AN D RI B BE: FORSTERITE-TEPH RO ITE SERI'S Table 7. Mean M-O distancesfor (Mg,Mn)-containing octahedra Mineral. Site Occupancy Forsterite M(1) Mo 2. 10r tlazen (1976) ' 00 M(t\ ;;1---1.00 2. L26 Fo--Te.- M(r) 2.116 )r 49 Thls study M/'\ ^"'0.89"60.$|o.szf;o.oa 2.209 11 tt91to9 M(1) z. Ld) This study u(2) fo.'..'1. sr"so. rz 2.227 00 Manganhumite M(1) 2.r70 Francls & Rtbbe (1978) f;0. zoMso. ro r.r(2)o "'r. oo 2.222 Table 8. Polyhedral distortions as measured by the bond angle hedra increase with increasing M-O distance. Poly- variance parameter (o)2 ofRobinson et al. (1971\ hedral distortions of the present structures (Table 8) conform to these general trends, but the distortions Polyhedron totoot Fo- - -'91 )l of Fo' are somewhatanomalous. The M(2) octahe- dron is more distorted than M(l), reversing the gen- Isio. ]x 42.4 48.3 38.0 eral rule for end members and disordered composi- lM(1)o_- l** 98.7 .3 tions. The tetrahedron in Fo' is also significantly 6- 99.9 L27 more distorted than in either end member. These [M/?)n']** 90.1 rr4.7 r24.1 o anomalies, which also hold for monticellite (Lager and Meaghet, 1978), are attributed to the large size tHazen (1976) di-fferencebetween M(l) and M(2) cations. 25 *o(tet) = X (o.-!09.47o)2 / 5 Reinterpretation of cation distribution in Zn,Mg l2 tephroite 2= xxO(oct) t (0.-90o)2/rr i=t Brown (1970)reported the M(2) site occupancyof the Franklin, New Jersey tephroite to be Table 9. Com.parison of site occupancy models for (Mn' 36sMgs3a5Zna225Fesr28)SiO4 Occupancy Scatterlng Powerx Effective Tonlc Brown (1970) M(1) ho. zL .40 0.774 2.r48 43zu8o.345Zto. l8oFto . 043 M(2) ho.86Bt"o. 25.32 0.821 2,224 oB5zoo.o45 Reinterpretat ion M(1) M8o. 2t.78 o.765 2.L5+ 345h0.ro oznn-zzlF"o.tza M(2) ht, oo 25.00 0. 830 2.223+l *Lnr"i **In.r. (radii from Shannon (I976)) ItO) tPrecllctecl from 0.755 + 1.38 (radtus of f tPredicted f rom Mn *"rFeoo.rZno*r,with a mean M(2)-O distanceof Burnham, C. W. (1973) Order-disorder relationships in some 2.2244. Qsmparison of this mean bond length with rock-forming minerals.Annual Rev.Earth Planet. Sci.,I,3lf- observedvalues ot 2.2294 for (M(2)-O) in Ten, 338. the Burns, R. G. (1970) Mineralogical Applications of Crystal Field and 2.2224 for (M(2).-O) in manganhumite Theory. Cam.bidge University Press,Cambridge, England. (Francis and Ribbe, 1978),both of which are com- Finger, L. W. (1970) FelMg ordering in olivines. CarnegieInst. pletely occupiedby Mn, suggeststhat the M(2) site in lAash. Year Book, 69,302-305. the Franklin tephroite is also completelyoccupied by - and E. Prince (1975) A systemof Fortran IV computer programs for crystal structure computations. U.S. Natl. Bur. Mn. The plausibility of a fully ordered distribution Stand. Tech. Note 854. may be tested by comparing the effective X-ray scat- - and D. Virgo (1971) Confirmation of Fe,/Mg ordering in tering factorsand ionic radii of the compositeoctahe- olivines. CarnegieInst. ll/'ash. Year Book, 70,221-225. drally coordinated atoms of the refined model with Francis,C. A. and P. H. Ribbe (1978)Crystal structuresof the hu- those of the fully ordered model. Only if these pa- mite minerals:V. Magnesianmanganhumite. Am. Mineral.,63, 874-877. rametersare nearly equal can the ordered model be Ganguli, D. (19'f7) Crystal chemical aspectsof olivine structures. realistic. This comparisonis made in Table 9. Scat- NeuesJahrb. Mineral. Abh., 130,303-318. tering factors were approximated by summing the Ghose, S. (1962)The nature of Mgz+-p"z+ distribution in some products of the atom fractions times their respective ferro-magnesiansilicate minerals.Am. M ineral.,47, 338-394. - atomic numbers, which equal the number of elec- and J. R. Weidner (1974) Sit€ preferenceof transition metal ions in olivine (abstr.) Geol.Soc. Am. Abstracts'trtithPro- trons in neutral atoms. The scattering factors of both grams,6,751. modelsare identical within the limits of resolution of --, C. Wan and I. S. McCallum (1976)Fe2+ + Mg2* order in X-rays for both M(l) and M(2). Similarly the mean an olivine from the lunar anorthosite 67U15and the significance effectiveradii ofthe divalent cationsare nearly iden- ofcation order in lunar and terrestrial olivines. Indian J. Earth tical. Thus the intensity data are equally satisfiedby Scr.,3,l-8. F. P. Okamura, H. Ohashi and J. R. Weidner the model reportedby Brown (1970)and the fully or- (1976) Site preference and crystal chemistry of transition metal deredmodel. In further support of the orderedmodel ions in pyroxenesand olivines. Acta Crystallogr.,.A3l Supple- may be cited the strong preferenceof Mg for M(l) ment, s76. observedin this study, the preferenceof Fe for M(l) Hazen, R. M. (1976)Effects of temperatureand pressureon the discussedabove, and the preferenceof Zn for M(l) crystal structureof forsterite.Ant Mineral., 61, 128tl-.1293. Intemational Tablesfor X-ray Crystallography, VoL IV (1974) Ky- relative to Mg (Ghose and Weidner, 1974).The or- noch Press,Birmingham, England. dered model therefore is not only possible but ap- Lager, G. A. and E. P. Meagher (1978) High+emperaturestruc- pearsto be crystal-chemicallypreferable. tural study of six olivines.Am. Mineral., 63,365-377. Rajamani,V., G. E. Brown and C. T. Prewitt (1975)Cation order- Acknowledgments ing in Ni-Mg olivine. Am. Mineral., 60,292-299. Robinson, K., G. V. Gibbs and P. H. Ribbe (1971) We are grateful to ProfessorCharles W. Burnham and Dr. Da- Quadratic elongation: a quantitative measureof distortion in coordination vid L. Bish of Harvard University, who assistedgenerously with polyhedra. Science,1 7 2, 567-570. data collection, and to the ResearchDivision of Virginia Polytech- Shannon, R. D. (1976) Revised effective ionic radii and systematic nic Institute and State University which provided funds for com- studies of interatomic distances in halides and chalcogenides. puting. Partial financial support was provided under NSF grant Acta Crystallogr., A 32, 75 1-767 . EAR77-21114 (Earth SciencesSection) to P.H.R. and G. V. Smyth, J. R. (1975) High temperature crystal chemistry of fayalite. Gibbs. Am. Mineral., 60, 1092-1097. - and R. M. Hazen (1973)The crystalstructures of forsterite References and hortonolite at several temperatures up to 900"C. Am Min- Basso,R., A. Dal Negro, A. Della Giusta and G. Rossi(1979) Fe/ eral., 58,588-593. Mg distributions in the olivine of ultrafemic nodules from As- Walsb D., G. Donnay and J. D. H. Donnay (1974)Jahn-Teller ef- sab (Ethiopia). NeuesJahrb. Mineral. Monatsh., l9'l-2O2. fect in ferro-magnesian minerals: pyrox€n€ and olivines. 8411. Birle, J. D., G. V. Gibbs, P. B. Moore and J. V. Smith (1968)Crys- Soc.fr. Mintral. Cristallogr., 97, l7Fl83. tal structuresof natural olivines.Am. Mineral., 53, 807-824. Wenk, H.-R. and K. N. Raymond (1973)Four new structure re- Brown, G. E. (1970) Crystal Chemistry of the Olivines. Ph.D. finements of olivine. Z. Kristallogr., 137, 86-105. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. - and C. T. Prewitt (1973)High-temperature crystal chemis- Manuscript received, February I, 1980; try of hortonolite. Am. Mineral., 58, 577-587. acceptedfor publication, May 7, 1980.