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Space probe to the Jupiter From JPL, NASARadioisotope
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
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