Citation
Gavini, Vikram (2007) Electronic structure calculations at macroscopic scales. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05152007121823
Abstract
Electronic structure calculations, especially those using densityfunctional theory have provided many insights into various materials properties in the recent decade. However, the computational complexity associated with electronic structure calculations has restricted these investigations to periodic geometries with small cellsizes (computational domains) consisting of few atoms (about 200 atoms). But material properties are influenced by defectsvacancies, dopants, dislocations, cracks, free surfacesin small concentrations (parts per million). A complete description of such defects must include both the electronic structure of the core at the fine (subnanometer) scale and also elastic and electrostatic interactions at the coarse (micrometer and beyond) scale. This in turn requires electronic structure calculations at macroscopic scales, involving millions of atoms, well beyond the current capability. This thesis presents the development of a seamless multiscale scheme, QuasiContinuum OrbitalFree DensityFunctional Theory (QCOFDFT) to address this significant issue. This multiscale scheme has enabled for the first time a calculation of the electronic structure of multimillion atom systems using orbitalfree densityfunctional theory, thus, paving the way to an accurate electronic structure study of defects in materials. The key ideas in the development of QCOFDFT are (i) a realspace variational formulation of orbitalfree densityfunctional theory, (ii) a nested finiteelement discretization of the formulation, and (iii) a systematic means of adaptive coarsegraining retaining full resolution where necessary, and coarsening elsewhere with no patches, assumptions, or structure. The realspace formulation and the finiteelement discretization gives freedom from periodicity, which is important in the study of defects in materials. More importantly, the realspace formulation and its finiteelement discretization support unstructured coarsegraining of the basis functions, which is exploited to advantage in developing the QCOFDFT method. This method has enabled for the first time a calculation of the electronic structure of samples with millions of atoms subjected to arbitrary boundary conditions. Importantly, the method is completely seamless, does not require any ad hoc assumptions, uses orbitalfree densityfunctional theory as its only input, and enables convergence studies of its accuracy. From the viewpoint of mathematical analysis, the convergence of the finiteelement approximation is established rigorously using Gammaconvergence, thus adding strength and validity to the formulation. The accuracy of the proposed multiscale method under modest computational cost, and the physical insights it offers into properties of materials with defects, have been demonstrated by the study of vacancies in aluminum. One of the important results of this study is the strong cellsize effect observed on the formation energies of vacancies, where cells as large as tens of thousands of atoms were required to obtain convergence. This indicates the prevalence of longrange physics in materials with defects, and the need to calculate the electronic structure of materials at macroscopic scales, thus underscoring the importance of QCOFDFT. Finally, QCOFDFT was used to study a problem of great practical importance: the embrittlement of metals subjected to radiation. The brittle nature of metals exposed to radiation is associated with the formation of prismatic dislocation loopsdislocation loops whose Burgers vector has a component normal to their plane. QCOFDFT provides an insight into the mechanism of prismatic dislocation loop nucleation, which has remained unclear to date. This study, for the first time using electronic structure calculations, establishes vacancy clustering as an energetically favorable process. Also, from direct numerical simulations, it is demonstrated that vacancy clusters collapse to form stable prismatic dislocation loops. This establishes vacancy clustering and collapse of these clusters as a possible mechanism for prismatic dislocation loop nucleation. The study also suggests that prismatic loops as small as those formed from a 7vacancy cluster are stable, thus shedding new light on the nucleation size of these defects which was hitherto unknown.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Densityfunctional theory; Electronic structure; Finiteelements; Gammaconvergence; Prismatic dislocation loops; Quasicontinuum; Vacancies in aluminum; Variational calculus 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Mechanical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  2 May 2007 
NonCaltech Author Email:  vikram.gavini (AT) gmail.com 
Record Number:  CaltechETD:etd05152007121823 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05152007121823 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1822 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  18 May 2007 
Last Modified:  26 Dec 2012 02:42 
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