Direct Measurement of the Absolute Seebeck Coefficient for Pb and Cu at 300 K to 450 K
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Direct Measurement of the Absolute Seebeck Coefficient for Pb and Cu at 300 K to 450 K Patrick L. Garrity1 and Kevin L. Stokes1 1
Advanced Materials Research Institute, University of New Orleans Lakefront, New Orleans, LA 70148, U.S.A.
ABSTRACT The utilization of thermal fluctuations or Johnson/Nyquist noise as a spectroscopic technique to experimentally measure transport properties is applied to Pb and Cu metal films. Through cross-correlation and autocorrelation functions obtained from power spectral density measurements, multiple transport coefficients are obtained through the Green-Kubo formalism. Supported rigorously by the underlying fluctuation-dissipation theory, this new experimental technique provides a direct measurement of absolute thermoelectric coefficients in addition to the electrical resistivity, electronic contribution to thermal conductivity, Lorentz number and various diffusion coefficients. This work reports the validation results of the experiment accomplished through the use of materials with thermoelectric properties widely accepted by the thermoelectric community, Pb and Cu. Further validation of the data was accomplished by comparing resistivity results to standard collinear four-probe resistivity measurements. Thermal fluctuation data for Pb at 300 K resulted in 5.9% and 2.02% agreement with the published Seebeck and four-probe resistivity data respectively. The Cu thermal fluctuation measurements at 300 K showed agreement within 3.76% and 6.14% for the published Seebeck and four-probe data respectively thus lending further credibility to the experimental method and underlying theory.
INTRODUCTION Typically considered a limitation or nuisance to electrical engineers or experimentalists, Johnson/Nyquist or thermal noise has traditionally been treated as white noise that contains no information other than perhaps the system temperature [1]. On the contrary, these fluctuations and subsequent relaxation of the number density of electrons or holes follows the fluctuationdissipation theorem with correlation functions that exhibits fine structure [2]. The experimental and theoretical quantities of crucial importance here are the correlation spectra, both autocorrelation and cross-correlation. Through the rigorous Green-Kubo formalism which equates transport coefficients to the time integral of a correlation function, we have previously validated the experimental measurement of electrical resistivity and the electronic contribution to thermal conductivity through autocorrelation function (ACF) measurements of thermal noise [2]. The ACF’s were obtained by inverse Fourier transforming power spectral density measurements of voltage noise. This new experimental technique termed Dynamic Electron Scattering or DES [2,3], exploits a perturbation-free technique that is applicable to any conducting or
semiconducting material. From a theoretical standpoint, Onsager’s hypothesis [4] and Kubo transport theory [5] predict the cross-correlation function (CCF) of charge and thermal energy spect
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