imperfections in solid materials_ch4
TRANSCRIPT
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Imperfections in Solid
Materials
R. Lindeke
ENGR 2110
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In our pervious Lecture when
discussing Crystals we
ASSUMED PERFECT ORDER
I n real mater ials we find:
Crystall ine Defects or lattice irregulari ty
Most real materials have one or more errors in perfection
with dimensions on the order of an atomic diameter to many
lattice sites
Defects can be classification:1. according to geometry
(point, line or plane)
2. dimensions of the defect
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ISSUES TO ADDRESS...
What types of defects arise in solids?
Can the number and type of defects be varied
and controlled?
How do defects affect material properties?
Are defects always undesirable?
What are the solidification mechanisms?
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Solidification- result of casting of molten material 2 steps
Nuclei form
Nuclei grow to form crystalsgrain structure
Start with a molten materialall liquid
Imperfections in Solids
Adapted from Fig.4.14 (b), Callister 7e.
Crystals grow until they meet each other
nuclei crystals growing grain structureliquid
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Polycrystalline Materials
Grain Boundaries
regions between crystals
transition from lattice of
one region to that of theother
slightly disordered
low density in grain
boundaries high mobility
high diffusivity
high chemical reactivityAdapted from Fig. 4.7, Callister 7e.
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Solidification
Columnar in
area with lessundercooling
Shell of
equiaxed grains
due to rapidcooling (greater
T) near wall
Grain Refiner - added to make smaller, more uniform, equiaxed grains.
heat
flow
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
Adapted from Fig. 4.12, Callister 7e.
~ 8 cm
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Vacancies:-vacant atomic sites in a structure.
Self-Interstitials:-"extra" atoms positioned between atomic sites.
Point Defects
Vacancy
distortion
of planes
self-interstitial
distortionof planes
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SELF-INTERSTITIAL: very rare occurrence
This defect occurs when an atom from the crystal occupies
the small void space (interstitial site) that under
ordinary circumstances is not occupied.
In metals, a self-interstitial introduces relatively (very!)
large distortions in the surrounding lattice.
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POINT DEFECTS
The simplest of the point defect is a vacancy, or vacant lattice site.
All crystalline solids contain vacancies.
Principles of thermodynamics is used explain the necessity of the
existence of vacancies in crystalline solids.
The presence of vacancies increases the entropy (randomness) ofthe crystal.
The equilibrium number of vacancies for a given quantity of
material depends on and increases with temperature as
follows:
Nv= Nexp(-Qv/kT)
Equi li brium no. of vacancies
Total no. of atomic sites Energy required to form vacancy
T = absolute temperature in Kelvin
k = gas or Boltzmanns constant
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We can get Qv from
an experiment. Nv
N= exp -
Qv
kT
Measuring Activation Energy
Measure this...
Nv
N
T
exponential
dependence!
defect concentration
Replot it...
1/T
N
Nvln
-Qv/k
slope
note:
A El
El
NN
A
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Example Problem 4.1
Calculate the equilibrium number of vacancies per cubic meter for copper at
1000C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight anddensity (at 1000 C) for copper are 63.5 g/mol and 8.4 g/cm3, respectively.
Solution.
Use equation 4.1. Find the value of N, number of atomic sites per cubic meter for
copper, from its atomic weight Acu, its density, and Avogadros number NA.
toequalie)1273(1000atvacanciesofnumbertheThus,
/8.0x10/5.63
)/10)(/4.8)(/10023.6(
328
336323
KC
matomsmolg
mcmcmgmolatomsx
A
NN
Cu
A
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325
5
328
/mvacancies2.2x10
)1273)(/1062.8(
9.0(
exp)/(8.0x10
exp
-
- KKeVx
eV
matoms
kT
QNN vv
Continuing:
And Note: for MOST MATERIALS just below
Tm Nv/N= 10-4
Here: 0.0022/8 = .000275 = 2.75*10-4
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Two outcomes if impurity (B) added to host (A):
Solid solutionof BinA(i.e., random dist. of point defects)
Solid solution of BinAplus particles of a new
phase(usually for a larger amount of B)
OR
Substitutionalsolid soln.
(e.g., Cuin Ni)
Interstitialsolid soln.
(e.g., Cin Fe)
Second phase particle
--different composition
--often different structure.
Point Defects in Alloys
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Imperfections in Solids
Conditions for substitutional solid solution (S.S.) HumeRothery rules
1. r (atomic radius) < 15%
2. Proximity in periodic table
i.e., similar electronegativities
3. Same crystal structure for pure metals
4. Valency equality
All else being equal, a metal will have a greater tendency
to dissolve a metal of higher valency than one of lower
valency (it provides more electrons to the cloud)
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Imperfections in Solids
Application of HumeRothery rulesSolidSolutions
1. Would you predict
more Al or Agto dissolve in Zn?
2. More Zn or Alin Cu?
Table on p. 106, Callister 7e.
Element Atomic Crystal Electro- Valence
Radius Structure nega-
(nm) tivity
Cu 0.1278 FCC 1.9 +2
C 0.071H 0.046
O 0.060
Ag 0.1445 FCC 1.9 +1
Al 0.1431 FCC 1.5 +3
Co 0.1253 HCP 1.8 +2
Cr 0.1249 BCC 1.6 +3
Fe 0.1241 BCC 1.8 +2
Ni 0.1246 FCC 1.8 +2
Pd 0.1376 FCC 2.2 +2
Zn 0.1332 HCP 1.6 +2
More Al because size is closer and val. Is
higherbut not too muchFCC in HCP
Surely Zn since size is closer thus
causing lower distortion (4% vs 12%)
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Imperfections in Solids
Specification of composition
weight percent100x
21
1
1mm
mC
m1= mass of component 1
100x
21
1'
1
mm
m
nn
nC
nm1= number of moles of component 1
atom percent
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Wt. % and At. % -- An example
'
'
Typically we work with a basis of 100g or 1000ggiven: by weight -- 60% Cu, 40% Ni alloy
6009.44
63.55 /400
6.8258.69 /
9.44 .581 or 58.1%9.44 6.82
6.82.419 or 41.9%
9.44 6.82
Cu
Ni
Cu
Ni
gn m
g mg
n mg m
C
C
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Converting Between: (Wt% and At%)
' 1 21
1 2 2 1
' 2 12
1 2 2 1
'
1 11 ' '
1 1 2 2
'
2 22 ' '
1 1 2 2
100
100
100
100
C AC
C A C A
C A
C C A C A
C AC
C A C A
C AC
C A C A
Converts from
wt% to At% (Aiis
atomic weight)
Converts fromat% to wt% (Ai is
atomic weight)
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Determining Mass of a Species per Volume
" 311
1 2
1 2
" 322
1 2
1 2
10
10
CC
C C
CC C C
iis density of pureelement in g/cc
Computed this way,
gives concentrationof speciesiin kg/m
3of
the bulk mixture
(alloy)
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And: slip between crystal planes result when dislocations move,
this motion produces permanent (plastic) deformation.
Are called Dislocations:
Schematic of Zinc (HCP):
before deformation after tensile elongation
slip steps which are
the physical
evidence of largenumbers of
dislocations
slipping along the
close packed plane
{0001}
Line Defects
Adapted from Fig. 7.8, Callister 7e.
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Linear Defects (Dislocations)
Are one-dimensional defects around which atoms aremisaligned
Edge dislocation: extra half-plane of atoms inserted in a crystal structure
b (the bergers vector) is (perpendicular) to dislocation
line
Screw dislocation: spiral planar ramp resulting from shear deformation
bis (parallel) to dislocation line
Burgers vector, b:is a measure of lattice distortion and is
measured as a distance along the close packed directions in
the lattice
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Edge Dislocation
Fig. 4.3, Callister 7e.
Edge Dislocation
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Dislocation motion requires the successive bumping
of a half plane of atoms (from left to right here).
Bonds across the slipping planes are broken and
remadein succession.
Atomic view of edge
dislocation motion from
left to right as a crystalis sheared.
(Courtesy P.M. Anderson)
Motion of Edge Dislocation
http://www.wiley.com/
college/callister/CL_E
WSTU01031_S/vmse
/dislocations.htm
http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htmhttp://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htm -
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Screw Dislocations
Adapted from Fig. 4.4, Callister 7e.
Burgers vector b
Dislocation
line
b
(a)
(b)
http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocations.htm -
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Edge, Screw, and Mixed Dislocations
Adapted from Fig. 4.5, Callister 7e.
Edge
Screw
Mixed
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Imperfections in Solids
Dislocations are visible in (T) electron micrographs
Adapted from Fig. 4.6, Callister 7e.
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Dislocations & Crystal Structures
Structure: close-packed
planes & directionsare preferred.
view onto two
close-packed
planes.
close-packed plane (bottom) close-packed plane (top)
close-packed directions
Comparison among crystal structures:FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none super-close many near close
Specimens thatwere tensile
tested.
Mg (HCP)
Al (FCC)
tensile direction
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Planar Defects in Solids
One case is a twin boundary (plane) Essentially a reflection of atom positions across the
twinning plane.
Stacking faults For FCC metals an error in ABCABC packing sequence
Ex: ABCABABC
Adapted from Fig. 4.9, Callister 7e.
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MICROSCOPIC EXAMINATION
Applications
To Examine the structural elements and defects that influence the
properties of materials.
Ensure that the associations between the properties and structure (and
defects) are properly understood.
Predict the properties of materials once these relationships have been
established.
Structural elements exist in macroscopic
and microscopic dimensions
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MACROSCOPIC EXAMINATION: The shape and average size or
diameter of the grains for a polycrystalline specimen are large
enough to observe with the unaided eye.
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Useful up to 2000X magnification (?).
Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal
orientation since different Xtal planes have different
reactivity.
Micrograph of
brass (a Cu-Zn alloy)
0.75mm
Optical Microscopy
Adapted from Fig. 4.13(b) and (c), Callister
7e. (Fig. 4.13(c) is courtesy
of J.E. Burke, General Electric Co.
crystallographic planes
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Grain boundaries...
are planer imperfections, are more susceptible
to etching,
may be revealed as
dark lines,
relate change in crystalorientation across
boundary.Adapted from Fig. 4.14(a)
and (b), Callister 7e.
(Fig. 4.14(b) is courtesy
of L.C. Smith and C. Brady,
the National Bureau ofStandards, Washington, DC
[now the National Institute of
Standards and Technology,
Gaithersburg, MD].)
Optical Microscopy
ASTM grain
size numberN= 2n-1
number of grains/in2at 100x
magnification
Fe-Cr alloy(b)
grain boundarysurface groove
polished surface
(a)
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GRAIN SIZE DETERMINATION
The grain size is often determined when the properties of
a polycrystalline material are under consideration. Thegrain size has a significant impact of strength and
response to further processing
Linear Intercept method
Straight lines are drawn through severalphotomicrographs that show the grain
structure.
The grains intersected by each line segment are
counted
The line length is then divided by an average
number of grains intersected.
The average grain diameter is found by dividing this
result by the linear magnification of the
photomicrographs.
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ASTM (American Society for testing and Materials)
VISUAL CHARTS(@100x) each with a number
Quick and easyused for steel
ASTM has prepared several standard comparison charts, all having differentaverage grain sizes. To each is assigned a number from 1 to 10, which is termed
the grain size number; the larger this number, the smaller the grains.
N = 2 n-1No. of grains/square inch
Grain size no.
NOTE: The ASTM grain size is related (or relates)
a grain areaAT 100x MAGNIFICATION
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Determining Grain Size, using a micrograph
taken at 300x
We count 14 grains
in a 1 in2area on
the image
The report ASTMgrain size we need
N at 100x not 300x
We need a
conversion method!
2
12100
M is mag. of image
N is measured grain count at M
now solve for n:
log( ) 2 log log 100 1 log 2
log 2log 41
log 2log 14 2log 300 4
1 7.98 80.301
n
M
M
M
m
MN
N M n
N Mn
n
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For this same material, how many Grains
would I expect /in2at 100x?
1 8 1 2
2 2
8 1
2 2
2 2 128 grains/in
Now, how many grain would I expect at 50x?100 100
N 2 128*50
N 128*2 512 grains/in
n
M
M
N
M
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0
100
200
300
400
500
600
0 2 4 6 8 10 12
Grain Size number (n)
Numbero
fGrains/in2
At 100x
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Electron Microscopes
beam of electrons ofshorter wave-length
(0.003nm) (when
accelerated across large
voltage drop)
Image formed with
Magnetic lenses
High resolutions andmagnification (up to
50,000x SEM); (TEM up
to 1,000,000x)
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Uses a moveable Probe of very small diameterto move over a surface
Atomscan be arranged and imaged!
Carbon monoxidemolecules arranged
on a platinum (111)
surface.
Photos produced from
the work of C.P. Lutz,
Zeppenfeld, and D.M.Eigler. Reprinted with
permission from
International Business
Machines Corporation,
copyright 1995.
Iron atoms arrangedon a copper (111)
surface. These Kanji
characters represent
the word atom.
Scanning Tunneling Microscopy (STM)
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Summary
Point, Line, andAreadefects exist in solids.
The number and type of defects can be varied andcontrolled Tcontrols vacancy conc.
amount of plastic deformation controls # of dislocations Weight of charge materials determine concentration of
substitutional or interstitial point defects
Defects affect material properties (e.g., grain boundariescontrol crystal slip).
Defects may be desirable or undesirable e.g., dislocations may be good or bad, depending on whether
plastic deformation is desirable or not.
Inclusions can be intention for alloy development