Imperfections in Solid Materials_Ch4

8/10/2019 Imperfections in Solid Materials_Ch4

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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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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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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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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



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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


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


Edge

Screw

Mixed


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Dislocations are visible in (T) electron micrographs



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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



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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

Documents

Imperfections in Solid Materials_Ch4