# 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.

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

27-201 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)

(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

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 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
- 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

**Laboratories Topics**

- 1/2 Line Defect Laboratory:
*Generation and Polygonization of Dislocations in Rock Salt* - 3/4 Area Defect Laboratory:
*Density and Grain Size of Annealed TiO*_{2}Polycrystalline Compacts - 5/6 Point Defect Laboratory:
*Electrical Conductivity of Oxygen Vacancy doped TiO*_{2}

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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

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*[top]

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 mixing
- 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 and volume and of a system held at constant temperature and pressure
- Conditions of equilibrium for multiphase, multi-component systems
- Heat capacities, Einstein model, Law of Dulong and Petit
- Third law of thermodynamics
- Phase equilibrium in one component systems
- Phase diagrams in one component 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 YBa*_{2}Cu_{3}O_{7-x}(superconducting phase) and Y_{2}BaCuO_{5}(pinning phase) in the Y-Ba-Cu-O system*Solid State synthesis (SSS) of YBa*_{2}Cu_{3}O_{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 YBa*_{2}Cu_{3}O_{7-x}with Y_{2}BaCuO_{5}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**

- Course Overview; what is a material property?
- Coordinate transformations and tensors
- Material tensors and symmetry
- Stereology and Microstructure Measurements
- Introduction to Lab I and II
- Linear Elasticity
- Electrical and Magnetic Properties I
- Electrical and Magnetic Properties II
- Optical and Non-Linear Properties
- Thermal and Other Transport Properties
- Tensor Properties in Polycrystalline Materials I
- Tensor Properties in Polycrystalline Materials II
- Strength and Ductility
- The Hall-Petch Effect and Creep
- Superalloys as examples of multiphase systems
- Fracture
- Transformation Toughening
- Composities
- Characterization of Microstructures

**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

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27-210: Materials Engineering Essentials (6 units)

**Lecture Topics**

TBD

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