Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

Microstructure control and iodine doping of bismuth telluride

On the materials scale, thermoelectric efficiency is defined by the dimensionless figure of merit zT. This value is made up of three material components in the form zT = Tα²/ρκ, where α is the Seebeck coefficient, ρ is the electrical resistivity, and κ is the total thermal conductivity. Therefore, in order to improve zT would require the reduction of κ and ρ while increasing α. However due to the inter-relation of the electrical and thermal properties of materials, typical routes to thermoelectric enhancement come in one of two forms. The first is to isolate the electronic properties and increase α without negatively affecting ρ. Techniques like electron filtering, quantum confinement, and density of states distortions have been proposed to enhance the Seebeck coefficient in thermoelectric materials. However, it has been difficult to prove the efficacy of these techniques. More recently efforts to manipulate the band degeneracy in semiconductors has been explored as a means to enhance α.

The other route to thermoelectric enhancement is through minimizing the thermal conductivity, κ. More specifically, thermal conductivity can be broken into two parts, an electronic and lattice term, κ_e and κ_l respectively. From a functional materials standpoint, the reduction in lattice thermal conductivity should have a minimal effect on the electronic properties. Most routes incorporate techniques that focus on the reduction of the lattice thermal conductivity. The components that make up κ_l (κ_l = 1/3Cνl) are the heat capacity (C), phonon group velocity (ν), and phonon mean free path (l). Since the difficulty is extreme in altering the heat capacity and group velocity, the phonon mean free path is most often the source of reduction.

Past routes to decreasing the phonon mean free path has been by alloying and grain size reduction. However, in these techniques the electron mobility is often negatively affected because in alloying any perturbation to the periodic potential can cause additional adverse carrier scattering. Grain size reduction has been another successful route to enhancing zT because of the significant difference in electron and phonon mean free paths. However, grain size reduction is erratic in anisotropic materials due to the orientation dependent transport properties. However, microstructure formation in both equilibrium and nonequilibrium processing routines can be used to effectively reduce the phonon mean free path as a route to enhance the figure of merit.

This work starts with a discussion of several different deliberate microstructure varieties. Control of the morphology and finally structure size and spacing is discussed at length. Since the material example used throughout this thesis is anisotropic a short primer on zone melting is presented as an effective route to growing homogeneous and oriented polycrystalline material. The resulting microstructure formation and control is presented specifically in the case of In₂Te₃-Bi₂Te₃ composites and the transport properties pertinent to thermoelectric materials is presented. Finally, the transport and discussion of iodine doped Bi₂Te₃ is presented as a re-evaluation of the literature data and what is known today.

Determination of optimum stocking density of Macrobrachium rosenbergii larvae using multiple feed in a commercial hatchery at Cox’s Bazar, Bangladesh

Experimental stocking density of Macrobrachium rosenbergii in larval rearing was conducted in A.G. Aqua Hatchery, Chakaria, Bangladesh to study the effect of different stocking densities on growth, survival rate and diseases stress under hatchery condition. The research work was conducted using six cemented rectangular tanks having 3m3 capacity (1.5mX2mX1m) each. Stocking density were maintained in three experimental setup as 200, 150 and 100ind/L of the T1, T2 and T3 respectively with one replicate each. The larvae were fed with Artemia nauplii, Custard, Maxima and brine shrimp flakes. Water quality was maintained by exchanging 20-30% (12ppt saline water) daily. During the study period, temperature, pH, DO, salinity, nitrite-nitrogen, ammonia and alkalinity were maintained from 28.5-31.5ºC, 7.5-7.8, 5.8-5.9mg/L, 12-13ppt, 0.14-0.2 mg/L, 0.22-0.3mg/L, and 140-160mg/L respectively. The growth rates of larvae at 11th stage were recorded in terms of body length 0.115, 0.136, and 0.169 mm/day whereas body weight were observed 0.000115, 0.000180, and 0.000240g/day. The survival rate of larvae were found 21.8%, 30.4% and 51.3% in treatments T1, T2 and T3 respectively. PL was obtained as 43, 45, and 51PL/L and days required of 41, 38 and 34 days in stocking density of 200, 150, and 100ind/L respectively. It was found that the minimum of 34 days was required to attain the PL (12th stage) using the stocking density of 100 individuals/L. Cannibalism, Zoothamnium, Exuvia Entrapment Disease (EED), and Bacterial Necrosis (BN) were found to be the threat to the commercial hatchery operation that might responsible for potential larval damages which can be reduced by lowering the stocking densities in larval rearing tank that also increased the survival and growth rate.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

Synthesis, Oxidation and Photophysics of Perfluoroborated Tetrakis(pyrophosphito)diplatinate (II) and Density Functional Theory (DFT) Study of Electrochemical CO2 Reduction by Mn Catalysts

In the first part of this thesis (Chapters I and II), the synthesis, characterization, reactivity and photophysics of per(difluoroborated) tetrakis(pyrophosphito)diplatinate(II) (Pt(POPBF₂)) are discussed. Pt(POP-BF₂) was obtained by reaction of [Pt₂(POP)₄]^4- with neat boron trifluoride diethyl etherate (BF₃·Et₂O). While Pt(POP-BF₂) and [Pt₂(POP)₄]^4- have similar structures and absorption spectra, they differ in significant ways. Firstly, as discussed in Chapter I, the former is less susceptible to oxidation, as evidenced by the reversibility of its oxidation by I2. Secondly, while the first excited triplet states (T₁) of both Pt(POP-BF₂) and [Pt₂(POP)₄]^4- exhibit long lifetimes (ca. 0.01 ms at room temperature) and substantial zero-field splitting (40 cm^-1), Pt(POP-BF₂) also has a remarkably long-lived (1.6 ns at room temperature) singlet excited state (S₁), indicating slow intersystem crossing (ISC). Fluorescence lifetime and quantum yield (QY) of Pt(POP-BF₂) were measured over a range of temperatures, providing insight into the slow ISC process. The remarkable spectroscopic and photophysical properties of Pt(POP-BF₂), both in solution and as a microcrystalline powder, form the theme of Chapter II.

In the second part of the thesis (Chapters III and IV), the electrochemical reduction of CO₂ to CO by [(L)Mn(CO)₃]^- catalysts is investigated using density functional theory (DFT). As discussed in Chapter III, the turnover frequency (TOF)-limiting step is the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^0/- (bpy = bipyridine) by trifluoroethanol (TFEH) to form [(bpy)Mn(CO)₄]^+/0. Because the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^- is faster, maximum TOF (TOF_max) is achieved at potentials sufficient to completely reduce [(bpy)Mn(CO)₃(CO₂H)]⁰ to [(bpy)Mn(CO)₃(CO₂H)]^-. Substitution of bipyridine with bipyrimidine reduces the overpotential needed, but at the expense of TOF_max. In Chapter IV, the decoration of the bipyrimidine ligand with a pendant alcohol is discussed as a strategy to increase CO₂ reduction activity. Our calculations predict that the pendant alcohol acts in concert with an external TFEH molecule, the latter acidifying the former, resulting in a ~ 80,000-fold improvement in the rate of TOF-limiting dehydroxylation of [(L)Mn(CO)₃(CO₂H)]^-.

An interesting strategy for the co-upgrading of light olefins and alkanes into heavier alkanes is the subject of Appendix B. The proposed scheme involves dimerization of the light olefin, operating in tandem with transfer hydrogenation between the olefin dimer and the light alkane. The work presented therein involved a Ta olefin dimerization catalyst and a silica-supported Ir transfer hydrogenation catalyst. Olefin dimer was formed under reaction conditions; however, this did not undergo transfer hydrogenation with the light alkane. A significant challenge is that the Ta catalyst selectively produces highly branched dimers, which are unable to undergo transfer hydrogenation.

Generation of millimeter-wave in optical pulse carrier by using an apodized Moire fiber grating

A novel scheme is proposed to transform a Gaussian pulse to a millimeter-wave frequency modulation pulse by using an apodized Moire fiber Bragg grating in radio-over-fiber system. The relation between the input and output pulses is analyzed theoretically by Fourier transformation method and the requirements for the proposed fiber grating are presented. An apodized Moire fiber Bragg grating is designed and its characteristics are studied. It is shown that the proposed device is feasible, and the new scheme is believed to be an effective solution for the generation of millimeter-wave sub-carrier in future radio-over-fiber systems. (c) 2006 Elsevier B.V. All rights reserved.

Talbot-SNOM method for non-contact evaluation of high-density gratings

A Talbot scanning near-field optical microscopy (SNOM) method for non-contact evaluating of high-density gratings was described. This method combines the Talbot self-imaging effect of the gratings and the conventional SNOM technique without damage. The significant advantages of this method are its simple structure, reliable and fast measurement for the surface quality of the tested gratings. Experimental results of three different kinds of gratings were demonstrated to indicate that this method is effective for evaluation surface quality of high-density gratings. (c) 2004 Elsevier B.V. All rights reserved.

Effects of density differences on lateral mixing in open-channel flows

This study investigates lateral mixing of tracer fluids in turbulent open-channel flows when the tracer and ambient fluids have different densities. Longitudinal dispersion in flows with longitudinal density gradients is investigated also.

Lateral mixing was studied in a laboratory flume by introducing fluid tracers at the ambient flow velocity continuously and uniformly across a fraction of the flume width and over the entire depth of the ambient flow. Fluid samples were taken to obtain concentration distributions in cross-sections at various distances, x, downstream from the tracer source. The data were used to calculate variances of the lateral distributions of the depth-averaged concentration. When there was a difference in density between the tracer and the ambient fluids, lateral mixing close to the source was enhanced by density-induced secondary flows; however, far downstream where the density gradients were small, lateral mixing rates were independent of the initial density difference. A dimensional analysis of the problem and the data show that the normalized variance is a function of only three dimensionless numbers, which represent: (1) the x-coordinate, (2) the source width, and (3) the buoyancy flux from the source.

A simplified set of equations of motion for a fluid with a horizontal density gradient was integrated to give an expression for the density-induced velocity distribution. The dispersion coefficient due to this velocity distribution was also obtained. Using this dispersion coefficient in an analysis for predicting lateral mixing rates in the experiments of this investigation gave only qualitative agreement with the data. However, predicted longitudinal salinity distributions in an idealized laboratory estuary agree well with published data.

Photoelectrochemistry of GaAs and Si liquid junctions

A quantitative study has been performed on the stability of GaAs surfaces in a 0.10 M K₂Se-0.01 M K₂Se₂ aqueous solution. In this electrolyte, n-type GaAs electrodes displayed significant photocorrosion in competition with faradaic charge transfer to Se^2-. Chemisorption of group VIIIB metal ions onto the GaAs surfaces yielded improved current-voltage behavior of the GaAs photoanodes, and also resulted in a significant reduction in photocorrosion. This behavior implies that the chemisorbed metal ions act to increase the rate of hole transfer to the Se^2- species. Related experiments on n-GaAs, pGaAs, and Sn-doped In₂O₃ electrodes in Te^2-/- aqueous solutions have also been performed.

The majority carrier (electrons) transfer rate constant at a highly doped n⁺-Si/Co(Cp)₂Cl-methanol junction has been measured directly using the chronoamperometry electrochemical technique. The reduction reaction rate of Co(Cp)₂+ was 0.03 cm-s^-1 at the Si electrode, and was more than 100 times slower than at a hanging mercury electrode. The slower rate was attributed to the smaller optical and static dielectric constants, and the lower density of electrons of the semiconductor. The experimental results were compared to the Marcus theory of charge transfer.

The unique properties of high purity Si/liquid junctions have been investigated under illumination conditions in which the photogenerated carrier concentration exceeds the dopant concentration. Under these high injection conditions, negligible electric fields exist at the semiconductor/liquid interface, and carrier motion is driven by diffusion. Studies of the current-voltage properties of the Si in methanol solutions containing various redox couples suggested that high efficiency photoelectrochemical cells could be established through selective collection of carriers at the semiconductor/liquid junction. The quasi-Fermi levels of electrons and holes were measured directly against the solution potential. Steady-state and transient photovoltage measurements, and theoretical modeliug of the carrier transport, generation, and recombination dynamics indicated that the quasi-Fermi levels were flat across the semiconductor sample. The recombination velocities at the Si/liquid junctions have also been measured, and were shown to vary with the solution potential following the Shockley-Read-Hall theory on recombination.

Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm

We describe the design, fabrication, and excellent performance of an optimized deep-etched high-density fused-silica transmission grating for use in dense wavelength division multiplexing (DWDM) systems. The fabricated optimized transmission grating exhibits an efficiency of 87.1% at a wavelength of 1550 nm. Inductively coupled plasma-etching technology was used to fabricate the grating. The deep-etched high-density fused-silica transmission grating is suitable for use in a DWDM system because of its high efficiency, low polarization-dependent loss, parallel demultiplexing, and stable optical performance. The fabricated deep-etched high-density fused-silica transmission gratings should play an important role in DWDM systems. (c) 2006 Optical Society of America.