Exam3 Cheat Sheet - Summary Materials Science PDF

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Summary

Cheat sheet for exam 3 fall 2017....

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Bonding Electrons

Ionic Transferred

Metallic Shared with all atoms

Covalent Shared by specific atoms

Directional? Strength Melting Temp Thermal Expansion

No Strongest Highest Lowest

No Intermediate Intermediate Intermediate

Yes Weakest Lowest Highest

Elastic Modulus EN Difference

Highest >2.0

Intermediate

Lowest 0.2-0.5 np, 0.5-1.9 polar

Melting T / Bond E alters depth (A greater)

*rounded crack tips share stress in deformed region, less felt stress Fracture toughness: resistance to brittle fracture when crack exists Units: MPa sqrt(m) or ksi sqrt(in)

TEC (a) alters asymmetry (C greater)

Rc/Ra covalent>ionic (electrostat rep) - Enthalpy makes defects less favorable - Entropy makes defects more favorable Crystallographic planes: 1. If plane passes through origin, choose a different origin 2. Find plane intercepts on each axis in terms of a, b, c 3. Take reciprocals of intercepts 4. Reduce to smallest integer values

For polymers, greater MW: - Greater tensile strength - Greater MT and GT temps - Less likely to crystallize - Bonding in inert gases is VDW - Bonding within polymer coval., between chains is VDW

Composition calc: (C = wt%)

For HCP: 1. If plane passes through origin, choose a different origin 2. Find plane intercepts on a1 (h), a2 (k), c (l) axes 3. Take reciprocals of intercepts 4. Reduce to smallest integer values 5. Find last index using i = - (h+k) 6. Write in plane notations (hkil) Struct CN APF N SC 6 0.52 1

R 0.5a

CP direction {001}

Stacking -

BCC 8 0.68 2 Sqrt(3)a/4 none FCC 12 0.74 4 Sqrt(2)a/4 {111} 12 tot ABCABC HCP 12 0.74 6 none {0001} ABABAB Electrical conduction: Ohm’s law: V=IR or j = σE Resistance: NOT a material property, inc w/ L, dec w/ A Resistivity (ρ) and conductivity (σ) are material properties Order of inc σ: polymers < semiconductors < metals *Energy bands from electrostatic forces of other atoms Electron transport in metals: *hole concept does not apply - Resistivity increases with temperature (atoms vibrate) - Resist. increases with imperfections (disloc, impurity, etc) Band gap: applied voltage required for current to flow - e in conduction band move toward + terminal, holes in valence band move toward - terminal (diff velocities) - Metals: none, semiconductors: wider band gap - conductivity increases with temp Extrinsic semiconductors: n ≠ p due to impurities - n-type (n>>p): column 15 elements (usually not N) - p-type (p>>n): column 13 elements - doping increases conductivity, lowers activation energy T tensile region, large atom -> compressive region - Like stresses repel, opposite stresses attract and cancel 3. Strain hardening/cold working (more disloc impede motion) - mechanical shaping processes increase yield strength - must apply more stress to reach curve to begin plastic def. - dislocation density increases, like dislocations repel - Increases yield strength, tensile strength, decreases ductility

Luminescence: reemission of light at different frequency Phosphorescense >10-8 s, Fluorescence Fick’s 2nd law Fick’s 1st Law: Fick’s 2nd Law:

4. Precipitation hardening/particle strengthening (2nd phase particles are difficult to shear) - given const. volume fraction, larger particles-> more space btw - greater undercooling, smaller precipitates - strength increases with precipitation time, but eventually decreases due to diffusion of precipitate particles to larger particles

Diffusion faster for: open crystals, lower Tm, secondary bonding, smaller atoms, cations, lower density Diffusion slower for: close-packed crystals, higher Tm, covalent bonding, larger atoms, anions, higher density Order of increasing fracture toughness: Mechanical behavior: polymers < ceramics < composites < metals - Young’s modulus (E), elastic shear modulus (G), and elastic bulk modulus Temperature effect on fracture mode: (K) are related —> only two are independent - colder -> more brittle, seen in BCC metals and polymers - Stiff materials (high E) and high TS are usually strong (high yield strength) - FCC and HCP metals are always ductile Yield strength: value of stress noticeable plastic deformation occurs - DBTT (ductile to brittle transition temp) -> DESIGN ABOVE Increasing ductility of metals: *Draw straight line from 0.002 strain to meet the curve with slope E - Heat treating/annealing reverses effects of cold working - inflection point of impact energy vs. temp curve Tensile strength: max engineering stress; when necking starts (metals), 1. Recovery (100-200C): annihilation reduces dislocation density Creep: strain over time at constant temp (>0.4Tm in K) and stress crack propagation starts (ceramics), or polymer backbones are aligned and greater temperature increases diffusion, reduce intern. energy Primary: creep rate decreases with time, strain hardening Ductility: plastic tensile strain at failure *Polymer >> metals 2. Recrystallization (200-500C): atoms diffuse, rearrange, and Secondary: steady-state creep rate, vacancies migrate -> failure Resilience: energy absorbed during elastic deformation form new crystals, small dislocation density and small grains Units- rate: hr^-1 Toughness: energy absorbed before fracture (area under the curve) - TR is between 0.3-0.6 * melting temperature K2: Mpa^-n/hr Ranking: thermoplastic > elastomer > thermoset - TR decreases with increasing %CW and increasing purity - Steady-state rate increases/rupture life decreases with: Hardness: resistance to permanent indentation of the surface 3. Grain growth (>500C): grains combine over time due to diffuIncreasing constant stress, increasing temperature Ultimate strength: strength at which fracture occurs *Metal >> polymer sion, grain boundaries and grain boundary energy are reduced Tertiary: creep rate increases with time, movement and annihilaPhase diagrams: n=2 tion of dislocations Isomorphous: both metals have the same crystal structure and similar Creep mechanisms: - dislocation creep (vacancies replace atoms in electronegativities and atomic radii -> two phases and three phase fields Hot working = deformation about TR -> decreases strength half plane, moves dislocations past obstacles) - Phase diagrams provide number and types of phases present, composiCold working = deformation below TR -> increases strength - diffusion creep (atoms diffuse to stressed surfaces) tion of each phase (tie line), and wt% of each phase (fraction of tie line) *Perfect single crystals reduce creep Eutectic: liquid two solids, Eutectoid: solid two other solids Prediction of creep rupture lifetime: Hypoeutectic: comp below eutectic comp and above max pure solid Composites: extrapolate using higher T Hypereutectic: comp above eutectic comp and below max pure solid Matrix: continuous phase, Dispersed phase: reinforcement * m = Larson-Miller parameter, units: Kh; C usually = 20 Free energy of nucleation: surface energy increases, bulk energy decreasCMC: ceramic matrix composites Fracture toughness (Kc) Fatigue: Key parameters: stress amplitude, mid-stress, frequency es, total free energy increases to critical radius then decreases MMC: metal matrix composites σy, tensile strength, creep resistance - Transformation is fastest at moderate temperatures - Responsible for ~90% of failures, materials fail at lower stress Fatigue life: Nf, # stress cycles to cause fatigue failure PMC: polymer matrix composites E, σy, tensile strength, creep resistance Fe-C system order increasing hardness/strength and decreases ductility: Three steps: crack initiation, crack propagation, final sudden failure Spheroidite, c pearlite, f pearlite, bainite, tempered martensite, martensite Techniques to improve fatigue life: *Martensite only forms from austenite NOT pearlite/bainite Types of fibers: whiskers (thin single crystals, strongest), fibers - reduce magnitude of mean stress, shifts entire curve downward (polymer or ceramic), wires (metal) For Fe-C system, to form: - surface treatments: increase surface compressive stress Fiber alignment: longitudinal along fibers, transverse perpendicular 1. % coarse pearlite and proeutectoid ferrite: 680C - Shot peening (surface plastic def), carburizing (C atom diffusion) - Aligned continuous, aligned discount, 2D/3D random discont 2. 50% fine pearlite and 50% bainite: 590C until 50% transforms, 470C - design changes, remove stress concentrators ex: round corners Critical fiber length for stress transference (Lc): 3. 100% martensite: rapidly quench to RT Generalized yielding Dislocation motion σ>σy σy, TS 4. 50% martensite and 50% austenite: quench to 290C and hold there - continuous: L > 15Lc, discontinuous: L < 15Lc Longitudinal loading: matrix and fiber in parallel Fracture Crack growth to rupture Kc Ttrans (C) Result Phase comp - Composite stress: σc = σmVm + σfVf Gamma (FCC Fe with C in solid Fatigue Cyclic crack growth S, Nf No transition Austenite solution) - Composite strain: εc = εm = εf *isostrain Alpha crystals w/ spherical Fe3C - Composite stiffness: Ec = EmVm + EfVf Creep High T deformation by diff Qc, n 700 (long time) Spheroidite particles Transverse loading: matrix and fiber in series Layered BCC ferrite and Fe3C 650 700 Coarse pearlite Slip: plastic def by dislocation motion (edge, screw, mix) phases (eutectoid) - Composite stress: σc = σm = σf *isostress Layered BCC ferrite and Fe3C - Atomic bonds broken and reformed 550-650 Fine pearlite - Composite strain: εc = εmVm + εfVf phases (eutectoid) - Edge: line of motion in direction of applied shear stress - Composite stiffness: 1/Ec = (EfVm + EmVf)/EmEf 250-550 Bainite Fe3C rods in alpha-ferrite matrix - Screw: line of motion is perp to direction of applied shear stress Calculate stiffness based on orientation: (assume long. Loading) BCT w/ BCC Fe lattice and C - Macroscopic parallel slips form on surface of single crystal due to Aligned parallel in-plane, K = 1 large source-drain current Ferroelectric ceramics: applied voltage across mat shifts Ti atom Piezoelectric materials: stress induces voltage, voltage induces dimensional change

Refraction: n = c/v where v = velocity of light in material Snell’s Law: Critical angle: φ1 when φ2 = 90 Internally reflected if φ1>φc Metals: absorb and reemit photons -> reflection Ir/Io = 0.9-0.95 - metals w specific colors selectively absorb some photons Semiconductors: absorb light if h > Egap - If Egap all visible light absorbed, opaque - If Egap>3.1 eV -> no visible light absorbed, transparent - If Egap = 1.8-3.1 eV -> some photons absorbed, colored - Color of material is the color not absorbed *Red is lowest energy - Adding impurity atoms changes color Minimum wavelength absorbed:

Factor of safety: Fat. Stress ratio: - Can reduce grain size by cold working then annealing...