Download Local states of Fe2+ and Mg2+ in magnesium-rich olivines

American Mineralogist, Volume 71, pages 127-135, 1986
Local statesof Fe2+and Mg2+ in magnesium-richolivines
JeN SreNer,t S. S. HArxrn, rNo J. A. Sewrcxrr'2
Deportment of Geosciences
Universityof Marburg
3550Marburg,FederalRepublicof Germany
Abstract
s?FeM0ssbauerspectraof a synthetic forsterite and of one natural olivine were studied
at temperaturesbetween 4.2 and 1223 K. Spectrawere also taken at pressuresbetween I
and 30 kbar at 568 K and in external magnetic fields between4 and 7 T at295 Kand 4.2
K. The signs of the electric field gradient at Ml and M2 arc positive. The averagevalue
of the two asymmetry parametersa is 0.20+0.05. The force constantsof Fe2+at Ml and
M2 are4.7+0.1 eY/42 and 4.2+O.l eY/A', respectively.The axial splittingd is I 120+50
cm-' for both sites. The comparison of the 57Fedata with the previous 'z5Mgdata allows
a more detailed analysis of total, lattice, and Fe2* valence field gradients at the Ml and
M2 sites.The observedapparentlack of site preferencefor Fe2+can be interpreted in terms
of the local electronic properties.
Introduction
physical
properties
Many
of olivines (Fe,Mg)rSiOoare
determined by the local statesof bonding at the atomic
positions and their dependenceson temperatureand pressure. The crystal structuresof olivines are orthorhombic
with space group Pnma. In this paper we are particularly
concernedwith the local propertiesofthe positions ofthe
bivalent cations, Fe2* and Mg2+, which are octahedrally
coordinated.There aretwo distinct positions,M I and M2,
with point symmetries 7 and m, respectively.The distribution of the Fe2* and Mg2+ ions is generallydisordered
over Ml and M2, although possible preferencesof Fe2+
for Ml or M2 under certain conditions have beendebated
in the past. Many questions,particularly the cationic exchangebetweenMl and M2 at elevatedtemperaturesand
its kinetics are still open. However, for the interpretation
ofsuch processes,detailed studies ofthe local site properties are desirable.
In the past, Mdssbauer spectroscopyof 57Fehas been
mainly used for studying iron rich olivines (Eibschiitz and
Ganiel, 1967;Kiindig etal.,1967; Bush et al., 1970).In
the presentwork we describeMdssbauer studies of synthetic and natural olivines with low concentrationsofiron
(0.0025and 0.1 mol. fraction). The experimentswere carried out in a wide rangeof temperatures(4.2-1223 K), at
high external fields (4-7 T), and at high pressure(30 kbar)
and elevatedtemperature (568 K).
In this paper, the measured magnitudes, signs, and
asymmetries of the electric field gradient (EFG) tensors
of 5?Fein forsterite are compared with the 2sMgnuclear
magneticresonancedata previously obtained for the same
mineral (Derighetti et al., 1978)and with theoreticalEFG
calculations.Suchcomparisonis interestingin view of the
relationship betweenlattice and valencecontributions to
the total EFG. This may be a steptowards a more general
considerationof local structureand chemical bonding. In
particular, the estimated axial field splittings of the iron
3d orbitals can tentatively explain the weak, ifany, preferential site occupancyby Fe'z+ions, which appearsto be
independent of the external state during the crystallization
of olivine.
The Mossbauerspectra,if measuredover a wide temperaturerange,also supply information about the dynamics of Fe2* ions. For this, the estimated Debye temperatures and force constants for both sites may be compared
with X-ray diffraction studies at high temperatures and
high pressuresprovided that sufrciently refined data are
available.
Samples
Twomaenesium-rich
olivineswith thefollowingcompositions
This forsterite
werestudied.Sample(1): (Feo.-M&eers)rsiOo.
samplewasobtainedby powderinga singlecrystalspecimenof
high perfectiongrown usingthe Czochralskimethod.High enpermittedthe recordingof Miissbauer
richmentof 57Fe(90.470)
despite
spectrawith a hightotal resonantabsorptioneffectof I 80/o
This
of iron.Sample(2):(FeootMgo
thelowconcentration
r)rSiOn.
samplewas kindly provided by T. Malysheva.It was a high
temperatureolivine separatedfrom a naturalgarnetperidotite.
at 295,78and4.2K were
Theabsorbers
for themeasurements
madeby mixing powderedsampleswith lucite powder.Pellets
with a diameterof 12 mm werepreparedby heatingat 420 K
I On leavefrom Institute of Physics,JagiellonianUniversity, and pressingat 2 kbar for 30 minutes. For high temperature
measurements
the samplesweremixed with boron nitride and
30-059Cracow.Poland.
2Presentaddress:Chalk River Nuclear Laboratories,Chalk distributedhomogeneously
on an iron-freeberyllium plate,also
River, Ontario,Canada.
l2 rnm in diameter.The absorberthicknesswasabout0.1 mg
0003{04v8 6/ 0 to24 | 27502.00
r27
128
STANEK ET AL.: LOCAL STATES OF Fd* AND Mg,* IN OLIVINES
--------------s
z
o
G
G
o
o
z
Fig. I . Design of the high pressure, high temperature cell. ( I )
sample,(2) graphiteheater,(3) cupperconnection,(4) pyrophilite
filler, (5) BnCanvils, (6) stainlesssteelrings, (7) thermocouplein
Al2O3 tube fixed in a steel screw.
2
U
E
sTFe/cm2
for sample (l) and about 4 mgFe/cm2 for sample (2)
so that the samples could be approximately treated as "thin"
absorbers.
Measurements
The Mtissbauer spectra in the temperature range between 295
and 1223 K were recorded using a vertically operating, water
cooled furnace with a tungsten filament. The vacuum during the
measurementsvaried from 5 x l0-5 to l0-3 Torr, dependingon
the temperature which was stabilized within 2 I(
Measurements in high, external magnetic fields were carried
out using a superconducting solenoid which allowed the taking
of spectra at liquid helium, liquid nitrogen, and room temperatures. The direction of the gamma rays was parallel to the magnetic field. The source was kept at a "zero field" position 4 cm
from the absorber. This fortunate source-to-absorber geometry
was possible due to a field compensation coil in the solenoid at
the side of the source. However, the experimental line width in
the absorber was generally broadened to widths of about 0.28
mm/s probably due to tlle fact that the magretic field at the
source was not exactly zero.
The apparatususedfor the measurementsofM0ssbauer spectra
at high pressureswas the equipment described by Amthauer et
al. (1979) modified for high temperaturework up to 600 I( This
temperature is needed for obtaining the resolution ofthe distinct
quadrupole splittings of 57Feat Ml and M2. The investigated
sample was mixed with BN powder, inserted into a graphite ring
(4 mm in diameter), and pressed between two B4C anvils. The
current through the graphite ring, being the main heating element,
was 40 A at 500 K. The temperature of the sample was measured
by a Pt-Pt (10o/oRh) thermocouple, which was used also for
temperature regulation (+2 K). The correction for the pressureinduced change of the thermoelectrical voltage given by the
thermocouple was considered (Bundy and Strong, 1962). The
pressure vs. applied force calibration was carried out at room
temperature using the known resistivity jumps of bismuth at 25.4
and27 kbar (Bundy and Strorg, 1962) and ofytterbium at 40
kbar (Drickamer, 1965). The constant force during experiments
was supplied by an automatically regulated hydrostatic press.
Thus, there was no change in pressure during heating from 300
to 500 IC
The design ofthe high pressure, high temperature cell which
hasnot beenpublished before is shown in Figulg | . lligh pressure,
-L
-2
t'
u..oi,r, rr.r1r
Fig. 2. Miissbauer spectra of sTFein polycrystalline forsterite
at temperatures as marked. The solid lines are Lorentzian line
fits with widths and intensities constrained to be equal for the
low and high velocity peaks of each doublet.
high temperature Mtissbauer spectroscopy measurements have
been attempted using a diamond cell heated with a laser beam
(Ming and Bassett,1974).The advantageofour designis that it
yields undistorted spectra based on thin absorbers with reasonably large areas. However, the range of temperatures at present
is limited to about 700 K due to the thermal properties ofstainless
steel(Thyrodur 2709) gasket.
All experiments were performed using a singleJine source of
s'Co in metallic Pd or Rh matrices. The activity of the source
varied from 20 to 40 mCi in the diferent experiments. The
instrumentalline width wassmallerthan 0.25 mm,rs.The velocity
scalein the Mdssbauer spectra was calibrated by use of a metallic
iron absorber.
Experimental results
Measurements at high temperatures
The temperature dependenceof the Miissbauer spectra
in forsterite doped with 5?Fe(sample l) was investigated
between 295 K and 1223 K. Spectrataken at 295, lO23
and 1223 K are shown in Figure 2. High temperature
measurementswere also carried out for the natural olivine
(Feo,Mgr)rSiOo(sample2).
r29
STANEK ET AL.: LOCAL STATES OF Fd* AND ME* IN OLIVINES
9.0,,
E
5
o
o
U
E
T
E
aO
o
sa
a
o
ao
o
a
a
T (K}
Fig. 3. Temperature
dependence
ofthe total areaunderthe
3oo
soo
57Fespectraof syntheticforsterite(samplel; O) and natural olTtKi
(sample 2;). 0 : 374 + 5 K for forsterite
ivine(Feo,Mg.r)rSiOn,
Fig. 5. Temperaturedependenceof the QS of 57Feat Ml (solid
"
anddD: 375+5 K for naturalolivine.
points) and M2 (open points) in natural olivine (Feo,Mgor)rSiOo
(sample 2).
Sincethe two quadrupole-splitFe2+doublets at the Ml
and M2 positions of olivine strongly overlap, the fitting
procedureis generallydifrcult. In our case,however, becauseofhigh crystalperfectionand absenceofany textural
effectsphysically reasonableconstraints can be assumed
for the fit. Consequently,the spectrawere fitted in three
diferent ways with the constraints
(a)
wl: wfr,wi: wa,Ii_:I[, r?:rh;
W|: Wfr: Wi: W?.,Ii.:Il',17:1tr' &)
( c)
wi.: wfr : wi: wa,Ii: Ifr : I7:Ih.
Here W and I are the line widths and intensities, the
superscriptsI and 2 refer to the M I and M2 sites,and L
and H are the low and high energylines, respectively,of
the doublets.The final values for the quadrupole splitting
QS, isomer shift IS and area A are the averagedresults
obtained from these fits. The errors given include the
differencesbetween the different schemesof fitting. The
data on the temperature dependenciesofthe total areas
E
F
L
I
o
?
E
t
ul
o
@
E
0.7
o
o
tO00 T t Kl
T (K}
Fig. 4. Temperaturedependenceof the 57Fethermal shifts in
Fig. 6. Temperaturedependenceofthe QS of 57Feat M I (solid
synthetic forsterite (sample 1). The solid lines represent least points) and at M2 (open points) in synthetic forsterite (sample
squaresfits basedon equation (2), yielding force constantsKl :
l). The solid lines are the least squaresfits basedon equation (3)
4.7 eV/4, (Ml, solid points), K2: 4.2 eV/4, (M2, open points).
and equation (7) yielding 6 : I 120+ 50 cm-' for both positions.
The solid and open squaresshow the temperature dependence The dashedline is the calculatedtemperaturedependenceofQS
of the thermal shifts for (Feo,Mgor)rSiOo(sarnple2) (they were for d : 1860 cm-' reported by Burns, 1970. The QS values at
not included in the fit).
4.2 K and at 78 K were not included into the fit.
STANEKET AL.: LOCAL STATESOF FE* AND Mg,, IN OLIVINES
130
where .ERis the recoil energyof the nucleus(1.95 x l0-3
eV for 57Fe),{ is the recoil free fraction ofthe absorber,
andCisaconstant.
Thp leastsquaresfit ofequation (l) to our data is shown
in Figure 3. The fit yielded 0D:374+5 K for synthetic
forsterite (sample l) as well as for natural olivine (sample
2). In our case,the ratio of A at Ml and M2 turned out
to be independentof f within a fitting error of 20loso that
0o may be assumedto be the same for iron at both sites.
This assumptionis in agreementwith earlier results(Bush
et al., 1970)obtained for fayalite, an iron-rich olivine, and
a magnesium-rich olivine. In that work it was also concluded that the recoil free fraction ofiron at the Ml and
M2 positions was the same within 2ol0.
The high temperatureMdssbauerspectraalso supplied
values for the force constantsof the Fe2* ions at the Ml
and M2 positions. In the higher temperature limit the
thermal shift, i.e., the temperaturedependenceof the shift
of the Mdssbauerspectrummay be approximated (Gupta
and Lal, 1972)by
t
z
o
F
L
E
I
d)
F
z
z
a
U
dIS
3h2 ,,dl.JJ-f,
i:_ffi*,"#
-4
(2)
-2
t'
u.roa9,r, ,..rr1
Fig. 7. Mdssbauer spectra of forsterite at I bar (A) and 30
kbar (B) at 568 K. The spectrawere not correctedfor the background count rate produced by the iron impurities in the BoC
anvils.
under the spectraare shown in Figure 3, the thermal shifts
are presented in Figure 4, and the temperature dependencies of the quadrupole splittings QS are plotted in Figures
5 and 6.
The spectraof synthetic forsterite (sample l) taken at
two different pressuresat 568 K are shown in Figure 7.
An increaseof l0o/oof the total area of absorption lines
was observed,but the spectradid not show any measurable changein QS.
While the overlap of the Ml and M2 paramagnetic
doubletsin olivines is nearly completebetween4 and295
K, a distinct separationof the doublets occursat temperatureshigher than 500 K. QS plots from a larger number
of spectraat temperaturesbetween 295 and 623 K (Fig.
5) revealthat the temperaturedependenciesof the QS are
almost linear over that range. There is no discontinuity
at any temperature. First, the areas of the doublets will
be analyzed in more detail. In the higher temperature
limit, i.e., for T > 0.50owhere do is the Debye temperature, the decreaseofthe total areaA under the absorption
spectrum of a thin absorber depending on temperature
can be expressedas
A:ct:c'*n(-*ff)
Here, E" is the energyof the gamma transition (14.4 keV),
M is the mass of 5?Fe,M : 9.465 x l0-" kg, and K is
the force constant.Substituting f obtained from the temperature dependenceofthe resonant area and fitting the
experimentalIS for eachdoublet, K(Ml) : 4.7+0.1 eY/
;i 11.45x loa dyn/cm'z)and K(M2):4.2+0.1 eY/42
(6.66 x lOadyn/cm'z)are obtained. The fits togetherwith
the experimental IS values are shown in Figure 4.
Measurements of forsterite in high,
external magnetic ftelds
The main pulpose of measuringMdssbauer spectrain
high, external magneticfields H was the determination of
the signof the principal componentV'' of the EFG tensor3
at the Ml and M2 positions. Such spectraalso allow us
to estimatethe asymmetryparameter4; ? : (Vxx - Y"")/
Vo, where V**, Vr" andYrtare the values of the second
derivative of the electrostaticpotential V at the crystallographic positions of 5?Fe,and X,Y ,Z refer to the diagonalized system.
The signofV,and value ofrl werefoundby comparison
of the experimental spectrawith those computed by means
of the "Gabriel-Ruby" program for calculatingcombined
quadrupole and magnetic hyperfine interactions in polycrystalline samples (Gabriel, 1965; Collins and Travis,
1967). The magnitudes of the quadrupole splittings observed in zero-field spectra and experimental line widths
of 0.28 mm/s were introduced as fixed parameters.Since
the spectrum consists of two overlapping doublets due to
(1) Fcf.
Dir"*rioo.
STANEK ET AL.: LOCAL STATES OF FdT AND ME, IN OLIVINES
l3l
r00
8
z.
(L
:<
z
Xon
a
(D
c
d}
z
z
z.
z
o
a
U
e.
YO
@
U
E
-6
6
mm/s)
Y E L O C I T(Y
Fig. 9. 57Fespectrumin polycrystalline forsterite at 4.2 K in
an external magnetic field of 7.15 T parallel to the transmitted
gamma rays.
magnetic fields developed by Varret (1976) may be applied. It is based on the assumption that H"o acting at the
Fe2+ nucleus can be described as
H"r: (l + E)H
Fig. 8. Computed(solid line) and experimental(dots)5?Fe
spectrain polycrystallineforsteritein externalmagneticfieldsof
4.0 T (A), and 6.0 T (B) at 295 K. The field wasparallelto the
gammarays.For the computedspectra,n:0.2 anda positive
signof Vo wereassumed.
(3)
where E is the "magnetization hyperfine tensor." Such
magnetization effectsbecome significant at low temperature and at the high field limit, when saturation of the
magnetization in the easy direction appears. This can
drastically change the line shape of the M6ssbauer absorption. Suchan approachhas been successfullyusedfor
Fe'?+at the M I and M2 sitesvarious simulations of spectra the description of 57Fespectraof Fe andZn fluorosilicates
had to be computed using positive and negative signs of
studied in external fields (Varret,1976).
V' as well as diferent 4 valuesfor both sitesand different
For a verification of the data obtained, an additional
external magnetic fields. a was varied between0 and I in
experimentat H : 7.l5 T and4.2 K wasmade.The specstepsof 0.05. The simulations showed that the spectrum trum obtained, shown in Figure 9, consistsof two broad
depends on 4 and the sign of V,' most critically at fields lines and can not be reproduced by the simple method
between4 and 7 T. The best agreementbetween experi- used in this paper due to enhancedmagnetic anisotropy
mental and computed spectrawas obtained for a positive ofFe2+ at lower temperaturesas discussedabove. In consign of Yu at the Ml as well as the M2 sites, and an sequence,this result suppliedno independentestimatefor
average4 : 0.20+0.05. Two experimentaland computed the 4 value (the sign is obvious from room temperature
spectrafor fields H : 4.0 T and 6.0 T are shown in Figspectra).
ure 8.
It is to be noted that the sign of the V,, component of
The application of the Gabriel-Collins procedure used the EFG tensor as well as the asymmetry parameter for
for the evaluation of Mdssbauer spectra needs further Fe2+in forsterite are the same at both sitesas in fayalite,
comment. It is only correct for diamagnetic ions, or for FerSiOo.The componentsof EFG tensorin fayalite N u >
paramagneticions which have isotropic properties as, for 0 and a :0.2 at Ml and M2 sites)were estimatedby
example Fe3+.Fe2+in forsterite is, however, anisotropic, Kiindig et al. (1967) on the basisof the Mdssbauerspectra
i.e., the effectivemagneticfield at 57Fe,H"n,is not parallel of the magnetically ordered state at 4.2 K.
to the external field H. Its magnitude depends on the
A drastic differenceis observed,however, betweenthe
orientation of the crystal with respectto the externalfield. EFG measuredat Fe2+and at Mg2+ions in forsterite. The
In this casea phenomenologicalmodel which describes components of EFG tensors at Mg2+ in forsterite have
the Mdssbauerspectrumof paramagneticpowdersin high been precisely determined by Derighetti et al. (1978) by
132
STANEK ET AL.: LOCAL STATES OF Fd* AND ME* IN OLIVINES
means of magnetic resonanceon dynamically polarized
25Mgnuclei in a single crystal. The given values of the
asymmetry parametersare larger: 0.4 atM2 and 0.96 at
Ml. The signs of the main EFG components were not
determined experimentally but a calculation basedon the
point charge model including ionic, dipole and quadrupole contributions as well as overlap effectslead to positive signs (Ragerand Schmidt, l98l). These results, togetherwith our data are the basis ofthe discussionofthe
relationship between lattice and valence EFG, presented
in the next section.
Discussion
Correlation betweenlattice qnd valencefteld gradient
A prirnary interestofthis study wasthe relation between
the EFG tensorsof sTFeand 25Mg(Derighetti et al., 1978)
at the two nonequivalent Ml and M2 sites.The 57Fetensors are described in their principal axes system X,y,Z
and consist of two contributions: (l) the dominating valence contribution V; with the principal axes system
X*,Y*,2* and(2) the lattice contribution Vl, with the principal axessystemx,y,z. According to the model of Ingalls
(1964) it is usually assumedthat the systemsX,Y,Z,
X*,Y*,Z* and x,y,z have identical orientation. For the
2sMgtensor,of course,Y; is assumedto be zero, i.e., V,, :
Vl,. A discussionof the sigrrsof the various tensors and
the ditrerent orientations of their principal axes appears
worthwhile.
For comparing the lattice tensors acting on 57Feand
'?sMgwith the total tensors,the data should be corrected
for the different Fe2+and Mg'z+Sternheimerantishielding
factors 7-. Thus at 57Fethe lattice tensor is
s00
1000
1s00
6 (cm-1
)
parameter
of a positivevalenceEFG
Fig. 10. Theasymmetry
for 295K in the functionofthe axialfield splitting6.
calculated
The ditrerentlinesreferto different6'ld ratios,as marked.The
points(i) and (ii) resultfrom two possiblerelative
experimental
ofthe valenceandlatticeEFG tensors.
orientations
is still open for discussion.The two gradients may differ
becauseof the different overlap contribution, which at
least in the Mg2+ caseis meaningful (Ragerand Schmidt,
l 9 8l ) .
For obtaining the valence EFG, V;, the lattice EFG
-3.5
:
:
expressedin the x,y,z frame must be subtracted
tensor
(Schmidt
where'y-(Mg'z+;
et al.,1979),?-(Fe'z+;
-10.972 (Sternheimer,1972),and i: x,y,z. Assuminga from the total EFG tensor.From a comparison of the data
positive sign of V-(Mg2+) (Ragerand Schmidt, l98l) and of Kiindig et al. (1967) and Derighetti et al. (1978),it is
found that at the M2 position V,' is parallel to V! (the
substituting the experimental data for Vu(Mg'?*)(Derighetti et al., 1978), yields the values for the 57Felattice Z axis coincides with the y axis). For further discussion
tensor components at both positions4 expressedin the it is reasonableto assumethat not only is Z parallel to y
but also (l) zllY and xllX, or, alternatively,(2) zllX, xllY.
principal axes system,x,y,z.
Using
the proper transformation matrix, describing the
The estimation of the errors in Vl(Fe'*) is difficult. The
rotation
by 90'around the x axis for case(l) and rotation
experimentalerrors of Vl,(Mg2+)are about l0re V/m2. The
errorsof calculated7-(Fe2+)and "y-(Mg'?*)arenot known; by 90" around x and y axesfor case(2) the Vl, tensor can
they can even reach 100/0,
but this causesonly systematic be transformed to the X,Y,Z frame, now being identical
:
shifts ofV|(Fe2+).In particular the value of the asymmetry to the X*,Y*,Z* axes system. By this procedure, Vii
Vo - Vl (for i + j, V,,,Vl,,Vj : 0).
parameter 4 is not affected.
The first transformation leadsto a highly asymmetrical
However, the question of how much the lattice EFG
measuredon Mg2+ ions can be identified with the lattice valenceEFG tensor for Fe2+with a":0.33 and should
EFG acting on Fe2+at the samecrystallographicposition be excludedfrom further discussion,accordingto the following considerations.
The asymmetry parameter of,the valencetensor, 4", of
a An energyshift of I mm,/s for the 14.4 keV transition in the
the Fe2+ion in a distorted octahedrally coordinated site
57FeMdssbauerspectrumis equal to 11.625MHz, or to 4.808 x
is causedby the unequal population of rhe 3d*,,3d-and
l0-e eV. An axial tensor of Vo: 10" V/m'z producesa quad3d,, levels. If the ground state of Fe2+is 3d*, the Yo is
rupole splitting of 57Feof 0.208 mm/s (assumingQ : 0.20 x
l0-20cm2for the quadrupole moment of 14.4 keV state of sTFe). positive. The a is determined by the temperature,by the
vl,(Fe,*):
#rffi
x v'(Ms,*) (4)
STANEKET AL.: LOCAL STATESOF FE* AND ME* IN OLIVINES
Table l. The components of the lattice (l), total and valence
(v) EFG tensorsin Ml and M2 sites,expressedin the total EFG
tensor principal axis system X,Y,Z in the units of 1020V/m,
1
qo(
--1
u$a
+2O
-6
_luzz
-23
ttl
t42
Vlo<
Vy"
Yzz
vV
')o(
vv
'w
,rV
'zz
-57
-59
-85
-88
+142
+147
-81
-79
44
-82
+165
+161
axial field splitting 6, and by the rhombic field splitting
6, : l2D, where D is rhombic field parameter according
to equation (5) (Ingalls, 1964)
J
?":;
z
P l x z )- P l y z )
t -Lrp6zl- Plyz))
-;')l14-.-{-('
.i',)/14
, *'[-('
r33
where QS is the experimental quadrupole splitting, and
n:0.2 is the experimentalvalue of the asymmetryparameter of the total tensor. Finally, VI : Vo - Vl,.
Considering the data collected in Table l, it can be
concluded that in spite ofthe fact that the lattice tensor
is highly asymmetric (especiallyat Ml) the valance contribution to the total tensoris, at room temperature,fairly
axial (a":0.018, as estimatedfrom Table l) i.e., it is
indicative ofa big axial field splitting.
The experimentalresultson forsterite appearto weaken
the prediction of Ingalls (1964) concerning the relation
betweenthe lattice and valencecontributions to the total
tensor (they should be of opposite signs and the x,y,z
system should be identical with the X,Y,Z system).
Temperature dependenceof the quadrupole splitting
(QS) and the axial fwld spliuing 6
The temperature dependenceof the valence tensor of
Fe2+ was described by Ingalls (1964). The ligand field
parameters(cf. also Gibb, 1968) can be estimated from
the decreaseof the QS with the increasingtemperatureif
the weakly temperaturedependentlattice contribution is
(5) subtractedfrom the total tensor. In our presentcase,the
lattice tensorsin forsterite are, ofcourse, known precisely
whereP I yx), P Ixz), P I xy) are the populations ofthe 3d"", at4.2Kfrom the 2sMgdataof Derighettiet al. (1978).In
3dn and 3d-, orbitals.
olivines, two opposing contributions to the temperature
?" was calculatedas a function of Dfor T : 294 K and dependenceofthe lattice tensormay be expected:(l) therfor different D,/Dratios. The result is shown in Figure 10. mal expansionof the lattice may reduce the tensor with
Assuming a" : 0.33 (case(l)) leadsto a 6 of lessthan 300 increasingtemperature;(2) the increasingmean static discm-'. Such small axial field splitting would lead to a very tortion of the oxygenoctahedraaround Ml and M2 with
fast decreaseof the quadrupole splitting with increasing increasingtemperature(Smyth and Hazen, 1973; Smyth,
temperature. This is inconsistent with our data (seethe
1975)may produce an increasingcontribution to the tenfollowing section).In summary, we believe that case(2), sor. This contribution may partly cancelor even outweigh
i.e.,xllY, yllZ, zllX, leadingtoanearlyaxialvalencetensor, ( l ) .
must be chosen.
For further discussion the high temperature (568 K)
The discussionofthe tensor at the Ml site is lessstraight- and high pressure (30 kbar) M0ssbauer measurements
forward. First,4' :0.964, i.e., Vl, = -Vl-, and the as- should be included. It is known that the ratio of the coefsignment of axes, as well as the discussion of the sign ficient of linear thermal expansiona, and the coefficient
becomeirrelevant. Second,becauseof the crystallographic of linear compressionB, are constant for a wide variety
point symmetry I at Ml, the systemsX,y,Z, and x,y,z of minerals (Hazen, 1976, 1977).Thus the processof the
do not coincide with any crystallographicaxis. Moreover, thermal volume decreaseis structurally similar to the dethe orientation of the total tensor obtained from Mdss- creaseof volume during compression. For forsterite, a
bauer measurementsis subject to considerableerror.
pressurediference of 30 kbar correspondsto a decrease
At any rate, accordingto Kiindig et al. (1967) and Deof the averageM-O bond of about 0.018 A. The same
righetti et al. (1978), the anglebetweenZ and,z or, alter- decreaseis achievedby a decreasein temperatureofabout
natively, Z and y, is about 15", i.e., the Z and z axes are 700 K (Hazen 1976).No pressuredependenceof the
QS
nearly parallel. Ifthe secondorientation is arbitrarily cho- was observedat 30 kbar (cf. Fig. 7). lt can, therefore, be
sen,i.e., Z parallel to y, Vlj at the Ml site may be treated concludedthat structural changesexpectedin our experas in the caseof M2.
imental temperature range (300-1220 K) have little inIn Table I the components of the lattice (Vl), valence fluenceon the lattice tensor, which can be assumedto be
(V;) and total (V,,) tensorsexpressedintheX,Y,Z system independentof temperature.
are presented.The Vl, componentsare calculatedfrom the
In the high temperature region, where the influence of
data of Derighetti et al. (1978) using equation (4) and spin orbital interaction on the tensor is negligible, the
transformed to the X,Y,Z system. The V' values were temperaturedependenceof an axially symmetric valence
obtained using the equation
tensor V2, at an octahedrally coordinated site of Fe2+
(Ingalls,1964)is
-i{.4.;,)I14}
F;,)I14...{-(,
"
os:f"o
n2
T;
J
(6)
Y2: -2Y:,": -2Vk: C x ,l ,--eipl;4u.4,?(7)
l+2exp(-6/kt1
134
STANEKET AL.: LOCAL STATESOF FE* AND ME, IN OLIVINES
responsible for the preference of Fe2+ for the M2 position
(Burns, 1970). The apparent lack of cation ordering in
olivines appears to be related to the equal 6 splittings of
Fe2+ at both M positions as concluded from present data.
(8)
V'(Z): VI(l") +'Vl,
Therefore, precise determination of Fe2+ ordering over
To obtain the explicit form ofthe temperaturedependence Ml and M2 in the olivine solid solution by Mdssbauer
of QS the V,,(7) componentsmust be inserted into equa- spectroscopy will require careful experimental study of
tion (6). The experimental values of QS are presentedin the relative Ml and M2 resonant absorption areas over
Figure 6. The least squaresfit ofthe function ofequation a large region of temperature.
(6) to the points of Figure 6 with the conditions described
The weak preferential site occupancy in olivines has
by equation (7) (solid lines in Fig. 6) leadsto d : I I 20 + 50 also been explained by a dynamical Jahn-Teller effect
(Welsch et al, 1974). However, in that work an incorrect
cm-'. This result is inconsistentwith d : 1860 cm-'
(dashedline in Fig. 6) ofBurns (1970).It shouldbe noted, order of /r, level splitting was assumed, i.e., from the
however, that the value of 1860 cm-' results, at least for distortion of the M2 octahedron it was concluded that the
the Ml site, from a numerical error in subtracting the ground state is a doubly degenerated (3d-.,3d-) level. The
energyof 8060 cm-' and,7200cm-' of the two absorption positive signs of V2 show that the ground states must be
bands in the polarized absorption spectraofolivine (Burns, 3d-, singlets for both positions. Thus, the values of sta1970). Our result can be related rather well to the ab- bilization energy of Welsch et al. (197 4) require reconsisorption minimum of ll24 cm-' in the infrared spectra deration.
Here d: 3D, is lhe Tr" orbital splitting, where D" is the
axial field parameter.The values of the total components
V' can be calculatedfor any temperature as
of forsterite (Runciman et al., 1973).
Preferentialsite occupancyof bivalent
iron in olivines
In view of the different point symmetriesof the Ml and
M2 positions and the somewhatdifferent geometricaldistortions of the Ml and M2 coordination octahedraa preferenceofFe2* is expectedfor one ofthe two positions, at
least in general.The EFG tensorsare distinct for the two
positions, particularly at temperatureshigher than 250C.
Moreover, the averageM-O distanceis somewhatshorter
for Ml (d : 2.095 A; ttran for M2 (d : 2.131A) (Went
and Raymond, 1973), yielding a slightly smaller volume
for the Ml octahedron.
The relative volumes of Ml and M2 octahedraare consistent with the result that the force constant K(Ml) is
greaterthan K(M2). This fact indicatesthat the Fe2* ions
at Ml are somewhat more tightly bonded to the oxygen
ions than alM2. This result doesnot support the conclusion of Hazen (1976) that the compressibility of M I octahedra is larger than that of M2. From our data for the
force constantswe find
Acknowledgments
We thank T. Malysheva, Vernadsky Institute of Chemistry,
Academy of SciencesUSSR, Moscow, for a natural sample of
olivine. One of us (J. Stanek) thanks the A. V. Humboldt Foundation for a fellowship. This work was supportedby a Grant of
German ResearchFoundation (SFB-I 27).
References
Amthauer, Georg, Fenner, J., Hafner, S. S., Holzapfel, W. B.,
and Keller, R. (1979)Effectofpressureon resistivity and Mdssbauer spectraof mixed valence compound in SnrSr.Journal
of Chemical Physics,7O, 4837-4842.
Bundy, F. P. and Strong, H. M. (1962) Behavior of metals at
high temperaturesand presswes.Solid State Physics (Advances
in Researchand Application), 13, 8l-146.
Burns, R. G. (1970) Mineralogical Application of Crystal Field
Theory. Cambridge at the University Press,79-84.
Bush, W. R., Hafner, S. S., and Virgo, David (1970) Some ordering ofiron and magnesiumat the octahedrallycoordinated
sites in a magnesiumrich olivine. Nature, 227, 1339-1341.
Collins, R. L. and Travis, J. C. (1967\ The electric fietd gradient
tensor. In I. J. Tensor, Ed., MdssbauerEffect Methodology, 3,
p. 123-161. Plenum, New York.
Derighetti, Bruno, Hafner, S. S., Marxer, H., and Rager,Helmut
(1978) NMR of '?eSiand 2'Mg in MgrSiOn with dynamical
polarisation technique. Physicsktters, 661', I5C-l52.
dv(M2) dv(Ml) /r(vrrlY
Drickamer, H. G. (1965) The etrectof high pressureon the elec0p
tronic structure of solids. Solid State Physics (Advances in
Researchand Application), 17, l-134.
In spite of the geometricaldifferencebetweenthe Ml and
M2 octahedra the electronic levels of Fe2+appear to be Eibschiitz, Marcu and Ganiel, U. (1967) M<issbauerstudies of
Fe2+in paramagneticfayalite. Solid StateCommunications, 5,
quite similar at both sites.This rather surprising result is
267-270.
confirmed by the spectraat high pressures.The hyperfine Gabriel, J. R. (1965) Computation of Mtissbauer spectra.In I.
parametersare not influenced significantly by pressures
J. Gruverman, Ed., MtissbauerEffect Methodology, l, p. l2l132.Plenum.New York.
up to about 30 kbar.
T. C. (1968) Estimation of ligand-field parametersfrom
Gibb,
The ordering of cations may be discussedin terms of
Miissbauer spectra.Journal of Chemical Society (A), 1439the crystal freld stabilization energy CSFE. For octahedral
1444.
coordination,
Gupta, G. P. and Lal, K. C. (1972) Temperatureshift, recoil-free
fraction, and force constant in Miissbauer studies. Physica Sta(9)
CSFE: ja. + jo
tus Solidi, 51, 233-239.
Hazen, R. M. (1976) Efect of temperature and pressureon the
where Aois the crystal field splitting and 6 is the axial field
crystal structure of forsterite. American Mineralogist, 60, 1280splitting (Burns, 1970). In pyroxenes, it was concluded
1293.
that the diference in D at the Ml and M2 positions is Hazen, R. M. (1977) Effectsof temperatureand pressureon the
' ,o :\ffi7 ='o
STANEK ET AL.: LOCAL STATES OF FdT AND Mgh IN OLIVINES
crystal structure of ferromagnesianolivine. American Minerafogist,62,286J95.
Ingalls, Robert (1964) Electric-field gradient tensor in ferrous
compounds.Physical Review (A), 133, 787-795.
Kiindig, Walter, Cape,J. A., Lindquist, R. H., and Contrabaris,
G. (1967) Some magnetic properties of FerSiOofrom 4 K to
300 K. Journal ofApplied Physics,38,947-948.
Ming, Li-chung and Bassett,W. A. (1974) Laser heating in the
diamond anvil pressup to 2000qCsustainedand 3000"Cpulsed
at pressureup to 260 kilobars. Review of Scientific Instrum e n t s , 4 5l,1 l 5 - 1 1 1 8 .
Rager,Helmut and Schmidt, P. C. (1981) Electric field gradient
calculation in forsterite, MgrSiOo. Physics and Chemistry of
Minerals, 7, 169-176.
Runciman, W. A., Sengupta,Dipankav, andGourley, J. T. (1973)
The polarized spectraof iron in silicates.II Olivine. American
Mineralogist,58, 45 1-456.
Schmidt, P. C., Weiss, Alarich, and Das, T. P. (1979) Effect of
crystal field and self-consistencyon dipole and quadrupole
polarizabilities of closed-shellions. Physical Review (B), 19,
552s-5534.
135
Smyth, J. R. and Hazen, R. H. (1973) The crystal structuresof
forsterite and hornolite at several temperaturesup to 900'C.
American Mineralogist,58, 588-593.
Smyth, J. R. (1975) High temperaturecrystal chemistry of fayalite. American Mineralogist, 60, 1092-1097.
Sternheimer,R. M. (1972) Quadrupole shieldingand antishielding factors for severalatomic ground states.Physical Review
(A),6, 1702-1707.
Varret, F. (1976) Miissbauer spectra of paramagneticpowders
under applied field: Fe2* in fluorosilicates.Journal of Physics
and Chemistry of Solids, 37, 265-27 l.
Welsch, D., Donnay, Gabrielle, and Donnay, J. D. H' (1974)
Jahn-Teller effectsin ferro magnesianminerals: pyroxeneand
olivines. Bulletin de la Soci6t6Francaisede Min6ralogie et de
Cristallographie,97, I 7f l 83.
Wenk, H. R. and Raymond, K. N. (1973) Four new structure
refinements of olivine. Zeitschrift fiir Kristallographie, 137,
86-l 05.
Manuscipt received,December3, 1984;
acceptedforpublication, September4, 1985.