Exam 2 Study Guide - Fundamentals of Materials | ENGR 220, Study notes of Materials science

Download Exam 2 Study Guide - Fundamentals of Materials | ENGR 220 and more Study notes Materials science in PDF only on Docsity! 1 Engineering 220: Exam II Study-guide Chapter 5: Diffusion: mass transport by atomic motion.  Focus on diffusion in solids: vacancy and interstitial diffusion.  Interdiffusion: in an alloy, atoms migrate from regions of high concentration to regions of low concentration  creates concentration gradient.  Self-diffusion: in elemental solid, atoms can also migrate. Diffusion Mechanisms: I. Vacancy diffusion a. Atoms exchange with vacancies. i. Basically atom fills vacancy and creates new vacancy in its place. The vacancy just moves around. b. Applies to substitutional impurities atom. c. Rate depends on: i. Number of vacancies (*affected by temperature) ii. Activation energy to exchange II. Interstitial diffusion a. Smaller solute atoms can diffuse between atoms. * More rapid than vacancy diffusion because atoms can move through open interstitial. Processing Using Diffusion: I. Case Hardening o Diffuse atoms into host atoms at surface. o Changes the properties of the surface without effecting properties of interior. o *great for making surface wear resistant but not making it brittle but maintaining interior. II. Doping a. Silicone with phosphorous for n-type semiconductors. i. Deposit phosphorous rich layers on surface ii. Heat iii. Causes doped semiconductor regions Quantify: I. Quantify the amount or rate of diffusion a. J=Flux=(moles (or mass) diffusing)/(surface area * time)= mol/cm2s or kg/m2s - Quantity of mass or number of atoms diffusing over a certain area over an amount of time - Measured empirically (by experiment) Steady-state diffusion:  Concentration profile is not a function of time. Non-steady state diffusion:  Concentration profile is function of time. 2 Steady-state diffusion: I. Across a plate  concentration vs. distance: gradient dC/dx (constant slope line) II. High pressure on the left, low pressure on the right = negative slope. III. Rate of diffusion independent of time. a. Fick’s First Law of Diffusion: J= –D*dC/dx (D= diffusion coefficient) - Linear  can calculate dC/dx = (C2 – C1)/(x2 – x1) - Units: - Flux: (mol or kg)/m2s - Concentration: (mol or kg)/m3 - D: m2/s Diffusion and Temperature:  Diffusion coefficient increases with increasing temperature.  D=Do*exp(– Qd/RT) (Arrhenius Equations**) o D = Diffusion coefficient [m2/s] o Do = pre-exponential [m2/s] o Qd = Activation energy [J/mol or eV/atom] o R = gas constant o T = absolute temperature [K] Non-steady state diffusion:  Flux and concentration gradient change with time  Implies net accumulation or depletion of diffusing species: all converge on same point after time.  Concentration of diffusing species is function of both position and time  Fick’s Second Law: o δC/δt = D*δC/δC/δt = D*δt = D*δC/δt = D*δ2C/δC/δt = D*δx2 o (C(x,t) – Co)/(Cs – Co) = 1 – erf(x/2*sq(D*t)) (erf(z)) = error function What effects Diffusion coefficient (D)? 1. Temperature: Higher temperature = higher diffusion coefficient 2. Diffusion Mechanism: Interstitial diffusion is much faster than vacancy diffusion 3. Activation Energy: Determined by diffusing species and material its diffusing through Diffusion: FASTER: a. Open crystal structures b. Materials with Secondary bonding c. Smaller diffusing atoms d. Lower density materials SLOWER: a. Close-packed structures b. Materials with covalent bonding c. Larger diffusing atoms d. Higher density materials 5 b. Failure will occur wear necking begins c. Comparison: i. Metals/Alloys: Typically higher tensile strength ii. Ceramics: Varies from low to high based on properties iii. Polymers: Lower tensile strength iv. Composites: Variable 9. Ductility: Plastic tensile strain at failure a. How much deformation can you have before it actually breaks? b. Measured in 2 ways: i. Percent elongation = %EL = ((Length @ failure – Initial length)/(initial length))*100 1. Higher %EL = more ductile = doesn’t fail suddenly ii. Reduction in cross sectional area: %RA= ((Initial area – final area [in neck region]/(initial area))*100 c. Behavior: i. Low ductility: 1. Small amount of strain before fracture ii. High ductility: 1. Large amount of strain before fracture 10. Toughness: Energy required to break a unit volume of material a. Approximate by area under stress/strain curve b. Comparison: i. Ceramics: small toughness 1. Because they can go to high tensile stresses before breaking, but low ductility ii. Metals: large toughness 1. Moderately high stresses and can withhold a lot of deformation before failure iii. Unreinforced polymers: very small toughness 1. Lots and lots of ductility, but occurs at very low tensile stress 11. Elastic Strain Recovery: When plastic deformation occurs, elastic strain recovery is the small amount of recovery when stress is removed. a. On stress/strain curve it’s the space between the line straight down from the peak and the actual sloped line of the curve. 12. Hardness: Resistance to permanently indenting the surface a. Resistance to cracking in compression or plastic deformation b. Related to strength: higher strength = higher hardness c. Better wear properties d. Tests (indenter used to test): i. Rockwell: No major damage to sample 6 ii. Brinell Hardness: Approximate tensile strength from hardness e. Lowest to highest: i. Most plastics ii. Brasses Al alloys iii. Easy to machine steel iv. Cutting tools v. Nitrided steels vi. Diamond 13. True Stress and Strain: Calculate stress and strain based off of cross-sectional area at each point in test. True stress/strain curve will continue up instead of curving downward a. True stress = σ)T = F/Ai b. True strain = ε)T = ln(li/lo) 14. Hardening: An increase in yield strength due to plastic deformation a. As you deform metal you can add strength b. Create dislocations, which move around and tangle – viola! More strength c. σ)T = K(ε)T)n (n = hardening exponent)(K = material property) 15. Variability in Material Properties a. Critical properties depend largely on sample flaws b. Can determine with statistics: i. Mean (x́) ii. Standard deviation (s) 16. Design or Safety Factors a. Design uncertainties mean playing it safe yo. b. Factor of safety = N i. σ)working = σ)y/N (*N is usually between 1.2 and 4) ii. σ)working = Force/Area Summary: A. Stress and strain are size independent measures of load and displacement, respectively. B. Elastic behavior: reversible behavior that often shows linear relationship between stress and strain. Minimize deformation  choose material with large elastic modulus (E or G). C. Plastic behavior: permanent deformation behavior occurs when tensile (or compressive) uniaxial stress reaches yield strength. D. Toughness: Energy needed to break a unit volume of material. Measured by area under stress/strain curve of material taken to failure. E. Ductility: Plastic strain at failure. 7 Chapter 7: Strengthening in Metals: Dislocations:  Metals: easiest material class for dislocations to move around o Non-directional bonding o Close-packed directions for slip  Ceramics: Dislocation motion difficult o Ionic: need to avoid nearest neighbor of like sign (+ or – ). Positive atoms like to stay next to negative atoms. o Covalent: directional (angular) bonding Dislocation motion & plastic deformation:  Metals: plastic deformation occurs by slip – an edge dislocation (extra half-plane of atoms) slides over adjacent plane half-plane of atoms. o If dislocations can’t move, deformation can’t occur!  Dislocation moves along a slip plane in a direction perpendicular to dislocation line (slip direction is the same as Burger’s Vector direction). o Edge dislocation: Burger’s vector = parallel. o Screw dislocation: Burger’s vector = perpendicular. Deformation mechanisms:  Slip System o Slip plane: plane on which easiest slippage occurs  Highest planar densities (and large interplanar spacing) (planes with most atoms squeezed into one area) o Slip directions: directions of dislocation movement  Highest linear densities (along directions in which atoms are “touching”, most atoms on them) (BCC through diagonal of cube, FCC along diagonal of face of the cube)  Stress and dislocation motion o Resolved Shear stress (τR)  Results from applied tensile stresses (σ) = F/A)  Specific plane where slip will occur most easily  τR = Fs/As (force/new area)  Fs = Fcos(λ) –> λ = angle between Fs and F  As = A/cos(ϕ) –> ϕ = angle between ns and F  τR = σ)cos(λ) cos(ϕ)  τR = 0, λ = 90o (horizontal slip)  τR = σ)/2, λ = 45o, ϕ = 45o (diagonal – max shear stress)  τR = 0, ϕ = 90o o Slip Motion in Polycrystals 10  Close-packed structures  2 types of interstitial sites: o Octahedral (CN# 8)  # octahedral sites: # of atoms o Tetrahedral (CN#4)  # tetrahedral sites: 2x # of atoms 1. Ceramic Crystal structure a. Determines what site cations will occupy? i. Size of sites ii. Stoichiometry iii. Bond hybridization - % covalency b. Size: i. Stable ii. Maximize # of oppositely charged ion neighbors iii. CN related to cation-anion radius ratio c. Different crystal structures: i. Cesium Chloride (A-X): n’= 1 ii. Zinc Blende (A-X): n’= 4 iii. Rock Salt (NaCl)(A-X): n’= 4 iv. Fluorite(Am-Xp): n’ = 4 1. Antifluorite: cations > anions v. Perovskite (AmBnXp): >1 type of cation. Cubic d. Ceramic Density calculation. i. Formula. 2. Polymorphic Forms of Carbon a. Diamond i. Tetrahedral bonding ii. Very high thermal conductivity b. Graphite i. Layered structure ii. Parallel hexagonal arrays iii. Van der Waals bonding between layers c. Fullerenes i. Soccer ball type d. Nanotubes Point Defects in Ceramics: 1. Vacancies: a. Exist in ceramics for both cations and anions 2. Interstitials: a. Exist for cations b. Not observed for anions because anions are large relative to interstitial sites. 3. Frenkel Defect a. Cation vacancy-cation interstitial pair 11 4. Shottky Defect a. Paired set of cation-anion vacancy