electronic and ionic conductivity in metal oxides
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PAUL SCHERRER INSTITUTPAUL SCHERRER INSTITUT
Electronic and ionic conductivity in
metal oxides
Kazimierz Conder
Laboratory for Developments andMethods, Paul Scherrer Institute,
5232 Villigen PSI, Switzerland
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1 10 100 100010
-11
10-9
10-7
10-5
10-3
10-1
101
103
105
107
La0.75
Ca0.25
MnO3
Na2O*11Al2O3
YBa2Cu
3O
7
Superconductors >1023
Cu
Pb
Graphite
Ge
Si
GlassInsulators
Semico
nductors
Me
tals
Conductivity[-1cm
-1]
Temperature [K]
Electrical conductivity
Conductivity of metals decreaseswith temperature. Increasedinteraction of electrons withlattice!
Superconductivity: by coolingresistivity drops to zero
Conductivity of insulators andsemiconductors increases withtemperature. Concentration ofcarriers increases!
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Electrical resistivity of ceramic (oxide) materials over 20 orders of magnitude
10-13 10-8 10-3 102 107
Conductivity,-1m-1
Insulators Semiconductors Conductors Superconductors
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18
18
18
18
18
18
18
18
18
18
18
18
Molecular: Ar
1"18
1#
18
1"18
1#
18
1"18
1#18
1"18
1#18
1"
1" 1"
1"1"
1" 1"
1"$ $ $
$ $ $
Ionic: KCl
Covalent: C (diamond) Metallic: K
%lectronic charge distribution in the basic solid types
&chemical bond point of view'
(fter ).*. (shcroft+ ).,. -ermin+ Solid State /hysics0+ /hiladephia+ 1"#
2 Cl
,elocalizedelectrons
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Metals, semiconductors, insulators
134
5og
-etal
Semiconductor:intrinsice6trinsic
Insulator
4
Semiconductors: electrons aree6cited over the band gap andoccupy energy levels inconductivity band. 7oles arecreated in valence band. 4heprocess is thermally activatedconductivity increase withtemperature.
( material with an energy gap 9. e; is an insulator.
Conductivity can be increased by a doping. 4hrough the dopingenergy levels within band gap will be created.
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Energy of
an electron: E = = (k)2/2m
k=2/ wave vector
E
k
E ~ k2
%lectrons with a &lattice parameter'can travel freely through a crystal
For more energetic electrons when a
wavelength
of the electron
Electron in a (1D) solid
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E
k
E ~ k2
a 63a' higher energy
,istribution of the electrondensities:
63a' lower energy
?@9a
Electrons which have awavelength commensuratewith the lattice arescattered on the !eriodic
!otential
E
>3a >3a
Aorbidden band
Electron in a (1D) solid
/otential energy of an electronin a periodic array of positive ions
*ave functions for ?@9a
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Band &Bloch*ilson'insulators
S
Partially filled energy band metal
Filled energy band insulator
splitted d orbitals(trigonal prismcoordination)
dxz, dyz
dxy, dx2-y2
dz2
insulator metal
Nb4+
4d1
Mo4+
4d2
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)o carriers no conductivity
-gD -g9 9pEsF D9 9p insulator
)a9D )a 9pEsF D9 9p )oble gas configuration:
insulator
4iD9 D9 9p4i$ EdF$sF insulator
Aree delectrons:metal
4iD 4i9 Ed9$sF D9 9p
)iD )i9 Ed8$sF D9 9p InsulatorBut whyGGG
Aree carriersG
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TiO- rutileTi
O
4i Ed9$sF
metal
NiO- NaCl structure )i Ed8$sF
Is insulator!
Why not a metal?
Ni
O
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CuD Cu9 Ed"$sF
CoD Co9
Ed#
$sF
-nD -n9 Ed$sF
Cr9DE CrE EdE$sF
Ddd number of d electronsall this o6ides should bemetals but are insulators
*hatever is the crystal
field splitting the orbitalsare not fully occupied!!!
Why not metal?
Ed#$s9Ed$s9
Ed"$s9Ed$$s9%lectron configurationsof elements
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H4he dlevels in most of the transition metalo6ides are partially filled+ therefore+ the bandtheory predicts electron delocalization and
metallic properties.H(ccording to band structure calculations halfof the nown binary compounds should beconducting.
HIn reality+ many o6ides show insulatingbehavior+ implying that the delectrons arelocalized.HShortrange Coulomb repulsion of electrons
can prevent formation of band states+stabilizing localized electron states.
Mott-Hubbard insulators
The Nobel Prize in Physics1977: Philip Warren
Anderson, Sir Nevill
Francis Mott and JohnHasbrouck van Vleck"for their fundamental
theoretical investigations
of the electronic structure
of magnetic anddisordered systems".
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-ott considered the idealized metalinsulator transition for )acrystal by changing the
interatomic spacing.
After: Feng Duan, Jin Guojun,
Introduction to Condensed Matter
Physics, Vol.1, World Scientific 2005
7ubbard J energy penalty for transferring an
electron between two adKacent sites assumed tobe independent on a
)a )a )a" )a#$
Bandwidth or band dispersion:energy difference between the highest
and lowest level. Bandwidth increaseswith better orbital overlap. Localizationof electrons narrow bands.
%lectron hoppingbetween atomsduring conduction
13a
a
conductivity
%
$
)a )a )a )a
)a" )a#
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U ~I -A
ionization energy(a few eV)
electron
affinity
Coulomb repulsion is described interms of a correlation energy,%u&&ard#$, which is the energypenalty for transferring an electronbetween two adKacent sites.
Ni2+ + Ni2+ Ni3+ + Ni+
d8 + d8 d7 + d9
Mott-Hubbard insulators
$
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At the !oint where '$, the &ands overla!*eyond this !oint, thereis no energy ga! and the
material is metallic
I+ $ ', the d &and o+ thetransition metal is s!litted intosu&ands For an electrontrans+er an energy &arrier $must &e overcome and the
material is insulatingMott#%u&&ard (M%) insulator
U
E
U=1/2(B1+B2)Bandwidth W
Ef
Upper Hubbard band
Lower Hubbard band
4he effect of the electron repulsion maes even the halffilled band
insulating when the interaction between atoms &band width *' is small.
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Pressure and temperature dependence
H%very material under highpressure will have metallicpropertiesHInsulator-etal transition canbe achieved increasingtemperature &thermallyinduced carriers' or doping 13a
metal
insulator
13ac
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/hase diagram of ;9DE
,.B. -c*han et al.+ /L5+ 9E &1""' 1E8$
H-i6ed o6ides &chemical pressure'-i." /0123 4." /50 23 Cr." /566 2
H/ressure e6periments for ;9DEand &;F."CrF.F$'9DE
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;9DE metalinsulator transition
,.B. -c*han et al.+ /L5+ 9E &1""' 1E8$ J. Feinleib and W. Paul,Phys. Rev. 155(1967) 841
=1$2
conductivity&ohmc
m'!1
134+ 1FE32
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5arger d orbitals
Hlow o6idation state &more electrons' for early 4- &good -- overlap'Hhigh o6idation state for late 4- &good -D- overlap: covalentbond'
Hfor covalent bonds: low electronegativity anionshalides+ D+ S+ Se+ 4e+ phosphides.....
*
* J
JHelectron configuration e.g. -n9 Ed has halffilled shellHother cations in the structure &as e.g. in perovsites (BDE'
Meneral rules
)iS+ CoS and CuSmetals)iD+ CoD and CuD (M%) insulators
4ransition metals 4-
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LaCuO3 is a metalCu 3d-band and O 2p-band
overlap.
o6ygen p
band
metal d
bands
Egap U is large
(Semi)Metal
Charge-transfer-
insulator(semiconductor)
Mott-Hubbard-
insulator
Egap
Different /Uratio!
Conductivityvia holes inO 2p-band
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D6ygen p band
-etal bands
U
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D6ygen pband
metal dbands
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CoO
Fe2O3
NiO
Cr2O3
Mn3O4
FeO
VO2
MoO2
Ti2O3
ReO3
TiOCrO2
V2O3VO
Fe3O4NbO
ReO2MnO2
10-14
10
-10
10-6
10-2
102
106
Conduc
tivity,
-1m
-1
1000 800 333 250 200 167 149 125 T, K
1000/T, K-11 2 3 4 5 6 7 8
Cu 5.9 107 at RT
metallic
After: Schaumberg, Keramik
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/erovsites
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d1 perovsites
Sr;DE metalCa;D
E
metal
5a4iDE insulatorgap F.9e;
N4iDE insulatorgap 1.F e;
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D6ygen nonstoichiometric Ed o6ides
Does the electrical
conductivity
depend on oxygencontent and cation
doping?
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9e+ect concentration n;/
4emperatureOoCP
(ctivation %nergy e;
1 9 8
1FF EQ1F1$ 1Q1F9# 1Q1F1F8
FF EQ1F# 1Q1F1E 8Q1FE
1FFF 1Q1F$ 1Q1F8 9Q1FE9
1FF 1Q1FE 9Q1F 9Q1F9E
9FFF Q1FE $Q1F 9Q1F18
kTE
Nn Vexp
0
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Fe1#FeFe " ?=
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-i=?#< semiconductor ty!e n
F()
%nergy
E+
4*
C*
,onor level
?-i
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9e+ect semiconductor ;i1#=
In )iD nicel vacancies are created when o6idized with o6ygen. 4hecharge of the additional o6ygen sites is compensated by o6idationof some nicel sites to )iE. 4hrough the o6idation the volume ofthe material increases.
p
+++ ONiNiNiO
Ni ONiVNiO 225.0//
2
+ hNiNi NiNiO
Ni
+++ hNiheNi NiNiO
Ni/
)iE sites are electron acceptors:
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A!!lication ceramic semiconductors
)4Cthermistors &;egative -emperatureCoefficient thermal resistor'
( )
=T
BT exp0 kEB A/=
-60 -40 -20 0 20 40 60 80 100 12010
0
10
1
102
103
104
105
106
107
108
50
500
500 k
50 k5 k
Resistivity[
]
Temperature [oC]
Conductivity is
thermally activated
4ill EFFoC spinels:-nED$
)i-n9D$CoAe9D$
4ill ca. 1FFFoC rare eartho6ides eg.:#FRSm9DEEFR4b9DE
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E
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Intrinsic su!erionic conductor#aluminum o
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#Aluminiumo
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7igh energy density+ high
efficiency of charge3discharge&8""9R' and long cycle life+and is fabricated fromine6pensive materials.
The sodium is separated by a
beta-alumina solid electrolyte(BASE) cylinder from the
container of molten sulfur.
Sodium Sulfur Cell
+ + eNaNa l 222 )(
)(52)( 252 ll SNaeSNa ++ +
+ Cathode
- Anode
)(52)()( 52 lll SNaSNa +
Discharging
Charging
)()()(52 52 lll SNaSNa +
7igh operating
temperatures of EFF toEF TC and the highlycorrosive sodiumpolysulfides and sodium.
+
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Solid =
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Solid electrolyte# Solid =
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0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
-3
-2
-1
0
1
2
3400500600700800900
T [C]
103/T [K-1]
log
(t)
[S/m]
intermediatetemperature
SOFC
ZrO2-based
GaO3-based
Bi2O
3-based
CeO2-based
S=FC Solid Ele8trolyteH7igh stability in air and alsostrongly reduced atmosphereat high temperature
4etragonal or cubic stabilizedrD9 &E+ resp. 8 molR N9DE inrD9'. 4hicness = 9FFm.
Stability other materials &e.g.doped CeD9' in reducedatmosphere is not sufficient./artial reduction gives
electronic conductivity!
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Oxygen sensor (lambda sensor)
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Cm7n &mn3$'D9 mCD9 n3979D
=
exhaustO
AirO
p
p
F
RTE
2
2ln4
V1 fuel e6cess
@1 stoichiometric combustion
1 o6ygen e6cess
,elivered amount of D9
Stoichiometic amount of D9@
Oxygen sensor (lambda sensor)
exhausOp 2Signal
lambda
sensor
Oxygen sensor (lambda sensor)
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Oxygen sensor (lambda sensor)
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Summary
Itinerant and localized electrons &holes' in solids
H-ott7ubbard transition
HStructure influence
H,oping &stoichiometry'
e
Ions in solids as charge carriers