SOLID STATE

ISOMORPHISM:
1. Two or more substances having same crystal structure are said to be
isomorphous.
2. They have same atomic ratio.
3. For example, (a) NaF and MgO (b) NaNO3 and CaCO3 are isomorphous pairs
and have the same atomic ratios,1:1 and 1:1:3, respectively of the constituent
atoms.

POLYMORPHISM:
1. A single substance that exits in two or more forms is said to be
polymorphous.
2. For example, calcite and aragonite are two forms of calcium
carbonate.
3. Polymorphism occurring in elements is called allotropy. For
example, allotropic forms of carbon are diamond, graphite and
fullerene.
CLASSIFICATION OF CRYSTALLINE SOLIDS

IONIC COVALENT MOLECULAR METALLIC

CRYSTALS NETWORK CRYSTALS CRYSTALS
↓ CRYSTALS ↓ ↓
Charged ↓ Molecules Cations and
ions Atoms ↓ mobile
↓ ↓ H2O, CH4 electrons
NaCl Diamond ↓
Na, Ca, K

1. IONIC CRYSTALS:

I. The constituent particles are charged

ions.
II. The particles of these crystals are held
by electrostatic force of attraction.
III. Ionic crystals are hard and bitter & have
high M.P.
IV. They are nonconductors of electricity in
solid state.
V. Examples: Nacl, K2SO4, KCl

2. COVALENT NETWORK CRYSTALS

 I. The constituent particles are atoms.
II. The particles of these crystals are held by covalent bonds.
III. They are hardest and most incompressible and posses high
M.P. and B.P.
IV. They are poor conductors of heat and electricity.
V. Examples: diamond, quartz (SiO2)

3. MOLECULAR CRYSTALS
The constituent particles are molecules and the bonds within the
molecules are covalent bonds.
The molecules are held together by various intermolecular force of
attractions.

Fig a. Fig. b. Fig. c.

(a) weak dipole dipole interactions in polar molecules such as

HCl, H2O, SO2 etc.
(b) very weak dispersion or London forces in non-polar
molecules such as CH4, H2 etc.
(c) intermolecular hydrogen bonds in solids such as NH3, HF
etc.
 4. METALLIC CRYSTALS

I. In these crystals, the attractive interactions between cations

and mobile electrons constitute the metallic bond.
II. They are formed by the atoms of the same metallic element.
III. The positive ions are arranged to form a kernel in the sea of
delocalized electrons.
IV. These are malleable and ductile.
V. Good conductors of heat and electricity.
VI. Examples: Na, K, Fe, etc.

CRYSTAL STRUCTURE / CRYSTAL LATTICE / SPACE LATTICE:

It is the ordered three-dimensional arrangement of particles.
LATTICE POINT: It is the position in the unit cell. A crystal
structure is obtained by attaching a constituent particle to each of
the lattice points.
BASIS: The constituent
particles that are attached to the
lattice points are called as the
basis of the crystal lattice.
Crystal is the structure that
results by attaching a basis to
each of the lattice points.
UNIT CELL: The smallest repeating structural unit of a crystalline
solid is called unit cell.
TYPES OF UNIT CELL :
I. Primitive or simple cubic unit cell
II. Body centered unit cell
III. Face centered unit cell
IV. Base centered unit cell

1. PRIMITIVE OR SIMPLE CUBIC UNIT CELL (SC)

I. In simple cubic unit cell, there are eight particles at 8 corners of
unit cell.
II. Every particle at the corner of unit cell is shared by 8
neighbouring unit cells.
III. Hence each unit cell will contain only 1/8th of the particle at its
corners.
IV. Hence total no. of particles present in simple cubic = 1/8 × 8 =
1 particle
2. BODY CENTRED CUBIC UNIT CELL (BCC)
I. It has one particle at every corner of the cell and in addition to
it, it has one more particle at the centre of its body.
II. Hence total no of particles present in body-centred cubic
structure =1/8 × 8 + 1 = 2 particles

3. FACE CENTRED CUBIC UNIT CELL (FCC)

I. It has one particle at every corner of the cell and in addition to
it, it has particles at the centre of its six faces.
II. Hence total no. of particles presents in FCC structure = 1/8 × 8
+ ½ × 6 =1 + 3 = 4 particles.
PACKING OF PARTICLES IN CRYSTAL LATTICE
COORDINATION NUMBER: The number of neighbouring Spheres
that touch any given sphere is its coordination number.

CLOSED PACKED STRUCTURES:

(A) Close packing in One dimension:

I. In this the spheres are arranged in one row touching one

another.
II. Each sphere in row has 2 neighbouring Spheres.
III. The coordination number of the particles in One dimension is
two.

(B) Close packing in two dimensions:

There are two ways to obtain close packing in two dimensions and
they are
(1) Square close packing:
 I. In this arrangement, spheres are placed one over the other in
such a way that each sphere in a row is placed over another
sphere of another row and so on.
II. This planar two-dimensional arrangement is called AAAA type
of arrangement.
III. Coordination number is 4.
IV. A square is obtained by joining the centres of these four
neighbouring Spheres and therefore this two-dimensional close
packing is called square close packing in two dimensions.

(2) Hexagonal close packing:

I. Firm and closest type of arrangement may be made by

arranging successive rows by placing the crests of spheres of
one row into depression or troughs of the spheres of the next
row. This two-dimensional arrangement is called ABAB type.
II. The coordination no. is 6.
III. A regular hexagon is obtained by joining the centers of these
closest six spheres and therefore this two-dimensional close
packing is called hexagonal close packing in two dimensions.

(C) CLOSE PACKING IN THREE DIMENSIONS:

Stacking of two-dimensional layers gives rise to three-dimensional
crystal structures.
(A) STACKING OF SQUARE CLOSED PACKED LAYERS:
(SIMPLE CUBIC STRUCTURE)

I. In this arrangement, AAAA type layers are placed one over the
other such that all the spheres of the successive layers are
exactly above the spheres of the lower layers.
II. Hence this arrangement is described as `AAAA’ type
arrangement.
III. Its unit cell is primitive cubic unit cell.
IV. Each sphere is surrounded by six spheres, 4 in the layer of the
sphere and one in layer above and one below the layer.
Hence, coordination no. is 6.

(B) STACKING OF TWO HEXAGONAL CLOSED PACKED

LAYERS:

I. Consider two ABAB type planar two-dimensional crystal

structures as shown in figure.
 II. First layer is labelled as A layer and the second layer is labelled
as B layer. Hence this arrangement is called as ABAB type
hexagonal closed packed arrangement.
III. In this the spheres of the first layer are placed into the
depressions of the second layer.
IV. This type of arrangement results in the formation of
TETRAHEDRAL VOIDS and OCTAHEDRAL VOIDS.
TETRAHEDRAL VOIDS:

I. The triangular voids that are covered by the spheres of the

second layer generate tetrahedral void.
II. A tetrahedral void is surrounded by four spheres - three in the
base and one at the top.
III. On joining the centers of the four spheres, a tetrahedron is
formed.
IV. No. of tetrahedral voids = 2 × No. of atoms
OCTAHEDRAL VOIDS:
 I. The overlapping of triangular voids from
the two hexagonal packed layers
together forms an octahedral void.
II. It is surrounded by 6 spheres.4 particles
at the base, 1 particle above and below
each.
III. No. of octahedral voids =No. of particles.
IV. Size of octahedral void > size of
tetrahedral void.

PLACING THIRD HEXAGONAL PACKED LAYER :

This can be done in two ways,
(1) Aligning the spheres of the third layer with the spheres of the
first layer. The resulting pattern of the layers will be ABAB. This
arrangement results in HEXAGONAL CLOSED PACKED structure
(hcp). Examples: Mg, Zn

(2) The third layer may be placed over the second layer such that
all the spheres of the third layer fit in the octahedral voids. The third
layer is therefore called C layer. If the stacking of layers is
continued then it is found that every fourth layer is same as the first
layer. Hence this pattern of stacking hexagonal closed packed
layers is called ABCABC type. This arrangement results in CUBIC
CLOSE PACKED structure (ccp) or (fcc). Examples: Cu, Ag
 PACKING EFFICIENCY:
Packing efficiency = Volume occupied by particles in unit cell × 100
Total volume of unit celldgdsggdgdsgg
(1) Packing efficiency of metal crystal in simple cubic lattice (SCC)
STEP 1: Radius of sphere (Particle)

From above fig. it is evident that

a = 2r or r = a/2 ---> (1) where
r = radius of atom
a = edge length of unit cell
STEP 2: Volume of sphere
Volume of sphere (particle) = (4/3×∏) r3
From equation (1) we get,
Volume of one particle = (4/3×∏) (a/2)3 =4/3 ×∏×a3/8 =∏a3/6 →(2)

STEP 3 :Total volume of particles

Simple cubic unit cell contains only one particle, therefore from
equation (2) we get
Volume occupied by particle in unit cell =∏a3/6

STEP 4:Packing efficiency

Packing efficiency = Volume occupied by particles in unit cell × 100
Total volume of unit celldgdsggdgdsgg
= ∏a3/6 ×100 = 100 ∏/6 = 100 ×3.142 = 52.36%
a3 6
Volume occupied = 52.36%
Empty space (void volume) =100-52.36 =47.64%
(2) Packing efficiency of metal crystal in body centred cubic
lattice (BCC)
STEP 1 : Radius of sphere (particle)
Volume occupied = 68%
Empty space (void volume) = 100 - 68 =32%
CRYSTAL DEFECTS OR IMPERFECTIONS:
The irregularities in the arrangement of constituent particles of a
solid crystal are called defects or imperfections.

There are three types of defects and they are - point defects, line
defects and plain defects. Only point defects will be discussed.
POINT DEFECTS:
These defects are produced due to irregularities produced in the
arrangement of basis at lattice points in crystalline solids.
There are three major point defects,
1. STIOCHIOMETRIC POINT DEFECTS
2. IMPURITY DEFECTS
3. NONSTIOCHIOMETRIC POINT DEFECTS
 STIOCHIOMETRIC POINT DEFECTS: In this the stoichiometry
remains unchanged, i.e. The ratio of number of atoms or number
of cations and anions of a compound remains the same as
represented by its chemical formula.
These are of four types:
A. VACANCY DEFECT
B. SELF INTERSTITIAL DEFECT
C.SCHOTTKY DEFECT
D.FRENKEL DEFECT

(A) VACANCY DEFECT :

I. In vacancy defect, a particle is missing from its regular site in
the crystal lattice.
II. Thus, some of the lattice sites are vacant because of missing
particles.
III. The mass of the substance decreases and volume remains
unchanged. As a result, the density of the substance
decreases.

(B) SELF INTERSTITIAL DEFECT :

When some particles of a crystalline elemental solid occupy
interstial sites in the crystal structure, it is called self interstitial
defect. This defect occurs in two ways,
First, an extra particle occupies an empty interstitial space in the
crystal structure.

This extra particle is same as those already present at the lattice

points. The extra particle increases the total mass of the substance
without increasing the volume. Hence its density increases.
Second, in an elemental solid a particle gets shifted from its original
lattice point and occupies an interstitial space in the crystal as
shown in the figure.

This defect is the combination of vacancy and interstitial defect.

The density of the substance remains unchanged.
(C) SCHOTTKY DEFECT:
I. In an ionic solid, equal number of cations and anions are
missing from their regular positions in the crystal lattice
creating vacancies.
 II. Vacancy created by a loss of cation is always accompanied
by a vacancy formed by a loss of anion.
III. There exist two holes per ion pair lost. Such a paired cation
and anion vacancy defect is a SCHOTTKY DEFECT.

CONDITIONS FOR THE FORMATION OF SCHOTTKY DEFECT

Schottky defect is found in ionic compounds with the following
characteristics:
I. High degree of ionic character.
II. High coordination number of anion.
III. Small difference between size of cation and anion.

CONSEQUENCES OF SCHOTTKY DEFECT:

i. As the number of ions decreases, mass decreases. However,
volume remains unchanged.
Hence, the density of substance decreases.
ii. As the number of missing cations and anions is equal, the
electrical neutrality is maintained.
(D) FRENKEL DEFECT:
i. Frenkel defect arises when an ion of an ionic compound is
missing from its regular lattice site and occupies interstitial
position between lattice points.
ii. Cations occupy interstitial sites as they are smaller in size.
iii. Smaller cation is displaced from its normal site to an interstitial
site. It, therefore, creates a vacancy defect at its original position
and interstitial defect at its new location in the same crystal.
iv. It’s a combination of vacancy defect and interstitial defect.

CONDITIONS FOR THE FORMATION OF FRENKEL DEFECT:

i. Frenkel defect occurs in ionic compounds with large difference
between the sizes of cation and anion.
ii. Should have low coordination number.

CONSEQUENCES OF FRENKEL DEFECT:

i. The density of solid remains unchanged as no ions are
missing from the crystal lattice.
ii. The crystal as a whole remains electrically neutral.
Example: ZnS, Agcl, AgBr, AgI, CaF2

(3) IMPURITY DEFECT:

Impurity defect arises when foreign atoms, that is atoms different
from the host atoms, are present in crystal lattice.
There are two kinds of impurity defects,
(A) SUBSTITUTIONAL IMPURITY DEFECT:
In this defect, the foreign atoms are found at the lattice points in
place of host atoms.
 Example: Brass is an alloy of Cu and Zn. In brass, host Cu
atoms are replaced by impurity of Zn atoms.

VACANCY THROUGH ALIOVALENT IMPURITY:

Vacancies are created by the addition of impurities of aliovalent

ions (i.e. ions with oxidation state different from that of host ions) to
an ionic solid.
(B) INTERSTITIAL IMPURITY DEFECT:

In this defect, the impurity atoms occupy interstitial spaces of

lattice structure. For example, in steel, Fe atoms occupy normal
lattice sites. The carbon atoms are present at interstitial spaces.
(4) NONSTOICHIOMETRIC DEFECTS:
This type of defect arises, when the ratio of number of atoms of
one kind to that of other kind or the ratio of number of cations to
anions becomes different from that indicated by its chemical
formula.
These are of two types,
(A) METAL DEFICIENCY DEFECT:
 I. This defect is possible only compounds of metal that show
different oxidation states.
II. In some crystals, the positive metal ions are missing from
their original lattice sites.
III. The extra negative charge is balanced by the presence of
cation of the same metal with higher oxidation state than that
of missing cation.
IV. The composition of NiO then becomes Ni0.97O1.0

(B) METAL EXCESS DEFECT:

There are 2 types of metal excess defects
(1) A NEUTRAL ATOM OR AN EXTRA POSITIVE ION
OCCUPIES INTERSTITIAL POSITION:
I. Example: ZnO
II. In first case in ZnO lattice one neutral Zn atom is present in
the interstitial space as shown

lll. In the second case, when ZnO is heated it decompose as

ZnO → Zn2+ + ½ O2 + 2e-
The excess Zn2+ ions are trapped in interstitial site in the lattice.
The electrons also occupy interstitial sites
In both the cases, nonstoichiometric formula of ZnO is
ZnO1+xO1.0
 (2) BY ANION VACANCIES (COLOUR OR F-CENTRES)
I. This type of defect imparts colour to the crystal
II. For example, NaCl crystal is heated in the atmosphere of
sodium vapour, Na atoms are deposited on the crystal surface.
III. Cl- ions diffuse to the surface creating vacancies at their regular
sites.
IV. These Cl- ions combine with Na atoms on the surface to form
NaCl, by releasing electron from Na atom. Na + Cl- → NaCl + e-
V. These electrons diffuse from the surface and occupy vacant
sites.
VI. The anion vacant sites occupied by electrons are F- centres or
colour centres.
VII. NaCl shows yellow colour due to the formation of F-centres. The
crystal of NaCl has excess of Na. The nonstoichiometric formula
of NaCl is Na1+xCl1.0