Carnegie Mellon University

Core Course Content

Follows is a list of the topical content of all core courses in Materials Science and Engineering.
Numbers describe approximate order of coverage by topics.
27-100 Engineering the Materials of the Future (Introduction to Materials)
27-201 The Structure of Materials
27-202 Defects in Materials
27-205 Materials Characterization Lab
27-215 Thermodynamics of Materials
27-216 Transport in Materials
27-217 Phase Relations and Diagrams
27-301 Microstructure and Properties I
27-367 Selection and Performance of Materials
27-210: Materials Engineering Essentials

27-100 Engineering the Materials of the Future
(Introduction to Materials, 12 Units)
Lecture Topics
  1. Materials Science and Engineering: Structure-Property-Processing-Performance; Materials Classifications.
  2. Atomic Structure and Bonding: Atomic Structure; Electronic Configurations and Quantum numbers; Bonding: metallic, ionic, covalent.
  3. Crystal Structures: Crystalline vs Amorphous Solids; Unit Cell, Lattice, and Crystal Systems; Common Cubic Crystal Systems; Packing Fractions, Density, and Close Packing; Crystallographic Directions and Planes.
  4. Defects: Points Defects — Composition of Alloys; Line Defects — Dislocations; Planar Defects;Volume Defects.
  5. Diffusion: Modes of diffusion; Activation energy: bonding and structure; Steady state and Fick's First Law; Diffusivity and Temperature.
  6. Phase Diagrams: Equilibrium and Other Definitions; Solutions and Solubility; Interpreting Phase Diagrams: Phases, Compositions, Relative Amounts; Simple Binary and Eutectic diagrams.
  7. Microstructure: Microstructure and Other definitions; Relationship to Phase Diagram and Processing; Controlling Microstructures; Equilibrium vs Non-equilibrium.
  8. Phase Transformations: Nucleation and Growth; Diffusion and Phase transformations;T-T-T or C-C-T diagrams; Diffusionless Transformations.
  9. Mechanical Properties of Materials: Stress and Strain; Deformation Modes; Yield and Fracture; Engineering Mechanical Properties.
  10. Deformation and Strengthening: Dislocations and slip systems; Plastic Deformation; Strengthening Mechanisms; Recovery, Recrystallization, and Grain Growth.
  11. Ceramics: Crystal Structures; Mechanical Properties; Processing; Applications.
  12. Polymers: Molecular Structures; Crystalline Structures; Glass Transition; Mechanical Properties.
  13. Electronic Materials: Electrical Properties; Energy Bands in Solids; Metal-Semiconductors-Insulators; Semiconductors; Diodes and Transistors; Ferroelectrics and Piezoelectrics.
  14. Composite Materials: Particle-reinforced composites; Dispersion-strengthened composites; Fiber-reinforced composites; Structural composites.
Laboratories Topics
  1. Introduction to Materials and Fabrication
    •  Casting of Brass
    •  Rolling Casting of Co-Block Polymer
    •  Slip Casting of Ceramics
    •  Lay-up of Fiberglass Composite
  2. Material Property Testing
    •  Tensile Testing of Metals, Polymers, and Composites
    •  Elastic Modulus Determination for Elastomers
    •  Three Point Bend Testing of Ceramics
    •  Determination of Glass Transition Temperature in Silicon Rubber
  3. Mechanical Deformation, Recrystallization and Phase Transformations
    •  Cold Rolling and Recrystallization of Brass
    •  Thermal Transformations in Steels
  4. Optical Microscopy of Cold Rolled and Recrystallized Brass
  5. Scanning Electron Microscopy of Fracture Surfaces

27-201 The Structure of Materials (6 + 3 Units)
Lecture Topics
  1. Macroscopic Properties
  2.  Periodic Table, Energy Levels
  3. Different Types of Bonding
  4. Crystal Structures – Bravais Lattice
  5. Lattices, Directions & Distances
  6. Lattice Geometry and the Metric Tensor, Crystal Planes
  7. Crystal Planes and Miller Indices
  8. Reciprocal Space and Reciprocal Metric Tensor
  9. Reciprocal Space and Computations
  10. Stereographic Projections
  11. Zones and Habits
  12. Symmetry Operations – I
  13. Symmetry Operations – II
  14. Point Groups – I
  15. Point Groups – II
  16. Space Groups – I
  17. Space Groups – II
  18. X-ray Diffraction-I
  19. X-ray Diffraction-II
  20. X-ray Diffraction-III
  21. Metal Structures-I
  22. Topologically Close Packed Phases and Quasicrystals
  23. Ceramic Structures
  24. Molecular Solids and Biomaterials
  25. Macromolecular Solids
  26. Special Topics
Laboratories Topics
  1. Introduction – Laboratory Safety
  2. Software, Hardware & Library Resources
  3. Carnegie Museum: Minerals and Gemstones
  4. Periodic Table, Solid Structures (TAPP, CrystalMaker Software)
  5. Plane Groups, Symmetry, Optical Diffraction
  6. Space Groups, Pauling’s Rules, X-Ray Diffraction
  7. X-Ray Diffraction

27-202 Defects in Materials (6 + 3 Units)
Lecture Topics
  1. Overview and Importance of Defects Line Defects
  2. Dislocations: crystal growth and plasticity
  3. Structure of dislocations: edge, screw, non-equilibrium nature
  4. Structure of dislocation: Burger’s Vectors
  5. Observation and quantification of dislocations
  6. Dislocation motion: sip, slip systems
  7. Dislocation motion: slip
  8. Dislocation motion: climb
  9. Elastic properties of dislocations
  10. Energy of dislocations
  11. Interaction of dislocations
  12. The origin of dislocations
  13. Multiplication of dislocations Area Defects
  14. Area defects and dislocation arrays
  15. Surface energy and conceptual models
  16. Surface energy anisotropy: conceptual models and polar plots
  17. Equilibrium crystal shape: Wulff construction
  18. Grain boundary crystallography and structure
  19. Grain boundaries energies: Read Shockley Model / High angle models
  20. Interfacial equilibrium: angles at triple points
  21. Point Defects
  22. Point defects in elemental solids: types and definition of their formation energy
  23. The equilibrium defect concentration in an elemental solid
  24. Measurements of point defects
  25. Point defects in compound solids: Kroger-Vink and defect reaction rules
  26. The equilibrium defect concentration of a compound solid: law of mass action
  27. Intrinsic electronic disorder and extrinsic doping reactions
  28. Non-stoichiometry and defect concentrations
  29. Solid-gas equilibrium and defect concentrations
Laboratories Topics
  1. 1/2 Line Defect Laboratory: Generation and Polygonization of Dislocations in Rock Salt
  2. 3/4 Area Defect Laboratory: Density and Grain Size of Annealed TiO2 Polycrystalline Compacts
  3. 5/6 Point Defect Laboratory: Electrical Conductivity of Oxygen Vacancy doped TiO2

27-205 Materials Characterization Lab (3 Units)
Lecture Topics
  1. Fundamentals of Materials Characterization
  2. Basics of Surface Analysis by Scanning Probe Microscopy - SPM
  3. Micro/nano-scale Imaging by Scanning Electron Microscopy - SEM
  4. Compositional Analysis by Energy Dispersive Spectroscopy - EDS
  5. Structural Analysis by X-ray Diffraction and Rietveld Method - XRD
Laboratories Topics
  1. Hands-on Training/Operation of Tabletop SEM/EDS
  2. Hands-on Training/Operation of SPM
  3. Hands-on Training/Operation of XRD and Rietveld methods

27-215 Thermodynamics of Materials (12 Units)

Lecture Topics
  1. Microstructure, phase transformations and phase diagrams
  2. Systems, boundaries, surroundings, equilibrium states, state functions and processes, extensive/intensive variables, reversible and spontaneous processes.
  3. Zero-th Law, work (W), heat (Q), internal energy (U), First Law, ideal gas, units, enthalpy (H), constant volume V) and constant  pressure (P) processes
  4. Heat capacities and processes for ideal gases
  5. Thermochemistry: primarily changes in H as a function of path
  6. Reversible and spontaneous processes and the Second law, introduction of the state function entropy (S)
  7. Entropy changes due to heat transfer and production of entropy within the system
  8. Review different statements of the Second Law, concept of maximum work, combined statement of the First and Second Laws; introduction to partial derivatives
  9. Statistical mechanics, configurational entropy and the entropy of mixing
  10. Statistical mechanics, the Boltzman distribution, application of statistical mechanics to ideal gases
  11. Thermodynamic variables and relations, Maxwell relations, chemical potential, Gibbs-Helmholtz equation
  12. Conditions for equilibrium of an isolated system, of a system held at constant temperature and volume and of a system held at constant temperature and pressure
  13. Conditions of equilibrium for multiphase, multi-component systems
  14. Heat capacities, Einstein model, Law of Dulong and Petit
  15. Third law of thermodynamics
  16. Phase equilibrium in one component systems
  17. Phase diagrams in one component space, Clapeyron equation, Clausius-Clapeyron equation; saturated vapor pressures
  18. Euler's theorem, partial molar quantities, the use of Euler’s theorem to write state functions in terms of their partial molar quantities, Gibbs-Duhem equation
  19. Equations of state for real gases; thermodynamics of ideal gases
  20. Chemical reactions involving gases
  21. Chemical activity and its relation to the chemical potential and Ideal Solutions
  22. Non-ideal and regular solutions
  23. Gibbs free energy (G) versus composition curves, standard states, changing standard states, tangency rule for equilibrium
  24. Constructing phase diagrams from thermodynamic data

27-216 Transport in Materials (9 Units)
Lecture Topics
  1. Course introduction
  2. Kinetics of homogeneous reactions
  3. Temperature dependency of reaction rates and analysis
  4. Mass transfer in solids: Random walk and Fick’s 1st law
  5. Diffusion coefficient (D), mechanisms of diffusion including fast paths
  6. Fick’s 2nd law, 1D steady state diffusion and 1D transient thin film source
  7. 1D transient semi-infinite-solutions – Method of Laplace
  8. Reciprocal 1D transient semi-infinite-solutions – Method of Laplace, continued
  9. Diffusion in binary systems-Kirkendall effect, Darken’s Analysis
  10.  Diffusion couples with variable D – Darkens Phenomenological Analysis
  11. Diffusion couples with variable D – Bolzmann-Matano
  12. Diffusion mechanisms and ion-migration in ceramic materials
  13. Mass transport in polymers, non-Fickian and anomalous diffusion and mass transport fluids and pores
  14. Combined mass transfer and interfacial reactions
  15. Heat transfer conduction - Steady state
  16. Heat transfer conduction - Transient solutions
  17. Heat transfer radiation
  18. Viscous properties of fluids, Equation of continuity, Navier Stoke’s equation
  19. Navier Stoke’s equation, pipe flow examples
  20. Laminar flow, boundary layer and heat transfer coefficient
  21. Turbulent and complex flow
  22. Natural convection

27-217 Phase Relations and Diagrams (9 + 3 Units)
Lecture Topics
  1. Review of Thermodynamics
  2. Phase Diagrams
    •  Phase Diagram Concepts and the Lever Rule
    •  Binary Phase Diagrams
    •  Development of Microstructure
    •  Free Energy Curves
    •  Calculation of Binary Phase Diagrams
    •  Ideal Solution Model
    •  The Quasichemical Model and the Regular Solution Model
    •  Compounds and Intermediate Phases, Solid Solutions and Hume-Rothery Rules
    •  Ternary Phase Diagrams
  3. Phase Transformations
    •  Interfaces and Homogeneous Nucleation
    •  Nucleation and Growth, Coarsening, and the Gibbs-Thompson Eq.
    •  Diffusional Transformations
    •  Diffusionless Transformations
High Temperature Ceramic Superconductor (HSTC) in the Y-Ba-Cu-O System: Processing-Structure-Property Relationship
  1. Crystal Maker, Crystal Diffract: Unit Cells and Diffraction patterns of YBa2Cu3O7-x (superconducting phase) and Y2BaCuO5 (pinning phase) in the Y-Ba-Cu-O system
  2. Solid State synthesis (SSS) of YBa2Cu3O7-x via powder processing (grinding, pressing, annealing)
  3. Preparation of SSS powder for X-ray diffraction, preparation of powder samples for melt process melt growth of YBa2Cu3O7-x with Y2BaCuO5 pinning phase, pressing and heat treatment
  4. Preparation of powder of the MPMG sample for x-ray diffraction,
  5. Levitation of a Nd-Fe-B magnet above the SSS and MPMG samples immersed in liquid nitrogen, levitation recorded by digital photography, preparation of SSS and MPMG samples for optical microscopy (grinding, polishing, etching)
  6. Group poster presentation

27-301 Microstructure and Properties I (6 + 3 Units)
Lecture Topics
  1. Course Overview; what is a material property?
  2. Coordinate transformations and tensors
  3. Material tensors and symmetry
  4. Stereology and Microstructure Measurements
  5. Introduction to Lab I and II
  6. Linear Elasticity
  7. Electrical and Magnetic Properties I
  8. Electrical and Magnetic Properties II
  9. Optical and Non-Linear Properties
  10. Thermal and Other Transport Properties
  11. Tensor Properties in Polycrystalline Materials I
  12. Tensor Properties in Polycrystalline Materials II
  13. Strength and Ductility
  14. The Hall-Petch Effect and Creep
  15. Superalloys as examples of multiphase systems
  16. Fracture
  17. Transformation Toughening
  18. Composities
  19. Characterization of Microstructures
Coming Soon


27-367 Selection and Performance of Materials (6 Units)
Lecture Topics
  1. Course Introduction, Influence of Design, The Design Process
  2. Overview of the Design Process
  3. Structurally Insensitive Properties, Relationship of Moduli, Microstructural sensitive properties
  4. Procedure for Selection of Materials, Material Charts, Attribute Limits, and Material Indices
  5. Type One Hybrid Materials,
  6. Hybrid Materials, Type Two, Type Three, Type Four
  7. Uncoupled Constraints Problems
  8. Multiple Constraints and Objectives
  9. Influence of Shape, Shape Factor
  10. Processes, Shaping Processes, Casting
  11. Shaping Processes, Powder, Forging, Molding
  12. Rolling, Special Methods, Composite Fabrication, Joining, Mechanical Fastening, Welding
  13. Process selection, Ashby charts, Economics
  14. Risk Reliability Safety and Quality, Standards, Quality Systems
  15. Fracture Mechanics
  16. Fatigue, Failure Analysis
  17. Design for Wear
  18. Design for Thermal Conditions
  19. Environmentally Conscious Material Selection
  20. Design Attributes, Psychology of Design

27-210: Materials Engineering Essentials (6 units)
Lecture Topics