This document discusses various types of imperfections in solids, including point defects and non-stoichiometric defects. It also covers close packing of spheres in one, two, and three dimensions. Specifically, it describes: 1) Point defects as irregularities from the ideal arrangement around an atom, including vacancies and interstitials. 2) Stoichiometric defects that do not disturb composition, such as Schottky and Frenkel defects in ionic solids. 3) Non-stoichiometric defects that do disturb composition, such as metal excess or deficiency defects involving vacancies or interstitials. 4) Close packing of spheres can form hexagonal or cubic structures in 3D depending

1. Point
defects
Stoichiometric
Defects
Non Ionic
solids
Vacancy
Defect
Interstitial
Defect
Ionic
solids
Frenkel
Defect
Schottky
Defect
Non-
Stoichiometric
Defects
Metal
Deficiency
Defect
Metal
Excess
Defect
anionic
vacancies
extra
cations
Impurity
Defects
Imperfections in Solids

2. Imperfections in Solids
Point defects are the irregularities or deviations from ideal arrangement
around a point or an atom in a crystalline substance
(a) Stoichiometric Defects
These are the point defects that do not disturb the stoichiometry of the
solid.
They are also called intrinsic or thermodynamic defects.
Stoichiometric Defects in Non-Ionic solids

3. Vacancy Defect can also develop when a substance is heated

4. Stoichiometric Defects in Ionic solids
Seen in Solids having high
Co-ordination number
Seen in Solids having low Co-
ordination number

5. Non – stoichiometric defects: These are the point defects that disturb
the stoichiometry of the solid.
Non-stoichiometric defects are of two types
(i) Metal Excess Defect
Metal excess defect due to anionic vacancies
 A compound may have an extra metal ion if the negative ion is absent from its
lattice site. This empty lattice site is called a Anionic vacancy. To maintain electrical
neutrality this site is occupied by an electron.
 The Anionic vacancy occupied by an electron is called F-centre or Farbenzenter.
 F- centre is responsible for the colour of the compound.
 Alkali halides like NaCl and KCl show this type of defect

6. Method: Crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium
atoms are deposited on the surface of the crystal. The Cl– ions diffuse to the surface
of the crystal and combine with Na atoms to give NaCl. This happens by loss of
electron by sodium atoms to form Na+ ions. The released electrons diffuse into the
crystal and occupy anionic sites. As a result the crystal now has an excess of
sodium.
Example
NaCl : yellow
LiCl : pink
KCl : violet (or lilac).

7. Metal excess defect due to Presence of extra cations:
A compound is said to have extra cations, if a cation is present in the interstitial
site. An electron is present in the interstitial site to maintain the electrical
neutrality.
Eg : Zinc oxide is white in colour at room temperature. On heating it loses oxygen
and turns yellow
Now there is excess of zinc in the crystal and its formula becomes Zn1+xO. The
excess Zn2+ ions move to interstitial sites and the electrons to neighbouring
interstitial sites

8. Non-stoichiometric defects Metal deficiency:
This defect arises because of absence of metal ions from its lattice sites.
This defect arises when a cation exists in more than one oxidation state and the
cation of higher oxidation state replaces the cation of lower oxidation state.
The electrical neutrality is maintained by an adjacent ion having a higher positive
charge.
Solids contain less amount of the metal as compared to the stoichiometric proportion
Eg : FeO which is mostly found with a composition of Fe0.95O. (Fe0.93O to Fe0.96O)
In crystals of FeO some Fe2+ cations are missing and the loss of positive charge is
made up by the presence of required number of Fe3+ ions.

9. (b) Impurity Defects
These are the defects in ionic solids due to the presence of impurities in them.
Eg : (1) NaCl with SrCl2 as impurity
 If molten NaCl containing a little amount of SrCl2 is crystallized, some of the
sites of Na+ ions are occupied by Sr2+. Each Sr2+replaces two Na+ ions.
 The cationic vacancies thus produced are equal in number to that of Sr2+ ions
(2) AgCl with CdCl2 as impurity.

10. Close Packed structures
In solids, the constituent particles are close-packed, leaving the minimum vacant
space these are called as Close packed structures
Three dimensional structure is studied in three steps or levels
Assumption:
1. Constituent particles are hard spheres
2. Spherical particles are of equal size.
3. In Metallic crystals the constituents particle are nearly of the above said type
Step1 : Close packing in one dimension
Step 2 :
Close packing in
two dimension
Square close packing in 2D
Hexagonal close packing in 2D

11. Step 3 :
Close
packing in
three
dimension
From Square close
packed
2D layer
Simple cubic unit cell
(with primitive unit
cell)
From Hexagonal
close packed 2D
layer
Hexagonal Close packed
structure (hcp)
(by Covering tetrahedral
voids)
Cubic close packed structure
(ccp) or Face –centered cubic
(fcc) structure
(by covering Octahedral voids)
The number of nearest neighbours of
a particle (in direct contact) is called
its coordination number.(C.N)

12. Close packing in one dimension
In 1D there is only one way of arranging spheres . In this arrangement
spheres are arranged in a row and touching each other
Coordination number is two
Close packing in two dimensions
It is generated by stacking the rows of close packed spheres in two ways:
i). Square close packing: When the spheres of
the second row are placed exactly above those of
the first row. This way the spheres are aligned
horizontally as well as vertically. The arrangement
is AAA type. Coordination number is 4.

13. ii. Hexagonal close packing: When the spheres of
the second row are placed above the first one in a
staggered manner such that its spheres fit in the
depression of the first row. The arrangement is ABAB
type.
Coordination number is 6.
Voids or interstitial site: The vacant space between the close packed
touching spheres
Triangular Voids : Voids are triangular in shape and centers lie at the corners
of an equilateral triangle.

14. Close packing in three dimensions:
They can be obtained by stacking the two dimensional layers one above the other. It
can be obtained in two ways:
From two dimensional square close packed layers:
The spheres of the upper layer (two dimensional
square close packed layers) are placed exactly
over the first layer such the spheres of the layers
are perfectly aligned horizontally and vertically. It
has a AAAA..type pattern.
The lattice is simple cubic lattice.
CN = 6

15. From two dimensional hexagonal close packed layers:
If a two dimensional layer (hexagonal close packed) is considered as A, the second
layer which is placed above the first layer in such a way that the spheres of the
second layer (considered as B) are placed in the depressions of the first layer(by
covering the triangular voids). This gives rise to two types of voids: tetrahedral voids
and octahedral voids.

16. If the number of close packed particles = N
Number of particles present in octahedral voids = N
Number of particles present in tetrahedral voids = 2N
Tetrahedral voids : The Void formed between
four touching spheres, a tetrahedron is formed
when the centres of these four spheres are joined
Octahedral voids : The interstitial void formed by
combination of two triangular voids (6 spheres) a octahedron
is formed when the centres of these six spheres are joined

17. 1. Covering the tetrahedral voids: Here, tetrahedral voids of the second layer may be
covered by the spheres of the third layer. It gives rise to ABABAB… type pattern.
The three dimensional structure is called hexagonal close packed structure.
Coordination number is 12. Example: Mg, Zn
Placing the third layer over the third layer: There are two possibilities:

18. 2. Covering the octahedral voids: Here, octahedral voids of the second layer may
be covered by the spheres of the third layer. It gives rise to ABCABCABC…
type pattern. The three dimensional structure is called cubic close packed
structure or face centred cubic structure.
Coordination number is 12. Example: Cu, Ag