arXiv subjects

T. A. Arias

Publications and source records attributed to T. A. Arias.

54 records · Page 3Linked to original sources

arXiv2001

Accurate Calculations of the Peierls Stress in Small Periodic Cells

The Peierls stress for a [111]-screw dislocation in bcc Tantalum is calculated using an embedded atom potential. More importantly, a method is presented which allows accurate calculations of the Peierls stress in the smallest periodic cells. This method can be easily applied to ab initio calculations, where only the smallest unit cells capable of containing a dislocation can be conviently used. The calculation specifically focuses on the case where the maximum resolved shear stress is along a {110}-plane.

cond-mat.mtrl-sci↗

arXiv2000

New Physics of the $30^\circ$ Partial Dislocation in Silicon Revealed through {\em Ab Initio} Calculation

Based on {\em ab initio} calculation, we propose a new structure for the fundamental excitation of the reconstructed 30$^\circ$ partial dislocation in silicon. This soliton has a rare structure involving a five-fold coordinated atom near the dislocation core. The unique electronic structure of this defect is consistent with the electron spin resonance signature of the hitherto enigmatic thermally stable R center of plastically deformed silicon. We present the first {\em ab initio} determination of the free energy of the soliton, which is also in agreement with the experimental observation. This identification suggests the possibility of an experimental determination of the density of solitons, a key defect in understanding the plastic flow of the material.

cond-mat.mtrl-sci↗

arXiv2000

A Priori Approach to Calculation of Energies of Solvation

We propose a systematic, {\em a priori} approach to the problem of the calculation of solvation energies using continuum dielectric models coupled to quantum mechanical description of reacting molecules. Our method does not rely on empirically scaled van der Waals radii to create a dielectric cavity, but rather uses the electron density of the reactants as the physical variable describing the cavity. In addition, the precise choice of cavity is made by ensuring that the dielectric reproduces the correct linear response of the solvent to electrostatic perturbations. As a model application which is interesting in its own right, we study the hydrolysis of methylene chloride, a representative model waste compound in supercritical oxidation experiments, and which has shown surprising solvation effects close to the critical point of pure water (T=394$^o$ C, P=221 bar). Using our {\em a priori} methodology, we find results in good agreement with available experimental reaction barriers. We then study, in a controlled manner, the relative importance of various further approximations that are routinely performed in the literature such as the use of spherical cavities, the replacement of the reactant by a dipole, or the neglect of self consistency in solving the electrostatic problem.

cond-mat.mtrl-sci↗

arXiv2000

New physics of grain boundaries in bcc metals from the atomic level: molybdenum as a case study

We present a systematic trend study of the symmetric tilt grain boundaries about the <110> axis in molybdenum. Our results show that multiple structural phases, some incorporating vacancies, compete for the boundary ground state. We find that at low external stress vacancies prefer to bind to the boundaries in high concentrations, and moreover, that external stress drives structural phase transitions which correspond to switching the boundaries on and off as pipe-diffusion pathways for vacancies. Finally, we present physical arguments which indicate these phenomena are likely to occur in the other bcc transition metals as well.

cond-mat.mtrl-sci↗

arXiv2000

New Algebraic Formulation of Density Functional Calculation

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for the construction of such for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures.

cond-mat.mtrl-sci↗

arXiv1999

Ab Initio Study of Screw Dislocations in Mo and Ta: A new picture of plasticity in bcc transition metals

We report the first ab initio density-functional study of <111> screw dislocations cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.

cond-mat.mtrl-sci↗

arXiv1999

Ab initio study of magnetic structure and chemical reactivity of Cr2O3 and its (0001) surface

We present the first ab initio density functional theory study of the oxygen-terminated Cr2O3 (0001) surface within the local spin-density approximation (LSDA). We find that spin plays a critical role for even the most basic properties of Cr2O3 such as the structure and mechanical response of the bulk material. The surface exhibits strong relaxations and changes in electronic and magnetic structure with important implications for the chemical reactivity and unusual spin-dependent catalytic activity of the surface. Unlike the bulk, the outermost chromium bilayer is ferromagnetically ordered, and the surface oxygen layer exhibits appreciable net spin polarization in the opposite sense. Surprisingly, despite this ferrimagnetic order, the chemically important states near the Fermi level exhibit ferromagnetic order and thus favor electronic spin alignment of species interacting with the surface. Finally, we also find a high density of unoccupied electronic surface states available to participate in the chemical reactivity of the surface.

cond-mat.mtrl-sci↗

arXiv1999

Tensor product expansions for correlation in quantum many-body systems

We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory which predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartee-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids. PACS 71.10.-w 71.15.Mb, Accepted for publication in Physical Review B

cond-mat.mtrl-sci↗

arXiv1999

Beyond Wavelets: Exactness theorems and algorithms for physical calculations

This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings of wavelet theory and the algorithms behind the fast wavelet transform. This article underscores the fact that traditional wavelet bases are fundamentally ill-suited for physical calculations and shows how to go beyond these limitations by the introduction of the new concept of semicardinality, which leads to the profound, new result that basic physical couplings may be computed {\em without approximatation} from very sparse information, thereby overcoming the limitations of traditional wavelet bases in the treatment of physical problems. The paper then explores the convergence rate of conjugate gradient solution of the Poisson equation in both semicardinal and lifted wavelet bases and shows the first solution of the Kohn-Sham equations using a novel variational principle.

cond-mat.mtrl-sci↗

arXiv1998

Multiresolution analysis of electronic structure: semicardinal and wavelet bases

This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on electronic structure, the advances described are useful for non-linear problems in the physical sciences in general. The new language and notations introduced are well- suited for both formal manipulations and the development of computer software using higher-level languages such as C++. The discussion is self-contained, and all needed algorithms are specified explicitly in terms of simple operators and illustrated with straightforward diagrams which show the flow of data. Among the reviewed developments is the construction of_exact_ multiresolution representations from extremely limited samples of physical fields in real space. This new and profound result is the critical advance in finally allowing systematic, all electron calculations to compete in efficiency with state-of-the-art electronic structure calculations which depend for their celerity upon freezing the core electronic degrees of freedom. This review presents the theory of wavelets from a physical perspective, provides a unified and self-contained treatment of non-linear couplings and physical operators and introduces a modern framework for effective single-particle theories of quantum mechanics.

cond-mat.mtrl-sci↗

arXiv1998

Solvation effects on kinetics of methylene chloride reactions in sub- and supercritical water: theory, experiment, and ab initio calculations

The nature of the CH2Cl2 neutral/acidic hydrolysis reaction from ambient to supercritical conditions (25 C to 600 C at 246 bar) is explored. Of primary interest is the effect of the changing dielectric behavior of the water solvent over this temperature range on this reaction. Experiments reveal that significant CH2Cl2 hydrolysis occurs under subcritical temperatures, while relatively little hydrolysis occurs under supercritical conditions. These trends cannot be explain by simple Arrhenius behavior. A combination of Kirkwood theory and ab initio modeling provides a means of successfully accounting for this behavior both qualitatively and quantitatively. The results show that increases in the activation energy and a changing reaction profile with a decreasing dielectric constant provide a mechanism for a slowing of the reaction at higher temperatures by as much as three orders of magnitude. These solvent effects are captured quantitatively in a correction factor to the Arrenius form of the rate constant, which is incorporated into a global rate expression proposed for CH2Cl2 hydrolysis that provides good predictions of the experimental data.

cond-mat.soft↗

arXiv1998

The Hopgrid algorithm: multilevel synthesis of multigrid and wavelet theory

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an efficient representation of functions which exhibit localized bursts of short length-scale behavior. Applications such as computing the electrostatic field in and around a molecule should benefit from both approaches. In this work, we demonstrate how a novel interpolating wavelet transform, which in itself is the synthesis of finite element analysis and wavelet theory, may be used as the mathematical bridge to connect the two approaches. The result is a specialized multigrid algorithm which may be applied to problems expressed in wavelet bases. With this approach, interpolation and restriction operators and grids for the multigrid algorithm are predetermined by an interpolating multiresolution analysis. We will present the new method and contrast its efficiency with standard wavelet and multigrid approaches.

physics.comp-ph↗

arXiv1998

The Geometry of Algorithms with Orthogonality Constraints

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.

physics.comp-ph↗

arXiv1998

The stabilizing role of itinerant ferromagnetism in inter-granular cohesion in iron

We present a simple, general energy functional for ferromagnetic materials based upon a local spin density extension to the Stoner theory of itinerant ferromagnetism. The functional reproduces well available ab initio results and experimental interfacial energies for grain boundaries in iron. The model shows that inter-granular cohesion along symmetric tilt boundaries in iron is dependent upon strong magnetic structure at the interface, illuminates the mechanisms underlying this structure, and provides a simple explanation for relaxation of the atomic structure at these boundaries.

cond-mat.mtrl-sci↗

arXiv1998

Multiscale Computation with Interpolating Wavelets

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution representation of a function from its sample values on a finite set of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases. The manuscript describes algorithms for the associated transforms which, for properly constructed grids of variable resolution, compute correctly without having to introduce extra grid points. We demonstrate that for the application of local homogeneous operators in such bases, the non-standard multiply of Beylkin, Coifman and Rokhlin also proceeds exactly for inhomogeneous grids of appropriate form. To obtain less stringent conditions on the grids, we generalize the non-standard multiply so that communication may proceed between non-adjacent levels. The manuscript concludes with timing comparisons against naive algorithms and an illustration of the scale-independence of the convergence rate of the conjugate gradient solution of Poisson's equation using a simple preconditioning, suggesting that this approach leads to an O(n) solution of this equation.

cond-mat.mtrl-sci↗

arXiv1998

Edge-driven transition in surface structure of nanoscale silicon

We present an ab initio exploration of the phenomena which will become important for freestanding structures of silicon as they are realized on the nanoscale. We find that not only surface but also edge effects are important considerations in structures of dimensions on the order of 3 nm. Specifically, for long nanoscale silicon bars, we find two competing low-energy reconstructions with a transition from one to the other as the cross section of the bar decreases. We predict that this size-dependent phase transition has a signature in the electronic structure of the bar but little effect on elastic properties.

cond-mat.mtrl-sci↗

arXiv1998

Paramagnetic structure for the soliton of the $30^\circ$ partial dislocation in silicon

Based on ab initio calculation, we propose a new structure for the fundamental excitation of the reconstructed 30$^\circ$ partial dislocation in silicon. This soliton has a rare structure involving a five-fold coordinated atom near the dislocation core. The unique electronic structure of this defect is consistent with the electron spin resonance signature of the hitherto enigmatic thermally stable R center of plastically deformed silicon. This identification suggests the possibility of an experimental determination of the density of solitons, a key defect in understanding the plastic flow of the material.

cond-mat.mtrl-sci↗

arXiv1998

A Multiscale Approach to Determination of Thermal Properties and Changes in Free Energy: Application to Reconstruction of Dislocations in Silicon

We introduce an approach to exploit the existence of multiple levels of description of a physical system to radically accelerate the determination of thermodynamic quantities. We first give a proof of principle of the method using two empirical interatomic potential functions. We then apply the technique to feed information from an interatomic potential into otherwise inaccessible quantum mechanical tight-binding calculations of the reconstruction of partial dislocations in silicon at finite temperature. With this approach, comprehensive ab initio studies at finite temperature will now be possible.

cond-mat.mtrl-sci↗