Exploratory phase stability analysis in Materials Science has two primary goals: (a) Characterizing the evolution of the materials single phase field in composition space to identify solubility and electronic dopability limits and (b) Accelerated prediction of new phases of technological importance. In this thesis we reorganize defect theory --- the thermodynamics and chemistry aspects --- towards advancing both these goals significantly. Although (a) can, in principle, be approached using computational as well as experimental techniques, both avenues can become quite prohibitive for phases in complex, multi-component composition space. Considering that a defect of interest (often the dominant defect) can often be chemically intuited based on the structure of a phase or similar compounds, it is often desirable to have strategies for solubility design requiring much less effort by relying entirely on thermodynamic intuition. The current thermodynamic rules of thumb (e.g. `$A$-rich conditions are suitable for solubility of $A$-interstitial defects') regarding defect solubility are limited only to interstitial and vacancy defects. We develop a thermodynamic visualization framework in composition space which applies to all defect-types (substitutional defects and paired defect complexes). This generalized framework, in-principle, \textit{only} requires the defect type as the input to identify (i) chemical conditions leading to maximum solubility and (ii) the special cases in which two distinct chemical conditions will lead to equal solubility. These solubility guidelines explain why the varying reports of solubility limits in the thermoelectric Mg$_2$Si-Mg$_2$Sn pseudobinary is thermodynamically impossible and correctly identify equilibrium yielding maximum solubility in Sn-doped ZnSb and Te-doped Mg$_3$Sb$_2$. The predictive nature of these thermodynamic guidelines can also help in warning against atypical pseudobinary systems in which the solubility limit can be quite dependent on chemical conditions. The thermoelectric LAST-type systems (like PbTe-AgSbTe$_2$) are identified, potentially, as one example of such systems. The study of point defect thermodynamics in previous literature has thus far relied substantially on treating the reference chemical potential contributions to the defect energy by plotting them in chemical potential space. Thermodynamic analysis in chemical potential space can be quite abstract and is a relatively advanced concept not used regularly by the materials community. Considering the fact that defects impact all transport and thermochemical properties, the audience for defect thermodynamics is possibly much larger than the fraction of researchers well versed with analyzing stability in chemical potential space. By solving the defect solubility problem in composition space we bypass the need to work in chemical potential space entirely and provide a visualization scheme suitable for a very broad audience. Due to its simplicity, we expect our thermodynamic analysis to serve as an intermediate analysis step --- for computationalists and experimentalists alike --- before attempting (a). Beside this general thermodynamic aspect of defects, we also focus on rationalizing the differences between the two very distinct physical chemistry and defect physics approaches for treating defects in semiconductors and insulators. While historically these approaches have been used for studying defects in ionic and electronic conductors separately, mixed conductors with applications as battery materials are now attracting the attention of researchers from both communities. Both approaches have their pros and cons. The pros for the physical chemistry approach is that (1) its data representation --- characterized by plotting defect concentration against changing chemical potential in the so-called Brouwer diagrams --- is more direct in communicating chemical control of defects and (2) it characterizes the defect formation with a single reaction equilibrium constant. The cons of this approach are that (1) it does not discuss the Fermi-level dependence of defect concentrations explicitly and (2) it often lacks a clear distinction between the behavior of paired and isolated components of complex defects, such as Schottky and Frenkel defects. An advantage of the defect physics approach is that it accounts for a Fermi-level dependence of defect energetics -- connecting it to key properties such as electronic dopability and formation of deep defect states. The cons to this approach are that (i) the Fermi-level dependency is never studied with experimental techniques for verification of computational results and (ii) the Fermi-level dependency requires plotting the multi-dimensional data in separate panels, making visualization cumbersome. Using MgO, PbTe and Mg$_3$Sb$_2$ as example systems we address the cons in both the approaches and develop a composite language for defects in semiconductors and insulators. The pursuit of (b) in modern exploratory phase stability analysis is often carried out using high-throughput first-principles computational approaches. The choices of structure and composition in approaches for discovery of semiconducting compounds are often based on chemical intuition from long-standing stability rules. While these rules reduce the computational cost significantly, they apply by default only to fixed stoichiometries \textit{and} combination of elements, thereby favoring exploration in specific multi-component chemistries over others. Choosing the example of Heusler compounds, we show that these rules for stability of semiconductors nedd to apply to fixed stoichiometries or electron counts (as expected by the 18-electron rule for the $XYZ$ stoichiometry for example). We therefore develop the generalized valence balanced rule for stability of semiconductor Heuslers which now allows for a flexibility in the ground state composition by accounting for defects in the structure as well. We use this valence balanced rule be explain the semiconducting electronic structure of the thermodynamically stable ground state stoichiometries in Nb$_{0.8}$CoSb (nominally 19-electron at NbCoSb), Ti$_{0.75}$NiSb (nominally 19-electron at TiNiSb), and 24-electron VFe$_2$Al. By virtue of this rule, we predict over 150 new defective compounds --- which includes over 100 low thermal conductivity quaternary double (e.g. Ti$_2$FeNiSb$_2$), triple and quadruple half-Heusler compounds --- in multi-component chemistries which would have been inaccessible using the conventional 18-electron rule.

Creator

• Anand, Shashwat

DOI

• https://doi.org/10.21985/n2-fg30-xt13

Subject

• Materials Science

Language

• en

Alternate Identifier

• etdadmin_upload_794325
• http://dissertations.umi.com/northwestern:15457

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright