There are two types of materials - crystalline and non-crystalline. Crystalline materials have atoms arranged in a regular pattern, making them anisotropic, while non-crystalline materials have atoms in a random arrangement, making them isotropic. Crystalline materials can exist as polycrystalline, with many regularly ordered grains, or single crystalline, with a single regularly ordered grain. An important concept in crystalline materials is the unit cell, which is the smallest repeating unit that extends in three dimensions to form the entire crystal structure. There are three main types of unit cells - simple cubic, body centered cubic, and face centered cubic - which differ in their atomic arrangements and packing fractions.

2. EXISTENCE OF MATERIALS
CRYSTALLINE
Atoms are
arranged in
regular
manner.
Anisotropic in
nature.
NON-
CRYSTALLINE
Atoms are
arranged in
random manner.
Isotropic in
nature.

3. CRYSTALLINE MATERIALS
Polycrystalline Form
Regular arrangement of ions up to
finite distance.
Large number of grains in the
material.
Single crystalline Form
Regular arrangement of
atoms/ions throughout the
material.
Single grain in the material.

4. IMPORTANT TERMS
LATTICE
1. The 3-D
arrangement of
points obtained by
replacing the atom
or group of atoms
are lattice.
2. The concept of
space lattice is
totally imaginary.

5. BASIS
1. Some atoms or
group of atoms or
group of ions by
which if we
replace the lattice
points then we get
a complete crystal
structure.
2. Eg. In case of
NACL, NA atoms
will act as basis.

7. UNIT CELL
1. Smallest entity
2. Repeated again
& again in 3-D
so that a
complete
structure is
formed.
3. Parallalopipe in
nature.

9. TYPES OF UNIT CELL
SIMPLE CUBIC
FACE CENTERED
BODY CENTERED

10. SIMPLE CUBIC STRUCTURE
1. In this type of
structure, atoms
are located at
the corners of
the cube .
2. All the atoms
which are at
distance ’a’
touch each
other.
3. Coordination
Number is=6

11. PACKING FRACTION OF SIMPLE CUBIC STRUCTURE
PF=Volume occupied by atom/
Volume of unit cell
No of atoms in unit cell=1/8*8=1
Volume of atoms
In a unit cell=4/3*pi*r^3
(It is clear from picture 2r=a)
PF= 4/3*pi*r^3/
a^3
=52.33%

12. BODY CENTERED CUBIC STRUCTURE
1.Atoms are
present at the
corners of the
cube & one atom is
present at the
centre of cube.
2. Atoms present
at the centre will
touch all the
atoms & corner
atoms will not
touch each other.
3. Coordination
Number is = 8

13. PACKING FRACTION OF BODY CENTERED CUBIC STRUCTURE
PF=Volume occupied by atom/
Volume of unit cell
No of atoms in unit cell=1/8*8+1
=2
Volume occupied by atoms
In a unit cell =2*4/3pi*r^3
=8/3pi*r^3
PF=8/3*pi*r^3/
a^3
=67.9%

14. FACE CENTERED CUBIC STRUCTURE
1. Atoms are present at
the corners of the
cube, one atom is at
the centre of each
face.
2. Each atom which is at
centre will touch four
corner atoms in its
plane , 4 face atoms
below its plane & 4
face atoms above its
plane.
3. Coordination Number
is =12

15. PACKING FRACTION OF FACE CENTERED CUBIC STRUCTURE
PF=Volume occupied by atom/
Volume of unit cell
No of atoms in unit cell=1/8*8+6*1/2
=4
Volume occupied by atoms
In a unit cell =4*4/3pi*r^3
=16/3*pi*r^3
PF=16/3*pi*r^3/
a^3
=73.2%
=74%