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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 assachusetts
02I 38
AND PAUL H. RIBBE
Department of Geological Sciences
Virginia Polytechnic Institute and State University
B lac ksbur g, Virginia 2406 I
Abstract
The crystal structures of the following metamorphic olivines, M;*[SiO4], in the forsteritetephroite (Fo-Te) serieswere refned in space group Pbnm:
Cation compositionM
Mg
Mn
Ca
Fol
Ten,
1.028
0.181
0964
1.780
0.006
0.013
Fe
0.002
0.026
a
Cell parameters(A)
b
c
4.794
4.879
10.491 6.t23
10.589 6.234
Rfactor
0.029
0.039
Treating minql ps and Ca as though they were Mn, the refined cation distributions (esds <
0.01) and mean bond lengthsare:
M(1) site
Mg
Mn
For,
Te",
0.92
O.l7
0.08
0.83
M(2) site
(M(lFo)
2.116I^
2.0294
Mg
Mn
0.1I
0.00
0.89
1.00
(M(2)-o) (si-o)
2.185A r.6374
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 distancescorrelatelinearly with Mgl(Mg+Mn) occupancy.
Introduction
However, the crystal structures of only two MgMn
olivines have previously been refined. One of
With the widespread availability of automated Xcontains I I mole percent of Zn SiOo, thereby
them
ray di-ffractometeruand least-squaresrefinement prothe octahedral site refinement (Brown,
complicating
grams, order-disorder has become a principal theme
The
is synthetic ForrTeo, which was
1970).
other
of contemporary crystal chemical investigations
(Ghoseand Weidneg 1974;
l000oc"
"heat
treated
at
(Burnham, 1973).Both natural and synthetic com1976)
and
thus
doesnot representa natet
al.,
Ghose
pounds with the olivine structure have been inThe present
Mg/Mn
distribution.
equilibrated
urally
tensivelystudied(for a review,seeGanguli,1977).At
Mg/Mn orexamine
were
undertaken
to
refinements
least 25 different room-temperature refinements of
uncomplicated
by addinatural
olivines
in
dering
the geologically-importantMg-Fe olivineshave been
substituents.
tional
carried out and 13 additional refinements extend the
observationalconditionsto 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 manganoanforsterite
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).Scatteringfactorsfor neuCa"*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 Crystalbands anhedralforsterite crystalsrange from 0.1-1.0 lography(1974,p.99, 149).The refinementswere inicm 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 concentratedon M(l)], and reasonableisotropic temoccurs as discreterounded 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 convenapatite in a calcite marble. For the purposesof site tional R factor dropped to -0.10. Site occupancyreoccupancy refinement these compositionswere ap- finements were undertaken by varying the Mg conproximated 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 isobut nonstandard spacegroup Pbnm. Unit-c.ell dinentropic temperature factors, and the R factors desions (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 crystalsusedfor 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 unand 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 NbStructure factors for which F"o"< 2oF"* were confiltered MoKc radiation (I : 0.70926A)and ttLeo:-20 sidered unobserved and were excluded from the rescanning technique at a rate of l" 20 per rrinute. finement. These are indicated in the structure factor
Twenty-second background measurementswere tables(Tables2a,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-squareequivalentsare 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 enThe olivine structure
velopesin the absorption correction. Linear absorption 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 diaaged 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 hexFull-matrix least-squaresrefinementsof Fo' and agonal closest-packedarray of oxygen anions with
one-half of the octahedral sites filled with divalent
cations and one-eighth of the tetrahedral sites occuTable L Crystal data
pied by silicon. The key structural feature is the serrated chain, parallel to c, of two symmetrically-indeto5,
YI
pendent, edge-sharing octahedra. The M(l)
Langban,
Sweden
Madagascar
octahedron is at the interior of the chain and the
4 . 7 9 4 ( 2 )* A
4.879(2) A
b
10.491(4)
1 0 . s 8 9( 4 )
M(2) octahedron forms the "elbows" of the chain.
c
Vol
Density
^Numbers
deviation
6.r23(2)
3 o az. ( z ) n 3
(ca1c. )
ln
3.67 glcc
parentheses
represent
(14) and refer
to the
6.234(3)
-aa
)zz.
'zar
L\z)
.3
A
4.UO g/cc
es!imated
standard
last
decimal olace.
I To obtain a copy of Table 2, order Document AM-80-141
from the BusinessOffice, Mineralogical Society of America, 2000
Florida Avenue, NW, Washington" DC 20009.Pleaserenit $1.00
in advance for ttre microfiche.
1265
FRANCIS AND RIBBE: FORS TERI TE-TEP H ROI TE SERI'S
Table 3. Atomic coordinates
t",
)l
Atom
x
M(1)
M(2)
v
0.9870(1)
o . 4 2 2 6( 2 )
b1
0 .7 s 8 (ss )
0 .2 3 0 (1s)
0(1)
0(2)
0(3)
t-
0 . 2 78 2( 3 )
o . 2 79 0( r )
0.0910(1)
0 . 0 8 6 (72 )
0 . 4 4 8 9( 2 )
0.1590(2)
Atom
v
M(1)
M(2)
0 . 9 8 7 7( 2 )
o . 4 2 6 5( 4 )
o . 7 s 74 ( L O )
0 . 2 1 6 2( r r )
0 . 2 8 s7 ( 8 )
5a
0( 1 )
0(2)
0(3)
,
t4
,,4
o . 0 3 74 ( 2 )
z
0.2801(1)
0 . 0 9 5 (12 )
0.0914(5)
o . 452s(5)
0 . 1 6 2 (53 )
,4
t4
,4
\
0 . 0 4 0 1( s )
The [SiO.] tetrahedron sharesits basal edgeswith
two M(l) and one M(2) octahedra.Its apex links to
the adjacentchain, which is related to the first by Dglide planes.
Cation ordering
Consideration of cation ordering in non-calcium
olivines began with the prediction of Ghose (1962)
that becausethe effective ionic radius of Fe (r :
0.78A) is larger than that of Mg (r : 0.72A) it should
be preferentially ordered into the larger M(2) site.
Refinementsof four compositionsacrossthe forsterite-fayalite seriesby Birle et al. (1968) and refine-
mentsby Brown (1970)failed to detectMglFe order.
Subsequentrefinementsby Finger (1970),Finger and
Virgo (1971),Brown and Prewitt (1972),Wenk and
Raymond (1973),Ghoseet aI. (1976),and Basseer a/.
(1979) have shown small but signfficant degreesof
ordering of Fe onto M(l) rather than M(2). This unexpected result, termed anti-ordering by Brown and
Prewitt (1973),has generally been attributed to the
greater distortion from ideal Oo symmetry of the
[M(l)O6] octahedron which results in a slightly
greater crystal field stabilization energy for Fe2* on
M(l) (Walsh et al.,1974) [althoughfor someMg-rich
olivines, Fe'* may show a slight preferencefor M(2)
(Wenk and Rayrrond, 1973). In general,site preference of divalent transition-metal cations relative to
Mg in olivine is determined by two competing factors: cation sizeand crystal field etrects(Rajamani et
al., 1975).
Divalent manganesetras t high spin d' 6snfiguration which is unaffected by crystal field effects.Thus
cation ordering in Mg-Mn olivines is predicted
(Brown, 1970;Burns, 1970,p.118)to be governedby
the size criterion with Mg (r : 0.72L) preferring
M(l) and Mn (r : 0.834) preferring M(2). The cation distributions determined in the present refinements and an earlier refinement of a synthetic manganoanforsterite(ForrTen) "heat treatedat 1000"C"
by Ghose and Weidner (1974)genfirm the predicted
preferences(Table 6). Another refinement, that of
from Franklin, New
Mn, r*MgororZnorrrFeo..r"SiOo
Jersey(Brown, 1970)is consistentwith but is not a
Table 4. Anisotropic temperaturefactors(Bi;),equivalentisotropictemperaturefactors(Beq) and their root-mean-square
equivalents(p)
Btz
R
- 1* 1
R
-22
R
-33
3.r(4)
6.L(2)
3.1(3)
2 , 2( 7 )
4.o(8)
3 .e ( 6 )
r.35(8)
1.16(4)
0 . 9 6( 6 )
L . 7( 2 )
2.s(z)
- o .r ( 2 )
3 . 6 6( 9 )
0.24(8)
0.0(r)
-0.2(3)
-0.5(3)
0.0(2)
5.8(4)
6. 7( 4 )
s . 4 ( 7)
2.9(18)
5 . 7( 1 8 )
7 .s ( 1 3 )
2. 2 ( L )
r . 3 7( 7 )
1 .4 ( 1 )
2.s(4)
1 .4( 4 )
1.9(3)
Brg
R
-23
se q ( e ' )
u(A)
to5r
M(1)
M(2)
Si
o(r)
o( 2 )
o(3)
r.r(2)
1.3(r)
2.s(2)
3 . 1( 4 )
3.8(4)
3 .6( 3 )
- 0 .s ( 2 )
0.0
0.0
0.0
o.o
0.0(3)
-0.34(9)
0.0
0.0
0 .0
0.0
0 . 4( 2 )
0.42
0.54
0.36
0.50
0.48
0.50
0.073
0. 083
0. 058
0.079
0.078
0.079
-0.7(3)
0.0
0.0
0.0
0.0
0.0(8)
-0.7(1)
0.0
0.0
0 .0
0.0
0.4(3)
0.76
0.68
0.61
0.81
0.59
O.77
0.098
0.093
0.089
0.r01
0.094
0.099
T"91
M(1)
M(2)
5a
o(1)
o(2)
o(3)
*8..
4.8(2)
s.0(2)
4.s(3)
5.7(10)
s.6(e)
4 . 9( 6 )
0.0(2)
0.1(2)
0.1(3)
o.r(8)
-o.2(7)
0.2(s)
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
Table 5A. Interatomic distances(A) and angles (o) of Fo'
Table 5B. Interatomic distances (A) and angles (o) of Tecr
Isioo1 tetrahedron
si-o(1)[1]
o ( 2 )[ 1 ]
o ( 3 )[ 2 ]
Mea
Isiool tetrahedron
1.611(3)*
1.651(2)
1.638(2)
1.637
O...O dlstaces
sr-o(1)[1] 1.613(5)*
o ( 2 )[ 1 ] 1 . 6 6 3 ( 6 )
o ( 3 )[ 2 ] r . 6 4 1 ( 4 )
M e a n1 . 6 4 0
Angles at Sl
o ( 1 ) - o ( 2[)r ] z . z s s ( : )
o ( 1 ) - o ( 3l)z l - 2 .t s z ( z )
o ( 2 ) - o ( 3[)2] ? . 5 5 0 ( 3 )
o ( 3 ) - o ( 3[)r l ' 2 . o o + ( g )
[M(1)06 ] ocrahedron
o ( 1 ) - o ( 2 )[ 2 ] b
o ( 1 )- o ( 2 ) [ 2 ]
o(1)-o(3)2
[ ]
o ( 1 ) - o ( 3 ) [2 ]
o ( 2 ) - o ( 3 ) [2 ]
o(2)-o(3) 2
I'Iean
I u ( 1 ) o uJ o c t a h e d r o n
M ( 1 ) - o ( 1 )[ 2 ] 2 . 1 8 3 ( 4 )
o(2)12) 2.L44(4)
o(3)12) 2.228<4)
M e a n2 . 1 8 5
Angles at M(1)
2.753(3)
3 . 0 8 7( 1 )
2 . 75 2 ( 3 )
3 . r . 2 6( 3 )
2 . s 5 0( 3 )
3 . 3 s 9( 3 )
2.940
bz,ttt(t)
8s.35(7)
94.65(7)
8 s .9 3( 8 )
9 4 .0 7( 8 )
ros.38(8)
74 . 6 2 ( 8 )
90.0
s6.26(1s)
o ( 1 ) - o ( 2 )[ 2 ]
93.74(L5)
o ( 1 ) - o ( 2 )[ 2 ] 1 3 , 1 5 8 ( 2 )
o(1)-o(3)[2] "2.7s0(6',) 85.20(16)
94.80(16)
o ( r ) - o ( 3 )[ 2 ] J . 2 4 7 ( 5 )
-2.580(6)
107.59(16)
o ( 2 ) - o ( 3 )[ 2 ]
72.3L(L6)
o(2)-o(3)[2] 3.530(6)
Mean 3 . 0 0 0 M e a n9 0 . 0
[M(2)06] octahedron
M ( 2 ) - o ( 1l t) l z . z g o ( z )
o ( 2 ) [ 1 ]2 . r z e ( 2 )
(2)
0 ( 3 )[ 2] 2 . 2 8 7
o3)lzl 2.L26(2)
u ( 2 ) - o ( r l)1 l
o ( 2 )[ 1 ]
0 ( 3 )[ 2 ]
0 ( 3 )t 2 l
l4ean 2.209
disteces
l.lean
Mean 3.L16
*Nunber
ln
deviation
7s.so(1)
e2.53(7\
e7.28(8)
eo.oe(7)
69.40(8)
89.r.2(6)
r11.70(e)
Uean
a.
Edges shared between tetrahedron
b.
Edge shared between octahedra.
and
octahedron,
valid test of the prediction, becauseMg had to be assignedto M(l) in order to simplify the computation.
The degreeof order for the three pure Mg-Mn olivines is illustrated in Figure l, with data for Mg-Fe
olivines included for comparison. Order is frequently
quantified by the use of a distribution coefficient Ko
lMe/(Me+Mn)M(2)l [Mn/(Ms+ Mn)M (r)l / IMe/
(Mg+Mn)M(1)l[Mn/(Mg+Mn)M(2)] written for
the ion exchange reaction Mg'z*M(l) f Mn2*
M(2)SMg3*M(2) + Mn'z*M(l). For a fully ordered
Angles
at M(2)
80.72(14)
o(1)-0(3)t2l "z.tso(o)
91.26(r2)
o ( 1 ) - o ( 3 )[ 2 ] 3 , 1 7 s ( s )
97.59(rs)
o ( 2 ) - o ( 3 )[ 2 ] 3 . 3 s s ( b )
o(2)-o(3)[2] ^3.350(5) 89.84(12)
' 2 . 6 1 7( 6 )
68.73(17)
o ( 3 ) - o ( 3 )l r l
87.e4(8)
o ( 3 ) - o ( 3 )[ 2 ] 3 . 1 0 2 ( 4 )
o ( 3 ) - 0 ( 3 )[ 1 ] 3 . 6 1 7 ( 6 ) ! L 4 . 7 7 ( 2 0 )
M e a n3 . 1 7 2 M e a n 8 9 ' 8 5
89,75
parentheses represents one estinated
stmdard
(d) and refers to the last decinal
place.
2.2s2(s)
2 .r 3 9( s )
2.318(4)
2 . r 4 7( 3 )
2.227
0.,.O disteces
Angles at M(2)
o(1)-o(3)lzlb z.tsz(t)
o ( 1 ) - o ( 3[)2 ] 3 . 1 e 7 ( 3 )
o(2)-0(3)[2] 3.315(3)
o ( 2 ) - o ( 3 ) [ 2 ]3^ . 3 s e ( 3 )
o ( 3 ) - o ( 3[)1 ] ' 2 . 6 0 4 ( 3 '
o(3)-0(3)[2] 3.010(3)
o(3)-o(3)[1] 3.s20(3)
A n g 1 e sa t M ( 1 )
o...o distances
IM(2)06 octahedron]
0,..O
1r.33
. (3)
LLs.4(2)
L 0 2 . 7( 2 )
105.8(3)
tog.2
o ( 1 ) - o ( 2 )[ r ] 2 . 7 3 7 ( 7 )
o ( 1 ) - o ( 3 ) [ 2 ] ^ 2. 75 0( 6 )
o ( 2 ) - o ( 3 )[ 2 ] : 2 . 5 8 0 ( 6 )
' 2 . 6 1 7( 6 )
o ( 3 ) - o ( 3 )[ 1 ]
Mean 2 . 6 6 9
M ( 1 ) - o ( 1 )l 2 l 2 . L 2 4 ( 2 )
o(2)l2l 2.o7s(2)
0(3)t2l 2.L48(2)
M e a n2 . 1 L 6
O.,.O distances
A n g l e sa t S l
0...O distmces
1 1 4 .6 ( 1 )
115.8(1)
101.8(1)
r . o s . 3( 1 )
1o9.2
llean 2.664
S,ERIES
*Number in Darentheses reDresents
refers to last
devlation
i6)
""a
a,
Edge
shared
between
tetrahedron
b.
Edge
shared
between
octahedra,
one estimated standard
decimal place.
and
octahedron.
distribution Ko : 0, for a completely random distribution Ko : l, and for an anti-ordered distribution
KD : @. These define the top and right edges,the
long diagonal, and the left and bottom edgesof the
parallelogramin Figure l.
The Mg-Mn olivines are strongly ordered by comparison with Mg-Fe olivines. The contrast between
'the
heat-treatedsynthetic crystal (Ko : 0.196) and
the metamorphiccrystals(Ko : 0.000,0.01l) demonstratesthat the degreeof Mg/Mn order is dependent
1267
FRANCI S A N D RI BBE: FORSTERITE-TEPH ROITE SER/ES
Table 6. Refined site occupanciesof Mg-Mn olivines
M(1)
ConDoslEion
l4n
4C
Fo53Tt47 *
o.124
Fo51Tt49
0.921(5) 0.079
roo9Tt91
o.172(9) 0.828
Mg
O.276(4)
Mn
K-**
0.339
0.661
0.196
0.110
0.890
0.011
1.000
0.000
radii (Brown,1970).This relationshipis illustrated in
Figure 2 for (Mg-Mn)-containing octahedra. The
data (Table 7) fall into two distinct populations describedby the following regressionequations:
(M(l)-0) :2.200 - 0.096VoMg; R : 0.997
(M(2) -0) :2.223 - 0.097VoMs; R:0.998
reflecting the inherent size differencebetweenM(l)
and M(2) octahedra due to the difference in number
**K-= [ Ms/ (Mg+lrn)M(2) ] [Mn/ (Ms+Mn)M(I ) ]
(Ms+Mn)M(1)
of sharededges.
lMs/
I IMn/ (Ms+un)M(2) ]
Quadratic elongation,a measureof distortion of_t
are in square brackets and refer to
Estimated standard deviations
the last decimal place.
ten used in the analysis of finite homogenousstrain,
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 precludetheir wide use angle (Robinson et al., l97l).
as petrogeneticindicators.
Using the bond anglevarianceparameteras a convenient 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 octashared polyhedral edges,have been thoroughly discussedby Birle et al. (1968)and Brown (1970).One
1976)
Effectivelonic Rodius( Shonnon,
surprisingresult of the latter study is the constancyof
Si-O distancesirrespective of octahedral cation
2.24
chemistry.The Si-O distancesobservedin this study
(Table 5) are typical, being statistically indistinguishablefrom the correspondingvalues for ten oli2.22
vines studiedby Brown. In contrast,mean M-O distancesare a linear function ofthe calculated effective
*chose
& weidner
(1974).
o42
E
-ordered
\
( K-n = O O O ) r
\ F o 5 1, K 9 = 9 . 6 1 1
r*\
\a..
6z.te
.-^\.
V.i
c|)
"" t'ii. .iuay)
t
!,
c
--synthetic
Foo3 KD=O 199
( G h o s eI W e i < l n e r1,9 7 4)
oo
2.r6
o
I
q
-50
or
82.t4
=
(D
;e
I
o
Fo - Te series
Fo - Fo series
roo
50
Mole % Forsterite
2 .t o
o
Fig. l. Plot of percent magnesiumon M(l) as a function of
mole percent forsterite component, which illustrates the degree of
cation order-disorder in the forsterite-tephroite series (squares)
and the forsterite-fayalite series (dots). Data from Table 7.
Rr^
to0
Mole 7" Forslerile
Fig. 2. Plot of mean M(l)-O (dots) and M(2FO (squares)
distances as a function of refined site occupancy in percent
magnesium (lower abscissa) and effective ionic radius (upper
abscissa).Lines represent regressionequations given in the text.
1268
FRANC I S AN D RI BBE: FORSTERITE-TEPH ROITE SERI'S
Table 7. Mean M-O distancesfor (Mg,Mn)-containing octahedra
Mineral.
Site
Occupancy
<M-O> (A)
Reference
Forsterite
M(1)
Mo
2. 10r
2. L26
tlazen (1976)
2.116
2.209
Thls study
z. Ld)
This study
' 00
;;1
---1.00
M(t\
M(r)
Fo--Te.)r
49
$|o.szf;o.oa
^"'0.89"60.
M/'\
11
M(1)
tt91to9
sr"so.
rz
fo.
'..'1.
00
u(2)
Manganhumite
M(1)
. ro
zoMso
f;0.
"'r. oo
r.r(2)
o
Table 8. Polyhedral distortions as measured by the bond angle
variance parameter (o)2 ofRobinson et al. (1971\
totoot
Fo- -
-'91
Isio. ]x
42.4
4 8 .3
38.0
l- M ( 1 ) o _l * *
98.7
99.9
L 2 7. 3
[M/?)n']**
o
9 0 .1
rr4.7
r24.1
Polyhedron
6-
)l
tHazen (1976)
25
*o(tet) = X (o.-!09.47o)2 /
5
l2
xxO(oct) 2= t
i=t
2.227
2.r70
2.222
Francls & Rtbbe (1978)
hedra increase with increasing M-O distance. Polyhedral distortions of the present structures (Table 8)
conform to these general trends, but the distortions
of Fo' are somewhatanomalous.The M(2) octahedron is more distorted than M(l), reversing the general rule for end members and disordered compositions. The tetrahedron in Fo' is also significantly
more distorted than in either end member. These
anomalies, which also hold for monticellite (Lager
and Meaghet, 1978), are attributed to the large size
di-fferencebetween M(l) and M(2) cations.
Reinterpretation of cation distribution in Zn,Mg
tephroite
(0.-90o)2/rr
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' 36sMgs3a5Zna225Fes
r28)SiO4
Occupancy
Scatterlng
Powerx
Electrons
Effective
Radius
Tonlc
(A)
<M-O>
obs.
(A)
pred.
Brown (1970)
M(1)
ho.
M(2)
43zu8o.
345Zto.l8oFto. 043
ho.86Bt"o.
oB5zoo.o45
zL .40
0.774
2.r48
25.32
0.821
2,224
M8o.
345h0. ro oznn-zzlF"o.tza
ht, oo
2 t . 78
o.765
2.L5+
2 5 .0 0
0. 830
2.223+l
Reinterpretat ion
M(1)
M(2)
*Lnr"i
**In.r.
(radii
from Shannon(I976))
ItO)
tPrecllctecl from 0.755 + 1.38 (radtus of
f tPredicted
f r o m < M (2) - 0 > = 2 . 2 2 3 - 0 . 0 9 7" / " V i g
FRANCI S A N D RI BBE: FORSTERITE-TEPH ROITE SER/ES
Mn *"rFeoo.rZno*r,with a mean M(2)-O distanceof
2.2244. Qsmparison of this mean bond length with
the observedvaluesot 2.2294 for (M(2)-O) in Ten,
and 2.2224 for (M(2).-O) in manganhumite
(Francis and Ribbe, 1978),both of which are completely occupiedby Mn, suggeststhat the M(2) site in
the Franklin tephroite is also completelyoccupiedby
Mn. The plausibility of a fully ordered distribution
may be tested by comparing the effective X-ray scattering factorsand ionic radii of the compositeoctahedrally coordinated atoms of the refined model with
those of the fully ordered model. Only if these parametersare nearly equal can the ordered model be
realistic. This comparisonis made in Table 9. Scattering factors were approximated by summing the
products of the atom fractions times their respective
atomic numbers, which equal the number of electrons in neutral atoms. The scattering factors of both
modelsare identical within the limits of resolution of
X-rays for both M(l) and M(2). Similarly the mean
effectiveradii ofthe divalent cationsare nearly identical. Thus the intensity data are equally satisfiedby
the model reportedby Brown (1970)and the fully orderedmodel. In further supportof the orderedmodel
may be cited the strong preferenceof Mg for M(l)
observedin this study, the preferenceof Fe for M(l)
discussedabove, and the preferenceof Zn for M(l)
relative to Mg (Ghose and Weidner, 1974).The ordered model therefore is not only possiblebut appearsto be crystal-chemicallypreferable.
Acknowledgments
We are grateful to ProfessorCharlesW. Burnham and Dr. David L. Bish of Harvard University, who assistedgenerouslywith
data collection, and to the ResearchDivision of Virginia Polytechnic Institute and State University which provided funds for computing. Partial financial support was provided under NSF grant
EAR77-21114 (Earth SciencesSection) to P.H.R. and G. V.
Gibbs.
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Manuscript received, February I, 1980;
acceptedfor publication, May 7, 1980.