Transcript Electrical Properties - Ohio State University

Transition Metal Oxides
Rock Salt and Rutile:
Metal-Metal Bonding
Chemistry 754
Solid State Chemistry
Lecture #25
May 27, 2003
Chemistry 754 - Solid State Chemistry
Rock Salt and Rutile:
Structure & Properties
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Octahedral Molecular Orbital Diagram
Rock Salt p*(t2g) and s*(eg) Bands
M-M Interactions
Properties 3d Transition Metal Monoxides
Magnetic Superexchange
Rutile p*(t2g) Bands, t and t
Properties MO2 (M=Ti, V, Cr, Mo, W, Ru)
Double Exchange in CrO2
Chemistry 754 - Solid State Chemistry
Rock Salt Crystal Structure
M
O
y
x
Chemistry 754 - Solid State Chemistry
Generic Octahedral MO Diagram
t1u (s* + p*)
(n+1)p
a1g (s*)
Oxygen
(n+1)s
eg (s*)
nd eg (dx2-y2, dz2)
t2g (p*)
O 2p p (6) - t2g, t1u
O 2p NB (6)-t1g, t2u
(n+1)d t2g (dxy, dxz, dyz)
t1g & t2u
Transition
Metal
t2g (p)
eg (s)
O 2p s (6)
a1g, t1u, eg
t1u (s + p)
a1g (s)
Chemistry 754 - Solid State Chemistry
Simplified Band Structure
(n+1)p
(n+1)s
nd eg (dx2-y2, dz2)
s* [4]
M-O s* [2]
Oxygen
M-O p* [3]
(n+1)d t2g (dxy, dxz, dyz)
O 2p p (12)
O 2p NB
Transition
Metal
Bands of interest
M-O p
O 2p s (6)
a1g, t1u, eg
M-O s
Chemistry 754 - Solid State Chemistry
3d Transition Metal Monoxides
Compound
M-M
Distance
Electrical
Properties
Magnetic
Properties
TiO (d2)
2.94 Å
Metallic
Pauli Paramagnetic
VO (d3)
2.89 Å
Intermediate
Intermediate
MnO (d5)
3.14 Å
Semiconductor
AFM TN = 122 K
FeO (d6)
3.03 Å
Semiconductor AFM TN = 198 K
CoO (d7)
3.01 Å
Semiconductor AFM TN = 293 K
NiO (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?
Chemistry 754 - Solid State Chemistry
Orbital Overlap in the t2g Band
G point (kx=ky=kz=0)
M
M
M
M
M
M-M bonding
M-O p nonbonding
M point (kx=ky=p/a, kz=0)
M
M
M
M
Band Runs
Uphill from
G M
M
M-O p antibonding
M-M nonbonding
Chemistry 754 - Solid State Chemistry
Orbital Overlap in the eg Band
G point (kx=ky=kz=0)
M
M
M
M
M
Band Runs
Uphill from
G M
M-O s nonbonding
M point (kx=ky=p/a, kz=0)
M
M
M
M
M
M-O s antibonding
Chemistry 754 - Solid State Chemistry
Band Structure Calculations
SrTiO3
Energy (vs. O 2s)
25
20
20
15
15
10
10
X
R
TiO
25
G
M
k
R
10
DOS (e/eV)
20
X
R
M
k
G
R
10
20
DOS (e/eV)
The eg s* band is more narrow in TiO because the Ti-O distance is considerably
longer and the overlap is smaller.
The t2g p* band is also slightly more narrow in TiO, except for near the G-point,
where Ti-Ti bonding lowers the energy
and widens
band.
Chemistry
754 -the
Solid
State Chemistry
Magnetic Structure
MnO, FeO, CoO and NiO are all antiferromagnets
with the structure shown below (for MnO).
=
eg
t2g
eg
A
F
M
t2g
=
O
Mn
The electrons align themselves in an antiparallel fashion due to AFM
superexchange interactions arising primarily from the ½ filled eg
orbitals. The magnetic ordering temperature increases from Mn 
Fe  Co  Ni due to increasing covalency (see Magnetism lecture).
The magnetic ordering has implications for the electronic transport
properties.Chemistry 754 - Solid State Chemistry
Mott-Hubbard Insulators
The AFM coupling of ions is shown
for FeO. The ½ filled eg orbitals
Fe
Fe
O
stabilize AFM coupling. Notice that
there is no mechanism for the
eg 
eg 
minority spin electrons (shown in
red) to move from one Fe ion to the
t2g  next without undergoing a spin flip
t2g 
(the t2g orbitals of the same spin are
occupied).
eg 
eg 
Consequently the AFM coupling of
ions forces a localization of the t2g
t2g 
t2g  electrons, even in the absence of a ½
filled or completely filled band. This
M-O-M Interaction is AFM ()
is essentially the opposite of doublewhen both TM have 1/2 filled
exchange. Such compounds are
5
5
3
3
configurations (d -d or d -d )
called Mott-Hubbard insulators.
Chemistry 754 - Solid State Chemistry
Rutile Crystal Structure
z
y
x
Chemistry 754 - Solid State Chemistry
MO2 with the Rutile Structure
Compound
M-M
Distance
Electrical
Properties
Magnetic
Properties
TiO 2 (d0)
2.96 Å
Semiconductor
Diamagnetic
VO 2 (d1) T>340K
2.88 Å
Metallic
Paramagnetic
Semiconductor
Diamagnetic
VO 2 (d1) T<340K 2.65;3.12Å
CrO 2 (d2)
3.14 Å
Metallic
MoO 2 (d 2)
2.52;3.10Å
Metallic
Ferromagnetic
TC = 398 K
Pauli Paramagnetic
RuO 2 (d 4)
3.14 Å
Metallic
Pauli Paramagnetic
Chemistry 754 - Solid State Chemistry
c/a Ratio in Rutile-Type Oxides
VO2 (T > 340K)
Metallic
V-V Even Spacing
VO2 (T < 340K)
Metallic
V-V Alternating
CrO2
Metallic
Cr-Cr Even Spacing
RuO2
Metallic
Ru-Ru Even Spacing
MoO2
Metallic
Mo-Mo Alternating
Chemistry 754 - Solid State Chemistry
M-M Overlap in the t2g Band
G point
kx=0
ky=0
kz=0
M
M
M
M
M
M
M
M
M
M-M s bonding
Z point
kx=0
ky=0
kz=p/a
M-M p antibonding
M-M d bonding
M
M
M
M
M
M
M
M
M
M-M s antibonding
M-M p bonding
M-M d antibonding
Chemistry 754 - Solid State Chemistry
Combined M-O & M-M Effects
•The M-O p* and M-M bonding interactions both make a
contribution to the t2g band.
•The M-O p* interactions are dominant, but the M-M s
interactions preturb the picture. The M-M p & d interactions
are of minimal importance.
•As we fill up the t2g band we can roughly think of the following
picture in terms of M-M bonding strength.
EF
M-M s*  d6 TM Ion
M-M p*  d5 TM Ion
M-O p*
M-M d/d*
M-M p  d2 TM Ion
M-M s  d1 TM Ion
DOS
M-O p* ~ M-M s > M-MChemistry
p > M-M
754d- Solid State Chemistry
Tetragonal Structure (TiO2,CrO2,RuO2)
Delocalized
Electrons
M-O s* [4]
+ M-M s*
d eg
d t2g
Transition
Metal
Z = 2 (M2O4)
M-O p* [2]
+ M-M s
EF RuO2
EF CrO2
EF VO2
EF TiO2
O 2p NB
M-O p
Oxygen 2p
M-O s
Chemistry 754 - Solid State Chemistry
Energy (vs. O 2s)
Band Structure Calculations
25
25
20
20
15
15
10
10
X
R
M
G
k
SrTiO3
R
12
DOS (e/eV)
Z

M
G
Z
k
R
X G
12
DOS (e/eV)
TiO2
Chemistry 754 - Solid State Chemistry
Calculated Band Structure (Tetragonal, Z=2)
TiO2
Energy (vs. O 2s)
25
VO2
25
25
20
20
20
15
15
15
10
10
10
Z

M
G
Z
R
X G
Z

M
G
Z
CrO2
R
X G
Z

M
G
Z
R
X G
k
Chemistry 754 - Solid State Chemistry
Density of States (Tetragonal Structure)
Energy (vs. O 2s)
TiO2
VO2
CrO2
25
25
25
20
20
20
15
15
15
10
10
10
4
8
12
4
8
12
4
8
12
DOS (electrons/eV)
Chemistry 754 - Solid State Chemistry
MoO2
Monoclinic Z=4
TiO2
Tetragonal Z=2
G point
M
a
M
M
M
Bonding
Z point
a
a
M
M
M
M
M
a
M
M
M-M Short=Bonding
M-M Long=Bonding
M
M-M Short=AB
M-M Long=AB
M
M
M
M
M
M
M
M
Antibonding
a
M
M
a
M
M
M-M Short=Bonding
M-M Short=AB
M-M Long=AB
M-M
Long=Bonding
Chemistry 754
- Solid
State Chemistry
Pierls Distortion
The dimerization which occurs in the rutile structure and it’s
effects on the band structure are similar to the Pierls
distortion we discussed for a 1D chain of Hydrogen atoms,
except that it occurs on top of the M-O p* interactions.
a
E
a
EF
E
a
EF
a
a
a
0
k
p/a
0
k
p/a
Chemistry 754 - Solid State Chemistry
Monoclinic Structure (VO2,MoO2)
Delocalized
Electrons
M-O Antibonding
d eg
d t2g
Localized
Electrons
M-M Bonding
M-O s* [8]
M-M s* [2]
M-O p* [8]
M-M s [2]
O 2p NB
M-O p
EF MoO2
EF VO2
Oxygen 2p
M-O s
Z = 4 (M4O8)
Chemistry 754 - Solid State Chemistry
CrO2
MoO2
Energy (vs. O 2s)
Tetragonal (Z=2)
Monoclinic (Z=4)
25
25
20
20
Mo-O p*
Mo-Mo s
15
15
10
10
Z

M
G
Z R
k
X G
13
DOS (e/eV)
Z
G
Y

k



C
13
DOS (e/eV)
Chemistry 754 - Solid State Chemistry
CrO2 and RuO2
Why are alternating long-short M-M contacts, indicative of
Metal-Metal bonding not observed in CrO2 and RuO2. The
electron count suggests that the M-M s levels should be full
and the M-M s* levels empty?
There is a competition between localized M-M bonding (prefers
dimers) and delocalized electronic transport in the M-O p* band
(prefers equal spacing).
Favors delocalized
transport in the M-O p*
band
Favors M-M bonding
and localized e-
Dominant in
CrO2 (poor overlap)
RuO2 (electron count)
Dominant in MoO2
VO2
Intermediate
Chemistry 754 - Solid State Chemistry
Double Exchange
CrO2 is ferromagnetic. A property which leads to it’s use in magnetic
cassette tapes. What stabilizes the ferromagnetic state?
M
M
M
M
M
M
tp*
Ferromagnetic: Delocalized
transport of tp* electrons allowed.
tp*
Localized t||
electrons
No M-M Bonding
Delocalized t2g p*
electrons
t||
t||
Antiferromagnetic: Delocalized
transport violates Hund’s Rule.
Localized t|| electrons polarize itinerant (delocalized) t2g p*
electrons. Magnetism and conductivity
are
correlated.
Chemistry 754
- Solid
State Chemistry