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Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Transition Metal Oxides Transition Metal Oxides Rock Salt and Rock Salt and RutileRutile::MetalMetal--Metal BondingMetal Bonding
Chemistry 754Chemistry 754Solid State Chemistry Solid State Chemistry
Lecture #25Lecture #25May 27, 2003May 27, 2003
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Rock Salt and Rock Salt and RutileRutile: : Structure & PropertiesStructure & Properties
�� Octahedral Molecular Orbital DiagramOctahedral Molecular Orbital Diagram�� Rock Salt Rock Salt ππππππππ*(t*(t2g2g) and ) and σσσσσσσσ*(*(eegg) Bands) Bands�� MM--M InteractionsM Interactions�� Properties 3d Transition Metal MonoxidesProperties 3d Transition Metal Monoxides�� Magnetic Magnetic SuperexchangeSuperexchange�� Rutile Rutile ππππππππ*(t*(t2g2g) Bands, t) Bands, t and tand t⊥⊥⊥⊥⊥⊥⊥⊥
�� Properties MOProperties MO22 (M=Ti, V, Cr, Mo, W, (M=Ti, V, Cr, Mo, W, RuRu))�� Double Exchange in CrODouble Exchange in CrO22
2
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Rock Salt Crystal StructureRock Salt Crystal Structure
OO
MM
x
y
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Generic Octahedral MO DiagramGeneric Octahedral MO Diagram
a1g (σσσσ)
t1u (σ σ σ σ + π)
eg (σσσσ)t2g (ππππ)
t1g & t2u
a1g (σ∗σ∗σ∗σ∗)
t1u (σ∗ σ∗ σ∗ σ∗ + π∗)
t2g (π∗π∗π∗π∗)
eg (σ∗σ∗σ∗σ∗)
nd eg (dx2-y2, dz2)
(n+1)d t2g (dxy, dxz, dyz)
(n+1)s
(n+1)p
O 2p π π π π (6) - t2g, t1uO 2p NB (6)-t1g, t2u
O 2p σ σ σ σ (6)a1g, t1u, eg
Transition Transition MetalMetal
OxygenOxygen
3
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Simplified Band StructureSimplified Band Structure
nd eg (dx2-y2, dz2)
(n+1)d t2g (dxy, dxz, dyz)
(n+1)s
(n+1)p
O 2p π π π π (12)
O 2p σ σ σ σ (6)a1g, t1u, egTransition Transition
MetalMetal
OxygenOxygen
M-O σσσσ
M-O ππππO 2p NB
M-O π∗π∗π∗π∗ [3]
M-O σ∗σ∗σ∗σ∗ [2]
σ∗σ∗σ∗σ∗ [4] Bands of interestBands of interest
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
3d Transition Metal Monoxides3d Transition Metal Monoxides
Compound M-MDistance
ElectricalProperties
MagneticProperties
TiO (d2) 2.94 Å Metallic Pauli ParamagneticVO (d3) 2.89 Å Intermediate IntermediateMnO (d5) 3.14 Å Semiconductor AFM TN = 122 KFeO (d6) 3.03 Å Semiconductor AFM TN = 198 KCoO (d7) 3.01 Å Semiconductor AFM TN = 293 KNiO (d8) 2.95 Å Semiconductor AFM TN = 523 K
AFM = Antiferromagnetic
How can we understand this behavior? Metallic conductivity for a fairly ionic Ti2+-O2- bond? Semiconducting behavior for
partially filled bands?
4
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Orbital Overlap in the tOrbital Overlap in the t2g2g BandBandΓΓΓΓ point (kx=ky=kz=0)
M
M
M M
M
M
M
M M
M
ΜΜΜΜ point (kx=ky=ππππ/a, kz=0)
MM--O O ππ nonbondingnonbonding MM--M bondingM bonding
MM--O O ππ antibondingantibonding MM--M nonbondingM nonbonding
Band Runs Uphill from
Γ Γ Γ Γ →→→→ ΜΜΜΜ
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Orbital Overlap in the Orbital Overlap in the eegg BandBandΓΓΓΓ point (kx=ky=kz=0)
ΜΜΜΜ point (kx=ky=ππππ/a, kz=0)
MM--O O σσ nonbondingnonbonding Band Runs Uphill from
Γ Γ Γ Γ →→→→ ΜΜΜΜ
M
M
M M
M
M
M
M M
M
MM--O O σσ antibondingantibonding
5
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Band Structure CalculationsBand Structure Calculations
DOS (e/eV)10 20
k
Ener
gy (v
s. O
2s)
10
15
20
25
10
15
20
25
DOS (e/eV) 10 20X R M Γ R
kX R M Γ R
SrTiOSrTiO33 TiOTiO
The The eegg σσσσσσσσ* band is more narrow in * band is more narrow in TiO TiO because the Tibecause the Ti--O distance is considerably O distance is considerably longer and the overlap is smaller.longer and the overlap is smaller.
The tThe t2g2g ππππππππ* band is also slightly more narrow in * band is also slightly more narrow in TiOTiO, except for near the , except for near the ΓΓ--point, point, where Tiwhere Ti--Ti bonding lowers the energy and widens the band.Ti bonding lowers the energy and widens the band.
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Magnetic StructureMagnetic StructureMnOMnO,, FeOFeO,, CoOCoO and and NiO NiO are all are all antiferromagnets antiferromagnets
with the structure shown below (for with the structure shown below (for MnOMnO). ).
The electrons align themselves in anThe electrons align themselves in an antiparallelantiparallel fashion due to AFM fashion due to AFM superexchangesuperexchange interactions arising primarily from the ½ filled interactions arising primarily from the ½ filled eegg
orbitalsorbitals. The magnetic ordering temperature increases from . The magnetic ordering temperature increases from MnMn →→Fe Fe →→ Co Co →→ Ni due to increasing covalency (see Magnetism lecture). Ni due to increasing covalency (see Magnetism lecture). The magnetic ordering has implications for the electronic transpThe magnetic ordering has implications for the electronic transport ort
properties.properties.
AFM
eg
t2g
==
eg
t2g
==MnO
6
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
MottMott--Hubbard InsulatorsHubbard Insulators
MM--OO--M Interaction is AFM (M Interaction is AFM (↑↓↑↓) ) when both TM have 1/2 filled when both TM have 1/2 filled configurations (dconfigurations (d55--dd55 or dor d33--dd33))
FeFe OO FeFeThe AFM coupling of ions is shown The AFM coupling of ions is shown for for FeOFeO. The ½ filled . The ½ filled eegg orbitals orbitals
stabilize AFM coupling. Notice that stabilize AFM coupling. Notice that there is no mechanism for the there is no mechanism for the
minority spin electrons (shown in minority spin electrons (shown in red) to move from one Fe ion to the red) to move from one Fe ion to the next without undergoing a spin flip next without undergoing a spin flip
(the t(the t2g2g orbitals orbitals of the same spin are of the same spin are occupied). occupied).
Consequently the AFM coupling of Consequently the AFM coupling of ions forces a localization of the tions forces a localization of the t2g2g
electrons, even in the absence of a ½ electrons, even in the absence of a ½ filled or completely filled band. This filled or completely filled band. This is essentially the opposite of doubleis essentially the opposite of double--
exchange. Such compounds are exchange. Such compounds are called Mottcalled Mott--Hubbard insulators.Hubbard insulators.
eg ↑↑↑↑
t2g ↑↑↑↑
eg ↓↓↓↓
t2g ↓↓↓↓
eg ↓↓↓↓
t2g ↓↓↓↓
eg ↑↑↑↑
t2g ↑↑↑↑
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
RutileRutile Crystal StructureCrystal Structure
z
x
y
7
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
MOMO22 with the with the Rutile Rutile StructureStructureCompound M-M
Distance Electrical Properties
Magnetic Properties
TiO2 (d0) 2.96 Å Semiconductor Diamagnetic
VO2 (d1) T>340K VO2 (d1) T<340K
2.88 Å 2.65;3.12Å
Metallic Semiconductor
Paramagnetic Diamagnetic
CrO2 (d2) 3.14 Å Metallic Ferromagnetic
TC = 398 K MoO2 (d2) 2.52;3.10Å Metallic Pauli Paramagnetic
RuO2 (d4) 3.14 Å Metallic Pauli Paramagnetic
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
c/a Ratio in c/a Ratio in RutileRutile--Type OxidesType Oxides
VOVO22 (T > 340K)(T > 340K)MetallicMetallic
VV--V Even Spacing V Even Spacing VOVO22 (T < 340K)(T < 340K)
MetallicMetallicVV--V AlternatingV Alternating
MoOMoO22MetallicMetallic
MoMo--Mo AlternatingMo Alternating
RuORuO22MetallicMetallic
RuRu--RuRu Even SpacingEven Spacing
CrOCrO22MetallicMetallic
CrCr--Cr Even SpacingCr Even Spacing
8
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
MM--M Overlap in the tM Overlap in the t2g2g BandBand
MM--M M σσ bondingbonding
M
M
MM
M
M
M
M
M
MM--M M ππ antibondingantibonding MM--M M δδ bondingbonding
ΖΖΖΖ point kx=0ky=0
kz=ππππ/a
MM--M M σσ antibondingantibonding
M
M
MM
M
M
M
M
M
MM--M M ππ bondingbonding MM--M M δδ antibondingantibonding
ΓΓΓΓ point kx=0ky=0kz=0000
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Combined MCombined M--O & MO & M--M EffectsM Effects��The MThe M--O O ππ* and M* and M--M bonding interactions both make a M bonding interactions both make a contribution to the tcontribution to the t2g2g band. band. ��The MThe M--O O ππ* interactions are dominant, but the M* interactions are dominant, but the M--M M σσσσσσσσinteractions interactions preturb preturb the picture. The Mthe picture. The M--M M ππππππππ & & δδδδδδδδ interactions interactions are of minimal importance.are of minimal importance.��As we fill up the tAs we fill up the t2g2g band we can roughly think of the following band we can roughly think of the following picture in terms of Mpicture in terms of M--M bonding strength.M bonding strength.
M-M σ σ σ σ →→→→ d1 TM Ion
EF
DOS
M-M π π π π →→→→ d2 TM IonM-M δ/δδ/δδ/δδ/δ∗∗∗∗
M-M π∗ π∗ π∗ π∗ →→→→ d5 TM IonM-M σ∗ σ∗ σ∗ σ∗ →→→→ d6 TM Ion
M-O ππππ∗∗∗∗
M-O π* ~ M-M σ > M-M π > M-M δ
9
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
+ M-M σσσσ
Tetragonal Structure (TiOTetragonal Structure (TiO22,CrO,CrO2,2,RuORuO22))
d d eegg
d td t2g2g
Oxygen 2pOxygen 2pTransition Transition
MetalMetal
M-O σσσσ
M-O ππππO 2p NB
M-O π∗π∗π∗π∗ [2]
M-O σ∗σ∗σ∗σ∗ [4]
+ M-M σ∗σ∗σ∗σ∗
Z = 2 (MZ = 2 (M22OO44))
EEFF TiOTiO22
EEFF VOVO22
EEFF CrOCrO22
EEFF RuORuO22
Delocalized Delocalized ElectronsElectrons
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Band Structure CalculationsBand Structure Calculations
10
15
20
25
DOS (e/eV) 12
DOS (e/eV)12
k
Ener
gy (v
s. O
2s)
10
15
20
25
kX R M Γ R Z α M Γ Z R X Γ
SrTiOSrTiO33 TiOTiO22
10
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
k
Ener
gy (v
s. O
2s)
10
15
20
25
Z α M Γ Z R X Γ
10
15
20
25
10
15
20
25
Z α M Γ Z R X Γ Z α M Γ Z R X Γ
TiOTiO22 VOVO22 CrOCrO22
Calculated Band Structure (Tetragonal, Z=2)Calculated Band Structure (Tetragonal, Z=2)
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
TiOTiO22 VOVO22 CrOCrO22
Density of States (Tetragonal Structure)Density of States (Tetragonal Structure)
DOS (electrons/eV)
4 8 12
Ener
gy (v
s. O
2s)
10
15
20
25
4 8 12
10
15
20
25
4 8 12
10
15
20
25
11
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
TiOTiO22Tetragonal Z=2Tetragonal Z=2
MoOMoO22Monoclinic Z=4Monoclinic Z=4
ΖΖΖΖ point
ΓΓΓΓ point
BondingBonding
AntibondingAntibonding
MM--M Short=BondingM Short=BondingMM--M Long=BondingM Long=Bonding
MM--M Short=ABM Short=ABMM--M Long=ABM Long=AB
MM--M Short=BondingM Short=BondingMM--M Long=ABM Long=AB
MM--M Short=ABM Short=ABMM--M Long=BondingM Long=Bonding
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
PierlsPierls DistortionDistortionThe The dimerization dimerization which occurs in the which occurs in the rutile rutile structure and it�s structure and it�s
effects on the band structure are similar to the effects on the band structure are similar to the Pierls Pierls distortion we discussed for a 1D chain of Hydrogen atoms, distortion we discussed for a 1D chain of Hydrogen atoms, except that it occurs on top of the Mexcept that it occurs on top of the M--O O ππ* interactions.* interactions.
a
a
a
a
a
a
E
k0 π/a
EF
E
k0 π/a
EF
12
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
M-O σσσσ
M-O ππππO 2p NB
M-M σσσσ [2]
M-O π∗π∗π∗π∗ [8]
M-O σ∗σ∗σ∗σ∗ [8]
M-M σ∗σ∗σ∗σ∗ [2]d d eegg
d td t2g2g
Z = 4 (MZ = 4 (M44OO88))
EEFF VOVO22
EEFF MoOMoO22
Oxygen 2pOxygen 2p
Monoclinic Structure (VOMonoclinic Structure (VO22,MoO,MoO22))
Delocalized Delocalized ElectronsElectrons
MM--O O AntibondingAntibonding
Localized Localized ElectronsElectrons
MM--M BondingM Bonding
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
DOS (e/eV)
13
k
Ener
gy (v
s. O
2s)
10
15
20
25
Z α M Γ Z R X Γ
10
15
20
25
DOS (e/eV) 13Z Γ Y α β ∆ ε C
k
MoOMoO22Monoclinic (Z=4)Monoclinic (Z=4)
CrOCrO22Tetragonal (Z=2)Tetragonal (Z=2)
Mo-Mo σσσσMo-O ππππ∗∗∗∗
13
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
CrOCrO22 and RuOand RuO22Why are alternating longWhy are alternating long--short Mshort M--M contacts, indicative of M contacts, indicative of MetalMetal--Metal bonding not observed in CrOMetal bonding not observed in CrO22 and RuOand RuO22. The . The
electron count suggests that the Melectron count suggests that the M--M M σσσσσσσσ levels should be full levels should be full and the Mand the M--M M σσσσσσσσ** levels empty?levels empty?
There is a competition between localized MThere is a competition between localized M--M bonding (prefers M bonding (prefers dimersdimers) and ) and delocalized delocalized electronic transport in the Melectronic transport in the M--O O ππππππππ** band band
(prefers equal spacing). (prefers equal spacing).
Favors MFavors M--M bonding M bonding and localized eand localized e-
Dominant in MoODominant in MoO22
Favors Favors delocalizeddelocalizedtransport in the Mtransport in the M--O O ππππππππ**
bandband
Dominant in Dominant in CrOCrO22 (poor overlap) (poor overlap)
RuORuO22 (electron count)(electron count)
VOVO22IntermediateIntermediate
Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry
Double ExchangeDouble ExchangeCrOCrO22 is ferromagnetic. A property which leads to it�s use in magnetis ferromagnetic. A property which leads to it�s use in magnetic ic
cassette tapes. What stabilizes the ferromagnetic state?cassette tapes. What stabilizes the ferromagnetic state?
Localized tLocalized t||||electronselectrons
No MNo M--M BondingM Bonding
M
M
MM
M
M
Delocalized Delocalized tt2g2g ππππππππ**
electronselectrons
Ferromagnetic:Ferromagnetic: DelocalizedDelocalizedtransport of transport of ttππππππππ** electrons allowedelectrons allowed..
tt||||
ttππππππππ**
tt||||
ttππππππππ**
AntiferromagneticAntiferromagnetic:: DelocalizedDelocalizedtransport violates transport violates Hund�sHund�s RuleRule..
Localized tLocalized t|||| electrons polarize itinerant (electrons polarize itinerant (delocalizeddelocalized) t) t2g2g ππππππππ**
electrons. Magnetism and conductivity are correlated.electrons. Magnetism and conductivity are correlated.
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