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Imperfections in Solids
Art Ian G. Bautista, ECE, ECT
Imperfections in Solids
- The properties of some materials are
profoundly influenced by the presence
of imperfections.
- It is important to have knowledge about
the types of imperfections that exist and
the roles they play in affecting the
behavior of materials.
2
3
Atom Purity and Crystal Perfection
- If we assume a perfect crystal structure
containing pure elements, then anything
that deviated from this concept or
intruded in this uniform homogeneity
would be an imperfection.
1. There are no perfect crystals.
2. Many material properties are improved by
the presence of imperfections and
deliberately modified (alloying and
doping).
- The simplest of the point defects is a
vacancy, or vacant lattice site, one
normally occupied from which an atom
is missing.
- A self-interstitial is an atom from the
crystal that is crowded into an interstitial
site, a small void space that under
ordinary circumstances is not occupied.
Point Defects in Metals
5
- Vacancies:
- vacant atomic sites in a structure.
- Self-Interstitials:
- "extra" atoms positioned between atomic sites.
Point Defects in Metals
Vacancy
distortion
of planes
self-interstitial
distortion
of planes
- In metals, a self interstitial introduces
relatively large distortions (strain) in the
surrounding lattice since the atom is
substantially larger than the interstitial
site.
Self Interstitials
7
Boltzmann's constant
(1.38 x 10 J/atom-K)
(8.62 x 10
eV/atom-K)
N
v
N
exp
Q
v
kT
No. of defects
No. of potential
defect sites
Activation energy –
energy required for formation of vacancy
Temperature
Each lattice site
is a potential
vacancy site
- Equilibrium concentration varies with temperature.
Equilibrium Concentration:
Point Defects
8
- Find the equil. # of vacancies in 1 m
3
of Cu at 1000C.
A
Cu
= 63.5 g/mol
r = 8.4 g/cm
3
Q
v
= 0.9 eV/atom N
A
= 6.02 x 10
23
atoms/mol
Estimating Vacancy Concentration
For 1 m
3
, N =
N
A
A
Cu
r x x 1 m
3
= 8.0 x 10
28
sites
8.62 x 10
eV/atom-K
0.9 eV/atom
1273 K
N
v
N
exp
Q
v
kT
= 2.7 x 10
N
v
= (2.7 x 10
)(8.0 x 10
28
) sites = 2.2 x 10
25
vacancies
9
-- vacancies exist in ceramics for both cations and anions
-- interstitials exist for cations
-- interstitials are not normally observed for anions because anions
are large relative to the interstitial sites
Adapted from Fig. 5.2, Callister & Rethwisch 3e.
(Fig. 5.2 is from W.G. Moffatt, G.W. Pearsall, and
J. Wulff, The Structure and Properties of
Materials , Vol. 1, Structure , John Wiley and Sons,
Inc., p. 78.)
Point Defects in Ceramics
Cation Interstitial
Cation Vacancy
Anion Vacancy
10
To maintain the charge neutrality, a cation vacancy-cation interstitial
pair occur together. The cation leaves its normal position and moves to the
interstitial site.
To maintain the charge neutrality, remove 1 cation and 1 anion;
this creates 2 vacancies.
Adapted from Fig. 5.3, Callister & Rethwisch 3e.
(Fig. 5.3 is from W.G. Moffatt, G.W. Pearsall, and
J. Wulff, The Structure and Properties of
Materials , Vol. 1, Structure , John Wiley and Sons,
Inc., p. 78.)
Point Defects: Frenkel and Schottky
Schottky
Defect
Frenkel
Defect
11
Point Defects in Polymers
- Defects due in part to chain packing errors and impurities such
as chain ends and side chains
Adapted from Fig. 5.7,
Callister & Rethwisch 3e.
Alloying
- Most metals are alloys. Alloying is done to
improve strength, corrosion resistance, ductility,
lower melting T.
- For example, sterling silver is an alloy of 92.5%
silver, 7.5% copper. At room temperature, “pure”
silver is highly corrosion resistant, but also very
soft. The addition of copper improves the strength
and maintains good corrosion behavior.
12
19
- Charge balance must be maintained when impurities are
present.
Na
Cl
- Substitutional cation impurity
without impurity Ca
2+ impurity with impurity
Ca
2+
Na
Na
Ca
2+
cation
vacancy
- Substitutional anion impurity
without impurity O
2 - impurity
O
2 -
Cl
anion vacancy
Cl
with impurity
Point Defects: Impurities
Drills:
