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.

Methods for melting temperature calculation

Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly.

We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the melting temperature is a design criterion.

We present in detail two examples of refractory materials. First, we demonstrate how key material properties that provide guidance in the design of refractory materials can be accurately determined via ab initio thermodynamic calculations in conjunction with experimental techniques based on synchrotron X-ray diffraction and thermal analysis under laser-heated aerodynamic levitation. The properties considered include melting point, heat of fusion, heat capacity, thermal expansion coefficients, thermal stability, and sublattice disordering, as illustrated in a motivating example of lanthanum zirconate (La₂Zr₂O₇). The close agreement with experiment in the known but structurally complex compound La₂Zr₂O₇ provides good indication that the computation methods described can be used within a computational screening framework to identify novel refractory materials. Second, we report an extensive investigation into the melting temperatures of the Hf-C and Hf-Ta-C systems using ab initio calculations. With melting points above 4000 K, hafnium carbide (HfC) and tantalum carbide (TaC) are among the most refractory binary compounds known to date. Their mixture, with a general formula Ta_xHf_1-xC_y, is known to have a melting point of 4215 K at the composition Ta₄HfC₅, which has long been considered as the highest melting temperature for any solid. Very few measurements of melting point in tantalum and hafnium carbides have been documented, because of the obvious experimental difficulties at extreme temperatures. The investigation lets us identify three major chemical factors that contribute to the high melting temperatures. Based on these three factors, we propose and explore a new class of materials, which, according to our ab initio calculations, may possess even higher melting temperatures than Ta-Hf-C. This example also demonstrates the feasibility of materials screening and discovery via ab initio calculations for the optimization of "higher-level" properties whose determination requires extensive sampling of atomic configuration space.

Vibrational predissociation spectroscopy of mass-selected ionic clusters

This thesis presents structural investigations of molecular ions and ionic clusters using vibrational predissociation spectroscopy. Experimentally, a pulsed beam of the mass-selected ion is crossed by a tunable infrared laser beam generated by a Nd:YAG pumped LiNbO_3 optical parametric oscillator. The resulting fragment ion is mass-analyzed and detected, with its intensity as a function of the laser wavelength being the "action" spectrum of the parent ion. In the case of SiH_7^+, we observed a vibrational band centered at 3866 cm^(-1) with clear P, Q, R branches, which is assigned as a perturbed H_2 stretch. The absence of a second H_2 band suggests that the ion forms a symmetric complex with a structure H_2•SiH_3^+•H_2 , in contrast to the species CH_7^+, which has the structure CH_5^+•H_2. The infrared spectra of NO_2^+(H_2O)_n clusters exhibit a marked change with cluster size, indicating that an intracluster reaction occurs with sufficient solvation. Specifically, in NO_2^+(H_2O)_n clusters where n≤3, H_2O binds to a nitronium ion core; but at n=4 the NO_2^+ reacts, transforming the cluster to a new structure of H_3O^+•(H_2O)_(n_2)•HNO_3. For protonated chlorine nitrate, we have observed two distinct isomers previously predicted by ab initio calculations: NO_2^+•(HOC1), the lowest energy isomer, and (ClO)(HO)NO^+, a covalently bonded isomer about 20 kcal/mol higher in energy. Both isomers decompose to NO_2^+ and HOCl upon photo-excitation. These results for HClONO_2^+ lend strong support to the involvement of an ionic mechanism in the reaction of ClONO_2 on polar stratospheric cloud surfaces, a critical step in the dramatic springtime depletion of ozone over Antarctica. Current research activities on halide-solvent clusters and metal-ligand complexes as well as technological improvements of the apparatus are also discussed.

Electronic structure and phonon thermodynamics of iron alloys

Inelastic neutron scattering (INS) and nuclear-resonant inelastic x-ray scattering (NRIXS) were used to measure phonon spectra of FeV as a B2- ordered compound and as a bcc solid solution. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2-ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy, which stabilizes the ordered phase to higher temperatures. Ab initio calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.

The phonon spectra of Au-rich alloys of fcc Au-Fe were also measured. The main effect on the vibrational entropy of alloying comes from a stiffening of the Au partial phonon density of states (DOS) with Fe concentration that increases the miscibility gap temperature. The magnitude of the effect is non- linear and it is reduced at higher Fe concentrations. Force constants were calculated for several compositions and show a local stiffening of Au–Au bonds close to Fe atoms, but Au–Au bonds that are farther away do not show this effect. Phonon DOS curves calculated from the force constants reproduced the experimental trends. The Au–Fe bond is soft and favors ordering, but a charge transfer from the Fe to the Au atoms stiffens the Au–Au bonds enough to favor unmixing. The stiffening is attributed to two main effects comparable in magnitude: an increase in electron density in the free-electron-like states, and stronger sd-hybridization.

INS and NRIXS measurements were performed at elevated temperatures on B2-ordered FeTi and NRIXS measurements were performed at high pressures. The high-pressure behavior is quasi- harmonic. The softening of the phonon DOS curves with temperature is strongly nonharmonic. Calculations of the force constants and Born-von Karman fits to the experimental data show that the bonds between second nearest neighbors (2nn) are much stiffer than those between 1nn, but fits to the high temperature data show that the former softens at a faster rate with temperature. The Fe–Fe bond softens more than the Ti–Ti bond. The unusual stiffness of the 2nn bond is explained by the calculated charge distribution, which is highly aspherical and localized preferentially in the t2g orbitals. Ab initio molecular dynamics (AIMD) simulations show a charge transfer from the t2g orbitals to the eg orbitals at elevated temperatures. The asphericity decreases linearly with temperature and is more severe at the Fe sites.

Theoretical studies of novel organic systems : biradicals, polyradicals, and conducting polymers

Chapter 1

Cyclobutanediyl has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C_(2h) and C_(2v) forms, which interconvert via a C_s transition state. For the singlet, only a C_(2h) form is found. It passes, via a C_s transition state, onto the C_(2v) surface on which bicyclobutane is the only minimum. The ring-flipping (inversion) process in bicyclobutane includes the singlet biradical as an intermediate, and involves a novel, nonleast motion pathway. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.

Chapter 2

The dimethylenepolycyclobutadienes (n) are the non-Kekulé analogues of the classical acenes. Application of a variety of theoretical methods reveals several novel features of such structures. Most interesting is the emergence of a parity rule. When n is even, n is predicted to be a singlet, with n disjoint NBMOs. When n is odd, theory predicts a triplet ground state with (n+1) NBMOs that are not fully disjoint.

Chapter 3

Bi(cyclobutadienyl) (2), the cyclobutadiene analogue of biphenyl, and its homologues tri- (3) and tetra(cyclobutadienyl) (4) have been studied using electronic structure theory. Ab initio calculations on 2 reveal that the central bond is a true double bond, and that the structure is best thought of as two allyl radicals plus an ethylene. The singlet and triplet states are essentially degenerate. Trimer 3 is two allyls plus a dimethylenecyclobutanediyl, while 4 is two coplanar bi(cyclobutadienyl) units connected by a single bond. For both 3 and 4, the quintet, triplet, and singlet states are essentially degenerate, indicating that they are tetraradicals. The infinite polymer, polycyclobutadiene, has been studied by HMO, EHCO, and VEH methods. Several geometries based on the structures of 3 and 4 have been studied, and the band structures are quite intriguing. A novel crossing between the valence and conduction bands produces a small band gap and a high density of states at the Fermi level.

Chapter 4

At the level of Hückel theory, polyfulvene has a HOCO-LUCO degeneracy much like that seen in polyacetylene. Higher levels of theory remove the degeneracy, but the band gap (E_g) is predicted to be significantly smaller than analogous structures such as polythiophene and polypyrrole at the fulvenoid geometry. An alternative geometry, which we have termed quinoid, is also conceivable for polyfulvene, and it is predicted to have a much larger E_g. The effects of benzannelation to produce analogues of polyisothianaphthene have been evaluated. We propose a new model for such structures based on conventional orbital mixing arguments. Several of the proposed structures have quite interesting properties, which suggest that they are excellent candidates for conducting polymers.

Chapter 5

Theoretical studies of polydimethylenecyclobutene and polydiisopropylidene- cyclobutene reveal that, because of steric crowding, they cannot achieve a planar, fully conjugated structure in either their undoped or doped states. Rather, the structure consists of essentially orthogonal hexatriene units. Such a structure is incompatible with conventional conduction mechanisms involving polarons and bipolarons.

Spectroscopic studies of gas-phase molecular clusters

Spectroscopic investigations of hydrogen-bonding and van der Waals' interactions m molecular clusters were studied by the techniques of infrared predissociation and resonance-enhanced multiphoton ionization spectroscopies (REMPI). Ab initio calculations were applied in conjunction for data interpretation.

The infrared predissociation spectroscopy of CN^-•(H_2O)_n (n = 2 - 6) clusters was reported in the region of 2950 - 3850 cm^(-1). The hydrogen bondings for the C-site and N-site binding, and among the water molecules were identified for n = 2 to 4. A spectral transition was observed for n = 5 and 6, implying that the anion was surface-bound onto the water aggregates in larger clusters.

The infrared predissociation spectroscopy of Br^-•(NH_3) and I^-•(NH_3)_n (n =1-3) clusters was reported in the region of 3050-3450 cm^(-1). For the Br^-•(NH_3) complex, a dominating ionic NH stretch appeared at 3175 cm^(-1), and the weaker free NH stretch appeared at 3348 cm^(-1). The observed spectrum was consistent to the structure in which there was one nearly linear hydrogen bond between Br^- and the NH_3 moiety. For the I^- •(NH_3) complex, five distinct IR absorption bands were observed in the spectrum. The spectrum was not consistent with basic frequency patterns of three geometries considered in the ab initio calculations - complex with one, two and three hydrogen bondings between I^- and the NH_3 moiety. Substantial inhomogenous broadening were displayed in the spectra for I^-•(NH_3)_n (n =2-3), suggesting the presence of multiple isomers.

The REMPI spectroscopy of the bound 4p ^2П 1/2 and ^2П 3/2 states, and the dissociative 3d ^2Σ^+ 1/2 state in the Al•Ar complex was reported. The dissociative spectrum at Al^+ channel suggested the coupling of the 4p ^2П 1/2,3/2 states to the repulsive 3d ^2Σ^+ 1/2 state. The spin-electronic coupling was further manifested in the dissociative Al^+ spectrum of the 3d ^2Σ^+ 1/2 state. Using the potential energy curves obtained from ab initio calculations, a bound → continuum Franck-Condon-intensity simulation was performed and compared with the one-photon 3d ^2Σ^+ 1/2 profile. The agreement provided evidence for the petturbation above the Al(3d)Ar dissociation limit, and the repulsive character of the 3d ^2Σ^+ 1/2 state.

Light-matter Interactions in Semiconductors and Metals: From Nitride Optoelectronics to Quantum Plasmonics

This thesis puts forth a theory-directed approach coupled with spectroscopy aimed at the discovery and understanding of light-matter interactions in semiconductors and metals.

The first part of the thesis presents the discovery and development of Zn-IV nitride materials.The commercial prominence in the optoelectronics industry of tunable semiconductor alloy materials based on nitride semiconductor devices, specifically InGaN, motivates the search for earth-abundant alternatives for use in efficient, high-quality optoelectronic devices. II-IV-N2 compounds, which are closely related to the wurtzite-structured III-N semiconductors, have similar electronic and optical properties to InGaN namely direct band gaps, high quantum efficiencies and large optical absorption coefficients. The choice of different group II and group IV elements provides chemical diversity that can be exploited to tune the structural and electronic properties through the series of alloys. The first theoretical and experimental investigation of the ZnSnxGe1−xN2 series as a replacement for III-nitrides is discussed here.

The second half of the thesis shows ab−initio calculations for surface plasmons and plasmonic hot carrier dynamics. Surface plasmons, electromagnetic modes confined to the surface of a conductor-dielectric interface, have sparked renewed interest because of their quantum nature and their broad range of applications. The decay of surface plasmons is usually a detriment in the field of plasmonics, but the possibility to capture the energy normally lost to heat would open new opportunities in photon sensors, energy conversion devices and switching. A theoretical understanding of plasmon-driven hot carrier generation and relaxation dynamics in the ultrafast regime is presented here. Additionally calculations for plasmon-mediated upconversion as well as an energy-dependent transport model for these non-equilibrium carriers are shown.

Finally, this thesis gives an outlook on the potential of non-equilibrium phenomena in metals and semiconductors for future light-based technologies.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.