MIAE 221 All key concept Notes best for both midterm and final exam prep 2026-2027 Concordia Univers

MIAE 221 All key concept Notes best for both midterm and final exam prep 2026-2027 Concordia University

MIAE 221 Chapter 2 - Bonds Between Atoms Atomic Structure Atomic number (Z) = Number of protons = Number of electrons for a neutral atom Atomic weight (A) = Number of protons + neutrons = Weight of 1 mole of atoms Mole = 6.022 × 10^23 atoms (Avogadro's number)

Electron Configuration s p d f—> 2, 6 10, 14 electrons Velence not filled means not stable:

Metals

Non-metals

Metals readily give up electrons to form

Nonmetals readily accept electrons to form

positive CATIONS (electropositive)

negative ANIONS (electronegative)

Low electronegatives

High electronegatives

e.g: Mg → (Mg^2+) + 2e^-

e.g: Cl + e^- → Cl^-

←smaller

Bonding Forces FN = FA + FR → Net force is force of attraction + force of repulsion → when = 0, then equilibrium F = k q1rq2 2 ← Force of attraction, k=8.99E9, q is charge Energy relates to force. If you take integral of force, it’ll give you net energy. If you take derivative of energy, it’ll give you force.

Equilibrium State When net force is 0, then the energy required to break the bond is bonding energy E0

electronegativity

larger→

Higher E0 → stronger bond → higher strength and melting point (T0)

Types of Atomic Bonds 1. Ionic: Non Directional Form between electropositive (metal) and electronegative (nonmetal) atoms Requires electron transfer Metal atom donates electron(s) and becomes a positive ion (cation) Nonmetal accepts electron(s) and becomes a negative ion (anion) Ions attract each other through electrostatic forces Examples: NaCl MgO CaF2

A=

(∣Z1∣)(∣Z2∣)(e2) 4πe0

e = 1.602 E -19

e0 = 8.85 E -12 Z = absolute values of charges With A known now, you can use it in EA:

EA = − Ar

→ [neg cuz attractive force] → A, B, and n are constants

ER = Bn

→ r is distance apart aka bond length

r

ENET = ER + EA 2. Covalent: Directional Form between nonmetal atoms with similar electronegativities

Atoms share valence electrons to attain stable configuration Directionally specific along axis between atoms Examples: H2 CH4 (methane) → C has 4 valence e-, needs 4 more, and H has 1 valence e-, needs 1 more.

C (diamond) SiC Hybridization: mixing of atomic orbitals, only for covalent bonded elements 3. Metalic Bonding: Non-directional Form in metals and their alloys between positive metal ion cores Valence electrons freely move as "electron gas" in a sea of electrons

Ionic-Covalent Mixed Bonding Some bonds are both covalent and ionic, you can compute % ionic: XA and XB are pauling electronegatives

Bonding Properties

Elastic Modulus [E] The elastic modulus, also known as Young's modulus, is a measure of the stiffness of a material.

It describes how much a material deforms under a given amount of stress.

Materials with higher elastic moduli are stiffer and require more force to deform.

Relationship to Properties Bond energy E_0 = binding energy = energy required to break the bond, aka the current energy Higher bond energy (E0)→ higher melting temp (Tm) Requires more energy to break bond Higher bond energy (E0) → higher elastic modulus Requires more energy to deform Lower bond energy (E0) → higher thermal expansion Requires less energy to change bond length (r)

Chapter 3 - Atomic Arrangement Solids: Non-Crystal (Amorphous) materials atoms bonded with no repeating pattern (short range order) Plastics, Glass non dense, random packing Crystals atoms bonded in 3D pattern with long range order Metals dense, ordered packing → lower energies

Metal Structures a = edge of unit cell R = radius APF = atomic packing factor

SC (simple cubic)

APF =

1× 4 πr3 3

a3

r = 12 a LD = 1a FCC (face centered)

APF =

4× 43 πr3 a3

2×a 4

r=

a = 2 2R LD =

2

BCC (body centered)

APF = r=

2× 4 πr3 3

a3

3×a 4

LD =

1

Densities Crystal Density (True Density) The density of a crystal is defined as the mass of a unit cell divided by its volume.

Density =

n×A VC × NA

n = # of atoms in unit cell (1, 2, 4) A = atomic weight (g/mol) Vc = Volume of unit cell (denominator of APF func)

N_A = avogadros constant 6.022…

Linear Density in the math notes

Planar Density in the math notes

Polymorphism and Allotropy Some elements/compounds can exist in more than one crystal form.

This can be due to changes in temperature or pressure.

When found in elemental solids, it's often called allotropy.

Example: Carbon can exist as Diamond (under high pressure) or Graphite (under low pressure).

Crystal Systems Crystals can be grouped based on the shape (geometry) of their Unit Cell.

There are seven possible crystal systems: Cubic: Most symmetric Tetragonal Hexagonal Orthorhombic Rhombohedral (Trigonal) Monoclinic

Triclinic: Least symmetric

Point Coordinates in the math notes

Crystallographic Directions in the math notes

Crystallographic Planes and Miller indices in the math notes

Anistropy Many properties depend on the direction in the crystal in which they are measured. For example, stiffness (rigidity), electrical conductivity, refractive index, coefficient thermal expansion, etc.

If properties vary with direction, it is said to be anisotropic.

If properties have no variation with direction, the property is isotropic.

Single crystals show anisotropic behavior since the atoms are aligned in an ordered way.

Polycrystalline materials are usually made of many randomly oriented grains, so the anisotropic effects are averaged out, giving isotropic properties.

Single vs Polycrystals

Single crystal: Properties vary with direction -> anisotropic A single crystal is a piece of material that is made up of one crystal; all the unit cells are aligned up in the same orientation.

Example: The modulus of elasticity (E) in BCC iron varies depending on direction. Along [100] it is 169 GPa, and along [111] it is 287 GPa. Polycrystals: Polycrystals contain many small crystals with different orientations joined together.

Properties may or may not vary with direction E.g. polycrystalline iron has E = 210 GPa (average value) If grains are randomly oriented -> isotropic overall If grains have preferred orientation -> anisotropic For example, rolled sheet metal tends to have grains aligned with the rolling direction, leading to anisotropic properties.

X- Ray Diffraction Used to determine crystal structure and interplanar spacing.

X-rays diffract off the atoms in the crystal. They constructively interfere at certain angles according to Bragg's law:

nλ = 2dhkl sin θ

Equation explanation is in math notes

dhkl =

a

By varying θ and measuring the diffraction intensity, the interplanar spacing d_hkl can be determined, and btw the hkl is the plane coordinate (110 for e.g) The pattern of peaks identifies the crystal structure.

Chapter 4 - Imperfections Types of Imperfections 1. Point Defects Vacancies missing atoms at lattice sites

Nv/N = exp(−Qv/kT ) NV = number of defects/vacancies, N = number of potential defect sites (atomic sites) QV = Activation Energy, K = constant, T = temp in kelvin Interstitial Atoms extra atoms squeezed between lattice sites Substitutional Atoms impurity atoms substituted for host atoms

2. Line Defects Dislocations Are line (one-dimensional) defects Result from thermal stresses, mechanical deformation, rapid cooling from liquid to solid misaligned planes of atoms caused by shear stress. Allow metals to deform plastically

Two types: Edge dislocation Imagine an “extra” half-plane of atoms inserted in a crystal burgers vector b is perpendicular to the dislocation line Screw dislocation Crystal is “cut halfway through & then slide sideways” burgers vector b is parallel to the dislocation line

3. Area Defects External Surfaces Crystal structure terminates; surface atoms lack neighboring atoms Grain Boundaries: regions where crystalline grains meet with different orientations.

Grain boundaries impede dislocation motion, so smaller grains strengthen metals. high mobility high diffusivity high chemical reactivity

Solid Solutions 1. Substitutional Solid Impurity atom replaces host atom Causes a distortion to surrounding lattice 2. Interstitial Solid Impurity atom places in voids between host atoms

Degree of Solution How much does the solute dissolve in the solvent. These deciding factors (Rothery rules): 1. Δr (difference in atomic radius) < 15% 2. Proximity in periodic table i.e. similar electronegativities Large differences results in intermetallic compounds 3. Same crystal structure for pure metals 4. Valences All else being equal, a metal will have a greater tendency to dissolve a metal of higher valence than one of lower valence e.g: Copper (FCC) - Nickel (FCC) r = 0.128 nm - 0.125 nm —> size% = 2.3% → most solubility Whereas: Copper (fcc) - Lead (fcc) r = 0.128 - 0.175 —> size% = 36.7% → less solubility

Grain Size Determination To measure grain size in metals: 1. Take a photomicrograph of the metal sample at 100x magnification 2. Draw some lines randomly across the photo of same l 3. Count the number of grain boundaries intercepted by each line (ng) 4. Find the average ng for all lines 5. Divide the line length (l) by the average ng

6. Divide this by the magnification (100x) This gives the average grain size diameter.

So in summary: Average Grain Size = (Line length / Average ng) / Magnification

Chapter 5 - Diffusion Diffusion is the movement of atoms or molecules from regions of higher concentration to regions of lower concentration. This occurs both in gases, liquids and solids.

There are two main types of solid-state diffusion: 1. Interdiffusion (also called impurity diffusion) Diffusion between two different chemical species.

For example, diffusion of Cu and Ni atoms in a Cu-Ni couple.

Atoms move from higher concentration to lower concentration regions.

2. Self-diffusion Movement of atoms of the same species within a pure material.

For example, diffusion of Fe atoms within pure iron.

There is no change in overall composition.

Diffusion Mechanisms 1. Substitutional aka Vacancy Diffusion Atoms swap with vacancies, slower, for similar-sized atoms.

Atoms exchange places with neighboring atoms.

Requires adjacent vacant site for atom to move into. Cant just go find an empty spot like interstitial can.

Increasing temperature increases number of vacancies Atom needs energy to break bonds and jump into vacant site 2. Interstitial Diffusion Atoms move through gaps in lattice. Faster, requires smaller atoms. like H, C, N, O which can fit in interstitial sites Faster than vacancy diffusion due to: More vacant interstitial sites available Less energy required to squeeze between atoms Example: Carbon diffusion in iron to harden steel

Quantifying Diffusion Rate Its called J or Flux

J = M/At

J = mol/cm^2 or kg/m^2s t = time A = surface area M = # moles or mass(kg)

Fick’s First Law Fick's first law applies to steady-state diffusion where concentration profile does not change with time

Fick’s Second Law Fick's second law applies to non-steady state diffusion where concentration C=C(x,t) changes with time and position:

An important solution is for semi-infinite solid: Initial concentration Co for all x Surface concentration Cs kept constant Concentration = Co at x = ∞

Temperature and Diffusion Rate Increasing temperature increases diffusion coefficient D

D = D0 exp (−

Qd

)

RT

Where: D0 = Pre-exponential constant Qd = Activation energy R = Gas constant T = Absolute temperature

Key Summary Diffusion faster in open structures, smaller atoms, lower density Diffusion slower in close-packed structures, larger atoms, higher density Many key heat treatments rely on diffusion Fick's laws allow diffusion distance and time calculations Increasing temperature significantly increases diffusion rate

Chapter 6 - Mechanical Properties of Metals Types of Load: 1. Tensile (pulling) 2. Compressive 3. Shearing (cut in half and sliding) 4. Tosional (twisting) We need a parameter which is independent of the size (i.e. length, width, thickness) of the components to represent the strength of the material rather than the component.

We can divide load (F) by minimum cross-sectional area (A0) to find tensile stress (σ)

σ = F /A0 Applied Force True Stress = Instantanious Cross Sectional Area

Force Engineering Stress = OriginalApplied Cross Sectional Area

Strain As something is pulled it gets longer and thinner (deforms). Can measure this using extensometers. The change in length during this load is normalized to the original length.

Engineering Strain =

Change in length Original Length

Yield Strain = єy

Shearing Stress (τ)

Shearing Strain (γ)

Elastic Deformation Hook’s Law: E is the slope of stress strain curve in the linear portion

Hooke’s Law 𝜎 = Eє є = △L/L0 If asks for total elongation, solve for delta L

Elastic Modulus (E) E tells us how much something will stretch elastically, i.e stiffness of the material. є is elastic strain Larger E means atoms are well bonded together, so we cant change the elasticity of a material since it relates to its bonds. The greater the slope, the stronger its bonded.

Poisson’s Ratio (v) Defines how much strain occurs in the lateral directions (x,y) when strained in z direction

v=

Lateral Strain Longitudinal Strain

=−

єx

=−

єz

єy єz

Yield Strength (σy) Yielding: Transition from elastic (recoverable) deformation to plastic (permanent) deformation. σy (Yield Stress): The stress level past which a material begins to deform permanently.

Hook’s Law: Valid until the yield point, beyond which it doesn't apply.

Elastic Deformation: The material returns to its original shape completely when the load is removed.

Plastic Deformation: The material does not return to its original shape completely when the load is removed.

Specifics of Yield Strength: Elastic to Plastic Transition: For some steels, there's a clear yield point phenomenon with a distinct transition from elastic to plastic.

In some alloys, this transition is gradual.

Yield Strength Measurement: 0.2% Offset Yield Strength: A common method for measuring yield strength. Calculated by the amount of strain (usually 0.002 or 0.2%) which results in a permanent set.

Proportional Limit (Point P): The exact point of transition from elastic to plastic deformation, which is difficult to measure.

Example: є_p = 0.2%. For 50mm sample:

△l = (єp)l0 = (0.002)(50) = 0.1mm This is the 0.2% offset yield strength ← P is the proportional limit aka point of change from elastic to elastic+plastic

Tensile Strength The peak of the stress strain curve graph

σTS = MaximumForce/OriginalArea

Example Tensile σ-ϵ graph for brass shown below:

Max load that can be handled by cylinder w/ original diameter 12.8mm

d0 2 6 12.8 × 10−3 )𝜋 = 570 F = 𝜎A0 = 𝜎( ) 𝜋 = 450 × 10 ( 2 2 Change in length originally at 250mm long, undergone tensile stress of 345 MPa.

△l = єeng l0 = (0.06)(250mm) = 15mm (0.06 is the A in the graph, aka strain at 345MPa)

Modulus of Elasticity E = slope = 150-0 / 0.0016 - 0 = 93.8 GPa Yield Strength at strain offset 0.002 = 250MPa

Ductility It's an indicator of how pliable a material is.

1. Percentage Elongation (%EL): Plastic tensile strength at failure

2. Percentage Reduction in Area (%RA): measuring the minimum diameter at the fracture site to calculate the area at fracture.

Note: %RA and %EL are often comparable (not identical)

Example

A cylindrical metal specimen (original diameter 12.8 mm, gauge length 50.80 mm) is tension-tested until fracture. The diameter at fracture is 6.60 mm, and the fractured gauge length is 72.14 mm. Calculate its ductility as percent reduction in area and percent elongation.

d0 is the original diameter of the specimen before testing. df is the diameter at the point of fracture.

This formula calculates using cross-sectional area of the cylindrical specimen (which is a circle in this case) [pi r^2]

Risilience Ability material to absorb energy during elastic deformation then give it back when unloaded U_r = Modulus of Resistence → strain energy per unit volume σy = yield strength єy = yield strain (elastic limit) E = modulus of elasticity

U_r is also just area under slope of the stress strain graph, point 0 to σy

Summary Stress and strain: These are size-independent measures of load and displacement, respectively Elastic behavior: This reversible behavior often shows a linear relation between stress and strain.

To minimize deformation, select a material with a large elastic modulus (E or G).

Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches σy.

Toughness: The energy needed to break a unit volume of material.

Ductility: The plastic strain at failure.

Chapter 7 - Strengthening Mechanisms Dislocation Motion Under applied shear stress, dislocations move by breaking bonds one by one, not simultaneously, requiring less energy. This movement involves breaking and forming only one set of bonds per step.

When two dislocations with the same characteristics (type and direction) are close, they push away from each other, while dislocations of opposite characteristics attract and can cancel each other out

Slip - The Movement of Dislocations Understanding 'Slip': Movement of dislocations under applied stress is called "SLIP". It occurs in the densely packed planes.

The direction of this movement is known as the "Slip Direction."

The plane swept out by the dislocation is called the "Slip Plane."

A combination of direction and plane forms a "Slip System."

Types of Dislocations Edge Dislocation: Movement parallel to the direction of shearing stress.

Screw Dislocation: Movement perpendicular to the direction of shearing stress.

Analogy: Caterpillar locomotion - movement is not simultaneous but sequential, similar to the movement of dislocations.

Dislocations in Various Materials Metals: Dislocation motion is easier due to non-directional bonding and close-packed directions for slip.

Covalent Ceramics (e.g., Silicon in diamond structure): Motion is hard due to directional (angular) bonding.

Ionic Ceramics (e.g., NaCl): Motion is challenging; it's essential to avoid ++ and -- neighbor interactions.

Chapter 9 - Phase Diagrams Phase diagrams are useful tools to determine, for a given T and composition of the system: The number and types of phases The wt% of each phase

And the composition of each phase

wt% = ( at% = (

m1 m1 + m2 nm1

) ∗ 100

nm1 + nm2

← Weight percent with mass m

) ∗ 100 ← Atomic percent with number of moles n Note: n = m/A ← A is atomic weight

Calculating wt% Example for two phases Given the following,

C0 = 35 wt% Ni Calculate the wt% at T_B. Answer:

WL =

S = R+S

43 − 35 = 73 wt% (35 − 32) + (43 − 35) Wa =

R R+S

= 27 wt%

Weight Fractions & Volume Fractions Ex. if W_solid is 0.75 in a 100kg mass, then there is 75kg of solid.

Volume fractions though is how much space each phase takes up in a mixture

M = pV

Volume Fractions

M = mass

Va =

(Wa/pa) (Wa/pa) + (Wb/pb)

p = density V = volume

This just means the volume occupied by phase a (liquid or whatever)

Weight Fractions Using Volume, we can do this:

Wa =

(Va ∗ pa) (Va ∗ pa) + (Vb ∗ pb)

Equilibrium & Non-equilibrium Cooling & Solidification Of Alloys Equilibrium cooling: Very slow cooling that allows time for diffusion and the alloy to come to an equilibrium state at each temperature Non-equilibrium cooling: Faster cooling that does not allow sufficient time for equilibrium Results of non-equilibrium cooling: Solidification may occur at different temperatures compared to equilibrium Get "cored" non-uniform microstructures May need homogenization heat treatment later to make the microstructure more uniform

Solid Solution Strengthening Solid solution strengthening increases strength (tensile strength) but decreases ductility (% elongation and % reduction in area). This is due to lattice strain caused by different sized solute atoms.

Eutectic Phases Eutectic systems are when two components can't mix well as solids. At a particular mix and temperature, the liquid turns into two different solid parts quickly.

Eutectoid Reaction: A phase transformation in which a single solid phase transforms into two other solid phases upon cooling. This reaction is crucial in the steel-making process.

Peritectic Reaction: Involves a reaction between a liquid and a solid phase to form a second solid phase. This reaction is essential in the formation of certain types of alloys.

Example:

Find: Composition of phases Co = 40 wt% Sn Ca = 11 wt% Sn Cb = 99 wt% Sn Phase Weight Fraction:

Wα =

CB − Co = 99 − 40 = 67 wt% S = CB − Cα R+S 99 − 11

Wβ =

CO − Cα = 40 − 11 = 33 wt% R = CB − Cα R+S 99 − 11

Graph: Goes from 0-100% Tin(sn) What are alpha (a) and beta (B): L → Liquid + Lead + Tin L + a → Liquid + C | B + L → Liquid + Sn a → C rich only | B→ Tin rich only General Eutectic Temperature and Composition → temp at the bottom pointy tip in L (here its 61.9 comp and 183 C) L = a + B → L is the general, a and B is the composition wt % of a and B:

Eutectic for a only: at eutectic temp, go left till you hit a. (18.3 wt%, 183 C here) Eutectic for B only: at eutectic temp, go right till you hit B. (97.8 wt%, 183 C here)

Another Example:

Formulas

Example: Phase Equilibria For a 99.6 wt% Fe-0.40 wt% C at a temperature just below the eutectoid, determine: Composition of Fe3C (cementite) and ferrite (a) Co = 0.40 wt% Molar mass of Fe3C → 179.56 Molar mass of C → 12.01 Thus, wt% of C in Fe3C is 12.09/179.56 ⇒ 6.7 wt% C wt % a ⇒ 0.4 - 0.022

NOT COMPLETE Chapter 12 - Ceramic Structure & Properties Cations (+) smaller than anions (-)

Crystal Structure of Ionic Ceramics Ionic Composition: Often involves two types of atomic species (e.g., Na and Cl), forming a crystal structure that must satisfy charge neutrality and size/coordination number requirements.

Cation-Anion Relationship: Cations (+) are smaller than anions (-). Each attempts to maximize the number of opposite neighbors.

Coordination number reflects the size ratio.

Examples of Structures: Standard types (AX) like NaCl, CsCl, ZnS; more complex structures (AmXp) like CaF2, UO2, Al2O3.

Glass is noncrystalline (anorphous)

Carbons Polymorphic: Diamond, Graphite Nano Carbons: Graphene, carbon nanotubes

Graphite

Diamonds

In plane covalent, between sheets vanderwalls

Covalent

Gives interplanar cleavage - lubrication

Low electrical conductivity, high thermal conductivity

High electrical conductivity, low thermal expansion

Interstitials Exists for cation, but not anions cuz anions are large relative to the interstitial sites

Point Defects in Ceramics Frenkel Defect: This is when an atom moves from its regular spot, creating an empty space (vacancy) and then squeezes itself into another spot where it doesn't usually belong (interstitial).

Schottky Defect: This is when there are missing atoms, both a positively charged atom (cation) and a negatively charged atom (anion), leaving two empty spots.

Mechanical Properties of Ceramic Brittle Low tensile strength High compressive strength High Hardness Elastic Behavior is linear

Plastic deformation is nearly impossible (too brittle)

Fracture Toughness K_1c = fracture toughness a = half the crack length Y = geometric shape parameter σ = stress amount (MPa) aka also flexural strength

Flexural Testing to Measure Strength Flexural Strength:

L is the length between the support points, b is the breadth (or width) of the rectangular cross-section d is the depth (or height) of the rectangular cross-section.

Porosity Effects

Stiffness, E: E = E0 × (1 − 1.9P + 0.9P 2) P = volume fraction of porosity E_0 = elastic modulus of fully dense material (at P=0)

Flexural Strength, σ: σf = σ0 e−nP

Chapter 13 - Ceramic Processing Glass Glasses don't have a specific solidification temperature like crystalline materials (e.g., ceramics and metals).

Instead, their viscosity increases as they cool down, making them "supercooled liquids."

Unlike metals, glasses don't undergo a sudden change in volume when they solidify at a melting temperature (Tm).

They gradually shrink as the temperature decreases, with a noticeable change in slope at the Glass Transition Temperature (Tg), also known as the fictive temperature.

Below T_g, glasses exist in a solid state.

Cryalline Materials: Crystallize at melting temp Tm and have abrupt change in volume at Tm

Glasses: Does not crystalize, volume varies smoothly with T, has glass transition temp T_g 1. Melting point: Temperature where glass becomes liquid.

2. Working point: Temperature for easy glass deformation.

3. Softening point: Maximum handling temperature without dimensional changes.

4. Annealing point: Temperature for stress removal due to rapid atomic diffusion.

5. Strain point: Temperature below which glass tends to fracture rather than deform. Glass transition temperature is higher.

Making Glass Tougher: Replace Na⁺ ions with larger K⁺ ions via hot alkaline potassium salt bath (400°C).

Cooling induces compressive stress at the surface and tensile stress at the center.

Enhances surface strength, flaw containment, and overall crack resistance.

Chapter 14 - Polymers Most polymers are hydrocarbons (H and C) and can be AMORPHOUS or PARTIALLY CRYSTALLINE Thermo Plastics Saturated Hydrocarbons are those where each carbon is bonded to four other atoms (single bonds) Unsaturated Hydrocarbons have double or triple bonds, relatively reactive, can form new bonds

Hydrocarbon Molecules Basic building block of polymers. Each carbon atom wants to form 4 covalent bonds. If double or triple bonds —> unsaturated.

Chemistry of Polymers Monomers joined by polymerization to form polymers Molecular weight (g/mol) varies since the chain can be large or small, so there are number-avg and weight-avg molecular weights for polymers.

Below formula calculates how many monomer units are on average in each polymer chain by dividing the average molecular weight of the polymer by the molecular weight of the monomer unit.

DP =

Mn

DP = Degree of polymerization: avg number of repeat units per chain

m

M_n = Number average molecular weight of the polymer. It is the total weight of all the polymer molecules in a sample divided by the total number of polymer molecules in the sample. m = molecular weight of the repeat unit

Molecular Structure (Order of Increasing Strength) 1. Linear Polymers: mers joined end-to-end to form long chain; includes plastics like PE and PVC. 2. Branched Polymers: Main chains with side branches, making them lighter.

3. Crosslinked Polymers: Chains covalently crosslink bonded together; makes materials stretchy like rubber.

4. Network Polymers: Highly bonded, 3D structures; used for heat-resistant materials.

Molecular Configuration Stereoisomerism (Tacticity): Arrangement of side groups in a polymer.

Isotactic: R groups are all on the same side.

Syndiotactic: R groups alternate sides.

Atactic: R groups are placed randomly.

Thermoplastics, Thermosets, Elastomers Permanent change, rigid covalent bonds

Copolymers Homopolymers: Chains of same repeating unit e.g.: -AAAAAACopolymer: Two or more chemically different repeating units A & B 1. Random copolymers a. Random arrangement of different Mers 2. Alternating copolymers a. Ordered, unlike groups attract 3. Block copolymers a. Ordered, like groups attract 4. Graft copolymers a. Grafts of one type on another chain

Molecular Weight - Chains If polymer is made of 10000 repeat units then the molecule has relative molecular mass or weight of 10000*28 = 280,000g/mol Number average molecular weight:

M_i = mean molecular weight of a size range x_i = fraction of total number of chains (# chains / # total of all chains) w_i = the weight fraction of total weight of chains

Weight-average molecular weight:

Note: the weight average molecular weight is larger than the number average molecular weight.

Example: We have a polyethylene sample containing: 4000 chains with molecular weights between 0 and 5000 g/mol 8000 chains with molecular weights between 5000 and 10,000 g/mol 7000 chains with molecular weights between 10,000 and 15,000 g/mol 2000 chains with molecular weights between 15,000 and 20,000 g/mol Determine both the number and weight average molecular weights.

Degree of Polymerization (DP) DP = average number of repeat units per chain Where m is the molecular weight of the repeat unit

% Crystallinity % of material that is crystalline

% crystalline =

pc(ps − pa) ps(pc − pa)

% crystallinity depends also on: Faster cooling → less crys Simple chain config → more crys

∗ 100

p_s = density of sample p_a = density of completely amorphous polymer (measured in lab) p_c = density of completely crystalline polymer (can be theoretical)

Copolymers → less crys

Chapter 15 - Polymer Processing Overview Polymers generally have very low densities, excellent formability and moldability, reduced manufacturing costs, good noise dampening, corrosion resistance, low friction, electrical insulation, and tailored properties.

Mechanical Properties Polymers exhibit elastic, plastic, and viscoelastic behaviors.

Modulus values are much lower than metals, tensile strength is lower, but elongation can be over 1000% unlike metals (~10-30%).

Mechanical properties depend on temperature, strain rate, environment.

Brittle behavior below Tg, rubbery above Tg.

Modulus of Elasticity (Tensile Modulus): • May be as low as 0.17 GPa or as high as 5 GPa (compare to 48-410 GPa for metals) • TS polymers up to 95 MPa (metals up to 1800 MPa)

Elongation: • Often deform plastically as much as 1200% (metals rarely over 100%) Temperature Dependence: • Mechanical properties are temperature dependent even close to room temp.

Strain Rate Dependence: • Decreasing strain rate has similar effect to raising temperature

Plastic polymer

Viscoelasticity

VISCOELASTIC: a rubbery solid with combined mechanical characteristics of elastic & viscous materials i.e. non-linear elastic behaviour Chain slippage depends on rate of strain, time & temperature Fast strain → no time for slippage, brittle failure Slow strain → chain slippage, ductile Combination of elastic (recoverable) and viscous (time-dependent, nonrecoverable) deformation.

Amorphous polymers mechanically behave: At low temps. [ below Tg] like a glass – brittle & elastic Elastic: instantaneous deformation & recovery At high temps. like a viscous liquid (e.g. grease, honey) Viscous: time-dependent, non-recoverable deformation At intermediate temps. [ > Tg] like a rubbery solid

Factors Affecting Strength Temperature & Strain Rate are critical. Higher temps improve ductility (above their T_g), brittle below their T_g.

Lower Strain rate is like higher temperature ↑T & ↓SR favour ductile behavior ↓T & ↑SR favour britle behavior Molecular weight - higher gives ↑ strength.

Tensile strength ↑ with molecular weight → more entangled (short strings vs long)

Crystallinity: ↑ strength through higher intermolecular bonding.

Decreasing degree of cross linking ↑ strength (inhibits chain motion ⇒ more brittle) Deforming (drawing) a polymer can ↑ its strength - because chains become oriented.

Strain Rate Speed at which load applied Low rate → slow loading → Ductile favored (chains can move) High Rate → Impact → More brittle (chains have no time to move)

Deformation of Semi-crystalline Polymers Elastic Bond-stretching/bending in the chains (RECOVERABLE) Plastic Amorphous regions elongate; chains slide and rotate and move past each other. Tilting of crystalline regions. Blocks orient towards tensile axis (NOT RECOVERABLE unless heated) When you stretch a metal wire, sometimes it starts to get thinner in one spot. That's called "necking." Once that happens, the wire keeps getting thinner at the neck when you pull, until it snaps there.

But when you stretch something like plastic or rubber, it can also neck. But that narrow spot doesn't keep getting thinner. Instead the rest of the plastic/rubber gets pulled out from the sides, because the neck part got tougher. The neck holds steady while the sides keep stretching more.

Finally the plastic snaps somewhere else instead.

So metals break at the neck, but plastics/rubbers break somewhere else after necking starts. The neck doesn't determine the breaking spot for them like it does for metals.

Inter-molecular bonding is much weaker than other types, hence yield strength of polymers is low compared to metals or ceramics.

Pre-deformation You can stretch out polymers like plastic or rubber before using them to change their properties. This is called drawing.

Stretches the polymer chains out straight Lines up the chains along the stretch direction

Drawing Stretching it makes the polymer: Stiffer in the stretch direction Stronger in the stretch direction Less stretchy overall though

Annealing If you heat up the stretched polymer, it does the opposite: The chains go back to curly Gets less stiff Gets less strong that way Gets more stretchy again Annealing semicrystalline polymers lead to: Increase crystallinity Increase crystallite size and perfection So heating reverses the effects of stretching it out. This is called annealing.

Deformation of Elastomers Rubber and stretchy polymers are called elastomers. Ability to be deformed to large elastic deformations and then spring back to original size.

Low modulus of elasticity, non-linear elastic deformation When you stretch rubber: The tangled polymer chains get pulled straighter This is an elastic deformation - it springs back It takes force to straighten the chains So rubber gets harder to stretch more When you let go: The chains immediately curl back up Like letting go of a stretched spring This releases the force you put in The rubber bounces back to its original shape Polymers come in 3 types: Crystalline - Very lined up structure there is a discontinuous change in specific volume at Tm Amorphous - Random, messy structure continuous, no Tm but there is an increase in slope at Tg, the glass transition temperature Semi-crystalline - Some areas lined up & some messy

intermediate to crystalline and amorphous, show both transitions

Melting and Glass Transition What affects the melting point (Tm) and glass transition temperature (Tg) of polymers?

Both Tm and Tg increase when polymer chains are stiffer Chain stiffness increases with: 1. Bulky side groups 2. Polar groups or side chains 3. Double bonds or aromatic groups in the chain Regularity of repeat unit structure affects Tm but not Tg More crystallinity means a stiffer and stronger polymer Relating Polymers to Spaghetti Amorphous polymers are like hot, fresh spaghetti with no clumps Semicrystalline polymers are like hot, fresh spaghetti with some clumps

Crystalline polymers are like spaghetti that's mostly clumps with some free strands Polymer crystals (e.g. spherulites) are layered like lasagna A polymer below its Tg is like 3-day old spaghetti left in the sun

Polymerization Addition Polymerization A molecule called a monomer gets activated to start the reaction Monomers join together in a chain reaction to build the polymer The reaction stops when the active sites get deactivated

Condensation Polymerization Two different molecules join together, losing a small molecule like water as a byproduct This repeating reaction builds up the polymer chain

Polymer Additives Additives are mixed with polymers to improve specific properties: Fillers - Improve strength, abrasion resistance, toughness. Examples: wood flour, talc, silica, clay, glass Plasticizers - Increase flexibility and toughness. Example: pPVC vs uPVC

Stabilizers - Prevent UV degradation. Examples: Antioxidants Lubricants - Ease processing. Example: sodium stearate Colorants - Dyes and pigments to change color Flame Retardants - Reduce flammability

Processing Plastics Thermoplastics Can be reversibly cooled and reheated (recycled) Heat to soften, shape, cool to set Examples: polyethylene, polypropylene, polystyrene Thermosets Form permanent molecular network when heated (chemical reaction) Degrades instead of melting when reheated Examples: urethane, epoxy

Chapter 18 - Electrical Properties Electrical Conduction Ohm’s Law: Relationship between resistance, voltage drop, and current.

Resistivity: A material property independent of sample size and geometry, affecting resistance.

Conductivity: Inversely related to resistivity, crucial for determining a material's ability to conduct electricity.

Example A copper wire 100 m long must experience a voltage drop of less than 1.5 V when a current of 2.5 A passes through it. If σ is 6.07E7 (Ohm/m), compute the minimum diameter of the wire.

Energy Bands

Electrical Conductivity n = “compute the electron concentration” |e| = coulombs constant p = hole concentration

𝜎=

1

p p = resistivity

𝜎 = Electrical conductivity

Intrinsic semiconductors have equal numbers of electrons and holes (absences of electrons) due to thermal excitation. When you introduce impurities into a semiconductor through a process called doping, you can control its electrical properties.

Two common types of doped semiconductors are n-type (where extra electrons are introduced, creating an excess of negative charge carriers) and p-type (where electron "holes" are introduced, creating an excess of positive charge carriers).

Intrinsic Semiconducters Intrinsic conductivity depends on temperature and as-present impurities Same # of holes as free electrons (n = p = n_i):

Extrinsic Semiconducters

Same formula as the normal one where n and p are different not the same Doping: substituting a Si atom in the lattice by an impurity atom (dopant) that has one extra or one fewer valence electrons Donor impurities have one extra electron (group V: P, As, Sb), donate an electron to Si. Acceptor impurities have one fewer electrons (group III: B, Al, In, Ga), accept electrons from Si which creates holes.

Semiconductor Formula Difference In semiconductors, we have two main types of "roads": N-type and P-type.

N-type semiconductors have extra electrons, which are negatively charged particles. P-type semiconductors have "holes" where electrons are missing, acting like positive charges. When put together, electrons move towards the holes, creating an electric current. N-type is like a road with extra cars, P-type is like a road with extra parking spaces.

N-Type Semiconductors

E.g. Si has 4 valence electrons. If add P atoms (5 valence electrons) there is one extra electron which is loosely bound and can easily be excited (with increasing T) into conduction band start to move under electric field.

These extra electrons are the main charge carriers now. Here, P is called a donor impurity.

Donor impurities → N-type (negative) conductivity by electrons

P-Type Semiconductors

E.g. Si has 4 valence electrons. If add B atoms (3 valence electrons) there is one extra hole which is loosely bound and can easily start to move under electric field. These extra holes are the main charge carriers now.

Here, B is called an acceptor impurity.

Acceptor impurities → P-type (positive) conductivity by holes

Resistivity (p) Increases with temperature, impurity conc, % Cold work

ptotal = pthermal + pimpurity + pdef pdef = %ColdWork

pthermal = p0 + aT a and p0 = constants for each metal

pimpurity = Aci(1 − ci) ci = impurity concentration in atomic % and A is constant

For two phase alloy: pimpurity = paVa + pB + VB V’s and p’s are volume fraction and individual resistivities for

Chapter 19 - Thermal Properties Temperature has significant influence on physical and mechanical characteristics of some engineering materials: Metals: High thermal expansion → applications e.g. thermostats Thermally conductive High temperature application → creep Ceramics: Most susceptible to thermal shock Thermal insulation High temperature applications Polymers: Soften in elevated temperatures Brittle in lower temper

A material responds to heat by: Increased vibrational energy Redistribution of this energy to achieve thermal equilibrium

Heat Capacity The ability of a material to absorb heat. Increases with temperature.

Polymers have the largest values.

The energy required to increase the temperature of the material:

cp = Heat capacity at constant pressure cv = Heat capacity at constant volume

Thermal Formulas Thermal Expansion The stress-free strain induced by heating by a unit T. Polymers have highest value Materials change size when temp is changed

Thermal Conductivity

Ability material to transfer heat, metals have highest values

Thermal Stress

Occur due to: Restrained thermal expansion/contraction Temperature gradients (uneven heating/cooling) that lead to differential dimensional changes Thermal Shock Resistance Occurs due to: nonuniform heating/cooling Ability of a material to be rapidly cooled & not crack. Maximize σfk/Eα.

If you set them equal to each other:

(Quench Rate)forfracture = Thermal Shock Resistance 𝜎 k (Quench Rate) = f forfracture Eal

Chapter 21 - Optical Properties E = energy of a photon λ = wavelength of radiation ν = frequency of radiation h = Planck’s constant (6.62×10 ³⁴ J.s) c = speed of light in a vacuum (3.00×10

m/s)

Absorption Light Interaction with Solids Incident light is reflected, absorbed, and/or transmitted.

I₀ is the intensity (W/m²) of incident light and subscripts refer to transmitted, absorbed or reflected

Incident Light intensity i_0 = sum of intensities of transmitted light, absorbed light, and reflected light

Electron Transition

An electron can jump from one energy state to a higher energy state if it absorbs a photon with the appropriate energy This higher energy state is called excited state

Required energy for electron transmission

c = λv = wavelength ∗ frequency

E_gap Energy Band Gap is the energy difference between a material's valence band and conduction band.

Large E_gap: Insulators and Transparent materials (e.g diamond) if E_gap > visible light (3.1ev), material is likely transparent Small E_gap: semiconductors (e.g silicon)

if hv > E_gap, absorption of light occurs.

Example Given: Semiconductor has energy band cap (Egap) of 1.8eV. Find: Maximum wavelength of light it can absorb Solution: 1. Convert E_gap to joules → 1 ev = 1.6E-19J

If E_gap < visible light (1.7ev), material absorbs light and is colored/opaque

2. Find wavelength E = hcλ, where E is the E_gap in J 3. Solve for λ

if hv > E_gap, electrons move from valence to conduction band, causing absorption

Reflection Reflection R (experimental approach)

Reflection R (theoretical approach)

From Material to Material:

From Material to Material:

The reflectivity percentage formula measures the reflection of light (R).

It calculates the percentage of light reflected by a surface (L_R) compared to the intensity of the light that hits the surface (L_0).

When light moves from one material to another (normal incident beam), the light reflection (R) can be calculated using the formula that

Reflectivity(%) = lR/l0

considers the indices of the materials:

R=

L is in Watts/m^2 So for a perfect mirror, LR = L0, such that R = 1, aka all of the light is reflected.

From Air to Material

R=

(n − 1)2 (n + 1)2

(n2 + n1)2

n has no units, constant based on material type

Total Internal Reflection

For the case of light passing from air (n = 1) to another material, the reflection coefficient R can be simplified to:

(n2 − n1)2

When light passes from a material with a higher refractive index (n_1) to a material with a lower refractive index (n_2), total internal reflection can occur when the angle of incidence (φ_1) is greater than the critical angle:

Refraction bending of light

ϕ1 = nn21

Light Scatter in Polymers Amorphous Polymers and pore-free Almost no scatter, these are transparent materials Semicrystaline Polymers Light scatter at boundaries, so translucent or opaque material Scattering can come from: Grain boundaries in poly-crystalline materials Fine pores in ceramics different phases of materials Example: Polystyrene is amorphous, so its clear and transparent. Low density polyethylene carton: opaque.

Translucency Scattering inside the material Partial transmission of light through materials with internal scattering.

Excessive scattering can lead to opacity.

Luminescence Re-emission of absorbed light at a lower frequency.

Two types Phosphorescence (longer trapped state [>10^-8 seconds]) Fluorescence (shorter trapped state [>10^-8 seconds]) Example: Glow-in-the-dark toys using phosphorescence.

Photoconductivity Absorption of light by a semiconductor can cause photon-induced electron transitions, increasing its conductivity.

Think of light sensors, they get hit with light which enables the circuit and flow of electrons

Lasers Coherent: If emitted light has same energy and phase as incident light To keep coherent emission, ensure that light between the mirrors returns in phase with itself: The distance of the mirrors should obey 2L = Nλ N is integer, λ is the laser wavelength, L is cavity length Fiber Optics has two types of design: Step-Index: Core is same material, but light takes diff paths. Some move fast, some bounce around and take longer. This isnt good for sending data.

Graded-index: Core material changes from cross center to the outside gradually, so like a highway, the outer lanes are faster than the inner, so they dont bounce. So its like creating lanes.

Final Exam format 30 MCQ (60 marks) 20 T/F (20 marks) 2 long answer