American Mineralogist, Volume 69, pages 928-936, IgB4
Cation arrangementin iron-zinc-+hromium spinel oxides
Clene
P. MnnsHaLL AND WeyNr, A. Dor-la,se
Department of Earth and Space Sciencis
University of California
Los Angeles, California 90024
Abstract
The distribution offerric and ferrous ions within the quaternaryFe2*-Fe3*-Zn-Cr spinel
solid solution seriesis documentedusing Mcissbauerspectroscopyand X-ray diffraction.
Along the binary joins Fecr2oa-Fe3oa, znCr2oa-Fe3oa and znFe2oyFqoa the cation
distribution changesfrom normal to inverse. From the different trends of iron distribution
versuscompositionobservedalongthesethreejoins and at other points within the Fe-ZnCr solid solution series, it was found that octahedralsite ferric/ferrous chargehopping may
be the most important phenomenonstabilizingthe inverse ion distribution. For spinels
whose compositions make charge hopping impossible or statistically unlikely, cation
dis-tributionis governed by the intrinsic spinel site preferences(tetrahedral site: Zn > Fe2*
Fe3* )) cr, octahedralsite: cr > Fe3i > Fe2* ) Zn), which result from the size and
bondingcharacteristicsof theseatoms.
Near the ZnFe2Oa-FqOa edge of this spinel quadrilateral, the normal to inverse
transitionproceedsessentiallyto the maximumextent allowedby the Zn content,because
the octahedra!F"t* produced by inversion can share electrons with the surrounding
octahedral Fe3* ions. Inversion along the FeCr2oa-Fe3oa edge of the quadrilateral,
however,is inhibiteduntil there is a sufficientoctahedralFe3+populationto makeelectron
sharing(with inversion producedoctahedralFe2+)statisticallylikely. A rapid changeof
site preferenceof iron ions occurs in the central range of this composition subspace,
offering a physical reasonfor the miscibility gap found along the chromite-magnetitejoin.
Introduction
ferrous iron in either site. The octahedra form edge
Cation arrangementin spinel-typeoxides has long been sharingchains along [110]. The tetrahedraare isolated
a topic of interest among mineralogists(Barth and posn- from one another, sharingeach of their corners with three
jak, 1932;Verwey and Heilmann, 1947;Robbins et al., octahedra.
Chromite (FeCrzOe), ZnCr2Oa and franklinite
l97l; Price et al., 1982),becausethe site distribution
(particularly of iron) has a strong effect on magnetic, (ZnFe2Oa\are all normal spinels, with divalent atoms on
electrical and thermochemical properties. Studies of a the tetrahedralsites. Magnetite (FeFe2Oa)is an inverse
variety of end member spinel compositions (Verwey and spinel with all ofits ferrous iron occupying the octahedral
Heilmann, 1947, Navrotsky and Kleppa, 1967;price et site. (The degreeof inversion, which in these spinelsis
al., 1982;Urusov, 1983; O'Neill and Navrotsky, l9g3) equal to the fraction of tetrahedral site occupied by
and binary solid solutions(Ol€s 1970;Dobsonet al. 1970; trivalent ions, is commonly denotedby I which can vary
Levenstein et al. 1972;Grandjean and Gdrard 197g,and from 0 to l.) Thus, this systemexemplifiesthe transition
Burns 1981,to mention a few) have brought into focus from one end member ordering stateto the other, acrossa
many problems concerning the compositional depen- quaternary solid solution series. By using Zn and Cr,
dance of cation distribution in spinels. This paper will which strongly prefer tetrahedral and octahedral sites
concentrate on changes in cation arrangement within a respectively (Navrotsky and Kleppa, 1967), the only
distributional variablesare the position and valenceofthe
quaternary solid solution series, the Zn{r-Fe2*-Fe3+
iron atoms present. These constraintsallow the cation
spineloxide system.
The spinel structure consists of an almost cubic close distribution vs. composition of the experimentally propacked array of oxygen atoms with cations in intersticies duced phasesto be found using X-ray powder diffraction
within the oxygen framework. Sixteen octahedral and (XRD) and Mdssbauerspectroscopy.
eight tetrahedral sites within one unit cell of 32 oxygens
Experimental procedures
are filled, in the system studied, with zinc in the tetraheSeventeenspinels were synthesized from mechanical
dral sites, chromium in the octahedral sites and ferric and mixtures of oxide powders within the Zn-Cr-Fe2*-Fe3+
0003-09)v84l09I 0-0928$02.
00
92E
MARSHALL AND DOLLASE: IRON-ZINC-CHROMIUM
Table I. X-ray data for synthesizedspinels
no.
/, comp
(Zn, Cr)
tcst=Fe
3l
7
6
1.0, 2.0 +
0.90,2.0 +
0.80,2.0 +
0.55,2.0 +
0 . 3 0 , 2 . 0+
tenp, dur. f 02
("c,
apror,
hours)
valu€s
ceII
/l/lult
dldension
6
.!2
(Angstrons )
1200,3
960,26
1000,24
940,25
940,25
alr
-14.5
-14.5
-14 5
-14.5
**
*
*
*
*
3 0 1 . 0 , r . 5 0+
28 0 7 5 , 1 . 5 0
0.25,1 50
1200,1E
1060,10
1060,4
air
-13.2
-14.0
** 6.3502(E)
*'r 8.36,6,0(r1)
** 8.3938(10)
t1
1.0, 1.0 +
0.50,1.0
850,24
1007,48
air
-13.r
#
#
E.3625(9)
8.3904(5)
38
25
1 . 0 , 0 . 5 5+ 1 2 0 0 , 3
0 75,0.50
985,3
0.25,0.50 1010,11
0 . 0 5, 0 . 5 0
9 8 5, 3
air
-10.0
-13.0
-13 0
**
**
*
#
8.4099(24)
8.3955(6)
8.3E69(r0)
8.3864(6)
air
-t2.1
-12.0
** E.4415(12)
** 8.4366(5)
** 8.4252(11)
l0
1.0, 0.0 +
0.75,0.0
36 0 . 5 0 , 0 . 0
32
1200,3
912,10
1025,4
8.3275(5)
8.3333(7)
8 3375(E)
8.3503(11)
E.3516(14)
conversion
of the starting
/l assuming conplete
/lJl Gu K o, = 1.540598' Cu K c2 = 1.54443
+ synthesized
with a Li-borate
flux
t NBS silicon
standard used
** Silver
netal used as standard
SPINEL
929
mm/sec/channelfor magnetic spectra. The sampleswere
placedin l-inch diameterpolyetheleneholderswith inert
adhesive. Velocity calibration utilized Fe metal and Nanitroprusside.
Room temperature Mdssbauer spectra were collected
for eachspinelsynthesized,(seeTable 2)' In paramagnetic spectra,doublets were constrainedto have equal areas
and peak widths. In magnetic spectra, the areasfor each
sextetwere constrainedto a3:2: I ratio, with corresponding peaksconstrainedto have equal peak widths. (For a
more detailed description of the experimental procedures, see Marshall, 1983.)
The calculated and measured cation arrangement of
thesespinelsis assumedto correspondto the temperature
of synthesisbecausethe quench rates were rapid relative
to ionic re-equilibration rates of similar spinels (Trestman-Mattset al., 1983).The electronicconfigurationsof
the iron atoms, however, probably does not quench
(O'Neill and Navrotsky, l9E4; Trestman-Matteset al.,
1983)and could representlower temperatures,although
the cation arrangementspredicted by Robbins et al.'
(1971) along the chromite-magnetite join correspond to
the theoretical thermodynamic arrangement(O'Neill and
Navrotsky, 1984) predicted for l000oc, the synthesis
temperature.
spinel quadrilateral, except along the magnetite--chromite
Experimental results
join, amply studiedby Robbinset al., (1970);Levinstein
et al., (1972);Ok et al., (1978);and others (compositions
The parametersobtained from the Mcissbauerspectra
on Figure2 and Table 1). One spinelwas synthesizednear are isomer shift (IS), quadrupolesplitting (QS) and peak
join (sample25). It showedcharthe magnetite-chromite
acteristicsconsistentwith the findingsof these authors.
Table 2. Mtissbauerdata for synthesizedspinels$
Most sampleswere pressed, then hung from platinum
wire in a controlled atmospheregas mixing furnace (COI
I
rel.
P9
ll
No.
#comp
llllls
QS
(m/
(no/
(m/
Udss, UCE
(Zn, Cx
koe
area
CO2)operatedbetween900'C and I100"C.
(!5)
calc.
beas
sec)
sec)
sec)
rest=Fe
,
!0 06 t0.02
All samples were quenched by dropping, under an
argon atmosphere. The samplesreached room tempera-0
0.0
31
1. 0 , 2 0
ture within minutes,althoughthe exact quenchrate was
o .o
0.0
0
,.0
0 30(r)
0 . 9 0 , 2 . 00 8 8 ( 2 ) 0 1 7
7
o.o
0-0
0
0.89(r)
0 . 3 0 (1 )
5
0 E 0 , 20 0 . 8 8 ( r ) 0 2 1
:not measured.If wiistite or hematitewas found in the X0 11(r)
0 30(1)
0
0.34(9) 0.28
00
0,0
10
0 . 3 7 6( 5 ) o
iiay:pattern, or if the diffraction pattern showed broad
I
0.55,2.00.85(1) 0.26
00
0.0
I 0
0.3se(8) 0
IO
0 . 3 0 , 2o o . 9 0 ( r ) o - 2 3
peaks, the samples were reground and rerun at slightly
0
.
0
0.0
0
1
.
0
3
4
8
0
.
2
7
8
(
7
)
0
.
3
6
4
(
9
)
0
30
1.0,1.60
o 03
0.343(1) 0.0
changedoxygen fugacities until no other phasescould be
0 . 7 5 , r . 5 00 . 9 6 6 ( 9 ) 0 . 2 8 4 0 3 9 7 ( 8 ) 0
(
9
)
o
6
s
7
(
l
)
o
,
0
4
0
3
0
s
)
0
.
4
0
E
2
8
5
o
detected. Final conditions are included in Table L The
o01
0605(1) 00
0 403(9) 0
29
0 2 s , 1 . 5 00 9 6 ( l ) 0 . 3 3
o 383(6) 0
0 3es(r)
0.3E(l) 0.43
compositionslisted in Tables I and2 are those assuming
0.0
0.0
complete conversion of the starting mixes to spinel. 1 5 0r .05,01, 100o0 0 . 313 9 ( 8 ) 0 . '3l 8 5 0 . 3 2 2 ( 4 ) 01 1?0
2
0.20
2l
Mdssbauer and X-ray data were consistent with this
0.0
0 0
1.0
33
r . 0 , 0 . 5 s 0 . 3 5 1 ( 4 )o 3 4 s 0 . 3 3 ( 3 ) o
assumption (to within 4% of the expected composition)
0.30* 0 25
0.rE(2)
0 73(3) 468
25
0 . 7 5 , 0 . s *0 . 2 6 ( 9 ) - 0 . 0 2
o.82(2')
2 14(3' 413
0 6,1(7) 0 0e
except for sample 26. For, that single sample, both the X0.71 0 66
0 32(1)
0 57(2) s07
38
0 . 2 5 , 0s o o . 2 r ( 5 ) o . 0 3
ray and Mcissbauermeasurementsare more consistent 25 o 0 5 , 0 5 0 00 .6256((56)) 00 .. 01 50 0r . 45 55 ((5l )) 44 49 97 0o 63 e3 (( 11 )) 0 E l O . 7 7
0.67(1)
t.36(2) 445
0.67(5) 0.11
with a compositionof Zn 0.7O,Cr 0.56, rather than the
0.0
0
1.0
0.0
originally intended composition, Zn 0.75, Cr 0.50. The
32 1 . 0 , 0 0 0 . 3 3 1 ( 4 )0 4 r 4 0 . 3 4 3 ( 5 )
?
?
01E
1',l
?
?
34 0 . 7 5, 0 . 0
corrected composition is shown in Figures 2 and 3.
0.11(1) 0.31 0 43
0.74(4) 499
16 0 . 5 0 , 0 . 0 0 2 0 ( 8 ) 0 . 0 6
2.34(4> 44O 0 E 9 ( 1 )
o 53(13) 0 02
Mtissbauer spectra were collected on a conventional
sourc€ uas Co ln Pd.
at rom tenperature,
constant accelerationspectrometerwith a moving sTCoin I neasur€d
oix to sPinel
/, assming conplete conversion of the startlnt
(errors
the
saoe
for QS)
powdered
are
The
mirror
rel
to
Fe.
Pd source and
sample absorbers.
llll
* Conposition would be 0.70,0.56 (ra!he! thd 0 75,0 50) if the
image spectra, accumulatedon a 512 channel multichanl,ldssbauer peak ereas are collect
# assuoinS excess ferlous lron on the octahedral site ls charSe hoPplnt
nel analyser,employedvelocity incrementsof about 0.03 ? velue
0as not obtalned.
mm/sec/channelfor paramagneticspectra and about 0.0E
930
MARSHALL AND DOLLASE: IRON_ZINC_CHROMIUM SPINEL
width at half height (pW). The IS is approximately partially or fully inverse(0.3 < I < 1, seeTable 2). These
constant for a particular iron valence state in a particular spectraare much more complicated and overlapped than
type of site. A literaturesearchof oxide spinelsgives the the paramagneticspectra and the errors in measurement
followingaveragesrelativeto iron metal:tetrahedralFe2+ are consequentlylarger.
: 0.91mm/sec(9 examples),octahedralFe2* : 1.02mml
In generalthe magneticspectralooked similar to those
sec (8 examples),tetrahedral Fe3+ : 0.28 mm/sec (6 of Robbinsetal. (1971).In every magneticspectrum,one
examples)and octahedralFe3* : 0.37 mm/sec(14 exam- sextet had an IS value correspndingto tetrahedralFe3+
ples). QS is a function of the electric field gradient and (around 0.27 mm/sec).For these,
QS is close to 0.0 as
therefore measuresthe symmetry of the site. In oxide would be expectedfrom the high symmetry of the site.
spinels, QS for either tetrahedral or octahedral Fe3* The peak width averagedaround 0.7 mm/sec, which is
tendsto be small (0.3-0.6mm/sec)and relativelyinsensi- wider than ideal.
tive to cation disorder. On the other hand, Fe2r in
The octahedralsite sextet in the magnetic spectrais
octahedraland especiallytetrahedralsites show small to more complicated. Whenever both ferric and ferrous iron
very large QS values, dependingupon disorder of near are present on the octahedral site, an intermediateIS
neighborsites.The PW reflectsthe similarity of the sites value of about0.63mm/secwas observed,corresponding
within each crystal; for a spinel where all of the tetrahe- to an intermediatevalence state resultingfrom electron
dral ferrous ions have an identical configuration of near- charge hopping between ferric and ferrous ions (Bauest neighbors,the peak width will be narrow (around0.3 minger et al., 1961;Dobson et al. 1970;Robbins et al.
mm/sec.). Broader peaks result from the existence of 1971;Murray and Linnett, 1976;Ok and Evans, 1976;
dissimilarsites,ditrering,for example,by havingdifferent Lotgeringand van Diepen, 1977andOk er al., 1978).The
secondor third nearestneighbors.
quadrupoleinteractionof this sextetvariesbetween0.06
The room temperatureMossbauerspectraof all para- to 0.25mm/sec.The peaksare broad, around 1.4mm/sec
magneticsamplesshowed spinelswith "normal" distri- for sampleswith approximately equal numbers of ferric
bution (\ : 0.0), i.e., in thesesamples,all ferric iron is in and ferrous ions, and up to 2.3 mm/sec when greatly
octahedral coordination and all ferrous iron is in tetrahe- different proportions offerric and ferrous ions occupy the
dral coordination.
octahedralsite. These extremely wide peaks are attributSamples along the ZnCr2Oa-ZnFe2Oobinary join able to variable amounts of charge transfer between iron
showedIS, QS and PW consistentwith octahedralferric ions, dependingon the ion distributionaround each site.
iron as was found also by Muthukumarasamyet al.,
Although a minor tetrahedralFe2+componentis pres(1980).Samplesalong the ZnCr2Oa-FeCr2Oa
binary join ent in some of the magneticspectrumsamples,its specshowtypical tetrahedralferrousiron valuesofIS, eS and tral contributionis too weak to show a third discernable
PW. Along this join the QS remainsalmost constantand sextet.Lack ofresolution ofthis sextetno doubt contribis very small (0.18 to 0.26 mm/sec.).This is expected utes to the apparent broadenedpeakwidths of the two
because,along this join the local site symmetry is high fitted sextets.
with all of the nearestneighborcationsfor this site being
Several room temperature spectra in the central range
the same (Cr atoms). The small changes in QS are of this composition spaceshowed both paramagneticand
probably due to variations among the second nearest magneticcontributionsof varying proportions.The paraneighborcations, i.e., the Fe and Zn on the tetrahedral magnetic component is due to the interaction of smaller
site.The largestQS on thisjoin occursat an approximate- magneticdomainswithin the samples,i.e. superparamagly half and half mixture of zinc and iron on the tetrahedral netism (Greenwoodand Gibb, 1971,p. 104).
site, where the highestdegreeof disorderwould occur.
The presenceof both paramagneticand magnetic comM<issbauerspectraof samples28 (Zns75Fe6
75Cr156Oa) ponentsyield severelyoverlapped,low resolution specand 29 (Zns25Fe1.25CrrsoOa)
show contributions from tra. Sample34 (Zno75Fe2.25O)
showsa largely paramagboth octahedral ferric and tetrahedral ferrous iron. The netic spectrum with enough magnetic component to
values of QS of the ferric iron are close to those obtained produce an undulating background, similar to that obalong the ZnCr2Oa-ZnFe2Oa
join. The QS for the ferrous served by Topsoe et al. (1974, Fig. 2-B). Sample 2l
iron, however, is higher than values obtained along the (Zns.56Fe1
5sCr16Oa)consistsof about half paramagnetic
join, as a result of decreasedlocal site and half magnetic components at room temperature,
ZnCr2Oa-FeCr2Oa
symmetry causedby mixing of different ion specieson the yielding a series of broad humps spanning the entire
nearestneighboroctahedralsite. The width of both the velocity range, similar to Figure 2, Grandjeanand Gerard
ferric and ferrous Mossbauer peaks are broader than the (1978).Although the paramagneticcomponentdecreased
averagewidth measuredalong the simpler binary joins. when the temperaturewas lowered (also seenby Topsoe
According to the site distribution calculations utilizing etal. 1974),individualpeakswere still difficult to resolve.
unit cell edge, (next section) these two samples also
Site distribution calculations
contain minor amounts of tetrahedral ferric and octahedral Fe25*, (i.e., they are partially inverse)which could Mtissbauer parameters
also contributeto the peak broadening.
Using the chemical compositions of the starting mix
The magneticspectrashowed spinelswhich were either and the relative peak areasof the Mossbauerspectra, site
MARSHALL AND DOLLASE: IRON-ZINC_CHROMIUM
distributions for each of the synthetic spinels were calculated. The calculation is straightforward for paramagnetic
spectra, where the ferric iron is confined to octahedral
sites and the ferrous iron is in tetrahedral sites. The
assumptionsinvolved are: all Zn is in tetrahedral coordination, all Cr is in octahedral coordination and all the
sites of the spinel structure are full.
For the magnetic spectra, only the tetrahedral ferric
iron to total iron area ratio was used for the calculation.
The Mcissbauerpeaks corresponding to the tetrahedral
site are narrower and better resolved than those correspondingto the octahedral peaks.
From the calculated site occupancy, the inversion
parametertr is found (i.e., the amount of tetrahedralferric
iron, seeTable 2, tr M<iss.meas.).The estimatederror in
the inversion parameteris t0.06 when errors in fit and
relative areas on the Mcissbauerspectra are taken into
account.
Cell dimensions
Distinguishingbetween tetrahedral and octahedralions
using Mcissbauerspectroscopyalone is somewhatimprecise, especiallywhen magneticor mixed magneticand
paramagnetic spectra are involved. Furthermore,
changesin site occupancythat involve lessthan 5Voof the
total iron are not generally distinguishableby Mcissbauer
measurements.For these reasons, estimations of site
occupancieswere also madeusingunit cell edgemeasurements.
Interatomic distances (such as the tetrahedral atomoxygen bond length and octahedral atom-oxygen bond
length) can be calculated from a knowledge of the spinel
cell dimension, a, and the single variable positional
parameterin the spinel structure, z. (The oxygen atom
lies on a 3-fold axis and has fractional coordinates
(u,u,u).) Conversely, the values of a and a can be
calculatedfrom a knowledge of the t-o (tetrahedralatomoxygen) and m-o (octahedral atom-oxygen) bond
Iengths. The operative equations are:
2 dl_" - d?-"
-
u""":#i**l
5
ffi-(d,-")
(1)
: averageoctahedral atom-oxygen distances for
that composition.
d1- : average tetahedral atom-oxygen distances for
that composition.
d*
931
a calc.: calculatedunit cell edge,
u calc.: calculated oxygen atom fractional coordinate.
Relatedequationswere derived to predict z and from this
in turn, a, for end membercompositionspinelsby Hill et
al., (1979\.(Thesewere also used by O'Neill and Navrotsky (1983)to calculate best fit cation radii for spinel
oxides.)
Thus, given a spinel composition and an appropriate set
of characteristic cation-oxygen bond lengths, the site
occupancy can be varied until the calculated cell dimension matchesthe observedcell dimension.ln considering
the possiblesite distributions,it was assumedthat where
Zn is present, it is in tetrahedral coordination and where
Cr is present,it is in octahedralcoordination.Whereboth
ferric and ferrous iron are present on the octahedral site,
it is assumedthat equal numbers of Fe2* and Fe3* are
involved in charge hopping, i.e., the extra electron is
sharedbetween two octahedral sites creating a net charge
of 2.5. The remaining iron, either Fe3* or Fe2*, is not
participatingin chargehopping.
This latter assumption is probably not strictly correct
as ratios other than l: I are possible,as shownby Ok and
Evans, (1976), Evans and Ok, (1977), and Ok et al.,
(1978), but it was initially employed to simplify the
calculations. Ignoring charge-hoppingon the octahedral
site altogether yield calculated unit cell edge dimensions
that were much larger than measuredvalues. Calculations
made with octahedral Zn or tetrahedral Cr also yielded
spuriousresults.
The values used for characteristic cation-oxygen distancesmust be chosencarefully.They shouldnot be very
different from those measuredin other natural crystalline
oxides (as given, for example, by Shannon 1976, ot
Brown and Wu, 1976).They must also be chosenso that
the difference between calculated and measuredunit cell
dimensionsof the end membersare less than the error in
measurement(0.0014).
5,
For tetrahedral ferric and octahedral Fe*2 measured
cation-oxygen distances from end member magnetite
(Fleet, 1981)were used.The other valueswere chosento
fit the measuredunit cell edge dimensions for the other
end members of this spinel quadrilateral and, where
known, their measuredsingle variable positional parameters, ,r. Unfortunately, this is an underconstrainedsystem
of equations (because the z parameters are not well
known) so the values chosenhere are not unique. That is,
other values of cation-oxygen distanceswithin 0.02A of
those chosenwill fit the end membersjust as well, as long
as the difference between Fe2+ and Zn t-o distance is
0.035A and the diference between Cr and Fe3* m-o
distanceis 0.0414. Calculatedcation-oxygen distances
for spinelsby O'Neill and Navotsky (1983)do not completely satisfy theseconstraints. The diference in their Cr
and Fe3+-Odistanceis 0.030Aand their tetrahedralFe+
oxygen distance is 1.865A rather than 1.8384 as measuredby Fleet (1981).
It is important that the cation-oxygen distancesbe fit to
(z)
where
SPINEL
932
MARSHALL AND DOLLASE IRON_ZINC-CHROMI UM SPINEL
8 4r0
I405
c I 400
.9
to
c 8 395
o
.E
I
!
o
o
z
c
390
8 385
8 380
5
:t"'""-';'ft"
crrFe3-"o.
i"T"'.t",il
Fig. L Unit cell edgeas a functionof composition
alongthe
chromite-magnetite
join. X's are measuredvaluesfrom
Levinstein
et al.(1972).
Solidlineis calculated
(l )
usingequation
asslmingchargehopping
onlyamongequalnumbers
of Fe2+and
Fe3+.Dashed
lineis calculated
usingtheassumption
thatall the
octahedral
iron atomsarechargehopping.
the end members,becausea changein 0.0007A in the
tetrahedral atom-oxygen distance or 0.004A in the octahedralatom-oxygendistancechangesthe calculatedunit
cell dimensionby 0.0014, which is the typical error in
measurement.Also, becauseof the strong site preferencesof chromium and zinc, it can be assumedfor the
end membersthat a negligibleamount of iron ion site
exchangehas occurred. For tetrahedralsites the values
usedare (in Angstroms):Fe2+2.015,Fe3+ l.ggg and Zn
1.980.The octahedralvaluesare: Fe2* Z.l54,Fe3* 2.026,
Fe2-5*2.059and Cr 1.9g5.
From the calculated site occupancies,the inversion
parameter\ is found (i.e., the amountof tetrahedralferric
iron), see Tabte 2 (\ UCE calc.) and Figure 3. The
estimatederror for this calculationis +0.02 when errors
in unit cell dimensionand cation-oxygen distancesare
both taken into account. For a complete tabulation of
thesecalculations,seeMarshall, 1983.
Discussion
Before consideringthe generalquaternarysystem,it is
useful to first review the binary joins. The ZnCr2Oa_
FeCr2Oajoin shows simple substitution of one ion for
anotheron the tetrahedralsite, as can be verified by the
Mtissbauer measurements.The simple substitution resultsin linear changesin unit cell edgewith composition.
The ZnFezO+-ZnCr2Oajoinsimilarly shows simple substitutionon the octahedralsite. Measuredunit cell dimensions of this study are in agreementwith those of Ol€s'
(1970).MeasuredMcissbauerparametersare consistent
with thoseof Muthukumarasamyet al. (1980).The calcuIated site occupanciesusing unit cell dimensionsare also
consistentwith simple substitutionalong both of these
binaryjoins.
The FeCr2Oa-Fe3Oa
join (chromite-magnetite),has
beenwell studied.Francombe(1957)and Levinsteinet al.
(1972)found extraordinarilynonlinearchangesin unit cell
dimensionwith composition.Robbinset al. (1971)and
Petric and Jacob(1982)presentedpredictedsite distribution along this binary join, on the basis of Mcissbauer
spectraand magnetiteactivity measurements
respectively. Ok et al., (1978)predictedsite occupanciesfor the
magnetite-richend members.
Calculatedunit cell dimensions(equation l) utilizing
predicted site occupanciesof Robbins et al. follow the
generaltrend for changesin unit cell with composition
(within 0.014) as measuredby Francombe(1957)and
Levinstein et al. (1972)(see Fig. l). The predicted site
occupanciesof Petric and Jacob (1982),however, show
trends in calculated unit cell edge very different than
thosemeasured.This discrepancycould be due in part to
the difference in experimental conditions (1100"C for
Robbins et al. vs. 1400'Cfor Petric and Jacob),but the
fact that Petric and Jacobneglectedto take into account
chargehoppingon the octahedralsite is also a factor.
In the present study, the "best fit" estimatesof site
occupanciesalong the magnetitechromitejoin are only
slightly different from the predictionsmade by Robbins
et al. (1971).For the composition range Crs.sFez.zOr
FeCr2Oa(see Fig. l), some ferric iron substitutioninto
the tetrahedralsite was necessaryto produce a good fit
(*O.OOOSA)
between calculatedand measuredunit cell
dimension. For the composition range Fe3Oa-Crsg
Fe22Oa,the calculated values using Robbins et al.'s
predictionsand the initial assumptionsin this stu^dyare
larger than the measuredvalues by up to 0.007A, well
beyond measurementerror.
The discrepancyis a result of assumingthat charge
hoppingonly involves equal numbersof Fe2* and Fe3*.
Wheneverboth Fe2+ and Fe3* ions are present on the
octahedralsite at appropriatehoppingtemperaturesand
in sub-equalamounts,the "extra" electronsare shared
amongall adjacentiron atoms,not only on a I : I basis.A
similar conclusion has been reached for magnetite-like
spinelsby other authors(Adler, 1968;Goodenough,1967;
Dobson1970;Evansand Ok, 1977;Wuand Mason,l98l;
Trestman-Mattset al. 1984).To test this hypothesis,the
unit cell dimensionwas recalculatedassumingthat all the
octahedraliron atomsparticipatein chargehopping(i.e.,
the electronsform a conductionband on the octahedral
site), and that the cation-oxygendistancefor the charge
hopping speciesis the same as measuredin magnetite
(Fleetet al., l98l) wherethe ratiois I : l. This assumption
produced a very good fit (10.00054) throughout the
compositionaljoin (seeFig. l, dotted curve). The cation
distributionnear the magnetiteend memberis essentially
identicalto the predictionsof Ok et al. (1978).
The ZnFe2Oa-Fe3Oajoin (franklinite-magnetite) has
also beenwell studied(Popovet al., 1963;Dobson et al.,
1970;Ok and Evans 1976;Srivastavaet al., 1976;Evans
and Ok, 1977),though no one study included both XRD
and Mcissbauerwork across the entire join, and the
MARSHALL AND DOLLASE: IRON-ZINC_CHROMIUM
SPINEL
933
almost complete substitution of ferric iron for Zn. Beand ZnFe2Oa,both ferric and fertween Zn6 75Fe2.25Oa
rous ions substitute for Zn, with the larger proportion
being ferrous (probably becauseof its more comparable
size to Zn ions).
In Figure 2, contours of unit cell edge over the entire
composition space studied are presented, incorporating
o'
data from this study and from Levinstein et al. (1972)and
s
o 05
oo
Popov et al. (1963)for the magnetite-chromite and magN
3
ro 0 5
netite-franklinitejoins respectively.Although Not all conc,
tt
tt
N
tours in Figure 2 are equally well constrainedby the data'
'C
0a
N
N
this particular configuration of contours is presented
becauseit is most consistentwith the site occupancyto
be discussedbelow. The changesin unit cell edgein this
composition spaceare due not only to changesin composition, but also reflect changesin site preference of the
0l
iron atoms. as the normal to inverse transition takes
place.
'' 16 I' r'2 r'0 08 06 04 02 F'F'".a
jilhoj
It is also interesting to note that on each ofthe normal
tus'rrr'
CrtFe3-tOn
to inverse binary joins in this system, the onset of
Fig. 2. Unit cell edgecontours(intervalof 0.014) over the magneticordering at room temperaturecoincides with an
Fe2*-Fe3*-Zn-Crspinelcompositionspace.Boldfacenumbers inflection in the unit cell dimension and a sharp increase
aredatapointsfrom this study.Datafor the ZnFez0+-FeFe2Oa
substituting on the tetrahedral
join are from Popovet al. (1963)and data for the FeCrzOn- in the amount of ferric iron
(i.e.,
)r).
in
increase
a
sharp
site
FeFe2Oajoin
are Levinsteinet al. (1972).
Figure 3 presentscontours of the amount of tetrahedral
ferric iron (that is, the inversion parameter,tr) throughout
Dobson and Srivastavastudiesare not completely consis- the composition space,as calculatedusing equation I and
tent. For these reasons,three spinelswere synthesized the measuredand interpolated unit cell edge dimensions
all
along this join, at 50Vo,75Vo,and lNVo franklinite mole shown in Figure 2. The assumption used was that
proportion.
Unit cell edge measurements of these samples and
ZnFe2-xCr*Oa
Zn?.2O1
those of Ok and Evans (1976)are consistentwith those
made by Popov et al. except for a constant of 0.0044
(Popov et al.'s data are consistently0.0044 larger than
this study's data and other published data on the end
members).The unit cell edgevs. compositionrelation is
0
not as sigmoidal as found on the chromite-magnetitejoin
o'
but does show a changein slope at 70 mole Vofranklinite,
oo
$o
N
which has been correlated with a change in entropy by
=
Popov et al, (1963).
o
o-o
l!
lt
N
!
The Mcissbauer measurementsof the present study
c"
N
'
join
with
Dobson
et
al.
those of
along this
are consisent
(1970). Franklinite shows a paramagnetic spectrum at
room temperature. Between Zns.75Fe2
25Oa and
Zn6.5,6Fe2.aOa,
spectra with paramagnetic and ferrimagnetic components are observed, with the paramagnetic
component decreasing with decreasing Zn component.
the spectra
For sampfesless zinc rich than Zns.6oFe2.aOa"
t2
o2
t"
r0
08
06
rcFoao.
,rcr1o,
are entirely magnetic with all of the octahedral ions
maSattta
CrrFe3-yO.
participating in charge transfer (as in Ok and Evans,
Fig. 3. Contoursofthe amountofinversion, I, over the Fe2*1976).Srivastavaet al. (1976)found mixed spectraat 80
Fe3*-Zn-Cr spinel composition space as calculated using
mole Vofranklinite and attributed the paramagneticcom- measured unit cell edge dimensions and equation (l)
ponent to interactions of small magnetic domains in the (corresponds identically to amount of tetrahedral ferric iron
crystals.
present).The large dots (O) representpoints where the unit cell
The tetrahedral site occupancy (calculated from cell edgewas measureddirectly. Crosses(+) representpoints where
dimensions and measured by Mtissbauer spectroscopy) unit cell edgevalues were linearly interpolatedbetweencontours
shows on Fig. 2.
along this join between Fe3Oaand Zns.75Fe2.25Oa
?nFe"-*CrrOo
I
s
934
MARSHALL AND DOLLASE: IRON_ZINC-CHROMIUM SPINEL
ZnFer-*CrrO
tranklinite
near the franklinite-magnetitejoin becausethe presence
of Zn in the tetrahedralsite limits the possibledegreeof
inversion.
In RegionIII, dl/dr - l, that is, the rate of changeof
0
inversionis essentiallyconstantwith changesin compoo 0
i:\t, \
sition. As the compositionbecomesmore magnetiterich
J
lll
o
in this region, ferrous ions substitutedirectly onto the
,"'
o 0
N
3I
I
octahedral site (ferric ions onto the tetrahedral site)
0
o
o
lt
allowing charge hopping among octahedraliron atoms.
l!
N
c
' 0
Chargehoppingstabilizesthe inversespinelby raisingthe
N
entropy (de-localizingelectrons)and lowering the strain
0
in the structure(more similar-sizedions on the tetrahe0
dral and octahedralsites).This regioncan be discussedin
0
terms of a different site preferencemodel than in Region
I. That is: tetrahedral Zn > Fe2* > Fe3* >> Cr and
14 t2
10 08 06 O4 O2
FeFe2O4
octahedral
Cr > Fe25+ > Fe3* > Fe2* >) Zn. The energy
magnetite
Cr"Fea_rOn
saved by octahedralcharge hopping (Fez's* more than
for the energylost by replacingferrous iron
Fig. 4. The rate of changeof inversionwith composition. compensates
Dashedlinesare compositional
joins alongwhichthe rate of with ferric on the tetrahedral site, and so the inverse
changeof inversion,dl/d-r is measured.
RegionI, dl/d-r < l. arrangementis preferred over the normal cation arrangeRegionII, d\/dx > l. RegionIII, dl/d,r: l.
ment at thesecompositions,
Many factorsinfluencethe normal to inversetransition
in spinel oxides. In this system, one important feature
octahedraliron is chargehoppingwhen there is a near I : I
stabilizingthe inverse spinel is the tendencyof the iron
ratio of ferric to ferrous iron. The cation distribution of
atomson the octahedralsite to chargehop. This concluany spinel in this composition space (formed near
sion is similar to that of Robbins et al. (1971) who
1000'C),can be determinedusing Figure 3.
concluded from the Mcissbauer spectra that along the
To discuss the degree of inversion as a function of
magnetite-chromite join between Fe:Oa and Fer s
composition,it is useful to divide the compositionspace
Cr1.2Oa,
the octahedralsite maintainedequal amountsof
into threeregions(aswas donein Robbinset al., 1971,for
ferric and ferrous iron. The main difference between
the magnetite-chromitejoin). Although the boundaries
theseconclusionsis the phrase"equal amounts". As was
between regions are not strictly constrained,Figure 4
previouslydiscussed(this study and Ok et al., 1978),a
showsthe generalform of the rate of changeof inversion
l: I correspondenceof ferric and ferrous ions is not
with composition,d\/dx. The diagram was constructed
essentialfor charge transfer,
by drawing compositionaljoins between points on the
ZnCr2Oa-ZnFe2Oa
joins and magand ZnCr2Oa-FeCr2Oa
Applications
netite (see dotted lines, Fie. a). Along each of these
compositionaljoins, the rate of inversion with composiOctahedralsite chargehoppingis an importantstabiliztion was calculated.Boundariesseparatingregionswith ing phenomenonfor iron rich inversespinels,and must be
d\/dr < l, dl/dr > I and dtr/dx - I were drawn. The taken into account in thermodynamicmodels of spinels
error in placementof these boundariesis not more than (or any mineral system with ferric and ferrous ions in
l0 mole Vo.
adjacentoctahedralsites).Ofgeologicimportanceare the
In Region I, both I and dl/d-r are small, that is, very thermodynamicmodelsusingspinelsas petrogeneticindilittle ferric iron substitutesonto the tetrahedralsite. This cators(Sack, 1982).
region can be described in terms of normal spinel site
In the spinel-olivine geothermometer(Irving, 1965),
preferencesarisingfrom cation size and bondingconsid- the partitioningof elementsbetweenolivine and spinelis
erations.In general,for the tetrahedralsite, the prefer- assumedto be dependentonly on the temperatureof
ences are: Zn > Fe2* > Fe3* >> Cr and for the formation and mole fraction of ions on the octahedralsite
octahedralsite: Cr > Fe3* > Fe2* >> Zn. The difference ofthe spinel.Roederet al. (1979),however, showedthat
in tetrahedralsite preferencebeween Fe2* and Fe3* is higher ferric iron spinels yield greater Fe2+/Mgratios,
not very large, as is shown by the presenceof small and that the Fe2*/Mg distribution between ferric rich
amounts of tetrahedral ferric iron.
spinelsand olivine is essentiallyindependantof temperaIn RegionII, dI/dr is greaterthan one. This is a region ture and therefore not useful as a geothermometer. In
of high rate of change of inversion with composition view of the present study, this observation of Roeder et
signifying a sudden transition from the normal spinel al. seemsnot only reasonablebut expected,becausea
orderingschemeof RegionI to the inversespinelordering ferric rich spinel will incorporate as much ferrous iron in
schemeof RegionIIL Note that this regionis not present its octahedral sites as possible, to satisfy its charge
znc(2o118
l6
14
o ,'n'"roa
MARSHALL AND DOLLASE: IRON-ZINC_CHROMIUM
hopping capacity. Consequently, the Fe2+/Mgration will
be dependentmore on the amount offerric iron presentin
the spinel than the temperature of formation.
The change in site preference which results in the
normal to inverse cation distribution is probably related
to miscibility gapsin reported spinel systems,as shown
theoreticallyby O'Neill and Navrotsky, (1984).One does
not find nor would one expect a miscibility gap along the
ZnCr2O4-ZnFe2Oaor ZnCr2O6FeCr2Oajoins because
the compositional changesresult in simple substitution of
one similar sized cation for another on the octahedraland
tetrahedral sites respectively.
Along the franklinite-magnetitejoin, although a change
in site preferencedoes occur, the site substitution rate is
still constant with composition. A miscibility gap is not
expected until much lower temperatures are reached
(O'Neill and Navrotsky, 1984).(This join does not fit
their model exactly, however, probably in part because
they did not take into account conduction electrons on
the octahedralsite.) Valentino and Sclar (1982)studied
this join at temperaturesas low as 500"C,and no miscibility gap was observed. Exsolution lamellaeof magnetitein
franklinite have been found by Burke and Kieft (1972),
but no temperatureswere estimated for this occurence.
Along the chromite-magnetitejoin, a rapid exchangeof
ferric and ferrous ions occurs (Region II, Fig. 4). Compositions within this region of high rate of site substitution
might be expectedto exsolve at lower temperaturesinto a
charge hopping species(inverse) and a non-charge hopping species(normal). Cremer (1969)studied the magnetite-chromite join and found a miscibility gap in this
region at 900"C, although other studies have placed the
(Evans and Frost, 1975).
miscibility gap as low as 5(X)oC
The miscibility gap has also been calculated thermodynamicallyby O'Neill and Navrotsky (198a).
Increased pressure should also favor exsolution. As
can be seenin Figure I , the volume of normal and inverse
spinels would be substantially smaller than that of the
homogenous solid solution. Similarly, Figure 4 shows
that the binary join connecting ZnCrzOqwith magnetite,
crosses Region II and, by analogy with the magnetitechromite join, a miscibility gap in this system is to be
expected.No studieshave yet been made at low temperatures or high pressuresalong this join.
Acknowledgments
The authorswouldlike to thankT. O. Mason,A. Navrotsky,
H. O'Neill andananonymous
reviewerfor usefulcomments
and
suggestions
in their reviews.
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