Solid state chemistry

1. Defects in Crystal
PHYSICAL CHEMISTRY
TYBSc.

2. A defect or imperfection is a
deviation from the orderly arrangement of
atoms or ions in a crystal lattice.There are two
types of defects-
• Point defects
• lattice defects.
A point defect involves the displacement of
individual atoms or ions from their normal
position in the crystal lattice.
Frenkel and Schottky defect falls in this
category.

3. Frenkel defect
In an ionic crystal,the positive ions are
balanced by an equal number of negative ions
so that the crystal, as a whole,is electrically
neutral.If an additional atom is trapped in the
crystal lattice,we call it an interstitial defect.
In frenkel defect,an ion is displaced
from its normal position to an interstitial
site,thus producing a vacant site or ‘hole’ in
the lattice.

4. A
A
c
v
c
c
c
c
c
v
A+
A+
A+
A+
A+
A+
A+
A
+
a. AN IDEAL CRYSTAL.
B
_
B
_
B
_
B
_
B
_
B
_
B
_ _
B A+
A+
A+
A+
A+
A+
A+
A+
B
_
B
_
B
_
B
_
B
_
B
_
B
_
b. A FRENKEL DEFECT.
Cation vacancy
Cation in interstitial site

5. In fig.b.,the positive ion has moved to an
interstitial site leaving behind a vacant site.
Such defects are found in crystals where
one ion is larger than the other eg.ZnS,AgCl
and AgBr.In these substances the anion is
larger than the cation and hence there is
enough space in the lattice for interstitisl
sites.

6. DETERMINATION OF AVOGADRO’S
NUMBER.
The Avogadro’s number(NA) is the number of molecules in one
gram-mole of a compound.Its value is 6.023x10
molecules/mol.The study of the crystal strucyure of NaCl
offers a accurate method to determine Avogadro’s number.
The unit cell of NaCl consists of eight simple cubes
which accounts for 14 Na+ions and 13 Cl- ions.
i.There are 8 Na+ ions at the 8 corners of of the unit cell and
one Na+ion at the centre of each of the 6 faces of the unit
cell.Each of the corner Na+ ions is shared by eight unit cells
meeting at the corner.
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Consequently,only1/8x8=1 Na+ ion belongs to the
unit cell.

7. ii.The Na+ ion at the centre of eavh face is shared equally by
two adjoining unit cells.Hence ½ of the mass of the Na+ ion
belongs to the unit cell.Consequently 1/2x6=3Na+ ions belong
to the unit cell.Thus atotal of 1+3=4Na+ ions belong to the
unit cell.
Similarly,there are 12Cl- ions at he middle of each of
the 12 edges of the unit cell & ion is shared equally by 4 unit
cells.Hence 1/4x12=3Cl- ions belongs to the unit cell.The Cl-
ion in the centre of the unit cell belongs exclusively to the
unit cell.Thus a total of 3+1=4Cl- ions belongs to the unit
cell.We can therefore conclude that a unit cell of NaCl
contains 4 molecules of NaCl.

8. Calculation of volume of unit cell
Since,the mass of NA (Avogadro’s number)of molecules of
NaCl is M(mol.wt.)
Therefore, the mass of NaCl is=M x4
The average mass per unit cell=4M
Volume associated with a unit cell is given by
V=Mass of unit cell =4M/NA = 4M ---------Eqn (1)
Density of NaCl
NA
NA
NaCl has F.C.C. Structure hence the length of the edge of
the unit cell is a i.e. 2d100 where a is the length of asimple
cube. Hence ,
ρ NA ρ

9. V=(a) =(2d100) ---------Eqn(2)
Combining eqn(1) &(2)
(2d100) = 4M
NAρ
i.e.d100=
3
4M
2 NAρ
And NA= 4M
(2d100). ρ
3 =
4M
2.d100 . ρ
3
This equation is used to calculate Avogadro’s number NA.

10. THANK YOU