Computational Materials Science

Parts 1 and 2 of the course text: Computational Materials Science: Fundamentals to Applications by R. LeSar (ISBN978-0-521-84587-8).

Home work and many of the illustrations utilize Jupyter notebooks. The notebooks give practical instruction about implementation of various models and methods. Non-mandatory exercises can be used for every chapter as a preparation for the exam.

Modeling and simulation. What is meant by computational materials science and engineering? Scales in materials structure and behavior. How to develop models

The random-walk model

Random-walk model of diffusion

Bulk diffusion

Random-walk models for materials

Simulation of finite and infinite systems

Sums of pair interactions

Perfect crystals

Cutoffs & Long-ranged potentials

Periodic boundary conditions

Electronic structure methods

Quantum mechanics of multielectron systems

Early density functional theories

The Hohenberg-Kohn theorem & Kohn-Sham method

The exchange-correlation functional

Wave functions

Pseudopotentials

Use of density functional theory

Interatomic potentials

The cohesive energy

Pair potentials

Ionic materials, Metals, Covalent solids

Systems with mixed bonding

Determining parameters in potentials

Molecular dynamics

Basics of molecular dynamics for atomic systems, integrating Newton's equations of motion

Ensembles, NVE (microcanonical), NVT (canonical), and others

Velocity rescaling and Thermostats

Molecular dynamics in other ensembles, calculating the stress tensor

Limitations of molecular dynamics, accelerated dynamics

Molecular dynamics in materials research

The Monte Carlo method

Random numbers, integration in many dimensions, ensemble averages

The Metropolis algorithm

The Ising model

Monte Carlo for atomic systems

Other ensembles

Time in a Monte Carlo simulation

Uses of the Monte Carlo method in materials research

computational materials science II (MS43205) is a follow-up course. In the follow-up the 2nd part of the textbook by LeSar is covered.