oxides for thermoelectricity - ucsb mrsecseshadri/2012-summerschool-talks/ucsb-2012-hebert.pdf ·...

111
Oxides for thermoelectricity Sylvie Hébert Laboratoire CRISMAT UMR6508 CNRS et ENSICAEN UCSB – ICMR Summer School on Inorganic Materials for Energy Conversion and Storage August 2012

Upload: others

Post on 23-Mar-2020

3 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxides for thermoelectricity

Sylvie HébertLaboratoire CRISMAT

UMR6508 CNRS et ENSICAEN

UCSB – ICMR Summer School on Inorganic Materialsfor Energy Conversion and Storage

August 2012

Page 2: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Laboratoire CRISMATCristallographie et Sciences des Matériaux

Caen

Page 3: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

CRISMAT : some figures

120 persons 47 researchers 15 post-doc 42 Ph-D students 125 publications per year

Search for new oxides : high Tc superconductors, colossal magneto-resistance, thermoelectrics, multiferroics…

And Beyond oxides

Page 4: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Thermoelectric Activities

7 permanent staff + 1 engineer + students / postdocs + the rest of the lab!

→ Synthesis / Processing

→ Low and high T thermoelectric properties

→ Modelization of the thermoelectric properties

→ Module and module testing

Ramzy Daou, Franck Gascoin, Christophe Goupil, Emmanuel Guilmeau, Sylvie Hébert, Antoine Maignan, Jacques Noudem

Page 5: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

TechniquesCristallography (8 diffractometers)

80 furnaces Thin-films (PLD’s)

5 TEM, 3 SEMthermomechanicaltests

+ SPS

Page 6: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Low T properties

3 SQUID magnetometersHmax =5.5T

2K < T < 400K

4 ‘PPMS’Hmax = 14T

2K < T < 400K

DC and AC magnetization

DC and AC magnetizationMagnetization up to 1000K (VSM)

ResistivitySpecific heat

Seebeck coefficient Thermal conductivity

F. Janin, Photothèque CNRS

Thermopower and thermal conductivity measurements developped by Jiri Hejtmanek (Prague), using PPMS environment

Page 7: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

High T properties

ZT = 2T/

ZEM 3 Ulvac RikoCombined Seebeck and resistivity

measurement(RT to 700°C)

seebeck

Electrical resistivity

Thermal conductivity

= diffusivity x density x Cp

Netzsch

Page 8: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Modules

Page 9: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxides for thermoelectricity

• Introduction : Oxides specificities / Models for oxides /

Best thermoelectric oxides

• Semi – conductors : the Heikes formula• Degenerate semi-conductors : best n type oxides

• NaxCoO2 and misfit compounds

• Nanostructuration• Modules

• Conclusion

Aim of this tutorial : Best thermoelectric oxides /

show the specificities of oxides

Increaseof thecarrier density

Page 10: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Introduction

Page 11: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Property MaterialsMetals CrO2, Fe3O4, SrRuO3

Insulators Cr2O3, CoO, Fe2O3, Al2O3

Metal-Insulator Transition VO2, V2O3

Superconductors Ba(Bi,Pb)O3, YBa2Cu3O7

Piezo- and Ferroelectrics Pb(Zr,Ti)O3, BaTiO3

Catalysts (chemical, photo-) TiO2 , LaCoO3, BiMoO4

Ferro-, Antiferro-, Ferrimagnets CrO2, MnO, MnFe2O4

Pigments TiO2, CoAl2O4, Co3(PO4)2

Sensors CaxZr1-xO2-x, SnO2

Negative Thermal Expansion ZrW2O8

Ionic Conductors (battery, SOFC) LixMnO2, CaxZr1-xO2-x

Thermoelectrics NaxCoO2

Non-Linear Optics LiNbO3

Rutile, TiO2

YBa2Cu3O7

LiNbO3

LiMnO2

ZrW2O8

NaxCoO2

Why oxides?Strong interplay between spin/charge/lattice

Large family of compounds,Can be cheap, environment friendly and resistant in air

From M. Subramanian,OSU

Page 12: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Specificities of oxidesHigh T synthesis and synthesis possible in oxydizing environment

Oxides can be stable at high T and in airNon toxic elements, abundance of elements…

Strong electronic correlations→ Difficult to calculate the band structure→ But could be interesting for the Seebeck!

Kinetic energy ~ Repulsive Coulomb energy

Strong renormalization of effective massesNarrow bands

D. Basov et al., Rev. Mod. Phys. 83, 471 (2011)A. Georges et al., Rev. Mod. Phys. 68, 13 (1996)

Introduction

Possible tuning of the electronic correlations

Page 13: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

A. Georges et al., Rev. Mod. Phys. 68, 13 (1996)

Influence of electronic correlations

U increasing

Modification of DOS→ Increase of S?

J. Merino et al., PRB61, 7996 (2000)

Calcul of U impact on theSeebeck coefficient

Introduction

DOS

SeebeckMetal

Insulator

Page 14: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Bibliography : Thermoelectric oxides•First papers in the 60’s : SnO2, SbO2…

Degenerate n type semi-conductors

•1980’s : thermopower is used as a probe for the cuprates

•1990’s : Doped ZnO as best n type thermoelectric oxide (Ohtaki et al.)

•1997 : NaxCoO2 (Terasaki et al.)

Introduction

Page 15: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

PRB46, 14928 (1992)

Correlation between Seebeck / doping / Critical temperature

Introduction

High Tc superconductors

YBa2Cu3O7-

Page 16: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

M. Ohtaki et al., JAP79, 1816 (1996)

Zn1-xAlxO (x = 0 – 0.1)

Broadband model for extrinsic n type semiconductor

Large mobility of the carriers : 3 – 7cm2/Vs

= 40Wm-1K-1 at 300K=5.4 Wm-1K-1 at 1000°C

ZT = 0.3

But is too high !!!

Introduction

Page 17: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Metallicity (crystals) ~ 0.2 m cmLarge S S ~ +80 V/KSmall (polycrystals) Wm

(crystals) ~ 5Wm-1K-1

Na0.7CoO2‘ Phonon Glass / Electron crystal ’

I. Terasaki et al., Phys. Rev. B 56, R12685 (1997)

Na0.7CoO2P= 50 10-4 WK-2m-1

Bi2Te3P= 40 10-4 WK-2m-1

At 300K

Power factor P=S2/ at 300K

Co3+ (3d6) / Co4+ (3d5)

NaxCoO2 : Na+xCo3+

xCo4+1-xO2 Measurements on polycrystals

Introduction

Page 18: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

ZT of oxides

p type :NaxCoO2, Misfitoxides

n type : TCOs

1992 1994 1996 1998 2000 2002 2004 2006 2008 20100.00.10.20.30.40.50.60.70.80.91.01.11.2

FujitaNa

xCoO

2

R. FunahashiCa

3Co

4O

9 Whisker

n-type Bulk p-type Bulk p-type single crystals

M.Ohtaki(Zn,Al,Ga)O

G. XuCa

3Co

4O

9

H. ItaharaCa

3Co

4O

9

R. FunahashiBiSrCoO

L. BoscherCa(Mn,Nb)O

3

D. BérardanGe:In

2O

3H. Kaga

ZnO-In2O

3M.Ohtaki(Zn,Al)O

M.OhtakiIn

2O

3-SnO

2

ZT

(10

00

K)

Year

2 different families for the best thermoelectric oxides• Type p : oxides related to NaxCoO2, metallic and large S

• Type n : ‘transparent conducting oxides’, degenerate semi-conductors

ZT (type p ) > ZT (type n)

Introduction

Page 19: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

High T properties of NaxCoO2

K. Fujita et al. JJAP40, 4644 (2001)

Introduction

Crystal and polycrystal measurements

Crystals : 1.5 ×1.5 × 0.03 mm3

ZT ~ 1 for crystals only at 800K

ZT = 1

Page 20: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxides

MisfitsNaxCoO2Large S

+ metallic small p type

Model systemTexturation problems

Transparent conductors, DelafossitesLarge S, small

Large Mostly n type (some p type)

Reduction of through nanostructuration?

Semi-conductorsLarge

SLarge

n and p type Increase of S

through Heikes?

Introduction

Page 21: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Modelization of thermoelectric propertiesin oxides

Page 22: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

)(

22

le

TSTSZT

•Mott’s formula :FEE

B

EET

ekS

))(ln(

3

22

(E) = en(E) (E)

Models

U increasingDOS

Seebeck

Possible increase of S due to strong correlations?

Page 23: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

)(

22

le

TSTSZT

(E)en(E)ρ 1 • Resistivity :

A large mobility is required (difficult for oxides!)

• Thermal conductivityElectronic part related to -1 (Wiedemann Franz), usually

smallLattice part has to be minimized

Models

Page 24: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Models

)(3

/ 22

FBel ENkTC

FEEB

EET

ekS

))(ln(

3

22

Mott’s formula : influence of electronic correlations

K. Behnia et al. JPCM 16, 5187 (2004)

Free electron gas

Very similar to the electronic specific heat

Relationship between Seebeck and specific heat at low T??

is a probe of electronic correlations

Scattering parameter

Carrier density

Page 25: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

csteeNTSq Av

K. Behnia et al. JPCM 16, 5187 (2004)

Low T limit

2q5.0

Universal value for the ratio of S /

Limit T 0

)(3

/ 22

FBel ENkTC

Models

Page 26: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

The Heikes formula

P. M. Chaikin et al. Phys. Rev. B 13, 647 (1976)

Models

‘Simple combinatorial problem’

Calculated for organic thermoelectrics

High T limit

Page 27: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

The Heikes formula

Te/

TeS/S

S)1()2(

Hubbard model

S(1) , S(2) : depend on v and Q, velocity and energy operatorsValid for narrow band systems (localized correlated particles)

Limit T : S ~ entropy / carrier

for T

)x

x1ln(e

kS B

-0.4 -0.2 0.0 0.2 0.4-600

-400

-200

0

200

400

600

S(V

/K)

x

x = concentration of carriers

Holes

Electrons

P. M. Chaikin et al. Phys. Rev. B 13, 647 (1976)

Models

Page 28: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0.0 0.2 0.4 0.6 0.8 1.0-300-200-100

0100200300400500600

Co3+ LS + Co4+ LS : =1/2

S Hig

hT(

V/K

)x

Extra term in the Heikes formula due to the spin degeneracy

Mixed valency cation Mn+ / M(n+1)+ :

Spin entropy

1S21S2

1n

n

J. P. Doumerc JSSC 110, 419 (1994)

)xx-1ln(

ekS B

S=0 S=1/2

Models

Page 29: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0.0 0.2 0.4 0.6 0.8 1.0-400-300-200-100

0100200300400

(HS+LS)+HS

(HS+LS+IS)+(HS+LS+IS)

HS+HS

LS+LSLS+(HS+LS)

S HT(

V/K

)x

NaxCoO2 : Spin and orbital degeneracy Co3+ (3d6)/Co4+ (3d5)

J. P. Doumerc JSSC 109, 419 (1994)W. Koshibae et al., Phys. Rev. B 62, 6869 (2000)

)x1

xggln(

ekS

4

3B

x : Co4+ concentration

g4/g3 = 6

Large S in NaxCoO2Origin of the metallicity ?

Models

Page 30: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Rhombohedral crystalline field Lifting of the t2g levels degeneracy

D. J. Singh, Phys. Rev. B 61, 13397 (2000)

a1g : localized moments / heavy holese ’g : mobile carriers / light holes

FEE

22))ln((

e3k

TS

dE

d

Peak of N(EF)

S = +110V/K at 300Kcalculated for NaCo2O4

T. Yamamoto et al., Phys. Rev. B 65, 184434 (2002)

avec = N(E)<vF(E)2>

Band structure?

Metallic and large S

Models

Page 31: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

M. R. Peterson et al., PRB76, 165118 (2007)

‘Thermoelectric effectsin a strongly correlated model for NaxCoO2’

t-J model : t = hopping and J = spin couplingKubo formalismValid at any T (different from the limit T →)

S = Stransport + SHeikes

Black : Heikes formulaRed : S = Stransport + SHeikes

Models

In a large part of the phase diagram (x, T, t), the Heikes formula gives a good estimate of S

Page 32: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

The Kelvin formulaM. R. Peterson et al., PRB82, 195105 (2010)

t- J model for NaxCoO2 with x ~ 0.7

Heikes formula valid for T > 6 – 8 t(blue curve)

Models

Page 33: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Models NaxCoO2

First models : crucial role of the CoO2 layers

• Lifting of the t2g orbitals : Seebeck calculated from the Mott’s formula + metallicity

• High T : the Heikes formula, effect of the spin and orbital degeneracies

Beyond the CoO2 layers : the impact of the block layer?

Page 34: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Electronic correlations + Disorder effectsNaxCoO2

P. Wissgott et al., PRB84, 085129 (2011)

DMFT calculations

Disorder potential induced by Na+ cations

Models

Correlations effect Disorder effect

Page 35: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Semi-conducteurs : The Heikes formula

Page 36: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type p : Pr1-xCaxCrO3 Orthochromites

Perovskite structure

Pr3+1-xCa2+

xCr3+/4+O3 : 3d3/3d2

S. Pal et al., Eur. Phys. J. B 53, 5 (2006)

0 100 200 300 40010-1

100

101

102

103

104

105

106

107

Pr1-xCaxCrO3

x=0.3

(

.cm

)

T(K)

x=0.05

x=0.0

Introduction of holes : Activated behavior with

a decrease of

Page 37: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type p : Pr1-xCaxCrO3

0

200

400

600

800

1000

1200

100 150 200 250 300 350T(K)

Pr1-xCaxCrO3

S(V

/K)

x=0.0

x=0.3

x=0.05

OrthochromitesPr3+

1-xCa2+xCr3+/4+O3 : 3d3/3d2

S. Pal et al., Eur. Phys. J. B 53, 5 (2006)

300 350 400 450 500 550 600 650 700100

150

200

250

300

350

400

Pr0.7Ca0.3CrO3

Pr0.95Ca0.05CrO3 Pr0.95Sr0.05CrO3

S(V

/K)

T(K)

Cr4+

Decrease of S induced by doping S constant from 200K to high T

Page 38: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0.0 0.1 0.2 0.3 0.4 0.5-100

0100200300400500600700800900

1000

x (Ca concentration)

S(

V/K

)

Pr1-xCaxCrO3 Pr1-xSrxCrO3 calculated value taking orbital degeneracy calculated value from Heikes formula

)ln(e

k)x

x1ln(ekS spinorb

BB

Marsh and Parris, Phys. Rev. B 54, 7720 (1996)

K/V9.694133ln

ek B

3d3, S = 3/2

orb=1spin = 4

3d2, S = 1

orb=3spin = 3

Type p : Pr1-xCaxCrO3

Heikes formula withspin and orbital degeneracies

Page 39: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type p : Pr1-xCaxCrO3 Power factor

PF ~ 2.10-4 Wm-1K-1

Typical for oxides

Page 40: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

LaCoO3

Heikes formula : possible change of sign

)x

x1ln(e

kS B

x = carrier concentration

-0.4 -0.2 0.0 0.2 0.4-600-500-400-300-200-100

0100200300400500600

S(V

/K)

x

Co4+

(3d5)Co2+

(3d7)Depending on x, S>0 or S<0

Small x |S| very large

Change of sign in LaCoO3

Page 41: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

LaCoO3 : A site substitutionLaCoO3 x~0 : La3+Co3+O3

Sr2+ x>0 : La1-xSrxCo3+Co4+O3

Ce4+ x<0 : La1-xCexCo3+Co2+O3

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-600-500-400-300-200-100

0100200300400500600

Co4+Co2+ x

S (

V.K

-1)

A. Maignan et al., EPJB 39, 145 (2004)

50 100 150 200 250 300 350-400

-200

0

200

400

600

800

1000

LaCoO3

Ce0.01

Sr0.02

S (

V.K

-1)

T(K)

Change of sign in LaCoO3

Page 42: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

LaCoO3 : B site substitution

100 150 200 250 300 350

-300

-200

-100

0

100

200

300

400

500

600

700

800

900

1000

LaCo0.995Ti0.005O3

LaCoO3

S (

V/K

)

T(K)

LaCoO3 x~0 : La3+Co3+O3

Ti4+ x<0 : La(Co3+Co2+)1-xTi4+

xO3

Change of sign in LaCoO3

Page 43: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Formule de Heikes pour S, avec

K. Berggold et al., PRB72, 155116 (2005)

50 100 150 200 250 300 350-400

-200

0

200

400

600

800

1000

LaCoO3

Ce0.01

Sr0.02

S (

V.K

-1)

T(K)-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

-600-500-400-300-200-100

0100200300400500600

Co4+Co2+ x

S (

V.K

-1)

A. Maignan et al., EPJB 39, 145 (2004)

Co3+ IS

Co4+ LS

)x1

xggln(

ekS

4

3B

Spin only degeneracyg3 = 3 / g4 = 2

Type p : LaCoO3

Page 44: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Change of sign in LaCoO3

K. Berggold et al., PRB72, 155116 (2005)

LaCoO3

Single crystals measurements

Page 45: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type p : LaCoO3 LaCoO3 perovskites

J. Androulakis et al., APL84, 1099 (2004)ZT = 0.18 at 300K

LaCoO3

La0.95Sr0.05CoO3

La1-xSrxCo3+1-xCo4+

xO3

Semi-conducting with 5% hole doping

Eg decreases from 250 meV from LaCoO3to 36meV for La0.95Sr0.05CoO3

ZT=0.18

300K

27m.cm à 300K

Similar as Berggold et al., but much larger S

Oxygen stoechiometry?

Page 46: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Resistivity of La1-xMxCoO3

0 50 100 150 200 250 300 350 400 45010-2

10-1

100

101

102

103

104

105

106

107

Ti0.01 LaCoO3

Ce0.01

Sr0.02

(o

hm.c

m)

T (K)

Asymmetry between hole and electron doping

Change of sign in LaCoO3

(n type ) > (p type)

Typical of many oxides

Page 47: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

An eg electron Co2+ cannot move in a background of LS Co3+ , requires to flip other spins, wrong spin-states LS Co2+ and IS Co3+ instead of LS

A t2g hole Co4+ can hopin a background of LS Co3+

A. Maignan et al, Phys. Rev. Lett. 93, 026401 (2004)

Change of sign in LaCoO3

Spin blockade mechanism

3d5 / 3d6

3d6 / 3d7

Page 48: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

The 112- family

A. A. Taskin et al., PRB73, 121101 (2006)

The 112 family

Co3+/Co4+ or Co2+/Co3+

Pyramidal and octahedral sitesPossible spin state transitions

Page 49: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

A. A. Taskin et al., PRB73, 121101 (2006)

Calculations of spin/orbital degeneracies taking into account the different sites (octahedral / pyramidal)

Explains the larger values for n type (HS Co2+) compared to p type (LS Co4+)

Quantitative analysis of SThe 112 family

Differences in orbitaldegeneracies

for octahedra / pyramids

Page 50: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

High Temperature properties of manganites

T. T. M. Palstra et al., Phys. Rev. B 56, 5104 (1997)

W. Kobayashi et al., J. Appl. Phys. 95, 6825 (2004)

Spin degeneracy + Orbital degeneracy

S independent on x in a large range of x

)1S21S2ln(

ekS

1

0B

-20V/K -20V/K

-80V/K

S0 = 3/2 (Mn4+)S1 = 2 (Mn3+)

‘Probe’ of Jahn Teller effect

Page 51: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Semi – conducting oxides

The Heikes formula

→ Possibility to get p and n type oxides

→Spin and/or orbital degeneracies have to be taken into account for a quantitative analysis

→Explains the asymmetry between n and p type

But too large resistivity !

Page 52: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Degenerate semi-conductors : Best n type oxides

Page 53: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type n : ZnO

M. Ohtaki et al., JAP79, 1816 (1996)

Zn1-xAlxO (x = 0 – 0.1)

Broadband model for extrinsic n type semiconductor

Large mobility of the carriers : 3 – 7cm2/Vs

= 40Wm-1K-1 at 300K=5.4 Wm-1K-1 at 1000°C

ZT = 0.3

too high!

Page 54: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Perovskite Ca1-xSmxMnO3

Partially filled 3d levels

Mn3+ t2g3eg

1, HS JT

V(Mn)=4-x

Type n : CaMnO3

Page 55: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type n Perovskite Ca1-xSmxMnO3

A-site doping

T(K)0 50 100 150 200 250 300

10-3

10-2

10-1

( c

m

0.00

0.05

0.075

0.10

0.12 Tp

x

T (K)0 50 100 150 200 250 300

S (

V K

-1)

-400

-300

-200

-100

0

Ca1-xSmxMnO3

0.00

0.05

0.10

x

VMn > 3.5Partially filled 3d levels

Mn3+ t2g3eg

1, HS JTMn4+ t2g

3, HS

Polaronic transport

Type n : CaMnO3

J. Hejtmanek et al., PRB60, 14057 (1999)

Page 56: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Manganese oxidesn type SrMn1-xMoxO3

0 100 200 300 400 500 600 700 80010-2

10-1

100

101

102

103

x=0

x=0.04x=0.02

(

cm)

T (K)0 100 200 300 400 500 600 700 800-500

-400

-300

-200

-100

0

x=0

x=0.02

x=0.04

S(V

/K)

T (K)

SrMnO3 : Mn4+

Mo6+ Mn3+/Mn4+

Metallic up to high T / S linear in TPower factor increases as T increases : PF = 9.10-4Wm-1K-2 for x=0.02 at 800K

Measurements by J. Hejtmanek (Prague))lnTk/3ekπS BB2 Eσ(E)/(

3d3 t2g3 / 3d4 t2g

3eg1

Page 57: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type n : CaMnO3 Ca0.9M0.1MnO3

M. Ohtaki et al., JSSC120, 105 (1995)

ZT ~ 0.1 à 900°C

S ~ T

Carrier concentration1019 -1021 cm-3

J. L. Cohn et al., PRB72, 024422 (2006)

Page 58: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

n type : SrTiO3

SrTiO3 = non magnetic insulatorLa3+ : doping of Ti3+ in a matrix of Ti4+

T. Okuda et al., PRB63, 113104 (2001)

Sr1-xLaxTiO3

PF = 28 -36 WK-2m-1

But electrical conductivity too large!!

~ n(Constant mobility) Boltzmann model for a parabolic band

Degenerate semi-conductor

ZT = 0.22 for Sr0.9Dy0.1TiO3at 573K

H. Muta et al., J. Alloys and Comp.350, 292 (2003)

n ~1020 – 1021 cm-3

3d0 / 3d1

Page 59: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

smaller than for p type oxidesLess sensitive to correlation effects

n type : SrTiO3 Sr1-xLaxTiO3

T. Okuda et al., PRB63, 113104 (2001)

Carrier concentration1019 -1021 cm-3

Page 60: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type p : delafossites CuCr1-xMgxO2 delafossitesCrO2 layers : edge shared octahedra

T. Okuda et al., PRB72, 144403 (2005), Y. Ono et al., ICT 2006

ZT = 0.04 at 950K

CuRh0.9Mg0.1O2 : ZT = 0.15 à 1000KH. Kuriyama et al., ICT2006

Possibility to get p type oxides

Page 61: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

10 20 30 40 50 60 70 80 90

0.0 0.1 0.2 0.30.00

0.05

0.10

0.15

0.20

In2Ge2O7

In2O3

I (a.

u.)

2

In2G

e 2O7 f

ract

ion

Nominal Ge fraction

No substitution occursor

Small Ge solubility limit

SampleIn1.9Ge0.1O3

RBragg= 2.98, Chi2=1.28

XRDIn2-xGexO3

C. Marcel et al., Active and Passive Elec. Comp., 1997, Vol. 19, pp. 217-223

D. Bérardan et al., Solid Stat. Comm. 146 (2008) 97.

Doping or microstructure effect??

Page 62: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

SampleIn1.8Ge0.2O3

EDS analyses: Ge is not detectable in the grains

No grain size modification

In2Ge2O7

MicrostructureIn2-xGexO3

Page 63: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

In2O3 doped with Ge

D. Bérardan et al., Solid Stat. Comm. 2008

Type n : In2O3

0,00 0,05 0,10 0,15 0,200,0

0,1

0,2

0,3

0,4

0,5

1273 K 873 K 573 K 298 K

ZTGe fraction (x)

300 400 500 600 700 800 900 1000 1100-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

S (

V.K-1

)

T (K)

x=0 x=0.002 x=0.004 x=0.006 x=0.01 x=0.015 x=0.02 x=0.04 x=0.06 x=0.1 x=0.2 x=0.3

300 400 500 600 700 800 900 1000 1100

1

10

(m

.c

m)

T (K)

x=0 x=0.002 x=0.004 x=0.006 x=0.01 x=0.015 x=0.02 x=0.04 x=0.06 x=0.1 x=0.2 x=0.3

0,00 0,05 0,10 0,15 0,201

2

3

4

5

6

7

8

9

10

(W

/m.K

)

Ge fraction (x)

300K 573K 873K 1273K

In2-xGexO3

ZT = 0.4 à 1273K

Page 64: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Doped CaMnO3 : New preparation techniques

Soft chemistry techniques

L. Bocher et al., Inorg. Chem. 47, 8077 (2008)

Reduction of Possible size effect?

Page 65: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Degenerate semi - conductors

• Classical behavior which can be described by the Boltzmann modelVery small enhancement of the effective mass

• Mostly n type (p tye in delafossites)

• Problem : too large thermal conductivityMicrostructure modification is necessary to enhance ZT

Page 66: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

NaxCoO2 and related metallic compounds(p type)

Page 67: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Cobalt bronzes family ofNaxCoO2

C. Fouassier et al., JSSC6, 532 (1973)

J. Molenda, C. Delmas, P. Dordor, A. Stoklosa, Solid Stat. Ionics 12, 473 (1989)

Na0.7CoO2-

T

S

T

NaxCoO2Misfits

Page 68: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Metallicity (crystals) ~ 0.2 m cmLarge S S ~ +80 V/KSmall (polycrystals) Wm

(crystals) ~ 5Wm-1K-1

Na0.7CoO2‘ Phonon Glass / Electron crystal ’

I. Terasaki et al., Phys. Rev. B 56, R12685 (1997)

Na0.7CoO2P= 50 10-4 WK-2m-1

Bi2Te3P= 40 10-4 WK-2m-1

At 300K

Power factor P=S2/ at 300K

Co3+ (3d6) / Co4+ (3d5)

NaxCoO2 : Na+xCo3+

xCo4+1-xO2 Measurements on polycrystals

Introduction

Page 69: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Heikes formula : doping influence?Band structure influence : peculiarity of CoO2 layers ?

Role of separating block layers?

b2

a NaxCoO2KxCoO2, …

Misfits

NaxCoO2Misfits Lamellar oxides with CoO2 layers

Triple AO layer (NaCl-type)

Misfit family : 2, 3 or 4 separating layers

Page 70: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

M. Blangero et al., Inorg. Chem. 44, 9299 (2005)

KxCoO2

Modification of the block layersNaxCoO2Misfits

Page 71: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0 50 100 150 200 250 30001234567

'Tl0.4SrCoO3+'

'Ca3Co4O9'

(10

-2

cm)

T(K)

Misfits

Modification of the block layersNaxCoO2Misfits

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

'Tl0.4

SrCoO3+

'

'Ca3Co

4O

9'

S(V

/K)

T(K)

Page 72: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0 50 100 150 200 250 300

0

20

40

60

80

100

120

140

160

As-prep.

Po2

S(V

/K)

T(K)

Unique behavior of CdI2 type layers: Comparison with other oxides

Perovskite Sr2/3Y1/3CoO8/3+

Corner shared octahedraedge shared octahedra

A. Maignan et al., JSSC178, 868 (2005)

Metallicity

Seebeck 0

NaxCoO2Misfits

Page 73: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxygen content influence

Ca3Co4O9+Co4+

M. Karppinen et al., Chem. Mater. 16, 2790 (2004)

NaxCoO2Misfits

Misfits : S the largest for the smallest ‘Co4+’ content

Page 74: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Doping effect in the misfit family

21 /4v

bbCo

Ca2CoO3NaCl-like

CoO2CdI2-like

Ca3Co4O9 Electronic neutrality :[Ca2CoO3±]RS[CoO2]b1/b2

2+ 2-3+ Co 2-

>0

Modification of vCo via and b1/b2

Link between vCo and S?

Page 75: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0 100 200 300 400

100

101

102

BSCO

BPSCO

(m

cm

)

T(K)

BiSrPbCoO single crystals : modification of

[Bi1.5Pb0.5Sr2O4-δ][CoO2]1.86[Bi1.74Sr2O4][CoO2]1.82

Metallic behavior down to 5K with = AT2

Characteristic of electronic correlations

Substitution of Bi3+ by Pb2+ : decrease of Increase of vCo

21 /4v

bbCo

Page 76: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0 50 100 150 200 250 3000

20

40

60

80

100

120

BSCO

BPSCO

S(V

/K)

T(K)0 100 200 300 400

100

101

102

BSCO

BPSCO

(m

cm

)

T(K)

Increase of ‘Co4+’ associated to a decrease of S

Generalized Heikes formula : increase of vCo

3.59 for BSCO and 3.65 for BPSCO

NaxCoO2Misfits BiSrPbCoO single crystals : modification of

)x1

xggln(

ekS

4

3B

Page 77: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

BiSrPbCoO single crystals : modification of

0 50 100 150 200 250 3000,000

0,005

0,010

0,015

BPSCO

BSCO

RH

(cm

3 /C)

T(K)

At 100K1.06 × 1021 cm-3 for BSCO 1.73 × 1021 cm-3 for BPSCO

W. Kobayashi et al., JPCM21, 235404 (2009)

t- J model : Linear T dependence of RHt ~10 – 40K

Justifies the Heikes formulaB. Kumar et al., PRB68, 104508 (2003)

Y. Wang et al., cond-mat/0305455G. Leon et al. , PRB78, 085105 (2008)

Increase of vCo3.113.18

NaxCoO2Misfits

Page 78: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

W. Kobayashi et al.

0 50 100 150 200 250 3000

2

4

6

8

10

12

14

BiBaCoO

BiSrCoO

BiCaCoO

(m

.cm

)

T(K)0 50 100 150 200 250 300

0

20

40

60

80

100

120

140

160

BiBaCoO

BiCaCoO

BiSrCoO

S (

V/K)

T(K)

0 50 100 150 200 250 3000.000

0.005

0.010

0.015

0.020

0.025

0.030

BiBaCoO

BiSrCoO

BiCaCoO

RH(c

m3 /C

)

T(K)

Influence of b1/b2

b1/b2

21Co b/b

4v

If b1/b2 , concentration of Co4+

S at 300K depends on Co4+

modified through b1/b2

NaxCoO2Misfits

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.0080

90

100

110

120

130

140

150

BiBa

BiSr

BiPbCa

BiCa

S 300K

(V/

K)

b1/b2

Carrier concentration ~ 1022 cm-3, larger than for conventional thermoelectrics

b1 : NaCl layers / b2 : CoO2 layers

Page 79: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Heikes formula

)xx-1

ggln(

ekS

3

4B

Co valency in BiCaCoO/ BiSrCoO / BiBaCoO?

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0-300

-200

-100

0

100

200

300

400

500

600

Spin degeneracyCo3+ S = 1/2 + Co4+ S=0 : =1/2

Heikes = 0

Spin and orbital degeneracyCo3+ LS + Co4+ LS : =1/6

S Hig

hT(

V/K)

x

3.05 -3.153.5 -3.7 for g4 / g3 = 6Hall effectHeikes (S at 300K)

NaxCoO2Misfits

Page 80: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Carrier concentration10

8

6

4

2

0

10

8

6

4

2

0

single hole-like fermi surface (a1g character)

21Co b/b

4v

kF=0.57±0.05 Å-1 for BiBaCoO

similar to kF of NaxCoO2 (x=0.7)

Collaboration with V. Brouet et al., LPS Orsay

Co3.3+ for BiBaCoO

Reliable data for vCo are obtained for BiBaCoO

Co3.2+ for BiSrCoOCo3.1+ for BiCaCoO

(=const)

V. Brouet et al., PRB76, 100403 (2007)

ARPES

NaxCoO2Misfits

Page 81: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Heikes formula

)x1

xggln(

ekS

4

3B

g3 / g4 = 1/2 instead of 1/6 Confirms the results in BiCaCoO : vCo = 3.24

M. Pollet et al., JAP101, 083708 (2007)

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0-300

-200

-100

0

100

200

300

400

500

600

Spin degeneracyCo3+ S = 1/2 + Co4+ S=0 : =1/2

Heikes = 0

Spin and orbital degeneracyCo3+ LS + Co4+ LS : =1/6

S Hig

hT(

V/K)

x

NaxCoO2Misfits

Co valency in BiCaCoO/ BiSrCoO / BiBaCoO

3.24M. Pollet et al.,

JAP101, 083708 (2007)

3.1 -3.3J. Bobroff et al., PRB76, 100407

(2007)

3.3V. Brouet et al.,PRB76, 100403

(2007)

3.05 -3.15W. Kobayashi et al.

3.33P. Limelette et al., PRL97, 046601

(2006)

3.5 -3.7

SusceptibilitéBiCaCoO

RMNARPESBiBaCoO

Effet HallSeebeck avec S(H)g3/g4 = 1BiCaCoO

Heikesg3/g4 = 1/6S à 300K

Page 82: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Orbital filling in NaxCoO2 and misfit cobaltiteswith edge-shared CoO6

Ligand field splitting :trigonal distortion

MB Lepetit

LS Co3+/Co4+ mixed-valency

metallicity

a1g

e’g

= 1/61 for Co3+ but 2 instead of 6 for Co4 +

= 1/2

NaxCoO2Misfits

Page 83: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

NaxCoO2Misfits Influence of electronic correlations

P. Limelette, PRB71, 233108 (2005)

csteeNTSq Av

For T→0

P. Limelette, PRL97, 046601 (2006)

S ~ T

Page 84: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Low T : Spin entropy

BiCaCoO : excess of S at low TA. Maignan et al., JPCM 15, 2711 (2003)

Observed also in NaxCoO2[Wang et al. Nature 423, 425 (2003)]

NaxCoO2Misfits

Page 85: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Scaling MR et MTEPLien avec la susceptibilité

Spin entropy at low TMisfit BiCaCoO

Na0.7CoO2

A. Maignan et al., JPCM15, 2711 (2003)

Y. Wang et al., Nature423, 425 (2003)

Scaling law for S(H) : paramagnetic spins S=1/2Brillouin function

P. Limelette et al., PRL97, 046601 (2006)

Decrease of S under field at low TDue to the alignement of paramagnetic spins

Peak of susceptibility

Page 86: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Misfits

CoO2 (type CdI2)

NaCl-like triple layer (RS)

Co3+ (3d6) / Co4+ (3d5)Low spin : t2g orbitals+ triangular network

0 50 100 150 200 250 300100

101

102

103

104

BiBaCoOBiSrCoO

BiCaCoO

(m

.cm

)

T(K)

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

BiBaCoO

BiCaCoO

BiSrCoO

S (

V/K)

T(K)

For T > 100K : metallicity + large S

• High T : Seebeck depends on Co4+

Heikes formula with spin / orbital degeneracye)

• Low T : electronic correlations : S ~ T+ spin entropy depending on doping

• High T limit : small t from Hall effect. Justifies the Heikesformula

S. Hébert et al., PRB64, 172101 (2001), P. Limelette et al., PRL97, 046601 (2006), W. Kobayashi et al., JPCM21, 235404 (2009)

Misfit oxidesNaxCoO2Misfits

Page 87: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

0 50 100 150 200 250 3000

20406080

100120140160

S(V

/K)

T(K)

Thermoelectric power of misfits

Spin entropy (depending on doping)Electronic correlations : S ~ T

High T Seebeck, depends on Co4+

(Heikes formula with = 1/2)

BiCaCoO

Page 88: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Power factor

0 100 200 3000

1

2

3

4

Temperature (K)

Pow

er F

acto

r (W

/cm

K2 )

BiSrCoO

BiPbSrCoO

BiBaCoO

BiCaCoO

enhancement for BiBaCoO and BiPbSrCoO

P is almost independent of carrier concentration

In conventional semiconducting thermoelectric material such as Bi2Te3, n is an important parameter to tune the properties.

How to modify the electronic properties?Influence of the block layer?

2.10-4 Wm-1K-2 at 300K

NaxCoO2Misfits

Page 89: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Role of the block layer?

• Role of Na+ : Curie-Weiss behavior obtained by introducing theelectrostatic potential of Na+ (Co3+ S = 0 / Co4+ S = 1/2)C. Marianetti et al., PRL98, 176405 (2007)

•Kagomé lattice in NaxCoO2 with x = 2/3 : strong electronic correlationsF. Lechermann et al., PRL107, 236404 (2011)

Curie-Weiss

NaxCoO2Misfits

Page 90: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

NaxCoO2Misfits High T measurements in Ca3Co4O9

Increase of S at high T

Measurements in air?

M. Shikano et al., APL82, 1851 (2003)

Page 91: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

NaxCoO2Misfits Thermal conductivity

Measurements of single crystals (Harman method)

A. Satake et al., JAP96, 931 (2004)

smaller in misfits

Influence of incommensurability?

Page 92: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

• Charge transfer between the layers : S300K mostly depends on the ratio Co3+/Co4+

• Low T : electronic correlations influence (S ~ T) + S(H) term

• Small

Power factor is constant : modification of the block layers? Influence on thermal conductivity?

NaxCoO2Misfits Conclusion

Page 93: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Nanostructuration

Page 94: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

2DEG SrTiO3

Nanostructuration :Increase of S

2D electron gas in SrTiO3H. Ohta et al., Nat. Mater. 6, 129 (2007)

‘ZT’ = 2.4!

of SrTiO3 single crystals

SrTi1-xNbxO3

Page 95: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

NaxCoO2 nanowires

Sol-gel electrospinning

F. Ma et al., J. Phys. Chem. C 114, 22038 (2010)

~ .m?Resistivityoverestimated by 3 orders ofmagnitude by themeasurementtechnique?

Same technique as for Ca3Co4O9

Lin et al., J. Phys. Chem. C 114, 10061

(2010)

Nanostructuration

Page 96: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

J. Ravichandran et al., PRB85, 085112 (2011)

Strong correlations + Size effects

Correlation effect :

Behavior different from the oneclassical observed through thesurface diffusion mechanism(Fuchs – Sondheimer model)

Thin films of BiSrCoO misfits

Decoupling of resistivity and Seebeck?

Page 97: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxide modules

Page 98: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Modules Oxide prototypes

W. Shin et al., JJAP39, 1254 (2000)

n : Ba0.4Sr0.6PbO3 Z = 2.10-4 K-1 at 673K (ZT = 0.13)p : Li0.025Ni0.975O Z = 0.75 10-4 K-1 at 1273K (ZT = 0.095)

One leg : 4.8 ×4.9 × 17.5 mm3

One pair : 7.91mWTH = 987KT = 552K

1st prototype in 2000

Page 99: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Oxide prototypes

I. Matsubara et al., APL 78, 3627 (2001)

n : Ca0.92La0.08MnO3 / p : Ca2.75Gd0.25Co4O98 pairs 3 × 5 × 30 mm3

Th = 1046K , T = 390K, P=63.5mW

Modules

TC = 370°CTH = 650°C

Stability

Page 100: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Modules La0.9Bi0.1NiO3 / Ca2.7Bi0.3Co4O9

R. Funahashi et al., APL 85, 1036 (2004)R. Funahashi et al., JAP99, 066117 (2006)

n : La0.9Bi0.1NiO3 / p : Ca2.7Bi0.3Co4O91 jonction : TH = 1073K, T = 500K, P = 94mW

140 pairesTH = 1072K, T = 551K

For mobile phoneTH = 1072K!

Page 101: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Modules

0.150.0162NCa0.95Sm0.05MnO3/ Ca0.95Sm0.05MnO3

Present work

0.570.0312PNCa3Co4O9 / Ca0.95Sm0.05MnO3Sudhakar et al.

0.820.0898PN(Gd) Ca3Co4O9 / (La) CaMnO3Matsubara et al.

0.30.0342PN(Li) NiO / (Ba, Sr) PbO3Shin et al.

0.150.031PNCa2.7Bi0.3Co4O9 / La0.9Bi0.1NiO3Funahashi et al.

MFPower (W)Nb CoupleTypeMaterialsName

Comparison of modules

Manufacturing factorMF = Rideal / Rint,

S. Lemonnier, C. Goupil et al.

Important to optimize the contacts quality!

Page 102: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Type n : SrTiO3 dopé au La450mW/cm2 pour T = 360K

Modules and prototypesDevices

Page 103: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Stability problems

Page 104: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Thermal stability

Oxides : can be synthesized in air or controlled atmosphere at 800°C – 1500°C

Misfits : 800 - 1000 °C in air, or controlled atmosphereLa1-xSrxCo3+

1-xCo4+xO3 : 1250°C

Pr3+1-xCa2+

xCr3+/4+O3 : 1500°C in O2CuCr1-xMgxO2 : 1200°C in airCa0.9M0.1MnO3 : 1300°C in air

Zn1-xAlxO : 1400°C in airSr1-xLaxTiO3: 1400°CIn2O3 : 1300°C in air

Oxygen stoechiometry?

Page 105: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Perovskites

B. Dabrowski et al., JSSC170, 154 (2003)

Type n : manganese oxides

CaMnO3Stable jusqu’à ~ 700 -800°C

sous O2

Thermal stability

Page 106: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Misfits

Oxygen stoechiometry?

Y. Morita et al., JSSC177, 3149 (2004)

N2 annealing

Thermal stability

Thermogravimetric+ titration analysis

Page 107: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Synthesis and measurements conditions : ZnO

D. Bérardan et al., GDR Thermoélectricité, Grenoble, juin 2010

Page 108: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

D. Bérardan et al., GDR Thermoélectricité, Grenoble, juin 2010

Page 109: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Seebeck coefficient : Major role of the spin and orbital term

Importance of electronic correlations

Conclusion

• n type oxides : degenerate semi-conductorsSeebeck described in a first approach by Mott’s formula

• p type oxides

)xx-1ln(

ekS B

ZT (n type) < ZT (p type)Thermal conductivity : coming from the lattice

Page 110: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

How to enhance ZT??

Investigation of thermal conductivity

Nanostructuration and electronic correlations?

Low dimensional structures

Microstructures

Anionic subsitutions (oxyselenides)

Page 111: Oxides for thermoelectricity - UCSB MRSECseshadri/2012-SummerSchool-Talks/UCSB-2012-Hebert.pdf · influence of electronic correlations K. Behnia et al. JPCM 16, 5187 (2004) Free electron

Collaborators

Laboratoire CRISMATWataru Kobayashi (Tsukuba), Hidefumi Takahashi (Nagoya),

Antoine Maignan, Christine Martin, Denis Pelloquin, Olivier Perez

Patrice Limelette, LEMA, ToursJulien Bobroff, Véronique Brouet, LPS Orsay

This work is supported by FP7 European Initial Training Network SOPRANO (GA-2008-214040)