Band Engineering in Thermoelectric Materials Using Optical, Electronic, and Ab-Initio Computed Properties

Thermoelectric materials have demanded a significant amount of attention for their ability to convert waste heat directly to electricity with no moving parts. A resurgence in thermoelectrics research has led to significant enhancements in the thermoelectric figure of merit, zT, even for materials that were already well studied. This thesis approaches thermoelectric zT optimization by developing a detailed understanding of the electronic structure using a combination of electronic/thermoelectric properties, optical properties, and ab-initio computed electronic band structures. This is accomplished by applying these techniques to three important classes of thermoelectric materials: IV-VI materials (the lead chalcogenides), Half-Heusler’s (XNiSn where X=Zr, Ti, Hf), and CoSb₃ skutterudites.

In the IV-VI materials (PbTe, PbSe, PbS) I present a shifting temperature-dependent optical absorption edge which correlates well to the computed ab-initio molecular dynamics result. Contrary to prior literature that suggests convergence of the primary and secondary bands at 400 K, I suggest a higher convergence temperature of 700, 900, and 1000 K for PbTe, PbSe, and PbS, respectively. This finding can help guide electronic properties modelling by providing a concrete value for the band gap and valence band offset as a function of temperature.

Another important thermoelectric material, ZrNiSn (half-Heusler), is analyzed for both its optical and electronic properties; transport properties indicate a largely different band gap depending on whether the material is doped n-type or p-type. By measuring and reporting the optical band gap value of 0.13 eV, I resolve the discrepancy in the gap calculated from electronic properties (maximum Seebeck and resistivity) by correlating these estimates to the electron-to-hole weighted mobility ratio, A, in narrow gap materials (A is found to be approximately 5.0 in ZrNiSn).

I also show that CoSb₃ contains multiple conduction bands that contribute to the thermoelectric properties. These bands are also observed to shift towards each other with temperature, eventually reaching effective convergence for T>500 K. This implies that the electronic structure in CoSb₃ is critically important (and possibly engineerable) with regards to its high thermoelectric figure of merit.

Influence of composition on the structure and properties of Fe-Pd-P and Ni-Pd-P amorphous alloys

Ternary alloys of nickel-palladium-phosphorus and iron-palladium- phosphorus containing 20 atomic % phosphorus were rapidly quenched from the liquid state. The structure of the quenched alloys was investigated by X-ray diffraction. Broad maxima in the diffraction patterns, indicative of a glass-like structure, were obtained for 13 to 73 atomic % nickel and 13 to 44 atomic % iron, with palladium adding up to 80%.

Radial distribution functions were computed from the diffraction data and yielded average interatomic distances and coordination numbers. The structure of the amorphous alloys could be explained in terms of structural units analogous to those existing in the crystalline Pd₃P, Ni₃P and Fe₃P phases, with iron or nickel substituting for palladium. A linear relationship between interatomic distances and composition, similar to Vegard's law, was shown for these metallic glasses.

Electrical resistivity measurements showed that the quenched alloys were metallic. Measurements were performed from liquid helium temperatures (4.2°K) up to the vicinity of the melting points (900°K- 1000°K). The temperature coefficient in the glassy state was very low, of the order of 10^-4/°K. A resistivity minimum was found at low temperature, varying between 9°K and 14°K for Ni_x-Pd_80-x -P₂₀ and between 17°K and 96°K for Fe_x-Pd_80-x -P₂₀, indicating the presence of a Kondo effect. Resistivity measurements, with a constant heating rate of about 1.5°C/min,showed progressive crystallization above approximately 600°K.

The magnetic moments of the amorphous Fe-Pd-P alloys were measured as a function of magnetic field and temperature. True ferromagnetism was found for the alloys Fe₃₂-Pd₄₈-P₂₀ and Fe₄₄-Pd₃₆-P₂₀ with Curie points at 165° K and 380° K respectively. Extrapolated values of the saturation magnetic moments to 0° K were 1.70 µ_B and 2.10 µ_B respectively. The amorphous alloy Fe₂₃-Pd₅₇-P₂₀ was assumed to be superparamagnetic. The experimental data indicate that phosphorus contributes to the decrease of moments by electron transfer, whereas palladium atoms probably have a small magnetic moment. A preliminary investigation of the Ni-Pd-P amorphous alloys showed that these alloys are weakly paramagnetic.

Structure and properties of an amorphous ferromagnetic alloy

The structure and the electrical and magnetic properties of an amorphous alloy containing approximately 80 at .% iron, 13 at.% phos phorus and 7 at.% carbon (Fe_(80)Fe_(13)C_7) obtained by rapid quenching from the liquid state have been studied. Transmission electron diffraction data confirm the amorphous nature of this alloy. An analysis of the radial distribution function obtained from X-ray diffraction data indicates that the number of nearest neighbors is approximately seven, at a distance of 2.6A. The structure of the alloy can be related to that of silicate glasses and is based on a random arrangement of trigonal prisms of Fe_2P and Fe_3C types in which the iron atoms have an average ligancy of seven. Electrical resistance measurements show that the alloys are metallic. A minimum in the electrical resistivity vs. temperature curve is observed between 10° K to 50° K depending on the specimen, and the temperature at which the minimum occurs is related to the degree of local ordering. The Fe-P-C amorphous alloys are ferromagnetic. The Curie temperature measured by the induction method and by Mossbauer spectroscopy is 315° C. The field dependence of the magneto-resistance at temperatures from liquid helium to room temperature is similar to that found in crystalline iron. The ordinary Hall coefficient is approximately 10^(-11) volt-cm/amp-G. The spontaneous Hall coefficient is about 0.6 x 10^(-9) volt-cm/amp-G and is practically independent of temperature from liquid helium temperature up to 300° c.

Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

I. The structure and properties of closed circular duplex DNA. II. Chemically interacting systems at equilibrium in a buoyant density gradient

I. The binding of the intercalating dye ethidium bromide to closed circular SV 40 DNA causes an unwinding of the duplex structure and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities and sedimentation velocities of both intact (I) and singly nicked (II) SV 40 DNAs were measured as a function of free dye concentration. The buoyant density data were used to determine the binding isotherms over a dye concentration range extending from 0 to 600 µg/m1 in 5.8 M CsCl. At high dye concentrations all of the binding sites in II, but not in I, are saturated. At free dye concentrations less than 5.4 µg/ml, I has a greater affinity for dye than II. At a critical amount of dye bound I and II have equal affinities, and at higher dye concentration I has a lower affinity than II. The number of superhelical turns, τ, present in I is calculated at each dye concentration using Fuller and Waring's (1964) estimate of the angle of duplex unwinding per intercalation. The results reveal that SV 40 DNA I contains about -13 superhelical turns in concentrated salt solutions.

The free energy of superhelix formation is calculated as a function of τ from a consideration of the effect of the superhelical turns upon the binding isotherm of ethidium bromide to SV 40 DNA I. The value of the free energy is about 100 kcal/mole DNA in the native molecule. The free energy estimates are used to calculate the pitch and radius of the superhelix as a function of the number of superhelical turns. The pitch and radius of the native I superhelix are 430 Å and 135 Å, respectively.

A buoyant density method for the isolation and detection of closed circular DNA is described. The method is based upon the reduced binding of the intercalating dye, ethidium bromide, by closed circular DNA. In an application of this method it is found that HeLa cells contain in addition to closed circular mitochondrial DNA of mean length 4.81 microns, a heterogeneous group of smaller DNA molecules which vary in size from 0.2 to 3.5 microns and a paucidisperse group of multiples of the mitochondrial length.

II. The general theory is presented for the sedimentation equilibrium of a macromolecule in a concentrated binary solvent in the presence of an additional reacting small molecule. Equations are derived for the calculation of the buoyant density of the complex and for the determination of the binding isotherm of the reagent to the macrospecies. The standard buoyant density, a thermodynamic function, is defined and the density gradients which characterize the four component system are derived. The theory is applied to the specific cases of the binding of ethidium bromide to SV 40 DNA and of the binding of mercury and silver to DNA.