Term
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Definition
Vacancies and Intersticials
Two Ions:
# Cation vacancies = # Anion vacancies (electroneutrality)
More cation than anion interstitials (size)
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Term
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Definition
cation vacancy - cation interstial pair
any time an atom/anion moves from latice site to its interstitial site |
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Definition
| Paired anion and cation vacancies |
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Term
| Substitutional Impurities/ Charge Neutrality (Ceramics) |
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Definition
If the replacing atom has a different charge than the replaced, then vacancies must occur.
EX. NaCl, with a Ca taking place of a Na.
Na +1, Ca +2, so there must be a cation vacancy as well to keep it balanced.
NaCl, Cl -, O 2- |
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Term
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Definition
More complicated in Ceramics b.c. electroneutrality.
Diffusion occurs through vacancy mechanism.
Diffusion of an anion must be accompanied by diffusions of cation(s) with equal charge.
Diffusion rate is limited by the slower moving ion
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Term
Ceramics vs Metal
Brittleness |
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Definition
Ceramics are more brittle
Crystalline - dislocation motion
Highly ionic solids - dislocation motion is difficult.
Few slip systems
Moving same charged ions close together - repel |
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Term
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Definition
Flaws/cracks within the structure.
Propagated stress is much lower than you would expect:
(Initiation sites)Stress concentration/riser (from small flaws)
No mechanisms for plastic deformation = unimpeded propogation fo cracks
K=Yo(pi*a)^1/2
Cracks can propogate slowly at lower stresses, but only in moist environments where corrosion processes are occuring at the crack tips |
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Term
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Definition
One point is different from the normal repeating structure
Vacanies = much mroe likely than self interstitials
Vacancy Atoms
Interstitial Atoms
Substitutional Atoms |
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Term
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Definition
Defect in the structure with one dimension
Dislocations |
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Term
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Definition
2 or more dimensions in the defect
Grain Boundaries |
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Term
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Definition
All crystalline solids have vacancies.
Increases entropy (degree of disorder) |
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Term
| Equilibrium Concentration |
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Definition
Equilibrium vacancy concentration varies with temperature.
Increasing Temp causes surface island of atoms to grow.
So higher temperature = more vancancies = more atoms moved to "surface island"
(Nv/N = exp(-Qv/kT))
Nv= Number of defects
N= Number of possible defect sites (lattice sites)
Qv= Activation energy
k= Boltzmann's constant |
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Term
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Definition
k
Used in Equilibrium Concentration equation (Nv/N = exp(-Qv/kT)) |
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Term
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Definition
| extra atoms positioned between atomic sites |
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Term
| Substitutional Impurities |
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Definition
Always 10^22-!0^23 impurity atoms/m^3
Alloys = Deliberately added for metals
Sterling silver = 7.5% Cu = stronger, but still corrosion resistant.
Adding impurity atoms results in solid solution/second phase formation
Solute = minority
Solvent = majority |
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Term
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Definition
Liquid Solutions:
Immiscible = won't mix (oil& water)
Miscible = will happily mix
Same with Solid:
Immiscible = Fe+Mg, will form two separate phases
Miscible:
Complete Solid Solution: They can exist on each others lattice sites. Same crystal structures
Partial: Only a certain amount will be miscible. After too much is added, it will no longer sit.
Substitutional Sold Solution: They will sit on the atomic sites
Interstitial Sold Solution: They will sit in the interstitial sites |
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Term
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Definition
When enough B is put into A, there will be a second phase particle, where there will be a different composition. Often different structure.
So the ratio will be different, and for example, have a spot that is BCC in a mainly FCC structure. |
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Term
| Substituional Solid Solution |
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Definition
Conditions:
1) Difference between atomic r < 15%
2) Similar electronegativities
3) Same crystal structure for pure metals
4) Valency: If all else is fine, then a metal of higher valency will dissolve a metal of lower valency |
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Term
Impurities in Solids
(Composition) |
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Definition
Weight %: C1 = m1/(m1+m2)
Atomic %: C1 = nm1/(nm1+nm2)
n= number of atoms |
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Term
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Definition
Line defects
Slips between crystal planes
Permanent (plastic) deformation
Atoms become misaligned
1) Edge Dislocation
2) Screw Dislocation |
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Term
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Definition
Extra half-plane of atoms inserted into a crystal structure
Allows plastic deformation at much lower stress than if they weren't present
b is perpendicular to dislocation line
Edge dislocation line (|), going into the screen
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: : : :
: : : : |
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Definition
b, measure of lattice distortation
When you go around in a nxn square, b is the vector that gets you back to your starting point. |
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Term
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Definition
requires the successive bumping of a half plane of atoms
Bonds across the slipping planes are broken and remade in succession
Shifts it one at a time, meaning much less energy needed, meaning much less stress. |
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Term
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Definition
Spiral planar ramp resulting from shear deformation
b is parallel to the dislocation line |
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Term
| Dislocation Close-Packed Directions # |
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Definition
FCC: Many close-packed planes/directions
HCP: Only one plane, 3 directions
BCC: None |
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Term
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Definition
Also a planar defect
Because surface atoms don't have all the bonds, there are a higher energy state due to surface energy
Driving force to reduce this (easily done in liquids, water -drop-) |
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Term
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Definition
Regions between crystales
less atomic bonding along the grain
Impurity atoms tend to segregate here
1) Tilt Boundaries
2) Phase Boundaries
3) Twin Boundaries |
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Term
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Definition
| When edge dislocations line up |
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Term
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Definition
| between two different phases in an alloy |
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Term
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Definition
| A reflection of atom positions across the twin plane |
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Term
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Definition
ABCABC packing sequence is disturbed
ABCABABC |
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Term
| Catalysts and surface defects |
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Definition
Increases the rate of reactions
Active sites on catalysts are normally surface defects |
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Term
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Definition
Mass transport by atomic motion.
1)Vacancy Diffusion
2)Interstitial Diffusion |
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Term
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Definition
In alloys, from regions of high to low concentration.
Time to reach equilibrium dependent on how easily atoms can move through vacancies and interstitial diffusion |
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Definition
| not easily visible, but still, even without concentration gradient, atoms still move |
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Term
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Definition
Diffuse carbon atoms into host iron atoms at surface
Carbon is much smaller than iron, making interstitial diffusion.
Presence of carbon makes surface harder |
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Term
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Definition
atoms exchanging position with vacancies
also applies to substitutional impurity atoms
rate depends on:
-Number of vacancies
-Temperature
-Activation energy to exchange |
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Term
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Definition
Smaller solute atoms can diffuse between atoms
Moves around in interstitial sites
More rapid than vacancy diffusion |
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Term
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Definition
J=Flux=moles diffusion/(SA*t)
mol/cm^2s or kg/m^2s
Measured empirically (by experiment)
make thin film, impose gradient, measure how fast moving through membrane |
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Term
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Definition
Concentration profile is not a function of time.
AKA rate of diffusion is independent of time.
Rate stays constant over time.
J=-D*(dC/dx)
D=Diffusion coefficient
dC/dx~=C2-C1/x2-x1
Units: mol/m^2s, then C=mol/m^3, then D=m^2/s |
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Term
| Fick's First Law of Diffusion |
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Definition
D=Do*exp(-Qd/RT)
Do=pre-exponential
Qd=activation energy
R=gas constant 8.314J/mol*K
T=temp in K |
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Term
| Non-Steady State Diffusion |
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Definition
Most practical cases
Flux & concentration gradient change with time
Implies net accumulation or depletion of diffusing species
Both function of time and Position
C=C(x,t)
Fick's Second Law |
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Term
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Definition
pd = partial deriv
pd^2= second pd, or pd of pd
pdC/pdt = D*(pd^2C/pdx^2)
Given that surface concentration is constant (Cs), and there is a point far away that stays at initial concentration(Co),
C(x,t)-Co/Cs-Co=
1-erf(x/(2*root(D*t))
erf(z)
If there is specific concentration desired (C1), then left hand side becomes constant, and so must the right:
x/(2*root(Dt)) or x^2/(4)Dt
x~= root(Dt) |
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Term
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Definition
Elastic means reversible.
Bonds are being stretched.
Linear-elastic: Relationship between force and change in length is linear. |
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Term
| Plastic Deformation (Metals) |
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Definition
Permanent.
Generally, elastic to a point, but after a certain point, a slip occurs.
After slip, it will still recover the amount of the elastic deformation |
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Term
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Definition
Up and down.
Tensile stress(o-) = Ft/A = N/m^2 |
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Term
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Definition
t=Fs/A
Stress in the Plane of the area
Area is always ORIGINAL area |
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Term
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Definition
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Term
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Definition
| equal stress in one direction as another direction. So F on L = F on Right |
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Term
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Definition
emf=d/L (change in length over original Length)
Tensile strain= same direction as pulling (up/down)
Lateral strain(emfL)= other direction., d/W
Shear strain(y)=x/y=tan() |
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Term
| Modulus of Elasticity (E) |
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Definition
Hooke's Law:
stress(o-)=E*emf
Units: (GPa or psi) |
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Term
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Definition
Pull on sample in one direction, what is strain in opposite?
v=-(emfL/emf)
if v> than .5, the density will increase. |
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Term
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Definition
How much deformation is possible before it breaks.
%EL = Lf-Lo/Lo |
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Term
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Definition
Ernergy needed to break a unit volume of material
Area under stress-strain curve |
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Term
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Definition
Resistance to permanent indenting
Large hardness:
resistance to plastic deformation or cracking in compression
better wear proppoerties |
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Definition
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