Size-Dependent Errors in Z Determination Using the Harman Method

The effect of sample size on the measured thermoelectric figure of merit (Z m ) determined by the Peltier–Seebeck or Harman method has been studied by progressively halving the area (A s ) and length (l s ) of bismuth telluride alloy samples. Measurements were carried out with A s values from 1 to 0.01 cm 2 , l a values from 2 to 0.5 cm, and three different gauges of current leads (cross-sectional area A w ). The relative decrease of Z m was found to vary approximately as sech [Formula: see text] with A w and l s constant, as In A w with A s and l s constant, and as T 4 / s 2 with A w and A s constant, where T is the absolute temperature. The variation with A s and A w appears to be due to conduction along the sample leads, while the variation with l s is well accounted for by radiation to and from the sample. With 40 A.W.G. wires, the error in the measured figure of merit is estimated to be about 5% for a sample of dimensions 0.5 × 0.5 × 1 cm and around 50% for a sample of size 0.1 × 0.1 × 2 cm.