Department of Materials Science & Engineering

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Core Course Content

The following pages list 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
27-299, -399, -499: Professional Development I, II, and III

27-100 Engineering the Materials of the Future
(Introduction to Materials, 12 Units)

Lecture Topics

Materials Science and Engineering: Structure-Property-Processing-Performance; Materials Classifications.
Atomic Structure and Bonding: Atomic Structure; Electronic Configurations and Quantum numbers; Bonding: metallic, ionic, covalent.
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.
Defects: Points Defects— Composition of Alloys; Line Defects— Dislocations; Planar Defects;Volume Defects.
Diffusion: Modes of diffusion; Activation energy: bonding and structure; Steady state and Fick's First Law; Diffusivity and Temperature.
Phase Diagrams: Equilibrium and Other Definitions; Solutions and Solubility; Interpreting Phase Diagrams: Phases, Compositions, Relative Amounts; Simple Binary and Eutectic diagrams.
Microstructure: Microstructure and Other definitions; Relationship to Phase Diagram and Processing; Controlling Microstructures; Equilibrium vs Non-equilibrium.
Phase Transformations: Nucleation and Growth; Diffusion and Phase transformations;T-T-T or C-C-T diagrams; Diffusionless Transformations.
Mechanical Properties of Materials: Stress and Strain; Deformation Modes; Yield and Fracture; Engineering Mechanical Properties.
Deformation and Strengthening: Dislocations and slip systems; Plastic Deformation; Strengthening Mechanisms; Recovery, Recrystallization, and Grain Growth.
Ceramics: Crystal Structures; Mechanical Properties; Processing; Applications.
Polymers: Molecular Structures; Crystalline Structures; Glass Transition; Mechanical Properties.
Electronic Materials: Electrical Properties; Energy Bands in Solids; Metal-Semiconductors-Insulators; Semiconductors; Diodes and Transistors; Ferroelectrics and Piezoelectrics.
Composite Materials: Particle-reinforced composites; Dispersion-strengthened composites; Fiber-reinforced composites; Structural composites.

Laboratories Topics

Introduction to Materials and Fabrication
• Casting of Brass
• Rolling Casting of Co-Block Polymer
• Slip Casting of Ceramics
• Lay-up of Fiberglass Composite
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
Mechanical Deformation, Recrystallization and Phase Transformations
• Cold Rolling and Recrystallization of Brass
• Thermal Transformations in Steels
Optical Microscopy of Cold Rolled and Recrystallized Brass
Scanning Electron Microscopy of Fracture Surfaces

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27-201 The Structure of Materials (6 + 3 Units)

Lecture Topics

Macroscopic Properties
Periodic Table, Energy Levels
Different Types of Bonding
Crystal Structures – Bravais Lattice
Lattices, Directions & Distances
Lattice Geometry and the Metric Tensor, Crystal Planes
Crystal Planes and Miller Indices
Reciprocal Space and Reciprocal Metric Tensor
Reciprocal Space and Computations
Stereographic Projections
Zones and Habits
Symmetry Operations – I
Symmetry Operations – II
Point Groups – I
Point Groups – II
Space Groups – I
Space Groups – II
X-ray Diffraction-I
X-ray Diffraction-II
X-ray Diffraction-III
Metal Structures-I
Topologically Close Packed Phases and Quasicrystals
Ceramic Structures
Molecular Solids and Biomaterials
Macromolecular Solids
Special Topics

Laboratories Topics

Introduction – Laboratory Safety
Software, Hardware & Library Resources
Carnegie Museum: Minerals and Gemstones
Periodic Table, Solid Structures (TAPP, CrystalMaker Software)
Plane Groups, Symmetry, Optical Diffraction
Space Groups, Pauling’s Rules, X-Ray Diffraction
X-Ray Diffraction

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27-202 Defects in Materials (6 + 3 Units)

Lecture Topics

Overview and Importance of Defects
Line Defects
Dislocations: crystal growth and plasticity
Structure of dislocations: edge, screw, non-equilibrium nature
Structure of dislocation: Burger’s Vectors
Observation and quantification of dislocations
Dislocation motion: sip, slip systems
Dislocation motion: slip
Dislocation motion: climb
Elastic properties of dislocations
Energy of dislocations
Interaction of dislocations
The origin of dislocations
Multiplication of dislocations
Point Defects
Point defects in elemental solids: types and definition of their formation energy
The equilibrium defect concentration in an elemental solid
Measurements of point defects
Point defects in compound solids: Kroger-Vink and defect reaction rules
The equilibrium defect concentration of a compound solid: law of mass action
Intrinsic electronic disorder and extrinsic doping reactions
Non-stoichiometry and defect concentrations
Solid-gas equilibrium and defect concentrations
Area Defects
Area defects and dislocation arrays
Surface energy and conceptual models
Surface energy anisotropy: conceptual models and polar plots
Equilibrium crystal shape: Wulff construction
Grain boundary crystallography and structure
Grain boundaries energies: Read Shockley Model / High angle models
Interfacial equilibrium: angles at triple points

Laboratories Topics

1/2 Line Defect Laboratory:
	Generation and Polygonization of Dislocations in Rock Salt

3/4 Point Defect Laboratory:
	Synthesis and Magnetic Properties of Y_xGd_3-xFe₅O₁₂ Garnets
5/6 Area Defect Laboratory:
	Density and Grain Size of Annealed TiO₂ Polycrystalline Compacts

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27-205 Materials Characterization Lab (3 Units)

Lecture Topics

Fundamentals of Surface Scanning Techniques - AFM
Fundamentals of Electron Beam Interactions - SEM
Fundamentals of Electron Beam Interactions - EDS
UV/VIS Spectroscopy Vacuum Systems
Vacuum Systems

Laboratories Topics

Operation of Electron Optics Equipment (SEM)
Operation of Spectroscopy Equipment (EDS)
Operation of Surface Microscopy Equipment (AFM)
Operation of UV/VIS Spectromete

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27-215 Thermodynamics of Materials (12 Units)

Lecture Topics

Microstructure, phase transformations and phase diagrams
Systems, boundaries, surroundings, equilibrium states, state functions and processes, extensive/intensive variables Reversible and spontaneous processes.
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
Heat capacities and processes for ideal gases
Thermochemistry: primarily changes in H as a function of path
Reversible and spontaneous processes and the Second law, introduction of the state function entropy (S)
Entropy changes due to heat transfer and production of entropy within the system
Review different statements of the Second Law, concept of maximum work, combined statement of the First and Second Laws; introduction to partial derivatives
Statistical mechanics, configurational entropy and the entropy of
Statistical mechanics, the Boltzman distribution, application of statistical mechanics to ideal gases
Thermodynamic variables and relations, Maxwell relations, chemical potential, Gibbs-Helmholtz equation
Conditions for equilibrium of an isolated system, of a system held at constant temperature (T) and V and of a system held at constant T and P
Conditions of equilibrium for multiphase, multi-component systems
Heat capacities, Einstein model, Law of Dulong and Petit
Third law, S(T) at constant V or P; DeltaS of a phase change
Phase equilibrium in one component systems
Phase diagrams in P-T space, Clapeyron equation, Clausius-Clapeyron equation; saturated vapor pressures
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
Equations of state for real gases; thermodynamics of ideal gases
Chemical reactions involving gases
Chemical activity and its relation to the chemical potential and Ideal Solutions
Non-ideal and regular solutions
Gibbs free energy (G) versus composition curves, standard states, changing standard states, tangency rule for equilibrium
Constructing phase diagrams from thermodynamic data

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27-216 Transport in Materials (9 Units)

Lecture Topics

Course introduction
Kinetics of homogeneous reactions
Temperature dependency of reaction rates and analysis
Mass transfer in solids: Random walk and Fick’s 1st law
Diffusion coefficient (D), mechanisms of diffusion including fast paths
Fick’s 2nd law, 1D steady state diffusion and 1D transient thin film source
1D transient semi-infinite-solutions – Method of Laplace
Reciprocal 1D transient semi-infinite-solutions – Method of Laplace, continued
Diffusion in binary systems-Kirkendall effect, Darken’s Analysis
Diffusion couples with variable D – Darkens Phenomenological Analysis
Diffusion couples with variable D – Bolzmann-Matano
Diffusion mechanisms and ion-migration in ceramic materials
Mass transport in polymers, non-Fickian and anomalous diffusion and mass transport fluids and pores
Combined mass transfer and interfacial reactions
Heat transfer conduction - Steady state
Heat transfer conduction - Transient solutions
Heat transfer radiation
Viscous properties of fluids, Equation of continuity, Navier Stoke’s equation
Navier Stoke’s equation, pipe flow examples
Laminar flow, boundary layer and heat transfer coefficient
Turbulent and complex flow
Natural convection

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27-217 Phase Relations and Diagrams (9 + 3 Units)

Lecture Topics

Review of Thermodynamics
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
Phase Transformations
•  Interfaces and Homogeneous Nucleation
•  Nucleation and Growth, Coarsening, and the Gibbs-Thompson Eq.
•  Diffusional Transformations
•  Diffusionless Transformations

Laboratories

High Temperature Ceramic Superconductor (HSTC) in the Y-Ba-Cu-O System: Processing-Structure-Property Relationship

Crystal Maker, Crystal Diffract: Unit Cells and Diffraction patterns of YBa₂Cu₃O_7-x (superconducting phase) and Y₂BaCuO₅ (pinning phase) in the Y-Ba-Cu-O system
Solid State synthesis (SSS) of YBa₂Cu₃O_7-x via powder processing (grinding, pressing, annealing)
Preparation of SSS powder for X-ray diffraction, preparation of powder samples for melt process melt growth of YBa₂Cu₃O_7-x with Y₂BaCuO₅ pinning phase, pressing and heat treatment
Preparation of powder of the MPMG sample for x-ray diffraction,
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)
Group poster presentation

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27-301 Microstructure and Properties I (6 + 3 Units)

Lecture Topics

What is Microstructure? Descriptions and definitions of microstructural elements. How do we measure microstructure? Outline of microstructural characterization for multiphase materials.
Review of properties: scalar properties, tensor properties, scalar approximations to tensor properties. Example of Properties: how stiff is a (multiphase) material? Elastic properties, Young's modulus, effect of crystal structure, simple composite structures, iso-stress vs. iso-strain models.
Where does Microstructure come from? Elementary theory of nucleation and growth in the solid state, application to precipitation of a new phase as discrete particles (diffusional transformation only)
What influence does microstructure have on phase transformation? Effect of vacancies, dislocations, boundaries [first part of Ch.5 of Porter & Easterling]
Important examples of solid state transformations. Age hardening aluminum alloys for aerospace [e.g. Ch. 12 in Haasen's Physical Metallurgy]. Crystallization in glass-ceramics and toughness (elementary Griffith theory) application to Pyrex. TTT curves.
How does microstructure affect properties? Shear Strength of crystals; effect of second phase particles on shear strength; how to exploit a phase transformation to develop precipitates; Orowan looping; age-hardening behavior.
More complex phase transformations: eutectoid decomposition and the Fe-C diagram, lamellar (pearlitic) structures,
Elementary magnetism (emphasizing domain walls, the B-H loop): effect of microstructure on hard versus soft magnets, contrast electrical steels with metallic glasses.
Transformation toughening of ceramics: example of zirconia in alumina; alternate example, ferroelectric ceramics, e.g. Pb-La-Zr-titanate (PLZT).
Composite materials: distinction between second phases arising from processing and composites as man-made multiphase materials. Types of composites (laminar versus fibrous). Applications of composites to aerospace, automotive, biomedical, sports, electronic, defense.
How are composites made? Fabrication methods for composites.
Elastic properties of composites: how to design the thermal expansion of a composite.
Review of transformation rules for tensors, symmetry; Overview of important linear material tensors; constitutive relations application to composites.
Design of composite materials for high strength, high [electrical] conductivity: application to very high field magnets.

Laboratories

Coming Soon

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27-367 Selection and Performance of Materials (6 Units)

Lecture Topics

Course Introduction, Influence of Design, The Design Process
Overview of the Design Process
Structurally Insensitive Properties, Relationship of Moduli, Microstructural sensitive properties
Procedure for Selection of Materials, Material Charts, Attribute Limits, and Material Indices
Type One Hybrid Materials,
Hybrid Materials, Type Two, Type Three, Type Four
Uncoupled Constraints Problems
Multiple Constraints and Objectives
Influence of Shape, Shape Factor
Processes, Shaping Processes, Casting
Shaping Processes, Powder, Forging, Molding
Rolling, Special Methods, Composite Fabrication, Joining, Mechanical Fastening, Welding
Process selection, Ashby charts, Economics
Risk Reliability Safety and Quality, Standards, Quality Systems
Fracture Mechanics
Fatigue, Failure Analysis
Design for Wear
Design for Thermal Conditions
Environmentally Conscious Material Selection
Design Attributes, Psychology of Design