5.0.Imperfections in Solids

8/3/2019 5.0.Imperfections in Solids

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MECH 221 PM Wood-Adams Fall 2008

ISSUES TO ADDRESS... What types of defects arise in solids?

Can the number and type of defects be variedand controlled?

How do defects affect material properties?

1

Are defects undesirable?

CHAPTER 4:

IMPERFECTIONS IN SOLIDS


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Imperfections in SolidsThere is no such thing as a perfect crystal!

Thermodynamically impossible

defects lower the energy of a crystal & make it more stable

always have vacancies and impurities, to some extent

Defect does not necessarily imply a bad thing

addition of C to Fe to make steel

addition of Cu to Ni to make thermocouple wires addition of Ge to Si to make thermoelectric materials

addition of Cr to Fe for corrosion resistance

introduction of grain boundaries to strengthen materials

and so on

Defect(in this context) can be either desirable or undesirable.

In general, a defect simply refers to a disruption in the crystalline

order of an otherwise periodic material.


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TYPES OF IMPERFECTIONS

Vacancy atoms

Interstitial atoms

Substitutional atoms

1- Point defects:

Dislocations2- Line defects

interstitial atom

Substitutional atom

Grain Boundaries

3- Area defects:


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MECH 221 PM Wood-Adams Fall 2008 3

Vacancies:-vacant atomic sites in a structure.

Vacancydistortionof planes

Self-Interstitials:-"extra" atoms positioned between atomic sites.

self-interstitialdistortion

of planes

POINT DEFECTS

Much less likely to form

because of large energy

required to squeeze the extra

atom in.


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Boltzmann's constant

(1.38 x 10-23 J/atom K)

(8.62 x 10-5 eV/atom K)

ND

N

= expQD

kT

No. of defects

No. of potentialdefect sites.

Activation energy

Temperature

Each lattice siteis a potentialvacancy site

4

Equilibrium concentration varies with temperature!

EQUIL. CONCENTRATION:

Vacancies


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We can get Q from

an experiment. ND

N

= expQD

kT

Measure this... Replot it...

1/T

NNDln 1

-QD/k

slopeND

N

T

exponential

dependence!

defect concentration

MEASURING ACTIVATION ENERGY


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Find the equil. # of vacancies in 1m of Cu at 1000C.

Given:

3

ACu

= 63.5g/mol = 8.4 g/cm3

QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole

8.62 x 10-5 eV/atom-K

0.9eV/atom

1273K

NDN

= expQDkT

= 2.7 10-4

ESTIMATING VACANCY CONC.


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Low energy electron

microscope view of

a (110) surface of NiAl.

Increasing T causessurface island of

atoms to grow.

Why? The equil. vacancy

conc. increases via atommotion from the crystal

to the surface, where

they join the island.

Island grows/shrinks to maintainequil. vancancy conc. in the bulk.

Reprinted with permission from Nature (K.F.

McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in

Solids and the Stability of Surface Morphology",

Nature, Vol. 412, pp. 622-625 (2001). Image is5.75 m by 5.75 m.) Copyright (2001) MacmillanPublishers, Ltd.

OBSERVING EQUIL. VACANCY CONC.


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impurity addition of an atom of a different species than the

host or matrix

Alloys other types of atoms are deliberately added to

give the material certain propertiesMay or may not result in the same crystal structure

May or may not result in secondary phases

Example 1: add 1% Sn to Pbi.e., of every 100 Pb lattice sites, 1 is occupied by an Sn atom

Result: ..

samecrystal structure as pure PbExample 2: add 25% Sn to Pb

Result: a microstructure (distinct regions of Sn)

solubility of Pb (in the solid state) is exceeded

single phase alloy

two-phase

Impurities


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Solid Solution

A homogeneous distribution of two or more elements.

solute atoms are added without altering the crystal structure

or resulting in formation of a new phase.

Solid solution is a particular type of alloy Two types: substitutional and interstitial

solvent the host material, usually the element or compound

present in the greatest amount.

solute the minor phase, added to the solvent. Usually the

element or compound present in minor concentrations.

phase is a region of uniform composition or crystal structure

What would a solid solution look like?


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Two outcomes if impurity (B) added to host (A): Solid solution ofB in A (i.e., random dist. of point defects)

Solid solution ofB in A plus particles of a new

phase (usually for a larger amount of B)

OR

Substitutional alloy(e.g., Cu in Ni) Interstitial alloy(e.g., C in Fe)

Second phase particle

--differentcomposition

--often different structure.

POINT DEFECTS IN ALLOYS


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Conditions for the formation of a

substitutional solid solution

The difference between theatomic radii of the two elements

must be less then 15%. The crystal structure of both

elements must be the same.

If the electronegativities arevery different then a compoundmay form instead of a solution

a metal is more likely to

dissolve a solute of highervalency (all other things beingequal).

An example of a

substitional solid solutionis that formed by Cu

(r0=0.128 nm, X=1.9) and

Ni (r0

=0.125 nm, X=1.8).

They are completely

soluble in one another at

all concentrations.


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Comparison between a substitutional solid

solution and an intermetallic compound

Solid solution: (1) random

placement of solute atoms

(2) metallic bonding

Intermetallic compound: (1)

Specific stoichiometry, (2) crystal

structure is such that thisstoichiometry is allowed (3)

bonding is partially metallic and

partially covalent (or ionic)


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Definition: Amount of impurity (B) and host (A)

in the system.

Weight %

Two descriptions:

Atom %

CB =mass of B

total massx 100 C'B =

# atoms of B

total # atomsx 100

Conversion between wt % and at% in an A-B alloy:

CB =C'BAB

C'AAA+ C'BABx 100 C'B =

CB/AB

CA

/AA

+ CB

/AB

Basis for conversion:

mass of B = moles of B x AB

atomic weight of B

mass of A = moles of A x AA

atomic weight of A

COMPOSITION


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Dislocations result from solidification from the melt, from

mechanical work (e.g., rolling, drawing, compressive impact, tensile

or shear stress), or from thermal stresses

It is very difficult to prepare a dislocation-free crystal!!!

2 Types:

EDGE DISLOCATIONS

SCREWDISLOCATIONS

Dislocations

Dislocations make metals weaker

than they should be, BUT also allow

metals to be deformed (ie. allowplastic deformation). (Chp. 6)

Linear Defects

before deformationafter tensile elongation

slip steps


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Think of edge dislocation as an extra

half-plane of atoms inserted in a crystal.

Misalignment of atomic planes due

to the extra half plane.

Edge Dislocation

Burger's vector (b) = magnitude + direction of lattice distortion.


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SCREW Dislocation

Crystal is "cut halfway through and then slide sideways

helical path through structure hence screw.

The motion of a screw dislocation can be thought of in terms of tearing a

sheet of paper.


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Usually, dislocations have both an edge and a screw character;

i.e., they are dislocations:

Pure edge here

Mixed mode here

Slip plane

Pure screw here

mixed

Dislocations


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Polycrystalline Materials

Most materials arepolycrystalline and are made

of many single crystals during solidification the

crystal nucleate and growfrom the liquid in a random

orientation the grains impinge on each

other when the solidificationis complete

junction of grains are grainboundaries


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Grain Boundaries

Occurs due to thecrystallographic mismatch whentwo grain meet

when mis-orientation is large

high angle grain boundary when mis-orientation is small,

low angle grain boundary atoms are less bondedand the

atomic packing is lower than inthe grain (lower coordination)

the result is an energy difference

interfacial energy or grainboundary energy


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Grain boundary energy is afunction of mis-orientation

grain boundaries are morechemically reactive

segregation of impurities dueto higher energy

total grain boundary areasmaller in coarse grainedthan

fine grainedmaterial low angle grain boundary is

described a an array ofdislocations

tilt boundary (edge ) twist boundary (screw)


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Observation of Grain Structure

Macrostructure can beobserved with naked eye

coarse grains can berevealed this way (e.g. Alstreetlight posts e.g. zincgalvanized garbage cans

microstructure is when thegrains can only beobserved with amicroscope microscopy

imaged using a camera forarchiving

photomicrograph

FIGURE 4.10 High-puritypolycrystalline lead ingot in which

the individual grains may be

discerned.


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Useful up to 2000X

magnification.

Polishing

removes surface

features (e.g.,

scratches) Etching changes

reflectance,

depending on

crystal orientation.

microscope

close-packed

planes

micrograph of

Brass (Cu and

Zn)

0.75mm

OPTICAL MICROSCOPY (1)


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Sample Preparation for Microscopy

Preparation requires

meticulous grinding and

polishing of the surface

the microstructure is revealed

by attack using etchants

(chemical reagents preferential attack of grain

boundaries

effect is that these features

scatter the incident light andcreate optical contrast


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Grain Size Determination

properties are affected by grain size

measurement ofgrain volume, diameter and area

average grain diameter can be determined using the linearintercept method

lines of same length placed on micrograph

measure number of grains intercepting each line average grain

diameter ASTM grain size (n) based number of grains/square inch

(N) at 100x magnification

expression relating two parameters:

N =2n-1

use comparison charts to determine size of microstructure

of interest at x100 magnification simple to implement

2 different

ways to

describe

grain size


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Example: Grain Diameter Determination

5 cm=1.97 in 250 X


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Example: Grain Size Determination

250 X

Image size:

5 in by 5.9 in


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Point, Line, and Area defects arise in solids.

The number and type of defects can be varied

and controlled (e.g., T controls vacancy conc.)

Defects affect material properties (e.g., grain

boundaries control 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.)

SUMMARY

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5.0.Imperfections in Solids