VIDYANIDHI V-TECHNO

Chapter 1
SOLID STATE

“Solid state of matter possesses fixed mass, volume, shape and rigidity “.
Solids are classified on the basis of arrangement of constituent particles. Due to their specific
arrangements, it shows wide range of properties and hence varied applications like as superconductors,
magnetic materials, polymers etc.

GENERAL CHARACTERISTICS OF SOLID STATE:

In nature the particular state of matter is governed by two opposing forces at given set of temperature and
pressure. These forces are intermolecular force of attraction and thermal energy. If intermolecular force
of attraction is high as compared to thermal energy, particles remains in closest position and hence very
less movement in particles is observed. In this case solid state is the preferred state of matter.
Let us revise the general characteristics of solid:
i) Fixed mass, volume and shape
ii) Strong intermolecular force of attraction
iii) Least intermolecular space
iv) Fixed position of constituent particles
v) Incompressible and rigid

CLASSIFICATION OF SOLIDS:
Solids are classified on the basis of arrangement of their
constituent particles. If the arrangement of constituent
particles is same throughout the solid (long range order) it
is called crystalline. If the arrangement of particles does not
follow any regular pattern throughout the solid (short range
order) it is called amorphous solid.

Characteristics of crystalline solid:

 It consists of large number of small crystals having a
definite geometrical shape.

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 The arrangement of constituent particles is regular throughout

the solid (long range order). That is a fixed pattern of
constituent particles repeat itself periodically over the entire
range of solid.
 They have sharp melting points.
 They are anisotropic in nature.
Anisotropy is defined as” Difference in properties when
measured along different axes or different directions”.
Crystalline solid show different values of some of the physical
properties like electrical resistance, refractive index etc.when
measured along the different directions. The anisotropy arises due to the different arrangement of particles
in different directions. Look the different arrangement of particles along the axis AB and CD in diagram
given below.

Characteristics of amorphous solid:

 The arrangement of constituent particles is irregular throughout the solid. Regular pattern of constituent
particle is visible in small areas only. That is it shows short-range order.
 Melting point is not sharp. Amorphous solid melts over a range of temperature.
 They have tendency to flow at slower rate.
 They are isotropic in nature.
“Isotropic means no difference in properties taken from any direction.”

Intext Questions:
Q.1 Classify the following solids as crystalline and amorphous.
Sodium chloride, quartz glass, quartz, rubber, polyvinyl chloride, Teflon
A.1 Crystalline solid: Sodium chloride, Quartz
Amorphous solid: Quartz glass, rubber, polyvinyl chloride, Teflon.
Q.2 why glass is considered as super cooled liquid?
A.2 Glass shows the tendency to flow at slower rate like liquid. Hence they considered as super cooled
liquid.
Q.3 why the window glass of old buildings show milky appearance with time?

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A.3 Glass is an amorphous solid. Amorphous solid has the tendency to develop some crystalline character
on heating. Due to heating in day over the number of years, glass acquires some crystalline character and
show milky appearance.
Q.4 why the glass panes fixed to window or doors of old building become slightly thicker at bottom?
A.4 Glass is super cooled liquid. It has the tendency to flow down very slowly. Due to this glass pane
becomes thicker at the bottom over the time.
Q.5 Sodium chloride is a crystalline solid. It shows the same value of refractive index along all the
direction. True/False. Give reason.
A.5 False
Crystalline solid shows anisotropy in properties. That is, it shows different values for the given physical
property in different direction. All the crystalline solids show anisotropy in refractive index. Therefore
sodium chloride will show different values of refractive index on different directions.
Q.6 Crystalline solid are anisotropic in nature. What does this statement means?
A.6 Anisotropy is defined as” Difference in properties when measured along different axis or from
different directions”. Crystalline solid show different values of some of the physical properties like
electrical resistance, refractive index etc.when measured along the different directions. The anisotropy in
crystalline solid arises due to the different arrangement of particles in different directions.

CLASSIFICATION OF CRYSTALLINE SOLIDS:

Classification with properties of solid in tabular form:

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Crystalline solid can be classified on the basis constituent particles and intermolecular force of attraction
in between them. Constituent particles are molecules, ions, metal kernel in sea of electrons and atoms.
Force of attraction operate in between the particles are dispersion force, dipole-dipole interaction,
hydrogen bonding, electrostatic attraction, metallic bonding and covalent bonding.

Q.2 what type of interactions hold the molecules together in a polar molecular solid.
A.2 The molecules in a solid are held together by van der Waals forces. The term van der Waals forces
include hydrogen bonding, dipole-dipole attraction and London dispersion forces. All molecules
experience London dispersion forces. In addition, polar molecules can also experience dipole-dipole
interactions. So, the interactions that holds the molecule together in polar molecular solid are London
dispersion force and dipole-dipole interactions.
Q.3 Write a feature that will distinguish a metallic solid from an ionic solid.
A.3 Metals are malleable and ductile whereas ionic solid are hard and brittle. Metallic solid has typical
metallic lustre. But ionic solid looks dull.
Q.4 Write a point of distinction between a metallic solid and an ionic solid other than metallic lustre?
A.4 Metals are malleable and ductile whereas ionic solid are hard and brittle.
Q.5 Write a distinguish feature of metallic solid.
A.5 The force of attraction in between the constituent particles is special kind of electrostatic attraction.
That is the attraction of positively charged kernel with sea of delocalized electrons.
Q.6 which group of solid is electrical conductor as
well as malleable and ductile?
A.6 Metallic solid
Q.7 why graphite is good conductor of electricity
although it is a network (covalent solid)?
A.7 The exceptional property of graphite is due to its
typical structure. In graphite, each carbon is
covalently bonded with 3 atoms in same layer. The
fourth valence electron of each atom is free to move
in between different layers.
This free electron makes the graphite a good
conductor of electricity.

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CRYSTAL LATTICE AND UNIT CELL

The characteristic feature of crystalline solid is regular and repeating arrangement of constituent particles
in space. The regular three dimensional arrangement of constituent particle in a crystal is known as
crystal lattice.
The smallest part of the crystal lattice is known as unit cell. Look at the role of unit cell in crystal lattice.

A unit cell is characterised by 6 parameters:

 3- edges a, b and c (refer the diagram given above). The edges may
or may not be perpendicular to each other.
 3 angles α (between b and c), β (between a and c) and γ (between a
and b).
Classification of unit cell:
i) Primitive unit cells: The constituent particles are only present at
corners of unit cell.
ii) Centred unit cells: The constituent particles occupy other
positions also beside the corners.
Centred unit cell can be further classified into 3-types:
a) Body- centred unit cells: Other than corner it contains one
constituent particle at the centre of the body of unit cell.
b) Face-centred unit cells: Other than corner it contains one
constituent particle at the centre of each face of unit cell.
c) End- centred unit cells: Other than corner it contains one
constituent particle at the centre of any two opposite faces of unit
cell.
On the basis of 6 parameters (3 edges and
3 angles) of unit cell mentioned above,
total seven types of primitive unit cells are
possible. The primitive unit cells show
variations in form of centred unit cells.
The total number of possible unit cells
(primitive and centred) in 3-dimensional
lattice is 14. This is called Bravais
Lattice. The detail of the lattice structure
in tabular form is given below.
Point to be noted is primitive unit cell
structure is 7 but total (primitive +
centred) is 14.

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The structure of above mentioned 14 Bravias lattice is as follows:

NUMBER OF ATOMS IN UNIT CELL

Primitive unit cell: In Primitive unit cell, atoms are present at
corner only. An atom is shared by 8 unit cell. Hence only 1/8th of
the atom belong to particular unit cell. There are total 8 corners in
each unit cell therefore, 1/8 part of 8 atoms would give the value
of number of atoms per unit cell. In brief 8 corners, 1 atom at each
corner, 1/8 of each atom in unit cell.

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Number of atoms present at different position is as follows:

 8 corners, 1 atom at each corner (1/8 of each atom in unit cell)
 1 atom at centre of body ( 1 atom completely present in the unit cell)
Total number of atom present in each unit cell:
= Contribution of atoms at corner + contribution of atom at the centre of the body
a) Face-centred unit cell -

Number of atoms present at different position is as follows:

 8 corners, 1 atom at each corner (1/8 of each atom in unit cell)
 6 faces, 1 atom at each face of unit cell ( ½ of each atom in the unit cell)
Total number of atom present in each unit cell:
= Contribution of atoms at corner + contribution of atom at the face of unit cell
Intext Questions:
Q.1 How many atoms can be assigned to its unit cell if an element forms (i) body centred cubic cell, and
(ii) a face centred cubic cell?

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A.1 (i) For body centred unit cell:

(ii) For face centred unit cell:
Q.2 How many lattice points are there in one unit cell of following lattices? (i) body centred cubic cell,
and (ii) a face centred cubic cell?
A.2 (i) For body centred unit cell:
8 lattice points at corner + 1 lattice point at centre of the body = 9 lattice points
(ii) For face centred unit cell:
8 lattice points at corner + 6 lattice point at face-centre of each face = 14 lattice points
Q.3 A cubic solid is made of two elements X and Y. Atoms Y are at the corners of the cube and X at the
body centre. What is the formula of the compound?
A.3 Number of X atom per unit cell = 1
Number of Y atom per unit cell = 1/8 x 8 = 1
Formula of compound = XY
Q.4 What is the number of atom in a unit cell of simple cubic crystal?
A.4 8 Corners x 1/8 atom at each corner =1 atom per unit cell
Q.5 A cubic solid is made of two elements X and Y. Atoms Y(anions) are at the corners of the cube and
X(cations) at present at face-centre of the cubic lattice. What is the formula of the compound?
A.5 Number of X atom per unit cell = 1/2 x 6 = 3
Number of Y atom per unit cell = 1/8 x 8 = 1
Formula of compound = XY3

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CLOSED PACKED STRUCTURE

As we the constituent particles in solid are in form of sphere. The spheres in solid are arranged in different
way to leave minimum vacant space. These arrangements of spheres in different layers form the closed
packed structure of solid. The crystals are formed in closed packed structures. Similarly spheres in solid
are also arranged in 3-dimension to form close-packed structure.
a) Close-packing in one-dimension:
 Spheres are arranged in a row with touching each other as shown below :

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In this type of arrangement spheres of both the layers are perfectly aligned horizontally and vertically.
This type of arrangement is known as AAA type closed packing of sphere in 3-dimension. The possible
smallest geometrical 3-dimensional shape would be cube. Thus this type of arrangement generate simple
cubic lattice with primitive type of unit cell.
(i) Hexagonal closed packing in three dimension:
 Placing second layer over the first layer-
- Spheres in the second layer are fit in the depression of first layer.

Let the number of close packed spheres be N, then:

The number of octahedral voids generated = N
The number of tetrahedral voids generated = 2N
 Placing the third layer above second layer –
- Covering tetrahedral voids: If all the tetrahedral voids of second layer is covered by third layer, then
third layer would be exactly aligned with the first layer as shown below:

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This forms the ABCABC... type of arrangement of sphere and is known as Cubic closed packing (ccp)
or face centred cubic (fcc) structure.
Coordination number: The number of nearest neighbour touching a particle in closed packed structure is
known as the coordination number of constituent particles.
In both type of crystal lattice (hcp, ccp or fcc) the coordination number for the constituent particle is 12.
Formula of compound:
Formula of the compound is deduced by calculating number of atoms present at lattice point and number
of atoms present in voids. Generally anions are bigger and they occupy the lattice point while cations are
occupied in voids.
In a given compound, it is not necessary that all the voids are occupied by constituent particles. Some time
only fraction of voids are occupied depend on the formula of compound. Therefore it is necessary to know
the position of voids in crystal lattice.

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Total number of octahedral voids = 1(body-centre) + 3 (edge-centre) = 4

As we know number of atom per unit cell for ccp is 4. Therefore:
The number of octahedral voids generated = N(number of atoms per unit cell)
Intext Questions:
Q.1 A compound is formed by two element A and B. Element B occupy all the ccp position and element
A occupy all the octahedral voids. Find the formula of compound.
A.1 In ccp number of atoms per unit cell = 4
Number of octahedral voids = same as number of atoms present at ccp = 4
Number of atoms of element B (at ccp) = 4
Number of atoms of element A (octahedral voids) = 4
Ratio of element A : B = 4 : 4 = 1 : 1
Formula of compound = AB
Q.2 A compound is formed by two elements A and B. The element B form ccp and element A occupy 2/3
of tetrahedral voids. What is the formula of compound?
A.2 Let the number of atoms of element B form ccp: N
The number of tetrahedral voids would be: 2N
Since 2/3 of tetrahedral voids are occupied therefore number of atom of element A would be: 2N x 2/3 =
4/3 N
Ratio of element A: B = 4/3: 1 or
Simple whole number ratio A: B = 4: 3
Formula of compound: A4B3.
Q.3 An oxide of aluminium is formed where oxide ions occupy all the hcp positions and aluminium ion
occupy 2/3 of octahedral voids. What is the formula of compound?

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A.3 Let the number of atoms of oxide form hcp: N

The number of aluminium ions in octahedral voids would be: N
Since 2/3 of octahedral voids are occupied therefore number of aluminium ion would be: N x 2/3 = 2/3 N
Ratio of element Aluminium ion: oxide ion = 2/3N: 1N or
Simple whole number ratio Aluminium ion: oxide ion = 2: 3
Formula of compound: Al2O3.
Q.4 What is the coordination number of each type of ion in rock-salt type crystal structure.
A.4 Rock salt (NaCl) has fcc type of crystal structure.
In fcc the cations in voids touches 6 nearest neighbour as well as anion at lattice point also touches 6
nearest neighbour.
Coordination number of Na+ = 6
Coordination number of Cl- = 6
Q.5 what is the two-dimensional coordination number of a molecule in square-closed packed layer.
A.54
PACKING EFFICIENCY:
Packing efficiency is defined as percentage of total space filled by the constituent particles in crystal.
Packing efficiency in hcp and ccp structures:
Let us consider the unit cell of ccp in which sphere ABCDEFGH are occupied at corner. And sphere
a,b,c,d,e,f are placed at centre of face.

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IMPERFECTION IN SOLIDS
Although in crystalline solid there is regular arrangement of constituent particles but yet the crystals are
not perfect. There is always some king of irregularity in arrangement of constituent particles in small
crystals. These
Irregularities are known as defects in crystal. There are 2 types of defects known in crystal lattice.
 Point defect
 Line defect
In our syllabus only point defects are included so we will focus our study on point defects only.
POINT DEFECTS:
 Impurity defect
 Stoichiometric defects
 Non- stoichiometric defects
Types of stoichiometric defects and Non- stoichiometric defects are mentioned in tabular form.
Stoichiometric defects Non- stoichiometric defects
Vacancy defect Metal excess defect
Interstitial defect Metal deficiency defect
Frenkel defect
Schottky defect

Impurity defect:
Impurity defect is arises due to addition of small amount of impurity in ionic solid. It actually creates
some kind of cationic vacancy in ionic solid. For example, if some SrCl2 is added in molten salt of NaCl
it takes the position of Na+ in the crystal. But charge on Sr is 2+. After removing 2 ions of Na+, Sr2+
occupy one point only. In this way it causes vacancy of 1 point.

Vacancy defect:
It arises when some of the lattice point remains unoccupied during the crystal formation.
 It occurs in non-ionic compounds
 It decreases the density of solid
 It can be created by heating

Interstitial defect:
It arises when some of the constituent particles occupy the interstitial sites other than the lattice points.
 It occurs in non-ionic compounds
 It increases the density of solid

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Impurity defect:
Impurity defect is arises due to addition of small amount of impurity in ionic solid. It actually creates
some kind of cationic vacancy in ionic solid. For example, if some SrCl2 is added in molten salt of NaCl
it takes the position of Na+ in the crystal. But charge on Sr is 2+. After removing 2 ions of Na+, Sr2+
occupy one point only. In this way it causes vacancy of 1 point.

Frenkel defect:
It is actually the combination of vacancy defect and interstitial defect in ionic compound. It arises when
smaller ion is dislocated from its normal site and occupies an interstitial site. It is also known as dislocation
defect.
 It occurs in ionic compounds
 It does not change the density of solid
 Shown by ionic compound having large difference in their constituent ions.
For example: ZnS, AgBr, AgI etc.

Schottky defect:
It is actually a vacancy defect. But it causes vacancy of cation and anion both.
It occurs in ionic compounds
It decrease the density of solid
Shown by ionic compound having similar size of cation and anion.
It is actually the combination of vacancy defect and interstitial defect in ionic compound. It arises when
smaller ion is dislocated from its normal site and occupies an interstitial site. It is also known as
dislocation defect.
It occurs in ionic compounds
It does not change the density of solidShown by ionic compound having large difference in their
constituent ions.
For example: ZnS, AgBr, AgI etc.

Schottky defect:
It is actually a vacancy defect. But it causes vacancy of cation and anion both.
 It occurs in ionic compounds
 It decrease the density of solid
 Shown by ionic compound having similar size of cation and anion
For example: NaCl, KCl, AgBr.
Important point: AgBr shows both Frenkel and schottky defect.

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Metal excess defect:

Due to anionic vacancies:

Anionic vacancies are created due to reaction of anion of the crystal with excess of metal present in the
atmosphere. For example when crystal of NaCl is heated in presence of sodium vapour, the sodium atoms
are deposited on the surface of crystal and later on forms the bond with Cl- ion by losing an electron.
In this way it creates a vacancy for Cl- ion. But the electron removed by sodium metal diffuse in the crystal
and occupies the anionic site. This creates an F-centre. The presence of unpaired electron at vacant anionic
site in metallic crystal is known as F-centre. This F-centre is responsible for imparting colour to the crystal.
Like as:
NaCl – yellow colour
LiCl – pink
KCl-violet.
 It occurs in ionic compounds
 It is responsible for imparting colour to the crystal through F-centres.
For example: NaCl, KCl, LiCl.
Due to presence of extra cations:
Excess cationic sites are generated due to the loss of anion of crystal after any reaction. The excess of
cation occupies the interstitial site. ZnO on heating loss oxide ion from the crystal. The excess of Zn2+
ions occupy the interstitial site and electron lost by oxide ion occpy the neighbouring site, in this way
maintain the electrical neutrality of crystal.
 It occurs in ionic compounds
 It is responsible for imparting colour to the crystal through free electrons.
For example: ZnO (white at room temperature, yellow on heating)
Metal deficiency defect:
Number of metal cations is less as required by metallic crystal. For example in FeO the actual composition
ranges from Fe0.93O to Fe0.95O.

ELECRTICAL PROPERTIES:
Solid are classified as conductor, semi-conductor and insulator on the basis of the magnitude of
electrical conductivity.
 Conductor: electrical conductivity range 104 to 107 ohm-1m-1
 Semi-Conductor: electrical conductivity range 10-6 to 107 ohm-1m-1.
 Insulator: electrical conductivity range 10-20 to 10-10 ohm-1m-1

CONDUCTION OF ELECTRICITY
As we know that free electrons are responsible for the conduction of electricity in metals. Electrons are
occupied in atomic orbital. The atomic orbital forms molecular orbital in metallic crystal. Molecular
orbital are very closer in energy and known as bands. To be a conductor there must be some electrons in

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conduction band. But electrons are mainly occupied in valance band. On the basis of conductivity solids
are classified in 3 types: Conductor, semi-conductor, insulator.
 In case of conductor there is an overlapping of valance band and conduction band.
 In semi-conductor there is small gap of energy between valance band and conduction band. Some of the
electron may jump and show some activity. The metal showing this type of activity is known as intrinsic
semi-conductors. For example : Silicon and Germanium
 In case of insulator there is a large energy difference between valance band and conduction band

Classification of semi-conductors:
The electrical conductivity of semi-conductors can be increased by adding some electron rich impurity or
electron deficient impurity. This is called doping.
n-type semiconductor: When the conductivity of semi-conductor is increased by adding electron rich
impurity. It generates n-type semi-conductor. For Example: when Silicon is doped with phosphorus,
phosphorus also occupies some lattice site. The covalency of Si is 4 but that of P is 5. So, one electron per
atom left unused and it delocalise from its location. This delocalise electron help in increasing conductivity
of semi-conductor.

p-type semiconductor : When the conductivity of semi-conductor is increased by adding electron

deficient impurity. It generates p-type semi-conductor. For Example: when Silicon is doped with boron,
boron also occupies some lattice site. The covalency of Si is 4 but that of B is 3. So, one of the position
of electron is left unused. This is called electron hole. The electron from neighbouring atom moves to fill
this hole but creates a new hole. This looks like movement of electron hole throughout the system.
Electrons moves through theses hole under the influence of electric fields. In this way electrical
conductivity increases.

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Application of n-type and p-type semiconductors:

By the combination of n-type and p-type semi-conductors many electronic devices are prepared.
 Diode (is a device that allows the current in one direction only) is used as amplifier
 pnp and npn sandwiching is done in making transistors
 As photo diode in solar cells
 In lasers

MAGNETIC PROPERTIES:
Electrons are charged particles and it generates a magnetic field around itself. The magnetic field arises
due to the spinning of electron at its own axis and movement of atomic orbital around nucleus.

Classification of magnetic properties:

I. Paramagnetism:
 Weakly attracted by magnetic fields
 Alignment of magnetic dipole in the same direction of magnetic field
 Loose magnetism in absence of magnetic field
 They have unpaired electrons
Ex. Cu 2+, Fe 3+
II. Diamagnetism:
 Weakly repelled by magnetic fields
 Alignment of magnetic dipole in the opposite direction of magnetic field
 They have all the electrons paired
Ex. H2O, NaCl
III. Ferromagnetism:
 strongly attracted by magnetic fields
 Permanently magnetised.
Ex. Fe, Co, Ni etc.
IV. Anti-Ferromagnetism:
 strongly repelled by magnetic fields
 Alignment of magnetic domains (group of metal ions)in the opposite direction of magnetic field..

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Ex. MnO
V. Ferrimagnetisms:
 Weakly attracted by magnetic fields
 Alignment of magnetic domains (group of metal ions)in the parallel and anti parallel direction with
direction of magnetic field and unequal in number.
 Loss magnetic moment on heating.
Ex. Fe3O4(magnetite)

Summary:
 Solids have definite mass, volume and shape. This is due to the fixed position of their constituent particles
and strong intermolecular force of attraction.
 Solids are classified as amorphous and crystalline.
 In amorphous solids, the arrangement of constituent particles has only short
 Range order. The melting point is not sharp. They are isotropic in nature. In crystalline solids there is
long range order in the arrangement of their constituent particles. The melting point is sharp. They are
anisotropic in nature.
 Properties of crystalline solids depend upon the nature of interactions between their constituent particles.
On this basis, they can be divided into four categories, namely: molecular, ionic, metallic and covalent
solids.
 The constituent particles in crystalline solids are arranged in a regular pattern which extends throughout
the crystal. This arrangement is often depicted in the form of a three dimensional array of points which is
called crystal lattice. Each lattice point gives the location of one particle in space. In all, fourteen different
types of lattices are possible which are called Bravais lattices. Each lattice can be generated by repeating
its small characteristic portion called unit cell
 A unit cell is the smallest portion of space lattice which when repeated in different directions , generate
the entire lattice. A unit cell is characterised by its edge lengths and three angles between these edges.
Unit cells can be either primitive which have particles only at their corner positions or centred. The centred
unit cells have additional particles at their body centre (body-centred),at the centre of each face (face-
centred) or at the centre of two opposite faces (end-centred)
 There are seven types of primitive unit cells. Taking centred unit cells also into account, there are fourteen
types of unit cells in all, which result in fourteen Bravais lattices

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 Close-packing of particles is obtained in two highly efficient lattices, hexagonal close-packed (hcp) and
cubic close-packed (ccp). The latter is also called facecentredcubic (fcc) lattice. In both of these packings
74% space is filled. Other types of packing are not close-packings and have less efficient packing of
particles. While in body-centred cubic lattice (bcc) 68% space is filled, in simple cubic lattice only 52.4
% space is filled
 The remaining space is present in the form of two types of voids-octahedral voids and tetrahedral voids
 Solids are not perfect in structure. There are different types of imperfections or defects in them. Point
defects and line defects are common types of defects
 Point defects are of three types - stoichiometric defects, impurity defects and non-stoichiometric defects
 Vacancy defects and interstitial defects are the two basic types of stoichiometric point defects. In ionic
solids, these defects are present as Frenkel and Schottky defects
 Impurity defects are caused by the presence of an impurity in the crystal. In ionic solids, when the ionic
impurity has a different valence than the main compound, some vacancies are created
 Nonstoichiometric defects are of metal excess defect and metal deficient defect
 On the basis of electrical conductivity solids are classified as conductor, semiconductor and insulator
 Sometimes calculated amounts of impurities are introduced by doping in semiconductors that change their
electrical properties. Such materials are widely used in electronics industry. They are of two types namely,
n-type semiconductor and p-type semiconductor
 Solids show many types of magnetic properties like paramagnetism, diamagnetism, ferromagnetism,
antiferromagnetism and ferrimagnetism

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