Electronic and Ionic Conductivity in Metal Oxides

8/12/2019 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

[email protected]


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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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3131

-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@


exhausOp 2Signal

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

Electronic and Ionic Conductivity in Metal Oxides

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