Core Course Content

The following pages describe the content of all core courses, broken down according to the number of lectures available.

27-201 Perfect Crystals

# Topic
1 Macroscopic Aspects of Crystals, Periodic Table
2 Different Types of Bonding
3 Material Properties, Crystal Systems
4 Bravais Lattices, Crystal Directions
3 Lattice Geometry and Metric Tensor, Plane Normals
4 Stereographic Projection, Reciprocal Space
5 Reciprocal Metric Tensor, Zone equation
6 Symmetry Operations
7 Point Groups
8 Space Groups
9 Representation of Crystal Structures
10 Important Crystal Structures
11 X-ray diffraction: geometry
12 X-ray diffraction: intensities
13 Important Crystal Structures and diffraction
14 Diffraction applications

27-202 Defects in Materials

# Topic
1 The equilibrium defect concentration in an elemental solid
2 The equilibrium defect concentration of a compound solid
3 The solid-gas equilibrium and defect concentrations
4 Impurities and defect concentrations
5 Dislocations: Crystal growth and plasticity
6 Structure and observation of dislocations
7 Dislocation motion: slip and climb
8 Elastic properties of dislocations
9 Dislocations in fcc materials
10 The origin and multiplication of dislocations
11 Surface Energy
12 Surface energy anisotropy and the equilibrium crystal shape
13 Grain boundary crystallography and structure
14 Special boundaries; Interfacial equilibrium

27-215 Thermodynamics of Materials

# Topic
1 Microstructure, phase transformations and phase diagrams
2 Systems, boundaries, surroundings, equilibrium states, state functions and processes, extensive/intensive variables
3 Zero-th law, first law, ideal gas, units, enthalpy, constant volume and constant pressure processes
4 Heat capacities and processes for ideal gases
5 Thermochemistry: mainly changes in H as a function of path
6 Reversible and spontaneous processes and second law, examples, motivation that S is state function
7 Entropy changes due to heat transfer and production of entropy within the system
8 Review statements 2nd law, concept of maximum work, combined statement 1st,2nd law; application partials to variables
9 Stat. mech. and configurational entropy; entropy of mixing
10 Stat. mech., Boltzman distribution, S(U,V); relation DeltaS-Q, and DeltaS>0 in free adiabatic expansion
11 Thermodynamic variables and relations, Maxwell relations, chemical potential, Gibbs-Helmholtz equation
12 Equilibrium in isolated system, system at constant T and V, constant T and P
13 Multiphase systems, example of equilibrium at constant T and V
14 Heat capacities, Einstein model, Dulong and Petit
15 Third law, S(T) at constant V or P; DeltaS of a phase change
16 Phase equilibrium in one component system
17 Clapeyron equation, Clausius-Clapeyron equation; determining vapor pressures, phase diagrams in P-T space
18 Equations of state for real gases; thermodynamics of ideal gases, partial molar quantities
19 Euler's theorem, Bibbs-Duhem equation, reactions involving gases
20 Reactions involving gases
21 Ideal Solutions
22 Non-ideal and regular solutions
23 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

# Topic
1 Introduction (Units, Momentum, Heat and Mass Transfer)
2 Rate Equations and Fluxes
3 Kinetics of Homogeneous Reactions
4 Integrated Rate Equations
5 Temperature Dependency of Reaction Rate
6 Reactions in Parallel and Series
7 Mass Transfer in Solids
8 Ficks 1st and 2nd Laws
9 1d Non Steady State Diffusion
10 Diffusion Couples, Darken's Analysis
11 Measurement of Diffusion Constants
12 Mass Transfer in Fluids
13 Combined Mass Transfer and Chemical Reaction
14 Reactions on a Surface
15 Rates of Evaporation
16 Heat Transfer - Conduction, Convection and Radiation
17 Transient Heat Flow
18 Momentum Transfer
19 Equation of Continuity , Navier Stokes Equation
20 Boundary Layer Theory, Stokes Law
21 Convection Heat Transfer

27-217 Phase Relations and Diagrams

# Topic
1 PD Basic concepts, unary and binary diagrams, lever rule
2 Review binary PD types, overview microstructure development in binary PDs
3 Ternary PDs, Gibbs triangle, tie lines, lever triangle, Higher order PDs.
4 The Gibbs phase rule-applications to unary, and binary PDs
5 Application of phase rule to ternary PDs, PDs in thermodynamic potential space
6 Free energy and equilibrium-unary diagrams-Clausius-Clapeyron equation.
7 Thermodynamics binary solutions, partial and relative partial molar quantities, ideal solutions
8 Regular solutions-quasi-chemical description
9 Reference (standard) states for G-X diagrams-common tangent construction
10 Construction of basic PD features from G-X diagrams
11 More about regular solutions, metastability
12 Disallowed PD features, Hume-Rothery rules for solid solutions, types of intermediate
phases (normal valence, electron and Laves)
13 Diffusion in solids, brief statement on phenomenology (Fick's first law, chemical potential
as driving force, uphill diffusion).
14 Atomic diffusion in elemental solids, random atom movements and Fick's first law,
role of vacancies, atomic jump frequency, mean square displacement
15 Self diffusion, vacancy formation and migration energies, interstitial and substitutional diffusion
16 Diffusion across intermediate phases, empirical rules for diffusivity in metals and alloys
17 Diffusion in ionic solids, charge considerations, review of Kroger-Vink notation, Schottky
and Frenkel pairs, charge neutrality
18 Self diffusion in ionics, intrinsic and extrinsic diffusivity
19 High diffusivity paths, dislocation pipe diffusion, grain boundary diffusion
(digression on grain boundaries and their structure) empirical rules
20 Surface diffusion, Laplace Eq., Gibbs-Thomson Eq., and surface curvature.
21 Fick's second law for surfaces, sinusoidal profile decay, application to sintering, empirical rules.

27-301 Microstructure and Properties I

# Topic
The objective of this pair of courses is to convey some of the essential
concepts in materials science and engineering that relate material
properties (strength, magnetism, thermal expansion) to microstructure
(crystal structure, dislocations structure, grain structure, precipitate
structure, composite structure) in multiphase materials. The relationships
will be illustrated with examples of both idealized and technological
materials. The course will draw upon many aspects of materials science
such as defects, phase transformations etc. Pre-requisites are 27-100,
structures, defects, thermodynamics, phase relations.
1 Material properties: definition and tensor character
2 Tensors and symmetry; examples and constitutive relations
3 Electrical properties of solids
4 Magnetic properties of solids
5 Thermal properties of solids
6 Elastic properties of solids
7 Non-linear properties; examples: shear strength in crystals, non-linear optics
8 Types of polycrystals; texture and grain size
9 Orientational averaging of property tensors; intrinsic vs. microstructure dependent properties
10 Effects of microstructure on electrical properties (GB in metal films, dislocations in semiconductors
11 Effects of microstructure on magnetic properties
12 Effects of microstructure on thermal properties
13 Effects of microstructure on elastic properties
14 Applications

27-302 Microstructure and Properties II

# Topic
Objectives: to develop basic concepts of the origin of microstructure and
how microstructure controls properties of multiphase engineering materials.
Examples drawn from mechanical behavior (hard vs. soft, tough vs. brittle),
magnetic properties (hard vs. soft). *assumption: nucleation & growth has
been discussed previously for solidification
1 What is Microstructure? Descriptions and definitions of microstructural elements.
How do we measure microstructure? Outline of microstructural characterization for multiphase materials.
2 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.
3 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)
4 What influence does microstructure have on phase transformation? Effect of vacancies, dislocations,
boundaries [first part of Ch.5 of Porter & Easterling]
5 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.
6 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.
7 More complex phase transformations: eutectoid decomposition and the Fe-C diagram, lamellar (pearlitic) structures,
8 Elementary magnetism (emphasizing domain walls, the B-H loop): effect of microstructure on hard versus soft magnets,
contrast electrical steels with metallic glasses.
9 Transformation toughening of ceramics: example of zirconia in alumina;
alternate example, ferroelectric ceramics, e.g. Pb-La-Zr-titanate (PLZT).
10 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.
11 How are composites made? Fabrication methods for composites.
12 Elastic properties of composites: how to design the thermal expansion of a composite.
13 Review of transformation rules for tensors, symmetry; Overview of important linear material tensors; constitutive relations
application to composites.
14 Design of composite materials for high strength, high [electrical] conductivity: application to very high field magnets.

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