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We propose a new formula for the mineral nickelskutterudite, based on our observation that either (or both) Co or Fe3+ are essential structure constituents. The crystal structure of nickelskutterudite, (Ni,Co,Fe) As-3, cubic, Im (3) over bar, Z = 8: a = 8.2653(6) angstrom, V = 564.65(7) angstrom, has been refined to R-1 = 1.4% for 225 unique reflections I > 2 sigma(1) collected on a Bruker X8 four-circle diffractometer equipped with fine-focus, sealed tube MoKa radiation and an APEX-II CCD detector. This is the first report of the crystal structure of nickelskutterudite. Nickelskutterudite, a member of the skutterudite group of isostructural minerals, adopts a distorted perovskite structure with notably tilted octahedra and an unoccupied to partially occupied icosahedral metal site. In the structure of nickelskutterudite, there is one metal (B) site occupied by Ni, Co, or Fe in octahedral coordination with six As atoms. Procrystal electron density analysis shows each As anion is bonded to two cations and two As anions, resulting in a four-membered ring of bonded As with edges 2.547 and 2.475 angstrom. The extreme tilting of BAs6 octahedra is likely a consequence of the As-As bonding. The nickelskutterudite structure differs from the ideal perovskite structure (A(4)B(4)X(12)) in that As4 anion rings occupy three of the four icosahedral cages centered on the A sites. There are reported synthetic phases isomorphous with skutterudite with the other A site completely occupied by a cation (AB(4)X(12)). Electron microprobe analyses of nickelskutterudite gave an empirical chemical formula of (Ni0.62Co0.28Fe0.12)(Sigma 1.02)(AS(2.95)S(0.05))(Sigma 3.00) normalized to three anions. Pure NiAs3 nickelskutterudite, natural or synthesized, has not been reported. In nature, nickelskutterudite is always observed with significant Co and Fe, reportedly because all non-bonded valence electrons must be spin-paired. This suggests that nickelskutterudite must contain Co3+ and Fe2+, consistent with previous models since Ni4+ cannot spin-pair its seven non-bonded electrons, Co3+ and Fe2+, which can spin-pair all non-bonded electrons, are required to stabilize the structure. No anion deficiencies were found in the course of this study so, including the structurally necessary Co and Fe, the chemical formula of nickelskutterudite (currently given as NiAs3-x, by the IMA) should be considered (Ni,Co,Fe)As-3.

Thesis advisor: Mark Reeder / A polynomial is said to be invariant for a group of linear fractional transformations G if its roots are permuted by G. We begin by using a simple group of linear fractional transformations that is isomorphic to S_{3} and finding its invariant polynomials to build up the tools necessary to attack a larger group. We then follow a construction from Toth of the icosahedral group I, and derive a general formula for all polynomials of degree 60 that are invariant under I. / Thesis (BA) — Boston College, 2004. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Mathematics. / Discipline: College Honors Program.

Computer simulations play a profound and fundamental role inmodern theoretical physics, chemistry and materials science. Tounderstand the complex physics of metally liquids, metals,quasicrystals and metally glasses a working model imposing thelocal and global order is needed. Experiments and theory havepredicted the local order in liquid metals to beicosahedral. The current work has been done using molecular dynamicscomputer simulations of a monatomic system using a simplepair-potential for the interactions. Two new pair-potentialshas been developed, the Zetterling-1(Z1) and Zetterling-2(Z2)potentials. They are specifically modeled to impose icosahedralorder. The basis for the development of the potentials was theold Dzugutov potential which is known to freeze into adodecagonal quasicrystal. The new Zetterling potentials have alonger interaction range and a narrower first minimum. The morenarrow first minimum will enhance the local icosahedralordering and the longer interaction range was introduced toincorporate a second maximum in the potential mimicing theFriedel oscillations found in metallic systems. These Friedeloscillations are due to the singularity which arises at theFermi surface due to the screening of the positive charge bythe electron gas. Five papers are included in the study. The first two papersare studies of icosahedral clustering in the liquid andsupercooled liquid. The simulations in Paper I was done usingthe old Dzugutov potential while the new potentials were usedin Paper II using both molecular dynamics and the Basin Hoppingalgorithm presented in Chapter 5. Paper III considers theconcept of dynamical ergodicity in the context of thesuper-cooled liquid behaviour. The simulations were made usingthe old Dzugutov potential. Paper IVr eports a moleculardynamics simulation using the Dzugutov potential undersuper-cooling. A formation of icosahedrally structured domainswith distinctly slow diffusion which grows with cooling in alow-dimensional manner and percolate around Tc, the criticaltemperature of the mode-coupling theory. A sharp slowing downof the structural relaxation relative to diffusion is observed.It is concluded that this effect cannot be accounted for by thespatial variation in atomic mobility. The low-dimensionalclustering is discussed as a possible mechanism of fragility.Paper Vin vestigates the crystallization of a simple monatomicliquid model which utilizes the Zetterling-1 potential. Thesystem forms a thermodynamically stable solid phase exhibitingcubic symmetry. Its diffraction pattern is identified as thatof γ-brass, a tetrahedrally packed crystalline structurewith 52 atoms in the unit cell. <b>Keywords:</b>simple liquids, molecular dynamics, pairpotential, icosahedral cluster.

<p>Computer simulations play a profound and fundamental role inmodern theoretical physics, chemistry and materials science. Tounderstand the complex physics of metally liquids, metals,quasicrystals and metally glasses a working model imposing thelocal and global order is needed. Experiments and theory havepredicted the local order in liquid metals to beicosahedral.</p><p>The current work has been done using molecular dynamicscomputer simulations of a monatomic system using a simplepair-potential for the interactions. Two new pair-potentialshas been developed, the Zetterling-1(Z1) and Zetterling-2(Z2)potentials. They are specifically modeled to impose icosahedralorder. The basis for the development of the potentials was theold Dzugutov potential which is known to freeze into adodecagonal quasicrystal. The new Zetterling potentials have alonger interaction range and a narrower first minimum. The morenarrow first minimum will enhance the local icosahedralordering and the longer interaction range was introduced toincorporate a second maximum in the potential mimicing theFriedel oscillations found in metallic systems. These Friedeloscillations are due to the singularity which arises at theFermi surface due to the screening of the positive charge bythe electron gas.</p><p>Five papers are included in the study. The first two papersare studies of icosahedral clustering in the liquid andsupercooled liquid. The simulations in Paper I was done usingthe old Dzugutov potential while the new potentials were usedin Paper II using both molecular dynamics and the Basin Hoppingalgorithm presented in Chapter 5. Paper III considers theconcept of dynamical ergodicity in the context of thesuper-cooled liquid behaviour. The simulations were made usingthe old Dzugutov potential. Paper IVr eports a moleculardynamics simulation using the Dzugutov potential undersuper-cooling. A formation of icosahedrally structured domainswith distinctly slow diffusion which grows with cooling in alow-dimensional manner and percolate around Tc, the criticaltemperature of the mode-coupling theory. A sharp slowing downof the structural relaxation relative to diffusion is observed.It is concluded that this effect cannot be accounted for by thespatial variation in atomic mobility. The low-dimensionalclustering is discussed as a possible mechanism of fragility.Paper Vin vestigates the crystallization of a simple monatomicliquid model which utilizes the Zetterling-1 potential. Thesystem forms a thermodynamically stable solid phase exhibitingcubic symmetry. Its diffraction pattern is identified as thatof γ-brass, a tetrahedrally packed crystalline structurewith 52 atoms in the unit cell.</p><p><b>Keywords:</b>simple liquids, molecular dynamics, pairpotential, icosahedral cluster.</p>

Doctor of Philosophy / Department of Chemical Engineering / James H. Edgar / The exceptional radiation resistance, high melting point, and wide energy bandgap (3.2 eV) of icosahedral boron arsenide, B[subscript]12As[subscript]2, make it an attractive candidate for applications in radiation intense environments, for example, in radioisotope batteries. These devices have potential lifetimes of decades rather than days or weeks that are typical of conventional chemical power cells. Solid state neutron detectors are another potential application of this semiconductor, as the boron-10 isotope has a high thermal neutron capture cross-section, orders of magnitude higher than most elements. To produce high quality crystalline B[subscript]12As[subscript]2 for these applications, this research focused on the epitaxy and electrical properties of B[subscript]12As[subscript]2 thin films. The major findings include the following. Twin-free heteroepitaxial B[subscript]12As[subscript]2 layers were obtained on m-plane 15R-SiC and c-plane 4H-SiC inclined 4° and 7° off-axis in the [1-100] direction. These substrates exposed asymmetric step-terrace surface structures that force B[subscript]12As[subscript]2 layers to adopt a single orientation, thus, twins were eliminated. Consequently, the crystal quality was greatly improved over films on on-axis c-plane 6H-SiC, yielding a maximum hole mobility of 80 cm[superscript]2V[superscript]-1s[superscript]-1, nearly 100 times higher than previously reported values. B[subscript]12As[subscript]2 epilayers grown at 1300°C had the lowest defect densities, smallest residual strains, highest mobility and highest deposition rate. Excess AsH[subscript]3 concentration was advantageous to prevent the loss of arsenic from the epilayer. Undoped B[subscript]12As[subscript]2 exhibited a variable-range-hopping conduction, indicating it was a highly disordered system. All films were p-type with a room temperature hole concentration on the order of 10[superscript]12~10[superscript]15cm[superscript]-3. The thermal activation energy of acceptors varied from 0.15 eV to 0.33 eV. The Hall mobility was dominated by impurity scattering at low temperatures and by polar phonon scattering at high temperatures. H, C, O and Si were the major impurities present in the undoped B[subscript]12As[subscript]2 films with concentrations on the order of 10[superscript]18~10[superscript]19 cm[superscript]-3. Si doping and annealing decreased the resistivity by up to two orders of magnitude. The density of localized states was small in the undoped B[subscript]12As[subscript]2 as the intrinsic acceptor levels (IALs) were compensated by the boron interstitials. However, in Si-doped B[subscript]12As[subscript]2, Si may prevent the interstitial boron atoms from compensating the IALs, yielding a decreased density of localized states. The Hall mobility of B[subscript]12As[subscript]2 epilayer was significantly reduced with increasing silicon concentration.

O objetivo deste trabalho é o estudo de métodos multigrid para a solução de equações elípticas na esfera, discretizadas em malhas esféricas geodésicas icosaédricas. Malhas esféricas geradas a partir de sólidos platônicos receberam crescente atenção ao longo da última década, por serem razoavelmente uniformes e não apresentarem concentração de pontos em torno dos pólos como as tradicionais malhas latitude-longitude. Em especial, as malhas geodésicas icosaédricas (geradas a partir de um icosaedro inscrito na esfera com suas faces projetadas na superfície) têm sido adotadas no desenvolvimento de diversos modelos atmosféricos. Nestes é comum a necessidade de resolução de equações do tipo Poisson como parte do método de integração, motivando o nosso trabalho. Adotamos uma discretização do operador de Laplace baseada em volumes finitos. Para tal escrevemos o laplaciano como o divergente do gradiente. O divergente é discretizado com base nos fluxos nos pontos médios das arestas das células computacionais (com o auxílio do teorema da divergência de Gauss) e no uso de diferenças centradas para aproximar as derivadas nesses pontos médios. Validamos a discretização para o operador de Laplace resolvendo uma equação de Poisson através dos métodos iterativos de Jacobi e Gauss-Seidel. Estes sabidamente não são eficientes computacionalmente, devido ao grande e crescente número de iterações necessárias para atingir a convergência ao refinar a malha. Uma alternativa muito eficiente para a resolução de equações elípticas é a métodologia multigrid. Investigamos alguns métodos multigrid propostos na literatura para a solução destas equações na malha esférica geodésica icosaédrica. A partir desse estudo, utilizando também como referência a Análise Local de Fourier para a equação de Poisson em malhas hexagonais uniformes, como uma aproximação para malhas geodésicas icosaédricas, escolhemos um algoritmo multigrid para implementação. Testamos algumas opções para as componentes do esquema multigrid. Obtivemos taxas de convergência muito boas com V(1,1) ciclos com relaxação por Gauss-Seidel, restrição full weighting e interpolação linear. / This work is dedicated to the numerical solution of elliptic equations on the sphere, discretized on geodesic icosahedral grids. Spherical meshes generated from projections of platonic solids received considerable attention in the last decade, once they are almost isotropic and do not present a concentration of grid points around the poles, as traditional latitude-longitude grids. In particular, the geodesic icosahedral spherical grids have been adopted in the development of several atmospheric models. In these models, the necessity to solve Poisson type equations is very common, providing a motivation for our present work. We have employed a discretization of the Laplace operator based on finite volumes. We write the Laplacian as the divergent of the gradient operator and use Gauss theorem to derive the discretization of the operator. We integrate the fluxes along the cell borders and approximate them through finite-differences. We first validated the discretization solving Poisson\'s equation with a simple (and very innefficient) Jacobi-Relaxation and Gauss-Seidel. We then investigated the use of multigrid type schemes for the solution of this equation. We have analysed some schemes proposed in the literature, also using an idealized Local Fourier Analysis on hexagonal (planar) grids to estimate the behaviour of the schemes on the icosaedral grids. We have implemented and tested a multigrid method, comparing the performance with different relaxation schemes and transfer operators. We have obtained a very efficient method employing V(1,1) cycles with Gauss-Seidel relaxation, and full-weighting and linear interpolation as transfer-operators.

O objetivo deste trabalho é o estudo de métodos multigrid para a solução de equações elípticas na esfera, discretizadas em malhas esféricas geodésicas icosaédricas. Malhas esféricas geradas a partir de sólidos platônicos receberam crescente atenção ao longo da última década, por serem razoavelmente uniformes e não apresentarem concentração de pontos em torno dos pólos como as tradicionais malhas latitude-longitude. Em especial, as malhas geodésicas icosaédricas (geradas a partir de um icosaedro inscrito na esfera com suas faces projetadas na superfície) têm sido adotadas no desenvolvimento de diversos modelos atmosféricos. Nestes é comum a necessidade de resolução de equações do tipo Poisson como parte do método de integração, motivando o nosso trabalho. Adotamos uma discretização do operador de Laplace baseada em volumes finitos. Para tal escrevemos o laplaciano como o divergente do gradiente. O divergente é discretizado com base nos fluxos nos pontos médios das arestas das células computacionais (com o auxílio do teorema da divergência de Gauss) e no uso de diferenças centradas para aproximar as derivadas nesses pontos médios. Validamos a discretização para o operador de Laplace resolvendo uma equação de Poisson através dos métodos iterativos de Jacobi e Gauss-Seidel. Estes sabidamente não são eficientes computacionalmente, devido ao grande e crescente número de iterações necessárias para atingir a convergência ao refinar a malha. Uma alternativa muito eficiente para a resolução de equações elípticas é a métodologia multigrid. Investigamos alguns métodos multigrid propostos na literatura para a solução destas equações na malha esférica geodésica icosaédrica. A partir desse estudo, utilizando também como referência a Análise Local de Fourier para a equação de Poisson em malhas hexagonais uniformes, como uma aproximação para malhas geodésicas icosaédricas, escolhemos um algoritmo multigrid para implementação. Testamos algumas opções para as componentes do esquema multigrid. Obtivemos taxas de convergência muito boas com V(1,1) ciclos com relaxação por Gauss-Seidel, restrição full weighting e interpolação linear. / This work is dedicated to the numerical solution of elliptic equations on the sphere, discretized on geodesic icosahedral grids. Spherical meshes generated from projections of platonic solids received considerable attention in the last decade, once they are almost isotropic and do not present a concentration of grid points around the poles, as traditional latitude-longitude grids. In particular, the geodesic icosahedral spherical grids have been adopted in the development of several atmospheric models. In these models, the necessity to solve Poisson type equations is very common, providing a motivation for our present work. We have employed a discretization of the Laplace operator based on finite volumes. We write the Laplacian as the divergent of the gradient operator and use Gauss theorem to derive the discretization of the operator. We integrate the fluxes along the cell borders and approximate them through finite-differences. We first validated the discretization solving Poisson\'s equation with a simple (and very innefficient) Jacobi-Relaxation and Gauss-Seidel. We then investigated the use of multigrid type schemes for the solution of this equation. We have analysed some schemes proposed in the literature, also using an idealized Local Fourier Analysis on hexagonal (planar) grids to estimate the behaviour of the schemes on the icosaedral grids. We have implemented and tested a multigrid method, comparing the performance with different relaxation schemes and transfer operators. We have obtained a very efficient method employing V(1,1) cycles with Gauss-Seidel relaxation, and full-weighting and linear interpolation as transfer-operators.

My research focuses on structures of the genomes of single-stranded RNA viruses. The first project is concerned with the sequence and secondary structure of HIV-1 RNA. Based on the secondary structure that Watts et al. determined, I performed a series of analysis and the results suggested that the abundance of Adenosines at the wobble position of the codons leads to an unusual structure with numerous unpaired nucleotides. The findings indicated how the virus balances evolutionary pressures on the genomic RNA secondary structure against pressures on the sequence of the viral proteins. The second project is the modeling of satellite tobacco mosaic virus (STMV). STMV is a T=1 icosahedral virus with a single piece of RNA that has 1058 nucleotides. X-ray crystallography studies of this RNA have revealed a structure containing 30 helices. The linkers between the helices, the possible structures at the interior of the icosahedron, and the sequence of the RNA were all missing in the crystal structure. To explore how the genome is organized within the protein capsid, I built a 3D model based on the RNA secondary structure predicted by Susan Schroeder. Being the first all-atom model of any virus, this model is highly correlated with the crystal structure; and the comparison with the in vitro structure of the same RNA supports the hypothesis that capsid protein plays an important role in RNA folding during assembly. The third project includes the modeling of bacteriophage MS2 (MS2) and the examination of the compactness of RNA in different viruses. MS2 is a T=3 RNA virus, and the cryo-EM studies have revealed a double-shell conformation of the genome. My final model of MS2 recaptures the double-shell structure of the RNA presented in the cryo-EM density. In addition, the predicted secondary structure that I used for the construction of the model shares a strong similarity with the in vitro structure determined in 1980s. This similarity contrasts with the striking difference between in vivo and in vitro RNA structures observed in STMV. Inspired by this finding, I examined the compactness of the RNA of several different viruses. The results strongly suggest that the RNAs of viruses requiring packaging signals have evolved to be structurally compact, which facilitates post-replicational RNA packaging. In contrast, viruses that do not depend on packaging signals probably adopt co-replicational RNA packaging.

This research investigated the tribological performance of a composite material, formed from an ultra high molecular weight polyethylene (UHMWPE) matrix and quasicrystalline Al-Cu-Fe alloy powders. An evaluation was conducted for the microstructure, material properties, and tribological performance of quasicrystalline materials formed from Al-Cu-Fe alloys. Arc melting was used as the fabrication technique for these alloys, and some samples were additionally heat treated in an argon environment. Vickers microhardness testing was done to make comparisons to wear rate behavior of the various alloys. Tribological studies were conducted using a linear pinon- desk configuration to evaluate friction and wear. Research indicated the annealed samples of Al-Cu-Fe that formed icosahedral quasicrystalline phases, where the quasicrystalline phase was most dominant of the observed alloys, displayed the greatest wear resistance and hardness. Abrasive wear was observed in each of the samples, as the brittle, hard nature of the quasicrystalline phase would not allow for the ductile adhesion. The addition of small amounts of Al-Cu-Fe quasicrystalline particles, crushed and pulverized from the arc-melted ingots, reduced the coefficient of friction and wear rate of UHMWPE, when added to the polymer.