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Hiroyuki KOIZUMI
1. Principle
Seebeck effect
Peltier effect
Thomson effect
Thermoelectric effect
Δ𝑇
𝐼
Δ𝑉
𝑄
𝐼 𝑄Heattransfer
Current
Voltagedifference
Temperaturedifference
Seebeck effect
Peltier effect
Thomson effect
Δ𝑉 = −𝑆Δ𝑇
𝑄 = Π𝐴 − Π𝐵 𝐼
𝑄 = −𝜅𝐼Δ𝑇
Thermoelectric effect
Peltier effect
Thomson effect
𝑄 = Π𝐴 − Π𝐵 𝐼
𝑄 = −𝜅𝐼Δ𝑇
Electricity Heat
Joule heating 𝑄 = 𝑅𝐼2Generation
Transfer (Q>0 = output)
Transfer
Peltier effect
Thomson effect
𝑄 = Π𝐵 − Π𝐴 𝐼
𝑄 = 𝜅𝐼Δ𝑇
Electricity Heat
Joule heating 𝑄 = 𝑅𝐼2Irreversible
Reversible
Reversible
Thermoelectric EMF(熱起電力)
Seebeck coefficient or Thermopower (熱電能)
Found by T.J. Seebeck
Seebeck effect (1821)ゼーペック効果
𝑇 𝑇 + Δ𝑇
Δ𝑉
Δ𝑉 = −𝑆 ΔT
𝑇𝐴 𝑇𝐵
𝑉𝐴𝐵
𝑉𝐴𝐵 = − 𝐴
𝐵
𝑆 𝑇 𝑑𝑇
Seebeck effect (1821)ゼーペック効果
8
Thermal equilibrium condition with Electron diffusion
No temperature gradient case
With temperature gradient case
heating
Same temperatures
Charge is carried by electron flow
MaterialSeebeck
coefficient/(μV/K)
Selenium 895
Tellurium 495
Silicon 435
Germanium 325
Antimony 42
Nichrome 20
Molybdenum 5.0
Cadmium, tungsten 2.5
Gold, silver, copper 1.5
Rhodium 1.0
Tantalum -0.5
Lead -1.0
Aluminium -1.5
Carbon -2.0
Mercury -4.4
Platinum -5.0
Sodium -7.0
Potassium -14
Nickel -20
Constantan -40
Bismuth -77
Wide variety
Dependency on 𝑇
P-type semiconductor
Carrier: positive hole
Δ𝑉 = −𝑆 Δ𝑇
High 𝑇
Lower hole density(stochastically, by random walk)
Negative potential
Low 𝑇
𝑆 > 0
N-type semiconductor
Carrier: negative electron
Δ𝑉 = −𝑆 Δ𝑇
High 𝑇
Lower electron density(stochastically, by random walk)
Positive potential
Low 𝑇
𝑆 < 0
P-N junctionPCarrier: positive hole
NCarrier: negative electron
Found by J.C.A. Peltier
Peltier effect (1844)ペルチェ効果
Q = Π𝐼
A
ΠA𝐼 Π𝐵𝐼
BQAB = (Π𝐴 − Π𝐵)𝐼
QAB
Π: Peltier coefficient
Metal N-type P-typeEnergy
Electron energy state in solids
Metal AEnergy
Electron energy state in solids
Metal Bcurrent
Energy gap
Metal AEnergyMetal Bcurrent
Energy gap
HeatHeating
Metal AEnergyMetal Bcurrent
Energy gap
HeatCooling
N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy release
N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy injection
20
𝜅: Thomson coefficient
(electric specific heat)
Predicted by William Thomson (Lord Kelvin)
Thomson effect (1854)トムソン効果
𝑇 𝑇 + Δ𝑇
Q = −𝜅𝐼Δ𝑇
𝐼
Current
Energy
𝑇 𝑇 + Δ𝑇
Low energycarrier
High energycarrier
Heat
Current
Energy
𝑇 𝑇 + Δ𝑇
Low energycarrier
High energycarrier
Heat
Seebeck effect
Peltier effect
Thomson effect
Δ𝑉 = 𝑆Δ𝑇
𝑄 = Π𝐵 − Π𝐴 𝐼
𝑄 = 𝜅𝐼Δ𝑇
Thermoelectric effectAll the phenomena are caused by the current carriers
They should be related each other
𝑇 𝑇 + Δ𝑇
Δ𝑉
𝑄in 𝑄out
𝑄ex
𝑄J
𝑄in = Π 𝑇 𝐼
Current𝐼
𝑄out = Π 𝑇 + Δ𝑇 𝐼
𝑄J = −𝐼Δ𝑉
Peltier effect
𝑄J + 𝑄in − 𝑄out − 𝑄ex = 0 Energy balance
Note, voltage drop with current is −Δ𝑉
Δ𝑉
𝑄in 𝑄out
𝑄ex
𝑄J
Current𝐼
Δ𝑉 = −𝜌Δ𝑥
𝐴𝐼 − 𝑆Δ𝑇
Resistance effect+Seebeck effect
𝜌 : resistivity
𝐴 : cross section
𝑇 𝑇 + Δ𝑇
𝑄ex = 𝜌Δ𝑥
𝐴𝐼2 −
dΠ
𝑑𝑇− 𝑆 Δ𝑇𝐼
𝑄ex = 𝜌Δ𝑥
𝐴𝐼2 −
dΠ
𝑑𝑇− 𝑆 Δ𝑇𝐼
Thomson effect
𝑄 = −𝜅𝐼Δ𝑇
Joule heating
𝑄 = 𝑅𝐼2
𝜅 =dΠ
𝑑𝑇− 𝑆
The first Thomson relation
Current𝐼
Two different materials
Temperature difference
Voltage differenceand current flow
Adjusting voltage to neglect 𝐼2 term
Voltage supply
to 𝐼2 ≅ 0
B A
𝑇H
𝑇C𝑉
Voltage supply
to 𝐼2 ≅ 0
B A
𝑇 + Δ𝑇
𝑇
𝑉 = 𝑆𝐵Δ𝑇 − 𝑆𝐴Δ𝑇 + 𝛿𝑉
𝑉
to flow a little current
to compensate the thermoelectric EMF
𝑄T,𝐵 𝑄T,𝐵
𝑄P,𝐵𝐴
𝑄P,𝐴𝐵
𝑄P,𝐵𝐴 = Π𝐵𝐴 𝑇 + Δ𝑇 𝐼
𝑄P,𝐴𝐵 = Π𝐴𝐵 𝑇 𝐼
𝑄T,𝐵 = −𝜅𝐵Δ𝑇𝐼
𝑄T,𝐴 = 𝜅𝐴Δ𝑇𝐼
Π𝐴𝐵 = Π𝐴 − Π𝐵
𝑉 ≅ −𝑆𝐴𝐵Δ𝑇
𝑉𝐼 = 𝑄P,𝐵𝐴 + 𝑄P,𝐴𝐵 + 𝑄T,𝐵 + 𝑄P,𝐴
𝑑Π𝐴𝐵𝑑𝑇
− 𝑆𝐴𝐵 = 𝜅𝐴𝐵
𝑆𝐴𝐵 = 𝑆𝐴 − 𝑆𝐵
𝜅𝐴𝐵 = 𝜅𝐴 − 𝜅𝐵
(The first Thomson relation)
Energy balance
Entropy balanceIrreversible process, Joule heating, is neglected by 𝐼2 ≅ 0
𝑄P,𝐵𝐴𝑇 + Δ𝑇
+𝑄P,𝐴𝐵𝑇
+𝑄T,𝐵
𝑇 + Δ𝑇/2+
𝑄T,𝐴𝑇 + Δ𝑇/2
= 0
Π𝐵𝐴 𝑇 + Δ𝑇
𝑇 + Δ𝑇+Π𝐴𝐵 𝑇
𝑇+
𝜅𝐴𝐵Δ𝑇
𝑇 + Δ𝑇/2= 0
𝑑Π𝐴𝐵𝑑𝑇
−Π𝐴𝐵𝑇= 𝜅𝐴𝐵
Π𝐵𝐴 𝑇 + Δ𝑇
𝑇 + Δ𝑇=Π𝐵𝐴𝑇+dΠ𝐵𝐴d𝑇
Δ𝑇
𝑇−Π𝐵𝐴𝑇2Δ𝑇 + 𝑂 Δ𝑇2
Δ𝑇 → 0
𝑑Π𝐴𝐵𝑑𝑇
−Π𝐴𝐵𝑇= 𝜅𝐴𝐵
𝑑Π𝐴𝐵𝑑𝑇
− 𝑆𝐴𝐵 = 𝜅𝐴𝐵
Energy balance(The first Thomson relation)Entropy balance
Π𝐴𝐵𝑇= 𝑆𝐴𝐵
The second Thomson relation
𝑑Π
𝑑𝑇− 𝑆 = 𝜅
Π
𝑇= 𝑆
Seebeck coefficient: 𝑆
Peltier coefficient: Π
Thomson coefficient: 𝜅
Three coefficients
Two relations
One of three coefficientsgives the other two coefficients
The only one directly measurable for individual materials
Onsager reciprocal relationsin Non-equilibrium thermodynamicsCheck it for more exact and more universal deviation.
Potential: 𝜙
Its conjugate: 𝑝
Its flow: 𝐽
𝐽1𝐽2⋮𝐽𝑁
=𝐿11 ⋯ 𝐿1𝑁⋮ ⋱ ⋮𝐿𝑁1 ⋯ 𝐿𝑁𝑁
∇𝜙1𝛻𝜙2⋮𝛻𝜙𝑁
𝐿𝑖𝑗 = 𝐿𝑗𝑖 Onsager reciprocal relations
𝑇, 𝜙𝑒 , 𝑃, 𝜇,⋯
𝑠, 𝑞, 𝑉,𝑚,⋯
(𝑝𝜙 has the unit of energy)
Intensive variables
Extensive variables
2. Thermocouple
Thermocouple thermometer
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
𝑉
𝑉𝐴𝐵 = − 𝐵
𝐴
𝑆 𝑇 𝑑𝑇
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
Unknown
𝑇𝐴
Known
𝑇𝐵
Unknown
𝑇𝐴
Known
𝑇𝐵
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
𝑉 Meter
Wire
Connection is (usually) necessary
Thermocouple
𝑉 Meter
𝑉𝑀𝐴 = − 𝑀
𝐴
𝑆w 𝑇 𝑑𝑇
𝑉𝐵𝑀 = − 𝐵
𝑀
𝑆w 𝑇 𝑑𝑇
Unknown
𝑇𝐴
Known
𝑇𝐵
What you measure is 𝑉𝐵𝐴 − 𝑉𝑀𝐴 − 𝑉𝐵𝑀
Thermocouple
𝑉
𝑉 = 𝐵
𝐴
𝑆+ 𝑇 − 𝑆− 𝑇 𝑑𝑇
Unknown
𝑇𝐴
Known
𝑇𝐵
What you measure is
Uniform temperature
Material-
Material+
𝑉
Use two materials(no other way)
Thermocouple
𝑉 = 𝐵
𝐴
𝑆+ 𝑇 − 𝑆− 𝑇 𝑑𝑇
Coupled propertiesare important
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
Thermocouple
T Range/℃ Remarks
-200 +1350High sensitivityHigh linearity
-40 +750High sensitivityEasily rusting
-270 +1300Wide range
stability
0 +1600High temperature
Expensive
-200 350Low temperature
Thermal noise
-110 +140Highest
sensitivity
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
Thermocouple
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
Color code
IEC BS
3. ThermoelectricPower Generation
44
Semiconductor thermoelectric circuit
Small heat engines Non-mechanical engine(Radioisotope generators) Recovery of waste heat (Energy Harvesting)
Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
45
Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Generated power W
Excited current IPtype
Ntype
Current𝐼
𝐼 =𝑉
𝑅 + 𝑟=𝑆 𝑇𝐻 − 𝑇𝐶𝑟 𝑚 + 1
𝑚 =𝑅
𝑟
𝑊 = 𝐼2𝑅 =𝑆2 𝑇𝐻 − 𝑇𝐶
2
𝑟 𝑚 + 1 2
h : hightA : cross section ρ : resistivity λ : thermal conductance
𝑟 =ℎp𝜌p
𝐴p+ℎn𝜌n𝐴n
Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
Current𝐼
Ohmic heating
Heat conduction
Peltier heat
h : hightA : cross section ρ : resistivity λ : thermal conductance
𝑄𝑂 = 𝑟𝐼2 𝑟 =
ℎp𝜌p
𝐴p+ℎn𝜌n𝐴n
𝑄𝐻 = Λ(𝑇𝐻 − 𝑇𝐶)Λ =
𝜆p𝐴p
ℎp+𝜆n𝐴nℎn
𝑄𝑃 = 𝑆𝑇𝐻𝐼
Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
Current𝐼
Heat balance on hot side
𝑄 +1
2𝑄𝑂 − 𝑄𝐻 − 𝑄𝑃 = 0
𝑄 = 𝑆𝑇𝐻𝐼 + Λ 𝑇𝐻 − 𝑇𝐶 −1
2𝑟𝐼2
Thermoelectric power generation
Theoretical thermal efficiency
𝑚opt = 1 +𝑍
2𝑇𝐻 − 𝑇𝐶
𝜂 =𝑇𝐻 − 𝑇𝐶𝑇𝐻
𝑚opt − 1
𝑚opt + 𝑇𝐶/𝑇𝐻
𝜂 =𝑊
𝑄= 𝑓(𝑇𝐻 , 𝑇𝐶 , 𝑚, 𝑍)
Maximum efficiency (impedance matching)
𝑍opt = S2 𝜆𝑝𝜌𝑝 + 𝜆𝑛𝜌𝑛
−2
𝑍 =𝑆2
Λ𝑟Figure-of-merit (熱電素子対の性能指数 )
Thermoelectric materials
49
Temperature dependence of ZT (dimensionless parameter)
p-type (left) and n-type (right) semiconductors
Design example
50
Specifications
p n
e [mV/K] 210 ‐170
r [mWm] 18 14
l [W/mK] 1.1 1.5
h [cm] 1.0 1.0
S [cm2] 1.3 1.0
TH=1,000K and TC=400K(S has been optimized)
Thermal efficiency
Output =4.5[W]
6
p n 380 10 [V/K]e e e
2
2 -1
max p p n n 0.00177[K ]Z e l r l r
opt 1.5m R r
max
1000 400 1.5 10.6 0.26 0.16
1000 1.5 400 1000
2 2
opt opt
opt
0.2280.004127
0.006886
TW R
R r
e
2.8mr W
=
Radioisotope Generator: RTG 原子力電池
Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)
Nuclear ReactorUse of nuclear chain reaction
Natural decay Chain reaction
Control the rateby the material and environment
Chain reactionUse of nuclear chain reaction
Electron
Nucleus
= Protons+ neutrons
Atom
Chemical energyUse of electron energy states
Electron
Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
540 W/kg
RTG~5 W/kg
SAP~50 W/kg(1 AU)
59
Radioisotope-Thermoelectric Generator
Electric output 290W/250W
Thermal Output 4,234Wt
TH 1000℃
Total mass 55kg
Pu mass 7.561kg
size 114cm×f42cm
Galileo RTG
Radioisotope Generator: RTG 原子力電池
Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)
VoyagerRTG was located with a distance from the main body.Power would be 73% of BOL after 39 years.
CuriosityRTG on the back (hip)
CassiniThree RTGswith a cover for each
New HorizonsThe latest RTG
Thank you