A brief lecture about crystal structure and its properties, types in materials.

1. Crystalline Structure
A lecture by
Aqeel A. Al-Taie
M.Sc. Of Physics
September, 2018

2. Outline
 Classification of Matter
 Solids: Crystalline and non-crystalline
 Lattice points
 Crystal lattice
 Basis
 Unit cell
 Crystal systems
 Bravais lattice
 Summary
Objectives
• Define the crystalline structure.
• Understand the elements of crystal structure.
• Describe how the structure of crystals is build up.
• Identify various types of crystal systems and lattices.

3. Classification of Matter
Matter
Solids Gases Liquids
Solids are classified in to two types:
Crystalline.
Non-Crystalline (Amorphous).

4. A crystal or crystalline solid is a solid material, whose
constituent atoms, molecules, or ions are arranged in
an orderly repeating pattern extending in all three
spatial dimensions.
- Examples: Diamond, Nacl, Kcl, Copper, Silver, and
Aluminium.
Amorphous (Non-crystalline) Solid is composed of
randomly orientated atoms, ions, or molecules that
do not form defined patterns or lattice structures.
- Examples: amorphous silicon, plastics, and glass.

5. Lattice Points: The points in the space,
replacing the atoms in the structure of a
crystal, with regular periodic arrangement
and have identical environment with
respect to other points.
. . . . . . . lattice points
. . . . . . .
. . . . . . .

6. Crystal Lattice: The regular orderly arrangement
of lattice points in space which resembles the
atoms or molecules in a crystal such that every
point has same environment with respect to all other
points.
* * * * * * * * * * atoms
* * * * * * * * * *
* * * * * * * * * *
Crystal lattice

7. Basis: The set of atoms or molecules attached
to each lattice point in a crystal lattice, identical
in composition, arrangement and orientation.
Crystal Structure = Basis (*) + Crystal lattice (.)

8. Unit Cell: The smallest block or geometrical figure
from which the crystal is build up by repetition in
three dimensions, (or) The fundamental grouping of
particles which are repeating entities.

9. The unit cell and consequently, the entire
lattice, is uniquely determined by the six
lattice parameters: a, b, c, α, β and γ. These
six parameters are also called as basic
lattice parameters.

10. Crystal Systems: On the basis of lattice parameters
(a, b, c, α, β and γ) or shape of the unit cell ,crystal
systems are classified into 7 categories.
No Crystal Structure Lattice Parameters
1 Cubic
a = b = c,
α = β = γ = 90°
2 Tetragonal
a = b ≠ c,
α = β = γ = 90°
3 Orthorhombic
a ≠ b ≠ c,
α = β = γ = 90°
4 Monoclinic
a ≠ b ≠ c,
α =β = 90°, γ ≠ 90°
5 Triclinic
a ≠ b ≠ c,
α ≠ β ≠ γ ≠ 90°
6
Rhombohedral
(Trigonal)
a = b = c,
α = β = γ ≠ 90°
7 Hexagonal
a = b ≠ c,
α = β = 90°, γ =120°

11. Bravais Lattices
- In 1950 Bravais showed that, there are
fourteen ways of arranging points in space
lattice, relating to the seven crystal systems
to describe crystals.
- These fourteen space lattices are called
‘Bravais lattices’.
Auguste Bravais
(1811-1863)

12. Bravais Lattices

13. Summary
- Crystalline structure is generally present in solids rather than
in fluids.
- There are a crystalline and non-crystalline solids.
- A crystalline solid is a material in which the basis are
arranged in a periodic, 3-D pattern; in oppose from non-
crystalline(amorphous) solid.
- The crystal structure is composed from a crystal lattice and a
basis.
- The smallest component in the crystal is called ‘Unit cell’, and
is governed by six lattice parameters; a, b, c, α, β and γ.
- Due to these parameters, there are 7 crystalline systems.
- According to the possible arrangement of the lattice points in
space lattice, there are 14 types of crystalline lattice, called
‘Bravais lattices’.

14. THANK YOU