fe review materials properties
TRANSCRIPT
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FE ReviewMaterials Properties
Jeffrey W. FergusMaterials EngineeringOffice: 284 Wilmore
Phone: 844-3405email: [email protected]
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Electrical Properties
• Electrical resistance– resistance (R) = resistivity (ρ) length (l) / area (A)– resistivity is a material property– conductivity (σ) = 1 / resistivity (ρ)
l
A– conductivity (σ) = 1 / resistivity (ρ)
• Temperature dependence – with increasing temperature…– metals: resistance increases (conductivity decreases)– semiconductors: conductivity increases (resistivity decreases)
• extrinsic: like metals in intermediate temperatures
– insulators: conductivity increases (resistivity decreases)
A
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Mechanical Properties
• Stress-strain relationships– engineering stress and strain– stress-strain curve
• Testing methods• Testing methods– tensile test– endurance test– impact test
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Stress
AF=σ=Normal
AF=τ=Shear
F F FA A A
Tension: σ>0 Compression: σ<0
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Strain
oo
ol
ll
ll ∆=−=ε=Strain θ==γ= tanha
strain Shear
a
lol lo l hθ
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Tensile Test
thickness
Control length (l)
Measure force (F) with load cell
oo
ol
ll
ll ∆=−=ε=Strain
lengthwidth
Measure force (F) with load cell
twF
AF
⋅==σ=Stress
Reduced section used to limit portion of sample undergoing deformation
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Stress-Strain Curve
Ultimate Tensile Strength
Yield Point
Elastic Limit
Force decreases due to neckingS
tres
s
Strain
Slope = E (Young’s Modulus)
Percent Elongation(total plastic deformation)
Elastic Limit
Proportionality Limit
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0.2% Offset Yield Strength
0.2% offsetyield strength
Str
ess
Strain0.2% strain
yield strength
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True/Engineering Stress/Strain
oE A
F=σoo
oE l
ll
ll ∆=−=εEngineering
(initial dimensions)
Stress Strain
iT A
F=σ ∫
==ε
i
o
l
l o
iT l
lln
ldl
( )1+ε=ε ET ln
( )EET ε+σ=σ 1ooii lAlA ⋅=⋅
True(instantaneous
dimensions)
Usingand
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True/Engineering Stress/Strain
True
True stress does not decrease
Str
ess
Strain
Engineering
Decrease in engineering stress due to decreased load required in the reduces cross-sectional area of the neck.
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Strain Hardening
Str
ess
Plastic deformation require larger load after deformation.
Str
ess
Strain
Onset of plastic deformation after
reloading
after deformation.Sample dimensions are decreased, so stress is even higher
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Bending Test
Four-point Three-point
h
wFF/2F/2
LL/2
By summing moment in cantilever beam
22
3
wh
FLmax =σ
Tension at bottom, compression at top
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Hardness
• Resistance to plastic deformation• Related to yield strength• Most common indentation test
– make indentation– make indentation– measure size or depth of indentation– macro- and micro- tests
• Scales: Rockwell, Brinell, Vickers, Knoop
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Impact
Toughness: combination of strength and ductility -energy for fracture
hi
hf
Fracture energy = mghi -mghf
Charpy V-notch
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Ductile-Brittle Failure
• Ductile– plastic deformation– cup-cone / fibrous
fracture surface
Ductile-Brittle Transition Temperature
(DBTT)• Brittle
– little or no plastic deformation
– cleaved fracture surface
Temperature
Fra
ctur
e E
nerg
y
(DBTT)
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Creep / Stress Relaxation
• Load below yield strength - elastic deformation only• Over long time plastic deformation occurs• Requires diffusion, so usually a high-temperature
processprocess• Activation energy, Q (or EA)
−⋅=
−⋅=ε=kTE
expART
QexpA A
ɺratecreep
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Creep /Stress Relaxation
CreepFF Stress Relaxation
FF
time
fixed strain
fixed load
time
Permanent deformation
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Fatigue
Fatigue Limit(ferrous metals)
Repeated application of load - number of cycles, rather than time important.
σmax
0
Number of Cycles to Failure
Str
ess (ferrous metals)
σmin
σave ∆σ
σmax
σmin
0
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Corrosion Resistance
• Thermodynamics vs. Kinetics– thermodynamics - stable phases– kinetic - rate to form stable phases
• Active vs. Passive– active: reaction products ions or gas - non protective– passive: reaction products - protective layer
• Corrosion resistance– inert (noble): gold, platinum– passivation: aluminum oxide (alumina) on aluminum,
chromia on stainless steel
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Electrode Potential
• Tendency of metal to give up electron• Oxidation (anode)
– M = M2+ + 2e- (loss electrons)
• Reduction (cathode)• Reduction (cathode)– M2+ + 2e- = M (gain electrons)
• LEO (loss electrons oxidation) goes GER (gain electrons reduction)
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Corrosion Reactions• Oxidation - metal (anode)
– M = M2+ + 2e-
• Reduction - in solution (cathode)– 2H+ + 2e- = H2
– 2H+ + ½O2 + 2e- = H2O– H O + ½O + 2e- = 2OH-– H2O + ½O2 + 2e- = 2OH-
• Overall Reactions– M + 2H+ =M2+ + H2
– M + 2H+ + ½O2 = M2+ + H2O– M + H2O + ½O2 = M2+ + 2OH- = M(OH)2
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Electromotive Force
• Gibbs Free Energy (∆G) =-nFE (Electromotive Force)– n = number of electrons, F = Faraday’s Constant– favorable: energy decrease (-) = positive voltage
• Fe2+ + 2e- = Fe: Ered = +0.440 V• Fe2+ + 2e- = Fe: Ered = +0.440 V• Fe = Fe2+ + 2e-: Eox = -0.440 V• H2O = 2H+ + ½O2 +2e-: Ered = +1.229 V• Fe + 2H+ + ½O2 = Fe2+ + H2O: E = 0.789 V
– E does not change with number of moles (∆G does)– E must be corrected for non-standard state
• concentration of H+ (i.e. pH), oxygen pressure…
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Galvanic Corrosion / Protection
• At joint between dissimilar metals– reaction rate of active metal increases– reaction of less active metal decreases
• Galvanic corrosion– high corrosion rate at galvanic couple
• presence of Cu increase the local corrosion rate of Fe
• Galvanic protection– galvanized steel
• presence of Zn decreases the local corrosion rate of Fe
– galvanic protection• Mg or Zn connected to Fe decrease corrosion rate
Zn
Fe
Fe Cu
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Waterline Corrosion
• Oxygen concentration in water leads to variation in local corrosion rates
Higher corrosion rate near oxygen accessoxygen access
Rings of rust left from water drops
Rust just below water surface
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Materials Processing
• Diffusion• Phase Diagrams
– Gibb’s phase rule– lever rule– lever rule– eutectic system / microconstituents– Fe-Fe3C diagram (ferrous metals)
• Thermal-mechanical processing
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Diffusion
• Atoms moving within solid state• Required defects (e.g. vacancies)• Diffusion thermally activated• Diffusion constant follows Arrhenius relationship
−=
−=kTE
expDRT
QexpDD A
oo
Gas constant
Boltzman’s constant Temperature
Activation Energy
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Steady-State Diffusion
• Fick’s first law (1-D)• J = flux (amount/area/time)• For steady state
∂∂−=
xC
DJ
∆∆−=
xC
DJ ∆x
∆C
∆x
sm
massm
m
mass
sm
J2
32=
−=
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Phase Equilibria
• Gibb’s Phase Rule• P + F = C + 2 (Police Force = Cops + 2)
– P = number of phases– F = degrees of freedom– C = number of components (undivided units)– 2: Temperature and Pressure– 2: Temperature and Pressure
• One-component system– F = 1 + 2 - P = 3 - P
• Two-component system– F = 2 + 2 - P = 4 - P
• Two-component system at constant pressure– F = 2 + 1 - P = 3 - P
“2” becomes “1” at constant pressure
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Pressure-Temperature Diagram
Single-phase area: can change T
Two-phase line: Change T (P) require specific change in P (T)
(F=1)
One component: H2OIf formation of H2 and O2 were considered there would be two
components (H and O)
water
ice
watervapor
Temperature
Pre
ssur
e
Single-phase area: can change T and P independently
(F=2)
Three-phase point: One occurs at specific T and P (triple point)
(F=0)
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Phase Diagrams
L
δ
δ + γ δ + L
Two-component @ constant pressureThree-phase - horizontal line
Eutectic
PeritecticL +solid (δ) → solid (γ)
α
γ
β (pure B, negligible
solubility of A)
α + γ
γ + β
α + β
γ + L β + L
Composition (%B)
Tem
pera
ture Eutectic
L → 2 solids (γ + β)
Eutectoidsolid (γ) → 2 solids (α + β)
BA
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Lever Law• Phase diagram give compositions of phases
– two-phase boundaries in 2-phase mixture
• Mass balance generate lever law
LiquidComp.
(XL)
SolidComp.
(XS)
AlloyComp.(Xalloy)
Opposite arm over total length
Right arm for solid
L
S
Composition (%B)A B
Tem
pera
ture
(XL)(XS) (Xalloy)
SL
alloyL
XX
XXsolid%
−−
=
SL
Salloy
XX
XXliquid%
−−
=
Right arm for solid
Left arm for liquid
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70 wt% Pb - 30 wt% Sn
256°C
First solid
( ) %27)(%3.18.)(%8.61)(%3.18)(%30
%8.61.% =−−=
PbSnliqSnPbSnalloySn
Snliq
At 183.1°C
(Pb)L
12.8 wt% Sn
( ) %73)(%3.18.)(%8.61)(%30.)(%8.61
%3.18.% =−−=
PbSneutSnalloySneutSn
SnPbprim
(Pb)L
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70 wt% Pb - 30 wt% Sn
256°C
First solid
( ) %15)(%3.18.)(%8.97)(%3.18)(%30
%8.97% =−−=
PbSnliqSnPbSnalloySn
Snβ
At 182.9°C
(Pb)
12.8 wt% Sn
( ) %85)(%3.18.)(%8.97)(%30.)(%8.97
%3.18% =−−=−
PbSnliqSnalloySnliqSn
SnphasePb
(Pb)
Eutectic(Pb)+β
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Microconstituents
( ) )(%3.18)(%30 =−= PbSnalloySn
( ) %73)(%3.18.)(%8.61)(%30.)(%8.61
%3.18.Prim% =−−=
PbSneutSnalloySneutSn
SnPb
Eutectic Microsconstituent ((Pb)+βSn)
Primary Pb
( ) %27)(%3.18.)(%8.61)(%3.18)(%30
%8.61% =−−=
PbSnliqSnPbSnalloySn
SnL
( ) %55)(%3.18.)(%8.97)(%3.18.)(%8.61
%8.97% . =−−=
PbSnliqSnPbSneutSn
Sneutinβ
( ) %45)(%3.18.)(%8.97.)(%8.61.)(%8.97
%3.18% . =−
−=PbSnliqSneutSnliqSn
SnPb eutin
Phases in Eutectic Microsconstituent
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Phases in Microconstituents
(Pb) 73 g primary (Pb)
27 g eutecticβ
12 g (Pb) (45% of 27 g)
(Pb) + βSn15 g βSn (55% of 27 g)
Total amounts in 100 g sampleTotal (Pb) = 73 + 22 = 85 g Total βSn = 15 g(same as directly from the lever law)
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Fe-Fe3C Phase Diagram
Austenite Cementite
Ferrite
Pearlite (ferrite + cementite)%C = 0.77%
HypereutectoidHypoeutectoid
Cast Irons
Steels
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Time-Temperature-Transformation (TTT) Diagram
fs727°C
800°C
Decomposition of Austenite at fixed temperature Pearlite: High Temp
slow nucleation
Coarse pearliteps
bs
ms
mf
pf
bf
200°C
100°C
KeyMain symbolf = ferritep = pearliteb = bainitec = cementite
(Fe3C)Subscriptss = startf = finish
Tem
per
atu
re
Log TimeMartensite
athermal (diffusionless)
Bainite: Diffusion slow
for pearlite
Coarse pearlite
Fine pearlite
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Quench / Hardenability / Tempering
• Quench - rapidly cool– in steel: cool fast enough to Ms to prevent pearlite / bainite
formation
• Hardenability• Hardenability– ease of forming martensite in steels– alloying elements inhibit pearlite / bainite formation, promote
martensite formation
• Tempering of steels– reheating martensite to form transition carbides– improve toughness
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Cold Working• Plastic deformation creates dislocations, which
increases strength / decreases ductility• Reduction in Area used to quantify degree of cold
working%
AAfA
RA%CW%i
i 100⋅−==
lwlw ⋅−⋅%
lwlwlw
RA%ii
ffii 100⋅⋅
⋅−⋅=
%l
llRA%
i
fi 100⋅−=
if wwfor ≅
%d
dd%
d
dd
RA%
i
fi
i
fi
100100
4
442
22
2
22
⋅−
=⋅⋅π
⋅π−
⋅π
=
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Cold Worked Properties
400
500
600
Str
ess
(MP
a) 10
12
14
16
Percen
t Elo
ng
ation
Yield StrengthTensile Strength
0
100
200
300
0 10 20 30 40 50 60 70 80
Percent Cold Work
Str
ess
(MP
a)
0
2
4
6
8
Percen
t Elo
ng
ation
Tensile StrengthPercent Elongation
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Balancing Strength / Ductility
300
400
500
600
Str
ess
(MP
a)
20
25
30
35
Percen
t Elo
ng
ation
Yield Strength
Tensile Strength
Percent Elongation
0
100
200
0 10 20 30 40 50 60 70 80
Percent Cold Work
Str
ess
(MP
a)
0
5
10
15
Percen
t Elo
ng
ation
Sy > 310 MParequires
%CW > 22%Elongation > 10%
requires%CW < 31%
Both Propertiesrequires
22% < %CW < 31%
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Balancing Strength / Toughness
400
450
500
550
600
Str
ess
(MP
a)30
35
40
45
50Yield Strength
Tensile Strength
Fracture Toughness Fractu
re To
ug
hn
ess (K
σy = 250 MPa13% CW
Sy > 250 MPaand
KIc > 16 MPa m½
requires13% < %CW < 39%
100
150
200
250
300
350
0 10 20 30 40 50 60 70Percent Cold Work
Str
ess
(MP
a)
0
5
10
15
20
25
Fractu
re To
ug
hn
ess (KIc ) (M
Pa m
0.5)
KIc = 16 MPa m0.5
39% CW
31% CWSy = 364 MPa
KIc = 22 MPa m0.5
13% < %CW < 39%
Examplefor 31% CW
Sy = 364 MPaKIc = 22 MPa m½
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Cold Work / Anneal / Hot Work• Annealing can eliminate effect of cold work
– recovery - stress relief, little change in properties– recrystallization - elimination of dislocations, decrease in
strength, increase in ductility– grain growth - increase in grain size, decreases both
strength and ductility
• Hot working• Hot working– deforming at high enough temperature for immediate
recrystallization– list cold-working and annealing at the same time– no increase in strength– used for large deformation– poor surface finish - oxidation– after hot working, cold working used to increase strength and
improve surface finish
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Organization from 1996-7 Review Manual(same topics in 2004 review manual)
• Crystallography• Materials Testing• Metallurgy
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Crystallography
• Crystal structure– atoms/unit cell– packing factor– coordination number– coordination number
• Atomic bonding• Radioactive decay
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Bravais Lattice
Crystal System Centering
P: Primitive: (x,y,z)
(x,y,z): Fractional coordinates -proportion of axis length, not absolute distanct
a
b
c
β α
γ
P: Primitive: (x,y,z)
I: Body-centered: (x,y,z); (x+½,y+½,z+½)
C: Base-centered: (x,y,z); (x+½,y+½,z)
F: Face-centered: (x,y,z); (x+½,y+½,z)(x+½,y,z+½); (x,y+½,z+½)
Centering must apply to all atoms in unit cell.
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Bravais Lattices (14)
Crystal System Parameters Primitive
(Simple) Body-
Centered Face-
Centered Base-
Centered
Cubic a=b=c
α=β=γ=90° X X X
Tetragonal a=b≠c
α=β=γ=90° X X
α=β=γ=90°
Orthorhombic a≠b≠c
α=β=γ=90° X X X X
Rhombohedral a=b=c
α=β=γ≠90° X
Hexagonal a=b≠c
α=β=90°, γ=120° X
Monoclinic a≠b≠c
α=γ=90°, β≠120° X X
Triclinic a≠b≠c
α≠β≠γ≠90° X
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Atoms Per Unit Cell
• Corners - shared by eight unit cells (x 1/8)– (0,0,0)=(1,0,0)=(0,1,0)=(0,0,1)=(1,1,0)
=(1,0,1)=(0,1,1)=(1,1,1)
• Edges - shared by four unit cells • Edges - shared by four unit cells (x 1/4)– (0,0,½)= (1,0,½)= (0,1,½)= (1,1,½)
• Faces - shared by two unit cells (x 1/2)– (½,½,0)= (½,½,1)
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Common Metal Structures
• Face-Centered Cubic (FCC)– 8 corners x 1/8 + 6 faces x 1/2 – 1 + 3 = 4 atoms/u.c.
• Body-Centered Cubic (BCC)– 8 corners x 1/8 + 1 center – 8 corners x 1/8 + 1 center – 1 + 1 = 2 atoms/u.c.
• Hexagonal Close-Packed (HCP)– 8 corners x 1/8 + 1 middle – 1 + 1 = 2 atoms/u.c.– 12 hex. Corner x 1/6 +2 face x 1/2 + 3
middle = 6 atoms/u.c.
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Packing Factor
• Fraction of space occupied by atoms• For FCC
cba
rFP i
⋅⋅= ∑
334 π
..
ar
raraa2
44diagonalface 22 =⇒⋅=+=
( ) ( )3434
• For BCCa
r ( ) ( )740
23
24
443
334
3
334
.r
a
r.F.P =π=
π⋅=
π⋅=
r3
4ar4aaadiagonalbody 222 =⇒⋅=++=
( ) ( )680
83
34
223
334
3
334
.r
a
r.F.P =π=
π⋅=
π⋅=
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Density
volumemass
.c.uvolume
moleatom
molemass
.c.uatom
Density =
⋅
⋅
=
For nickel:- Atomic weight = 58.71 g/mole
( ) 338249158
1052393106020
71584
cm
g.
cmx.moleatom
x.
moleg
..c.u
atom
Density =⋅
⋅
=−
- Atomic weight = 58.71 g/mole- Lattice parameter = 3.5239 Å=3.5239 x 10-8 cm- Avogadro’s No. = 6.02 x 1023 = 0.602 x 1024 = atoms/mole
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Close Packed (CN=12)
Highest packing density for same sized spheresFCC and HCP structures
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Cube Center (CN=8)
Same atoms: BCCDifferent atoms: CsCl
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Octahedral Site (CN=6)
In FCC:- Center (½,½,½)- Edges (0,0,½),(0,½,0),(½,0,0)- 4 per unit cell- All filled - NaCl structure
8-sided shape
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Tetrahedral Site (CN=4)In FCC:- Divide cell into 8 boxes - center of small box- (¼,¼,¼),(¾,¼,¼),(¼,¾,¼),(¾,¾,¼)(¼,¼, ¾)(¾,¼, ¾),(¼,¾, ¾)(¾,¾, ¾)-8 per unit cell-All filled - CaF2 structure; half-filled - ZnS-All filled - CaF2 structure; half-filled - ZnS
4-sided shape
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Radius Ratio Rules
Critical Radius for CN 8 = 0.732CN 8
Critical radius is size of atom which just fits in siteDefine minimum for bonding (i.e. atoms must touch to bond)
Critical Radius for CN 8 = 0.732
Critical Radius for CN 6 = 0.414
Critical Radius for CN 4 = 0.225
CN 6
CN 4
CN 3planar
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Close Packed Plane
A BA BA C
HCP: ABABABABABABABABFCC: ABCABCABCABCABCSame packing density (0.74)Same coordination (CN=12)
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Miller Indices
Planes
Directions
(hkl)
{hkl}
[hkl]
<hkl>
specific
family
specific
family
- No commas- No fractions- Negative indicated by bar over number<hkl> family
A family of planes includes all planes which are equivalent by symmetry - depends on crystal system.- For cubic: (110),(011) and (101) are all {110}- For tetragonal: (011) and (101) are {101}
but (110) is not (c≠a)
over number
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Miller Indices - Directions
ba
c
-1/3
1/2-1
x1/2
y-1
z-1/3 (x 6)
[ ]263
1
1/4
1/2
x1
y1/4
z1/2 (x 4)
[ ]214
[ ]263
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Miller Indices - Planes
41
21
ba
c
41
21
ba
c
x1/44
y∝0
z-1/2-2
( )204
interceptreciprocal
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Miller Indices - Planes
31
21
ba
c
41
31
21
ba
c
41
x1/44
y-1/3-3
z-1/2-2
( )234
interceptreciprocal
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Atomic Bonding
• Covalent– sharing electrons– strong– directional
• Metallic– metal ions in sea or
electrons– moderately strong– directional
• Ionic– trading of electrons– electrostatic attraction or
ions– strong– non-directional
– non-directional
• Secondary– Van der Waals– H-bonding– electrostatic attraction of
electric dipole (local charge distribution
– weak
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Radioactive Decay
• Loss of electrons/protons/neutrons– alpha - 2 protons / two neutrons (i.e He nucleus)– beta - electrons– gamma - energy
• Exponential decay
−= t
expNNtime
• Exponential decay
τ
−= texpNN o
( ) ( )22 2
121
21
21
ln
tln
N
Nln
texpNNN
o
ooo −=τ⇒=
−=
τ⇒==
( )
⋅−=
⋅−=21
21
69302t
t.expN
tlnt
expNN oo half life
amount
original amount
time constant