Materials Science and Engineering Lecture Notes Flashcards

Comprehensive vocabulary flashcards covering crystallography, mechanical properties, phase diagrams, heat treatments, imperfections, failure mechanisms, and materials classes (metals, polymers, ceramics).

Lattice

An infinite, periodic 3D array of points in space where each point has identical surroundings; an abstract concept where atoms sit at or near lattice points.

Unit Cell

The smallest repeating structural unit of a crystal, described by three edge lengths ($a$, $b$, $c$) and three angles ($\alpha$, $\beta$, $\gamma$).

Bravais Lattices

The 14 distinct lattice types possible in 3D, grouped into 7 crystal systems; course focus includes SC, BCC, and FCC.

Simple Cubic (SC)

A crystal structure with 1 atom/cell where atoms touch along the cube edge ($a = 2r$), having an APF of $0.52$ and a CN of $6$. Polonium ($Po$) is the only example.

Body-Centered Cubic (BCC)

A crystal structure with 2 atoms/cell where atoms touch along the body diagonal ($a = \frac{4r}{\sqrt{3}}$), an APF of $0.68$, and a CN of $8$. Examples include $Fe$ (below $912^\circ\text{C}$), $W$, $Cr$, and $Mo$.

Face-Centered Cubic (FCC)

A crystal structure with 4 atoms/cell where atoms touch along the face diagonal ($a = \frac{4r}{\sqrt{2}}$), an APF of $0.74$, and a CN of $12$. Examples include $Al$, $Cu$, $Ni$, $Ag$, $Au$, and $Fe$ (above $912^\circ\text{C}$).

Hexagonal Close-Packed (HCP)

A crystal structure with 6 atoms/cell, ABAB layer stacking, an APF of $0.74$, and a CN of $12$. Ideal $\frac{c}{a} \approx 1.633$. Examples include $Mg$, $Ti$ (below $882^\circ\text{C}$), and $Zn$.

Atomic Packing Factor (APF)

The fraction of unit cell volume occupied by atoms, calculated as $\text{APF} = \frac{\text{atoms/cell} \times (\frac{4}{3})\pi r^3}{a^3}$. Values: SC=$0.52$, BCC=$0.68$, FCC/HCP=$0.74$.

Coordination Number (CN)

The number of nearest-neighbor atoms touching a given atom. SC=$6$, BCC=$8$, FCC=$12$, HCP=$12$.

Lattice Parameter

The edge length of a unit cell (symbol: $a$ for cubic), measured in Angstroms or $nm$ and determined by X-ray diffraction.

Miller Index [hkl] — Direction

Integer notation for a crystal direction derived by reading vector components along $a$, $b$, $c$ axes and clearing to integers; negative values are indicated by a bar over the number.

Miller Index (hkl) — Plane

Integer notation for a crystal plane found by taking reciprocals of axis intercepts and clearing to integers. Parentheses denote a specific plane, while ${hkl}$ denotes a family.

Key Directions

Specific vectors in a crystal: $[100]$ is the cube edge, $[110]$ is the face diagonal, and $[111]$ is the body diagonal. In BCC, $[111]$ is the close-packed direction.

d-spacing

The perpendicular distance between adjacent parallel $(hkl)$ planes. For cubic structures: $d = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$.

Metallic Bonding

The electron sea model involving delocalized valence electrons, making metals conductive, ductile, malleable, and lustrous.

Ionic Bonding

Electrostatic attraction between positive and negative ions; properties include being hard, brittle, high melting point, and electrically insulating (e.g., $NaCl$, $MgO$).

Covalent Bonding

Shared electron pairs between atoms; properties include being hard, having a high melting point, and often being insulating (e.g., diamond, $Si$, $SiC$).

Van der Waals Bonding

Weak induced dipole interactions resulting in low melting points and softness (e.g., polymer chains, noble gases).

Engineering Stress ($\sigma$)

Force divided by the original cross-sectional area: $\sigma = \frac{F}{A_0}$. Units are $Pa$ or $MPa$.

Engineering Strain ($\epsilon$)

The change in length divided by the original length: $\epsilon = \frac{\Delta L}{L_0}$; it is dimensionless.

Elastic Deformation

Reversible deformation where atoms displace but return to original positions when the load is removed; corresponds to the linear region of the stress-strain curve.

Plastic Deformation

Permanent deformation where atoms move to new positions via dislocation motion and cannot be recovered upon unloading.

Young's Modulus ($E$)

The slope of the linear elastic region measuring stiffness ($\sigma = E \cdot \epsilon$). Typical values: Steel $\approx 200\,GPa$, Al $\approx 70\,GPa$. It does not change with heat treatment.

Poisson's Ratio ($\nu$)

The negative ratio of lateral strain to axial strain ($\nu = -\frac{\epsilon_{lat}}{\epsilon_{axial}}$). Typically $0.25$-$0.35$ for metals.

Yield Strength ($\sigma_y$)

The stress at the onset of significant plastic deformation, found by drawing a line parallel to the elastic region offset by $\epsilon = 0.002$ (0.2% offset method).

Ultimate Tensile Strength (UTS)

The maximum engineering stress on the stress-strain curve, after which necking begins and engineering stress drops.

Ductility

The amount of plastic deformation before fracture, measured by $\text{\%Elongation} = (\frac{L_f - L_0}{L_0}) \times 100\%$ or $\text{\%RA} = (\frac{A_0 - A_f}{A_0}) \times 100\%$.

Resilience (Modulus of Resilience)

Energy absorbed per unit volume during elastic deformation only; represented by the area under the elastic region: $U_r = \frac{\sigma_y^2}{2E}$.

Toughness

Total energy absorbed per unit volume up to fracture, represented by the area under the entire stress-strain curve. High toughness requires the material to be strong and ductile.

Necking

Localized reduction in cross-sectional area after UTS, beginning when the strain hardening rate cannot compensate for area reduction.

Rockwell C (HRC)

Hardness test using a diamond cone (Brale indenter) and $150\,kg$ load; scale ranges $20$-$70\,HRC$ for hardened steel and hard alloys.

Rockwell B (HRB)

Hardness test using a $1/16"$ steel ball and $100\,kg$ load; scale ranges $0$-$100\,HRB$ for soft metals like Al, Cu, and annealed steel.

Brinell (HB)

Hardness test using a $10\,mm$ ball and $500$ or $3000\,kg$ load; measures indentation diameter. Good for castings and coarse materials ($HB \approx \frac{\text{UTS(MPa)}}{3.45}$ for steels).

Vickers (HV)

Hardness test using a $136^\circ$ diamond pyramid; precise and applicable to any material and hardness range, including thin films.

Phase

A region of a material with uniform composition and crystal structure, separated from others by phase boundaries.

Gibbs Phase Rule

The equation $F = C - P + 1$ (at constant pressure), where $F$ is degrees of freedom, $C$ is components, and $P$ is phases. At a eutectic, $F = 0$ (invariant).

Liquidus Line

The line on a phase diagram above which only liquid exists.

Solidus Line

The line on a phase diagram below which only solid exists.

Eutectic Point

The specific composition and temperature where liquid transforms simultaneously into two solids ($L \rightarrow \alpha + \beta$). It is the lowest melting point in a binary system.

Eutectoid Point

The specific composition and temperature where one solid transforms into two solids ($\gamma \rightarrow \alpha + \beta$) entirely in the solid state. For iron-carbon: $0.77\%\,C$, $727^\circ\text{C}$.

Tie Line

A horizontal line at constant $T$ through a two-phase region; its endpoints give the compositions of the two phases in equilibrium.

Lever Rule

Calculates the weight fraction of phases: $W_{\alpha} = \frac{C_{\beta} - C_0}{C_{\beta} - C_{\alpha}}$. Always check that $W_{\alpha} + W_{\beta} = 1$.

Ferrite (\alpha)

BCC iron with up to $0.022\,wt\%\,C$; soft, ductile, magnetic below $768^\circ\text{C}$, and the stable room-temperature phase in low-carbon steels.

Austenite (\gamma)

FCC iron with up to $2.14\,wt\%\,C$, stable between $727$-$1495^\circ\text{C}$, and non-magnetic.

Cementite (Fe3C)

Iron carbide at $6.67\,wt\%\,C$; extremely hard and brittle.

Pearlite

A eutectoid microstructure comprised of alternating lamellae of ferrite and cementite with a striped appearance, formed by slow cooling at $0.77\%\,C$, $727^\circ\text{C}$.

Martensite

A very hard, brittle BCT phase formed by rapid quenching of austenite; carbon is trapped in the lattice, resulting in a needle/lath microstructure.

Bainite

A metastable microstructure from intermediate cooling rates with a feathery or acicular appearance; tougher than martensite at similar strength.

Spheroidite

Rounded cementite spheres in a ferrite matrix formed by long anneals below $727^\circ\text{C}$; the most ductile steel microstructure.

Hypoeutectoid Steel

Steel containing less than $0.77\,wt\%\,C$; slow cooling results in a microstructure of proeutectoid ferrite and pearlite.

Hypereutectoid Steel

Steel containing between $0.77\,wt\%$ and $2.14\,wt\%\,C$; slow cooling results in proeutectoid cementite and pearlite.

Steel vs Cast Iron

Steels contain less than $2.14\,wt\%\,C$, while cast irons contain $2.14$-$6.67\,wt\%\,C$, undergoing a eutectic reaction at $4.3\%\,C$.

Annealing (steel)

Heating above the critical temperature followed by slow furnace cooling to produce a soft, ductile pearlite microstructure.

Normalizing

Heating above the critical temperature followed by air cooling, producing finer pearlite that is slightly harder than annealed steel.

Quenching

Rapid cooling in water or oil to suppress diffusion and form hard, brittle martensite.

Tempering

Reheating quenched martensitic steel to $150$-$650^\circ\text{C}$ to allow carbon diffusion, forming tempered martensite and improved toughness.

TTT Diagram

Time-Temperature-Transformation diagram; shows the microstructure formed versus time and temperature after quenching from austenite.

Vacancy

A point defect where an atom is missing from a lattice site; density increases exponentially with temperature: $N_v = N \cdot \exp(-\frac{Q_v}{kT})$.

Substitutional Impurity

A solute atom replacing a host atom on a lattice site; high solubility requires similarity in radius (<15% diff), crystal structure, electronegativity, and valence.

Interstitial Impurity

A small solute atom located in the gap between host atoms (e.g., Carbon in Iron).

Edge Dislocation

An extra half-plane of atoms in the lattice where the Burgers vector is perpendicular to the dislocation line; represented by the symbol $\perp$.

Screw Dislocation

A lattice displacement parallel to the dislocation line creating a spiral ramp; the Burgers vector is parallel to the dislocation line.

Burgers Vector (b)

A vector characterizing the magnitude and direction of lattice distortion at a dislocation. For FCC slip: $b = \frac{1}{2}a \langle 110 \rangle$.

Slip System

The combination of a slip plane and a slip direction. FCC has ${111} \langle 110 \rangle$ (12 systems), making it more ductile than HCP (3 systems).

Grain Boundary Strengthening

A strengthening mechanism where smaller grains (more boundaries) impede dislocation motion, increasing yield strength and improving toughness.

Hall-Petch Equation

The relationship $\sigma_y = \sigma_0 + k_y \cdot d^{-1/2}$ where yield strength ($\sigma_y$) increases as grain diameter ($d$) decreases.

Solid Solution Strengthening

A mechanism where solute atoms (interstitial or substitutional) distort the lattice and impede dislocation motion.

Strain Hardening (Cold Work)

Increased dislocation density from plastic deformation causing dislocations to tangle and making further deformation harder; quantified as $\text{\%CW} = (\frac{A_0 - A_d}{A_0}) \times 100\%$.

Precipitation Hardening

Strengthening by fine second-phase particles (e.g., $CuAl_2$ in Al-Cu alloys) that impede dislocation motion; requires solution heat treat, quench, and aging.

Recrystallization

The nucleation and growth of new strain-free grains in cold-worked metal at $T > \sim 0.4\,T_m$, restoring ductility and reducing strength.

Ductile Fracture

Fracture characterized by significant plastic deformation, cup-and-cone morphology, and high energy absorption; slow and predictable.

Brittle Fracture

Fracture with little or no plastic deformation, characterized by flat cleavage facets or chevron markings; fast, catastrophic, and low energy.

Fracture Toughness (KIc)

Resistance to fracture in the presence of a crack, given by $K_{Ic} = Y \cdot \sigma \cdot \sqrt{\pi a}$. Units: $MPa\cdot\sqrt{m}$.

Ductile-to-Brittle Transition (DBTT)

A shift in failure mode from ductile to brittle as temperature decreases, observed in BCC metals (like steel) but not FCC metals; measured by Charpy impact tests.

Charpy Impact Test

A method where a notched specimen is struck by a swinging hammer to measure energy absorbed during fracture, used to determine DBTT.

Fatigue

Failure under cyclic loading at stresses below the yield strength; cracks typically nucleate at surface defects.

S-N Curve (Wöhler Curve)

A plot of cyclic stress amplitude ($S$) versus cycles to failure ($N$, log scale) used to determine fatigue life and endurance limit.

Endurance Limit (Se)

The maximum cyclic stress below which a material (typically steel or Ti) can endure infinite cycles; for steels, $S_e \approx 0.5 \times \text{UTS}$.

Fatigue Crack Striations

Marks on a fracture surface where each striation represents incremental crack advance during one load cycle.

Creep

Time-dependent permanent deformation under constant stress at high temperatures ($T > 0.4\,T_m$ in Kelvin).

Steady-State Creep Rate

The minimum creep rate during the secondary stage: $\frac{d\epsilon}{dt} = K \cdot \sigma^n \cdot \exp(-\frac{Q_c}{RT})$; most important for engineering design.

Band Gap (Eg)

The energy gap between valence and conduction bands: Conductors ($\sim 0\,eV$), Semiconductors ($0.1$-$3\,eV$), and Insulators ($>5\,eV$).

Intrinsic Semiconductor

A pure semiconductor (e.g., $Si$, $Ge$) where conductivity arises from thermal excitation and electrons equal holes.

n-type Semiconductor

A semiconductor doped with Group V donor atoms ($P$, $As$) that provide extra electrons, making electrons the majority carriers.

p-type Semiconductor

A semiconductor doped with Group III acceptor atoms ($B$, $Al$) that create holes, making holes the majority carriers.

Matthiessen's Rule

The total resistivity is the sum of contributing factors: $\rho_{total} = \rho_{thermal} + \rho_{impurity} + \rho_{deformation}$.

Thermal Conductivity (k)

The rate of heat transfer following Fourier's Law: $q = -k\cdot(\frac{dT}{dx})$. Heat is carried by electrons in metals and phonons in ceramics/polymers.

Thermal Expansion (\alpha)

The fractional change in length per degree: $\frac{\Delta L}{L_0} = \alpha \cdot \Delta T$. Stronger bonding leads to a lower $\alpha$.

Thermoplastic

Polymers with linear or branched chains that can be remelted and recycled (e.g., PE, PVC, nylon).

Thermoset

Crosslinked 3D network polymers that decompose rather than melt, making them chemically resistant and non-recyclable (e.g., epoxy, Bakelite).

Elastomer

Lightly crosslinked polymers capable of large elastic deformations ($>200\%$), such as vulcanized natural rubber.

Addition Polymerization

A process where monomers at a time add to a growing chain without byproducts, requiring $C=C$ double bonds.

Condensation Polymerization

Step-growth polymerization where monomers react in pairs, releasing small molecules (usually $H_2O$).

Polydispersity Index (PDI)

The ratio of weight-average to number-average molecular weight ($PDI = \frac{M_w}{M_n} \geq 1$). A $PDI$ of 1 means all chains are identical.

Degree of Polymerization (DP)

The number of repeat units per chain: $DP = \frac{M_n}{m_{mer}}$, where $m_{mer}$ is the molecular weight of one mer.

Glass Transition Temperature (Tg)

The temperature range below which a polymer/glass is brittle/glassy and above which it is rubbery/viscous.

Tacticity

The regularity of side group arrangement in a polymer: isotactic and syndiotactic promote crystallinity, while atactic is amorphous.

Ceramic

Inorganic, non-metallic compounds of metallic and nonmetallic elements formed via ionic/covalent bonding; hard, brittle, and insulating.

Sintering

Firing compacted ceramic powder below its melting point to bond particles via diffusion, reducing porosity and increasing density.

Silicate Tetrahedron (SiO4 4-)

The fundamental unit of silicates where one $Si$ is bonded to four $O$ atoms, sharing corners only.