THE AMERICAN
MINERALOGISI',
VOL 53, MAY_JUNE,
CRYSTAL STRUCTURES OF NATURAL
1968
OLIVINES
, . B . M o o n E , A N DJ . V . S u r r H ,
J . D . B r n m t , G . V . G r n n s 2P
Departmentof the GeophysicalSciences,(Jn'ittersityof Chicago
Chicago,Illinois 60637, U.S.A.
Ansrnncr
Atomic parameters were obtained by 3D least-squares X-ray difiraction analysis of
ooo,CzIo
oor), dike
nso,Mrio
forsterite (Mgo go,Feo1s), plutonic hyalosiderite (Mgo u:u,Feo
hortonolite (Mgo as,Feoas,Mnoor,Caoor), and fayalite (Feo gz,Mgoor,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 structure type rather than on the Mg, Fe substitution. Simple electrostatic rules allied with papking 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
Three(1926) on a forsterite crystal with composition Mgo noFeo.ro.
dimensionalrefinement of another forsterite crystal by Belov, Belova,
Andrianova, and Smirnova (1951) yielded Si-O and M-O distancesfar
outside the usual ranges for silicates. More recently Hanke a\d Zemarn
(1963) determined the atomic parameters of forsterite from a two-dimensionalanalysis,and Born (1964) followed this by showing that the
observedposition ol M(2) falls on the maximum of the total attractive
plus repulsiveenergyfor half-ionizedatoms.Hanke (1963)has describeda
similar two-dimensionalanalysisof a fayalite crystal. A preliminary description of the present work has already appeared (Gibbs, Moore and
Smith, 1964). Geller and Durand (1960) determined the parametersof
isostructural lithiophilite, LiMnPOn and found Li to occupy the smaller
M(1) position and Mn the larger M(2) position.Onken (1965)refinedthe
crystal structure of monticellite,CaMgSiOaand showedthat Mg and Ca
are ordered in the M(l) and M(2) sites respectively.Caron, Santoro,
and Newnham (1965) determined the magnetic structure of glaucochroite, CaMnSiO+, and their neutron diffraction studies showed that this
mineral is isomorphous with monticellite.
Sahamaand Torgeson(19a9) and Bloss (1952) concludedfrom heats
of solution and densities that the olivine system showed ideal substituI 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. MOOREAND J. V. SMITH
tion. Yoder and Sahama (1957) from a plot of the spacingof the (130)
planes versus composition suggestedthat the variation oI cell parameters
with composition did not deviate greatly from Vegard's rule, though
Jambor and Smith, C. H. (1964)reported that there is a relatively sharp
break from a linear relation of spacingversus composition, and suggested
that ordering of Mg and Fe might explain the nonlinear relation. Henriques (1957) gave equations for relating the cell dimensionsof olivine to
the Mg, Mn and Fe contents.Smith and Stenstrom (1965) have shown
that when allowance is made for lattice expansionby Ca and Mn, there
is a continuous almost linear, relation between d(130) and atomic percent
Mg. Louisnathan and Smith (submitted for publication) have shown
that the cell edgeshave near-linear variations with the atomic fraction of
Mg, and have determined the regressioncoefficientswith 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 the
absorption frequenciesof infrared radiation. Saksena(1961) calculated
approximately the positions of the absorption bands for vibrations in
this SiOr tetrahedron, and Duke and Stephensshowed that the multiplicity of the bands was consistent with the symmetry of the potential
field.
Contradicting the above evidence for ideal substitution in the olivine
structure is the study by Eliseev (1958)who estimatedoptically the Mg:
Fe ratios of several olivines and claimed that the measured cell volumes
deviated greatly from Vegard's rule. He suggestedthat, because the b/c
ratio approaches /3 as the Fe-content increased, the oxygen atoms in
fayalite more nearly approach the ideal configuration of hexagonal close
packing than those of forsterite. Similarly he claimed that the forsterite
structurebecomesmore ideal at higher temperaturesbecauseof approach
of the axial ratio to l3.He also observedthe presenceof extra reflections
in the-powderpatterns of olivine at spacingsoI 4.703,4.030,3.330, and
I.776 L, which he claimedwere the result of "secondarydiffraction" in a
unit cell with c doubled over the value found by all other workers.
Ghose (1962), noting the suggestionof Eliseev that olivine disobeyed
Vegard's rule, suggestedthat the Mg and Fe2+atoms were ordered and
by analogy with monticellite, predicted that the larger Fe2+atom would
concentrateinto the M(2) site occupied by Ca in monticellite.
The present investigation was carried out to resolve the question of
ordering, to determine the distortions of the crystal structure and to provide accurate bond lengths as part of a program aimed at understanding
the chemical forces in silicates.
ExronrlmNr.q.rWe 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
however the large amount of Al and Fe+3 casts doubt on the apMgo.nsFeo.szMno.orCas.sll
pliiability of the analysis to the olivine. Microprobe analysis of the single crystal used for
The hyalocollection of difiraction data yielded a composition Mgo.rsFeo.EgMno.orCao.or.
siderite from the Skaergaard intrusion corresponds to sample YS-15 in Smith (1966) and
obtained by microprobe analysis was adopted'
the composition Mgo.sasFeo.aaffn6.6s6C&6.662
Fayalite was found to be zoned by electron microprobe techniques afiording an average
and ranges of Mg 0.00 to 0 08 and of Mn 0'03 to
composition Mgo.o:sFeo.szzMrro.oazC&o.ooz
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 reflections, 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 polarizaiion factors. 2026 independent intensities were gathered lor fayalite but 308 were omitted
because of asymmetrical backgrounds and 304 because of indistinguishability from background. Nonspherical absorption corrections were applied to forsterite, but were not needed
for the other three becauseof favorable shape and small size of the crystals'
Full matrix isotropic least-squares refinements were made using the Busing-MartinLevy 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 have
a strong influence on the estimated temperature factors. An estimate of the efiect was obtained by using separate scattering factor curves for Fe and Mg in place of the averaged
curves. Applying Mg to the M(l) site and Fe to the M(2) site of hortonolite gave in the
first 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 would
shift the temperature factors of the octahedral sites by about 0.1. The range of B values
between the four structures could be accounted for merely by errors in the composition
(averageB: Fo 0 34, Hy 0.35, Ho 0.41, Fa 0.38); indeed the argument may be reversed to
claim that the listed Mg and Fe compositions are accurate to 0.01 in spite of the difficulty
of analyzing zoned crystals.
Table 1 lists the atomic parameters and their standard errors, Table 2 the interatomic
distances and Table 3r the observed and calculated structure amplitudes. The final discrepancy factors for reflections used in isotropic refinements are 0.08 for forsterite, 0.07 for
dike hortonolite, 0 08 for plutonic hyalosiderite and 0.07 for fayalite. A three-cycle anisotropic refinement for fayaiite rapidly converged to R:0.05 and yielded apparently significant deviations from spherical symmetry of the ellipsoids: however, these deviations
will not be discussed at this time because the effect of differential absorotion has not been
evaluated in detail.
Drscussror.t
The idealizedolivine structure (Fig. 1a) consistsof a hexagonalclosepacked array of oxygen atoms in which one-half of the available octahedral voids are occupied by M atoms and one-eighth of the available
tetrahedral voids by Si atoms. To enumerate all the possibilities of arranging atoms in the voids is beyond the scopeof the present paper but
will be pursued elsewherebecauseof its importance. For example, there
are severalrecently-determinedstructures which have metal atoms occupying the voids in hexagonally close-packedoxygen atoms. In particular, welinite, recently determinedby Moore (in preparation) has the
propertiesMnzSizOr+,
d 8.155,c 4.785 4., P6", here half of the octahedral
voids are occupied but only one-fourteenth of the tetrahedral voids. This
arrangementis shown idealizedin Fig. 1b. An interesting arrangement
with the olivine stoichiometry MzTOa is shown in Figure 1c. The relations to hypothetical structures based on occupancy of voids in cubic
closepacked oxygen atoms (such as in spinel and kyanite) are also of interest, especially in view of the pressure dependenceof transitions such
as the well-known olivine-spinel transition.
Returning to the olivine structure it may be seenfrom Figure 1a that
the key structural unit is the serrated chain of octahedra lying parallel to
the a-axis. In any oue yz layer only half the octahedral voids are oc1 Table 3 has been deposited as Document No. 9901 with the American Documentation
Institute, Auxiliary Publications Department, Photoduplication Service, Library of Congress, Washington, D.C. 20420. Copies may be secured by citing the document number and
remitting in advance $3.75 for photoprints or $2.00 for microfilm.
STRUCTURES OF OLIVINES
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J. D. BIRLE, G. V. GIBBS, p. B. MOORE AND I. V. SMITH
812
T.tlr,e 2. INrERAroMrcDrsrexcns (A) rN Or.rvrNn
Atoms
Forsterite
Hyalosiderite(S) Hortonolite(CM)
Fayalite
Si, tetrahed.ron
1 Si
1
2
-O(1)
-o(2)
-O(3)
mean
1 O(1)-O(2)
_O(3)
2
2 O(2)-O(3).
1 O(3)-O(3)'
mean
r.614(4)
1.6s4(4)
1.63s(3)
1.613(3)
1.6s0(6)
1.634(3)
| 627(7)
1 .6s9(6)
1.636(4)
|.619(2)
r.634
t.634
1.639
1.638
2.743(5)
2.7s7(4)
2.ss6(4)
2.s86(6)
2.740(6)
2 . 7 4(74 )
2.ss4(6)
2.603(s)
2.7s8(e)
2.763(7)
2.s7r(6)
2.606(8)
2.72s(3)
2.7se(s)
2.s7s(3)
2.60s(4)
2.659
2.658
2.669
2.666
(2)
r.6s7
(2)
r.6s7
M(1) octahed.ron
2 M(1)-o(1)
2
2
-o(2)
-O(3)
mean
2 O(r)-O(2)b
-O(2)
2
-o(3)b
2
-O(s)
2
2 O(2)-O(3)"
-O(3)
2
mean
2.oer(2)
2.O7s(2)
2.142(3)
2.rr6(s)
2.0e1(s)
2.174(3)
2.100(4)
2.104(4)
2.183(4)
2 12s(2)
2.123(2)
2.228(2)
2.r03
2.127
2.t29
2.r59
2.8s7(s)
3.032(1)
2.8s7(4)
3.12s(4)
2.ss6(4)
3.3ss(4)
2.886(6)
2.062(r)
2.88s(4)
s.r77(6)
2.ss4(6)
(4)
3.417
2 .880(e)
3 .063(1)
2.88e(7)
s.164(7)
2.s7r(6)
s.43r(7)
2.e06(3)
3.0e8(1)
2.e28(3)
3.222(3)
2.s7s(4)
3 .s08(4)
2.964
2.997
3.000
3.039
M (2) oclahetlron
1 M(2)-O(1)
-O(2)
1
_O(3)
2
2
-o(3)
mean
2 O(1)-O(3)b
-O(3)
2
2 O(2)-o(3)
2
-o(3)
1 O(3)-O(3)"
-O(3)
2
-o(3)
2
mean
2 . t 7 7( 4 )
2.ose(4)
2.217(3)
2.070(3)
2.r17(s)
2.0e0(3)
2.262(3)
2.060(3)
2.202(6)
2.o7r(6)
(4)
2.267
2.060(4)
2.232(2)
2.110(2)
2.29r(2)
2.072(2)
2.r35
2.152
2.154
2.178
2.8s7(4)
3.028(4)
3.194(4)
(4)
2.e37
2.s86(6)
3.408(6)
2.99s(3)
2.886(4)
3.032(1)
3.25s(6)
2.e40(4)
2.603(s)
3.4s2(s)
3.011(s)
2.880(7)
3.0s7(6)
3.246(6)
2.e28(6)
2 606(8)
3.438(8)
3. 0 1 1 ( s )
2.906(3)
3.084(3)
3.303(3)
2.es6(3)
2.60s(4)
s 494(3)
3.024(2)
3.001
3.023
3.024
3.054
STRUCTURES OF OLIVINES
Tlr;e
Forsterite
1 O(1)-Si
-M(1)
2
-M(2)
1
r.614(4)
2.@r(2)
2 . r 7 7( 4 )
I O(2)-Si
-M(1)
2
-M(2)
1
I .6s4(4)
2.075(2)
2.0s9(4)
1 O(3)-Si
-M(1)
I
-M(2)
1
-M(2)
1
1.63s(3)
2.142(3)
2. 2 r 7( s )
2.070(3)
2-(Conti'nueil)
Hyalosiderite(S)
O(1) bond.s
1 . 613(3)
2.116(3)
Hortonolite(CM)
Fayalite
r . 6 2 7( 7 )
2.100(4)
2.202(6)
r.6re(2)
2.r2s(2)
2.232(2)
1 6s0(6)
2.091(3)
2.0e0(3)
I .6s9(6)
2.104(4)
2.O7r(6)
(2)
| .6s7
2.123(2)
2.rr0(2)
O(3)bonds
1.634(3)
2.r74(s)
2.262(3)
2.060(3)
1.636(4)
2.r8s(4)
(4)
2.267
2.060(4)
(2)
| .637
2.228(2)
2.2er(2)
2.072(2)
2.r77(s)
O(2) bond.s
tetrahedron and octahedron
" edges shared between
b edges shared between octahedra
an atom designaN.rribers in parentheses are standard errors. The number preceding
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
Qz-
(c)
(b) welinite' and
Frc. 1. Octahedral populations in the crystal structures of (a) olivine,
octahedra
unshaded
and
Shaded
stoichiometry.
olivine
with
(c) a hypothetical structure
distinguish the two levels normal to the plane of the drawings'
These predict a shortening of shared edgesand a lengthening of cationbonds to oxygen atoms of shared edgesbecauseof cation-cationrepulsion.
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 distancesaveragedover 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-oxygendistancescannot 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, MOOREAND T. V. SMITH
oxygen is bonded to one Si and three M atoms. The longest Si-o distance
is to o(2) which has the shortestM-o distances.rn the M(2) octahedron
part by the o(1)-o(2) edgesof two M(l) octahedra.These edgesare the
shortest of the unshared edges of the M(l) octahedron. Thus one can
envisage a compromise between conflicting electrostatic and spatial
factors such that the first o(3)-o(3) edge shortens and the second one
lengthenswhile the two o(1)-o(2) edgesshorten somewhat.of coursea
detailed analysis would require simultaneous consideration of all the
edges:perhaps such an analysis will become feasible in the future.
Burnham (1963) on the basis of a study of alumino-silicatesconcluded
that "in many casesthe minimum-energy configuration of a structure is
not primarily dictated by edge-sharingconsiderations". rn olivine, the
range of lengths of unshared edgesfor the M polyhedra is comparable to
the differencebetween the averageshared and the averageunshared edge.
Thus the simple concept of edge sharing would account for about half of
the length variations. Born (1964) on the basis of various simplifying
assumptionsincluding the positions of the Si and o atoms has been able
to predict the position of. M(2). perhaps the safest conclusion at this
time is that while Pauling's rules give a simple qualitative explanation of
817
STRUCTURES OF OLIVINES
Mfi)
@F
72
Y
)'.
@
72
@
@
I
( o oF
,8<
A
_{:9
Frc'2,o.Tetrahedralarrangementsandtheneighboringoctahedralsites.Distances
in a portion
along r are given in fractional.rnitr. b. Actual distortions observed for olivine
of an octahedral serrated band.
easeof sequential calculations.
818
T. D. BIRLE, G. V. GIBBS, P. B. MOARE AND J. V. SMITH
qq
si.;J5
M(2).3-;o
oo
o(3)
78
M ( , t ) o4 4 4
n,'t,
l. rl!
49242
2
M(2).
1493 27
6(21
tt,rtz)o
Jie
;A'
oo
M(11.4
2.72
327
M' 'f i ) a
44
272
1 5 0 3.27
i7
sit slos
(a.)
r',rrl
. !f;,
Si
M ( 2.) o
49
3.23
q?
2.72
o-z 3 2 7
o(.t))
2.85
o(2)
o (3)
78
78
'o\
s
r 209
33
u ( e ) o T3 s s
ot 366
6{
M(2).;23
22
07 272
'to7 3 27
r'ltilo
!on,t
(b)
819
STRUCTURES OF OLIVINES
si t
43
3.4o
,roo 5 66
Mfi).
oo359
57
sit328
50
M ( 1 ) . 32 3
o(1L,si 9 3
o(2)
72
282
o7 327
27
oo
M(1).50
3.23
Mfi).
100
o(3)
28
sl'
43
3 40
(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:tetrahedral site.
J. D. BIRLE, G. V. GIBBS, P. B. MOORE AND J. V, SMITH
o (3 ) M(1 )
t...3.'14
z.o]
\
n /^\ \ \
wlal
2 74 /,/
itat.P;'i
\:i
/oM(2)
o(1).
3.O4
o(3)\r
3.22 \
M({)\.
- -.-{
2.09t
o(3) .-\
3.392'
\t
I
I
o ( { )o s i
.2.74
-/l
I
1.65
821
STRUCTURES OF OLIVINES
Si
a
o(r)
M(2
o'..
2.76_
gi2i.. z.++
322
t.
\\
\
z-
.-6(\\
z.azl
,tc
6tsl
? ?n
---:'.-.
l
9l2l
M ((22)) i 2 3. e3 3 o ( 1 )
; .\-
2 00 66 i!
314
O(3)s.+r
tc)
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
distancesage given. O: octahedral site, T: tetrahedral site.
Figure 5 is an alternative way of displaying the distortion in the olivine
structure (again basedon an averageof forsterite and hortonolite). Each
of the subdiagrams is a stereographic projection of the first and second
neighborsof oxygen atoms, the former being tetrahedrally or octahedrally-coordinatedatoms, 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) in
olivine. 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 content
shows that most distances in the hyalosiderite and the hortonolite are
intermediate between those of forsterite and fayalite. The M(1) and
M(2) octahedraincreaseconsiderably in size with entry of the larger Fe
ions. The octahedra become more irregular as the Fe content increases,
and in contradiction to Eliseev's suggestion, fayalite is more distorted
from regular close-packing than is forsterite. The SiOr tetrahedron was
found to be larger in fayalite but the increaseis not significant in terms of
822
J. D. BIRLD, G. V. GIBBS,p. B. MOOREAND J. V. SMITH
the errors. The Si-O distances fall within the expectationslisted by
Smith and Bailey (1963): it is worth noting that the averagedistancein
olivine, 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 averagedistance in monticellite, 1.624 A, Onken (1965), is
smaller than in the forsterite-fayalite structures. This confirms earlier
indications that the mean Si-O distancesdependson the nature of other
cations and the structure type as well as on the degreeof polymerization of the Si-O group.
The surprisingaspectof olivine is the absenceof evidencefor ordering
of the octahedralcationsin Mg, Fe olivines.Of course,the minor cations
such as Ca and Mn causesome complicationand it is possiblethat they
occupy one site preferentially.In monticellite (Onken, 1965)magnesium
occupiesM(1) preferentially: perhaps the larger B value oI M(l) in
fayalite results from preferential occupancyby Mg. For the other three
structuresM(2) has the larger B value which might be taken to indicate
preferential occupancy by Mg. However it is thought that a larger B
value would be expectedtor M(2) in comparisonwith M(1) becauseof
the greater irregularity of the M(2) oxyget polyhedron: indeed, preferential occupancyof M(2) by Mg and of M(l) by Fe seemsunlikely
from a crystal chemical view-point since the larger Fe ion should prefer
the larger M(2) polyhedron if a preference does indeed occur. Lack of
ordering is consistentwith the other physical evidencefor near-ideal solid
solution summarized in the introduction. That lack of ordering is a surprise results from comparisonwith orthopyroxenewhere the two octahedra probably have lessdistortion than the onesin olivine but in which
strong ordering occurs(Ghose,1962).SIow cooling should have occurred
in the Skaergaardintrusion, while even the olivine from the Camas M6r
olivine gabbro dike (30 yards across) should have received some opportunity for annealing. Volcanic orthopyroxenes are partly ordered
(Hafner, pers. comm.).Presumablythere is somekey differencebetween
the crystal structures: the near closepacked structure of olivine may inhibit movement of octahedral cations more than the less closely-packed
structure gf pyroxene. Perhaps preferential occupancy in olivine becomes
stable thermodynamically only at temperatures too low for efiective
ionic migration: the frequent occurrence of orthoclase in plutonic and
metamorphic rocks shows how difficult is the ordering of AI and Si in
K-feldspar.
The presentstudv was begun becauseof literature reports of anomaIous properties in olivine that suggestedthat parameters might depend
on petrologic history and hence serve as petrogenic indicators. Actually
the structural parameters are quite regular and apparently immune to
STRUCTURES OF OLIVINES
823
crystallization history. Only the chemical parameters seemto 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-packedoxygen 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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824
J. D, BIRLE, G. V. GIBBS, P. B. MOORE AND J. V. SMITH
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M anuscriptrecei.ted.,
August8, 1967; accepted,
for publication,October13, 1967.