Unraveling the interplay between composition, electronic band structure and electronic transport properties in n-type Mg2X (X: Si, Sn) materials

Abstract

Mg2X (X: Si, Sn) based solid solutions are state-of-the-art thermoelectric (TE) materials in the intermediate temperature range (300 K – 900 K). Particularly, the n-type Mg2Si1-xSnx (with x = 0.6 – 0.7) shows excellent TE properties. These materials possess features such as a low mass density, abundant and economic precursors, and less interference to human and environmental health. All these characteristics makes these materials a prominent choice for the fabrication of modules for power generation. Even though these materials show a high TE performance, there is an obvious need for further research to understand the composition-synthesis-microstructure-property relationships for these materials. The motivation comes from the fact that the employed synthesis routes usually take days-to-weeks to prepare one batch of these materials, poor reproducibility of TE properties, and a large difference (beyond measurement uncertainty) in the TE properties of samples with nominally the same composition, as per the literature reports. The discrepancy could arise from the employed method, where the systematics are poorly understood i.e. more than one synthesis conditions (duration, number of repetitions of high temperature heating or milling etc.) could be responsible for the cited deviation in the TE properties. These aspects need to be systematically addressed. Therefore, for the development of efficient Mg2Si1-xSnx modules, a synthesis route with optimized parameters should be established which can be achieved by utilizing a technique to prepare Mg2Si1-xSnx materials with excellent reproducibility in relatively less time, identifying the synthesis parameters which influence the TE properties, and analyzing the TE properties to identify the microscopic material parameters affected due to a variation in synthesis parameters. Besides, for a long-term functioning and sustenance of maximum efficiency of Mg2Si1-xSnx based modules, the high temperature stability of Mg2Si1-xSnx materials is a significant challenge to overcome. Previous studies reveal that the high temperature (800 K – 875 K) stability of n-type Mg2Si1-xSnx materials is compromised by Mg loss. However, these studies lack proper methodology as the high-temperature annealing causes material degradation beyond the actual composition, which results in the formation of secondary phases. As a result, a comparison of TE properties measured before and after annealing hold no significance as the properties measured after annealing are representative of mixed-phase material. These studies also lack a proper detailing of the degradation mechanism and no conclusions about the mechanism can be drawn from the reported microstructure. These investigations highlight the fact that the practically relevant topic of thermal stability of Mg2Si1-xSnx materials needs to be addressed well. In this regard, the measurement of TE properties should be conducted by simulating the operation conditions of TEGs made from these materials. A measurement of TE properties of these materials at high temperatures of annealing would show a direct effect of heat-treatment on the TE properties. Moreover, a modelling-based analysis of measured properties will provide the extent of changes in the microscopic material parameters. Such an investigation would enable a systematic understanding of the different stages of the degradation mechanism of Mg2Si1-xSnx materials. Therefore, the focus of this work is to investigate the composition-synthesis-microstructure-property relationships in n-type Mg2X (X: Si, Sn) solid solutions, and the effects of long-term heat treatment on the thermoelectric transport properties of these materials, using semiconductor physics-based models. Carrier concentration (n) is one fundamental parameter that needs to be optimized for achieving best TE properties of any material. Therefore, a pre-existing in-house Hall facility is successfully advanced for high temperature measurements (T=300 K – 723 K) of Mg2Si1-xSnx materials. The Hall facility is capable to simultaneously measure the Hall coefficient (R_H) and the electrical conductivity (σ) in a van der Pauw configuration. The uncertainty in the signals corresponding to the σ measurement was addressed, partially resolved and quantified. The effect of non-ideal contact geometry on the R_H measurement was investigated using finite element simulations. For certain relevant cases, R_H values deduced from simulation and analytical expression showed a relative deviation (R.D.) >5 %, and so, the results of the analytical expression could be furthermore corrected using simulation results. Room temperature and T-dependent measurement of R_H and σ on Mg2(Si,Sn) and p-type FeSi2, respectively, in the Hall facility at DLR and other international research labs showed good agreement in their absolute measured values with R.D.≤8 %. For a better understanding of composition-synthesis-microstructure-property relationship, Sb-doped Mg2Si0.4Sn0.6 was synthesized using mechanical alloying. Employing an in-depth microstructure analysis, the formation mechanism of this material was studied in detail using mechanical alloying. The Mg-Sn phase forms readily followed by slow Si diffusion in the ductile matrix. However, the investigations showed that the powder sample was not phase pure even after extensive milling and therefore a high-temperature compaction step was added, enabling a successful synthesis of the desired composition. The effect of synthesis parameters (milling time, sintering time and temperature) was studied systematically. TE properties were hardly influenced by milling duration. However, carrier concentration reduced with an increase of sintering time and temperature which led to an observable effect on TE properties. Maximum TE performance, characterized by a TE figure-of-merit zT~1.4, was achieved for samples sintered at 973 K for 20 min. A TEM based microstructural analysis was performed on the samples sintered for different durations (10 min, 20 min and 40 min) at 973 K. This analysis was done with an objective to identify the reason of the sensitivity of TE properties to the sintering duration. An increase in the sintering duration resulted in Mg-depleted grain boundaries and local compositional inhomogeneities in the material. The transport properties of these samples were analyzed upto 700 K by using a single parabolic band (SPB) model under the assumptions of acoustic phonon (AP) and alloy scattering (AS) mechanisms. Analysis revealed carrier loss, a lowering in carrier mobility (μ) and a reduction in lattice thermal conductivity (κ_lat) with increasing sintering duration. A lower mobility for the sample (sintered for prolonged duration 40 min) was due to a combined effect of increasing electron-phonon interaction (higher deformation potential constant E_Def) and local compositional inhomogeneities, which are both associated with Mg loss. The altered temperature dependence of electrical conductivity could be reproduced by considering grain boundary (GB) scattering together with AP and AS, thus, linking the observed changes of the microstructure with the TE transport. The compensation between both a lower κ_lat and μ of the sample sintered for 40 min led to a similar TE performance as short-term sintered samples, with 〖zT〗_max=1.3±0.18 for all samples. The absence of any strong influence of sintering duration on 〖zT〗_max indicates that Mg2Si1-xSnx materials, and hence the TE modules made from them, can accommodate some Mg loss without their performance being degraded. Theoretical investigations have suggested scandium (Sc) as an impurity element for Mg2X materials that introduces resonant levels in the band structure, which could greatly enhance the Seebeck coefficient (S) and the overall TE performance. Correspondingly, the effect of the substitution of Mg by Sc in Mg2X binaries and their solid solutions was experimentally investigated. The TE properties showed no enhancement due to an addition of Sc to Mg2X material, thus, disproving the results of the theoretical study. The effect of long-term annealing on the transport properties of Mg2Si1-xSnx was further investigated at different temperatures. Chosen temperatures were near and beyond the operation temperature range of Mg2Si1-xSnx based TE modules. It is clear from the last investigation that the Mg loss is inevitable. The missing part is the extent and the speed of Mg loss at higher temperatures. It is furthermore unclear whether the microscopic mechanism of degradation is temperature dependent or not. Considering this, the electrical transport properties of six thermoelectrically identical samples were measured in-situ in two different setups: S and σ (three samples), and R_H and σ (other three as-prepared samples) during annealing at 710 K, 773 K and 848 K. All samples were largely single phase with no hints of de-mixing after annealing for several hundred hours. In-situ measured properties were analyzed using a SPB and a two parabolic band (2PB, one conduction and one valence band) model. The analysis revealed a loss of majority carriers due to ongoing Mg loss as annealing progressed. Besides, a lowering of μ, due to an increase in E_Def, and a reduction in the density-of-states effective mass (m_D^*) is also observed. This change in said microscopic material parameters could be directly related to an ongoing Mg loss or a lifted degeneracy of conduction bands in Mg2Si0.4Sn0.6, respectively. A microscopic, multi-step model of Mg loss was developed which qualitatively explains the Mg-transport from sample to the annealing atmosphere. Time constants (and rates) were estimated from the change of majority charge carriers and the electrical conductivity measured in situ at different temperatures. Rates were plugged in the Arrhenius expression to determine the activation energy of the complete degradation process. The activation energy was compared with the height of energy barriers associated with Mg-transport to judge the limiting step in the transport chain of multi-step model. Mg-transport was found to be dominated by Mg-vacancies owing to their low energy of formation and migration energy. With the established mechanism, the observed changes in the transport properties and the differences in rate and the frequency factor were found to be dependent on the design of measuring setups. This governs the degradation process by allowing one or more steps to act as a dominant mechanism of multi-step transport chain. The findings in this thesis provide a description of previously unknown synthesis mechanism of high performance n-type Mg2(Si,Sn) solid solutions using mechanical alloying. The effect of synthesis parameters on material properties is analyzed which explains discrepancies in the material properties reported in different literature reports. An effect of high-temperature degradation of n-type Mg2(Si,Sn) is understood by analyzing in situ measured transport properties which revealed the affected microscopic material parameters and the extent of their deterioration. Finally, the kinetics of Mg-loss in n-type Mg2(Si,Sn) solid solutions is known by utilizing the change in the majority charge carrier concentration and a model of Mg-loss in n-type Mg2(Si,Sn) is developed.