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.

Thermal and electrical currents in nanoscale electronic interferometers

We theoretically study thermal transport in an electronic interferometer comprising a parallel circuit of two quantum dots, each of which has a tunable single electronic state which are connected to two leads at different temperature. As a result of quantum interference, the heat current through one of the dots is in the opposite direction to the temperature gradient. An excess heat current flows through the other dot. Although locally, heat flows from cold to hot, globally the second law of thermodynamics is not violated because the entropy current associated with heat transfer through the whole device is still positive. The temperature gradient also induces a circulating electrical current, which makes the interferometer magnetically polarized.

Transport properties of hot-pressed bulk carbon nanotubes compacted by spark plasma sintering

Electrical and thermal transport properties of the carbon nanotube bulk material compacted by spark plasma sintering have been investigated. The electrical conductivity of the as-prepared sample shows a lnT dependence from 4 to 50 K, after which the conductivity begins to increase approximately linearly with temperature. A magnetic field applied perpendicularly to the sample increases the electrical conductivity in the range of 0-8T at all testing temperatures, indicating that the sample possesses the two-dimensional weak localization at lower temperatures (?50 K), while behaviors like a semimetal at higher temperatures (?50 K). This material acts like a uniform compact consisting of randomly distributed two dimensional graphene layers. For the same material, the thermal conductivity is found to decrease almost linearly with decreasing temperature, similar to that of a single multi-walled carbon nanotube. Magnetic fields applied perpendicularly to the sample cause the thermal conductivity to decrease significantly, but the influence of the magnetic fields becomes weak when temperature increases.

Heat transport in low dimensions : introduction and phenomenology

Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.)

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Design of composites for thermal management: Aluminum reinforced with diamond-containing bimodal particle mixtures

A new design route is proposed in order to fabricate aluminum matrix diamond-containing composite materials with optimized values of thermal conductivity (TC) for thermal management applications. The proper size ratio and proportions of particulate diamond–diamond and diamond–SiC bimodal mixtures are selected based on calculations with predictive schemes, which combine two main issues: (i) the volume fraction of the packed particulate mixtures, and (ii) the influence of different types of particulates (with intrinsically different metal/reinforcement interfacial thermal conductances) on the overall thermal conductivity of the composite material. The calculated results are validated by comparison with measurements on composites fabricated by gas pressure infiltration of aluminum into preforms of selected compositions of particle mixtures. Despite the relatively low quality (low price) of the diamond particles used in this work, outstanding values of TC are encountered: a maximum of 770 W/m K for Al/diamond–diamond and values up to 690 W/m K for Al/diamond–SiC.

Synthesis, characterisation and thermoelectric properties of the oxytelluride Bi2O2Te

Bi2O2Te was synthesised from a stoichiometric mixture of Bi, Bi2O3 and Te by a solid state reaction. Analysis of powder X-ray diffraction data indicates that this material crystallises in the anti-ThCr2Si2 structure type (space group I4/mmm), with lattice parameters a = 3.98025(4) and c = 12.70391(16) Å. The electrical and thermal transport properties of Bi2O2Te were investigated as a function of temperature over the temperature range 300 ≤ T/K ≤ 665. These measurements indicate that Bi2O2Te is an n-type semiconductor, with a band gap of 0.23 eV. The thermal conductivity of Bi2O2Te is remarkably low for a crystalline material, with a value of only 0.91 W m-1 K-1 at room temperature.

The interplay of metal-atom ordering, Fermi leveltuning and thermoelectric properties in cobalt shandites Co3M2S2 (M = Sn, In)

A combination of structural, physical and computational techniques including powder X-ray and neutron diffraction, SQUID magnetometry, electrical and thermal transport measurements, DFT calculations and 119Sn Mössbauer and X-ray photoelec-tron spectroscopies has been applied to Co3Sn2-xInxS2 (0 ≤ x ≤ 2) in an effort to understand the relationship between metal-atom ordering and physical properties as the Fermi level is systematically varied. Whilst solid solution behavior is found throughout the composition region, powder neutron diffraction reveals that indium preferentially occupies an inter-layer site over an alternative kagome-like intra-layer site. DFT calculations indicate that this ordering, which leads to a lowering of energy, is related to the dif-fering bonding properties of tin and indium. Spectroscopic data suggest that throughout the composition range 0 ≤ x ≤ 2, all ele-ments adopt oxidation states that are significantly reduced from expectations based on formal charges. Chemical substitution ena-bles the electrical transport properties to be controlled through tuning of the Fermi level within a region of the density of states, which comprises narrow bands of predominantly Co d-character. This leads to a compositionally-induced double metal-to-semiconductor-to-metal transition. The marked increase in the Seebeck coefficient as the semiconducting region is approached leads to a substantial improvement in the thermoelectric figure of merit, ZT, which exhibits a maximum of ZT = 0.32 at 673 K. At 425 K, the figure of merit for phases in the region 0.8 ≤ x ≤ 0.85 is amongst the highest reported for sulphide phases, suggesting these materials may have applications in low-grade waste heat recovery.

Ball milling as an effective route for the preparation of doped bornite: synthesis, stability and thermoelectric properties

Bornite, Cu5FeS4, is a naturally-occuring mineral with an ultralow thermal conductivity and potential for thermoelectric power generation. We describe here a new, easy and scalable route to synthesise bornite, together with the thermoelectric behaviour of manganese-substituted derivatives, Cu5Fe1-xMnxS4 (0 ≤ x ≤ 0.10). The electrical and thermal transport properties of Cu5Fe1-xMnxS4 (0 ≤ x ≤ 0.10), which are p-type semiconductors, were measured from room temperature to 573 K. The stability of bornite was investigated by thermogravimetric analysis under inert and oxidising atmospheres. Repeated measurements of the electrical transport properties confirm that bornite is stable up to 580 K under an inert atmosphere, while heating to 890 K results in rapid degradation. Ball milling leads to a substantial improvement in the thermoelectric figure of merit of unsusbtituted bornite (ZT = 0.55 at 543 K), when compared to bornite prepared by conventional high-temperature synthesis (ZT < 0.3 at 543 K). Manganese-substituted samples have a ZT comparable to that of unsubstituted bornite.

Up-scaled synthesis process of sulphur-based thermoelectric materials

The scale up of Spark Plasma Sintering (SPS) for the consolidation of large square monoliths (50 × 50 × 3 mm3) of thermoelectric material is demonstrated and the properties of the fabricated samples compared with those from laboratory scale SPS. The SPS processing of n-type TiS2 and p-type Cu10.4Ni1.6Sb4S13 produces highly dense compacts of phase pure material. Electrical and thermal transport property measurements reveal that the thermoelectric performance of the consolidated n- and p-type materials is comparable with that of material processed using laboratory scale SPS, with ZT values that approach 0.8 and 0.35 at 700 K for Cu10.4Ni1.6Sb4S13 and TiS2, respectively. Mechanical properties of the consolidated materials shows that large-scale SPS processing produces highly homogeneous materials with hardness and elastic moduli that deviate little from values obtained on materials processed on the laboratory scale.

The impact of charge transfer and structural disorder on the thermoelectric properties of cobalt intercalated TiS2

A family of phases, CoxTiS2 (0 ≤ x ≤ 0.75) has been prepared and characterised by powder X-ray and neutron diffraction, electrical and thermal transport property measurements, thermal analysis and SQUID magnetometry. With increasing cobalt content, the structure evolves from a disordered arrangement of cobalt ions in octahedral sites located in the van der Waals’ gap (x ≤ 0.2), through three different ordered vacancy phases, to a second disordered phase at x ≥ 0.67. Powder neutron diffraction reveals that both octahedral and tetrahedral inter-layer sites are occupied in Co0.67TiS2. Charge transfer from the cobalt guest to the TiS2 host affords a systematic tuning of the electrical and thermal transport properties. At low levels of cobalt intercalation (x < 0.1), the charge transfer increases the electrical conductivity sufficiently to offset the concomitant reduction in |S|. This, together with a reduction in the overall thermal conductivity leads to thermoelectric figures of merit that are 25 % higher than that of TiS2, ZT reaching 0.30 at 573 K for CoxTiS2 with 0.04 ≤ x ≤ 0.08. Whilst the electrical conductivity is further increased at higher cobalt contents, the reduction in |S| is more marked due to the higher charge carrier concentration. Furthermore both the charge carrier and lattice contributions to the thermal conductivity are increased in the electrically conductive ordered-vacancy phases, with the result that the thermoelectric performance is significantly degraded. These results illustrate the competition between the effects of charge transfer from guest to host and the disorder generated when cobalt cations are incorporated in the inter-layer space.

Study of the temperature distribution in Si nanowires under microscopic laser beam excitation

The use of laser beams as excitation sources for the characterization of semiconductor nanowires (NWs) is largely extended. Raman spectroscopy and photoluminescence (PL) are currently applied to the study of NWs. However, NWs are systems with poor thermal conductivity and poor heat dissipation, which result in unintentional heating under the excitation with a focused laser beam with microscopic size, as those usually used in microRaman and microPL experiments. On the other hand, the NWs have subwavelength diameter, which changes the optical absorption with respect to the absorption in bulk materials. Furthermore, the NW diameter is smaller than the laser beam spot, which means that the optical power absorbed by the NW depends on its position inside the laser beam spot. A detailed analysis of the interaction between a microscopic focused laser beam and semiconductor NWs is necessary for the understanding of the experiments involving laser beam excitation of NWs. We present in this work a numerical analysis of the thermal transport in Si NWs, where the heat source is the laser energy locally absorbed by the NW. This analysis takes account of the optical absorption, the thermal conductivity, the dimensions, diameter and length of the NWs, and the immersion medium. Both free standing and heat-sunk NWs are considered. Also, the temperature distribution in ensembles of NWs is discussed. This analysis intends to constitute a tool for the understanding of the thermal phenomena induced by laser beams in semiconductor NWs.

Weak coupling of acoustic-like phonons and magnon dynamics in incommensurate spin ladder compound Sr14Cu24O41

Intriguing lattice dynamics has been predicted for aperiodic crystals that contain incommensurate substructures. Here we report inelastic neutron scattering measurements of phonon and magnon dispersions in Sr14Cu24O41, which contains incommensurate one-dimensional (1D) chain and two-dimensional (2D) ladder substructures. Two distinct acoustic phonon-like modes, corresponding to the sliding motion of one sublattice against the other, are observed for atomic motions polarized along the incommensurate axis. In the long wavelength limit, it is found that the sliding mode shows a remarkably small energy gap of 1.7-1.9 meV, indicating very weak interactions between the two incommensurate sublattices. The measurements also reveal a gapped and steep linear magnon dispersion of the ladder sublattice. The high group velocity of this magnon branch and weak coupling with acoustic phonons can explain the large magnon thermal conductivity in Sr14Cu24O41 crystals. In addition, the magnon specific heat is determined from the measured total specific heat and phonon density of states, and exhibits a Schottky anomaly due to gapped magnon modes of the spin chains. These findings offer new insights into the phonon and magnon dynamics and thermal transport properties of incommensurate magnetic crystals that contain low-dimensional substructures.

Controlling Nanostructures for in-situ TEM Characterization

Low dimensional nanostructures, such as nanotubes and 2D sheets, have unique and promising material properties both from a fundamental science and an application standpoint. Theoretical modelling and calculations predict previously unobserved phenomena that experimental scientists often struggle to reproduce because of the difficulty in controlling and characterizing the small structures under real-world constraints. The goal of this dissertation is to controlling these structures so that nanostructures can be characterized in-situ in transmission electron microscopes (TEM) allowing for direct observation of the actual physical responses of the materials to different stimuli. Of most interest to this work are the thermal and electrical properties of carbon nanotubes, boron nitride nanotubes, and graphene. The first topic of the dissertation is using surfactants for aqueous processing to fabricate, store, and deposit the nanostructures. More specifically, thorough characterization of a new surfactant, ammonium laurate (AL), is provided and shows that this new surfactant outperforms the standard surfactant for these materials, sodium dodecyl sulfate (SDS), in almost all tested metrics. New experimental set-ups have been developed by combining specialized in-situ TEM holders with innovative device fabrication. For example, electrical characterization of graphene was performed by using an STM-TEM holder and depositing graphene from aqueous solutions onto lithographically patterned, electron transparent silicon nitride membranes. These experiments produce exciting information about the interaction between graphene and metal probes and the substrate that it rests on. Then, by adding indium to the backside of the membrane and employing the electron thermal microscopy (EThM) technique, the same type of graphene samples could be characterized for thermal transport with high spatial resolution. It is found that reduced graphene oxide sheets deposited onto a silicon nitride membrane and displaying high levels of wrinkling have higher than expected electrical and thermal conduction properties. We are clearly able to visualize the ability of graphene to spread heat away from an electronic hot spot and into the substrate.

A Generalized Methodology to Characterize Composite Materials for Pyrolysis Models

The predictive capabilities of computational fire models have improved in recent years such that models have become an integral part of many research efforts. Models improve the understanding of the fire risk of materials and may decrease the number of expensive experiments required to assess the fire hazard of a specific material or designed space. A critical component of a predictive fire model is the pyrolysis sub-model that provides a mathematical representation of the rate of gaseous fuel production from condensed phase fuels given a heat flux incident to the material surface. The modern, comprehensive pyrolysis sub-models that are common today require the definition of many model parameters to accurately represent the physical description of materials that are ubiquitous in the built environment. Coupled with the increase in the number of parameters required to accurately represent the pyrolysis of materials is the increasing prevalence in the built environment of engineered composite materials that have never been measured or modeled. The motivation behind this project is to develop a systematic, generalized methodology to determine the requisite parameters to generate pyrolysis models with predictive capabilities for layered composite materials that are common in industrial and commercial applications. This methodology has been applied to four common composites in this work that exhibit a range of material structures and component materials. The methodology utilizes a multi-scale experimental approach in which each test is designed to isolate and determine a specific subset of the parameters required to define a material in the model. Data collected in simultaneous thermogravimetry and differential scanning calorimetry experiments were analyzed to determine the reaction kinetics, thermodynamic properties, and energetics of decomposition for each component of the composite. Data collected in microscale combustion calorimetry experiments were analyzed to determine the heats of complete combustion of the volatiles produced in each reaction. Inverse analyses were conducted on sample temperature data collected in bench-scale tests to determine the thermal transport parameters of each component through degradation. Simulations of quasi-one-dimensional bench-scale gasification tests generated from the resultant models using the ThermaKin modeling environment were compared to experimental data to independently validate the models.