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Materials Midterm2
Ch 4-12 Materials Science and Engineering
56
Engineering
Undergraduate 2
05/17/2013

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Cards

Term
Point Defects (Ceramics)
Definition

Vacancies and Intersticials

Two Ions:

# Cation vacancies = # Anion vacancies (electroneutrality)

More cation than anion interstitials (size)

 

Term
Frenkel Defect
Definition

cation vacancy - cation interstial pair

any time an atom/anion moves from latice site to its interstitial site

Term
Shottky Defect
Definition
Paired anion and cation vacancies
Term
Substitutional Impurities/ Charge Neutrality (Ceramics)
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-

Term
Cation Diffusion
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

 

Term

Ceramics vs Metal

Brittleness

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

Term
Ceramic Brittle Fracture
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

Term
Point Defects
Definition

One point is different from the normal repeating structure

Vacanies = much mroe likely than self interstitials

Vacancy Atoms

Interstitial Atoms

Substitutional Atoms

Term
Line Defect
Definition

Defect in the structure with one dimension

Dislocations

Term
Area Defect
Definition

2 or more dimensions in the defect

Grain Boundaries

Term
Vacancy Defect
Definition
All crystalline solids have vacancies.
Increases entropy (degree of disorder)
Term
Equilibrium Concentration
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
Term
Boltzmann's constant
Definition
k
Used in Equilibrium Concentration equation (Nv/N = exp(-Qv/kT))
Term
Self-Interstitial
Definition
extra atoms positioned between atomic sites
Term
Substitutional Impurities
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
Term
Solid Solutions
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
Term
New Phase
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.
Term
Substituional Solid Solution
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
Term
Impurities in Solids
(Composition)
Definition
Weight %: C1 = m1/(m1+m2)
Atomic %: C1 = nm1/(nm1+nm2)
n= number of atoms
Term
Dislocation
Definition
Line defects
Slips between crystal planes
Permanent (plastic) deformation
Atoms become misaligned
1) Edge Dislocation
2) Screw Dislocation
Term
Edge Dislocation
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
|
: : : : :
: : : :
: : : :
Term
Burger's vector
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.
Term
Dislocation motion
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.
Term
Screw Dislocation
Definition
Spiral planar ramp resulting from shear deformation
b is parallel to the dislocation line
Term
Dislocation Close-Packed Directions #
Definition
FCC: Many close-packed planes/directions
HCP: Only one plane, 3 directions
BCC: None
Term
Surfaces (Defect)
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-)
Term
Grain Boundaries
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
Term
Tilt Boundaries
Definition
When edge dislocations line up
Term
Phase boundaries
Definition
between two different phases in an alloy
Term
Twin Boundary
Definition
A reflection of atom positions across the twin plane
Term
Stacking Fault
Definition
ABCABC packing sequence is disturbed
ABCABABC
Term
Catalysts and surface defects
Definition
Increases the rate of reactions
Active sites on catalysts are normally surface defects
Term
Diffusion
Definition
Mass transport by atomic motion.
1)Vacancy Diffusion
2)Interstitial Diffusion
Term
Interdiffusion
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
Term
Self-Diffusion
Definition
not easily visible, but still, even without concentration gradient, atoms still move
Term
Case Hardening
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
Term
Vacancy Diffusion
Definition
atoms exchanging position with vacancies
also applies to substitutional impurity atoms
rate depends on:
-Number of vacancies
-Temperature
-Activation energy to exchange
Term
Interstitial Diffusion
Definition
Smaller solute atoms can diffuse between atoms
Moves around in interstitial sites
More rapid than vacancy diffusion
Term
Rate of Diffusion
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
Term
Steady-State Diffusion
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
Term
Fick's First Law of Diffusion
Definition
D=Do*exp(-Qd/RT)
Do=pre-exponential
Qd=activation energy
R=gas constant 8.314J/mol*K
T=temp in K
Term
Non-Steady State Diffusion
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
Term
Fick's Second Law
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)
Term
Elastic Deformation
Definition
Elastic means reversible.
Bonds are being stretched.
Linear-elastic: Relationship between force and change in length is linear.
Term
Plastic Deformation (Metals)
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
Term
Tensile stress
Definition
Up and down.
Tensile stress(o-) = Ft/A = N/m^2
Term
Shear stress
Definition
t=Fs/A
Stress in the Plane of the area
Area is always ORIGINAL area
Term
simple compression
Definition
F/A (a negative force)
Term
Bi-axial Tension
Definition
equal stress in one direction as another direction. So F on L = F on Right
Term
Strain
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()
Term
Modulus of Elasticity (E)
Definition
Hooke's Law:
stress(o-)=E*emf
Units: (GPa or psi)
Term
Poisson's ratio (v)
Definition
Pull on sample in one direction, what is strain in opposite?
v=-(emfL/emf)
if v> than .5, the density will increase.
Term
Ductility
Definition
How much deformation is possible before it breaks.
%EL = Lf-Lo/Lo
Term
Toughness
Definition
Ernergy needed to break a unit volume of material
Area under stress-strain curve
Term
Hardness
Definition
Resistance to permanent indenting
Large hardness:
resistance to plastic deformation or cracking in compression
better wear proppoerties
Term
Hardness Tests
Definition
Rockwell
Brinell Hardness
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