SSP UNIT-I CRYSTAL STRUCTURE ENGINEERING PHYSICS.pdf

SOLID STATE PHYSICS
UNIT - I
CRYSTAL STRUCTURE
INTRODUCTION
It deals with the study and interpretation of geometric form and
macroscopic properties of the solid in terms of the microscopic properties of the
crystal in the solid by using X-rays, electron beams and neutron beams. Solids
are classified into two categories based on the arrangement of atoms or
molecules:(i) Crystalline solids and (ii) Amorphous solids.
Crystalline solids
In crystalline solids, atoms are arranged in a regular manner, i.e., the atomic
array is periodic in which a basic unit is repeated infinitely in the body of the
solid. Each of the atoms are at regular intervals along the arrays in all directions
of the crystal. The crystalline solids have different periodic arrangement in all the
three directions and the physical properties vary with direction and are also called
as “an-isotropic substances”. the structure may be made up of metallic crystals or
non-metallic crystals. The metallic crystals find wide application is engineering
because of their strength, conductivity, reflection, etc.
Examples of metallic crystal: copper, silver, aluminium, tungsten, etc.
Amorphous Solids (Non-metallic Crystals)
In amorphous solids, the atoms or molecules are arranged randomly. The
amorphous solids have no regular structure and have same physical properties in
all directions and hence, they are known as “isotropic substances”. such materials
have no specific electrical property but have only plasticity.
Examples are: glass, plastics and rubber.
FUNDAMENTAL TERMS OF CRYSTALLOGRAPHY
The structures of all crystals are described in terms of lattice with a group
of atoms, each in a lattice point. The group is termed as basis. The basis is
repeated in space to form the crystal structure. The following are the various
crystallographic terms in detail.

Space lattice
A space lattice is defined as an infinite array of points in three dimensional space
in which every point has surroundings identical to that of every other point in the
array.
Basis
Crystal structure is formed by associating with every lattice point – a unit
assembly of atoms or molecules identical in composition, arrangement and
orientation. This unit assembly is called basis
Crystal structure
A crystal structure is obtained by arranging the basis in each and every
lattice point. It can be written as
Crystal structure = lattice + basis
Unit cell
Unit cell is the smallest volume enclosed structure which when repeated in
3D and 2D space forms a crystal. In the construction of a wall, brick are arranged
one above the other. Therefore in the case of a wall, a brick is said to be a unit
cell. Similarly, in the case of a crystal, a smallest unit is arranged one above the
other. This smallest unit is known as unit cell. Thus, a unit cell is defined as a
fundamental building block of a crystal structure.
Crystallographic Axes
Consider a unit cell consisting of three mutually perpendicular edges OA,
OB and OC. Draw parallel lines along the three edges. These lines are taken as
crystallographic axes and they are denoted as x, y and z axes.

Primitives
Consider the unit cell, let OA be an intercept along the x-axis. Similarly
the intercepts made by the unit cell along the y and z axes are OB and OC I.e.,
OA, OB and OC are the intercepts made by the unit cell along the crystallographic
axes. These intercepts are known as primitives. In crystallography, the intercepts
OA, OB and OC are represented as a, b and c respectively.
Lattice parameters
In order to represent a unit cell, the six parameters such as three primitives
a, b and c of unit cell and the three inter-facial angles α, β and γ are essential
which are known as lattice parameters.
Primitive cell
It is the smallest unit cell in volume constructed by primitives. It consists of only
one full atom as shown in below fig.
If a unit cell consists of more than one atom, then it is not a primitive cell. A
simple cubic unit cell is said to be a primitive cell, whereas a body centred cubic
unit cell is not a primitive cell.

TYPES OF CRYSTALS
Crystals are classified into seven systems on the basis of the shape of the unit cell.
These are classified in terms of lengths of unit cells and the angle of inclination
between them.
The seven crystal systems are: Cubic, Tetragonal, Orthorhombic, Monoclinic,
Triclinic, Trigonal and Hexagonal.
Bravais lattice
Bravais, in 1948, showed that there are 14 different types of unit cells under the
seven crystal system which forms Bravais lattices. They are commonly known as
Bravais lattices. Below table shows the seven crystal systems, the number of 14
possible Bravais lattices and the corresponding lattice symbols of the crystal
types.

Bravais lattices (14 types of unit cells)
Miller indices
Miller devised a method to represent a crystal plane or direction. In this
method, to represent a crystal plane, a set of three numbers are written within the
parentheses. Similarly, crystal direction is represented as a set of three numbers
written within the square brackets. Miller index is one in which the crystal plane
is represented within the parenthesis.

Rules to find the Miller Indices of a Plane:
To find the Miller Indices of a given plane, the following steps are to be followed:
1. The intercepts made by the plane along x,y,z axes are noted.
2. The coefficients of the intercepts are noted separately.
3. Inverse is to be taken.
4. The fractions are multiplied by a suitable number, so that all the
fractions become integers, and
5. Write the integers within the parentheses.
Notes
1. While writing Miller indices, comma or dot between any two
numbers should be avoided.
2. The positive x-axis is represented as (1 0 0), y-axis as (0 1 0) and z-
axis as (0 0 1). Similarly, the negative x-axis as (10 0), negative y-
axis as (0 1 0) and negative z-axis as (0 0 1).
3. The Miller indices for a plane (1 0 1) is read as ‘one zero one’ and
not as one hundred and one.
For example, Miller indices of the plane shown in below given fig. can be found
by the following method.
The given plane ABC makes intercepts 2a, 3b and 2c along the x, y and z axes
respectively.
 The intercepts are 2a, 3b, 2c.
 The coefficients of the intercepts are respectively 2, 3and 2.
 The inverse are 1/2, 1/3, 1/2 respectively. The LCM is 6.
 Multiply the fractions by 6, they become integers as 3, 2 and 3.

 The integers are written within the parenthesis as (323). Therefore,
(323) is the Miller indices of the given lane ABC.
Salient Features of the Miller Indices
(i) A plane parallel to one coordinate axis is taken as that plane will
meet the axis at infinity. Therefore the intercept is taken as infinity.
The index number (Miller indices) for that plane in that coordinate
axis is zero.
(ii)A plane passing through the origin is defined in terms of a parallel
plane having non-zero intercepts.
(iii) Equally spaced parallel planes have the same Miller indices.
(iv) Planes which have negative intercepts are represented by a bar, like
(1¯0 0). The Miller indices (1¯0 0) indicate that the plane has an
intercept in the negative x-axis.
Important Feature of Miller Indices
The Miller index notation is especially useful for cubic systems. Its
desirable features are:
(i) The angle θ between any two crystallographic directions [u1 v1 w1]
and [u2 v2 w2] can be calculated easily. The angle θ is given as
cos θ =
𝑢1𝑢2+𝑣1𝑣2+𝑤1𝑤2
(𝑢1
2+𝑣1
2+𝑤1
2)1/2(𝑢2
2+𝑣2
2+𝑤2
2)1/2
(ii) The direction [hkl] is perpendicular to the plane (hkl).
(iii) The relation between the interplaner distance and interatomic
distance is given as
d =
𝑎
√ℎ2+𝑘2+𝑙2
(iv) If (hkl) is the Miller indices of a crystal plane, then the intercepts
made by the plane with the crystallographic axes are given as a/h,
b/k and c/l, where a, b and c are the primitives.
Procedure to Find the Miller Indices of a Direction
To find the Miller indices of a direction, choose a perpendicular plane to
that direction. Find the Miller indices of that perpendicular plane. The
perpendicular plane and the directions will have the same Miller indices value.
Therefore, the Miller indices of the perpendicular plane is written within a square
bracket to represent the Miller indices of the direction.

To find the Miller indices of a line (direction), find the direction ratios of that line
and then, write them within the square brackets. It represents the Miller indices
of that line.
The Miller indices of some of the important cubic crystal planes are as shown
below.
Relation between interplanar distance and cubic edge
Consider a cubic crystal with cube edge a. Let (h k l) be the miller indices for the
plane ABC as shown in the figure. The intercepts made by the plane are a/h, a/k,
a/l. Consider another plane PQR parallel to the above ABC, passing through the
origin O. A perpendicular line drawn from the origin o to the plane ABC
represents the distance between two parallel planes. Let ON be the distance d
between the two parallel planes.

Let αʹ, βʹ, γʹ be the angles made by line ON respectively with x, y and z axes. The
direction cosines, cos αʹ, cos βʹ, cos γʹ are written as
cos αʹ = ON/OA =d/(a/h) = dh/a ……….(1)
cos βʹ = ON/OB =d/(a/k) = dk/a ……… .(2)
cos γʹ = ON/OC =d/(a/l) = dl/a …….….(3)
From the properties of the direction cosines of any line, we can write
Cos2 αʹ + Cos2 βʹ + Cos2 γʹ = 1
i.e.,
(𝑑ℎ/𝑎)2
+ (𝑑𝑘/𝑎)2
+ (𝑑𝑙/𝑎)2
= 1
𝑑2
𝑎2
(ℎ2
+ 𝑘2
+ 𝑙2
) = 1
or
d =
𝑎
√ℎ2+𝑘2+𝑙2
……….(4)
Equation (4) gives the relation between the interatomic distance a and the
interplanar distance d.
CRYSTAL STRUCTURES OF MATERIALS
The following are the some of the important parameters which can be used
to describe the crystal structures of materials.
(a) Atomic radius
(b)Coordination number
(c) Density of packing

(a) Atomic radius
It is half the distance between any two successive atoms. For a simple cubic
unit cell , the atomic radius r is given by
r = a/2
Where a is the interatomic distance.
(b) Coordination number
It is the number of nearest neighbouring atoms to a particular atom. For a simple
cubic unit cell, the coordination number is 6.
(c) Density of packing
It is the ratio between the total volume occupied by the atoms or molecules in a
unit cell and the volume of unit cell. i.e.,
Density of packing =
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑎𝑡𝑜𝑚𝑠 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑋 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚
Simple cubic (SC) crystal structure
A simple cubic (SC) unit cell consists of eight corner atoms as shown in
the figure. In actual crystals, each and every corner atom touches with each other
and is shared by eight adjacent unit cells. Therefore, one corner atom contributes
1/8 of its part to one unit cell. Hence the total number of atoms present in a unit
cell is
1
8
X 8 =1
Arrangement of atoms in SC unit cell

Atomic radius
For simple cubic unit cell, the atomic radius is given by,
r =
𝑎
2
….. (1)
Coordination number
The coordination number of a simple cubic unit cell can be calculated as
follows:
Let us consider any one corner atom. For this atom, there are four nearest
neighbours in its own plane. There is another nearest neighbour atom in another
plane which lies just above this atom and yet another nearest neighbour atom in
another plane which lies just below this atom. Therefore, the total number of
nearest neighbour atom is six and hence, the coordination number is 6.
Packing density
The packing density of a simple cubic unit cell can be calculated as follows; For
simple cubic, the total number of atoms is present in a unit cell is 1. Therefore,
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑎𝑡𝑜𝑚𝑠 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑋 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚
1(
4
3
)𝜋𝑟3
𝑎3
…… (2)
Substituting the value of r from equation (1) in equation (2)
Packing density =
1(
4
3
)𝜋(
𝑎
2
)3
𝑎3
Packing density = π/6
Packing density = 0.52 ….. (3)
Therefore, 52% of the volume of the simple cubic unit cell is occupied by atoms
and the remaining 48% volume of the unit cell is vacant.
Body Centred Cubic (BCC) crystal structure
A body centred cubic (BCC) structure has eight corner atoms and one body
centred atom. The diagrammatic representation of a body centred cubic structure
is shown in the figure below. In a body centred crystal structure, the atoms touch

along the diagonal of the body. In a BCC unit cell, each and every corner atom is
shared by eight adjacent unit cells. Therefore, the total number of atoms
contributed by the corner atoms is
1
8
X 8 =1.
Arrangement of atoms in BCC unit cell
A BCC unit cell has one full atom at the centre of the unit cell. Therefore, the
total number of atoms present in a BCC unit cell is 2
Atomic radius
For a body centred cubic unit cell, the atomic radius can be calculated by the
following way:
From the above figure
AH = 4r and DH = a
From the triangle AHD,
AD2
+DH2
=AH2
……(1)
To find AD, consider the triangle ABD
From the triangle ABD,

AB2
+BD2
=AD2
……(2)
a2
+ a2
= AD2
AD2
= 2 a2
AD = √2 a ..….(3)
Substituting the values of AD, AH and DH in equation (1), we get
AD2
+DH2
=AH2
……(1)
2a2
+ a2
= 16 r2
r2
= (3/16) a2
r =
√3
4
a
Therefore the atomic radius, r =
√3
4
a ….. (4)
Packing density
The packing density of a body centred cubic unit cell can be calculated as follows:
The of atom present in a unit cell is 2
Density of packing = Total volume occupied by the atoms in a unit cell
Volume of the unit cell
= Number of atoms present in a unit cell X volume of one atom
2(
4
3
)𝜋𝑟3
𝑎3
Packing density =
2(
4
3
)𝜋𝑟3
𝑎3
…… ……(4)
Substituting the value of r from equation (3) in equation (4), we get,
Packing density =
2(
4
3
)𝜋(√3/4)
3
𝑎3
𝑎3
Packing density =
√3𝜋
8
Packing density = 0.68

Therefore, 68% of the volume of the body cubic unit cell is
occupied by atoms and the remaining 32% volume of the unit
cell is vacant.
Face Centred Cube (FCC) structure
A face centred cubic (FCC) unit cell consists of eight corner atoms and six
face centred atoms. A face centred cubic unit cell is shown in the figure. The
atoms in a face centred cubic unit cell touches along the face diagonal. Each and
every corner atom is shared by eight adjacent unit cells. Hence the total number
of atoms contributed by the corner atoms is
1
8
X 8 =1
Arrangement of atoms in FCC unit cell
Each and every face centred atom is shared by two unit cells. Therefore a face
centred atom contributes half of its part to one unit cell. The total number of atoms
contributed by the face centred atom is
1
2
X 6 =3
Therefore, the total number of atoms present in an FCC unit cell is 4.
Coordination number
The coordination number can be calculated as follows: Let us consider a corner
atom. In its own plane, that corner atom has four face centred atoms. These face
centred atoms are its nearest neighbours. In a plane which lies just above this
corner atom, it has four face centred atoms as nearest neighbours. In a plane which
lies just below this corner atom,it has four more face centred atoms as its nearest
neighbours. Therefore, for an atom in an FCC unit cell, the number of nearest
neighbours is 12.

Atomic radius
The atomic radius can be calculated from figure as follows. In the
figure consider the triangle ABC
AC2
=AB2
+ BC2
(4r)2
= a2
+ a2
16r2
= 2 a2
r = a/(2√2) …(1)
Packing density
The packing density of the FCC unit cell can be calculated as follows: The
number of atoms present in an FCC unit cell is 4. Therefore, from below equation
Density of packing = Total volume occupied by the atoms or molecules in a unit cell
4(
4
3
) 𝜋𝑟3
𝑎3
…… (2)
Substituting the value of r =
𝑎
2√2
from equation (1) in equation (2), we get,

4(
4
3
)𝜋 ( 𝑎/2√2)
3
𝑎3
=
𝜋
3√2
Density of packing = π/(3√2) =0.74
Therefore, 74% of the volume of the Face Centred Cubic unit cell is occupied by
atoms and the remaining 26% volume of the unit cell is vacant.
Hexagonal Closed Packed (HCP) structure
The hexagonal closed packed (HCP) structure is shown in the figure. An HCP
structure consists of three layers of atoms. The bottom layer has six corner atoms
and one face centred atom. The middle layer has three full atoms. The upper layer
has six corner atoms and one face centred atom.
In the bottom layer, the central atom is surrounded by six other atoms
having equal radius. The sequence of arrangement of atoms in HCP structure is
top layer, middle layer and bottom layer and the sequence is repeated. The total
number of atoms present in the case of HCP structure is 6, to calculate this, first
consider the bottom layers of atoms. The bottom layer consists of six corner
atoms and one faced atom. Each and every corner atom contributes 1/6 of its part
tone unit cell. Thus, the total number of atoms contributed by the corner atoms is
(
1
6
) 6 = 1. The face centred atom contributes ½ of its part to one unit cell.
Therefore, the total number of atoms present in the case of the bottom layer is
1+ (
1
2
) = (
3
2
). Similarly, the upper layer also has 3/2 number of atoms. The middle
layer has three full atoms. Therefore, the total number of atoms present in a unit
cell is
3
2
+
3
2
+ 3 = 6.

Atomic radius
The atomic radius of an HCP crystal structure can be calculated as follows; let us
consider any two corner atoms, each and every corner atom touches each other as
shown in the figure below.
Therefore, we can write a = 2r….. (1)
Atomic radius r = a/2
Coordination number
The coordination number of an HCP structure can be calculated as follows
: Let us consider a face centred atom in the bottom layer. This face centred atom
is surrounded by six corner atoms. These corner atoms are the nearest neighbours.
The middle layer has three atoms which are nearest neighbours to the face centred
atom. A unit cell, which lies below the reference unit cell, also has three middle
layer atoms. These three atoms are also the nearest neighbours for the face centred
atom. Therefore, the total number of nearest neighbours is 6+3 + 3=12.
Coordination number = 12.
Packing density
Density of packing = Total volume occupied by the atoms or molecules in a unit cell
Area of the base = 6 X area of the triangle INO
Area of the base = 6 X ½ X IN X OR
Area of the base = 3 X a X
√3
2
X a =3
√3
2
a2
Volume of unit cell = area of the base X height

=
3√3
2
a2
X c
The density of packing of an HCP structure can be calculated as follows:
Packing density = 6 X (4/3) X π X r3
(
3√3
2
) a2
X c ……..(1)
Substituting the value of r =
𝑎
2
in equation (1), we get,
Packing density =
2𝑋 6 𝑋 4 𝑋𝜋𝑋(
𝑎
2
)3
3𝑋3√3 𝑎𝑋𝑎𝑋𝑐
…… (2)
c/a = √(
8
3
) = 1.633 …… (3)
Substituting the value of (c/a) from equation (3) in equation (2) , we have
Packing density =
2𝜋
3√3
(
√3
8
) =
𝜋
3√2
= 0.74 = 74% ….. (4)
Packing density = 0.74
Therefore, 74% of the volume of the HCP unit cell is occupied by atoms and the
remaining 26% volume of the unit cell is vacant.
Relation between c and a (c/a ratio):

Let ‘a’ be the distance between the two neighbouring atoms and ‘c’ be the
height of the HCP unit cell. The bottom layer of the unit cell is assumed to be the
combination of 6 triangles, then consider one among that triangle INO. The
normal drawn from the origin O bisects the line IN at a point R. then from the
triangle IRO,
Cos30ͦ =
𝑂𝑅
𝑂𝐼
OR = OI Cos30ͦ = a
√3
2
If S is the orthocentre of the triangle INO, then the line OS is 2/3 of the line OR
OS = 2/3 OR
OS = 2/3X a
√3
2
=
𝑎
√3
Consider the middle layer atoms located at a distance of c/2 from the bottom layer
of the cell. Then from the triangle SOP
OP2
= OS2
+ SP2
a2
= (
𝑎
√3
)
2
+ (
𝑐
2
)
2
a2
-
a2
3
=
c2
4
2a2
3
=
c2
4
𝑐
𝑎
= √(
8
3
) = 1.633
Structure of the Ceramics
Most of the ceramics have crystalline structures, which are formed by the
chemical reactions between the non-metallic and metallic elements. The ceramic
material is formed due to the ionic bonding between the two elements resulting
in the existence of coulombic force of attractions between the negatively charged
anions and positively charged cations. The cations and anions are formed
respectively due to the loss of valence electrons from the metallic elements and
conversions of non-metallic elements. Understanding of the structures of the
ceramic materials provides an explanation for the contributions of the positively

charged and negatively charged ions, to explore the strength of the electrostatic
attractive and repulsive forces.
The following are the structures of the technical ceramic compounds:
(i) NaCl structure
(ii)Fluorite structure, and
(iii)Perovskite structure
Compounds with NaCl structure
One of the important ceramic compounds displaying the NaCl structure is
MgO. The Na+ ions are replaced by Mg2+ ions and the Cl- ions are replaced by
O2-ions. As a result, the properties of MgO in the NaCl structure, such as melting
points, hardness increases, leading to many industrial applications
Crystal structure of NaCl
Compounds with Fluorite structure
Most of the properties of the ceramics depend on their structures. The
structure of calcium fluoride (CaF2) is shown below. The compounds such as
uranium oxide (UO2) and zirconium oxide (ZrO2) crystallize in the CaF2
structure.
Crystal structure of CaF2

Crystal structure of UO2 and ZrO2
The structures of UO2 and ZrO2 are more apparent by showing a sizable
hole in the center of the unit cell. In the case of UO2, the hole is about 0.21 nm
and is equal to the size of helium atom, which is a nuclear fission product. The
crystal structure of UO2 can prevent the formation of fission products like He
without fracturing and premature replacement. In the case of ZrO2, the hole
adjacent to the unit cell provides a path for the O2- ion diffusion at elevated
temperature. As a result it is used in modern automobiles as an oxygen sensor. It
is also used to monitor the fuel air mixing to reduce pollution.
Compounds with Perovskite structure
Crystal structure of CaTiO3
The structure of CaTiO3 is known as perovskite structure. The substitution
of Barium in the place of Calcium results another technical ceramics BaTiO3
which finds applications in radio, television to increase dielectric constants due
to large dipole moment.
Difference between crystalline and non-crystalline ceramics
Crystalline ceramic materials are not reactive to a great range of
processing. It can be made either in the desired shape by reactions or by
"forming" powders into the desired shape, and then sintering to form a solid body.

Example: Bonechina, Earthernware, Porcelain, Stoneware, etc., It is used
in the field of medicine, electrical and electronic industries.
Non crystalline ceramics, like glasses, can be formed from melts. The glass
is shaped when either fully molten, by casting, or when in a state of toffee-like
viscosity, by methods such as blowing to a mold. If later heat treatments cause
this glass to become partly crystalline, the resulting material is known as a glass-
ceramic. The glass ceramic is widely used as cooktop.
Properties of ceramics:
 High strength
 High fracture toughness
 High hardness
 Excellent wear resistance
 Good frictional behaviour
Ceramic materials
A ceramic material is an inorganic, non-metallic, mostly crystalline oxide,
nitride or carbide material. Elements, such as carbon and silicon, may be
considered as ceramics.
Properties of Ceramics:
Ceramic materials are brittle, hard, strong in compression, weak in
shearing and tension.
Classification of Ceramics:
Based on the properties and applications of ceramic materials, they are
classified as
(i) Traditional ceramics
(ii)Advanced/modern/technical ceramics
Traditional ceramics: Traditional ceramics are made up of clay, silica, and
feldspar. The structure of clay is plate-like. This plate-like structure of clay
provides strength. Silica is the purest of abundant materials which takes the
structure of crystalline quartz. Feldspar is sodium, potassium aluminium
silicates.
Advanced /modern/ technical ceramics: The modern ceramics are pure
compounds such as magnesium oxide, aluminium oxide, barium titanate, silicon

carbide and silicon nitride. Thus the starting materials for the modern ceramics
are synthesized by chemical reactions.
Example: Al2O3, MgO, ZrO2, BeO, SiO2, MgAl2O4, BaTiO3
Graphite
Graphite is a crystalline allotrope of Carbon. It is a native element mineral.
It is the most stable form of carbon. It is used in thermo chemistry.
Properties of Graphite
(i) Black lustrous and opaque
(ii)High melting point
(iii)Insoluble in water
(iv) High thermal and electrical conductivity
(v)High thermal stability
Structure of Graphite
Graphite has a giant molecular structure. As its covalent bonds are very
strong and there are many of them, it requires a lot of energy to separate atoms.
This makes graphite's melting point and boiling point very high.
Each carbon atom is only covalently bonded to three other carbon atoms,
rather than to four as in diamond. Graphite contains layers of carbon atoms. The
layers slide over each other easily. The individual layers are called grapheme.
Carbon atoms are arranged in honey comb lattice pattern. Graphite contains
delocalised electrons (free electrons). These electrons can move through the
graphite, carrying charge from place to place and allowing graphite to conduct
electricity.
Structure of Graphite

The arrangement of carbon atoms in their bonding to form graphite sheet
molecules is known as ‘structure of graphite’. When carbon forms three covalent
bonds per atom, sheets of graphite are produced as shown in fig. The structure of
graphite consists of flat layer sheets of covalently bonded carbon atoms loosely
bounded by van der Waals forces to neighbouring sheets. Here each atom has
three instead of four close neighbours. The large distance between sheets is
responsible for weakness of the van der Waals bond and therefore the sheets slide
over one another. This gives graphite its lubricating property. The weak inter-
sheet bond makes graphite soft and therefore it is used for making lead pencils.
A similar lattice is formed by antimony, talc and mica.
Crystal growth
A crystal is a solid material whose atoms, molecules are arranged in an
orderly repeating pattern extending in all spatial dimensions. Crystal growth is a
major stage of crystallization process and consist in the addition of new atoms,
ions or polymer strings into the characteristic arrangement of crystalline Bravais
lattice. Process of crystal growth occurs in 2 stages, first stage – nucleation stage,
a small nucleus containing newly forming crystal is created. It occurs relatively
slow. The second stage of growth rapidly occurs. Crystal growth spreads
outwards from nucleating site which forms motif leading to the formation of
crystal lattice. The crystal growth occurs either by spontaneous nucleation in the
solution volume, at container walls and at seed rods or with the help of a seed
crystal dipped into a supersaturated solution. For bulk crystal growth we use the
slow cooling method. Based on the phase transformation process, crystal growth
techniques are classified as
(i) Solution growth
(ii) Melt growth
(iii) Vapour growth
(iv) Solid growth
Solution Growth Technique
Materials which have high solubility and have variation in solubility with
temperature, can be grown easily by solution method. There are two methods in
solution growth depending on the solvents and the solubility of the solute.
They are,

1. Low temperature solution growth.
2. High temperature solution growth.
Low temperature solution growth: In the low temperature solution growth,
crystals can be grown from solution if the solution is supersaturated. i.e it contains
more solute than it can be in equilibrium with the solid.
Three different methods to produce supersaturation.
1. Slow cooling of the solution.
2. Slow evaporation of the solvent.
3. Temperature gradient method.
It is possible to grow large crystals of high perfections as the growth occurs close
to equilibrium conditions. It also permits the preparation of different
morphologies of the same materials by varying the growth conditions.
Slow cooling of the solution
Nearly saturated solution of the compound to the boiling point of the solvent is
prepared. The solution is transferred into a clean container. The container is
placed into a heat bath at about the same temperature and allowed to cool slowly.
As temperature decreases solubility decreases and crystals start growing.
Substances that are soluble in a solvent at high temperature than at a low
temperature are good for crystal growth.
Merits
1) Simple-convenient method
2) Strain-dislocation free
3) Growth of prismatic crystals-varying the growth condition
Demerits
1) Growth substance-should not react
2) Variable rate of evaporation – affect quality
3) Applicable – fairly suitable in solvent.

Slow Evaporation of the solvent
slow evaporation method
This is most successful method. The compound can be dissolved in single solvent
or mixture of 2 solvents and left for slow evaporation. It can be done either under
atmosphere conditions or under inert atmosphere. Typical growth conditions
involve temperature stabilization to about ± 0.005°C and rates of evaporation of
a few ml /hr. The evaporation techniques of crystal growth have the advantage
that the crystals grow at a fixed temperature. But inadequacies of the temperature
control system still have a major effect on the growth rate. This method is the
only one, which can be used with materials, which have very small temperature
coefficient of stability.
It is similar to slow cooling method. The temperature is fixed constant and
provision is made for evaporation. With non-toxic solvents like water, it is
permissible to allow evaporation into the atmosphere. Saturated solution of the
compound is prepared in a suitable solvent. A couple of milliliters of the prepared
solution is transferred into a clean container, ideally with a large surface, and
cover. Aluminium foil with some punched holes may be used as the cover since
air tight closing is not to be done. The container is set aside and the solvent is
allowed to evaporate over for few days. The saturated solution is slowly
evaporated and the small crystals grow. The crystals get bigger as the solution
becomes more concentrated.
Advantages:
1. Easy technique
2. Crystals can grow at a fixed temperature.

Disadvantages:
1. Needs a lot of material, too much nucleation leading to simultaneous
growth of many crystals.
2. Not so good for air-sensitive compounds, requires temperature
stabilization.
Melt Growth Techniques
Growth from melt by solidification is the most widely used method for the
preparation of large single crystals. The melt does not undergo decomposition
and phase transformation at melting point. The following are the different melt
growth techniques, they are
1. Czochralski technique
2. Bridgman technique
3. Kyropoulos technique
4. Zone melting technique
5. Verneuil technique
Czochralski Technique

Czochralski Technique
It is a crystal pulling technique of growing a crystal gradually by
condensing the melt. It is nothing but liquid-solid phase transition by a seed
crystal. Large single crystals of silicon are grown by this method. The pure
material which is to be grown in the form of a single crystal is taken in the
crucible. It is heated by using induction heater above the melting point. Thus
melt is obtained in the crucible. A defect free single crystal called seed crystal
is introduced into the melt by crystal holder. A small portion of seed crystal
which is immersed in the melt is initially melted. The temperature is then
adjusted. The seed crystal is rotated and pulled out of the melt by maintaining
the grown crystal and melt near the surface of the melt. The diameter of the
grown crystal is controlled by the temperature of the melt and rate of pulling.
The large size cylindrical shaped grown crystal is known as ingot.
Advantages
1. A crystal which is free from crystal defects can be produced by this
technique.
2. Large single crystal can be produced by this technique.
3. It allows chemical composition of the crystal.
4. It enables easy control of atmosphere during growth.

Limitations
1. High vapour pressure of the materials can be produced.
2. It may produce contamination of melt by the crucible.
Bridgman technique
Bridgman technique
It is common technique for growing single crystals. It involves selective
cooling of the molten material. Solidification occurs along a particular direction.
Here the melt in a sealed crucible is progressively frozen from one end. It can
be achieved by Moving the crucible down the temperature gradient, Moving the
furnace over crucible. By keeping both furnace and crucible stationary and
cooling the furnace steadily along the crucible.
Description: In this method, the material to be grown in the form of a single
crystal is taken in a cylindrical crucible. The crucible is made of platinum and
tapered conically with pointed tip at the bottom. The crucible is suspended in
the upper furnace until the material in the crucible is completely melted into
molten liquid. The crucible is slowly lowered from upper furnace to lower
furnace with the help of motor.
The temperature of the lower furnace is maintained below the melting
temperature of the melt inside the crucible. Since the pointed tip enters the lower
furnace first, the melt at this point starts to solidify to form crystal. As the
crucible is continuously lowered, the solidification of melt continues to form

crystal. Thus, a bulk single crystal can be grown in the crucible by lowering at
steady state.
Advantages:
1. It is a simple technique.
2. Control over vapour pressure.
3. Crucible can be evacuated and sealed.
4. Control of shape and size of growing crystals.
5. Stabilization of thermal gradients.
Limitations:
1. Confinement of crystals.
2. Crystal perfection is not better than that of seeds.
3. No visibility.

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