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Aufbau Principles
electrons occupy orbitals of increasing energy
Hund’s Rule
electrons occupy all degenerate orbitals before putting 2 electrons in the same orbital
Pauli Exclusion Principle
No 2 electrons can have same set of 4 quantum #s
Primary bonds
- Ionic bond
- Covalent bond
- Metallic bond: atomic orbitals combine to form delocalized electron cloud shared by many atoms
Secondary bonds
- Van Der Waals: weak bonding induced by fluctuating/permanent molecular dipoles
- Hydrogen bonding: bonding between protons and available electron pair
Effects of bonding on melting temperature
- Tm larger if bond energy larger
- Tm is depth of potential energy curve
Effects of bonding energy on modulus of elasticity
- E is larger if bonding energy is larger
- E is related to curvature at unstretched length
Effects of bonding energy on coefficient of thermal expansion
- It’s larger if bonding energy is smaller
- Thermal expansion is mean interatomic distance which increases with thermal energy
- Related to symmetry of potential structure
Melting temperature hardness relationship
- Materials with high Tm are harder
- Hardness is resistance of surface to plastic deformation and is influenced by height of total force curve (bonding energy)
Ionic + covalent bonds in ceramics leads to…
- Large bond energy
- Large Tm
- Large E
- Small thermal expansion coefficient
Metallic bonds in metals leads to…
- Variable bond energy
- Moderate Tm
- Moderate E
- Moderate thermal expansion coefficient
Covalent + secondary bonds in polymers leads to…
- Directional properties
- Secondary bonding dominates
- Small Tm
- Small E
- Large thermal expansion coefficient
Valence band
Has highest energy electrons at 0 degrees K
Conduction band
Next band at energy > valence band
Fermi energy
- At 0 degrees K all electrons have energy smaller or equal to Fermi energy
- Energy where probability of occupancy is 50% for any T>0K
Movement of electrons in conductors
Energy needed is very small to move in a conduction region and become a free electron
Movement of electrons in insulators
Large energy band gap exists between full valence band + conduction region
Movement of electrons in semi-conductors
Same as insulators w/small band gap
Consequences of imperfections in a crystal
- Resistance of pure metals near absolute 0 temperature is very small
- Resistance increases with T
What happens when normal atoms are replaced with impurity atoms?
- Local strains are produced that scatter electrons
- Resistance increases even at absolute 0 temperatures
- Very good conductors must be pure
- Bad conductors are usually alloys
Does metal deformed by work hardening have lower or higher resistivity than the same metal in the stabilized state?
Higher
Intrinsic semiconductors
- Fermi energy is in the middle of the band gap
- Area above gap ~ # electrons in conduction
- Area below gap ~ # missing electrons in valence band (AKA holes in valence band)
Extrinsic semiconductors
- Fermi energy position changes according to doping
n-type extrinsic semiconductors
- Surplus of 1 electron for each atom added which goes easily to conduction band so required energy is small
- Have higher fermi levels than p types
- Happens when you add phosphorus to silicon
p-type extrinsic semiconductors
- Missing 1 electron for each atom added creating a hole
- Hole easily goes to valence band so required energy is small
- Happens when you add boron to silicon
Transistor
- Constituted of 3 semiconductor sections
- Current can flow between emitter + collector only if potential applied at base
- Applied in amplifiers + electronic switches
Peltier effect
- When current forced through bi-metal junction, electron going from point A to B gains energy at interface so energy taken from material (cooling effect)
- When electron goes from B to A it loses energy at interface –> heating effect
- When electron goes from p to n type it gains energy and energy taken from material so cooling effect (from lower to higher Fermi energy)
Amorphous
- Non-dense + random packing
- Solids w/out long range order/crystallinity
- When fast solidification doesn’t allow time to organize crystal structure the result is liquid like appearance
Crystalline
- Dense + regular packing
- Have lower energy than amorphous solids
Single crystal
Imply long range orders
Polycrystals
Imply several crystals packed together
Metallic crystal structures
- Densely packed
- Simplest crystal structures
Why are metallic crystal structures densely packed?
- Only 1 element present so all atomic radii are same
- Metallic bonding non-directional
- Nearest neighbour distances are small in order to lower bond energy
- Electron cloud shields cores from each other
Unit cell
Smallest repetitive volume which contains complete pattern of crystal
Atomic packing factor
APF = volume of atoms in unit cell / total unit cell volume
Coordination number
of first touching neighbours in hard sphere model
Simple cubic structure
- 1 atom/unit cell
- CN = 6
- a = 2R
- APF = 0.52
Body centred cubic structure
- 2 atoms/cell
- CN = 8
- APF = 0.68
- a = 4R/sqrt(3)
Face centred cubic structure
- a = 2Rsqrt(2)
- CN = 12
- APF = 0.74
- 4 atoms/unit cell
- Atoms touch along diagonal - close-packed direction
Hexagonal close packed structure
- 6 atoms/unit cell
- APF = 0.74
- CN = 12
2 types of voids in FCC
- Octahedral void (CN = 6) + 4/unit cell
- Tetrahedral void (CN=4) + 8/unit cell
Polymorphism
When metals + non-metals have >1 crystal structure
Anisotropy in single crystals
Properties vary w/direction
Anisotropy in polycrystals
- Properties may/may not vary w/direction
- If grains randomly oriented then isotropic. If grains oriented then anisotropic
Transitions in crystalline solids
- Before/after melting: atomic vibration increases w/T + volume expansion
- At melting: crystal formation + high APF + sudden volume decrease
Poisson ratio of 0.5
No volume change with strain
Poisson ratio of 0
No lateral strain with axial strain
Negative Poisson ratio
Positive lateral strain with positive axial strain
Ductility
- Measure of degree of plastic deformation that has been sustained at fracture
- If fracture strain less than 5% then brittle
Resilience
Capacity of material to absorb energy when deformed elastically
Modulus of resilience
Strain energy / unit volume required to stress a material to the point of yielding
Toughness
Capacity of material to absorb energy up to point of fracture
Hardness test
- Initial stress is high + plastic deformation occurs
- As point goes in stress decreases + equilibrium reached
- Shallower mark = harder material
Ceramics
- Brittle - elastic deformation until point of fracture
Polymers
Can be brittle, plastic or elastic depending on structure
Activation polarization
- Activation energy required to have electrons transferred from electrode into analyte
- Overvoltage is driving force for rxn
Concentration polarization
- Rxn rate limited by diffusion in solution
- Affects cathode only
Passive region
Oxide layer formed on surface which prevents passage of current
Transpassive
Potential high enough to break oxide layer
6 forms of corrosion
- Uniform
- Galvanic
- Stress
- Crevice
- Pitting
- Intergranular
Uniform attack
Homogenous corrosion over whole surface
Galvanic corrosion
Occurs when 2 metals/alloys having diff composition are electrically coupled while being exposed to electrolyte
How to avoid Galvanic corrosion?
- Choose metals close in galvanic series (low EMF potential)
- Avoid unfavourable anode-cathode area ratios (have large anode)
- Electrical insulation
- Connect to more anodic metal
Crevice corrosion
Occurs due to concentration diffs in ions + occurs in low concentration region
Pitting
Concentration difference driven like crevice corrosion but corrosion pit forms as deep well driven by gravity
Intergranular corrosion
Occurs at grain boundaries when metals are heated
Selective leaching
1 element of alloy is selectively removed by corrosion process
Erosion-corrosion
Occurs from combined chemical attack + mechanical abrasion from fluid motion - removes protective layer
Stress corrosion
- Metals which normally resist corrosive environment may corrode when stress applied in addition to corrosive environment
- Small cracks form + propagate in direction perpendicular to stress - stress need not be externally applied
Hydrogen embrittlement
Reduction in ductility + tensile strength that occurs when atomic hydrogen penetrates structure of the material
P-B ratio
Used to determine whether you have good conformal oxide coating
If P-B ration < 1?
Oxide takes less volume than metal
If P-B ratio = 1?
Oxide takes same volume as metal
If P-B ratio > 1?
Oxide takes greater volume than metal
Kinetics of oxides on well-adhering films
- Oxide growth limited by ionic diffusion as described by Fick’s law
- Parabolic growth kinetics
Kinetics of oxides on porous films
- Growth is linear
- P-B ratio < 1 or > 2
Kinetics of thin oxides growing close to room temperature
Logarithmic growth kinetics
Safety factor equation
Sigma_w = sigma_y/N
Effect of depth of bond force curve on elastic modulus
Slope of bond force is proportional to E because when you have a steeper slope you need more force to get the same interatomic distance
Thermal electromotive force
- Potential diff of 2 metals subject to same temp
- Diff in potential due to diff in resistivity + can be related to temp input
- Use thermocouple to measure
Linear defects / dislocations
1-D defects around which atoms are misaligned
Edge dislocation
- Extra half-plane of atoms inserted in crystal structure
- Burger’s vector is perpendicular to dislocation line
Screw dislocation
- Spiral planar ramp resulting from shear deformation
- Burger’s vector is parallel to dislocation line
Equiaxed grains
- Same size in all directions
- Form due to rapid cooling near wall
Why do dislocations preferentially move in the [1 1 1] plane of FCC instead of the [1 0 0] plane?
Smaller b so less energy needed for motion
Grain boundaries
- Regions between single crystals that mark the transition from lattice of 1 region to that of the other
- Slightly disordered + low density inside leading to high mobility, high diffusivity + high chem reactivity
Columnar grains
- Elongated grains
- Occur in area w/less undercooling
Does a large number of boundaries + defects produce a softer or harder material?
Harder
Do small grains make a stronger or weaker material?
Stronger because dislocations are stopped by grain boundaries
Is the total interfacial energy greater for fine or for large grains?
For fine grains because the boundary area/unit volume is smaller for large grains
At high temperatures what happens to grains?
They grow in size to minimize interfacial energy - large grains eat small grains
Do large grains have larger or smaller CN’s than small grains?
Larger
Diode
- p-n rectifier junction
- Current only flows in 1 direction
