Microstructural Evolution of Materials Part 1: Statistical Mechanics (edX)

Microstructural Evolution of Materials is intended for engineering and science students and professionals with an interest in materials statistics, kinetics, and microstructural transformations.

Part 1 of the course will introduce important concepts in statistical mechanics that are especially relevant to materials scientists. Topics include solid solutions, the canonical ensemble and heat capacity.

Part 2 of the course focuses on point defect evolution, including diffusion, substitutional diffusion, ionic defects, and ionic conductivity.

Part 3 of the course discusses surfaces and surface-driven reactions. Topics include surface energy, faceted and non-faceted growth, and growth and ripening.

Part 4 of the course focuses on phase transformations, including nucleation and growth, precipitate growth, interface stability, and glass transition.

What you'll learn:

At the end of this course, you will be able to:

- Explain the entropy of a solid solution from a quantum mechanical perspective

- Understand the trends in heat capacity of a monatomic gas and an atomic solid

- Use the canonical distribution to explain both the effect of gravitational force on the density of a gas and the origin of Curie’s law of paramagnetism

Syllabus

Introduction

- What is an ensemble?

- The Microcanonical Ensemble

- Fluctuations in a System

- Statistical Interpretations of Entropy

Solid Solutions

- Particle Distinguishability

- Gibbs Theorem

- Ideal Solid Solutions and Ideal Gasses

- Regular Binary Solution Theory

- Determining Phase Composition in Binary Solution

Canonical Ensemble

- Deriving the Canonical Distribution for N=5

- Deriving the Canonical Distribution

- The Partition Function

Canonical Ensemble: Application

- Example: Effect of Gravitational Force on Gas Density

- Example: Paramagnetism Materials

Heat Capacity

- Heat Capacity of an Ideal Gas

- Heat Capacity of Atomic Solids

- The Debye Model