THE AMERICAN MINERALOGISI', VOL 53, MAY_JUNE, 1968

CRYSTAL STRUCTURES OF NATURAL OLIVINES

J. D. Brnmt, G.V. Grnns2, P. B. MoonE, AND J. V. SurrH,Department of the Geophysical Sciences, (Jn'ittersity of Chicago

Chicago, I l l inois 60637, U.S.A.

Ansrnncr

Atomic parameters were obtained by 3D least-squares X-ray difiraction analysis of

forsterite (Mgo go,Feo 1s), plutonic hyalosiderite (Mgo u:u,Feo nso,Mrio ooo,CzIo oor), dike

hortonolite (Mgo as,Feo as,Mno or,Cao or), and fayalite (Feo gz,Mgo or,Mns ,r).

The closeness in value of the isotropic temperature factors calculated for the M sites

indicates substitutional disorder of the Mg and Fe atoms in all four structures. Poiyhedra

distortions are closely similar in all four structures showing that they depend on the struc-

ture type rather than on the Mg, Fe substitution. Simple electrostatic rules allied with papk-

ing considerations permit qualitative explanation of the structural distortions. The M(l)

octahedron has six short shared edges to give a distorted and elongated trigonal antiprism.

The M(2) octahedron has a triangle of three short shared edges. Metal-oxygen distances

tend to compensate e.g., the longest Si-O distance and the shortest (MS,Fe)-O distance go

to the same oxygen.

INrnorucrroN

The type structure of olivine was determined by Bragg and Brown(1926) on a forsterite crystal with composition Mgo noFeo.ro. Three-

dimensional refinement of another forsterite crystal by Belov, Belova,

Andrianova, and Smirnova (1951) yielded Si-O and M-O distances far

outside the usual ranges for silicates. More recently Hanke a\d Zemarn

(1963) determined the atomic parameters of forsterite from a two-di-

mensional analysis, and Born (1964) followed this by showing that the

observed position ol M(2) falls on the maximum of the total attractive

plus repulsive energy for half-ionized atoms. Hanke (1963) has described a

similar two-dimensional analysis of a fayalite crystal. A preliminary de-

scription of the present work has already appeared (Gibbs, Moore and

Smith, 1964). Geller and Durand (1960) determined the parameters of

isostructural lithiophilite, LiMnPOn and found Li to occupy the smaller

M(1) position and Mn the larger M(2) position. Onken (1965) refined the

crystal structure of monticell i te, CaMgSiOa and showed that Mg and Ca

are ordered in the M(l) and M(2) sites respectively. Caron, Santoro,

and Newnham (1965) determined the magnetic structure of glaucoch-

roite, CaMnSiO+, and their neutron diffraction studies showed that this

mineral is isomorphous with monticellite.Sahama and Torgeson (19a9) and Bloss (1952) concluded from heats

of solution and densities that the olivine system showed ideal substitu-

I C.I.C. exchange student from Ohio State University, Department of Mineralogy'2 Present address: Department of Geological Sciences, Virginia Polytechnic Institute.

807

808 r. D. BIRLE, G. V. GIBBS, p. B. MOORE AND J. V. SMITH

tion. Yoder and Sahama (1957) from a plot of the spacing of the (130)planes versus composition suggested that the variation oI cell parameterswith composition did not deviate greatly from Vegard's rule, though

Jambor and Smith, C. H. (1964) reported that there is a relatively sharpbreak from a linear relation of spacing versus composition, and suggestedthat ordering of Mg and Fe might explain the nonlinear relation. Hen-riques (1957) gave equations for relating the cell dimensions of olivine tothe Mg, Mn and Fe contents. Smith and Stenstrom (1965) have shownthat when allowance is made for lattice expansion by Ca and Mn, thereis a continuous almost linear, relation between d(130) and atomic percentMg. Louisnathan and Smith (submitted for publication) have shownthat the cell edges have near-linear variations with the atomic fraction ofMg, and have determined the regression coefficients with Mg, Ca and Mn.Lehmann, Dutz and Koltermann (1963) and Duke and Stephens (196a)have shown that there is a linear relation between the Fe content and theabsorption frequencies of infrared radiation. Saksena (1961) calculatedapproximately the positions of the absorption bands for vibrations inthis SiOr tetrahedron, and Duke and Stephens showed that the multi-plicity of the bands was consistent with the symmetry of the potentialfield.

Contradicting the above evidence for ideal substitution in the olivinestructure is the study by Eliseev (1958) who estimated optically the Mg:Fe ratios of several olivines and claimed that the measured cell volumesdeviated greatly from Vegard's rule. He suggested that, because the b/cratio approaches /3 as the Fe-content increased, the oxygen atoms infayalite more nearly approach the ideal configuration of hexagonal closepacking than those of forsterite. Similarly he claimed that the forsteritestructure becomes more ideal at higher temperatures because of approachof the axial ratio to l3.He also observed the presence of extra reflectionsin the-powder patterns of olivine at spacings oI 4.703,4.030, 3.330, andI.776 L, which he claimed were the result of "secondary diffraction" in aunit cell with c doubled over the value found by all other workers.Ghose (1962), noting the suggestion of Eliseev that olivine disobeyedVegard's rule, suggested that the Mg and Fe2+ atoms were ordered andby analogy with monticellite, predicted that the larger Fe2+ atom wouldconcentrate into the M(2) site occupied by Ca in monticellite.

The present investigation was carried out to resolve the question ofordering, to determine the distortions of the crystal structure and to pro-vide accurate bond lengths as part of a program aimed at understandingthe chemical forces in silicates.

ExronrlmNr.q.r-

We are grateful to Professor D. Jerome Fisher, Professor C. E. Tilley, Dr. H. S. Yoder,

and Mr. Paul E. Desautels respectively, for supplying forsterite from a nodule from Minas

STRUCTURES OF OLIVINES

Gerais, Brazil, hyalosiderite from the Skaergaard intrusion, Kangcrdlugssuag, Greenland,

hortonolite from a wide dike at camas M6r, Muck, scotland and fayalite in lithophysae

from Obsidian Clifi, Yellowstone National Park, Wyoming. The forsterite was estimated

by optical methods to have a composition near Mgo.eoFeo.ro. This estimate checks well

with estimated compositions by microprobe techniques for other forsterites from inclusions

in basaltic rocks (Smith, 1966). In contrast to this homogeneous forsterite' the hortonolite

from an olivine gabbro dike in camas M6r, Muck, Scotland was found to be strongly zoned.

Conventional bulk chemical analysis by J. H. Scoon (Tilley, 1952) yielded a composition

Mgo.nsFeo.szMno.orCas.sll however the large amount of Al and Fe+3 casts doubt on the ap-

pliiability of the analysis to the olivine. Microprobe analysis of the single crystal used for

collection of difiraction data yielded a composition Mgo.rsFeo.EgMno.orCao.or. The hyalo-

siderite from the Skaergaard intrusion corresponds to sample YS-15 in Smith (1966) and

the composition Mgo.sasFeo.aaffn6.6s6C&6.662 obtained by microprobe analysis was adopted'

Fayalite was found to be zoned by electron microprobe techniques afiording an average

composition Mgo.o:sFeo.szzMrro.oazC&o.ooz and ranges of Mg 0.00 to 0 08 and of Mn 0'03 to

0.04. CeIl dimensions were estimated from plots of cell dimensions os composition obtained

from data by Louisnathan and Smith (submitted for publication). The consistency of the

data indicate that the cell dimensions are accurate to about I in 1000. We chose forsterite,

a 4.762, b l0 225, c 5.994; dike hortonolit e, a 4.187, e lo.34l, c 6.O14; plutonic hyalosiderite

were made to explain the reflections on the basis of target contamination in the X-ray tube

or of contamination of the sample. Unless confirmation is obtained of Eliseev's extra re-

flections, it seems safe to assume that all olivine crystals obey the symmetry of Pbnm and

have the normal cell size.

Intensities for the forsterite, hyalosiderite and hortonolite were collected for each

crystal using a manual weissenberg equi-inclination counter difiractometer with moving

crystal and fixed scintillation counter. The fayalite data were gathered automatically on a

PAILRED unit. Monochromatized MoKa radiation was used for all four crystals and the

polarization efiect of the monochromator was ignored in applying the Lorentz and polariza-

iion factors. 2026 independent intensities were gathered lor fayalite but 308 were omitted

because of asymmetrical backgrounds and 304 because of indistinguishability from back-

ground. Nonspherical absorption corrections were applied to forsterite, but were not needed

for the other three because of favorable shape and small size of the crystals'

Full matrix isotropic least-squares refinements were made using the Busing-Martin-

Levy ORFLS program. The atomic form factor curves were taken from Beryhuis et d.,

(1955) and from Freeman (1959) after arbitrary modification for half-ionization. For the

reflections were given equal weight during the refinement. For fayalite extinction was small

but thirty of the strongest reflections were omitted. The number of independent reflections

used in the final refinements was as follows: forsterite (414), dike hortonolite (367), plutonic

hyalosiderite (924), and fayalite (1384).

The final isotropic temperature factors for these four olivines are comparable with those

from similar structure types, and the factors for the two octahedral sites are consistent

with disorder of the Mg and Fe atoms. Because of the large difference between the scatter-

810 I. D. BIRLE, G. V. GIBBS, P. B. MOORE AND T. V. SMITH

ing factors for Mg and Fe, errors in the Mg and Fe contents applied to the sites would havea strong influence on the estimated temperature factors. An estimate of the efiect was ob-tained by using separate scattering factor curves for Fe and Mg in place of the averagedcurves. Applying Mg to the M(l) site and Fe to the M(2) site of hortonolite gave in thefirst cycle of refinement temperature factors of -4.9 and f 5.0 for the two octahedral sites.Thus, an error of 1 percent in the Mg:Fe ratio of the hortonolite and hyalosiderite wouldshift the temperature factors of the octahedral sites by about 0.1. The range of B valuesbetween the four structures could be accounted for merely by errors in the composition(average B: Fo 0 34, Hy 0.35, Ho 0.41, Fa 0.38); indeed the argument may be reversed toclaim that the listed Mg and Fe compositions are accurate to 0.01 in spite of the difficultyof analyzing zoned crystals.

Table 1 lists the atomic parameters and their standard errors, Table 2 the interatomicdistances and Table 3r the observed and calculated structure amplitudes. The final dis-crepancy factors for reflections used in isotropic refinements are 0.08 for forsterite, 0.07 fordike hortonolite, 0 08 for plutonic hyalosiderite and 0.07 for fayalite. A three-cycle aniso-tropic refinement for fayaiite rapidly converged to R:0.05 and yielded apparently sig-nificant deviations from spherical symmetry of the ellipsoids: however, these deviationswill not be discussed at this time because the effect of differential absorotion has not beenevaluated in detail.

Drscussror.t

The idealized olivine structure (Fig. 1a) consists of a hexagonal close-packed array of oxygen atoms in which one-half of the available octa-hedral voids are occupied by M atoms and one-eighth of the availabletetrahedral voids by Si atoms. To enumerate all the possibilities of ar-ranging atoms in the voids is beyond the scope of the present paper butwill be pursued elsewhere because of its importance. For example, thereare several recently-determined structures which have metal atoms oc-cupying the voids in hexagonally close-packed oxygen atoms. In par-ticular, welinite, recently determined by Moore (in preparation) has theproperties MnzSizOr+, d 8.155, c 4.785 4., P6", here half of the octahedralvoids are occupied but only one-fourteenth of the tetrahedral voids. Thisarrangement is shown idealized in Fig. 1b. An interesting arrangementwith the olivine stoichiometry MzTOa is shown in Figure 1c. The rela-tions to hypothetical structures based on occupancy of voids in cubicclose packed oxygen atoms (such as in spinel and kyanite) are also of in-terest, especially in view of the pressure dependence of transitions suchas the well-known olivine-spinel transition.

Returning to the olivine structure it may be seen from Figure 1a thatthe key structural unit is the serrated chain of octahedra lying parallel tothe a-axis. In any oue yz layer only half the octahedral voids are oc-

1 Table 3 has been deposited as Document No. 9901 with the American DocumentationInstitute, Auxiliary Publications Department, Photoduplication Service, Library of Con-gress, Washington, D.C. 20420. Copies may be secured by citing the document number andremitting in advance $3.75 for photoprints or $2.00 for microfilm.

STRUCTURES OF OLIVINES

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T.tlr,e 2. INrERAroMrc Drsrexcns (A) rN Or.rvrNn

Atoms Forsterite Hyalosiderite(S) Hortonolite(CM) Fayalite

1 Si -O(1)1 -o(2)2 -O(3)

mean

1 O(1) -O(2)2 _O(3)2 O(2) -O(3).1 O(3) -O(3)'

mean

2 M(1)-o(1)2 -o(2)2 -O(3)

mean

2 O(r) -O(2)b2 -O(2)2 -o(3)b2 -O(s)2 O(2) -O(3)"2 -O(3)

mean

1 M(2)-O(1)1 -O(2)2 _O(3)2 -o(3)

mean

2 O(1) -O(3)b2 -O(3)2 O(2) -o(3)2 -o(3)1 O(3) -O(3)"2 -O(3)2 -o(3)

mean

Si, tetrahed.ronr .614(4) 1.613(3)1.6s4(4) 1.6s0(6)1.63s(3) 1.634(3)

r .634 t .634

2.743(5) 2.740(6)2.7s7(4) 2.747 (4)2.ss6(4) 2.ss4(6)2.s86(6) 2.603(s)

2.659 2 . 6 5 8

M(1) octahed.ron2.oer(2) 2.rr6(s)2.O7s(2) 2.0e1(s)2.142(3) 2.174(3)

2.r03 2 . 1 2 7

2.8s7(s) 2.886(6)3.032(1) 2.062(r)2.8s7(4) 2.88s(4)3 .12s (4 ) s . r77 (6 )2.ss6(4) 2.ss4(6)3.3ss(4) 3.417 (4)

2.964 2.997

M (2) oclahetlron2. t77 (4) 2. r17(s)2.ose(4) 2.0e0(3)2.217(3) 2.262(3)2.070(3) 2.060(3)

2. r35 2 . 1 5 2

2.8s7(4) 2.886(4)3.028(4) 3.032(1)3.194(4) 3.25s(6)2.e37 (4) 2.e40(4)2.s86(6) 2.603(s)3.408(6) 3.4s2(s)2.99s(3) 3.011(s)

| 627(7)1 .6s9(6)1 .636(4)

1 .639

2.7s8(e)2.763(7)2 .s7 r(6)2.606(8)

2.669

2.100(4)2.104(4)2.183(4)

2 . t 29

2 .880(e)3 . 063 (1)2.88e(7)s.164(7)2.s7r(6)s .43 r (7 )

3.000

2.202(6)2.o7r(6)2.267 (4)2.060(4)

2 .154

2 .880(7)3.0s7(6)3.246(6)2.e28(6)2 606(8)3.438(8)3 .011(s)

3.024

| .619(2)r .6s7 (2)r.6s7 (2)

1 . 6 3 8

2.72s(3)2.7se(s)2. s7s(3)2 . 60s (4)

2.666

2 12s(2)2.123(2)2.228(2)

2 . r59

2.e06(3)3.0e8(1)2.e28(3)3.222(3)2.s7s(4)3 . s08(4)

3.039

2.232(2)2.110(2)2 .29 r (2 )2.072(2)

2 .178

2.906(3)3.084(3)3.303(3)2.es6(3)2.60s(4)s 494(3)3.024(2)

3.0543.001 3.023

STRUCTURES OF OLIVINES

Tlr;e 2-(Conti'nueil)

Forsterite Hyalosiderite(S) Hortonolite(CM) Fayalite

1 O(1) -Si2 -M(1)

1 -M(2)

I O(2) -Si

2 -M(1)

1 -M(2)

1 O(3) -Si

I -M(1)

1 -M(2)

1 -M(2)

r.614(4)2.@r(2)2.r77 (4)

I .6s4(4)2.075(2)2 .0s9(4)

1 .63s(3)2.142(3)2 .2r7 (s)2.070(3)

O(1) bond.s1 . 613 (3)2.116(3)2 .r77 (s)

O(2) bond.s1 6s0(6)2 .091 (3)2.0e0(3)

O(3) bonds1 .634(3)2.r74(s)2.262(3)2 .060(3)

r .627 (7)2. 100(4)2.202(6)

I .6s9(6)2.104(4)2.O7r(6)

1 .636(4)2.r8s(4)2.267 (4)2.060(4)

r .6re(2)2 . r2s(2)2.232(2)

| .6s7 (2)2 .123(2)2.rr0(2)

| .637 (2)2.228(2)2 .2er (2 )2.072(2)

" edges shared between tetrahedron and octahedronb edges shared between octahedra

N.rribers in parentheses are standard errors. The number preceding an atom designa-

tion is the multiplicity of the second atom with respect to the first'

Note that the error does not include the efiect of error in the cell dimensions.

814 r. D. BIRLE, G. V. GIBBS, P, B, MOORE AND J. V. SMITH

C +

Qz-

STRUCTURES OF OLIVINES

Q z -

( c )

Frc. 1. Octahedral populations in the crystal structures of (a) olivine, (b) welinite' and

(c) a hypothetical structure with olivine stoichiometry. Shaded and unshaded octahedra

distinguish the two levels normal to the plane of the drawings'

These predict a shortening of shared edges and a lengthening of cation-

bonds to oxygen atoms of shared edges because of cation-cation repul-

sion.The principal distortions do indeed correlate with the sharing of

polyhedral edges. From Table2 it may be seen that the distortions are

essentially the same in all four structures and that substitution of Mg for

Fe has little effect. In the following part of the discussion and in the

figures distances averaged over the forsterite and hortonolite will be used.

From Figure 3 it may be seen that the silicon tetrahedron is almost a

trigonal pyiamid elongated parallel to the r-axis ' The M(l) octahedron

which Iies on an inversion center approximates to a trigonal antiprism

metry of M(2) is C".The cation-oxygen distances cannot be interpreted simply but there

are some crude relationships. From Table 2 it may be seen that each

816 J. D, BIRLE, G. V. GIBBS, P, B, MOORE AND T. V. SMITH

oxygen is bonded to one Si and three M atoms. The longest Si-o distanceis to o(2) which has the shortest M-o distances. rn the M(2) octahedron

part by the o(1)-o(2) edges of two M(l) octahedra. These edges are theshortest of the unshared edges of the M(l) octahedron. Thus one canenvisage a compromise between conflicting electrostatic and spatialfactors such that the first o(3)-o(3) edge shortens and the second onelengthens while the two o(1)-o(2) edges shorten somewhat. of course adetailed analysis would require simultaneous consideration of all theedges: perhaps such an analysis will become feasible in the future.

Burnham (1963) on the basis of a study of alumino-silicates concludedthat "in many cases the minimum-energy configuration of a structure isnot primarily dictated by edge-sharing considerations". rn olivine, therange of lengths of unshared edges for the M polyhedra is comparable tothe difference between the average shared and the average unshared edge.Thus the simple concept of edge sharing would account for about half ofthe length variations. Born (1964) on the basis of various simplifyingassumptions including the positions of the Si and o atoms has been ableto predict the position of. M(2). perhaps the safest conclusion at thistime is that while Pauling's rules give a simple qualitative explanation of

STRUCTURES OF OLIVINES 817

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Frc '2,o.Tetrahedralarrangementsandtheneighbor ingoctahedrals i tes.Distancesalong r are given in fractional.rnitr. b. Actual distortions observed for olivine in a portion

of an octahedral serrated band.

ease of sequential calculations.

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STRUCTURES OF OLIVINES

4 3s i t

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(c)

Frc. 3. Interatomic distances about the three polyhedra in olivine: (a) the silicate

tetrahedron, (b) the M(1) octahedron, and (c) the M(2) octahedron. Shared edges are

showed in bold lines. Heights are given as percentages of r-coordinates. Polyhedral edge

distances as well as the distances from the anion centers to neighboring anions and cations

are presented.

(a) (b)

Frc. 4. Stereographic projections of first and second nearest neighbors of oxygen atoms

in regular hexagonal (Ieft) and cubic (right) close-packing. O:octahedral site, T:tetra-

hedral site.

503.23

J. D. BIRLE, G. V. GIBBS, P. B. MOORE AND J. V, SMITH

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STRUCTURES OF OLIVINES

O(3)s .+ rtc)

Fre. 5. Stereographic projections of first and second nearest neighbors of oxygen atoms

in olivine (a), (b) and (c). About O(1), O(2), and O(3) respectively in olivine. Interatomic

distances age given. O: octahedral site, T: tetrahedral site.

Figure 5 is an alternative way of displaying the distortion in the olivinestructure (again based on an average of forsterite and hortonolite). Eachof the subdiagrams is a stereographic projection of the first and secondneighbors of oxygen atoms, the former being tetrahedrally or octahed-rally-coordinated atoms, the latter being oxygen atoms. Diagrams (a)

and (b) in Figure 4 refer to regular hexagonal and cubic close-packing,respectively; (a) (b) and (c) in Figure 5 refer to O(1), O(2) and O(3) inolivine. It may be seen that only one-eighth of the tetrahedral voids,and one-half of the octahedral voids are occupied.

Comparison of the four structures in terms of increasing Fe contentshows that most distances in the hyalosiderite and the hortonolite are

intermediate between those of forsterite and fayalite. The M(1) andM(2) octahedra increase considerably in size with entry of the larger Feions. The octahedra become more irregular as the Fe content increases,and in contradiction to Eliseev's suggestion, fayalite is more distortedfrom regular close-packing than is forsterite. The SiOr tetrahedron wasfound to be larger in fayalite but the increase is not significant in terms of

821

822 J. D. BIRLD, G. V. GIBBS, p. B. MOORE AND J. V. SMITH

the errors. The Si-O distances fall within the expectations l isted bySmith and Bailey (1963): it is worth noting that the average distance inolivine, 1.636, is greater than those for the two tetrahedra in kyanite,t.623 and 1.633 A, which is based on cubic close packing, (Burnham,1963). The average distance in monticell i te, 1.624 A, Onken (1965), issmaller than in the forsterite-fayalite structures. This confirms earlierindications that the mean Si-O distances depends on the nature of othercations and the structure type as well as on the degree of polymeriza-tion of the Si-O group.

The surprising aspect of olivine is the absence of evidence for orderingof the octahedral cations in Mg, Fe olivines. Of course, the minor cationssuch as Ca and Mn cause some complication and it is possible that theyoccupy one site preferentially. In monticell i te (Onken, 1965) magnesiumoccupies M(1) preferentially: perhaps the larger B value oI M(l) infayalite results from preferential occupancy by Mg. For the other threestructures M(2) has the larger B value which might be taken to indicatepreferential occupancy by Mg. However it is thought that a larger Bvalue would be expected tor M(2) in comparison with M(1) because ofthe greater irregularity of the M(2) oxyget polyhedron: indeed, pref-erential occupancy of M(2) by Mg and of M(l) by Fe seems unlikelyfrom a crystal chemical view-point since the larger Fe ion should preferthe larger M(2) polyhedron if a preference does indeed occur. Lack ofordering is consistent with the other physical evidence for near-ideal solidsolution summarized in the introduction. That lack of ordering is a sur-prise results from comparison with orthopyroxene where the two octa-hedra probably have less distortion than the ones in olivine but in whichstrong ordering occurs (Ghose, 1962). SIow cooling should have occurredin the Skaergaard intrusion, while even the olivine from the Camas M6rolivine gabbro dike (30 yards across) should have received some op-portunity for annealing. Volcanic orthopyroxenes are partly ordered(Hafner, pers. comm.). Presumably there is some key difference betweenthe crystal structures: the near close packed structure of olivine may in-hibit movement of octahedral cations more than the less closely-packedstructure gf pyroxene. Perhaps preferential occupancy in olivine becomesstable thermodynamically only at temperatures too low for efiectiveionic migration: the frequent occurrence of orthoclase in plutonic andmetamorphic rocks shows how difficult is the ordering of AI and Si inK-feldspar.

The present studv was begun because of l i terature reports of anoma-Ious properties in olivine that suggested that parameters might dependon petrologic history and hence serve as petrogenic indicators. Actuallythe structural parameters are quite regular and apparently immune to

STRUCTURES OF OLIVINES

crystallization history. Only the chemical parameters seem to be of value.

Perhaps some more subtle structural indicators, for example lamellae

may be found of value. In the meantime, the olivine structure serves

as an excellent example of the distortions consequent on the stuffing of

close-packed oxygen arrays.

AcrNowr-BncnuBnts

This work was supported by NSF grants G-14467 , GP-443, and GA-572 P' B' Moote

held an NSF Predoctoral Fellowship during the earl-v stages of this work.

RnrsnnNcss

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823

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M anuscript recei.ted., August 8, 1967 ; accepted, for publication, October 13, 1967 .