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Materials Science and Engineering
Hatem Zurob

Rexem Lally Pinzon – MATLS CRIB SHEET N ρ CHAPTER 2: ATOMIC STRUCTURE AND INTERATOMIC BONDING N= a *Bond length – distance at A N a avogadro’s # ρ – density A – atomic mass which the attractive and repulsive force balance. SOLUBILITY INCREASES if: – Fnet 0 , net= min ~ equilibrium -diff. sizes of atoms-same crystal structure -same electronegativity *High bonding energy – high melting -low valences point *Solid solubility: *High curvature – high elastic modulus (E) Line Defects (Dislocations) – always thermodynamically unstable * Symmetric energy well near bond *Edge dislocation – Burger’s Vector is perpendicular to dislocation line length – low coefficient of thermal *Screw dislocation – Burger’s Vector is parallel to dislocation line expansion. Planar Defects – boundaries that divide crystal regions *External Surfaces – crystal edge (unbonded electrons) ~ has higher Increasing strength (Weak to strong): energy Van der Waals – Hydrogen Bonding – *Grain Boundaries – smaller angle, more good bonds (polycrystalline) Metallic Bonding – Covalent bonding – *Twin Boundaries – mirror lattice symmetry ~ orientation is diff ~ low Ionic bonding energy Solidification CHAPTER 3: STRUCTURE OF CRYSTALLINE SOLIDS *Nucleation – appearance of solid in liquid *Hexagonal Packing – bonding to 6 atoms; lowers the overall energy (E *Growth – solid consumes liquid by adding atoms to nucleus. efficient) *Impingement – 2 solids meet each other forming a grain boundary *Square Packing – bonding to 4 atoms; not energy efficient Nucleation Barrier – surface terms>volume term at small values of r gamma – J/m 2 Gsoln negative CHAPTER 5: DIFFUSION Diffusion – [High] – [Low] ~ changing of atom’s location - helps overcome activation energy; temp is the motivation for diffusion *Diffusion mechanism – there must be an empty adjacent site vacancy - There must be a sufficient energy DIFFUSION IS FASTER FOR: -Open crystal structures -lowering melting T matls -Secondary bonding -Smaller diffusing atoms -high-temp First Fick’s Law: T – temp (K) t – time 2 Q – 2 activation energy 3 √ 3a c D – diffusion coefficient (m /s) J – flux V hex= q=J × A 2 Removal rate: A – area ***High q ~ temp. sensitive 3 V cubea CHAPTER 18: ELECTRICAL PROPERTIES OF SOLIDS Ohm’s law: I = V/R Resisitivity, ρ(Ωm):R = ρl/A A – area l – length *APF – the space that occupies in a cell -1 *Coordination # - # of bonds It can produce; same for every atoms in the unit cell. Conductivity (Ωm) : σ = 1/ρ Current density: J = σE =σ(V/l) E – # of atoms electric field Mass volume N a Avogadro Miller Direction Indices – [u v w] - Multiply/divide by a common factor (NO FRACTIONS) Miller Planes Indices – (h k l) - Take reciprocal and get rid of fractions Families of direction – (h k l) ●[u v w] = hu +kv + lw = 0 X-RAY DIFFRACTION – determines atomic interplanar distances & crystal structure Energy Bragg’s law: Band Structure: n – order λ – wavelength d – interplanar spacing *Fermi Energy (Ef) – energy of the last (highest) filled state at 0K. Electron Mobility (e ) – increase µ, decrease temp and purity of material a – lattice spacing -free electron accelerate in the opposite direction to the field - depends on ~impurity atoms ~vacancies ~thermal vibration CHAPTER 4: IMPERFECTIONS IN SOLIDS ~dislocation f ~interstitial atoms Point Defects – defects at a single atom position: Vacancies and self- Drift VelocityV = µ E E – electric fieldµe (m /Vs) interstitials d e *Vacancies - lattice site with missing atom or ion. Electrical Resistivity of Metals *High Conductivity – low resisitivity; large # of e have been excited N v −Q v into empty states above f X =v =exp⁡( ) T – temperature *Influence from temp – T increase, n increase, N RT µedecrease a – material constant *Influence from impurities – C is %at/100 (K) A – composition-independent constant Nv– vacancy/atom N – atom/m 3 Q v eV/atom or J/mol Xv– fraction of atoms R – 8.314 J/mol*k or 8.62*10 *Matthiessen’s Rule –conductivity decrease if: eV/atom*K ~increase in Temp, impurity atoms, # dislocation Electrical Conduction in Semi-conductors *Self-Interstitial – an atom that is crowded into an empty site bet. *Intrinsic Semi-conductions – determined by pure materials Atoms. lel – 1.602*1019n and p – m -3
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