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