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