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

##### Start Date
Self Paced
Course Auditing
Categories
Effort
Certification
Languages
University-level Calculus. Structure of Materials (Ideally, 3.012Sx: Structure of Materials. Thermodynamics (ideally, 3.012Tx: Thermodynamics of Materials)
Misc

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Discover the principles of statistical mechanics that explain materials science phenomena. This module is Part 1 of a four-part series on the Microstructural Evolution in Materials. Taken together, these four modules provide similar content to the MIT Course 3.022: Microstructural Evolution of Materials. This series introduces various kinetic phenomena in various classes of materials. The course explains how materials develop different microstructure based on different processing techniques, and it relates these microstructures to the properties of the material.

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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

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