imperfections 4

8/11/2019 Imperfections 4

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Chapter 4:

Imperfections in the

Atomic

and lonic Arrangements

2011 Cengage Learning Engineering. All Rights Reserved. 4 - 1

Chapter 4: Imperfections in the Atomic and lonic Arrangements


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Point Defects

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Most materials contain atomic structural defects and impurities within.

The properties of many materials are profoundly influenced by these

imperfections.

The heart of much materials research/development involves controlling them.

W.D. Callister, Jr., Materials Science and Engineering, An Introduction, Eighth Edition, John Wiley & Sons, New York (2010).

Figure 4.1 Two-dimensional

representation of a vacancy and

a self-interstitial. (Adapted from

W.G. Moffatt, G.W. Pearsall, and

J. Wulff, The Structure and

Properties of Materials, Vol. I,

Structure, p. 77. Copyright

1964 by John Wiley & Sons,

New York. Reprinted by

permission of John Wiley &

Sons, Inc.)

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Equilibrium vacancy concentration:

This increases with temperature exponentially

Nvnumber of vacancies

Nnumber of atom sites

Qvvacancy formation energy (J or eV)

kBoltzmanns constant (1.38x10-23J/atom-K or 8.62x10-5eV/atom-K)

TTemperature (K)

For most metals just below their melting temperature

Thus, only about one in 10,000 lattice sites will be empty (not very many!)

e.g.: Lead (FCC): Melting temperature 327C; energy for vacancy formation:

0.55 eV/atom

Nv=Nexp

Qv

kT

Nv

N 10

4

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Self-Interstitial:

An atom that is crowded into an interstitial site of identical atoms

This is not very probable because of the large lattice distortions required tomake it fit

Impurities:

Virtually all materials are not 100% pure (99.9% purity or more is very

expensive)

There are almost always atoms of a different species that enter into the mix

For metals, we oftentimes introduce these intentionally (Cr added to Fe for

oxidation and corrosion resistance)

These types of metals are called alloys

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Solid solutions:

Figure 4.2 Two-dimensional

schematic representations of

impurity atoms. (Adapted from

W.G. Moffatt, G.W. Pearsall, andJ. Wulff, The Structure and

Properties of Materials, Vol. I,

Structure, p. 77. Copyright

1964 by John Wiley & Sons,

New York. Reprinted by

permission of John Wiley &

Sons, Inc.)


The solvent is the major concentration element (host atom) while the solute

is the minor concentration element

Original crystal structure is maintained with no new structure being formed

The solid solution is generally homogeneous throughout with a random but

uniform distribution 7


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Substitutional atoms:

Impurity atoms replace host atoms at their lattice sites

Atomic radius must be close to that of the host

This is favored amongst atom types of the same crystal structure

This is favored amongst atoms with small electronegativity difference

Interstitial atoms:

Impurity atoms fit within the voids of the crystal structure

Atomic radius must be substantially smaller than that of the host

When C is added to Fe we get steel! This discovery changed the world

RC= 0.071 nm RFe= 0.124 nm

The maximum concentration of C in Fe is only about 2% 8


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Composition:

In a foundry, they weigh the elements, then melt them together to make

alloys

These smelters prefer to work with units of weight (or mass)

In a crystallography lab, they focus upon the interaction of individual atoms

These materials scientists tend to work with units of atoms

So how can these people communicate?

They bring into account the atomic weight (mass) and adjust units accordingly

A - atomic weight (mass) (g/mol)

NA - Avogadros number (6.02 x 10

23

atom/mol)

weight(%)=wt.%=weightofelement

totalweight

atomic(%)= at.%=#atomofelement

total#atom

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We know that

So (3)

Activity:

A material is composed of two primary elements 1 and 2. Express the weight

percent of element 1 (C1) as a function of atomic masses (A1and A2) and the

atom percents (C1and C

2).

C'1=N

1

N1+N

2

We have the atom percents, and we know that

so (1) and (2)

at.%=#atomofelement

total#atom

C'2=N2

N1+N2

wt.%=weightofelement

totalweight

C1=A1N1

A1N1+A2N2Replacing N1andN2in (3) by their expression from (1) and (2) we get:

C1=C'1A1

C'1A1+C'2A210


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Line Defects

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Dislocations:

Linear one-dimensional defects of

misaligned atoms (edge, screw,

and mixed types)

Edge dislocation:

Dislocation line - line formed by the extra half plane of atoms

Burgers vector - magnitude and direction of the lattice distortion (here, the

Burgers vector is perpendicular to the dislocation line)


Figure 4.3 The atom positions

around an edge dislocation;

extra half-plane of atoms shown

in perspective. (Adapted from

A.G. Guy, Essentials of Materials

Science, McGraw-Hill Book

Company, New York, 1976, p.

153.)

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Screw dislocation:

A shear stress applied to the crystal

leads to this type of misalignment

Here, the Burgers vector is parallel to

the dislocation line

Figure 4.4 (a) A screw dislocation within a crystal. (b)

The screw dislocation in (a) as viewed from above.

The dislocation line extends along line AB. Atom

positions above the slip plane are designated by open

circles, those below by solid circles. [Figure (b) from

W.T. Read, Jr., Dislocations in Crystals, McGraw-HillBook Company, New York, 1953.]

W.D. Callister, Jr., Materials Science and Engineering, An

Introduction, Eighth Edition, John Wiley & Sons, New York

(2010).14


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Figure 4.5 (a) Schematic representation of a

dislocation that has edge, screw, and mixed

character. (b) Top view, where open circles denote

atom positions above the slip plane and solid

circles, atom positions below. At point A, the

dislocation is pure screw, while at point B, it is pureedge. For regions in between where there is

curvature in the dislocation line, the character is

mixed edge and screw. [Figure (b) from W.T. Read,

Jr., Dislocations in Crystals, McGraw-Hill Book

Company, New York, 1953.]

W.D. Callister, Jr., Materials Science and Engineering, AnIntroduction, Eighth Edition, John Wiley & Sons, New York

(2010).

Mixed dislocation:

Most dislocations are of the mixed

type (neither pure edge or pure screw)

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Dislocation lines can be seen with a transmission electron microscope:

Figure 4.6 A transmission electron micrograph of a

titanium alloy in which the dark lines are

dislocations. 51,450x (Courtesy of M.R. Plichta,

Michigan Technological University.)


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Surface Defects

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Grain boundaries:

Figure 4.7 Schematic diagram showing small- and

high-angle grain boundaries and the adjacent atom

positions.


Consist of irregular boundaries separating individual crystals (many dislocations)

Grains tend to grow at elevated temperature to minimize grain boundary area

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Twin boundaries:

A special type of boundary in the form of a mirror image


Figure 4.9 Schematic diagram showing a

twin plane or boundary and the adjacent

atom positions (colored circles).

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Other defects:

Stacking faults - ABCABC -> ABCABABC

Phase boundaries - we shall see this in later chapters

Ferromagnetic domain walls - separates regions of different magnetization

direction

Atomic vibrations - these vary randomly throughout

Porosity

Foreign inclusions and impurities

Cracks

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Microscopic Examination

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Photograph of polycrystalline copper:

Figure 4.12 Cross-

section of a

cylindrical copper

ingot. The small

needle-shaped

grains may beobserved, which

extend from the

center radially

outwards.


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How optical microscopy works:


Figure 4.13 (a) Polished and etched grains as they might appear when viewed with an optical microscope. (b)

Section taken through these grains showing how the etching characteristics and resulting surface texture

vary from grain to grain because of differences in crystallographic orientation. (c) Photomicrograph of a

polycrystalline brass specimen. 60x. (Photomicrograph courtesy of J.E. Burke, General Electric Co.)

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How optical microscopy works:


Figure 4.14 (a) Section of a grain boundary and its surface groove produced by etching: the light reflection

characteristics in the vicinity of the groove are also shown. (c) Photomicrograph of the surface of a polished

and etched polycrystalline specimen of an iron-chromium alloy in which the grain boundaries appear dark.

100x. (Photomicrograph courtesy of J.E. Burke, General Electric Co.)

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ASTM grain size number:

N: grain/in2on a polished and etched material at 100X magnificationn: ASTM grain size number

N= 2n 1

W.F. Smith and J. Hashemi, Foundations of Materials Science and Engineering, Fifth Edition, McGraw-Hill, NY (2010).

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