Advanced Characterization and Microstructural Analysis

Timetable of Lectures

Week 1 --- Anthony Rollet Introduction to Microstructure, including texture: examples of engineering problems involving texture; orientation as rotation; PFs Measurement of pole figures, theoretical construction of PFs Homework: construction of PFs; projections

Week 2 --- ADR Concept of Orientation Distribution; Euler angles; discrete vs. functional ODs How to fit a discrete OD to experimental data (PFs); popLA demonstration (rolled Cu) Homework: use popLA to analyze a given set of PF data (Cu fiber textures in thin films, provided by Mr. Ali Gungor, CMU)

Week 3 --- ADR Texture Components; different representations; relationships between them Fiber textures, example of fiber textures in thin film Al, HTSC Homework: measurement of a set of PF data (each site to provide a specimen: CMU specimens = 6111 aluminum alloy, provided by Prof. D. Embury, McMaster Univ.)

Week 4 --- ADR Volume fractions; invariant measure; how to extract useful information from data sets Different methods of representing ODs; square, polar plots Homework: exercises on conversion between different representations of orientation (last year’s hwk #1)

Week 5 --- ADR Symmetry; Groups (elementary theory); Sample vs. Crystal Symmetry Effect of symmetry on Representation of Texture Homework: calculation of ODs from measured textures; calculation of volume fractions

Week 6 --- ADR In-class demonstration of effect sample symmetry with popLA Common Textures in metals (bulk, thin films), ceramics (thin films) Homework: literature search

Week 7 --- ADR Functions to represent texture; Fourier transforms; spherical harmonics Fundamental equation of texture Homework: plotting spherical harmonics Week 8 --- ADR Tensors; recapitulation of algebra of tensors; transformations Anisotropy; basic equation(s) for linear anisotropy; Elastic Anisotropy Homework: mastery of tensor algebra

Week 9 --- ADR / Brent Adams Brent Adams: Applications of elastic anisotropy; limits on elastic anisotropy Grain Boundaries; degrees of freedom; misorientations; Rodrigues vectors, space Homework: exercises on elastic anisotropy (probably from Courtney or Nye); conversion between different representations of g.b. crystallography

Week 10 --- Peter Kalu Microscopy; overview of different methods; Optical Microscopy Electron Microscopy; Transmission Electron Microscopy Homework: Take Home Exam

Week 11 --- CMU Spring Break

Week 12 Scanning Electron Microscopy (SEM) Grain Boundaries; properties: energy, mobility Homework:

Week 13 --- Greg Rohrer / Peter Kalu Atomic Force Microscopy (AFM) EBSD / Orientation Imaging Microscopy Homework:

Week 14 --- ADR Stereology; Delesse’s Principle; Elementary results Herring’s Relations for Triple Junctions; extension to velocities Homework: Exercise in Geometric Probability; exercise on TJ relationships

Week 15 --- ADR Plastic Anisotropy; Schmid’s Law; Rate Sensitive Yield; Yield Surfaces Taylor Model for large strain plastic deformation and texture development Homework: construction of single crystal yield surfaces

Week 16 Demonstration of polycrystal plasticity calculations (LApp) Wrap-up Homework:

Exam: Take-home