Imperfections in Solids
• Perfect crystals do not exist; even the best crystals have 1ppb defects.
– Defects are imperfections in the regular repeating pattern and may be
classified in terms of their dimensionality (Point vs. Extended).
– Classification is given by;
1. Point Defects
2. Line Defects
1.
2.
Point Defects
The irregularities or deviations from ideal arrangement around a point or an
atom in a crystalline substance.
Line defects
The irregularities or deviations from ideal arrangement in entire rows of
lattice points.
1. Point Defects
Point defects can be classified into three types :
(i) Stoichiometric Defects (E.g. Vacancy Defect, Interstitial Defect)
(ii) Impurity Defects
(iii) Non-Stoichiometric Defects (E.g. Metal Excess Defect, Metal
Deficiency Defect )
(i) Stoichiometric Defects
a) Vacancy Defect
– given a perfect crystal (e.g. of Cu), an atom can be placed on the outside
of the cell to produce a vacancy (≡ □); remember atom migration.
– e.g. TiO has 1:1 stoichiometry and NaCl structure, but has 15% vacancies
on the Ti sites and 15% vacancies on the O sites. Both sets of vacancies
are disordered.
b) Interstitial Defect
When some constituent particles (atoms or molecules) occupy an interstitial
site, the crystal is said to have interstitial defect. This defect increases the
density of the substance.
*Ionic Crystals shows the following Defects
– in pure metal compounds, don’t need to worry about
electroneutrality.
– in an ionic crystal, the interior and surface must remain ≈ neutral.
c) Schottky Defect
– take anions and cations and place them on surface in equal
numbers.
– stoichiometric effect: equal numbers of anion and cation vacancies.
– may be randomly distributed, but tend to cluster because ofoppositely charged vacancies.
– most important with alkali halides.
– at room temp, ~1 in 1015 pairs vacant in NaCl,
so 1mg sample has ~10,000 Schottky Defects.
– This defect causes the decrease in density ofthe substance
b) Frenkel Defect
– take cation out of position and cram it
into an interstitial site (void between
normal atomic position).
– Ag+ surrounded by 4Cl- stabilizes this
defect.
– tendency for vacancy and interstitial to
form nearby pair.
– also a stoichiometric deffect (vacancies
= interstitials).
(ii)Impurity Defect
Due to Impurities and Doping
• Impurities are elements present in the material that are different
from those in the compound formula.
• Dopants are intentionally added impurities (to make alloys or
affect changes in properties). Alloy formation most likely when
dopant anions and cations are close in size to original material.
• Isovalent dopants: substitution species have the same charge.
NaCl:AgCl → Na1-xAgxCl (alloy on cation site)
AgBr:AgCl → AgBr1-xClx (alloy on anion site)
• Aleovalent dopant: substitution species has different charge.
NaCl:SrCl2 could be either Na1-2xSrx xCl or Na1-xSrxClClxi
– either could happen; experimentally, first is found.
Figure shows the impurity defect in NaCl by Sr2+ ion
Due to Vacancy:
Missing atom from an atomic site
 Atoms around the vacancy displaced
 Tensile stress field produced in the vicinity
Tensile Stress
Fields ?
Due to Interstitial Atom:
Relative
size
Interstitial
Compressive
Stress
Fields
Impurity
Substitutional
Compressive stress
fields
 SUBSTITUTIONAL IMPURITY
 Foreign atom replacing the parent atom in the crystal
 E.g. Cu sitting in the lattice site of FCC-Ni
 INTERSTITIAL IMPURITY
 Foreign atom sitting in the void of a crystal
 E.g. C sitting in the octahedral void in HT FCC-Fe
Tensile Stress
Fields