Composite Thermoelectrics - Exact Results and Calculational Methods
- PDF / 380,787 Bytes
- 7 Pages / 420.48 x 639 pts Page_size
- 105 Downloads / 260 Views
COMPOSITE THERMOELECTRICS - EXACT RESULTS AND CALCULATIONAL METHODS DAVID J. BERGMAN AND OHAD LEVY Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel. ABSTRACT A theoretical study of composite thermoelectric media has resulted in the development of a number of simple approximations, as well as some exact results. The latter include exact upper and lower bounds on the bulk effective thermoelectric transport coefficients of the composite and upper bounds on the bulk effective thermoelectric quality factor Ze. In particular, as a result of some exact theorems and computer simulations we conclude that Z. can never be greater than the largest value of Z in the different components that make up the composite. I. INTRODUCTION The thermoelectric figure of merit Z is one of the main material parameters which affect the performance of practical thermoelectric devices: If a material were available in which the dimensionless product TZ is much greater than 1, where T is the absolute temperature, then a thermoelectric heat pump based on this material could be built with an efficiency approaching that of an ideal reversible Carnot cycle [1,2]. Since the highest value of this product which has ever been observed is less than 2, we are clearly very far from this ideal situation [2]. While much effort was directed in the past towards obtaining materials with increased values of Z by the doping of semiconductors or the alloying of metals, it seems that no thought was given to the possibility of achieving this goal by mixing together different materials macroscopically, i.e., as a composite medium. We have undertaken a theoretical study of this problem. In doing this we exploited the fact that in the field of composite media, it is often possible to find very strong connections between the behavior on the microscopic and on the macroscopic scales. What we have found is that it is apparently impossible to enhance the value of Z by mixing together a number of different homogeneous components so as to form a macroscopically inhomogeneous or composite medium. This negative result, while unfortunate from a practical point of view, is useful in that it shows us what not to do if we wish to try to increase the thermoelectric figure of merit. This negative result was not trivial to obtain. It does not seem possible to derive it from some general principle like the second law of thermodynamics. It has been possible to show it rigorously for certain classes of composites, including all two-component composites as well as multicomponent composites in which the value of the Seebeck coefficient is small in all components. In the general case, we have not been able to prove this negative result rigorously. Instead of that, we performed a large number of simulations of a discrete network model for a thermoelectric composite medium. These simulations included all possible network configurations of a certain type, and in none of them did we find an enhanced value of Z. H
Data Loading...
