Download SOLIDE STATE Introduction : Crystalline and

1
SOLIDE STATE
Introduction :
Five states of matter – solid, liquid, gas, plasma and BEC (Bose-Einstein condensate)
Solid states chemistry – study of structure of solids and their properties
Solid substance – Definite shape-mass-volume. If we study variation in properties of
solids by carrying out changes in it, we can have many uses of solids. E.g. substance used
in super conductors and plastics for packing can be prepared by this way.
Solids differ from liquid and gas in one aspect that is fluidity. Hence liquid and gases are
called fluids.
But in solids, the ions, molecules are in some definite form and arranged in a systematic
manner. Hence, they have definite shape and so it is not a fluid.
Solids are of two types – Crystalline and Amorphous.
In a crystalline solids, arrangement of atoms or ions is systematic or regular; while in
amorphous solids arrangement of constituent particles is irregular.
We will study in this unit, the arrangement of atoms or ions and their relationship with
their properties and what changes we can make in these properties ( i.e. in arrangement )
so that innumerable solid substances with desired and useful properties can be obtained.
Crystalline and Amorphous Solid Substances :
1
Solids can be classified as crystalline or amorphous on the basis of the nature of order of
arrangement present in the arrangement of their constituent particles.
Crystalline solid – Usually consist of large number of small crystals. Each small crystal
units have a definite characteristic geometrical shape.
In a crystal, arrangement of constituent particles (atoms, molecules, ions) is ordered. It
has long range ordered structure i.e. regular pattern of arrangement of particles which
repeats itself periodically over the entire crystal. E.g. NaCl, Quartz etc.
Amorphous solid – Usually consists of particles of irregular shape. The arrangement of
constituent particles (atoms, molecules or ions) in such a solid has only short range order.
In such an arrangement, a regular and periodically repeating pattern is observed for short
distance only.
Such short range ordered arrangements are scattered and disordered.
For example… Glass, rubber and plastic are typical examples of amorphous solids.
Quartz and Quartz glass are the two
structures of same substance where Quartz
is crystalline (fig - a) and Quartz glass is
amorphous (fig – b).
Both have identical composition, yet in the
case of quartz glass (b) there is no long
range order (i.e. amorphous).
Due to the difference in the arrangement of
the constituent particles, the two types of
(a)
(b)
solids differ in their properties.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Differences between Crystalline and Amorphous Solids :
1.
2.
3.
4.
5.
6.
7.
8.
Shape :
Definite shape and possessing characteristics geometry
Irregular shape
Melting point :
Definite and sharp melting point which is the characteristic of the crystal of the solid
Becomes soft gradually during the small temperature range i.e. have no definite and
sharp melting point
Fusion enthalpy :
Definite and characteristic fusion enthalpy
No definite and characteristic fusion enthalpy
Cleavage Property :
Divided into two parts by cutting the crystal with sharp cutting tool like knife. The
surface of the new part obtained is plain and soft i.e. it is an original one
Divided into two parts by cutting the crystal with sharp cutting tool like knife; but the
surface of new part obtained is not as the original one. i.e. it is irregular
Nature :
True solid
Pseudo solid or super cooled liquids(Highly viscous liquid)
Order of arrangement of constituent particles :
The order is maintained till a long range
The order is maintained in a short range
Effect of Temperature
The graph (temperature → time) obtained on cooling after heating is not a curvature. The
temperature remains definite during crystallization
The graph (temperature → time) obtained on cooling after heating is a curvature.
Temperature range is obtained during crystallization.
Properties:
Their properties like electrical conductivity, thermal
conductivity, mechanical strength and refractive
index are different in different direction –
Anisotropic in nature.
Their properties like electrical conductivity, thermal
conductivity, mechanical strength and refractive
index are same in all direction – Isotropic in nature.
Classification on the basis of Binding Forces :
(1)
2
Most of the solid substances are crystalline viz. metals like copper, iron, silver, etc., non
metals like phosphorus, sulphur, Ionic solids like sodium chloride, potassium chloride and
molecular solids like naphthalene.
The classification of crystalline solids on the basis of intermolecular attraction forces
involved in them, can be made into following four types…
Molecular solids :
Non-polar molecular solids :
Polar molecular solids :
Molecular solids containing H-bond :
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(2)
(3)
(4)
Ionic Solids :
Metallic Solids :
Covalent Solids :
(1)
Molecular solids :
In molecular solids the constituent particle present in them is molecule.
Non-polar Molecular Solids :
This type of solids includes elements like Ar, He or molecules formed by non-polar
covalent bonds like dihydrogen, dichlorine, dibromine, diiodine etc.
Possess weak Dispersion forces or London forces and hence low melting points
Soft - non conductor of electricity
They are in liquid or gaseous state at normal temperature and pressure.
Polar Molecular Solids :
These solids generally possess polar covalent bond. E.g. SO2, NH3, CS2 and CHCl3 etc.
Molecules are bound by strong polar-polar interactions
Soft and non conductor of electricity
Melting points are higher than those of non-polar molecular solids
Exist in liquid or gaseous state at normal temperature and pressure
e.g. solid SO2 and solid NH3
Molecular Solids Containing Hydrogen Bond :
Atoms like H form polar covalent bond by combining with electronegative atoms like F, O
or N e.g. ice
Non conductor of electricity
Volatile liquids or soft solids at room temperature and pressure
In molecule of ice, 4 molecules of water are attracted by H-bond
It gets separated from the hydrides of other elements of the same group because of H bond
(2)
Ionic Solids :
Constituent particles are ions.
Such solids are formed by three dimensional arrangements of cations and anions bound by
strong columbic (electrostatic) forces.
Hard and brittle
Melting points and boiling points are higher
Since ions are not free to move in solid state, they are non conductor of heat and electricity
in solid state.
Their aqueous solution or molten state can conduct electricity.
(3)
Metallic Solids :
Possess solid state and constituent atoms are arranged in systematic way.
Metals are orderly collection of positive ions (positively charge kernels) surrounded by and
held together by a sea of free electrons.
Electron sea model of metal
Hard and brittle
Freely moving delocalized electrons are mobile and are evenly spread out throughout the
crystal – hence metals are good conductors of heat and electricity
Metals have luster and in some cases have colours
Ductile and malleable
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(4)
Covalent or Network Solids :
Crystalline solids. Giant molecules – due to formation of covalent bonds between adjacent
atoms throughout the crystal
Covalent bonds are strong and directional in nature, therefore atoms are held very strongly
at their position.
Hard and brittle. Extremely high melting points – may decompose before melting.
Non conductor of electricity (generally)
For example… Diamond, graphite, silicon carbide etc.
Graphite is soft & good conductor of electricity. Structure of graphite – sp2 hybridized
carbon, free electron, layered structure and good solid lubricants
Diamond is hard and non conductor of
electricity. Structure of diamond – sp3
hybridized carbon, no free electron, tetrahedral
structure and extremely hard.
Thus, it can be concluded that in the two
allotropes of the same element, if intermolecular
forces and hybridization formed are different,
there is a great change in their properties.
Thus, as a summary…
Different types and Properties of Crystalline solids
Type of Solid
Constituen Attraction
Example Physical Meltin Electrical
t Particles
Forces
Mature
g Point Conductivity
Molecular Solid Molecules Dispersion
Ar,CCl4,
Soft
Very
Non-conductor
Non Polar
or London
H2,I2,CO2
low
Polar
forces
Molecules DipoleHCl,SO2, Soft
Low
Non-conductor
Hydrogen
Dipole inter NH3
bondPossessing
attraction
Molecules Hydrogen
H2O(ice) Hard
Low
Non-conductor
bond
Ionic Solid
Ions
Coulombic
NaCl,
Hard but High
Solid state, nonor
MgO,
brittle
conducting but
molten or aqueous
Electrostatic ZnS,
solution conductor
CaF2
Positive
Compa
Hard but
ion in sea
r-Metallic
Fe, Ca,
ductile
Conductors in solid
of
atively
Metallic Solid
bond
Mg, Ag
and
and molten states
delocalized
very
malleable
electrons
high
SiO2
Non Conductor
(Quartz)
Covalent or
Covalent
Very
SiC(Carboru
Atoms
Hard
Network Solid
bond
high
-ndum)
C(Diamond)
Conductor
C(Graphite)
(Exception)
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Crystal Lattice :
The smallest particle of a substance is known as atom or molecule.
Similarly, the smallest portion which describe crystal of solid is called the unit cell. This
smallest portion possessing the chief characteristics of a crystalline solid.
Such unit cells when arranged with each other in three dimensional directions, the
formation of crystal results.
This type of arrangement is called crystal lattice.
If constituent particles of solid
crystal are assumed to be
spherical then in crystal
formation this particles are
arranged as under.
In crystalline solid, each type of crystal is described by crystal lattice OR space lattice.
(network OR pattern)
A crystal lattice is defined as a pattern of points which describe the arrangement of
constituent particle (atoms, molecules, ions) in a crystal.
Each point represents the position of centre of the constituent particle.
What is unit cell ?
A crystal is made up of many small repeat units, stacked together in three dimensions.
These units are called unit cells.
The unit cell shows all the characteristics as well as geometrical shape of crystal.
There are 14 kinds of unit cell. Out of 14 types of unit cells, three unit cells have cubic
symmetry.
Thus, the systematic three dimensional arrangement of points in space is called crystal
lattice or space lattice.
There are seven different crystal systems and in which there are 14 different possibilities of
such three dimensional lattices (arrangement); which are known as Bravais lattice. (i.e. 14
kinds of unit cell)
3.
Some of the Characteristics of Crystal lattice are…
Each point in a lattice is called lattice point or lattice site.
Each point in a crystal lattice represents one constituent particle which may be an atom, a
molecule (group of atoms) or an ion.
Lattice points are joined by straight lines to bring out the geometry of the lattice.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
1.
2.
(1)
(2)
The Characteristics of Unit cell are…
Its dimensions along the three edges, a, b and c. These edges may or may not be mutually
perpendicular.
Angles between the edges, α (i.e. between edges
a
b and c), β (i.e. between edges a and c) and γ (i.e.
between edges a and b).
Thus, a unit cell is characterized by six
b
parameters… i.e. edges a, b and c; angles α, β
and γ
Types of Unit cell :
Unit cells are broadly divided into two categories…
Primitive Unit Cells
Centered Unit Cells
Body – Centered Unit Cells
Face – Centered Unit Cells
End – Centered Unit Cells
Primitive Unit Cells :
When constituent particles are present only
on the corner positions of a unit cell, it is
called as primitive unit cell.
c
(1)
(2)
(a)
(b)
(c)
(1)
(2)
(a)
(c)
(a)
(b)
(c)
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a
Centred Unit Cells :
When a unit cell contains one or more constituent particles present at positions other than
corners in addition to those at corners, it is called a centred unit cell.
Centered unit cells are of three types…
Body – Centered Unit Cells
(b)
Face – Centered Unit Cells
End – Centered Unit Cells
Body-Centered Unit Cells :
Such a unit cell contains one
constituent particle (atom, molecule or
ion) at its body-center besides the ones
that are at its corners.
Face-Centered Unit Cells :
Such a unit cell contains one
constituent particle present at the
center of each face, besides the ones
that are at its corners.
End-Centered Unit Cells :
In such a unit cell, one constituent
particle is present at the center of
any two opposite faces besides the
ones present at its corners.
End-centred
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
b
g
Seven Primitive Unit Cells and their Possible Variations as Centered Unit
Cells :
Crystal
System
Possible
Variations
Primitive
Body centred
Face centred
Axial Distance or
Distance of Edge
Axial Angle
Example
a=b=c
α = β = γ = 90°
NaCl, ZnS
(zinc blende), Cu
Primitive
a=b=c
α = β = γ ≠ 90°
Calcite (CaCO3),
Cinnabar (HgS)
Possible
Variations
Primitive
Body centred
Face centred
End centred
Primitive
End centred
Axial Distance or
Distance of Edge
Axial Angle
Example
a≠b≠c
α = β = γ = 90°
Rhombic sulphur,
KNO3
BaSO4
a≠b≠c
α = γ = 90°
β ≠ 120°
Triclinic
Primitive
a≠b≠c
α ≠ β ≠ γ ≠ 90°
Crystal
System
Possible
Variations
Axial Distance
or
Distance of Edge
Axial Angle
Tetragonal
Primitive
Body centred
a=b≠c
α = β = γ = 90°
Hexagonal
Primitive
a=b≠c
α = β = 90°
γ = 120°
Cubic
Rhombohedral
Or Trigonal
Crystal
System
Orthorhombic
Monoclinic
Monoclinic sulphur,
Na2SO4.10H2O
K2Cr2O7,
CuSO4.5H2O,
H3BO3
Example
White tin, SnO2,
TiO2, CaSO4
Graphite, ZnO,
CdS
What is Close Packing ?
If constituent particles of solid crystal are assumed to be spherical then in crystal formation
this particles are closely packed together. This is known as closed packing structure. The
empty spaces in this structure are known as voids OR holes.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
What is co-ordination number ?
The co-ordination number of each sphere (atom, molecule, ion) is the number of nearest
neighbours immediately surrounding each such sphere.
“Co-ordination number of an atom is the number of other atoms or groups directly linked
to that atom.”
Different types of three dimensional closed packing of constituent particles in (metallic)
crystal :
In three dimensional closed packing, there are four possibilities of arrangement if particles
are assumed to be uniformly sized spheres.
1)
Simple cubic packing
2)
Body centered cubic packing (BCC)
3)
Hexagonal close packed arrangement (HCP)
Cubic close packed arrangement (FCC)
4)
(1)
Simple Cubic Packing :
In simple cubic packing each sphere is touched by six neighbours− four in its own layer,
one above and one below.
The stacking (packing) pattern is thus a−a−a−a.
Each sphere has co-ordination number 6 − four neighbours in one plane, one above and
one below.
52% of the available volume is occupied by the spheres in simple cubic packing.
8
In simple cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell.
Each atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each
cube.
Now there are 8 corners or atoms.
Therefore, Number of atoms present in each unit cell of Simple cube…
= 8 corner atoms × (1/8) atom per unit cell =
1 atom
Thus, Simple cubic unit cell has one atom per unit cell.
52% of the available volume is occupied by the spheres in simple cubic packing.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
In simple cubic lattice, the atoms are only at the corners.
The particles touch each other along the edges.
(as shown in figure)
∴
Relation between edge length of a cube ‘a’ and radius of each particle ‘r’ will be …
a=2r
3
∴
Volume of unit cell (cube) a = (2 r)3 = 8 r3
Each unit cell possess only one atom.
4
∴ Volume occupied by one atom = πr 3
3
Volume of one atom
∴ Packing efficiency =
× 100
Volume of unit cell
4 3
πr
3
=
× 100
8 r3
π
=
× 100
6
(2)
9
= 52.36 %
Body Centered Cubic Packing :
In body centered cubic packing the spheres in the first layer ‘a’ remains slightly away from
one another. The spheres in ‘b’ layer fit into the depression between spheres in a−layer. The
third layer is arranged on second layer ‘b’ exactly the same way as layer − a.
The stacking (packing) pattern is thus a−b−a−b.
Each sphere has co-ordination number 8 − four A A A A A
neighbours above and four below.
B
B B B
68% of the available volume is occupied by the A A A A A
B B B B
spheres in body centered cubic packing.
A
A A
A A
Iron , Sodium and 14 other metals crystallize in
this way. This structure is also known as Body
centered cubic (BCC) packing.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
In Body centered cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell. Each
corner atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each cube.
In addition, one atom is located at the center of the unit cell, which is not shared by any other
cube.
Therefore,
Number of atoms present in each unit cell of Body centered cube
= ( 8 corner atoms × (1/8) atom per unit cell ) + 1 center atom
= 2 atom.
Thus, Body centered cubic unit cell has two atom per unit cell.
68% of the available volume is occupied by the spheres in body centered cubic packing.
As shown in figure, the atom in the centre of body touches two other atoms diagonally present
at the corner of body diagonal.
∴
For, ∆ AFD, ∠ ADF is right angle…
AF2 = AD2 + FD2
Where,
AF = c = Body diagonal
FD = b = Face diagonal
AD = a = Edge length
∴
c2 = a2 + b2
But, as derived in FCC unit cell… b2 = 2a2
∴
c2 = a2 + 2 a2
∴
c2 = 3 a2
Now, as shown in figure…Body diagonal c = 4 r
∴ c= 3a=4r
4
r
3
4
∴ Volume of unit cell (cube) a 3 = (
r)3
3
∴ a=
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Each bcc unit cell possess only two atoms.
4
∴ Volume occupied by two atoms = 2 × πr 3
3
Volume of two atoms
∴ Packing efficiency =
× 100
Volume of unit cell
4
2 × πr 3
3
=
× 100
4 3
(
r)
3
π 3
× 100
8
= 68 %
Hexagonal Close Packed Arrangement :
In Hexagonal close packed arrangement there are two alternating hexagonal layers a−b−a−b.
The a−b layers offset from each other so that the spheres in one layer fit in the small triangular
depression of neighbouring layer.
The stacking pattern is thus a−b−a−b .
Each sphere has co-ordination number 12 − six neighbours in the same plane, three above and
three below .
74% of the available volume is occupied by the spheres in hexagonal close packed
arrangement.
Zinc, Magnesium and 19 other metals crystallize in this way.
=
(3)
Unit cell of Hexagonal close pack
structure is not in syllabus.
Only cubic unit cells are in the
syllabus.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(4)
Cubic Close Packed Arrangement :
In Cubic close packed arrangement there are three alternating hexagonal layers a−b−c−a−
b−c. The a−b layers offset from each other so that the spheres in one layer fit in the small
triangular depression of neighbouring layer. The third layer is offset from both a & b
layers.
The stacking pattern is thus a−b−c−a−b−c.
Each sphere has co-ordination number 12 − six neighbours in the same plane, three above
and three below.
74% of the available volume is occupied by the spheres in cubic close packed arrangement.
Silver, Copper and 16 other metals crystallize in this way. This structure is also known as
Face centered cubic (FCC) packing.
In Face centered cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell.
Each atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each
cube. In addition there are six atoms at the faces of the cube and each is shared by two unit
cells. So atom present at each face contributes ½ to each unit cell.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Therefore,
Number of atoms present in each unit cell of Face centered cube…
= ( 8 corner atoms × (1/8) atom per unit cell ) + ( 6 atoms at faces × ½ atom per unit cell)
= 4 atom.
Thus, Face centered cubic unit cell has four atom per unit cell.
74% of the available volume is occupied by the spheres in cubic close packed arrangement.
As shown in figure, the atom in the centre of body touches two other atoms diagonally
present at the corner of face diagonal.
∴
In ∆ ABC, ∠ ABC is right angle…
AC2 = AB2 + BC2
Where, AC = b = Face diagonal
AB = BC = a = Edge length
2
2
2
b =a +a
∴
∴ b
=
2a
Now, as shown in figure…Face diagonal ‘b’ = 4 r
∴ b= 2a=4r
∴ a=2 2 r
∴ Volume of unit cell (cube) a 3 = (2 2r)3
Each FCC unit cell possess four atoms.
4 3
πr
3
Volume of four atoms
∴ Packing efficiency =
× 100
Volume of unit cell
4
4 × πr 3
3
=
× 100
4 3
(
r)
3
∴ Volume occupied by four atoms = 4 ×
=
π 2
× 100
6
= 74 %
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
NOTE :
In hcp & ccp both arrangements coordination number of sphere is 12. Hence close packing
is equally efficient in both these types.
Therefore, in hcp also…
∴ Packing efficiency =
Volume of four atoms
× 100
Volume of unit cell
π 2
× 100
6
= 74 %
=
Density of Unit Cell :
Suppose, edge length of a unit cell of a cubic crystal determined by X-ray diffraction is ‘a’;
‘d’ is the density of the solid substance and ‘M’ is the molar mass then…
In case of cubic crystal…
Volume of unit cell = a3
Mass of the unit cell = no. of atoms in the unit cell × mass of each atom
=z×m
(Here ‘z’ is the number of atoms present in one unit cell and ‘m’ is the mass of a single
atom)
Mass of an atom present in the unit cell (m) = M/NA Where, M is molar mass and NA is
Avogadro constant.
Therefore density of the unit cell is…
Density of unit cell
Mass of unit cell
Volume of unit cell
z×m
a3
z×M
a3 × NA
=
=
∴
d
=
Thus, as a summary…
Structure
Simple cubic
Body centered cubic
Hexagonal close packed
Cubic close packed
Stacking
Co-ordination
Space used %
Unit cell
pattern
Number
6
52
Primitive cubic
a− a− a− a
8
68
Body centered cubic
a−b−a−b
12
74
Non-cubic
a−b−a−b
12
74
Face centered cubic
a−b−c−a−b−c
Type of Cell
Simple Cubic
Body Centered Cubic (BCC)
Face Centered Cubic (FCC)
End Centered Cubic
14
No. of Atoms at
Corners
8 × (1/8) = 1
8 × (1/8) = 1
8 × (1/8) = 1
8 × (1/8) = 1
No. of Atoms in
Faces
0
0
6 × (1/2) = 3
2 × (1/2) = 1
No. of Atoms in
Total
Center of Cube
0
1
1
2
0
4
2
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Tetrahedral hole and Octahedral hole :
In cubic closed packed arrangement there are two types of holes.
Tetrahedral holes :
Holes which are directly beneath second layer of spheres and are surrounded by 4 spheres
are called tetrahedral voids. OR The hole produced when a sphere is placed on the three
spheres in one plane giving tetrahedral arrangement is called tetrahedral hole OR void.
Octahedral holes :
The holes which are not covered by second layer and are surrounded by six spheres are
called octahedral holes OR voids. OR The hole produced when two spheres are placed one
above and other below the central hole of the four spheres in a plane and in mutual contact
is called octahedral void OR hole.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
CRYSTAL STRUCTURE OF IONIC SOLIDS
Relation between Size of ions and Co-ordination number and Stability of Ionic crystal :
The number of spheres that can be arranged around a central sphere depends on the size of
the central sphere.
Cations are generally smaller than anions. In a packing arrangement of anions, holes are
produced in which cation will fit.
As the size of cation increases, more anions
having same size can be accommodated
around cation. i.e. co-ordination number of
cation increases.
Hence stability of ionic crystal increases.
Relationship between co-ordination number, radius ratio and crystal lattice structure :
The co-ordination number of each sphere (atom, molecule, ion) is the number of nearest
neighbors immediately surrounding each such sphere.
In ionic solids each ion is surrounded by definite number of oppositely charged ions which
is called co-ordination number of that ion.
Co-ordination number generally depends on the size of cation. (Which is present in the
hole)
It is also related to the radius ratio. The ratio of radius of cation to radius of anion is known
as radius ratio.
radius of cation r+
Radius Ratio =
radius of anion r−
As the size of cation decreases (i.e. as the radius ratio decreases) the space around the
central cation also decreases hence less anion can be accommodated around it. Thus, coordination number of cation decreases.
For example, in CsCl, NaCl and ZnS the size of cation decreases in following order… Cs+ >
Na+ > Zn2+. Therefore radius ratio also decreases in following order. CsCl > NaCl > ZnS.
(Hence their co-ordination number decreases… i.e. 8 > 6 > 4 )
Note :
Radius ratio in CsCl – 0.92; in NaCl – 0.525; in ZnS – 0.407
16
Geometry of crystal lattice also changes as radius ratio changes.
Radius ratio rc / ra
Co-ordination
Arrangement of anions around cations
number of cation
i.e. r+ / r−
3
0.15 to 0.22
Triangular
4
0.22 to 0.41
Tetrahedral (ZnS)
6
0.41 to 0.73
Octahedral, Face centered cube (FCC), NaCl
8
0.73 and above
Octahedral, Body centered cube (BCC), CsCl
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Sodium Chloride (NaCl) :
Coordination number : Na+ - 6 and Cl− - 6
No. of formula unit in one unit cell : 4
For NaCl type arrangement : 2r+ + 2r− = a =
Edge length
Cesium Chloride (CsCl) :
Coordination number : Cs+ - 8 and Cl− - 8
No. of formula unit in one unit cell : 1
For CsCl type arrangement : 2r+ + 2r− = c =
Body diagonal
Zinc Blend (ZnS) :
Coordination number : Zn2+ - 4 and S2− - 4
No. of formula unit in one unit cell : 4
Fluorite Structure (CaF2) :
Coordination number : Ca2+ - 8 and F− - 4
Ca2+ ions forms ccp lattice and F− in
tetrahedral hole
No. of formula unit in one unit cell : 4
Antifluorite Structure (Na2O) :
Coordination number : Na+ - 4 and O2− - 8
O2− ions forms ccp lattice and Na+ in
tetrahedral hole
No. of formula unit in one unit cell :
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Imperfections OR Defects in Solids :
All crystalline solids have short range as well as long range order in the arrangement of
their constituent particles, yet crystals are not perfect.
Any kind of irregularities from perfectly ordered arrangement of constituent particles in
crystals is called “imperfection” or “defect”.
Usually a solid consists of an aggregate of large number of small crystals. These small
crystals have defects or imperfection in them.
This happens when crystallisation process occurs at fast or moderate rate.
Single crystals are formed when the process of crystallisation occurs at extremely slow rate
(which is quite impossible). Even these crystals are not free from defects.
Thus, defects are basically irregularities in the arrangement of constituent particles.
The perfectly pure crystalline state is observed only at 0 K (i.e. at −273 °C).
The defects may also arise due to the heat absorbed by the crystals from the surroundings
(i.e. due to increase in temperature) or due to the presence of impurities in the crystals.
It is not possible to explain many properties of solids such as the mechanical strength or
electrical conductivity etc. in terms of pure structure alone.
Imperfections not only modify the properties but also sometimes impart new properties to
the solids.
Broadly speaking, the defects are of two types…
(1) point defects and (2) line defects.
Point defects are the irregularities or deviations from ideal arrangement around a point or
an atom in a crystalline substance.
Whereas the line defects are the irregularities or deviations from ideal arrangement in
entire rows of lattice points.
These irregularities are called crystal defects.
We shall confine our discussion to point defects only.
Types of Point Defects :
(C)
Point defects can be classified into three types…
Stoichiometric Defects :
(1)
Vacancy Defect - Schottky Defects
(2)
Interstitial Defect - Frenkel Defects
Non-stoichiometric defects
(1)
Metal Excess Defect
(a)
Metal excess defect due to anionic vacancies
(b)
Metal excess defect due to the presence of extra cations
(2)
Metal Deficiency Defect
(a)
Metal deficiency defect due to cationic vacancies
(b)
Metal deficiency defect due to the presence of extra anions
Impurity Defects
(A)
Stoichiometric Defects :
These are the point defects that do not disturb the stoichiometry of the solid.
If imperfections in the crystal are such that the ratio between the cations and anions
remains the same as represented by the molecular formula, i.e. stoichiometry of the solid is
not disturbed, the defects are called “Stoichiometric defects”.
They are also called intrinsic or thermodynamic defects.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(A)
(B)
(1)
Basically these are of two types, vacancy defects and interstitial defects.
Vacancy Defect :
When some of the lattice sites are vacant, the crystal is said to
have vacancy defect.
This results in decrease in density of the substance. This defect
can also develop when a substance is heated.
This type of vacancy defects is generally shown by non-ionic
solids.
Whereas, Ionic solids must always maintain electrical neutrality. Hence, rather than simple
vacancy defect, this type of defect in Ionic solids known as Schottky defects.
Schottky Defect :
It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the
number of missing cations and anions are equal.
Schottky defect is shown by ionic substances in which the cation and anion are of almost
similar sizes and having high coordination number. e.g. NaCl, KCl, CsCl and AgBr.
Number of such defects in ionic solids is quite significant.
For example, in NaCl there are approximately 106 Schottky
pairs per cm3 at room temperature.
In 1 cm3 there are about 1022 ions. Thus, there is one Schottky
defect per 1016 ions.
Effect on density : As the number of ions decreases as a
result of this defect, the mass decreases whereas the volume
remains the same. Hence, like vacancy defect, the density of
the solid decreases.
(2)
Interstitial Defect :
When some constituent particles (atoms or molecules) occupy an interstitial site, the
crystal is said to have interstitial defect.
This defect results in the increase in the density of the substance
(because mass increases but volume remains the same).
This type of interstitial defects is generally shown by non-ionic
solids.
In ionic solids interstitial defect is known as Frenkel defect.
Frenkel Defect :
This defect is shown by ionic solids. The smaller ion (usually cation) is dislocated from its
normal site and it occupies interstitial site.
It creates a vacancy defect at its original site and an
interstitial defect at its new location.
Frenkel defect is also called dislocation defect.
It does not change the density of the solid.
Frenkel defect is shown by ionic substance in which there is
a large difference in the size of ions and having low
coordination number, for example, ZnS, AgCl, AgBr and AgI
due to small size of Zn2+ and Ag+ ions.
It is important to note that AgBr shows both, Frenkel as well
as Schottky defects.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Some other consequences of Schottky and Frenkel defects :
Density of the crystals, having Schottky defect, decreases.
Solids having these defects conduct electricity to a small extent by an ionic mechanism.
Crystals having these defects have ‘holes’ due to the absence of ions in certain lattice
points. When electric current is applied, a nearby ion moves from its lattice site to occupy a
‘hole’. This creates a new ‘hole’ and another nearby ion moves into it and so on. This
process continues and a ‘hole’, thereby migrates from one end to the other end. Thus, it
conducts electricity.
Due to presence of holes, the stability (or the lattice energy) of the crystal decreases.
In Frenkel defect, similar charges come closer. This results in the increase of dielectric
constant of the crystals.
Difference between Schottky and Frenkel Defect :
SCHOTTKY DEFECT
FRENKEL DEFECT
1)
It is due to equal number of cations
and anions missing from the lattice
sites.
2)
This results in the decrease in the
density of the crystal.
This type of defect is found in ionic
compounds (like alkali halides)
having high coordination number;
and cations and anions of similar
sizes, e.g. NaCl, CsCl etc.
1)
2)
3)
3)
It is due to the missing of cations
from the lattice sites and these
occupy the interstitial sites.
It has no effect on the density of
the crystal.
This type of defect is found in
crystals with low coordination
number and in which the
difference in the size of cations
and anions is very large, e.g.
silver halides.
(B) Non-Stoichiometric Defects :
(1)
(2)
If imperfections in the crystal are such that the ratio between the cations and anions
becomes different from that represented by the molecular formula, i.e. stoichiometry of
the solid is disturbed, the defects are called “non-stoichiometric defects”.
A large number of non-stoichiometric inorganic solids are known which contain the
constituent elements in non-stoichiometric ratio due to defects in their crystal structures.
These defects are of two types…
Metal Excess Defect
Metal Deficiency Defect
(1)
Metal Excess Defect :
Metal Excess Defect due to Anionic Vacancies :
Alkali halides like NaCl and KCl show this type of defect.
When 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.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
A negative ion missing from its lattice site, leaving a hole which is occupied by an
electron, thereby maintaining the electrical neutrality.
As a result the crystal now has an excess of sodium.
The anionic sites occupied by unpaired electrons are
called F-centers (from the German word
Farbenzenter for colour centre).
They impart yellow colour to the crystals of NaCl.
The appearance of colour is due to excitation of
these electrons (i.e. F-centers electrons) when they
absorb energy from the visible light falling on the
crystals.
Similarly, excess of lithium makes LiCl crystals pink
and excess of potassium makes KCl crystals violet
(or lilac).
This defect is similar to Schottky defect and is found
in crystals having Schottky defects.
Metal Excess Defect due to the Presence of Extra Cations at Interstitial sites :
Metal excess defect may also be caused by an extra cation occupying the interstitial sites
of crystal.
For example, when zinc oxide (white in colour at room temperature) is heated, 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 to
maintain electrical neutrality.
This defect is similar to Frenkel defect and is found in crystals having Frenkel defects.
ZnO(s) ï
ï
ï ï
heating
Zn 2+ + 2 eï +
1
O 2(g)
2
It is important to note that, crystals with either type of metal excess defects contain some
free electrons. Hence such materials acts as semi conductors.
(2)
Metal Deficiency Defect :
Metal Deficiency Defect due to Cationic Vacancies :
There are many solids which are difficult to prepare in the stoichiometric proportion and
contain less amount of the metal as compared to the stoichiometric composition.
For example… FeO which is mostly found with a composition - Fe0.95O. It’s composition
may vary from 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.
This defect occurs when the metal shows variable valency, i.e. in transition metals.
The defect usually occurs due to the missing of a cation from its lattice site and the
presence of the cation having higher charge (e.g., 3+ instead of 2+) in the adjacent lattice
site. E.g. FeO, FeS and NiO
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Metal Deficiency Defect due to the Presence of Extra Anions :
This type of defect involves the presence of an extra anion in an interstitial position, the
electrical neutrality is maintained by an extra charge on a cation.
No example of crystals possessing this defect is known at present because anions are
usually larger in size, so it is improper to expect them to fit into the interstitial sites.
(C)
Impurity Defects :
These defects arise when foreign atoms are present in the crystal..
If foreign atoms are present at the lattice site in place of host atoms then we get
substitutional solid solution.
If foreign atoms are present in the vacant interstitial sites then we get interstitial solid
solutions.
The formation of the substitutional solid solution depends upon the electronic structure
of the impurity while the formation of the interstitial solid solution depends upon the size
of the impurity.
Addition of impurities changes the properties of the crystal.
The process of adding impurities to a crystalline solid so as to change its properties is
called doping.
Impurity Defect in Ionic Solids :
In ionic solids, the impurities are introduced by adding impurity of ions.
If the valency of impurity ions are different than valency of the host ions, vacancies are
created.
For example, If molten NaCl containing a little amount of SrCl2 as impurity is
crystallized, some of the sites of Na+ ions are occupied by Sr2+. (i.e. Na+ ions are
substituted by Sr+2 ion)
Each Sr2+ replaces two Na+ ions to maintain
electrical neutrality. Sr2+ ions occupies the site of
one ion and the other site remains vacant.
The cationic vacancies thus produced are equal in
number to that of Sr2+ ions. These vacancies result in
the higher electrical conductivity of the solid.
Similar defect and behaviour is observed when
CdCl2 is added to AgCl.
(1)
(2)
22
Impurity Defects in Covalent Solids :
In case of covalent solids such as silicon or germanium (i.e. Group 14 elements) have 4
valence electrons.
The impurities added to such covalent solids (elements) may be…
Of elements of group-15 (i.e. having more than 4 valence electrons, like P, As – which
have 5 valence electrons )
OR
Of elements of group-13 (having less than 4 valence electrons, like B, Al, Ga – which have
3 valence electrons)
Thus, the impurities added may be electron rich or electron deficit.
This type of (impurities) defects thus introduced in the crystals are called electronic
defects.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(a)
Doping with Electron Rich Impurities :
Group 14 element like silicon or germanium has 4 electrons in the valence shell.
Hence, it normally forms four covalent bonds with the four neighbouring atoms.
When it is doped with Group 15 element like P or As, the silicon or germanium atoms at
some lattice sites are substituted by atoms of P or As.
Since, these atoms have 5 electrons in the valence shell, after forming four normal
covalent bonds with the neighbouring atoms, the fifth extra electron is free and gets
delocalized.
These delocalized electrons increase the conductivity of silicon or germanium.
As the increase in conductivity is due to negatively charged electrons, the silicon or
germanium crystals doped with electron rich impurities are called n-type
semiconductors.
(b)
23
Doping with Electron Deficit Impurities :
Group 14 element like silicon or germanium has 4 electrons in the valence shell.
Hence, it normally forms four covalent bonds with the four neighbouring atoms.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
24
When it is doped with Group 13 element like B or Al or Ga, the silicon or germanium
atoms at some lattice sites are substituted by atoms of B or Al or Ga.
Since, Group 13 elements have only three valence electrons, they can form only three
covalent bonds with the neighbouring silicon atoms.
Thus, a hole is created at the site where fourth electron is missing. This is called electron
‘hole’ or electron vacancy.
An electron from the neighbouring atom can jump to fill up this electron ‘hole’ but then
an electron hole is created at the site from where electron has jumped.
As it continues, the electron holes will move in opposite direction to that of the flow of
electrons.
Now, when an electric field is applied, the electrons move towards the positively charged
plate and while the electron holes move towards the negatively charged plate as if they
carry positive charge.
Hence, silicon and germanium doped with electron-deficit impurities are called p-type
semiconductors.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Applications of n-type and p-type Semiconductors :
Various combinations of n-type and p-type semiconductors are used for making
electronic devices.
Diode is a combination of n-type and p-type semiconductors and is used as a rectifier.
Transistors are made by sandwiching a layer of one type of semiconductor between two
layers of the other type of semiconductor.
For example…‘npn’ and ‘pnp’ type of transistors are used to detect or amplify radio or
audio signals.
The solar cell is also an efficient photo-diode used for conversion of light energy into
electrical energy.
Germanium and silicon are group 14 elements and therefore, have a characteristic valence
of four and form four bonds as in diamond. A large variety of solid state materials have
been prepared by combination of groups 13 and 15 or 12 and 16 to simulate average
valence of four as in Ge or Si.
Typical compounds of groups 13 – 15 are InSb, AlP and GaAs.
Gallium arsenide (GaAs) semiconductors have very fast response and have
revolutionized the design of semiconductor devices.
ZnS, CdS, CdSe and HgTe are examples of groups 12 – 16 compounds.
In these compounds, the bonds are not perfectly covalent and the ionic character depends
on the electronegativities of the two elements.
Electrical Properties :
(1)
25
Solids exhibit an amazing range of electrical conductivities, extending over 27 orders of
magnitude ranging from 10–20 to 107 ohm–1 m–1.
Solids can be classified into three types on the basis of their conductivities.
Conductors :
The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors.
Metals have conductivities in the order of 107 ohm–1m–1 are good conductors.
They are further classified as metallic conductors and electrolytic conductors.
In the metallic conductors, the flow of electricity is due to flow of electrons (electronic
conductors) without any chemical change occurring in the metal.
The conductivity of metals depends upon the number of valence electrons available per
atom.
In case of electrolytic conductors like NaCl, KCl, etc., the flow of electricity takes place to
a good extent only when they are taken in the molten state or in aqueous solution.
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(2)
(3)
The flow of electricity is due to flow of ions. However, in the solid state, they conduct
electricity only to a small extent which is due to the presence of defects (holes, electrons,
etc.).
Thus, metals conduct electricity in the solid as well as molten state, electrolytes conduct
electricity only in aqueous solution or molten state.
Insulators :
These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm–1m–1.
Semiconductors :
These are the solids with conductivities in the intermediate range from 10–6 to 104ohm–
1m–1.
The Energy Band Model of Metal :
It can be explained on the basis of molecular orbital theory.
A metal lattice has an extremely large number of atoms. The atomic orbitals of these
atoms with the same symmetry and same energy overlap, resulting in the formation of
energy bands. Depending upon the different types of atomic orbitals which overlap,
different energy bands are obtained. These energy bands can be joined together OR can
also be separate.
The highest occupied energy band is called the valence band while lowest unoccupied
energy band is called conduction band.
The energy gap between the top of the valence band and the bottom of the conduction
band is called energy gap − Eg.
26
Sodium Magnesium
In the case of metals, the valence band may be half filled OR there may be an overlapping
between the valence bands and the conduction bands. This makes it possible for the
electrons to go into the vacant conduction bands and hence is responsible for high
electrical conductivity of metals. Thus, metals are good conductors.
In case of Insulators, the energy gap is very large and therefore the vacant conduction
band is not available to the electrons of completely filled valence band.
For example…in diamond the energy gap is very large. Hence electrons cannot move
from valence band into conduction band. This makes diamond as an insulator.
In semi conductors like Si (Silicon) and Ge (Germanium), value of energy gap Eg between
valence band and conduction band is small and increase in temperature gives thermal
energy, hence some of the electrons of the valence band move into the conduction band.
Thus, it shows electrical conductivity and it acts as a semiconductor. (like Si and Ge)
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
Distinction among (a) Metals (b) Insulators and (c) Semiconductors. In each case, an
unshaded area represents a conduction band.
Effect of Temperature on Electrical Conductivity :
Electrical conductivity of metals decreases with increase of temperature because on
heating, the positive ions of the metal atoms start vibrating and produce hindrance in the
flow of electrons.
The electrical conductivity of semiconductors increases
with increase in temperature
because more electrons can jump to the conduction band.
Substances like silicon and germanium which show this type of behaviour are called
intrinsic semiconductors.
In fact, all pure substances that show conductivity similar to that of silicon and
germanium are called intrinsic semiconductors.
The conductivity of intrinsic semiconductors is so low that as such they have no practical
use.
The conductivity can be increased by doping, either by adding electron rich impurities or
electron deficit impurities.
The semiconductors thus obtained are called n-type and p-type semiconductors, as
already discussed.
Conductivity of Transition Metal Oxides :
It is interesting to learn that transition metal oxides show marked differences in their
electrical properties.
For example…TiO, CrO2 and ReO3 behave like metals. Rhenium oxide, ReO3 is like
metallic copper in its conductivity and appearance.
Certain other oxides like VO, VO2, VO3 and TiO3 show metallic or insulating properties
depending on temperature.
It is interesting to point out that the variation in
conductivity is very large even
among similar
compounds.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
1)
2)
3)
Thus,
1)
2)
3)
For example… monoxides of transition metals, all of which possess NaCl structure,
show large variations in electrical properties.
Similar variations are observed among other oxides too.
TiO is metallic, MnO, FeO, CuO etc. are insulators whereas VO is metallic or insulating
depending upon temperature.
CrO2 is metallic, MnO2 is insulator whereas VO2 is
metallic or insulating depending
upon temperature.
ReO3 is metallic whereas VO3 and TiO3 are metallic or insulating depending upon
temperature.
TiO, CrO2 and ReO3 are metallic.
MnO, FeO and CuO are insulators.
VO, VO2, VO3, and TiO3 change from metallic to insulator at a certain temperature.
Similar variation is observed among the sulphides of transition elements.
Magnetic Properties of Solids :
Every substance has some magnetic properties associated with it.
The origin of these properties lies in the electrons. Each electron in an atom behaves like a
tiny magnet.
Its magnetic moment originates from two types of motions (i) its orbital motion around
the nucleus and (ii) its spin motion around its own axis.
Electron being a charged particle and undergoing these motions can be considered as a
small loop of current which possesses a magnetic moment.
Thus, each electron has a permanent spin magnetic moment and an orbital magnetic
moment associated with it.
Thus, each electron may be considered as a small magnet having a resultant permanent
magnetic moment (dipole).
As magnetic moment is a vector quantity, the net magnetic moment of an electron may be
represented by an arrow.
Thus, a material may be considered to contain a number of magnetic moments (dipoles);
where magnetic dipoles may be thought of small bar magnets composed of north and
south poles.
Magnetic dipoles are analogous to electric dipoles having positive and negative electric
charges.
Magnitude of this magnetic
moment (dipole) is very
small and is measured in the
unit called Bohr Magneton
(BM or µB). It is equal to
9.27 × 10–24 A m2.
1)
2)
3)
Based on the behaviour in the external magnetic field, the substances are classified into
five different categories …
Paramagnetic
Diamagnetic
Ferromagnetic
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
4)
5)
Antiferromagnetic
Ferrimagnetic
Note : Properties possessed by above types of substances are known as Paramagnetism,
Diamagnetism, Ferromagnetism, Antiferromagnetism and Ferrimagnetism respectively.
Paramagnetism :
Paramagnetic substances are weakly attracted by a magnetic field. They are magnetized
in a magnetic field in the same direction.
They lose their magnetism in the absence of magnetic field.
These have permanent dipoles because of the presence of some species (atoms, ions or
molecuels) having one or more unpaired electrons. O2, Cu2+, Fe3+, Cr3+, TiO, Ti2O3, VO,
VO2, CuO are some examples of such substances.
Diamagnetism :
Diamagnetic substances are weakly repelled by a magnetic field. H2O, TiO2, NaCl and
C6H6 are some examples of such substances.
They are weakly magnetized in a magnetic field in opposite direction.
Diamagnetism is shown by those substances in which all the electrons are paired and
there are no unpaired electrons.
Pairing of electrons cancels their magnetic moments and they lose their magnetic
character.
Ferromagnetism :
A few substances like iron, cobalt, nickel, gadolinium and CrO2 are attracted very
strongly by a magnetic field.
These Substances show permanent magnetism even in the absence of the magnetic field.
Such substances are called ferromagnetic substances.
Such substances remain permanently magnetized, once they have been magnetised.
These substances are very strongly attracted by a magnetic field. The reason for such a
magnetic behaviour by these substances is that in the solid state, the metal ions of these
substances are grouped together into small regions called domains.
Thus, each domain acts as a tiny magnet (having definite magnetic moment).
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(1)
(2)
(3)
(4)
In an unmagnetized piece of any ferromagnetic substance, the domains are randomly
oriented such that their magnetic moments cancel each other.
However, when the substance is placed in a magnetic field, all the domains get oriented
in the direction of the magnetic field and a strong magnetic effect is produced.
This ordering of domains persist even when the magnetic field is removed and the
ferromagnetic substance becomes a permanent magnet.
In fact, ferromagnetism is a case of large amount of paramagnetism.
The ferromagnetic material CrO2, is used to make magnetic tapes used for audio
recording.
Antiferromagnetism :
Substances which are expected to possess paramagnetism or ferromagnetism on the basis
of magnetic moments of the domains but actually they possess zero net magnetic moment
are called anti-ferromagnetic substances. E.g. MnO
In MnO domain structure is similar to ferromagnetic substance, but their domains are
oppositely oriented and cancel out each other's magnetic moment.
Ferrimagnetism :
Substances which are expected to possess large magnetism on the basis of the magnetic
moments of the domains but actually have small net magnetic moment are called
ferrimagnetic substances.
Ferrimagnetism is observed when the magnetic moments of the domains in the substance
are aligned in parallel and anti-parallel directions in unequal numbers.
They are weakly attracted by magnetic field as compared to ferromagnetic substances.
Fe3O4 (magnetite) and ferrites like MgFe2O4 and ZnFe2O4 are examples of such
substances.
These substances lose ferrimagnetism on heating and become paramagnetic.
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e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
(5)
(1)
(2)
It may be noted that all magnetically ordered solids, i.e. ferromagnetic and antiferromagnetic solids change into paramagnetic at high temperature. This is due to
randomization of domains (spins) on heating.
Ferrimagnetic substance, Fe3O4 becomes paramagnetic at 850 K.
It is important to note that each ferromagnetic substance has a characteristic temperature
above which no ferromagnetism is observed.
This is known as curie temperature.
Like electrical conductivity, the magnetic behaviour of the compound of transition
elements with similar structure may not be same. E.g.
TiO, VO and CuO are paramagnetic whereas MnO, FeO, CoO and NiO are
antiferromagnetic.
TiO2 is diamagnetic, VO2 is paramagnetic, CrO2 is ferromagnetic whereas MnO2 is
antiferromagnetic.
Sem – IV – 2015
Prasham Sheth
Alay Majmudar
Pooja Patel
Yash Patel
Kirtana Prabhu
Kathan Shah
Nidhi Patel
Dhruv Shah
Meet Shah
Rutu Nikhal
Anusha Patel
Esha Gor
Siddhi Shah
Freya Shah
Rashmi Menon
31
99
96
94
93
91
91
90
90
90
89
87
87
87
86
80
Sem – II – 2015
Gresha Vora
Vedant Shah
Sanket Bhardwaj
Aayushi Joshi
Jugal Shah
Mihir Chaudhary
Dhairya Shah
Aransha Shah
Saloni Chudgar
Abhi Shah
Chahat Shah
Rutvik Panchal
Tapash Bhavsar
Rutva Joshi
Aditi Parmar
Zeel Mehta
Dwij Shah
98
98
97
96
93
93
91
90
89
85
85
85
84
83
82
82
80
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433
JEE
score
CHEMISTRY
PHYSICS MATHS
Pooja Patel
158
68
41
49
DAIICT
Prasham
Sheth
152
70
29
53
Nirma
Computer
Alay
Majmudar
146
69
33
45
Nirma
Computer
It doesn’t matter how many resources you have.
If you don’t know how to use them,
it will never be enough.
32
e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433