Title

Analysis of transport properties of mechanically alloyed [Pb_1-xSn_xTe]

Author

Rajalakshmi Krishna, Michigan Technological University

Date of Award

2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Materials Science and Engineering (PhD)

College, School or Department Name

Department of Materials Science and Engineering

First Advisor

Peter Dane Moran

Abstract

The work described in this thesis had two objectives. The first objective was to develop a physically based computational model that could be used to predict the electronic conductivity, Seebeck coefficient, and thermal conductivity of Pb_1-xSn_xTe alloys over the 400 K to 700 K temperature as a function of Sn content and doping level. The second objective was to determine how the secondary phase inclusions observed in Pb_1-xSn_xTe alloys made by consolidating mechanically alloyed elemental powders impact the ability of the material to harvest waste heat and generate electricity in the 400 K to 700 K temperature range.

The motivation for this work was that though the promise of this alloy as an unusually efficient thermoelectric power generator material in the 400 K to 700 K range had been demonstrated in the literature, methods to reproducibly control and subsequently optimize the materials thermoelectric figure of merit remain elusive. Mechanical alloying, though not typically used to fabricate these alloys, is a potential method for cost-effectively engineering these properties. Given that there are deviations from crystalline perfection in mechanically alloyed material such as secondary phase inclusions, the question arises as to whether these defects are detrimental to thermoelectric function or alternatively, whether they enhance thermoelectric function of the alloy.

The hypothesis formed at the onset of this work was that the small secondary phase S_nO₂ inclusions observed to be present in the mechanically alloyed Pb_1-xSn_xTe would increase the thermoelectric figure of merit of the material over the temperature range of interest. It was proposed that the increase in the figure of merit would arise because the inclusions in the material would not reduce the electrical conductivity to as great an extent as the thermal conductivity. If this were to be true, then the experimentally measured electronic conductivity in mechanically alloyed Pb_1-xSn_xTe alloys that have these inclusions would not be less than that expected in alloys without these inclusions while the portion of the thermal conductivity that is not due to charge carriers (the lattice thermal conductivity) would be less than what would be expected from alloys that do not have these inclusions. Furthermore, it would be possible to approximate the observed changes in the electrical and thermal transport properties using existing physical models for the scattering of electrons and phonons by small inclusions.

The approach taken to investigate this hypothesis was to first experimentally characterize the mobile carrier concentration at room temperature along with the extent and type of secondary phase inclusions present in a series of three mechanically alloyed Pb_1-xSn_xTe alloys with different Sn content. Second, the physically based computational model was developed. This model was used to determine what the electronic conductivity, Seebeck coefficient, total thermal conductivity, and the portion of the thermal conductivity not due to mobile charge carriers would be in these particular Pb_1-xSn_xTe alloys if there were to be no secondary phase inclusions. Third, the electronic conductivity, Seebeck coefficient and total thermal conductivity was experimentally measured for these three alloys with inclusions present at elevated temperatures. The model predictions for electrical conductivity and Seebeck coefficient were directly compared to the experimental elevated temperature electrical transport measurements. The computational model was then used to extract the lattice thermal conductivity from the experimentally measured total thermal conductivity. This lattice thermal conductivity was then compared to what would be expected from the alloys in the absence of secondary phase inclusions.

Secondary phase inclusions were determined by X-ray diffraction analysis to be present in all three alloys to a varying extent. The inclusions were found not to significantly degrade electrical conductivity at temperatures above ~ 400 K in these alloys, though they do dramatically impact electronic mobility at room temperature. It is shown that, at temperatures above ~ 400 K, electrons are scattered predominantly by optical and acoustical phonons rather than by an alloy scattering mechanism or the inclusions. The experimental electrical conductivity and Seebeck coefficient data at elevated temperatures were found to be within ~ 10 % of what would be expected for material without inclusions. The inclusions were not found to reduce the lattice thermal conductivity at elevated temperatures. The experimentally measured thermal conductivity data was found to be consistent with the lattice thermal conductivity that would arise due to two scattering processes: Phonon phonon scattering (Umklapp scattering) and the scattering of phonons by the disorder induced by the formation of a PbTe-SnTe solid solution (alloy scattering). As opposed to the case in electrical transport, the alloy scattering mechanism in thermal transport is shown to be a significant contributor to the total thermal resistance. An estimation of the extent to which the mean free time between phonon scattering events would be reduced due to the presence of the inclusions is consistent with the above analysis of the experimental data.

The first important result of this work was the development of an experimentally validated, physically based computational model that can be used to predict the electronic conductivity, Seebeck coefficient, and thermal conductivity of Pb_1-xSn_xTe alloys over the 400 K to 700 K temperature as a function of Sn content and doping level. This model will be critical in future work as a tool to first determine what the highest thermoelectric figure of merit one can expect from this alloy system at a given temperature and, second, as a tool to determine the optimum Sn content and doping level to achieve this figure of merit.

The second important result of this work is the determination that the secondary phase inclusions that were observed to be present in the Pb_1-xSn_xTe made by mechanical alloying do not keep the material from having the same electrical and thermal transport that would be expected from “perfect" single crystal material at elevated temperatures. The analytical approach described in this work will be critical in future investigations to predict how changing the size, type, and volume fraction of secondary phase inclusions can be used to impact thermal and electrical transport in this materials system.

Recommended Citation

Krishna, Rajalakshmi, "Analysis of transport properties of mechanically alloyed [Pb_1-xSn_xTe]", Dissertation, Michigan Technological University, 2010.

https://doi.org/10.37099/mtu.dc.etd-restricted/39