a straightforward technique for the measurement of the
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A straightforward 2ω technique for themeasurement of the Thomson effect
Isaac Haık DunnSupervisor: Antoine Maignan
Cosupervisors: Ramzy Daou, Mohamed Fall
Normandie Universite, ENSICAEN, CNRS, Crismat-Greensystech
October 18th, 2018
1
Outline
Thermoelectricity and the Thomson effect
Our 2ω methodPhysical descriptionPhysics of the systemGetting µ
Validation of the methodSimulationsSeebeck measurement
Conclusion
2
Thermoelectricity and the Thomson effect
+++
-- -
-- --
-- -
+++
+
+++
A
BB
Seebeck Peltier Thomson
BA
+-
A
+-
3
T(x)
0 1 2 3 4 5Position (mm)
295
300
305
310
Temperature
(K)
∆T = 10 K
300 302 304 306 308 310Temperature (K)
1.02
1.03
1.04
1.05
Resis
tance(Ω
)
∆RJ
∆RT
∆TJ
∆TT
Joule + ThomsonJouleNo current
4
Physics of the system
Question: How to relate V we measure with µ?
Easy: ∆V = RI =
∫ L
0[ρ0 + ρ1T (x)]Jdx
Heat eq.
κ∂2T
∂x2− µJ ∂T
∂x+ (ρ0 + ρ1T )J2 = 0
Solve for T (x), obtain ∆V in function of µ.
6
Physics of the system
Question: How to relate V we measure with µ?
Easy: ∆V = RI =
∫ L
0[ρ0 + ρ1T (x)]Jdx
Heat eq.
κ∂2T
∂x2− µJ ∂T
∂x+ (ρ0 + ρ1T )J2 = 0
Solve for T (x), obtain ∆V in function of µ.
6
Physics of the system
Question: How to relate V we measure with µ?
Easy: ∆V = RI =
∫ L
0[ρ0 + ρ1T (x)]Jdx
Heat eq.
κ∂2T
∂x2− µJ ∂T
∂x+ (ρ0 + ρ1T )J2 = 0
Solve for T (x), obtain ∆V in function of µ.
6
Physics of the system - AC method
When I = I0 sin(ωt)Joule heat ∝ RI 2 produces T oscillations at 2ω.
Thomson heat ∝ I produces T oscillations at 1ω.We measure V (t).Impact of the T oscillations on V :From Ohm’s law V = RI ≈ (R0 + R1T )I0 sin(ωt)Means V oscillations at 3ω (Joule) and 2ω (Thomson).
7
Physics of the system - AC method
When I = I0 sin(ωt)Joule heat ∝ RI 2 produces T oscillations at 2ω.Thomson heat ∝ I produces T oscillations at 1ω.
We measure V (t).Impact of the T oscillations on V :From Ohm’s law V = RI ≈ (R0 + R1T )I0 sin(ωt)Means V oscillations at 3ω (Joule) and 2ω (Thomson).
7
Physics of the system - AC method
When I = I0 sin(ωt)Joule heat ∝ RI 2 produces T oscillations at 2ω.Thomson heat ∝ I produces T oscillations at 1ω.We measure V (t).Impact of the T oscillations on V :From Ohm’s law V = RI ≈ (R0 + R1T )I0 sin(ωt)Means V oscillations at 3ω (Joule) and 2ω (Thomson).
7
T(x) revisited (alternating current)
0 1 2 3 4 5Position (mm)
295
300
305
310
Temperature
(K)
∆T = 10 K
Tavg.
300 302 304 306 308 310Temperature (K)
1.02
1.03
1.04
1.05
Resis
tance(Ω
)
∆RJ
∆RT
∆TJ
∆TT
2ω
1ω
8
Validation of the method
SimulationsWe solve the heat eq.
∇ · (κ∇T )︸ ︷︷ ︸Fourier
−µ ~J · ∇T︸ ︷︷ ︸Thomson
+ ρJ2︸︷︷︸Joule
+AεσS-B(T 4ref. − T 4)︸ ︷︷ ︸
Radiation
= CV∂T
∂t︸ ︷︷ ︸Transient
we extract µ and compare it with the closed-form expression wehave found
10
Validation of the method - µ results
0 100 200 300 400Temperature (K)
−16
−14
−12
−10
−8
−6
−4
−2
0
2
4
Tho
msoncoeffi
cient(µ
V/K)
NiNi, simPt, simPt, RobertsPt, AmagaiPt
−10
−9
−8
−7
11
Validation of the method
Seebeck coefficient measurementWe measure S(T ) obtained from standard Seebeck measurement,and compare it to S(T ) obtained from Kelvin relation:
S(T ) =
∫ T
0
µ(T ′)
T ′ dT ′
with µ(T ) obtained from 2ω method.
12
Validation of the method
0 100 200 300 400Temperature (K)
−24
−22
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
Seebeckcoeffi
cient(µ
V/K)
Ni (measured)Ni (Thomson)Pt (measured)Pt (Thomson)
13
Conclusion
I We developed a new method to obtain µ with at least±0.5 µV/K. Advantage of being simple, fast, and accurate.Easily extendable to high temperatures (> 1000 K) and othermaterials. Higher accuracy can be achieved by the use oflower frequencies.
I The method was validated through the use of simulations and comparison withSeebeck coefficient measurements.
I We present corrections for κ when the current is high. Very useful for thestandard 3ω method. Similar corrections for µ, though it is much less affected.
I We also give a clue on the impact of radiation effects, µ being very littleimpacted while κ can potentially require corrections at high temperature.
14
Conclusion
I We developed a new method to obtain µ with at least±0.5 µV/K. Advantage of being simple, fast, and accurate.Easily extendable to high temperatures (> 1000 K) and othermaterials. Higher accuracy can be achieved by the use oflower frequencies.
I The method was validated through the use of simulations and comparison withSeebeck coefficient measurements.
I We present corrections for κ when the current is high. Very useful for thestandard 3ω method. Similar corrections for µ, though it is much less affected.
I We also give a clue on the impact of radiation effects, µ being very littleimpacted while κ can potentially require corrections at high temperature.
14
Conclusion
I We developed a new method to obtain µ with at least±0.5 µV/K. Advantage of being simple, fast, and accurate.Easily extendable to high temperatures (> 1000 K) and othermaterials. Higher accuracy can be achieved by the use oflower frequencies.
I The method was validated through the use of simulations and comparison withSeebeck coefficient measurements.
I We present corrections for κ when the current is high. Very useful for thestandard 3ω method. Similar corrections for µ, though it is much less affected.
I We also give a clue on the impact of radiation effects, µ being very littleimpacted while κ can potentially require corrections at high temperature.
14
Conclusion
I We developed a new method to obtain µ with at least±0.5 µV/K. Advantage of being simple, fast, and accurate.Easily extendable to high temperatures (> 1000 K) and othermaterials. Higher accuracy can be achieved by the use oflower frequencies.
I The method was validated through the use of simulations and comparison withSeebeck coefficient measurements.
I We present corrections for κ when the current is high. Very useful for thestandard 3ω method. Similar corrections for µ, though it is much less affected.
I We also give a clue on the impact of radiation effects, µ being very littleimpacted while κ can potentially require corrections at high temperature.
14
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