week 2

Imperfections in Solids
Imperfections
• Thus far it has been tacitly assumed that perfect order exists
throughout crystalline materials on an atomic scale.
• However, such an idealized solid does not exist; all solids contain
large numbers of various defects or imperfections.
• As a matter of fact, many of the properties of materials are
profoundly sensitive to deviations from crystalline perfection;
• The influence is not always adverse, and often specific
characteristics are deliberately fashioned by the introduction of
controlled amounts or numbers of particular defects.
Imperfections
• Crystalline defect refers to a lattice irregularity having one
or more of its dimensions on the order of an atomic
diameter.
• Classification of crystalline imperfections is frequently made
according to geometry or dimensionality of the defect.
• Various types of defects are:
1. Point defects
a) Vacancies & self-interstitials
b) Impurities/Alloys
2. Linear defects (dislocations)
3. Interfacial (2D) defects
4. Bulk or Volume Defects
1. Point defects
• The simplest of the point defects is a vacancy, or vacant
lattice site,
• One normally occupied from which an atom is missing
• All crystalline solids contain vacancies and, in fact, it is not
possible to create such a material that is free of these
defects.
• The necessity of the existence of vacancies is explained using
principles of thermodynamics; in essence, the presence of
vacancies increases the entropy (i.e. the randomness) of the
crystal.
Scanning probe
micrograph that
shows a vacancy on
a (111)-type surface
plane for silicon.
Approximately
7,000,000×.
(Micrograph courtesy
of D. Huang, Stanford
University.)
1. Point defects
• The equilibrium number of vacancies ( 𝑁𝑣 ) for a given
quantity of material depends on and increases with
temperature according to:
• Thus, the number of vacancies increases exponentially with

temperature;
• For most metals, the fraction of vacancies/N just below the
melting temperature is on the order of 10-4; that is, one
lattice site out of 10,000 will be empty.
Impurities in Solids
• A pure metal consisting of only one type of atom just
isn’t possible;
• Impurity or foreign atoms will always be present, and
some will exist as crystalline point defects.
• In fact, even with relatively sophisticated techniques, it
is difficult to refine metals to a purity in excess of
99.9999%.
• Even at this level, on the order of 1022 to 1023 impurity
atoms will be present in one cubic meter of material.
• Most familiar metals are not highly pure; rather, they
are alloys, in which impurity atoms have been added
intentionally to impart specific characteristics to the
material.
• Ordinarily, alloying is used in metals to improve
mechanical strength and corrosion resistance.
• For example, sterling silver is a 92.5% silver 7.5% copper
alloy. In normal ambient environments, pure silver is
highly corrosion resistant, but also very soft. Alloying
with
copper significantly enhances the mechanical strength
without depreciating the corrosion resistance
appreciably.
Pure 100% (in practice, 99.9% or better) gold is
24 karat by definition, so all colored golds are
less pure than this, commonly 18K (75%), 14K
(58.5%), 10K (41.6%), or 9K (37.5%).
Solid Solutions
• The addition of impurity atoms to a metal will result in the
formation of a solid solution and/or a new second phase,
depending on the kinds of impurity, their concentrations, and the
temperature of the alloy.
• A solid solution forms when, as the solute atoms are added to
the host material, the crystal structure is maintained and no new
structures are formed.
• A solid solution is also compositionally homogeneous; the
impurity atoms are randomly and uniformly dispersed within the
solid.
Solid Solutions
• Impurity/solute atoms in a solid solution may take
substitutional or interstitial positions in crystal
structure.
• Substitutional solid solutions form when, solute or
impurity atoms replace or substitute for the host atoms
• Several features of the solute and solvent atoms
determine the dissolvable concentration of the former
in the latter, as follows:
1. Atomic size factor: Appreciable quantities of a solute may be
accommodated in this type of solid solution only when the
difference in atomic radii between the two atom types is less
than about ±15%. Otherwise the solute atoms will create
substantial lattice distortions and a new phase will form.
Solid Solutions
2. Crystal structure: For appreciable solid solubility the crystal
structures for metals of both atom types must be the same.
3. Electronegativity: The more electropositive one element and
the more electronegative the other, the greater the likelihood
that they will form an intermetallic compound instead of a
substitutional solid solution.
4. Valences: Other factors being equal, a metal will have more of
a tendency to dissolve another metal of higher valency than
one of a lower valency.
Solid Solutions
• In interstitial solid solutions, impurity atoms fill the voids or
interstices among the host atoms.
• For metallic materials that have relatively high atomic packing
factors, these interstitial positions are relatively small.
• Consequently, the atomic diameter of an interstitial impurity
must be substantially smaller than that of the host atoms.
• Normally, the maximum allowable concentration of interstitial
impurity atoms is low (less than 10%). Even very small impurity
atoms are ordinarily larger than the interstitial sites, and as a
consequence they introduce some lattice strains on the adjacent
host atoms.
• Carbon forms an interstitial solid solution when added to iron;
the maximum concentration of carbon is about 2%. The atomic
radius of the carbon atom is much less than that for iron: 0.071
nm versus 0.124 nm.
• Solid solutions are also possible for ceramic materials
Dislocations or linear defects
• A dislocation is a linear or one-dimensional defect around which
some of the atoms are misaligned.
• One type of a dislocation is represented in Figure where an extra
portion of a plane of atoms is present, or half-plane terminates
File:Dislocation edge d2.svg
within the crystal.

• Dislocations are generally of two types:
• Edge dislocation and
• Screw dislocation
Burger vector (𝒃) represents the

magnitude and direction of the
lattice distortion resulting from a
dislocation in a crystal lattice
• Edge dislocation is a type of line defect in crystal lattices in which the
defect occurs either due to the presence of an extra plane of atoms or
due to the loss of a half of a plane of atoms in the middle of the lattice.
This defect causes the nearby planes of atoms to bend towards the
dislocation. Therefore, the adjacent planes of atoms are not straight.
• The atoms above the dislocation line are squeezed together, and those
below are pulled apart; this is reflected in the slight curvature for the
vertical planes of atoms as they bend around this extra half-plane.
• The magnitude of this distortion decreases with distance away from the
dislocation line; at positions far removed, the crystal lattice is virtually
perfect.
• The edge dislocation is represented by the symbol T which also
indicates the position of the dislocation line.
• Screw dislocation is another type of line defect in which the
defect occurs when the planes of atoms in the crystal lattice trace
a helical path around the dislocation line. Visualizing this type of
defects in crystals is difficult.
https://www.youtube.com/watch?v=iKKxTP6xp74
https://www.youtube.com/watch?v=RD40OtchSVg
Screw dislocation
Comparison of dislocation
motion in lattice
• Screw dislocation, may be thought of as being formed by a shear
stress that is applied to produce the distortion
• the upper front region of the crystal is shifted one atomic
distance to the right relative to the bottom portion.
• The atomic distortion associated with a screw dislocation is also
linear and along a dislocation line, AB Figure.
• The screw dislocation derives its name from the spiral or helical
path or ramp that is traced around the dislocation line by the
atomic planes of atoms.
• Sometimes the symbol  is used to designate a screw
dislocation.

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Imperfections in Solids

• Thus, the number of vacancies increases exponentially with

within the crystal.

Burger vector (𝒃) represents the

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