Solid state.pdf

• Paramagnetic- Weakly attracted by magnetic field. eg. O2
, Cu2+
etc.
• Diamagnetic- Weakly repelled by magnetic field. H2
O, NaCl, etc.
• Ferromagnetic- permanent magnetism even in absence of magnetic
fields eg. Fe, Ni, CO, CrO2
, etc.
• Ferrimagnetic- Magnetic moment is smaller than that of
ferromagnetic substances. eg.
• Antiferromagnetic- Zero magnetic moment due to equal no. of anti-
parallel domains. eg. MnO, etc.
• Conductors- Valence bond is partially filled or it overlaps with higher
energy unoccupied conduction bands.
• Semi-conductors- Small energy gap between valance and conduction
bands.
• Insulators- Large energy gap between valance and conduction bands.
• n-type semiconductor: (by doping e-
rich impurities
• p-type semiconductor: (by doping e-
deficient impurities
ELECTRICAL PROPERTIES
MAGNETIC PROPERTIES
MAGNETIC & ELECTRICAL PROPERTIES
Crystal
Structure
Lattice
Points
C.N. Number of Formula
Units per unit cell
Example
Cl-
,-CCP
Na+
-OV
6:6 4
LiCl, KCl
RbCl, AgCl
S2-
-CCP
Zn2+
-Alternate TV
4:4 4
ZnS, Bes,
CuCl, CuI
Cl-
-Corners
Cs+
-Body centre
8:8 1 CsBr, CsI,
CsCN
Ca2+
-CCP
F-all TV
8:4 4
SrF2
, BaF2
,
SrCl2
O2-
-CCP
Li+
-all TV
4:8 4
K2
O, Li2
O,
K2
S
STRUCTURE OF VARIOUS IONIC CRYSTALS
Rock salt
NaCl type
Zinc-Blende
Zns type
CsCl type
(BCC type)
Fluorite type
(CaF2
)
Anti-Fluorite
type (Na2
O)
Packging Efficiency
(P.E.)
Density
3
A
Z M
d
N a
×
=
×
Coordination No.
(C.N.)
3
3
4
Z r
3
PE 100
a
× π
= ×
It is no. of nearest
Neighbours of a
lattice point
DEFECTS IN CRYSTALS
IN NON-IONIC
SOLIDS
IN IONIC
SOLIDS
Interstitial
Defects
Vacancy
Defects
NON STOICHIOMETRIC
DEFECT
• Some of the
lattice sites
are vacant
• Decrease in
density
• Some particles
occupy an
interstial site
• increase in
density
Frenkel
Defects
Schottky
Defects
• Equal no. of
cations and
anions are
missing
• Decrease in
density
• Smaller ion is
dislocated from
it's normal site
to an interstitial
sites
• no change density
Metal deficiency
Defects
Metal excess
Defect
• It may arise either
due to anionic
vacancies or due to
presence of extra
cations at interstitial
Sites
• Generate F-centres
which are responsible
for colour in crystal
• Occurs due to cationic
vacancy and presence
of a cation having
higher charge.
• Appearance in oxides
of d-block metals.
STOICHIOMETRIC
DEFECTS
O2-
Fe3+
Fe3+
e-
TETRAHEDRAL
VOIDS (TV)
Surrounded by 4 spheres
Present on body diagonal line at a
distance of from corner of FCC
unit
C.N. = 4
a 3
4
OCTAHEDRAL VOIDS (OV)
Surrounded by 6 spheres
Present on edge centre and body
body centre of FCC unit
C.N. = 6
Types of Crystal Lattice/
14 Bravis Lattices
Cubic
Tetragonal
Orthorhombic
Monoclinic
Hexagonal
Rhombohedral
Triclinic
a = b = c
a ≠ b ≠ c
a = b ≠ c
a ≠ b ≠ c
a = b ≠ c
a = b = c
a ≠ b ≠ c
α = β = γ = 90°
α = β = γ = 90°
α = β = γ = 90°
α = γ = β ≠ 90°
α = β = 90° γ = 120°
α = β = γ ≠ 90°
α ≠ β ≠ γ ≠ 90°
Simple Cubic
Unit Cell (S.C.C.)
Body Centered Cubic
Unit Cell (B.C.C.)
Face Centered Cubic
Unit Cell (F.C.C.)
Hexagonal Closed Packed
Unit Cell (H.C.C.)
Lattic
points
Effective Number
of atoms (Z)
Packing Efficiency
(PE)
52% 68% 74% 74%
12 12
6 8
Coordination No.
Corners Corners + Body
Center
Corners + All
Face Center
Corners + Face Centers
+ 3 atoms in middle layers
 
1
8 1
8
 
 
× =
1
8 1 2
8
× + =
 
 
 
1 1
8 6 3
8 2
× + × =
 
 
 
1 1
12 2 3 6
6 2
× + × + =
 
 
 
CRYSTALLINE & AMORPHOUS
SOLIDS
CRYSTALLINE AMORPHOUS
• Have a long range
order of particles
• Anisotropic
• True solids
• Sharp melting point
• NaCl, Quartz, ZnS
• Do not have ordered
structure or have a very
short order
• Isotropic
• Pseudo solids
• Diffused melting point
• Glass, Rubber, etc.
Molecular Covalent/Network
Ionic Solid Metallic Solids
A regular 3-D arrangement of constituent
particles.
UNIT CELL
CRYSTAL LATTICE / SPACE
LATTICE
Fe3
O4
, MgFe2
O4 .
TYPES OF
UNIT CELLS
Smallest repeating
unit which repeats
itself over and over
again to generate
entire crystal.
SOLID
STATES
VOIDS

SOLID STATE (FULLY SOLVED) FOR CBSE (IIT-JEE) EXAMS (2021 - 2022)
 ACTIVE SITE EDUTECH  CONTACT:  Page 1 of 30
SOLID STATE
Matter exists mainly in three states, viz. solids, liquids and gases. The existence of matter
in any of these three forms depends upon two factors
1. Intermolecular forces of attraction (keeps particle closer)
2. Thermal energy (keeps particles apart)
Some common properties of solids, which distinguish them from liquids, gases, are:
Solids are rigid and have definite shapes.
Solids have definite volume irrespective of the size or shape of the container in which they
are placed.
Solids are almost incompressible.
Solids diffuse very slowly as compared to liquids and gases. Constituent particles are very
closely packed in solids permitting very little space for their movement.
Solids have a much higher density (mass to volume ratio) than that of gases and liquids.
Most solids become liquids when heated. Some undergo sublimation on heating. The
temperature at which a solid changes into liquid is called the melting point and the process
is called as melting. Due to the varying natures of solids their melting temperatures vary
considerably.
CLASSIFICATION OF SOLIDS
Solids are divided into two classes, namely
crystalline and amorphous solids. A solid is said to
be crystalline if the constituents arrange
themselves in regular manner throughout the three-
dimensional network. The ordered arrangement of
building constituents extends over a large distance
(long range order). On the other hand, in amorphous
solids, the arrangement of building constituents is not regular (short range order).
Properties Solid Liquid Gases
(i) Motion of partical.
No free motion
only vibration allow.
Randommotion to
a limited extent is allowed.
Totally random.
(ii) Inter molecular
forces
Very strong
Intermediate
strength
Very weak (~ zero)
(iii) Average separation
(volume)
x
Average separation is almost
constant so almost fixed
volume.
No fixed volume.
(iv) Shape
Definate shape as
location of partical are
fixed.
Average separation is fixed
but location of partical is not
fixed so no definate shape..
No fixed shape.
(v) Effect of change in
pressure & temperature.
Are incompressible.
Liquid are also almost
incompressible.
Highly compressible.
(vi) Heat capacities
Heat capacity is
almost independent
of process.
Same as solid.
Heat capacity is dependent
on process.

 ACTIVE
i) Crystall
(atoms, io
Example
General c
i) A cryst
molecules
ii) The tot
maximum
hydrogen
iii)A cryst
having a d
iv)Crystall
crystal, t
v) Crystall
vi)Crystall
vii) Crysta
viii)Crysta
is called a
SOLID S
E SITE EDU
ine solids:
ons or mole
e: Diamond
characteri
talline solid
s) are arran
tal intermo
stability,
n bonds and
talline solid
definite ch
ine solid h
thus exhibit
ine solids h
ine solids a
alline solid o
alline solid s
anisotropy
STATE (FU
UTECH 
A crystal
ecule) are a
d, Quartz, N
istics of C
d is a homo
nged in a de
olecular fo
the force
d Van der W
d usually co
aracteristi
has regula
ting short-
have sharp
are true so
on cutting
shows diff
y and the su
LLY SOLV
lline solid
arranged in
NaCl, K2SO
Crystalline
ogeneous s
efinite rep
orce of at
es responsi
Waal’s force
onsist of a
ic geometr
ar arrangem
- and long-
melting po
lids.
gives a clea
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ubstances
VED) FOR C
CONTAC
is a homog
a definite
O4 etc.
e solids:
solid in whi
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ttraction i
ble for th
es.
a large num
ical shape.
ment of p
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
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nstituent p
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.
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stituent pa
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properties like electrical conductivity, refractive index, thermal expansion etc. have different value
in different direction.
ix)Two or more crystalline substances having same crystal structure are said to be isomorphous.
Isomorphous substance contains constituent atom of same atomic ratio.
Example: a) NaF and MgO (Ratio is 1:1)
b) NaNO3 and CaCO3 (Ratio is 1:1:3)
c) K2SO4 and K2SeO4 (Ratio is 2:1:4)
d) Cr2O3 and Fe2O3 (Ratio is 2 : 3)
Exceptional: NaCl and KCl have all properties identical [same atomic ratio, similar molecular
formula or similar chemical properties] but are not isomorphous.
x) A single substance that crystallizes in two or more forms under different conditions is called
polymorphous. (allotropic forms)
. Example: a) Carbon has two allotropes graphite and diamond.
b) Sulphur has two polymorphic forms monoclinic and rhombic.
c) CaCO3 and SiO2 have two allotropic forms.
ii) Amorphous solids: Substances that appear like solids but do not have perfectly ordered
crystalline structure and no regular arrangement of constituent particles in structure is called
amorphous solids.
Example: Tar, glass, plastic, rubber, butter etc.
General characteristics of amorphous solids:
i) Amorphous substances appear like solids but they do not have perfectly ordered crystalline
structure, hence they are not real solids.
ii) An amorphous solid does not have regular arrangement of constituent particles.
iii)The arrangement of constituent particles like atoms or molecules has only short-range order
hence periodically repeating regular pattern is only over a short distance.
iv) Regular patterns are scattered and hence the arrangement is disordered.
v) Amorphous solids are called supercooled liquids of very high viscosity or pseudo solids.
vi) Physical properties do not change with change in directions hence amorphous solids are isotropic
in nature.
vii) Amorphous solids behave like fluids and very slowly float under gravity.
viii) Amorphous solids do not have sharp melting points.
ix)When cut, they split into pieces with irregular and rough surfaces.
Uses of amorphous solids:
i) Most widely used amorphous solid are the inorganic glasses viz. construction, house-ware,
laboratory ware, etc.
ii) Used as rubber in making tyres, shoe soles, etc.
iii)Used in plastics.
iv)Amorphous silica used for converting sunlight into electricity (in photovoltaic cell).

Anisotropy: The ability of crystalline solids to change their physical properties when measured in
different directions is called anisotropy.
Explanation: This property is due to different arrangement of
constituents in different directions.
Different types of particles fall on the way of measurements in
different directions. Hence, the composition of crystalline solids
changes with directions changing their physical properties.
Isotropy: The ability of amorphous solids to have same physical
properties when measured in different directions is called isotropy.
Explanation:This property is due to no regular arrangement of
particles in any direction. Hence the properties like electrical
conductivity, thermal expansion are identical in all the direction.
Difference between Crystalline and Amorphous Solid:
True solid Pseudo solids, super cooled liquid [In
between solid & liquid]
1 The constituent partical (atoms, molecule, ion)
follow a definite repetiting arrangement.
1 No particular pattern is followed
partical are random arranged.
2 These have long range order. 2 They have short range order no long
range order are found.
3 These are produced by slow cooling under
controlled condition of liquid. The crystalline
structure is also dependent on conditions.
Same substance can have different crystalline
structure in different condition.
Different crystalline structure of the same
substance are called its polymorphic forms &
this is known as polymorphism.
3 Rapid or suddenly cooling of the liquid
generate the amorphous solid.
4 These have fixed or sharp melting point and
enthalpy of fusion.
4 These have a range of temperature in
which they melts as. There melting
point and enthalpy of fusion is not
fixed.
solid
Time
Temp.
(T )
0
Transition
From liquid to solid
t1 t2
Liquid
t1 t2
solid
only
Time
T1
Temp.
T2
Liquid Liquid + solid
(Transition)
These are anisotropic : Physical properties
will have different values in different direction.
5
Cooling Curve :
These are isotropic :
All different physical properties are
same in all different direction.
Reason : Due to random arrangement
of partical.
Ex. : Ag, Fe, Cu, NaCl, H O (s), Dimond,
Quartz, Sucrose (Sugar)
2
Ex. : Glass, Plastic, Amorphous silica,
Rubber, Starch.
5
Crystalline solid Amorphous solids
A
B
A A
B
B
A
B B
A
B

Types of crystalline solids: They are classified into four main types as follows:
i) Molecular solids: They are further classified into three types:
a. Polar molecular solids.
b. Non-polar molecular solids.
c. Hydrogen bonded molecular solids.
ii) Ionic solids.
iii)Metallic solids.
iv)Covalent solids.
Molecular solids:
i) Here the constituent particles are molecules of same compound.
ii) Depending upon the type of molecules involved in crystal formation and the nature of
intermolecular force of attraction between the neighboring molecules, they are further sub-divided
as :
a) Non-polar molecular solids:
1. These are those crystalline solid in which the constituent particles are either atoms [Noble gases]
or non-polar molecules [H2, Cl2, I2, CH4, etc.] or weakly polar molecules like CO or other
hydrocarbons.
2. They are formed at relatively lower temperature and are in usually gaseous state at normal
temperature.
3. In these atoms or non-polar molecules are held by weak London forces.
4. These are generally soft, having low m.p and b.p and are non-conductor of electricity.
5. As polar molecules exist in gaseous state, polar molecular solids is obtained by subjecting the gas
high pressure and low temperature.
b) Polar-molecular solids:
1. They crystalline solid in which the constituent particles are polar molecules [HCl, SO2,]
2. In polar molecule there is separation of charges, in which the opposite charges of neighboring
molecules are brought closer.
3. The forces holding these molecules are dipole-dipole forces of attraction, this force of
attractionis stronger than London forces.
4. These solids show following characteristic:
i) They are soft.
ii) Their melting point and boiling point are comparatively higher than non-polar molecular solids
but lowerthan ionic and metallic.
iii) They also exist as liquid or gases at room temperature.
iv) They are non-conductor of electricity.
v) They possess permanent dipole moment.
c) Hydrogen bonded molecular solids:
1. In these solids, the constituent particles are such molecules which contain hydrogen atom linked
to a highly electronegative atom [O, N or F]. Example: solid ice, NH3, etc.
2. In these, molecules are held by hydrogen bond in which the H atom of one molecule is bonded to
electronegative atom of another molecule.

3. This intermolecular force of attraction existing among the molecules is strong hydrogen bonds.
4. Characteristic of hydrogen bonded molecular solid :
i) They exist as volatile liquid or soft solids at room temperature.
ii) They are non-conductors of electricity.
iii) Their melting point and boiling are usually higher than non-polar molecular solids and polar
molecular solids.
5. They solidify on cooling.
Ionic solids:
i) In these crystalline solids, the constituent particles are positive and negative ions i.e. cations and
anions. e.g. Na+
and Cl–
ions in case of NaCl.
ii) These ions in the solid are held in their lattice points by strong electrostatic force of attraction
resulting into well-ordered three-dimensional arrangement of ions.
iii)All salts are crystalline in nature and are called Ionic solids.
iv)In Ionic solids, the charges on the ions and the arrangement of ions are in such a manner that
they balance each other and hence the molecule is electrically neutral.
v) The arrangement of ions in the solid depends upon:
a) Size of cation and anion
b) charges on the ion
c) ease with which anion is polarized (i.e. polarizability of anions).
vi)Ionic solids are hard and brittle and have high melting point and boiling point.
vii) They are electrical insulators in solid state because their ions are not free to move.
viii)In aqueous solution or in molten state as the ions become free, they are good conductor of
electricity.
ix)They are soluble in polar solvent but insoluble in non-polar solvent.
x) On application of shearing force, ionic crystals undergo distortion and fracture in crystal
structure.
Metallic solids:
i) In metallic solids the constituent particles are positively charged metal ion and free electron.
ii) Due to low ionization energy of metal atom the metal atom loses their valence electron and
becomes positively charged ions.
iii)Thus electrons lost are delocalized over the crystal space and flows throughout the crystal like
water in sea, hence also called sea of free electrons.
iv)The force of attraction between positively charged metallic ion and negatively charged sea of
delocalized electron is called metallic bond.
v) If energy is supplied, valence electron from sea of electrons move from one place to another, this
presence of mobile electrons makes all the metal good conductor of heat and electricity.
vi)On application of shearing force, the layers slide on one another and hence the structure is not
fractured imparting the properties of malleability and ductility.
vii) They have high melting point, boiling point and density.
viii)The mixtures of metals can be fused together to form alloys, which exhibit all properties of
metals.

ix)They possess lusture and colour. [Gold metal exhibit yellow lusture and copper has reddish
lusture].
x) Metallic bonds are stronger than ionic and covalent bond.
Covalent solids or Network solids:
i) These are crystalline solids in which the constituent particles are non-metal atoms linked to the
adjacent atoms by covalent bonds throughout the crystal forming a giant three-dimensional
structure.
ii) Hence covalent solids are called giant solids and the constituting molecules are called giant
molecules.
iii)Since covalent bonds are strong and directional, atoms are held strongly at their lattice positions.
iv)They are hard or brittle depending on the event of bonding.
v) They have high melting points.
vi)They act as good conductors of electricity or insulators depending upon the availability of free
electrons.
Examples diamond, graphite, Silicon carbide (carborundum), fullerene, boron nitride, etc.

 ACTIVE
Space lat
It may be
solid subs
The posit
lattice po
Character
1. Lattice
position o
Lattice p
2. Each po
molecule
3. Lattice
Unit Cell:
dimensio
Characte
1. Edges o
The thre
along thr
2. Angles
unit cell
the help
a) The ang
b) The ang
c) The ang
SOLID S
E SITE EDU
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oint in a c
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: It is th
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or edge le
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ree axes. T
between
represen
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gle α is be
gle β is be
gle γ is be
La
P
STATE (FU
UTECH 
rystal latt
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h are occu
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Crystal la
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attice
Point
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straight lin
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ll: A unit
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ges may or
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CONTAC
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CT: 
CONCEPT
nal arrange
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
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Lattice p
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 ACTIVE
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SOLID S
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CT: 
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D TYPES O
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(b) Body Centered(BCC):When atoms are present at 8 corners as well as in the body centre
in a cubic unit cell then this arrangement is known as BCC.
(c) End-Centered:Inadditiontoparticlesatthe corners, there are particles at the centers of
two oppositefaces.
SEVEN CRYSTAL SYSTEMS
By considering the symmetry of the axial distance and the axialangles between the edges,
the various crystals can be divided into 7 systems. Although each system is expected to have
4 different unit cell, but actually all of them cannot exist in each case and only 14 different
type of lattices called Brava is lattice had been established.
There are 14 possible three-dimensional lattices. These are called Bravais Lattices.
Serial No. Crystal System Possible variations Edge lengths Axial angles Examples
1 Cubic
Primitive
a = b = c α= β = γ = 90o
NaCl
Body – Centered ZnS
Face – Centered Cu
2 Tetragonal
Primitive
a = b ≠ c α= β = γ = 90o SnO2
Body – centered TiO2
3 Orthorhombic
Primitive
a ≠ b ≠ c α= β = γ = 90o
Rhombic Sulphur
Body – Centered KNO3
Face – Centred BaSO4
End – Centred MgSO4.7H2O
4 Hexagonal Primitive a = b ≠ c
α= β = 90o
γ = 120o
Graphite, ZnO
5 Rhombohedral or Trigonal Primitive a = b = c α= β = γ ≠90o Calcite (CaCO3)
Cinnabar (HgS)
6 Monoclinic
Primitive
a ≠ b ≠ c
α= γ = 90o
β ≠90o
Monoclinic sulphur
End – Centred Na2SO4.10H2O
7 Triclinic
Primitive
a ≠ b ≠ c α≠ β ≠ γ ≠90
K2Cr2O7, H3BO3











CALCULATION OF NUMBER OF PARTICLES IN A UNIT CELL (Z)
In a crystal, atom located at the corner and face center of a unit cell are shared by other
cells and only a portion of such an atom actually lies within a given unit cell.
(i)A face-centered point is shared by two unit cells and only one half of it is present in given
unit cell, hence the contribution of the particle per unit cell is 1/2.
(ii) A point along an edge is shared by four-unit cells and only one-fourth of it lies within one
cell,hence the contribution of the particle per unit cell is 1/4.
c
a
b P
I F
a = b = c
All sides are
of equal length;
all angles are
90°
Three
angles
changed
a = b = c
All sides are
of equal length;
all angles
= = = 90°
  
c a
b P
Trigonal (Rhombohedral)
Cubic
a = b = c
One side is
different length;
all angles are
90°
One side
is
changed
General case :
All sides are
different lengths;
all angles are
different
a
One side length changed
two angles fixed at 90°
one fixed at 120°
c a
b P
a



Special case
a = b c
= = 90°
= 90°

 

Hexagonal
Three unit cells are
shown to give the
hexagon
Two side lengths made
the same; one angle
fixed at 120°
All sides are of
different lengths
= = 90°
90°
 
 
c
a
b
c
a
b P
C


One angle
changed
a b c
Three sides are of
different lengths;
all angles are 90°
 
Length of another side is
changed
Triclinic
Tetragonal
Orthorombic
Monoclinic
c a
b P I F C
c a
b P

5 6
3
2
8 7
1 4

1 2
4 3

i.
ii.
iii.
 ACTIVE
(iii)A poin
therefor
contribu
(iv) A bod
point to
Calculati
In this t
 Numbe
unit cell
= 8 x =
Calculati
This type
centre o
Numbe
= 2 partic
Calculati
This type
centre o
Numbe
SOLID S
E SITE EDU
nt that li
re, only o
ution of th
dy-center
the cell.
ion of num
type of uni
er of part
=1 partic
ion of num
e of unit c
f the unit
er of partic
cles.
ion of num
of unit c
f 6 faces
er of partic
STATE (FU
UTECH 
es at the
ne eighth
he particle
ed point
Typ
Face‐
Edge
Corne
Body
mber of p
it cell, the
ticles per
le
mber of p
cell has 8
t cell.
cles per u
mber of p
ell has 8
of the un
cles unit c
=1 +3
=4 parti
2
LLY SOLV
e corner
h of each
e per unit
lies entire
e of Lattice p
center
er
Center
particles p
ere are eig
unit cell =
particles p
particles
nit cell =8
particles p
particles a
it cell.
cell =8 x
cles.

8
7
6
5
2
1 3
4


8
1
VED) FOR C
CONTAC
of a unit
such poin
t cell is 1/
ely within
point Con
1/2
1/4
1/8
1
per unit ce
ght partic
= No. of p
per unit ce
at the co
8 x +1x
per unit ce
at the cor
+ 6 x

 

 



5
2
7
4
CBSE (IIT-J
CT: 
t cell is s
nt lies wit
/8.
the unit
ntribution to
2
4
8
ell in a p
les at the
particles i
ell in a B
rners and
1
ell in a F
rners and


6
3
EE) EXAM

shared am
thin the g
cell and
o one unit ce
primitive c
corners o
n unit cel
Body- cen
d 1 particle
Face- cen
6 particle
S (2021 - 2
 Pa
mong eigh
given unit
contribute
ell
cubic unit
of the unit
l x share
ntred cubi
e at the
ntred cubi
es at
2022)
ge 1 of 30
ht-unit ce
cell, hen
es one co
cell:
t cell.
of partic
ic unit cel
c unit cel
lls and
ce the
mplete
les per
ll:
l:

 ACTIVE
Type of u
SC
BCC
FCC
CALCULA
Note: In
corners of
sphere at
similarly,
The relat
crystals o
1] Simple
d = AB = a
r = a/2
2] Face C
d = in r
AC2
= a2
+
AC √2
d
AC
2
3] Body C
In right an
AC √2
In right a
AD2
= AC
AD
(i) Close p
Initiallyt
There ar
SOLID S
E SITE EDU
unit cell Lat
c
8
8
8
ATION OF
a simple
f face cen
the corne
in bcc, all
tionship b
of pure ele
e Cube:
a
Centered
right angled
+ a2
= 2a2
. a
√2. a
2
a
√
Centered C
ngled ABC
. a
angled AD
C2
+ DC2
= (√
3a  AD
packing in
the sphere
re two way
STATE (FU
UTECH 
Calcula
ttice points
orners
F NEARES
cube, the
ntered cub
er touches
the atoms
etween th
ements) an
Cube:
d ABC AC
a
√2
∵ r
Cube: d
C, AC2
= AB
DC
√2.a) 2
+ a2
D √3. a 
n two dime
es arrange
ys to build
LLY SOLV
ation of nu
at Lattice p
center
0
0
6
ST NEIGH
atoms at
be and bod
s the thre
s at the co
he neares
nd the edg
C2
= AB2
+ B
d
2
a
2√2
B2
+ BC2
= 2
2
 d
√3.
2
ensions:
e themselv
d a crystal
VED) FOR C
CONTAC
umber of
points at face‐
red
HBOURS
the corn
dy centere
ee spheres
orners tou
t neighbo
ge of unit
BC2
a2
a
r
d
2
ves in a ro
plane
CBSE (IIT-J
CT: 
particles
Lattice poin
centered
0
1
0
ers touch
ed cube do
s at the fa
uch the ce
or distanc
cell (a) are
√3
4
a
ow to form
EE) EXAM

in a unit
ts at body Z
each oth
o not touc
ace centre
entral sphe
e (d) and
e given be
m an edge o
S (2021 - 2
 Pa
cell
Z = no. of latti
cell
8
8
1
8
8
1
8
6
her. But, t
h each oth
es of thre
ere.
the radi
elow:
of the cry
2022)
ge 1 of 30
ice points per
1
8
1
1 1 2
1
2
4
he atoms
her. In fcc
ee adjuring
us of ato
ystal.
unit
at the
c, each
g faces
m (for

(a) Sphere is packed in such a way that the rows have a horizontal as well as vertical
alignment. In this arrangement, the spheres are found to form square. This type of packing
is also called square close packing.
The number of spheres which are touching a given sphere is called co-ordination number.
Thus, the coordination number of each sphere in square close packing is four.
(b) The sphere is packed in such a way that the spheres in the second row are placed in the
depressions between the spheres of the first row and so on. This gives rise to hexagonal
close packing of spheres and the coordination number of each sphere is six.
(ii) Close packing in three dimensions:
It is clear from the figure (X) that there are two types of voids or hollows in the first layer.
These are marked as b and c. All the hollows are equivalent but the sphere of second layer
may be placed either on hollows which are marked b or on the other set of hollows marked c.
The second layer is indicated as dotted circles in figure (Y).

When a third layer is to be added, again there two types of hollows available. One type of
hollows marked ‘c’ are unoccupied hollows of the first layer. The other type of hollows are
hollows in the second layer (marked a). Thus, there are two alternatives to build the third
layer.
(i) When the third layer is placed over the second layer so as to cover the tetrahedral or ‘a’
voids, a three-dimensional closest packing is obtained where the spheres in every third
layer are vertically aligned to the first layer. This arrangement is called ABAB.,…pattern
or hexagonal (HCP) close packing(calling first layer as A and second layer B).
c
a a
a a
a a
c
c c
b b
b b
c
a a
a a
a a
a a
a a
a a
c
c c
b b
c
a a
a a
c
b b
b b
c
a a
a a
a a
c
c c
b b
b b
(X) (Y)

(a) For HCP geometry Coordination number = 12
(b) For HCP geometry no. of atoms per unit cell
12 corners
1
6
2 face centres
1
2
3 inside the body 1 6
(c) For HCP geometry packing efficiency = 74 %
(ii) When the third layer is placed over the second layer such that the spheres cover the
octahedral or ‘a’ voids, a layer different from A and B is formed. This pattern is called
ABCABC……pattern or cubic close packing (CCP).
The ABC ABC....... packing has cubic symmetry and is known as cubic close packing (ccp). The
cubic close packing has face centered cubic (fcc) unit cell.
Cubic close packing (ccp)
(i) For CCP geometry coordination number = 12
(ii)For CCP geometry no. of atoms per unit cell = 4(as calculated before)
(iii)For CCP geometry packing efficiency = 74 %
VOIDS
In the close packing of spheres, certain hollows are left vacant. These holes or voids in the
crystals are called interstitial sites or interstitial voids.
(i) Triangular (ii) tetrahedral
(iii) Octahedral (iv) cubical void
(i) Triangular: The vacant space (void) formed by touching three spheres.
0.155















(ii) Tetrahedral:The vacant space among four spheres having tetrahedral arrangement is
called tetrahedral site or tetrahedral hole. For tetrahedral void 0.225.
(iii) Octahedral: This type of site is formed at the centre of six sphere. The void formed
by two equilateral triangles with apices in opposite direction is called octahedral site or
octahedral hole. For octahedral void
rvoid
rsphere
0.414
iv) Cubical void:Vacant space (void) formed by touching eight spheres
rvoid
rsphere
0.732
Note:If a close packing (array) is made up of n number of atoms or ions then it has n no.
ofoctahedral voids and 2n no. of tetrahedral voids.
DENSITY OF UNIT CELL
The length of edge of the cell= a cm
Volume of unit cell = a3
cm3
Density
Mass of unit cell = number ofatoms in a unit cell  mass of each atom = Z.m

 Mass of one atom m ′
 Density Z → Number of atoms per unit cell.









O
O
O
O
O
O
O
O


















O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O











O
O
O
O
O
O
O
O
O
O
O
O
Octahedral void
O
O
O
O

PACKING EFFICIENCY
Packing efficiency is the % of total space occupied by particles. Both types of close packing
(hcp and ccp) are equally efficient and occupy 74% of available value. In bcc, the efficiency
is 68% while is simple cubic structure, it is 52.4%
Packing ef iciency
Vol. occupied by all atoms in unit cell
Total vol. of unit cell
v
V
Let a be the cube edge length and r the radius of atom.
V =volume of unit cell = a3; Volume of sphere,v πr
a. Packing efficiency in CCP or FCCarrangement:
Both type of close packing (hcp and ccp) are equally efficient. Let us
calculate the efficiency of packing in ccp structure.
In ccp, the unit cell is face centred. In face centred cubic unit cell, there
are four spheres per unit cell. Let ‘r’ is the radius of sphere and ‘a’ be the
edge length of the cube.
Volume of the sphere =
Total four spheres per unit cell of fcc, volume of it = 4 x
In a face centred cubic unit cell, the spheres at corners are in
contact with the sphere at the centre of the face and the particles
at the corners are not in touch with each other.
Therefore we can find the radius of the sphere as follows:
From Δle
ABC, AC2
= AB2
+ BC2
 b2
= a2
+ a2
b2
= 2a2
b = √2
Since b = 4r, we have
4r = √2
r =
√
r =
√
or a =
√
 a =
√
or a =
√ √
√
 a = 2 2 r
Packing Efficiency = 100
√
3 100
√
100
√
100 74.04%
Packing Efficiency = 74.04% OR 74%

b) HCP arrangement:
Volume of unit cell base area height 6√34 4 2/3 24√2r
no. of atoms in hcp 12
1
6
2
1
2
3 1 6 v 6
4
3
4πr 8πr
Packing ef iciency
8πr
24√2r
100
π
3√2
100 74%
c) BCC arrangement:
InBody centred cubic unit cell, atoms are located at the corners of the cube and 1 particle at the
centre of the cube.
Number of particles per unit cell of BCC structure = 2
 Volume occupied by spheres = 2× πr = πr
Where r  radius of the spheres.
Edge length of cube = a
In a body centred cubic unit cell, the spheres at the corners are not touching
each other but are in contact with the sphere at the centre of the cube.
From the figure, we can find, Face-diagonal as, from Δle
ABC,
AC2
= AB 2
+ BC2
= a2
+a2
b2
= 2a2
For body diagonal consider the Δle
ACD, Body diagonal CD can be calculated as CD2
= AC2
+ AD2
c2
= b2
+ a2
= 2a2
+a2
CD = c = √3 = √3
CD =√3 = 4r
4r = √3
r=
3
4
a or a =
√
r
Volume of unit cell = a3
=
√
 a =
√
Packing Efficiency =
Volume of space occuped by atoms in one unit cell
Volume of one cubic unit cell
100
πr
64
√
x 100 =
8πr √
64 x 3 r
x 100
Packing efficiency = 67.98 % ≃ 68 %
d) Simple cubic arrangement: In simple cubic unit cell, atoms arelocated only at the corners of the
cube. The particles touch one another along the edge.
If edge length of the cube= a, and radius of each particle is r; then a is
related to r as a = 2r
The volume of the cubic unit cell = a3
= 2r3
= 8r3
Since a simple cubic unit cell contains only 1 atom
The volume of the occupied space = 3
4
πr
3
A
C
D
a
c
b
a

Volume of space occuped by atom
Volume of cubic unit cell
100% =
4/3πr
8r
×100 =
4πr
8r
×100
= ×100 = 52.36%
RADIUS RATIO RULES
In ionic crystals, the coordination numbers as well as the geometrical shapes of the crystals
depend mainly on the relative sizes of the ions. The ration of the radii of the positive and
negative ions is called radius ratio.
Radius ratio
Radius of postive ion cation
Radius of negative ion anion
r
r
Common coordination numbers are 3, 4, 6 and 8.
Limiting radius ratio Co‐ord. No. Shape Example
i) < 0.155 2 Linear BeF2
ii) 0.155 – 0.225 3 Trigonal planar B2
O3
iii) 0.225 – 0.414 4 Tetrahedral ZnS
iv) 0.414 0.732 6 octahedral NaCl
v) 0.732 0.999 8 B.C.C. CsCl
STRUCTURE OF IONIC COMPOUNDS
(A) Ionic Compounds of AB type:
These compounds can have following three type of structures.
1] Rock salt structure (NaCl):
a) Cl¯ is forming a FCC unit cell in which Na
+
is in the
octahedral voids. The co-ordination number of Na
+
is 6 and that
of Cl¯ would also be 6.
b Ratio of ionic radii
r
r
0.525
c No. of sodium ions 12 At edge centre
1
4
1 At body centre 1 4
No. of Cl ions 8 At corners
1
8
6 At face centres
1
2
4
(Thus formula is Na4
Cl4
i.e. NaCl)
d) Most of the halides of alkali metals and oxides of alkaline-earth metal have this type of
structure.e.g. NaI, KCl, RbI and RbF. FeO also has rock-salt structure in which oxide ions
are arranged in ccp and Fe
2+
ions occupy octahedral voids.
Cl–
Na+
Crystal structure of NaCl

 ACTIVE
2] Caesiu
(a)CsCl ha
i.e., each C
b
c No. of C
No. of
No. of
(d) Compo
3] Zinc b
(a)Sulph
b
c No. of
No. of
No. of
(Form
(d) Ionic
(B) Ionic
Fluorite
(a) The
tetrahed
(b) In un
No. of
No. of
(c) Com
BaCl2
, Ba
SOLID S
E SITE EDU
um chlorid
as body-ce
Cs+ ion is
0.933
l ions
f Cs+ ions =
f CsCl unit
ounds havin
blende str
ide ions a
0.40
S2–
ions
f Zn
2+
ions
f ZnS units
ula is Zn4
S
c solids ha
Compound
structure
cations ar
dral voids.
nit cell no.
f fluoride
f CaF2
unit
mpounds h
aF2
, PbF2
a
STATE (FU
UTECH 
de structu
entered cu
touching e
8 At corne
= 1 (At the
per unit c
ng this typ
ructure or
are face
8 at corn
= 4 (with
s per unit
S4
, i.e. ZnS
ving zinc b
ds of AB2
e (CaF2
):
re arrange
Calcium f
of calcium
ions = 4 (w
ts per unit
having flu
and CdF2
.
LLY SOLV












(a
ure (CsCl)
ubic (bcc)
eight Cl– io
ers
1
8
e body cen
cell = 1
pe of stru
r Sphaleri
centered
ners
1
8
in the bod
cell = 4
S)
blende str
type:
ed in cubi
fluoride ha
m ions 8
within the
t cell = 4
uorite str
VED) FOR C
CONTAC















)
:
) arrangem
ons and ea
1
ntre) × 1 =
ucture are
ite struct
and zinc
6 at face
dy) × 1 = 4
ructure ar
ic close pa
as 8: 4 co-
8 at corners
body) × 1
ructure a
CBSE (IIT-J
CT: 
Cs+
Cl—






(b)
One unit c
ment. This
ach Cl– ion
= 1
CsBr, CsI
ture (ZnS)
c is prese
centres
e CuCl, Cu
acking (cc
-ordination
s 6
= 4
re SrF2
,
EE) EXAM





cell
s structur
ns in touch
I, TlCl, and
):
ent in alte
1
2
4
Br, CuI &
cp) while t
n. (ccp)
at face cent
S (2021 - 2
 Pa
e has 8: 8
hing eight C
d TlBr.
ernate te
AgI
the anion
tres
2022)
ge 1 of 30

8 co-ordin
Cs+ ions. (
etrahedral
occupies
4
Ca2+
F—

nations,
(bcc).
voids.
all the

(C) Ionic Compounds of A2B Type:
Antifluorite Structure:
In Antifluorite structure e.g., (Na2
O)
(a) The anions are arranged in cubic close packing (ccp)
while the captions occupy allthe tetrahedral voids.
(b) Na2
O has 4: 8 co-ordinations
(c) Compounds having ant fluorite structures are: Li2
O, K2
O,
Rb2
O and Rb2
S
Sr. Type of crystal Ions occupying voids ions forming close
packing
Coord no.
(cation: anion)
1. Rock salt (AB) (NaCl) Na
+
ions occupy
octahedral voids
Cl
‐
6: 6
2. Cesium chloride (AB)
(CsCl)
Cs+ ion occupy cubic
hde
Cl‐
8: 8
3. Sphalerite (AB) (ZnS) Zn
2+
occupy tetrahedral
voids alternatively
S
2‐
4: 4
4. Fluorite (AB2) (CaF2) F
ˉoccupy tetrahedral
voids
Ca
2+
8: 4
5. Antifluorite (A2B)
(Na2O)
Cations occupy
telrahedrd voids
Anions 4: 8
IMPERFECTIONS OR DEFECTS IN SOLIDS
At absolute zero, crystals tend to have a perfectly ordered arrangement. This arrangement
corresponds to state of lowest energy. As the temperature increases, the crystals start
deviating from the perfectly ordered arrangement. Any deviation from the perfectly
ordered arrangement constitutes a defect or imperfection. These defects are sometimes
called thermodynamic defects because the number of these defects depends on the
temperature. Crystals may also possess addition defects due to the presence of impurities.
Many properties of crystalline solids such as electrical conductivity and mechanical strength
can be explained in terms of imperfections. Imperfections not only modify the properties of
solids but also give rise to new properties. The defect which arises due to the irregularity in
the arrangement of atoms or ions are called atomic imperfections.
These imperfections in the crystalline solid are called defects in crystalline solid. The
defects in crystalline solids are of two types viz.,
a. Point defect
b. Line defect
Point Defect: This defect is produced because of the faulty arrangement of a point i.e.
constituent practice like atom, ion or molecules in a crystalline solid.
The point defects are classified into three types:
Types of point Defects:
i) Stoichiometric defects.These are those defects in which the stoichiometry of the solid
is not disturbed as a result of the defect.
O2–
Na+


ii) Non-stoichiometry defects. These are those in which the stoichiometry is disturbed due
to the defect.
iii) Impurity defect. These arise when some foreign material is added into the crystal.
Types of Stoichiometric defect
(i) Vacancy defect is a stoichiometric defect generated
during crystallization, in which some of the places of the
constituent particle remain unoccupied. This defect
results in the decrease of density of thecrystal than
expected. This defect possibly occurs when a substance is
heated.
(ii) Interstitial defect: Interstitial defect is a type of
stoichiometric defect, in which the constituent particles
(atoms or molecules) occupy an interstitial site (occupies
the space between the lattice site). This defect results in
the increase of density of the crystal than expected.
In case of ionic solids, always electrical neutrality must be maintained. The above two
defects in case of ionic solids can be explained as follows:
a) Schottky defect:
It is due to equal number of cations and anions missing from their lattice sties. As a result,
density decreases. This type of defect is shown by ionic compounds which have high
coordination number and small difference in the size of cations and anions, e.g., NaCl, KCl,
KBr, AgBr and CsCl.
b) Frenkel defect:
It arises when cations are missing from their lattice sites and occupy interstitial sites. As a
result, density remains unchanged. This defect is also called dislocation defect as smaller
ions (usually cations) are dislocated from normal sites to interstitial sites.

 ACTIVE
Types of
These ar
i) Metal
These de
a) By anio
lattice si
maintainin
electrons
Crystal:
Ex: When
atoms get
the cryst
Cl¯ ions c
are releas
b) By pre
Excess m
neighbou
For exam
The Zn2+
neighborin
freeelect
b) Metal
This defe
transition
3 Fe
2+
ion
neutrality
Instead, w
SOLID S
E SITE EDU
Non-stoi
re of two t
excess: T
efects ari
on vacanc
ite leaving
ng electr
are calle
n NaCl is
t deposite
al lattice
combine w
sed are tra
esence of
metal ions
uring inter
mple, when
ions occu
ng sites i
rons from
Deficienc
ect occurs
n metals, e
ns may be
y. That is
we have Fe
STATE (FU
UTECH 
chiometri
types
These def
se in two w
ies: It ar
g a hole
rical neut
ed F-cent
heated in
ed on the
leave the
ith the so
apped by t
extra cat
s are entr
rstitial sit
n ZnO is h
upy certai
n the latt
ma lower en
cy due to
s when t
e.g., in FeO
e replaced
why we
exO with x
LLY SOLV
cDefects
fects aris
ways:
ises due t
which is
trality. T
tres as th
the atmo
surface o
ir sites an
odium atom
the anion
tions in th
rapped int
es to main
eated, it l
in interst
tice. On h
nergy stat
cations va
he metal
O, FeS, Ni
d by 2 Fe
never hav
x = 0.93 t
VED) FOR C
CONTAC
:
se when t
to a negat
s occupied
The lattic
hey are r
osphere of
of the cry
nd diffuse
ms and th
vacancies.
he interst
to the vac
ntain elect
loses O2
a
itial sites
heating th
te.
acancies:
shows va
O etc. Th
e
3+
ions to
ve the ide
o 0.96.
CBSE (IIT-J
CT: 
there are
ive ion mis
d by elec
ce sites
responsibl
f sodium v
ystal. The
e to the s
ese Na at
.These are
titial sites
cant inter
trical neut
nd turns y
swhereas
he crystal
ariable va
is is becau
o maintain
ea compos
EE) EXAM

excess m
ssing from
ctron the
occupied
eforcolou
vapors, so
Cl¯ ions f
surface. T
toms ioniz
e called f
s:
rstitials s
trality.
yellow due
electrons
turns ye
acancy, i.e
use in FeO
n electrica
sition FeO
S (2021 - 2
 Pa
metal ions
m the
reby
d by
r of
dium
from
These
es and th
centers
ites and e
to the fo
released
llow, due
e.,
O,
al
O.
2022)
ge 1 of 30
s in the c
e electron
electrons
llowing re
will occu
to transit
crystal.
ns that
in the
action:
py the
tion of

 ACTIVE
Types of
Impurities
i) In ionic
one Sr
2+
ii) In cov
a) Doping
(having 4
valence e
electron i
b) Doping
with Grou
14 replace
to occupy
charge. H
PROPERT
(i) Electric
conductivit
(a) Metals
(b) Insulat
(c) Semi-co
Electrical
insulators,
range of 10
and holes (
conduction
SOLID S
E SITE EDU
Impurity
s are adde
c solids: F
ion there
valent soli
g with ele
valence
lectrons).
s present
g with elec
up 13 eleme
ed by that
these ho
ence, we g
TIES OF S
cal Propert
ty.
(conductor
tors
onductors
conductivit
it is of th
0
2
–10
–9
ohm
–
(positive) o
n and throu
STATE (FU
UTECH 
defects:
ed to chan
For examp
by creatin
ids:
ectron ric
electros)
For ever
making it
ctron def
ents like B
t of Group
les. Thus,
get p-type
SOLIDS
ties: Solids
rs)
ty of meta
e order of
1
cm
–1
. Elect
or through
gh (positiv
LLY SOLV
nge the pr
ple, SrCl2
m
ng a whole
ch impurit
may be d
ry atom o
n-type se
ficit impur
B, Al or Ga
p 13, a hole
holes mov
e semicond
s can be br
als is very
10
–12
ohm
–1
c
trical condu
the motion
e) holes is
VED) FOR C
CONTAC
operties o
may be add
e (a cation
ties: For
doped wit
f Group 1
emiconduct
rities: For
a (having 3
e is create
ve toward
ductors.
roadly clas
y high and
cm
–1
. Semi-
uctivity of
n of ions. T
called p-ty
CBSE (IIT-J
CT: 
of the crys
ded to Na
vacancy) a
example,
th Group
14 replace
tor
r example
3 valence e
ed. On app
s the nega
sified into
is of the
conductors
solids may
The conduc
ype conduct
EE) EXAM

stals. The
aCl. Two N
and impart
Group 14
15 elemen
ed by tha
, when Gr
electrons)
plying elec
ative plate
three type
order of
s have inte
y arise thro
ction throug
tion. Pure i
S (2021 - 2
 Pa
e process i
Na+ ions wi
ting condu
4 element
nts like P
at of Grou
roup 14 ele
), for ever
ctric field
e as if the
es, on the
10
6
–10
8
ohm
rmediate c
ough the m
gh electron
onic solids
2022)
ge 1 of 30
s called do
ll be repla
uctivity.
ts like Si
P ores (ha
up 15 one
ements is
ry atom of
, electron
ey carry p
basis of ele
m
–1
cm
–1
where
conductivity
otion of ele
ns is called
where con
oping.
aced by
or Ge
aving 5
e extra
doped
f Group
ns move
positive
ectrical
eas for
y in the
ectrons
d n-type
nduction

can take place only through movement of ions are insulators. The presence of defects in the crystal
structure increases their conductivity.
The conductivity of semi-conductors and insulators is mainly due to the presence of interstitial
electrons and positive holes in the solids due to imperfections. The conductivity of semi-conductors
and insulators increases with increase in temperature while that of metals decrease.
(ii) Magnetic Properties:
 Diamagnetic Materials: Materials which are weakly repelled by the magnetic field are called
diamagnetic materials. e.g. Cu+, TiO2
, NaCl and benzene. They do not have unpaired electrons.
 Paramagnetic Materials:The materials which are weakly attracted by magnetic field are called
paramagnetic materials. These materials have permanent magnetic dipoles due to presence of
atoms, ions or molecules with unpaired electron. e.g. O2
, Cu
2+
, Fe
2+
etc. But these materials lose
their magnetism in the absence of magnetic field.
 Ferromagnetic Materials: The materials which show permanent magnetism even in the absence of
magnetic field are called ferromagnetic materials. These materials are strongly attracted by the
magnetic field. e.g. Fe, Co, Ni and CrO2
. Ferromagnetism arises due to spontaneous alignment of
magnetic moments of ions or atoms in the same direction.

Alignment of magnetic moments in opposite directions in a compensatory manner and
resulting in zero magnetic moment gives rise to anti-ferromagnetism.
for example,MnO,Mn2
O3
andMnO2
.
 Alignment of magnetic moments in opposite directions resulting in a net magnetic moment
due to unequal number of parallel and anti-parallel magnetic dipoles give rise to ferri-
magnetism e.g. Fe3
O4
.
Ferromagnetic and ferrimagnetic substances change into paramagnetic substances at
higher temperature due to randomization of spins. Fe3
O4
, is ferrimagnetic at room
temperature and becomes paramagnetic at 850 K.
(iii) Dielectric Properties:
The electrons in insulators are closely bound to the individual atoms or ions and thus they do not
generally migrate under the applied electric field. However, due to shift in charges, dipoles are
createdwhichresultsin polarisation. The alignments of these dipoles in different ways i.e.
compensatory way (zero dipole) or non-compensatory way (net dipole) impart certain characteristic
properties to solids.
If the dipoles align in such a way that there is net dipole moment in the crystals, these crystals are
said to exhibit piezoelectricity or piezoelectric effect i.e. when such crystals are subjected to
pressure or mechanical stress, electricity is produced. Conversely, if an electric field is applied to
such a crystal, the crystal gets deformed due to generation of mechanical strain. This is called
inverse piezoelectric effect.
Some crystals which on heating, acquire electric charges on opposite faces, are said to exhibit
pyroelectric effect.
The solids, in which dipoles are spontaneously aligned in a particular direction, even in the absence of
electric field are called ferroelectric substances and the phenomenon is known as Ferroelectricity.
If the alternate dipoles are in opposite direction, then the net dipole moment will be zero and the
crystal is called anti-ferroelectric.
Ferroelectric solids – Bariumtitanate (BaTiO3
), sodium potassium tartrate (Rochelle salt) and
potassium hydrogen phosphate (KH2
PO4
). Anti-ferroelectric – Lead Zircon ate (PbZrO3
).
SuperConducting Materials:The materials which offer no resistance to the passage of
electricity is called superconductor or super conducting material. In this state, the materials
become diamagnetic and are repelled by the magnets. Most of the metals become super
conducting at low temperatures (2 – 5K). Highest temperature at which super conductivity is
known is 23K in alloys of niobium (e.g. Nb3
Ge). Many complex metal oxides have been found to
possess super-conductivity at somewhat higher temperatures.]
Material Temperature
Nb3
Ge 23 K
Bi2
Ca2
Sr2
Cu3
O10
105 K
Ti2
Ca2
Ba2
Cu3
O10
125 K

Band theory of solids:
1.According to band Theory, the atomic orbitals of atom in the crystal combine to form
molecular orbital which spreads over the complete crystal structure.
2.As the number of atoms in crystal increases, the number of molecular orbital containing
electrons increased. As the number of molecular orbitals increases the energy difference
between the adjacent orbitals decreases.
3.Until finally the energy gap becomes very small and molecular discrete energy levels
merge into one another to form continuous band of molecular orbitals which extend over
the entire length of crystal.
4.All the molecular orbitals are very close to each other and are collectively called a band.
5.There are two types of bands of molecular orbitals as follows :
1. Valence band:The atomic orbitals with filled electrons from the inner shells form
valence bands, where there are no free mobile electrons since they are involved in
bonding.
2. Conduction band: Atomic orbitals which are partially filled or empty on overlapping
form closely placed molecular orbitals giving conduction bands where electrons are
delocalized and can conduct, heat and electricity.
6.In metallic crystals, the valence bands and conduction bands are very close to each other
and a very little energy is required to excite electrons from valence bond in to the
conduction band. In conduction band the electron are delocalized and are free to move
from one end to the other end of the metal piece, this migration of electron makes the
metal good conductor of heat and electricity.
7.In substance which are bad conductor of heat and electricity, the spacing between the
valence band and conduction band is relatively more so that more energy is required to
promote electrons from valence band to conduction bond, hence electrons remains in
valence band and thus cannot move freely thus do not conduct heat and electricity and act
as insulators.
8.If the energy difference between valence band and conduction band is moderate, then the
substance in ordinary condition is non-conductor, but if heated it becomes conductor due to
transition of electrons into conduction band. Such conductors are semiconductors.

Conduction of electricity in Semiconductors: The substance which have poor electrical
conductance at low temperature but increases with increase in temperature is called semiconductor.
A substance containing filled band with electrons and a completely empty band behaves as a
semiconductor.
Example: Si, Ge, etc.
In excitation, empty conduction bands contain electrons to conduct electricity. However electrons
can be added to conduction band by adding impurity (like Arsenic with extra electrons to silicon
conduction band) and hence can become conductor of electricity.
Electron rich impurity:
n-type semiconductor: If the impurity from Group 15 i.e. (Arsenic) is added to group 14 (i.e.
silicon), some of the sites of silicon in the crystal are occupied by arsenic atoms each with one extra
electron in the conduction band and will be available for transport of electricity. Such type of
semiconductor with impurity having extra negative charge due to extra electron of impurity atom is
called n-type semiconductor.
Electron deficient impurity:
p-type semiconductor: If the impurity from Group 13 i.e. (Boron) added to Group 14 (i.e. silicon)
then some atoms of born will occupy some of the sites of silicon atoms. At all sites of boron atoms
one valence electron will be shorter as compared to silicon atoms and there will be a positive hole in
the lattice. Hence an electron from neighbouring silicon atoms jumps into the electron hole and
continues till the electron hole is transferred to the edge of the crystal lattice and movement of
electron takes place. This type of semiconductor is called p-type semiconductor.
Semiconductor Type
1 B doped with Si p‐type
2 As doped with Si n‐type
3 P doped with Si n‐type
4 Ge doped with In p‐type

 ACTIVE
Do yo
SOLID S
E SITE EDU
u want fu
C
STATE (FU
UTECH 
ull version
Contact u
https
LLY SOLV
ns of all C
us throug
O
s://wa.me
NCERT
VED) FOR C
CONTAC
Chemistry
h the fol
984453
Or click b
e/message
T SOLUTI
CBSE (IIT-J
CT: 
(Organic
llowingWh
32971
below link
e/NZ7T43
ONS
EE) EXAM

+ Inorgan
hatsApp
34AHPHO
S (2021 - 2
 Pa
nic + Phys
Number
OD1
2022)
ge 1 of 30
sical) note
es?

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