Projects

These are little projects and papers that I've worked on. While they don't necessarily seem worthy of printed publication, making them available here seems appropriate.

These projects are not necessarily intended to be related and may not be thoroughly documented, but I hope that if you come to this page through a very specific and technical search phrase, you'll find this information useful. Don't hesitate to contact me if you need additional clarification about any of the work below.

I have a relatively large collection of work to put here from my time as a graduate student. As I restore this work from backup, the offering will grow.

Lecture notes

These are select notes from lectures that I've given at the University of Texas.

Introduction to the electronic structure of crystals

In this set of notes the concept of electronic structure is discussed, as is the basic background material, including the derivation of Bloch's theorem, and the definition of the Brillouin zone. I gave this lecture to a class of physics graduate students so I covered the subject quickly, under the assumption that they have seen it before. The lecture to follow this one gave them examples of the tight-binding and the plane wave/pseudopotential methods (below).
pdf file Electronic Structure Introduction

The Tight-Binding Method

In these notes the tight-binding formalism is explained. An example of an s-valent dimer molecule is given using the notation given in Pettifor's text Bonding and Structure of Molecules and Solids (there are of course many notations and parameterizations which can be used). The quantum number k is introduced by deriving the band structure for a simple 1D chain of s-valent atoms. To facilitate this, I used the notation of Chadi and Cohen, which is also given in Yu and Cardona's text, Fundamentals of Semiconductors. At the end of the notes I derived an expression for a 1D chain of sp-valent atoms, I encoded this in a Mathematica notebook to allow the students to experiment with the parameters.


pdf file Tight-Binding formalism
mathematica file 1D sp-valent Mathematica model

The Plane wave Method

Here the plane wave method is explained. The empirical pseudopotential method (EPM) is shown. The structure factor for diamond cubic and zinc-blende crystals is derived, following the notation of the 1966 Cohen and Bergstresser paper.


pdf file Plane wave formalism

Introduction to Crystals and the Reciprocal Lattice

This lecture was given to a graduate level class of chemical engineers. The basic mathematics of crystals was covered as was an introduction to the reciprocal lattice. As an application of this formalism diffraction was presented. The simple 1D model of Bragg's Law is shown to be compatible with the reciprocal lattice formalism. The Ewald construction is presented as is the Brillouin zone "Bragg Reflection" construction.


pdf file Crystals and Diffraction

Ewald Summations

In this lecture the Madelung constant is discussed. A method to calculate the Madelung constant by an Ewald lattice summation is presented. This lecture follows closely the appendix of Kittel's text Introduction to Solid State Physics.


pdf file Ewald Summation

Introduction to kinetic Monte Carlo

This is a two day lecture. It began with the derivation of the Boltzmann distribution and a discussion of the implications of the Ergodic assumption. The 1D Ising model is presented as an example system. The Monte Carlo method is presented, including the derivation of detailed balance condition. Using an expression for detailed balance, the Metropolis algorithm is shown to be a good method for "measuring" a canonical ensemble. Correlation functions are presented as is a discussion of the importance of making uncorrelated "measurements." It is shown how time can be incorporated to the Metropolis algorithm by discretizing events and generated a rate table. These lectures follow from the work of Reif Fundamentals of Statistical and Thermal Physics Laudau and Binder A Guide to Monte Carlo Simulations in Statistical Physics and Prof. Chrzan's MSE215 lecture notes.


pdf file kinetic Monte Carlo

Extraneous Projects

Implementation of the Alternating Direction Implicit Method to Solve Two Dimensional Heat Conduction with Mathematica

I've found from searching the Internet and several introductory texts that there doesn't appear to be any good examples showing the implementation of the ADI method. The few examples that do exist don't incorporate heating, apply homogeneous boundary conditions, and are written in old style FORTRAN77, which is difficult to read. With the below webpage and Mathematica notebook, I demonstrate the basics of how the ADI method works and how to apply Newton's law of cooling as a boundary condition. Although I do not use Mathematica to derive the general functions, I show how to use basic level programming techniques to solve for the temperature distribution.

In 3D, the ADI finite difference method is called Brian's method. I believe that I have this somewhere in my archive as a fully documented C function. If anyone would want a copy of this, I can give you what I have.


The ADI method in 2D
mathematica file Notebook for the ADI method in 2D

Solving Heat Conduction in One Dimension with Newton's cooling as Boundary Conditions using the Implicit Finite Difference Method

Along the same lines as the ADI method (above), here is a short Mathematica notebook that presents the a method for Solving Heat Conduction in One Dimension with Newton's cooling as Boundary Conditions using the Implicit Finite Difference Method.
mathematica file Notebook for 1D conduction using Implicit Finite Difference Method

Calculating the Concentration of Zirconium Point Defects in Silicon by Ab Initio Methods

As part of Prof. Haller's MSE223 course (U.C. Berkeley, Semiconducting Materials) we were to write a term paper on any topic in the field of semiconductors. Because I wanted to learn more about the methods to calculate parameters related to the concentration and motion of point defects in semiconductors I chose to write on this topic. I had seen a practice talk by Ravinder Sachdeva on the topic of Zr and Hf diffusion in Si so I chose as a proof of principle to apply the methods to calculate the equilibrium concentration of Zr in Si. Because I didn't have sufficient time to double check these results against experiment and other calculations, I don't know how much weight I would give to them; however, the methods presented here are sound. This draft is the paper prior to revisions suggested by the grading process. Here you can view the paper as html, postscript and pdf.

U.C. Berkeley MSE204, Midterm 1, Fall Semester 2000

Here is my solution to Prof. Gronsky's first midterm for his course Theory of Electron Microscopy and X-Ray Diffraction, from the fall semester of 2000. In general this was an enjoyable course, and I thought this midterm in particular was well designed. In addition to html, the solution is available as postscript, pdf, or Mathematica notebook.

Calculating 1D Concentration Profiles of Melt Zone Refined Materials

One of the topics presented in MSE223 (U.C. Berkeley, Semiconducting Materials) was melt zone refinement. Prof. Haller mentioned in class that it would be interesting to calculate the ultimate distribution. While I know that Pfeund has already done this, I thought it would be nice to have a Mathematica notebook that would allow the calculation of the 1D concentration profile as a function of melt zone pass number. Between classes over the first half of the Fall 2002, I wrote such a notebook.

The methods and results are presented as html and the Mathematica notebook for those interested.

Here is a comparison of my results to that of Burris et al., 1951. The match is fantastic. Using this software I generated a series of concentration curves that can be used for reference.

Somewhere in my archive I have a FORTRAN version of this software. I'll look for this and post it here.

Isotropic Elasticity Solution for the Equilibrium Separation of Partial Dislocations

Dislocations in semiconductors dissociate into partial Shockley partials separated by intrinsic stacking fault. The attractive restoring force between the two partials is the energy of the stacking fault. Here I calculate the equilibrium separation of a 90 and 30 degree partials in GaAs. While this isn't an astounding calculation, it's my first elasticity calculation. I've included the html and Mathematica notebook.

VASP and PARSEC data formatting tools

Pseudopotentials

I'm in the process of building a pseudopotential library. I have about a dozen norm-conserving pseudopotentials that I've constructed. Here I have posted good potentials for PbTiO3. Others will follow soon (I hope).

Nudged Elastic Band Tutorial

Alloy theory methods

This is a presentation that I gave to the Vanderbilt/Rabe joint group meeting. This is an overview talk, covering the virtual crystal approximation, cluster expansion method, and special quasirandom structure method. Toward the end I give details about generating SQS, because I am using these in my current research. At some point I would like to include additional information about the VCA method.

This is in powerpoint format. I'm in the process of learning to create presentations using LaTeX and in the future I will use nonproprietary format.

powerpoint format

PDF format