This document discusses crystal structures and crystallography. It defines key terms like lattice points, space lattice, unit cell, crystal systems, lattice planes, and miller indices. It describes common crystal structures like simple cubic, body centered cubic, face centered cubic, and provides examples like NaCl and diamond. It also discusses x-ray diffraction techniques like Laue and Bragg diffraction and defines Bragg's law.

1. Ice Fluorite Quartz
K.S. Mahesh Lohith
Asst. Professor
Centre for Emerging Technologies
Sri Bhagawan Mahaveer Jain College of Engineering.
Ruby Garnet

2. Introduction
Solids
Crystalline Amorphous
Single Crystals Polycrystals

3. Crystal Structure
Definition
• Crystal
• Crystal Structure
• Lattice Points
• Space Lattice or Crystal Lattice
• Basis or Pattern

4. Lattice Points and Space Lattice

5. Bravais and Non-Bravais Lattice
Aluminium
Sodium
Chloride

6. Unit Cell and Lattice Parameters

7. Primitive and Non-Primitive cells
Primitive Non-Primitive

8. Crystal Systems
• Cubic or Isometric
• Tetragonal
• Orthorhombic
• Monoclinic
• Triclinic
• Triagonal or Rhombohedral
• Hexagonal

10. Cubic or Isometric Crystal System
Simple(Primitive) Body Centered Cubic (BCC) Face Centered Cubic (FCC)

11. Tetragonal
Simple Body Centered
Wulfenite

12. Orthorhombic
Aragonite Sulphur

13. Monoclinic
Orthoclase Gypsum Mica

14. Triclinic
Microcline
Wollastonite

15. Triagonal or Rhombhohedral
Quartz
Calcite
Tourmaline

16. Hexagonal
Beryl

17. Crystal Directions and Planes
• The Directions are described by
giving the co-ordinates of the
first whole numbered point
through which each of the
direction passes.
Direction OA= [1 0 0]
Direction OB= [1 1 0]

18. Crystal Planes or Lattice Planes
A crystal may be regarded as made of up an
aggregate of set of parallel equidistant planes
called called Lattice planes. Miller evolved a
method to designate the plane with three
integers called miller indeces.

19. Determination of Miller Indeces
• Determine the Co-ordinates of the intercepts made by the plane along
the crystallographic axis.
• Express them as multiples of lattice parameters
• Take the reciprocal
• Express them interms of smallest set of integral values by multiplying
the fractions with the LCM
x
y
z
x = 1
y = 2
z = 3

20. Planes of a Simple Cubic Lattice

21. Planes of Simple Cubic Lattice

22. Definitions
• Co-ordination number
• Nearest neighbour distance
• Atomic Packing Factor or Packing Fraction
• Lattice Constant
Number of equidistant nearest neighbours that an atom has in a crystal structure i
is called Co-ordination number
The distance between the nearest neighbours is called nearest neighbour distance
The fraction of space occupied by the atoms in the unit cell is called Packing Fraction
For a cubic lattice the interfacial intercepts are equal in magnitude and hence called
Lattice constant.

23. Atomic Packing Factor
or
Packing Fraction
n= number of atoms per cell
Va= Volume of the each atom
V = Volume of the Unit cell

24. APF for Simple Cubic Structure

25. APF for BCC Lattice

26. APF for an FCC Lattice

27. Crystal Structure of NaCl
The Bravais lattice is fcc with the basis containing one sodium and one chlorine ion.
Since the structure is symmetric the Chlorine and sodium ions positons can be
interchanged. The co-ordination number is 6. Bond length is 2.82 angstroms.

28. Crystal Structure of Diamond
(Carbon)
Crystal Structure of diamond is
FCC with the basis containing
two carbon atoms. The
coordination number is 4. the
bond length is 1.54 angstroms

29. X-rays
X-rays are electromagnetic radiations of wavelenths varying from
0.01 angstroms to 10 angstroms. Since the dimensions of the atoms is
of the order of few angstroms. Crystals provide an excellent facility to
diffract x-rays. There are two kinds of x-ray diffraction.
1) Laue Diffraction
2) Bragg Diffraction.

30. Bragg Diffraction or Reflection
W.H Bragg considered crystal interms of set of equidistant parallel planes.
When x-rays are inclined on to the crystal the diffraction occurs if the condition
for constructive interference is satisfied. This is given by Bragg's Law
'd' is interplanar spacing
'λ' is the wave length of x-rays
'θ' is the glancing angle
'n' is the order of diffraction

31. Bragg's X-ray Spectrometer