introduction to thermoelectric materials and...

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Thermoelectric Generator (PbTe)

Introduction to Thermoelectric Materials and Devices

3rd Semester of 20122012.03.21, ThursdayDepartment of Energy ScienceSungkyunkwan University

1 Thermoelectric Phenomena and Conversion Efficiency

2 Thermoelectric Transport Theory I : Electrical Properties

3 Thermoelectric Transport Theory II : Thermal Properties

4 Thermoelectric System : Current and Future of Modules

5 Materials Preparation : Bulk and Film

6 Measurement of Thermoelectric Properties

7 Applications : Power Generation and Heat Cooling

8 Mid-term Exam

9 Thermoelectric Materials : State-of-the-art

10 Thermoelectric Materials : Intermetallics

11 Thermoelectric Materials : Oxides

12 Thermoelectric Materials : Phonon Glass and Electron Crystal (PGEC) Materials

13 Theory and Modeling in Nanostructured Thermoelectrics

14 High efficiency in Low Dimensional Materials

15 Hybrid Energy Conversion Systems of Thermoelectrics

16 Final Exam

Plan

Thermoelectric Energy Conversion Efficiency

ellat

: Power Factor /2

lat : Lattice Thermal Conductivity

el : Electronic Thermal Conductivity

TZT

2

or S : Seebeck Coefficient

(Thermoelectric Power)

: Electrical Resistivity

: Thermal Conductivity

Dimensionless Figure of Merit, ZT

lateltot

TLel

T

cBB

lat dxx

xxkk /

0 2

43

2 ]1)[exp(

)exp()(

2

)(

)(4)()(3*

02

*1

2*

2

*

0

2

2

F

FFF

e

kL B

Thermal Conductivity

L = 2.44108 W/K2

Electronic thermal Conductivity : Wiedemann–Franz law

lat : Lattice Thermal Conductivity

el : Electronic Thermal Conductivity

Metallic conductor

Semiconductor

Lattice thermal Conductivity : Debye-Callaway Model

lateltot

Thermal Conductivity

lat : Lattice Thermal Conductivity

el : Electronic Thermal Conductivity

(a) The binary -FeSi2, Cr, Co, Cu, and (b) Ge doped -FeSi2.

Quiz

Dumbbell-shape, Rubber (Bonding), Metal Ball (Atoms), Ball Size=Atomic Mass

Phonon :Particles derived from the vibrations of atoms in a solid

Phonon

Phonon :Particles derived from the vibrations of atoms in a solid

Angular frequency of Phonon, Dispersion Curve

Acoustic Phonon

Coherent movements of atoms ofthe lattice out of their equilibriumpositions2 Transverse Mode (TA)1 Longitudinal Mode (LA)

Optical Phonon

Out of phase movement of theatoms in the lattice, one atommoving to the left, and its neighbourto the right:Freedoms in the primitive cell3N-3 (N : number of atom)

lvC svlat 3

1

Thermal Conductivity

Particle of phonon with velocity of s

T

Bv dxx

xxTNkC

/

0 2

4

]1)[exp(

)exp()(9

kTx

Cv : Specific Heat CapacityVs : Velocityl : Phonon Mean Free Path (Phonon-phonon, Imperfection)

At high temperature, T >

Bv NkC 3

At low temperature, T <

34 )(5

12

D

Bv

TNkC

Debye’s T3 law

Constant value

Heat Capacity

ThermalConductivity

Mean Free Path

Temperature

Lattice Thermal Conductivity : Variation Method by G.A. Slack

22 Dlat MB

Number of Atoms, n=1

B : constant, M : Mean atomic mass, : Mean atomic size, : Gruneisen Parameter

Number of Atoms, n2

Tn

MB Dlat

23/2

2

: Gruneisen Parameter

The effect that changing the volume of a crystal lattice has on its vibrational properties,as a consequence, the effect that changing temperature has on the size or dynamics of the lattice

vmT CVB /3

BT : Bulk Modulus, Vm : Molar volume, Cv : Specific heat capacity

Only Acoustic Phonon!

Lattice Thermal Conductivity : Debye-Callaway Model

T

c dxx

xxI

/

0 2

4

1]1)[exp(

)exp(

)()(2 3

2

21

3

2 I

II

kk BBlat

T

N

c dxx

xxI

/

0 2

4

2]1)[exp(

)exp(

T

N

c

N

dxx

xxI

/

0 2

4

3]1)[exp(

)exp()1(

1

kTx

U : Umklapp, N : Normal, PD : Point Defect, B : Boundaries, S : Strains, D : Dislocations, P : Precipitates, BP : Bipolaron

Scattering Process

Relaxation time based model by Klemens and Callaway

Inverse Relaxation time

111111111 BPPDSBPDUNc

Lattice Thermal Conductivity : Debye-Callaway Model

111111111 BPPDSBPDUNc

)3/exp(321TTBU

2

2

2

m

hB

Umklapp scattering (Phonon-Phonon Scattering, q1+q2=q3+G, Thermal Resistance)

T

M

h

kBlat 2

333/1 )

2(4

5

3

Normal scattering (Phonon-Electron Scattering, q1+q2=q3)

A scattering process which conserve the total momentum of a system

A scattering process which do not conserve the total momentum of a system

321TBN

TBN

21

At Low Temp.

At High Temp.

TBN

21

At High Temp.

At Low Temp.

Leibfried and Schomann Model

)4/( 3

0 A

41 APD

2)/)(1( avMM

Lattice Thermal Conductivity : Debye-Callaway Model

0 is the unit cell volume, is the sound velocity

Point Defect Scattering (Alloy Disorder, ABC A1-XA’XBC)

M is the difference between the mass of the impurity and that of host.

is relative concentration of impurity atom

For a compound AxByCz, the composite , denoted by (AxByCz),

)()()(

)()()(

)()()(

)( 222 Cm

m

zyx

zB

m

m

zyx

yA

m

m

zyx

xCBA

av

C

av

B

av

Azyx

)/()( zyxzmymxmm CBAav

111111111 BPPDSBPDUNc

Temperature Dependence of Thermal Conductivity in Crystals

Thermal Conductivity

300 400 500 600 700 800 900 1000

3

4

5

6

7

8

9

10

11

TiNi0.9

Pt0.1

Sn

TiNi0.95

Pt0.05

Sn

Ti0.9

Zr0.1

NiSn

Ti0.9

Hf0.1

NiSn

TiNiSn

TiNiSn0.9

Si0.1

TiNiSn0.95

Si0.05

Therm

al C

onductivity (

W/m

K)

Temperature (K)

The Most Effective Element is Hf

300 400 500 600 700 800 900 1000

3

4

5

6

7

8

9

TiNi0.9

Pt0.1

Sn

TiNi0.95

Pt0.05

Sn

Ti0.9

Zr0.1

NiSn

Ti0.9

Hf0.1

NiSn

La

ttic

e T

he

rma

l C

on

du

ctivity (

W/m

K)

Temperature (K)

TiNiSn

TiNiSn0.9

Si0.1

TiNiSn0.95

Si0.05

Lattice Thermal Conductivity

Ti (MTi=48) : Hf (MHf=179) and Zr (MZr=91)

Hf

LvB /1

Lattice Thermal Conductivity : Debye-Callaway Model

Boundary

L : Grain size

111111111 BPPDSBPDUNc

T

e

k

Tk

E

b

b B

B

g

BP

22

2][]4[

)1(

Dislocation

3

2

3/4

01

V

VNDcore

Precipitate

1111)( lsP v : cross section of particle

: density of particle

Bipolar Thermal Conductivity (At high temperature)

22106.0 bNDscrew

1111 edgescrewcoreD ND : dislocation line density

b : the magnitude of Burgers vector

Appl. Phys. Lett. 79, 4316 (2001)

BPlateltot

Scattering Processes on in Debye-Callaway Model

Phys. Rev. 132, 2461 (1963)

How to Reduce Thermal Conductivity?

Phonon Scattering by imperfections = Limiting the phonon mean free path

Phys. Rev. A 136, 1149 (1964)

Minimum Lattice Thermal Conductivity

Proposed by G.A. Slack

opactot

minminmin

)()3

4(

2

33/22

3/1

min

c

Bac

n

k

nc : Number of atoms in a primitive unit cell

)1

1(2 3/1

2

min

c

Bop

nh

k

For Example, IrSb3

cmKmWtot

/12.287.1min

cmKmW /160

40 times

3 : Average volume per atom in 1024 cm3

: Debye Temperature

)/(72.297 v

Anderson’s Expression

333

12

)(

3

LT vvv

TZT

2

40 times??

At high temperature

Temperature Dependence of Thermal Conductivity in Crystals

Temperature Dependence T3 at low temp., T1 at high temp

Phys. Rev. 132, 2461 (1963)

Dominant Mechanism : Umklapp Scattering

Temperature Dependence of Thermal Conductivity in Crystals

Polycrystalline Samples with Constituent Substitution PRB. 63, 014410 (2000)

Dominant Mechanisms : Umklapp, Boundary, Point Defect Scattering

Co1-xFexSb3

Boundary, Point Defect Scattering

Thermal Conductivity

300 400 500 600 700 800 900 1000

2

4

6

8

10

12

(8%)

(21%)

(53%)

Th

erm

al C

on

du

cti

vit

y (

W/m

K)

Temperature (K)

IrSb3

La0.1

Ir4Ge

0.3Sb

11.7

La0.3

Ir4Ge

0.9Sb

11.1

La1Ir

4Ge

3Sb

9

Rattling Effect

Thermal Conduction in Amorphous

The tetragonal unit cell of Tl5Te3 as seen perpendicular to the c axis. The four differentcrystal sites and their coordination polyhedra are shown. The tellurium atoms are depictedin black with the coordination for the 4a site and the 8h site shown in the lower right andon top, respectively. The thallium atoms are shown in white on the 16l site, coordination asin the lower left, and checkered on the 4c site, where they are octahedrally coordinated(center). In the ternary compounds the additional atoms are substituted on the 4c site.

Temperature Dependence of Thermal Conductivity in Crystals

Tl9BiTe6

Temperature Dependence of Thermal Conductivity in Crystals

Deviation from T3 dependence in Single Crystal of 12CaO7Al2O3CaO : ~ 15 W/mKAl2O3 : ~ 30 W/mK

T2 dependence at low temperature : Amorphous-like thermal conduction

Phonon Mean Free Path : 0.7 nm

Thermal Conduction in Amorphous

T 3

T 2

Amorphous-like Thermal Conduction in Crystals

Amorphous-like Thermal Conduction in Crystals : Ionic Materials

Nolas et al. APL, 2000

A8B16C30A= Na, Ba, Sr, Eu, etcB = Al, GaC= Si, Ge, Sn

Amorphous like thermal conductivity

Low thermal conductivity High ZT over 1

Amorphous-like Thermal Conduction in Crystals : Clathrate

Thermal Conduction in Amorphous

Thermal Conduction in Amorphous

Two-level system or Tunneling state

A particle in an asymmetric potential well.Two minima differ in energy by an amount 2, which we will call the asymmetry.

Two lowest states with relative energies of =(o2 + 2)1/2, where 2o, the coupling energy, is theenergy difference between the two lowest energystates in the symmetric case.

The contribution of the tunneling states to thethermal properties depends critically on thenumber of states with energy between and + d.

Static Description

Atoms occupying one of two adjacent minima are assumed to tunnel quantum mechanically tothe other, leading to a splitting of the ground state

The inevitable variations in local environment present in the amorphous solid give rise to adistribution of these splittings which is almost constant in energy,

In a perfect crystal, each atom is constrained by symmetry to occupy a single potentialminimum.

At low temperatures a quantum mechanical description is necessary, and tunnelling of theatom from one minimum to another gives rise to the very small energy splittings (less than 104

eV) needed if the states are to be observed in thermal experiments at 1 K and below.

Many defects, however, can be represented microscopically as interstitial or substitutionalimpurity atoms or molecules moving in a multi-minima potential provided by the neighbours.

)2/coth(2 4

2

0

5

21

TkEE

vBTS

Presentation Articles by Group 1

By SYED WAQAR HASAN @ 2012.03.22

Seebeck Coefficient

• Variable-Range Hopping conduction• Electron-Electron Interaction• Electron Localization• Sign Change of Seebeck coefficient

By YunOk Kim @ 2012.03.29

Presentation Articles by Group 1

By HyunA Moon @ 2012.03.29

Seebeck Coefficient

By DongMok Lee @ 2012.04.05