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Amertcan Mineralogist, Volume 59, pages 319-334, 1974
The ElectronicStructureof Rutile,Wustite,and
Hematitefrom MolecularOrbitalGalculations
J. A. Tossrr-r,,r D. J. Vlucslrq,2
Departmznt of Earth and Planetary Sciences,MassrchusettsInstitute ol Technology
K. H. JosNsoN
Department ol Metallurgy and Materials Science,
M assachus et ts I nstitut e ol T echnology
Abstract
Molecular orbital (MO) calculations are presented for metal-oxygen polyhedral clusters
containing Ti'*, Fez*, and Fes in octahedral coordination with oxygen. These polyhedra are
used as models for the minerals rutile, wustite, and hematite. The calculations are used to
elucidate the nature of the electronic structure of these minerals and to assign and interpret
their X-ray and UV photoelectron, X-ray emission and absorption, and optical absorption and
reflectance spectra. In all cases agreement with experiment is good. Comparisons are made
between the Fez* and Fe8' octahedral clusters using the calculations and X-ray emission and
optical spectral data. Variations in the energies and intensities of peaks in the FeKB, FeZ
and OKa X-ray emission spectra are adequately explained by the calculations. Spectral methods for determining the energies of the different MO's are suggested,and necessaryconditions
for the spectral assessmentof mineral stability are discussed.
Introduction: Chemical Bonding Models for
Transition Mefals in Oxides and Silicates
The nature of chemicalbonds involving transition
metals in oxide and silicate minerals is of great
importance to mineralogists because of its effect
upon the chemical and physical properties of minerals. These in turn influence the nature of the
physicalprocesses
studiedby geophysicists.
Although
such concepts as ionic radius are very useful in
explaining the coordination symmetriesof transition
metal ions in oxide and silicateminerals (pauling,
1929, 1960), the systematicsof elementfractionation and site enrichment and the optical absorption
spectra of transition metal bearing minerals can
be explained only through the use of quantum
mechanics(Burns, 1970; Burns and Fyfe, 1967).
The quantum mechanicalmethodsusually employed
are thoseof atomic quantummechanics,commonly
in the form of crystal field theory (Bethe, 1929;
Orgel, 1952). Crystal field theory has very sucr Present address: Division
of Geochemistry, Department
of Chemistry, University of Maryland, College park, Maryland 20742.
zPresent address: Department
of Geological Sciences,
University of Aston, Gosta Green, Birmingham B47ET,
England.
cessfully explained the optical absorption spectra
of minerals, and the concept of the crystal field
stabilization energy has been instrumental in explaining element partitionings and site enrichments.
It is well known, however,that crystal field theory
is not a completely adequatetheory for transition
metal compounds. It describes only the predominantly metal d or "crystal field" orbitals but ignores
the substantialcovalencypresentin thesecompounds
(Cotton and Wilkinson, 1972). The evidencefor
covalency ranges from the presenceof transferred
hyperfine splittings in the Esn spectra of transition
metal compoundsto the failure of the Born-Mayer
lattice-energyequationfor the accuratecalculation
of heats of formation of transition metal oxides
(Gaffney and Ahrens, 1970). Another important
evidenceof covalencyis the reduction of the Racah
B and C interelectronicrepulsion parametersin the
spectra of oxides and silicatescontaining transition
metals when compared to their free ion values
(Manning, l97O). This effect drisesfrom covalency
but may be accommodatedwithin the ligand field
theory, which is essentiallya parameterizedmodification of crystal field theory (Orgel, 1960).
Although molecular quantum mechanicsis therefote lormally necessaryfor the description of the
319
320
TOSSELL, VAUGHAN,
AND ]OHNSON
electronic structure of transition metal compounds, tion on the stabilities of the bonding orbitals as a
it has been little employed in mineralogy for two function of chemical and geometrical parameters.
reasons.First, the electrons most easily studied The successof these approximatecalculationsis in
experimentally have been the d electrons of the part a result of the relative simplicity of the systems
transition metal, and the optical absorption spectra studied.For transitionmetalsystems,however,more
generated by transitions between them could be sophisticatedmethods are required. In this work,
describedfairly well by crystal field or ligand field a new firsrprinciples molecular orbital approach,
theory. Second,crystal field theory provided a well- namelythe Scr X,a ScatteredWave ClusterMethod
defined quantitative method for obtaining informa- (Slater and Johnson, 1972; Johnson and Smith,
tion on energeticsfrom optical spectra at a time 1972; Johnson,1973), is used.This methodyields
when quantitative molecular quantum mechanics molecular orbitals for transition metal compounds
afforded little agreement either between difterent which are in better quantitative agreement with
molecular quantum mechanicalcalculationsor be- experimentthan thoseobtained from ab initio Lcto
tween calculationand experiment.It was possible calculations(Johnson,1973).
Molecular quantummechanicalcalculationsusing
to use qualitative molecular orbital theory but in
practice the qualitativetheory was ambiguousand the Scr Xc method on polyhedral clusters containing Tia*, Fe'., and Fe3*in octahedralcoordination
unconvincing.
Both reasonsfor not using molecular quantum with oxygen are reported in this paper. In the next
mechanicsin mineralogyhave now largely lost their section, the Scn Xa method will be describedand
validity. New types of spectroscopywhich yield then the variousspectralmethodsbriefly discussed.
information on electronsother than those of the The molecular orbital results and spectral interpremetal d shell have been developedand applied to tationsfor TiOz (rutile), FeO (wustite), and FezOg
minerals.Important examplesinclude X-ray emis- (hematite) will then be presented.In the final
sion studies(Urch, l97l), and the X-ray absorp- section, a general discussionwill be given of the
tion and photoelectron (Nordling, 1972) spectro- electronic structure of oxides of transition metals
scopies discussed below. Qualitative MO theory and of spectralmethodsfor studyingthe nature of
has been used to interpret X-ray emissionspectra the electronicstructure and for assessingmineral
for sometime (Dodd and Glenn, 1969; Smith and stability.
O'Nions, 1972a, 1972b), but such interpretations
CalculationalMethod
are necessarilyuncertain.Fortunately,at the same
The Scn Xa method is a computationally effitime as new spectralmethodswere being applied
in mineralogy,new quantum mechanicalmethods cient,first-principlesmolecularorbital methodbased
and computer programs were being developedto on the division of matter into componentpolyatomic
yield electronic wave-functionsin much closer clusters(Johnson,1973).In this respectit is simagreementwith experiment than formerly. Sub- ilar to the model of Pauling (1929). For example
stantialadvanceshave been made in the application the Scp Xa model for rutile (TiO2) is the TiOo8Self Con- cluster, a Tia. ion surroundedby six O'z- ions. This
of the traditionalHartree-Fock-Roothaan
sistentField Linear Combinationof Atomic Orbitals- model should also be appropriate for Tin* in any
MolecularOrbital (Hrn scr rceo-rvro)theory (Roo- octahedralsite, for example,those in ilmenite and
thaan, 1951) to transition metal complexes(Mos- titanaugite.
The sevenstepsin the method are:
kowitz et aI, 1970; Aack et a:1,1972). Approximate
( 1) The spacewithin and around the cluster is
serni-empiricalrclo-uo theory has been successgeometrically partitioned into three contiguous
fully applied to the study of the geometries and
regions,namely,(I) the atomicregions,spherical
energeticsof several classesof silicate minerals
regions centeredon each of the atomic nuclei
(Louisnathanand Gibbs, 1972). Similar calculaand touching along the metal-ligandaxis, (II)
tions have been used with reasonablesuccessto
the interatomic region, the region outside the
interpret the X-ray emissionspectraof oxide minatomic regions but within an "outer sphere" eneralscontainingMg, Al, and Si (Tossell, 1973a,b\
(Vaughan
closing
all the atomicspheres,and (III) the extraof
Be
and
Tossell,
and
and B oxyanions
molecular region, the region beyond the "outer
1973). The metal KB and OKc X-ray emission
potentialof the resphere."Also, the electrostatic
spectraof thesemineralscontain valuableinforma-
MO CALCULATIONS
FOR RUTILE, WUSTITE, AND HEMATITE
321
maining atoms in the crystallinelattice is approxi- miliar Hartree-Fock-RoothaanLceo-uo method in
mated by a sphericalshell of positive charge (the two very important ways. First, in the Scr. Xo
"Watson sphere"), that is equal in magnitudeto approach the Schriidinger equation is solved nuthe charge of the cluster and that passesthrough merically rather than by expansionin a finite anathe nuclei of the ligandsin the cluster.After the lytical atomic orbital basis set. Lc,lo methodsrecalculation is completed,a correction is made to quire the choice of a finite basis set of atomic
the absolutevaluesof the orbital energiesequal to orbitals and the size of the basis set seriously
the differencebetweenthe "Watson sphere',stabil- affectsthe accuracyof the results.Second,in Harization and the accurate Madelung potential tree-Focktheory, as a result of the HF treatment
(Vaughan,Tossell,andJohnson,I974).
of the exchangepotential, the empty orbitals are
(2) The potential energy at each point is then treated as "virtual" orbitals which encounter their
evaluated,using electrostaticsto calculate the own self-repulsionand are therefore somewhattoo
Coulomb part of the potential and the Xa sta- diffuse (Huzinaga and Arnau, l97l). In the Scr
tistical approximationof Slater (1,972) ro evalu- Xa method, the filled and empty orbitals are treated
ate the exchange-correlationcontribution. The equivalently by the Xa approximation so that the
Xa approximation employs a proportionality be- empty orbitals are good representations
of excited
tween the exchange-correlationpotential at a state orbitals.
point and the cube root of the density of like-spin
The method has previously been applied to
electronsat that point. The proportionalitycon- two important minerals; SiO2, o'-quartz(Tossell,
stant, c, in this approximation is determined Vaughan,and Johnson,1973a) and Fe2O3,'-hemafrom first principles for the component free tite (Tossell, et al, 1973b). A companion paper
atoms, these ,a values then being transferred to discussingthe electronicstructureof Fe2. in tetrathe correspondingatomic regionsof the cluster. hedral coordinationwith oxygen and sulfur is in
Appropriately weighted values of ,a ?re used in press (Vaughan,Tossell,and Johnson,1974). For
the interatomicand extramolecular
regions(John- the SiOaa-molecular cluster, the Scr Xa model
son,1973).
for c-quartz, good agreementwas found with the
(3) The potential is simplified to a muffin-tin experimental X-ray photoelectron, SiKB and OKo
form by spherical averaging in the atomic and X-ray emission and UV spectra of quartz. The
extramolecularregionsand volume averagingin valenceregion MO's of SiO*"- were found to be
the interatomic region.
divisible into three filled sets: (1) O 2s non(4) The one-electronSchriidinger equation is bonding orbitals (4ar and 3t); (2) Si 3s, 3p
solved numericallyin each region and the solu- and O 2p bondingorbitals (5ar and 4t2, separated
tions are expandedin a rapidly convergentcom- by 34 ev); and (3) O 2p nonbondingorbitals(1e,
posite partial-wave representation.
5t.2,7t1),closelyspacedin energy,and an empty set
(5) The wavefunctionsand their first derivatives (4) diffuseSi-O antibondingorbitals (6a1,612).No
are joined continuously throughout the various significantSi 3d participationwas found in either
regions of the cluster using multiple-scattered- the O 2p nonbondingorbital set or in the bonding
wave theory (Johnson, 1973).
orbital set. The small calculatedseparationof the
(6) The spatial distribution of the electron nonbondingorbitals was in good agreementwith
density is calculatedand is used to generatea the experimentalX-ray photoelectrondata (DiStenew potential for the next step in the iterative fano and Eastman,1971). Lceo calculations,which
process.The entire numerical procedure is re- found much greater Si 3d participation,obtained
peated in successiveiterationsuntil self-consist- erroneouslyhigh values for the energy separation
ency is attained.
of theseorbitals (Collins, Cruickshank,and Breeze,
(7) The final self-consistentsolution for the 1972). It appearsthat the large Si 3d participation
ground state of the cluster is expressedin terms found in this Lcno calculationis thereforean artiof one electron molecular orbitals. These are fact of the inadequacyof the basis set used.This
characterizedby their orbital energies(or eigen- is Supportedby the Scr Lceo results of Gilbert
values), by their occupation numbers, and by et aI (1973) who find a maximum of 5 percent
their electron density distributions.
Si 3d participation in the MO's of Si2O using a
The Scr X,a method differs from the more fa- larger basis set. Using the X-ray photoelectron,
TOSSELL, VAUGHAN,
X-ray emission, and UV spectra of SiOz together
with the Scr Xo calculation, it was possible to
determine the positions of all the orbitals in the
system, usually to within one electron volt. We
have recently learned that high resolution OKa
spectraof SiOz (Klein and Chun, 1972) show a
main peak (arising from the 1tr orbital) and three
features at lower energy which can be identified
with the le * Stz,4tz and5ar orbitals (the existence
and energy of the weak 541 peak confirming the
prediction of Urch, 1970). This interpretationis
consistent with the X-ray photoelectron data of
DiStefanoand Eastman (1971) and with the ScrXa calculation.
SpectroscopicStudy of Electronic Structure of
Transition Metal Oxides and Silicates
AND
JOHNSON
advanceshave recentlybeen made by Wetme et al,
1973) and in the need to superimpose several
different series of X-ray emission and absorption
spectra to determine the positions of all the MO's
of the material. This requiresthat a common energy
scale be constructed(Fischer, l97l).
In photoelectronspectroscopy,a "photoelectron"
is ejected by an incident photon. Its kinetic energy
is measuredaccurately,and the photon energy less
the photoelectron kinetic energy gives the binding
energy (- the negativeof the eigenvalue)of the
orbital from which the electron was ejected' X-ray
and UV photoelectronspectra show intensity from
all the orbitals in the valence region of a material.
However. on all but the newest machines, the
spectral resolution is often insufficient to show
much structure in the valenceregion (e.g', Prins
and Novakov, 1972) and complications can arise
from satellitepeaks (Hi.ifnerand Wertheim,1973).
X-ray photoelectronspectroscopycan also be
used to study the shifts of inner-shell orbital energies yielding information on molecular charge
distributions. However, as opposedto X-ray emission inner-orbital spectra, which show shifts only
as a function of oxidation state and nearest
neighbor coordination, the inner-shellphotoelectron
peaks are significantly influenced by charges on
distant atoms (Shirley, l97O). The influence of
distant charges and the problems associatedwith
sample charging and reference level effects make
the interpretation of inner-shell energy shifts for
mineralsvery difhcult (Adams, Thomas, and Bancroft, 1972).
The spectral techniques discussed above are
largely complementary,and an adequatewavefunction should be capable of explaining all the ob
servedspectra.The purposeof using ScF Xo wavefunctions to interpret the spectra of minerals is
twofold. First, an adequate explanation of the
spectra establishesthe validity of the calculation.
Second,the interpretationsof the spectra are clarified, making it possible to identify those spectral
features which yield the most direct information
about the nature of the bonding and other quantities of interest.
Optical absorption spectroscopy, and related
techniquessuch as diffuse reflectancespectroscopy,
give information on the relative energies of the
highestoccupiedand lowest empty orbitals in transition metal oxidesand silicates.Experimentalspectral
energies may be used to define parameters,such
as lO Dq, which can be used within the framework
of crystal field theory to assessthe stability of
metal-oxygenpolyhedra (Burns, l97O). The major
deficienciesof optical absorption spectroscopyare
the small range of energiesspannedby the technique
and the complexity of the spectra. The range of
energies studied can be expanded by the use of
UV reflectancespectroscopy.The UV reflectance
techniqueis of particular value for studyingligand +
metal charge-transferspectra.
In X-ray emission spectroscopy,an electron is
ejectedfrom a core orbital by an X-ray or an energetic electron. A higher energy outer electron then
drops into the core "hole" and a photon is generated
with energy approximately equal to the difference
in eigenvalue(energy) of the outer and core orbitals. X-ray emission spectroscopymay be used
to study both the inner shellsand the valenceregions
of transition-metaloxides. Systematicstudieshave
been made of transition-metal oxide KB (Kiister
and Mendel, l97O) and L (Fischer, 1971.,1972)
X-ray emissionspectra.X-ray emissionspectra are
often easier to interpret than optical spectra beThe Electronic Structure and Spectra
cause there are fewer spectral features spread over
of Rutile' TiOz
a wider energy range and becausesymmetry selecTitanium. the second most abundant transition
tion rules are more rigorously followed. The major
deficienciesin the X-ray emission technique are metal in the earth's crust, is commonly found as
in the poor energy resolution (although important the TiOz polymorph, rutile. Its oxidation state is
MO CALCULATIONS
FOR R(]TILE,
WUSTITE, AND HEMATITE
usually *4 and its coordinationis commonly six_
fold, although *3 oxidation and four-fold coordination do occur. Rutile is tetragonal,but the distortion
of the coordination polyhedra is fairly small (2
Ti-O distances
are 1.988A;4 are1.944A), (Grant,
1959) and should have little effectupon the spectra.
323
T i06-8
ri
h l r i - o t =t . e 6 5 i e
7ob
MO Diagram for TiousThe calculated MO diagram for the TiOu'molecular cluster is shown in Figure 1. Although
all electronsof the cluster (78 for TiO6'-) ur" i.rcluded in the Scr Xa calculation,only the O 2s type
orbitals and the valence orbitals are shown in the
MO diagram, since the orbitals of lower energy
are essentiallyatomic in nature. The orbital ener_
gies are given in eu and the energy levels of the
free atoms (from atomic Scn X,a calculations) are
included for comparison. The orbitals are labeled
according to the irreducible representationsof the
octahedral(O5) group under which they transform.
These O,, representationsare such that the cen_
tral atom s orbitals belong to the are representation, the p orbitals belong to t1u, and the d orbitals
belong to eo and t2o. Appropriate symmetry combinations of the ligand orbitals belong to all the
irreducible representations.
The Scr Xa program
calculates the electron density in each region of
the molecular cluster and such quantities as the
amount of "Ti 3d" characterin an eo MO can be
assessed
from the percent electron density inside
the Ti sphere.
The MO's in TiOz and other transition metal
oxides fall into five sets, distinguishableby their
energies and by the spatial distribution of their
electron density. The orbitals with eigenvalues
around -22 ev (5a10,4t1u, Ieo) are essentially
O 2s nonbondingorbitals with a slight metal_orbital
admixture.The main bonding orbitals of the sys_
tem-Stu, 6a10,lt2o, and,2eo-possessappreciable
metal and oxygen character.A strong indication of
the bonding nature of these orbitals is the large
amount of electrondensity in the interatomic region
(-30-40 percent). The lt2u, 6tru, and lllo orbitals
are all primarily O 2p nonbonding orbitals with
relatively little metal character and little density
in the interatomic region. The l/ro is the highest_
energy filled orbital. The two lowest-energyempty
orbitals are the 2tro and 3eo ,,crystal field', orbitals,
which have both Ti 3d and O 2p character.The
empty orbitals of the conduction band-7as and
7tr,,-are diffuse Ti-O antibonding orbitals. The
3es
ll,
-5
c
x
U
T i 4 s -Ti3d
2tzc
lttc
(,
E
lrl
z -lo
trl
J
F
d
E,
o
6lr,
Itzu
2"c
-
o?p
-
o2s
lf2s
6ot9
5ftu
-t5
-20
lec
4t tu
5 o tc
Frc. 1. TiOo& MO diagram (R(Ti - O) - 1.965 A);
the highest occupiedorbital is the lhs.
spatial distributions of the orbitals are listed in
Table 1. For no orbital is there as much as 1 percent densityin the extramolecularregion (III), so
this region has been omitted from the table.
The TiO68- MO diagram differs from traditional
textbook MO diagrams in the following respects.
The order of the t2s and eo orbitals is the same in
both the bonding and crystal field sets and the
a1oand /t, orbital energiesare quite similar in both
the bonding and conduction band sets. There is
also a well-definedset of O 2p nonbondingorbitals.
TOSSELL, VAUGHAN,
324
"sets" is the 2eo (Ti-O ".-tronding") which has an
energyand chargedistribution intermediatebetween
those characteristicof the bonding and O 2p'nonbonding sets.
TesI-E 1. Percentage Spacial Distribution of
Electron Density in TiOuF MO's
REGION II
REGION I
AND |OHNSON
(interatonic)
TiO
Rutile: X-Ray and UV Photoelectron Spectra
Table 2 summarizesthe observedX-ray (Hiifner
62
l
37
TaL
and Wertheim,1973)and UV (Derbenwick,1970,
59
39
t.rn
2
reproducedin Fischer, 1972) photoelectronspectra
orbitals
Ti3d "crystal field"
of rutile. The resolution in the X-ray spectrum is
69
31
0
3e
g
lower becauseof the greater intrinsic width of the
18
13
69
tt2n
exciting X-ray line, but the width of the valence
band is about 5 ev in both spectra.In the UV
02p nonbonding orbitals
photoelectron spectrum, the bonding and O 2p
It_
0
87
Lq
nonbondingorbital sets in the valenceband can
l6
I
83
6t.
tu
be resolved.
2L
It^
0
79
'Ihere are experimentaluncertaintiesin the abso'
zu
orbita ls
T i - o bondi
lute values of the photoelectron binding energies
2t
2I
58
2e^
due to charging and referencelevel effectsin TiOz.
l+
57
3I
L2
In addition, our approximate treatment of the
zg
Madelung correction to the TiOo'- orbital energies
55
3
6a. ^
precludes accurate calculation of absolute binding
2
6I
37
lu
energies.Therefore in Table 2 we have simply set
orbitals
0 2 s nonbondi
the energy of the 1/1norbital equ,alto that of the
I1
Ie
lowest-binding-energyphotoelectron peak and adg
justed the other orbital energiesaccordingly. The
14
2
84
4tIU
relative energiesof the valenceband orbitals appear
L7
2
8I
5a.
Lg
to be reproduced quite well. The separation between the O 2s orbitals and the middle of the
valence band we calculated to be about 14 ev,
In general the orbitals are very much "grouped"
which compares favorably with the experimental
rather than being continuously distributed as sugX-ray photoelectronvalue of -16 ev' Therefore
gestedby many qualitative MO diagrams.The only
the orbital energiesin the O 2s and valenceregions
orbital not easily assignableto one of the orbital
seemto be reproducedreasonablywell by the Scr
Xc calculation.
antibonding
Ti-o
orbitals
IJ
Tlnlp
2.
Experimental and Calculated UV
Photoelectron Spectra of Rutile
(energiesin eu)
Experimental
Experimental
n 6 :L
r o1: f i r r a
l r h6l
F*
calculate
relative
d
E
and X-ray
Rutile: OPtical SPectra
MO assigment
uV Photoelectron
o
0
-4.8
-4.6
tar,
6r. , It^
a2P
02s**
IUZDg
X-ray
o2P
o2s
Photoelectron
a5 ev wide
\-16
ev***
spectrm
ev wide
5.4
13.9 ev***
* Experimental
UV data from Derbenwick
X-ray data from Hiifner and wertheim
**
**t
As shown by Fischer
erroneous.
(1972),
, 2e
1t2n,6u1n,5tr,
this
Ig
Ie^,
(1970);
(19?3),
labeling
IU
4tr,,,5ar^
experimental
is
definitely
of o2p peak
E taken with respect
to center
Relative
(calculated)
(experimental)
region
or to center
of valence
'
Table 3 showsthe observedand calculatedoptical
absorptionand UV reflectivity spectraof rutile- Since
Tia- has no / electrons,the optical absorptionspectrum exhibitsonly an edge,at3.03 ev (Cronemeyer,
1952). An analogouspeak is observedin the photoconductivity spectrum at about the same energy
(Cronemeyer,1952). For sometime it has beenassumed that the absorptionedge in TiOz and related
compounds arose from a ligand -+ metal chargetransfertransition (Kahn and Leyendecker,1964).
This is verified by our calculationwhich assignsthe
absorptionedgeto the ltlo + 2tzstransition,i.e., A
2p nonbonding+ Ti 3d. In the Scn Xo method,
transition energiesare calculated not from ground
MO CALCULATIONS
FOR RUTILE, WUSTITE, AND HEMATITE
325
stateeigenvaluedifferencesbut by usingthe ..transi- Tlsrs 3. Experimental and Calculated Optical Spectra of
tion state" conceptof Slater (1972). In the ,.transiRutile
(energiesin eu)
tion state", half an electronis consideredto be excited from the initial into the final orbital and the '
AE
AE
calculationis then iterated to self-consistency
MO assigment
for
the "transition state" electronicconfiguration.The
Optical
Absorption
absorption
1'
3.03*
transition energy is expressedas the difference of
rg
zq
edge
(02p nb-Ti3d)
the "transition state" eigenvaluesof the initial and
final states.Although this procedureis formally re(02pnb+Ti3d)
quired for all types of spectraltransitions,it seems
18.8
8.4
5tr,,+2t)^
to have a large effecton the relativespectralenergies
(Ti-ob +Ti3d)
10.7
only for optical spectra.The calculated ,,transition
O2P+3s
r4.0
(6tlu, tt2u)+(?afq,
I3.3
7t1r)
state" energyfor the ltlo + 2t2oexcitationis 3.2 ev,
(02onb+Ti-O ab)
in excellentagreementwith experiment(the ground
(Ieg,4t]u,5atg)+2t29
18.5
( 0 2snb+ri 3d )
stateexcitationenergyis 2.6 ev).
rding' nonbonding' and antibonding
The UV reflectivity spectrum of TiOg is more
orbitafs
respectively.
* Cronemeyer (1952).
informative than the optical absorptionspectrumbut
** Cardona and Harbeke (1965).
somewhatmore difficult to interpret. There are in_
tensepeaksat -4.'7 ev (A) and 8.8 ev (C), weaker
sharp peaksat 14.0 ev (E) and 17.4 ev (F), a
shoulder (D) at IO.7 ev, and some weaker peaks may be associated
with transitionsto the 3eoorbital.
(B) noted by Cardonaand Harbeke (1965). The
Overall, the agreementof the calculatedspectrum
possibilitythat peaksA and C result from transi- with experiment quite good.
is
It is clear that, if
tions from the O 2p nonbondingorbitals to the 2t2o our interpretationis correct,
the reflectivity specand 3eo orbitals, respectively,is unlikely because trum givesdirect information on
the relative energies
their separationis 4.1 ev whereasthe ,,crvstalfield,, of all five orbital sets.
splitting of the 2t2o and 3eo orbitals strouta be 2.7Rutile: X-Ray Emissionand Absorption Spectra
2.9 ev for Tia*with a Ti-O distanceof 1.959A (the
crystal field splitting is equal to 2.5 ev for aqueous
In Table 4, the observed and calculated X-ray
Ti3*, with a slightly longer Ti-O distance (Figgis, emission and absorption spectra of rutile are pre1966, p. 2I8)). A secondpossibiliry is that the sented.Although the individualexperimental
spectra
2t2o orbital is the final state for both A and C and are the sameas thoseusedby Fischer (1972), there
that the initial states are in the nonbonding and are some doubts about his energy alignment of the
bondingorbital setsof the valenceband, respectively. various spectralseriesand thereforeeach spectrum
The calculatedseparationof the 6ttu (O 2p non_ will be discussed
individually.
bonding) and 5hu (bonding) orbitals, both of which
The TiKB emissionspectrumshowsa number of
can participate in symmetry-allowedtransitions to peaks,which arisefrom transitionsin which an electhe ztpsorbital, is 4.3 ev, in excellentagreemeniwith tron in a ts (Ti p fype) orbital drops into hole in
a
Ihe -4.1 ev separationbetweenpeaksA and C. It the Ti ls shell.The main peak, KB1,arisesfrom the
was demonstratedin the previoussectionthat our 3tru MO which is essentiallya Ti 3p orbital. The
calculated valence orbital energies were in good satellite peak KB' is assignedto a discrete energyagreementwith the UV photoelectronspectrum; loss processin which a KB1 photon excitesan electherefore the calculationsand photoelectronspectra tron from the lt2o orbital into the Ttru orbital, i.e.,
both support this assignmentof peaks A and C in an exciton process.This interpretation is very simithe reflectivityspectrum.peaks E and F can also lar to that suggested
by Kiister and Mendel (1970)
be adequatelyassignedto discrete transitionsbe- on qualitativeexperimentalgroundsand yieldsgood
tween MO's using the suggestedqualitativeassign- values for the relative KB' energiesin TiO2, FeO,
mentsof Cardonaand Harbeke (1965). The only and FezOs.In particular the Tttu conductionband
peaks not readily assignablefrom our calculation orbital is found to be at higher energy (KB' lower
are D (assignedby Cardona and Harbeke to Or- with respectto KuBl)in TiOg than in the iron oxides
2p --> 3s) and the weak B peaks,some of which and at higherenergyin FeeO3than in FeO. The KB"
Observed
Feature
Peak
A
Peak
C
Peak
D
Peak
F
*r*
.ir.rl.fad
by adalogy
Experimental
Calculated
I1 ,4
:e
with
d.^,..d
<rrrp
Itlg+2t2q
Frr^ciri^n
-
-.,-- ,---
..-
cv
TOSSELL, VAUGHAN,
326
AND
IOHNSON
The TiLo spectrum (nominally arising from Ti
3d, 4s -->Ti 2h,n transitions) showstwo broad intensepeakswith maximaseparatedby -4.2 ev. The
higher-energyLa emission peak (designatedF in
Calculated
Experinental
ExperimentaL
M
o
a
s
s
i
g
m
e
n
t
E
E
*
r
e
l
a
t
i
v
e
reiative
peak label
Fischer, 1972) is assignedby us to a ltto + 7i2p
transition. Fischer assignsthis peak to the tt2o otTiKB Emission
(
1
5
.
8
l
t
,
^
+
7
t
l
I
s
3
t
(
L
B
)
a-I6
1. . + T i
,i)
KB'
bital, discountingthe possibility of 1/1, participation
s
3
t
l
u
*
T
i
l
00
KB,
becauseneither the Ti 3d not 4s orbitals belong to
4tlu+TiIs
r
7
.
1
r s. 2
KB''
this representation.This approachemploys the nor5
tlu+Ti1s
30.4, 29.1, ,^^, 27.A
mal assumptionthat the selection rules governing
31-4
X-ray emissionare atomic in nature, i.,e., fot L
6 tIu+Tils
3 2 .I
spectrathe upper level must be an s or / state-HowTiL Enission
ever, we believe that the correct selectionrules are
ttrn*Ti'2V 3y2
o
0 (Pr)
actually molecular in nature, i.e., determinedby the
2e +'I i'2o' J- / z,^
g
01, point group. Sincethe Ti 2p level and the dipole
-3.8
-4,2
Lt2q+TiL2p
3/2
moment operator are both of fr, character, the al-4'6
6ar"*Ti2e3y2
G
lowed upper states are therefore a1o* €s * tzs *
-15.3
-r8.8
le_+Ti2p 1 /.
c
t1o.The use of molecular selectionrules admits the
-16.7
-2r.3
Sarn*'Ii2p37Z
D
possibilitythat the highestfilled orbital is in fact the
oKo
ltro and therefore removesthe necessityfor assign(rt19,6tlu.
o
0
maj.n peak
rt,.,,2e^)+0ls
ing the TiO2 absorptionedgeto a symmetry-forbid-3-4
(OS)
den lt2o --s 2tzatransition, as in Fischer (1972)' In
lrt2n, 6a1nt
Iow energy
{-2.6
shoulder
-2. ? (FI)
5ttu) +0Is
generalwe believe that in casesin which the upper
atomic levelsnominally involved in the X-ray transiOK absorption**
I'iK, TiL,
core hole+2t2g
2.6
3.1
b
tions are filled (e.g., the O 2p levels which generate
core hole+3en
6.2
intensity in the OKc emissionspectrum) the atomic
TtIu
core hole*7atd'
I2.5
11.5
d
selectionrules are adequate.However when the ap
propriate atomic levels are essentiallyempty (e.9.,
-G;-?;;^;-'r.
1962 (Bs);
and shuvaev,
Mendel, 19?o (Kt{); fron Blokhin
s
m
i
t
h
'
a
n
d
(
r
r
)
o
'
N
i
o
n
s
Ti 3d andTi 4s in TiOz), absolutespectralintensirgzi
' and from
i;;l li;;l..,
ties are reduced and transitions forbidden by the
energy
state
** E vaLues calcufated
to lt19(grountl
relati.ve
differences
) .
atomic selection rules-but weakly allowed by the
molecular selectionrules---cangenerateappreciable
peak clearly arisesfrom the 4tu orbital, which re- relatiae intensity and therefore yield spectral feasemblesO 2s. The Kdr peak is somewhatmore dif- tures.
The lower energyI'o peak is resolvedby Fischer
ficult to assigndefinitively. The two Kp5 peaks observed by Blokhin and Shuvaev (1.962) possibly into two components(A and G). Our calculations
correspondto the 5/r, and 611,orbitals. However, indicate that the Zen, lt2o, and 6a1oorbitals have the
the experimental splitting of the Kps doublet is proper energiesto contribute to this peak. The peak
much smaller (-1.7 ev) than the calculated6ttu- maximum probably occurs very near the energy of
5/1, separation(4.3 ev) or that inferred from the the lt2o orbital. Assigning the maxima of the two
reflectivitysp€ctrum(4.1 ev). It seemsmore prob- La peaks to the l4n and 1l2oorbitals, we obtain a
able that the 6ts 2p nonbondingorbital (with very calculatedseparationof 3.8 ev, in good agre€ment
little Ti 4p character) will generate only a weak with the experimentalvalue of 4.2 ev. The peaks C
feature,KB5,similar to the weak high energyshoulder and D at lower energycan be adequatelycorrelated
observedin the SiKB spectrum of SiOz (Klein and with the leo and 5a1oO 2s orbitals.
The OKa spectrum of TiOz shows a main peak
C:hun, 1972). The K,B spectrum of Blokhin and
Shuvaevdoes show a weak shoulder at about the which is accompaniedby a shoulderat about 2.6 ev
expectedenergy.The doubling of the KBi peak may lower energy (Fischer, 1972; Smith and O'Nions
arise from a splitting of the 5t1, orbital. This may I972a\. Since the seven highest filled orbitals all
result from interaction between the metal-oxygen possesssubstantialO 2p characterthey should all
contribute to the OKc spectrum.The position of the
polyhedra(Tossell,1973a).
Tesrn
4.
Experimental and Calculated X-ray Emission
and Absorption SPectraof Rutile
(energiesin eo)
lRM)
J \ED,
F
9
Jl
-
MO CALCALATIONS
FOR RUTILE,
WUSTITE,
AND HEMATITE
327
OKc intensity maximum should correspondto some ite L* spectrumwas very similar to Fischer's
rutile
weighted average of the "l,ts, 6t1u, lt2u, and 2eo spectrum.
orbital positions. Simply weighting the energiesof
thesefour orbitalsby their degeneracies,
we calculate
The Electronic Structure and Spcctra
the OK,amaximumto lie 1.1 ev lower in energythan
of \ilustite, FeO, and Hematite, Fe2O3
the higher energy TiLc peak. As shown in Fischer
MO Diagrams For FeOuro-and FeO6sThe O 2s and valenceMO structure of FeO61o-,
the Xq model for FeO, is shown in Figure 2a. T'lte
previouslypublished (Tossell et al, I973b) MO diasepar:ationof 3.4 ev between the peaks resulting gram for FeO6e-(the FezOamodel) is also shown
from the two orbital sets and approximate main (Fig. 2b) so as to permit comparisonsbetween
the
peak/shoulderintensity ratio of ll/7 is obtained. Fe2* and Fe3* species.Since the iron
oxides have
in fair agre€mentwith experiment. An analogou.s ground stateswith total spins,S 0, an
unrestricted
+
weightingof the experimentalenergiesfrom the UV Scr calculation,in which the spin-up and spin-down
plrotoelectronspectrumleadsto a 3.2 ev separation. electrons occupy different
orbitals, must be perA more detailed analysiswill require the calculation
of spectraltransitionintensities.
The TiK, TiL, and OK X-ray absorption spectra
r e o j l o R ( F e - o=) 2 . t 7 i
all show similar featuresfor TiOs. This suggeststhat
s p r r u ls P r N l
o
selectionrules are greatly relaxed for traniitions to
conduction-bandorbitals. The two low energypeaks
(b and c) were assignedby Fischer to the 2t2o and,
tlu
7t,,,
3eoorbitals.The experimentalseparationis 2.1 ev,
-o,s
zoi,i
somewhatsmallerthan the -2.g ev expected.How_
everFischer(1970) alsofindsa low value for 2t2n_
3eosplittingin Ti2O* (1.9 ev us 2.5 ev from optical
spectra) and so the assignmentseemssound. It is
tzg
not clear why the X-ray 2t2o - 3eo splittings are
F
e
4
s
systematicallysmaller than their optical values in
;-5
thesematerials.Our calculated2tzg- 3eoseparation
lt9
is somewhatlarger (-l.S ev). The peak d observed (9
I lu
Fe3d
eg
E
in the TiK absorptionspectrumof Albrecht (1966)
trJ
','u z.
ozo
is assigaedto the 7/1&conduction-bandorbital with UJ
'29
.-to
3' l ut s
€n
@
J
F
(n
o
Although our assignmentof the TiL emission
spectrumdiffers from that of Fischer,we agreethat
the 2t2sf orbital, one third filled in TiB. oxides, will
contributeintensityto the higher energyL emission
peak. Therefore an increasein the relative intensitv
of the higher energyL emissionpeak does indicate
an increasingamountof Tis-. Such an analysiswas
usedby Pavicevic,Ramdohr,and ElGoresy (1972)
to showthe presenceof TiB-in lunar ilmenites.They
used the TiOz and TL1OBLa spectra of Fischer
(1971) as referencespectra for Tia- and TiB* in
octahedralcoordination,notingthat their pure ilmen_
Frc. 2a. FeOe'* MO diagram ( R ( F e - O ) - 2 . 1 7 A )
The highest occupied orbital is the 2t,o[, containing one
electron.
TOSSELL, VAUGHAN,
328
reofe
R(Fe-o)=2.06i
t
x
(,
t
U
z
U
-3
Fe4s-
.3^a g -
lttg -,f
Fe5d 616 -il212^-r/-'
tri
/
-tzs
I
t_rlg
,-
ltu
12,
9s-
AND
IOHNSON
somewhatlaryer (2.9 us 2.7 ev for the 3eostate).
The conductionband levelsare lower than in TiO2,
and the FeO610-conduction band levels are about
1.8 ev lower than those in FeO6r. The difference
in the energiesof the crystalfield levelswith respect
to the O 2p nonbondingorbitalsis primarily a result
of the differencein Fe oxidation state. The differcnce in conduction band levels results mainly from
the oxidation state differencealthoughthe Fe-O distance (2.06 A in FeOoe-and 2.17 A in FeOe'o-)
alsohassomeeffect.
ValenceregionX-ray and UV photoelectronspectra arenot availablefor FeO becauseof its instability
with respectto FezOg.Therefore,the optical and
X-ray emission spectra of ferrous compounds will
be discussedfirst.
Optical Spectrafor OctahedralFe2*
. _to
2e^
In oxide and silicatemineralsin which ferrous iron
_o,1n
,-'/
t l 2-'--/
;/-| lu
F
is octahedrally coordinated, a crystal field 'Tro +
z(D
e r od
l- 5 t t/ u
5E, transition with an averageenergy (A) of (r
10,000 cm-l (Burns, 1970) is normally observed.
The "Ayy" value for R(Fe-O) = 2.17 A is 9300
cm-1 from the analysisof Faye (1972). The value
for the 2trn1 --> 3erJ transition from a transition
state calculation is l3,7OO cm-1. This suggestsan
error in our calculated 2t2ul, --> 3eoJ,separationof
about 0.5 ev. Although this error is small in absolute
.
'-eg
leo f .t U
-magnitude, it is nonethelessa large percentageof
41t,, -ot^
the experimental result.'?The lowest optically al3ot9
- 02 s
lowed O'?- -+ Fe2* charge transfer transition is
from 6trul, -> 2tzol. The calculated transitionFrc. 2b. FeOu* MO diagram (R(Fe - O) : 2.06 A).
state energy is 37,50Ocm-' which compareswell
The highest occupied orbital is the 3eol, containing two
experimental spectra which show an absorpwith
electrons.
tion edgearound 35,000 cm-' (Figgis, 1966)' The
lowest optical L -> M chargetransfer transitions in
formed. Note that the spin splittings are quite large the ferric caseare calculatedto occurat 25,30Ocm-'
(6t6'-> 2t2o{) and 29,4@ cm-' (1t2,{'+ 27t011
for the es and t2s orbitals. The lowest-energy orbitals
and the transition is observedat 28,570 cm-l (Tanin Figure 2 arc again the set of three predominantly
O 2s orbitals. The 6a1n and 511, bonding orbitals don and Gupta, 1970). The lower value of the
charge-transferenergy in Fe3- oxides is a result of
have eigenvaluesaround - 11 ev. We find the lt2nl
and zesF bonding orbitals around -9 ev in FeOo'o- the lower relative energyof the crystal field orbitals
in the ferric case.Very weak, spin-forbiddentransiat higher energy than in FeOoF by about 1 ev. The
Itlo, 6t1,,, and 1t2,,orbitals are at about the same tions are observed in Fe'* minerals in the region
cm-' (Burns,I970,Fi9.3.2).
from about2O-23,O00
energy in both species and are again O 2p nonbondThe calculated transition-stateenergiesof the 3enl
ing orbitals. In the Fe2* species the "crystal field"
"2u
i,-
,zs
-O2o
J
orbitals, 2t2o and 3en, are at or above the top of the
O 2p nonbonding set while in the Fe3' case the 2t2gf
orbital lies deeply within this set. The 2t2ol + 3eof
eigenvalue difference is somewhat smaller in the ferrous case (1.7 as 2.2 ev) and the spin-splitting is
'The observed Scn Xa overestimation of the crystal field
splitting by 0.5-0.8 ev in transition metal oxides can be
eliminated by a slight modification of the procedures described in the "Calculational Method" section. Such modified calculationswill be reported in the future.
MO CALCULATIONS
FOR RUTILE,
WUSTITE, AND HEMATITE
329
's 3esI and 2t2ol -->Ztzsf transitions,21,50O
cm-l are quite similar. A detailedassignmentof the Fe2O3
and 22,400 cm-1respectively,are in excellentagree- La emissionand absorptionspectramay be found in
ment withexperiment.
Tossellet ol (1973b). Briefly, the main La emission
peak is assignedto the 2t2ol orbital and the main
X-Ray EmissionSpectrafrom OctahedralIron
absorption peak to 2t2of. This assignmentis conIn Table 5, the calculatedand experimentalFe sistent with the 2t2ol + 2t2ol, separationobserved
Kp X-ray emission spectral energiesof FeO and in the optical spectrum of FezOs.A weak peak
on
FerOr are listed. In the FeKB spectra,the KB, peak the high energyside of the La emissionpeak,
obdecreases
in energywith respectto Kfu as the oxida- servable only under conditions of negligible selftion stateof iron increases,
primarily becausethe,ltn absorption, has been assignedto the 3eof orbital.
orbital lies higher in the ferric state.This increasein The low intensityof this peak is probably a result
the KB'-KQ1 separation from FeO to Fe2O3 was of self-absorptionby the nearby 2t2ol orbitaL Alternoted by Kijster and Rieck (1970) and related to natively, this high energystructuremay be attributed
the larger d.c. resistivityof Fe2O3.The calculatidns to double ionization satellite intensity (Liefeld,
also show that the KBs Wak energyincreaseswith 1968). The shoulderobservedon the low energy
an increasein the Fe oxidation state. This results side of the main L,a emissionpeak is here assigned
from a drop in energyof the Fe ls orbital while the to orbitals lt2ol and/or 6a1o.Ifthe primary intensity
4, 5, and 6tr, orbitalsremain fairly constantin en- of this shoulderarisesfrom 1,t2nl,then its energy
ergy. This calculatedtrend is in agreementwith ex- with respectto the main peak will have little deperiment.The KB;' peak,arisingfrom the 6tr, O 2p pendenceon Fe oxidationstate.On the other hand.
nonbonding orbital is probably too weak to be ob- if the 6a1oyields appreciableintensity, the separaservedin both FeO and Fe2Os.
tion of the shoulder from the main peak should inIt is observedexperimentallythat the FeKB ab- creasefrom ferrous to ferric compounds.At present,
sorption edge is -5.8 ev higher in FezOgthan in no experimentalinformation exists on this point.
By
FeO (Dodd and Glenn, 1968). We calculatethe K analogywith TiO2, low energysatellitepeaksarising
absorption edge to lie higher in FeOue- than in from the predominantlyO 2s MO's, namelyleo and
FeO61r by 4.0 ev. This difierence in enersv arises 5a1n,ate expected.Calculatedenergiesof theseorfrom two separablebut complementaryeftelcis:(1)
bitals indicate an - L ev smaller separationof the
the Fe 1s orbital is 2.2 ev lower with respectto the O 2s derived peaksand the main peak in ferric state
ltro orbital in the Fes'case,(2) the 7ttu conduction relative to the ferrous. This is a consequenceof the
band orbital is 1.8 ev higherwith respectto the 1/ro lower relative2t2o| energyfor Fe3*.Apparently,no
in the FeS.case.
attempt has been made to observefeaturesin this
The FeZ,aspectraof ferrous and ferric compounds regionof the FeLa spectrum.
Taslr 5. Experimental and calculated FeKp x-ray Emission spectra: Feo us Fezoa
(energiesin eu)
FeO
Peak
Label
KB:
Experimental
rel-ative
Ea
-lJ.
Calculated
retative
E
- f
I
I .
0
0
33.0
JZ
KB.
4 7. 4
44.0
K B) . '
-
d
1A
KB"'
48.1
or. /
Mende1
2
/
MO assignment
3tlu+FeLs
0
a
47.4
and
CaIcu Iated
relative
E
-t
J
KB ''
Koster
Experimenta.I
rel-ative
Ea
-
(ft?^++7tr,,+ )
n
I{R
o
'F"a 2n - 3
(f970).
34.5
4tIu+Fe 1s
4 5. 5
5tr,r+Fe 1s
4 9. 5
5tlu+Fe Is
60.9
7tlu+Fe 1s
TOSSELL, VAUGHAN,
330
AND IOHNSON
band orbital 1at,, (and perhaps 7tn).These spectral
features are shown strikingly in Fischer's Cr oxide
X-ray absorption spectra (Fischer, I97I). The separation of lhe La and LB absorption maxima in Fe
oxides is - I 1.2 ev at 2 kY operating voltage
(O'Nions and Smith, l97l). The 2t2r{ and 3e,,t
orbitals are at the right energy to absorb X-ray intensity on the high energy side of the Ls erhission
peak in both the Fe'* and Fe3. cases. On the other
hand, the 7d1,, and 7t1,, conduction band orbitals
for Fe'z.occur at a minimum in the emission spectra
(betw.eenthe L" and LB peaks) while in Fe8* compounds the conduction band orbitals fall right on
top of the Lp emission peak. Therefore the LB peak
will be preferentially self-absorbed in Fe3. compounds to produce lower LB/Lo intensity ratios.
The separation of the 2t2,,1 and 7a1,,1orbitals is
mainly a function of oxidation state although preliminary Scp Xo results do show it to have a weak
metal-oxygen distance dependence. Therefore the
LB/La intensity ratio does measure the percent Fe3*.
Fischer and Baun (1968) have explained how such
3e9l
a technique ("difterential self-absorption") can be
2l2sl 2l2qt Tots
used to obtain L absorption spectra explicitly, and
Fe+2
A
Dodd and Ribbe ( 1.972) have obtained preliminary
results for minerals.
In the OKo spectra of the iron oxides, experiment
shows a broad peak at 524.6 ev in hematite and, in
wustite, a main peak at 524.L ev with a shoulder at
Fet3
527.2 ev (Smith and O'Nions, 1972a). Our calculation on the ferric cluster shows the crystal field and
O 2p nonbonding and bonding orbitals to be fairly
well mixed in energy, thus explaining the broad feaII
tureless spectrum observed in Fe2O3. On the other
I
hand, in the ferrous case the 3eol and 2tz, orbitals
are well separatedfrom the O 2p nonbonding levels,
F
as shown in Figure 2a. The 2.8 ev separation be(n
tween the weighted average energies of the O 2p
L
B
I
cfJ
F
nonbonding
orbitals (plus the 2t2ul and 2eol,) and
t1
z
tl \
the 3e,,1, 2t2ol, crystal field orbitals compares well
/l
\,
\
with the experimental separation of 3.1 ev. There\
fore the OKo X-ray emission spectrum of wustite
I
7177
.
shows a high energy shoulder directly attributable to
the Fe2*crystal field orbitals.
7oo
7lo
72o
73o
Although no valence region photoelectron spectra
ENERGY (eV )
are availablefor FeO, the valenceregion photoelecFrc. 3. ExperimentalFe La,8 X-ray emissionspectrum tron Spectrum Of Fe::Os haS been interpreted with
of Fe"O,and calculatedXa energiesof empty MO's gen- fair succesb (Tossell et al, 1973b). The separation
eratingIa absorptionpeaksin Fe"* and Fe'r'oxides.
of the upper valence orbitals and the O 2.1orbitals
A. Feou--emptyorbitalenergies
was calculated within an accuracy of about I ev
B. FeO"',emptyorbitalenergies
(O'Nions
and the upper valenceregion was reproducedreasonand Smith,l97l)
C. Fe,O,Ia,6 spectrum
The ratio of the LB/La peak intensitydecreases
linearly and quantitativelyas iron oxidation state
increaseswithin somesolid solutionseries(O'Nions
and Smith, 1971; Pavicevicet al, 1972). O'Nions
and Smith (197I) explainthis by assumingthat the
LB peak arises from transitions from antibonding
MO's only (e.9., 2te0I) while both antibonding
(2tznI) and bonding(e.g.,2e,,,1t.2,,,
5/r,,)MO's
6a1,,,
contributeto La. However,it is apparentfrom the
shapeof the La spectra(O'Nions and Smith, 1971)
that even if this assumptionwere true, the percent
of the L,a intensityarisingfrom the bondingorbitals
is quite small (certainly(10 percent).An alternative explanationis that in Fe'. compounds,there is
a preferentialself-absorptionof the Lp peak. This
interpretationis supportedby our calculations(Fig.
3 ). Featuresin the La absorptionspectrumresult
from transitionsfrom the Fe Zpg2stateto the crystalfield+ype orbitals 2t2ol,and 3e,,J,and the conduction
+
/l
MO CALCULATIONS
FOR RUTILE, WUSTITE, AND HEMATITE
ably well. The crystal field splitting of the 2trol and
3eof orbitals was a prominent feature of the experimental spectrum. The measuredcrystal field splitting
was -1.9 ev or about 15,000 cm-1, in reasonable
agreement with the measured values of 13,70016,500 cm-1 for 1O Dq in octahedral ferric cornpounds (Burns, 1970, Table 2.4).The separationwe
calculated was somewhat larger, about 2.7 ev. The
only ambiguous feature in the spectrum, a peak
around 15 ev in binding energy, is now believed
due to photoemission by the MgKa3,a satellite line
from the MgKa X-ray. Calabrese and Hayes (1973)
have shown for a series of transition metal oxides
that the spectral region shows only weak satellite
intensity. The study of the valence region X-ray (or
UV) photoelectron spectrum of a stable ferrous mineral such as fayalite would provide a good test for
our FeO610-calculation. The fayalite photoelectron
spectrum should be interpretable in terms of a
superposition of the calculated spectra of the FeO61oand SiOla- polyhedra.
Transition Metal Oxides: Elucidation of
Structures from Spectral Data
In the iron and titanium oxides, the non-core
orbitals can be divided into: (1) a set of O 2s nonbonding orbitals (5a1o,4t1,,,le); (2) a set of metaloxygen bonding orbitals with substantial density in
the interatomic region (5t1,,, 6a10, h2,, 2eo); (3) a
set of O 2p nonbonding orbitals (1t",,, 6tr,,, llro);
(4) the "crystal field" orbitals (2t20,3e") with metal
3d andO 2p character; and (5) the conduction band
orbitals (1aro,7ty) which are metal-oxygen 4s and
4p antibonding and diffuse in character. The orbital
sets most affecting the stability of the system are the
bonding and the crystal field sets. The O 2s and
O 2p nonbonding sets are quite constant in energy
while the conduction band set is empty and therefore does not affect the ground state energy.
The energies of the various orbital sets may be
determined experimentally in the following manner. The O 2s orbitals are most easily identified by
X-ray photoelectron spectroscopy. In conjunction
with a photoelectron measurementof the M 3s or 3p
level they could give useful information on the
charge distribution in the M-O bond. Measuring
binding energies of M and O orbitals together would
eliminate the problems of charging and reference
level effects and greatly simplify comparison of calculated and observed photoelectron shifts. The O 2s
orbitals can also be identified in MKB X-rav emis-
331
sion spectraand perhapsin ML spectra.The energy
,of the O 2s derivedKp spectralpeaks (and perhaps
the L peaks) are good indicatorsof the transition
metal'soxidationstate.
The metal-oxygenbonding orbitals, althoughvery
interesting, are most difficult to locate experimentally. The best method for studyingthem appears
to be MKB X-ray emissionspectroscopy.but the
appropriatepeak (KB,i) is very weak.Theseorbitals
may be resolvablein OKa spectraif they are fairly
compactand well separatedfrom the O 2p nonbonding orbitals (as in TiOr). Also, since the bonding
orbitals are quite diffuse, they should show substantial intensity in UV photoelectronspectra for
reasonsdiscussedby Lohr and Robin (1970) (this
is the casein TiOr). In many cases,the structureof
the bonding orbitals may also be seen in the UV
reflectance
spectrum.
The O 2p nonbondinglevelsare easilyfound from
OKa X-ray emissionspectroscopy.Although they
showlittle variationin energyfor the clustersstudied
here, this may be due to the length of the O-O
edges.The shortestO-O edgein any of the clusters
studiedwas 2.16 A. At smallerdistances.it is conceivablethat O-O antibondingdoes cause a sub'
stantialrise in the energyof this orbital set. Note
that it is preciselythis effectwhich is the basisof the
radiusratio rules.
As is well known, the "crystal field" orbitals are
most easilystudiedby optical absorptionand reflectance spectroscopy.Transitionswithin the crystal
field set as well as transitionsfrom the O 2p nonbonding set (and in some casesthe M-O bonding
set) to the crystalfield orbitalscan be thus studied.
The crystal field orbitals can also be studied by
X-ray photoelectronspectroscopy
and X-ray absorp
tion spectroscopy.
The conductionband levelscan
best be studiedby far UV spectroscopybut can also
be studied usefully by MKB X-ray emission spectroscopy. Therefore, every set of levels can be
studiedspectroscopically.
SpectralEvaluation of Mineral Stability
A worthwhilegoalwould be to evaluatethe stability of a transition metal-oxygencluster directly from
the spectroscopicvaluesof the energylevels.One
major problem in implementingthis procedureat
the present time is the difficulty in studying the
M-O bonding orbital set, since these orbitals are
spread out in energy and diffuse in space (thus
generatingfairly small X-ray intensities).A second
332
TOSSELL, VAUGHAN,
seriousproblem is in the very high spectral energy
resolution required.An averageerror of only 0.1
ev in FeOo'.- valenceorbital energy would produce
an error in total energyof -16 kcal/Fe-O bond.
Of course,in most cases,it is not the total energy
of a systembut rather the relative energiesof related
systemswhich are of interest.For related systems,it
is possiblethat the energy variations in one of the
orbital sets will essentially determine the relative
energiesor stabilities.This will certainly be the case
if all the other orbital sets are constantin energy.It
will also occur if the energy variations of the other
orbital setscompensatefor each other. For example,
qualitative considerationsand preliminary Scr X"
calculations show clearly that reducing the Fe-O
distance will destabilize the crystal field orbitals
(i.e., raise their energy baricenter), stabilize the
bonding orbitals, and increasethe crystal field splitting). The total energywill be a complicatedfunction of all theseefiects.Oxygen-oxygenantibonding
effectsmay alsobe important in somecases.As noted
by Burns (1970), crystalfield stabilizationenergies
are a small fraction of total lattice energies(usually
< 10 percent) but have a strong influence upon
relative stabilities and thus are good predictors of
element fractionation and site enrichment. This is
understandablein terms of the competition between
crystal field orbital destabilizationand bonding orbital stabilization.It is possiblethat a model which
included the crystal field splitting, the separationof
the O 2p nonbonding and cfystal field levels, and
the energyof one of the bonding orbitals would give
accuraterelative stabilities in all cases,and thus be
able to predict element fractionations and site enrichments.Such a model would require experimental
data from optical absorptionspectrafor crystal field
splittings, from UV reflectancespectrafor accurate
O'- + Fe charge transfer energies,and from FeKB
and L (or in simple minerals OK") X-ray emission
spectrafor bondingorbital energies.
Predictionof the Spectraand Electronic Structure
of Minerals at High Pressures
An important area of application of theseresults
is in the interpretation and prediction of the spectra
and electronic state of Fe in minerals at high pressure. Methods have been developed by Gaffney
(1972) and by Wood and Strens (1972) for calculating crystal field spectra from crystal structure
data. These methods, which rely upon an assumed
R-5 distance-deoendence
law for the crvstal field
AND IOHNSON
splitting and upon empirical parameterization,yield
crystal field spectra in fairly good agreementwith
experiment.However, the high pressureoptical and
conductivity studies of Mao and Bell (1972'l indicate that the major change in the high pressure
spectrum of fayalite (in both olivine and spinel
polymorphs) is an enormous reduction in energy
and an increasein intensity of the 6 -+ Fe charge
transfer band. Such changesare outside the scope
of semi-empiricalcrystal field calculations. Similar
shifts in the O'* -+ Fe3' charge transfer peak of
Fe3* chemical compounds have been observed by
Drickamer and correlated with Fe3*.+ Fez* reduction observedat high pressureby Miissbauer spectroscopy (Drickamer and Frank, 1.972). A similar
reduction of Fe3*to Fe2*has been observedin the
mineral magresioriebeckite (Burns, Tossell, and
Vaughan, 1972). Scp X,a calculationsare presently
being performed on Fe-O clustersat different Fe-O
distancesin order to interpret those results.
Acknowledgments
We thank R. G. Burns for a critical reading of this
manuscript, and T. L. Gilbert and G. K. Wertheim for
copies of their manuscripts in advance of publication. This
research was supported by the National Aeronautics and
Space Administration under Grant no. NGL 22-0@-187,
and by the National Science Foundation through the M.I.T.
Center for Materials Sciencesand Engineering.
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