# 1 Notes Outline Master

```Course overview and web page mechanics
http://www.stevens.edu/e344/e344_home.html
Assessment Performance Criteria Section 1 – Intro and Broad Goals
After an introductory course in Materials Science &amp; Engineering, students will be able to:
1.1 Identify the major classes of engineering materials and give practical examples of
each
1.2 identify the materials properties characteristic of some engineering application and
use these to guide the selection from one of the major materials classes, or from within a
particular class, to best satisfy the needs of that application
1.3
show for a typical engineering material how processing, structure, and properties
are inter-related and how they define performance in an engineering application.
1.
2.
3.
4.
How big is an atom
what does an atom look like
how do atoms interact with each other (bonding; many-atom assemblies)
how do large numbers of atoms arrange themselves in space to form a solid?
Orders of magnitude
atto, femto, pico, (Angstrom), nano, micro, milli, (centi)
m, g, sec…
kilo, mega, giga, tera
Section 2: Atomic Structure and Bonding
Real Space 1: Planetary model of Na.
(how big is a sodium atom? Note 052212A)
- plum-pudding model (1902)
- Rutherford Au scattering experiment
(1911 – introduced concept of nucleus surrounded by electron clouds)
Real Space 2: Wave model of electrons in atoms (Real-space picture)
- Bohr model: electrons orbitals are standing waves
1
electron waves can move between discrete orbitals
w/well-defined energy changes
Energy Space: Energy-level diagram for hydrogen
-filled level
- empty levels
- forbidden levels
Schrodinger equation and quantum mechanics
- can predict the electron orbitals/wave functions
- introduces 4 quantum numbers
- Pauli exclusion principal
spdf notation to describe atomic electron configuration
Energy-level diagram for sodium
Transitions between energy levels
X-Ray &quot;&quot; &quot;&quot; &quot;&quot;
Interactions between two sodium atoms
U(r) curves
Lennard-Jones potential
Information contained within U(r) curves
- equilibrium interatomic spacing
- melting temperature (deep potential energy well)
- thermal expansion (asymmetry)
l = T*l (see section 19.3 in Callister 8th)
Ex. Airplane: l = (50 m) * (2E-05 m/m-K) (100 K) = 10 cm
Real space planetary model of two bonded atoms: Molecular orbitals
Energy space picture: Conflict with Pauli exclusion principal
leads to splitting of valence electron energy levels
Hypothetical energy-level diagram for 2 Na atoms
- for 3 sodium atoms
- for 4 sodium atoms
- for N sodium atoms
Energy band diagram for Na:
2
- why is sodium (metal) a good electrical conductor?
- why is sodium (shiny) opaque to visible light?
14. Mg: overlapping conduction band and valence band
15. Energy band diagram for an insulator/semiconductor
- why is silica (E ~ 9 eV) a good electrical insulator?
- why is silica transparent to visible light?
Section 3: Metals, Alloys, and Elements of Structure
What is the difference between a metal and an alloy?
What are some examples of metals?
What are some of the important properties of metals?
What are some examples of where metals/alloys are used?
- what properties are important to these applications
What are the major ways in which we process (make objects out of) metals?
- deformation processing (exploits ductility)
- solidification processing (exploits accessible melting temperatures)
Crystallinity
Examples of crystalline minerals
Long-range order
2-D crystals;
- simple square, parallelograms,
- body-centered square (concept of a basis)
- # atoms per cell
Amorphous materials
- short-range order
Close-packed planes; close-packed directions
Stacking of close-packed planes
- ABABAB = HCP
3
- ABCABCABC = FCC
- stacking fault = one of many possible defects in a crystalline material
3-D unit cells
- FCC; SC; BCC
- APF
The 14 crystal classes
- a, b, c; 
Miller index notation
- points
- directions
- planes
Diffraction
- Braggs Law
- calculation of atomic radius of Na (BCC
Isotropy; anisotropy
Defects in crystals
- point defects
- line defects
- planar defects
Section 4: Ceramics (and Semiconductors)
Definition of a ceramic: A ceramic material is an inorganic, nonmetallic, material
where two or more elements, typically a combination of a metal and a non-metal,
are bonded together by strong and directional ionic, covalent, or, more generally,
mixed ionic-covalent bonding.
Ionicity of a bond (Callister 8th eq. 2.10)
% ionic character = (1-exp(-[0.25]{Xa - Xb}2)) X 100
Ex) % ionicity of MgO = (1-exp(-[0.25]{1.2 – 3.5}2)) X 100 = 73.4
See Table 12.1 Callister
Examples of ceramics
Typical uses
Macroscopic properties of ceramic materials
4
Structure of ceramic materials
- crystalline unit cells
- cation-anion ratio
- charge neutrality
Three primary ways to process ceramic materials
- glass formation and the manipulation of viscous liquids
- powder processing
- processing by chemical reaction
Section 5: Polymers
Main (inter-related) categories:
Thermoplastics:
melt when (re)heated =&gt; melt processing of (viscous) liquids; recyclable
Thermosets:
shaped and then cured; do not melt when reheated (reusable/recyclable)
Rubbers:
High elastic deformation
Gels:
Designed to interact with solvents (hydrogels interact with water)
-------Polymer = many units
Monomer unit of PE
Molecular weight
Conformation of a PE molecular
Sp3 bonding
Sp2 bonding
Show/pass ball and stick model of PE
Rope demo of conformation
Rg: How big is a polymer molecule?
Other types of monomer units
-PVC
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-PP
-PS
-PTFE
-PMMA
-PMAA
-PAA
Homopolymers; blends; and copolymers
- block, alternating, random
- macrophase vs microphase separation
Tacticity
Branching
viscosity
Tg
crystalline vs amorphous
Condensation polymerization
- nylon
- proteins and natural polymers
Rubber
- natural; synthetic
- possible to have rubber without covalent crosslinks
Gels
- lightly crosslinked and designed to interact with solvent
- hydrogels are designed to interact with water
Thermosets
- typically crosslinked during synthesis of (short) molecules rather than linking of
macromolecules (like rubber)
- example = epoxy
Recycling vs. reusing
If time permits: Composite materials (ch. 16 in Callister)
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Composite material = any multiphase material (natural or, more commonly,
synthetic) exhibiting a significant portion of the properties of the constituent phases
in order to realize a composite material with better properties than either
constituent alone.
Metal-matrix
Ceramic-matrix
Polymer-matrix…
Filler = glass, carbon, high-performance polymer fiber (alternately particulate).
Matrix = epoxy or other polymer
Nanocomposites
Section 8: Mechanical Properties
definition of engineering tensile stress, tensile strain, poisson ratio
True stress/strain
Shear stress/strain
Tensile test
ASTM = American Society for the Testing of Materials
Information from a tensile test (y, E, T, %elongation, toughness, resilience)
Reconstructing stress-strain diagram from 4 parameters
Hardness
Estimate of E from 1st principles (Cu)
Estimate of yield strength of Cu from 1st principles.
Dislocations
- types; draw an edge dislocation
- mathematical representation of a dislocation
- burger's vector, line direction
Slip systems
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Strengthening mechanisms
- strain hardening
- grain-boundary strengthening and Hall-Petch
- solid soln strengthening
- ppt hardening
Failure
1. Ductile
2. Brittle
stress concentrators:
 a 1/ 2
m  2o  
 t 

where m = max stress in front of crack tip
o = magnitude of applied tensile stress
a = crack half width
t = radius of curvature of elliptical crack
Non destructive evaluation (NDE)
KIC = Y crit(*a)1/2
3. Fatigue
S/N curve (see figure 8.19); fatigue limit; fatigue strength
Vignette – femoral nail
4. Creep
Qc 
eq. 8.20 in Callister 8th
RT 

&Yacute;s  K 2 n exp 


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 E 
&Yacute;s  K 2 n exp  c 
or: 
kB T 

Section 9: Fundamentals of Phase Transformations
Case Study 1: Recovery, Recrystallization, and Grain Growth
Cold rolling
- decrease plate thickness
- changes shape of grains from ~equiaxed to ~ pancaked.
- increases dislocation density
- decrease ductility
Changes upon annealing
- define annealing
- define what high temperature means (already done in discussion of creep)
- high temperature enables atomic motion (i.e. diffusion)
Recovery = rearrangement of dislocations to minimize energy
Recrystallization of new, equiaxed, low dislocation density grains
energetic driving force = lowering of strain energy
Grain growth – grain size increases
- energetic driving force = lowering of total grain-boundary energy
difference between cold work and hot work
Fundamentals of Nucleation
Volume Free Energy
Surface Energy
Homogeneous nucleation
Heterogeneous nucleation
Fundamentals of Diffusion
Concentration profiles
9
Fick's first law
- flux is proportional to the concentration gradient
- proportionality constant = D
- units on D
Values of Diffusivity
Fick's 2nd law
erf soln
vacancy mechanism of diffusion
Temperature dependence of diffusion
bulk, interstitial, surface, grain-boundary diffusion
Section 10: Phase Diagrams
definition of a phase
a homogeneous and mechanically separable
portion of matter with a well-defined chemical composition
ex: granite and other rocks
Phase diagram as a map of the phases stable
tells what phase or phases are stable at given T, P, composition, etc.
water P-T diagram
- ice skates
- density of solid &lt; density of liquid (ice floats; unlike most metallic systems]
Solid Solutions and the Hume-Rothery Rules [Page 95 in Callister 8th]
Cu – Ni diagram: Example of an isomorphous alloy system
Pb-Sn eutectic diagram
- stuff that can be identified immediately from diagram
- example of cooling from (PB) phase field into 2-phase field
- example of eutectic solidification
- example of hypo/hyper eutectic solidification
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Phase diagrams indicating very limited solubility
- water-salt (p. 301 in Callister 8th)
- Sn-Bi
phase diagrams with compounds
ex: Ge-Te phase-change optical storage
The Fe-Fe3C and Fe-C phase diagrams
- polymorphism
- austenite
- ferrite
- cementite
Limits of solubility
- why is carbon so much more soluble in FCC than in BCC?
Eutectoid rxn vs Eutectic rxn
Example of a 1080 steel
- Pearlite (see figs 9.27 and 10.15 in Callister 8th for micrographs)
- fine pearlite (forms by faster cooling through eutectoid temp)
- coarse pearlite (forms by slower cooling through eutectoid temp)
- spherodite (forms by very slow cooling thru eutectoid temp
or by annealing just below eutectoid temp).
A sqrt(Dt) analysis indicates that C can diffuse in Fcc at 1000 K for ~500 microns.
Example of a 1040 steel (note fig 9.30 in Callister 8th shows micrograph)
hypo eutectoid alloy
proeutectoid ferrite forms
eutectoid composition transforms to pearlite w/ remaining proeutectoid
ferrite
Fe-Fe3C phase diagram
- Hardness as a function of wt%C
- pearlitic microstructure
- spherodized microstructure
- martensitic microstructure
Callister 8th page 362: Martensite = non-equilibrium, single phase structure that
results from a diffusionless transformation of austenite.
Quenching from the gamma phase field limits carbon diffusion
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FCC wants to transform to BCC but can't because of carbon
Instead, FCC transforms to BCT (distorted BCC) via &quot;Bain transformation&quot;
Carbon stuck in former octahedral site (super saturated)
TTT and CCT diagrams
Hardenability = how easily an alloy forms martensite (see Glossery in Callister)
Jominy test (QUIZ???)
Tempering
How to select a set of kitchen knives; Samurai sword
PPT hardening and the Al-Cu phase diagram
see figs. 11.24 (Al-Cu phase diagram); 11.22 (schematic heat treatment) and
11.27 (hardness curves)
Temper designations
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