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Materials Science and Engineering

MATLS 1M03

Hatem Zurob

Winter

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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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