Analysis of transport properties of mechanically alloyed [Pb1-xSnxTe]

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 Pb1-xSnxTe 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 Pb1-xSnxTe 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 SnO2 inclusions observed to be present in the mechanically alloyed Pb1-xSnxTe 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 Pb1-xSnxTe 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 Pb1-xSnxTe 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 Pb1-xSnxTe 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 Pb1-xSnxTe 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 Pb1-xSnxTe 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.

Petrogenesis of rift-related tephrites, phonolites and trachytes (Central European Volcanic Province, Rhon, FRG): Constraints from Sr, Nd, Pb and O isotopes

The volcanic rocks of the Rhön area (Central European Volcanic Province, Germany) belong to a moderately alkali basaltic suite that is associated with minor tephriphonolites, phonotephrites, tephrites, phonolites and trachytes. Based on isotope sytematics (87Sr/86Sr: 0.7033–0.7042; 143Nd/144Nd: 0.51279–0.51287; 206Pb/204Pb: 19.1–19.5), the inferred parental magmas formed by variable degrees of partial melting of a common asthenospheric mantle source (EAR: European Asthenospheric Reservoir of Cebriá and Wilson, 1995). Tephrites, tephriphonolites, phonotephrites, phonolites and trachytes show depletions and enrichments in some trace elements (Sr, Ba, Nb, Zr, Y) indicating that they were generated by broadly similar differentiation processes that were dominated by fractionation of olivine, clinopyroxene, amphibole, apatite and titaniferous magnetite ± plagioclase ± alkalifeldspar. The fractionated samples seem to have evolved by two distinct processes. One is characterized by pure fractional crystallization indicated by increasing Nb (and other incompatible trace element) concentrations at virtually constant 143Nd/144Nd ~ 0.51280 and 87Sr/86Sr ~ 0.7035. The other process involved an assimilation–fractional crystallization (AFC) process where moderate assimilation to crystallization rates produced evolved magmas characterized by higher Nb concentrations at slightly lower 143Nd/144Nd down to 0.51275. Literature data for some of the evolved rocks show more variable 87Sr/86Sr ranging from 0.7037 to 0.7089 at constant 143Nd/144Nd ~ 0.51280. These features may result from assimilation of upper crustal rocks by highly differentiated low-Sr (< 100 ppm Sr) lavas. However, based on the displacement of the differentiated rocks from this study towards lower 143Nd/144Nd ratios and modeled AFC processes in 143Nd/144Nd vs. 87Sr/86Sr and 207Pb/204Pb vs. 143Nd/144Nd space assimilation of lower crustal rocks seems more likely. The view that assimilation of lower crustal rocks played a role is confirmed by high-precision double-spike Pb isotope data that reveal higher 207Pb/204Pb ratios (15.62–15.63) in the differentiated rocks than in the primitive basanites (15.58–15.61). This is compatible with incorporation of radiogenic Pb from lower crustal xenoliths (207Pb/204Pb: 15.63–15.69) into the melt. However, 206Pb/204Pb ratios are similar for the differentiated rocks (19.13–19.35) and the primitive basanites (19.12–19.55) implying that assimilation involved an ancient crustal end member with a higher U/Pb ratio than the mantle source of the basanites. In addition, alteration-corrected δ18O values of the differentiated rocks range from c. 5 to 7‰ which is the same range as observed in the primitive alkaline rocks. This study confirms previous interpretations that highlighted the role of AFC processes in the evolution of alkaline volcanic rocks in the Rhön area of the Central European Volcanic Province.