Jorge García-Cañadas

Transcription

1 Thermoelectric Network Workshop - oughborough University, 14 th April 15 - Measurement of thermoelectric properties by means of impedance spectroscopy Jorge García-Cañadas Cardiff School of Engineering Cardiff University (United Kingdom)

2 Thermoelectric Network Workshop - oughborough University, 14 th April 15 - Outline 1. Introduction. Impedance spectroscopy fundamentals 3. Theoretical background and validation 4. Acknowledgements

3 1. Introduction The task of characterisation It requires measuring the variation with T of 3 parameters: S, σ and λ Usually 3 different equipments are required. A variety of home-made techniques are frequently used, no standard methods are followed. ZT is usually obtained from the measurement of S, σ and λ and collects the errors of all these 3 measurements. High errors K Biswas et al. Nature 489, (1) Thermal conductivity is difficult to measure and involves very expensive equipments.

4 1. Introduction Why exploring impedance? It is widely used in a lot of different fields (solar cells, fuel cells, corrosion, supercapacitors, biosensors, etc.). Powerful and very reliable equipment are available in the market. It allows the separation of the physical processes occurring in a device. It can be used under actual operating conditions.

5 . Impedance spectroscopy fundamentals Perturbation and system response A small amplitude sinusoidal voltage wave of a certain frequency is applied The system responds with a current wave proportional to the voltage that can be shifted in time (phase) Voltage -Z V dc V ac I ac time V I ac ac arc Z Z Z' Z Z'' tan Z ' ''

6 . Impedance spectroscopy fundamentals The impedance spectrum Z is obtained for a range of frequencies (1 MHz to 1 mhz), obtaining one point in the spectrum per each frequency frequencies Impedance spectrum (Nyquist plot) Parameters vs frequency (Bode plots)

7 . Impedance spectroscopy fundamentals Equivalent circuits Z 1 1 jc max 1 C 1 =1 Ω =4 Ω

8 Considerations Thermoelectric element with certain area A and length contacted by metallic contacts of length M. Adiabatic conditions (no heat exchanged with surroundings). All thermal and parameters independent on temperature. System is initially at thermal equilibrium at temperature T i. Joule effect is neglected both in the bulk and at the junctions. Constant T plane metallic contact T T i metallic contact thermoelectric element - M / x (Blue line indicates T profile of n-type thermoelement at a certain moment in time under an applied positive current)

9 Impedance function Z t V I V I S T( ) T() time domain (t) S T( ) T() I {ΔT}=θ {I}=i T ( ) T () Z j S i frequency domain (jω) To know the impedance function we need to know the T difference at x= as a function of frequency Solve heat equation θ() Constant T plane ΔT T i T - M / V=V()-V(), =total ohmic resistance, ω=πf, f is the frequency, j = x 1

10 1. No contact influence approximation Very thin contact considered ( M ) In the thermoelectric material: T x 1 T t Boundary conditions: at <x< I A T x Constant T plane T i T ST I A x T( /, t) T i T at x= (adiabatic) at x=/ (heat sink) T x thermoelectric element I A / x α =thermal diffusivity, λ =thermal conductivity, π=st=peltier coefficient

11 1. No contact influence approximation Z( j) j j tanh.5. 5 W CT W constant-t Constant T Warburg (W CT ) / S Ti A Thermoelectric resistance 1 p C 4S / Characteristic frequency of thermal diffusion dc A T Thermoelectric capacitance i S Ti A (simulation for Bi Te 3 element 1 mm area and 1.5 mm length) It can provide all thermal constants If S is known S=Seebeck coefficient, α =thermal diffusivity, λ =thermal conductivity, d=mass density, C p =Specific heat

12 Experimental validation An impedance analyser equipment (potentiostat) was used. The sample is suspended using thin probes of a low thermal conductivity material (Stainless Steel) to provide adiabatic conditions and reduce the cold finger effect. A thin contact is formed with Ag paint. ow contact resistance c should be achieved to minimise Joule effect at the junctions (I c ). Ag paint layers Bi Te 3 Stainless steel probes

13 p-bi Te 3 thermoelement (1.4 x 1.4 mm, 1.6 mm length) 8 W CT W constant-t Experimental Fitting Parameter calculation using S=195 µv/k (hot-probe) iterature values* -Z'' (m ) 6 4 =437.3 mω ω =1.78 rad/s =6.68 mω C =84.1 F S Ti 1.37 W / m K A ( / ) 3 3.6x1 cm / s C p.45 J / gk d 1.5 W/m K 3.7x1-3 cm /s.54 J/gK Z' (m ) (Impedance spectrum from 3 to.5 Hz) It can provide all thermal constants in a 5 min measurement If S is known. No thermocouples used to measure T differences. d=7.53 g/cm 3, (*) Data from Custom Thermoelectric manufacturer

14 . Heat equations with contact influence Heat conduction and absorption by the metallic contacts have to be considered In the metal: T x 1 M T t Boundary conditions: at - M <x< M T x I A Constant T plane T x metallic contact T T i ST I A T T M x, M x, at x= metallic contact thermoelectric element T x M at x=- M (adiabatic) - M H x T ( ) T() at x= (T continuity) M α M =thermal diffusivity of metal, λ M =thermal conductivity of metal

15 . Heat equations with contact influence Z Z W Z Wa CT Z Wa C j C j coth C.5. 5 Adiabatic Warburg (W a ) W a W CT C S Ti A Thermoelectric resistance from contact C C Characteristic frequency of thermal diffusion at the contact C C C (simulation for 1 mm and 1.5 mm length Bi Te 3 thermoelement contacted with Cu contacts. mm length) α C =thermal diffusivity of contact, λ C =thermal conductivity of contact ω C

16 Thermoelectric module (5 legs, 1 x 1 mm, 1.5 mm length) Z j 5 1 Z 1 1 Wa Z WCT S Ti C C m C A λ C =3 W/mK S=193.5 µv/k S Ti A λ =1.6 W/mK Z eff T p 5 Z eff T=.6 S Ti 5 A A (Impedance spectrum from 1, to.1 Hz) Complete module characterisation is achieved J. García-Cañadas, G. Min, Impedance spectroscopy models for the complete characterization of thermoelectric materials, J. Appl. Phys. 116 (14) 17451

17 4. Acknowledgements European Commission and European Space Agency for financial support under Accelerated Metallurgy project (AccMet NMP4-A ). Dr. Gao Min for his contribution and ourdes Márquez-García for assistance with sample preparation. European Thermodynamics td as module and materials provider. - Moving to Universitat Jaume I in Castellón (Spain) in September jorge.garcia.canadas@gmail.com