1. Ice Fluorite Quartz
K.S. Mahesh Lohith
Asst. Professor
Centre for Emerging Technologies
Sri Bhagawan Mahaveer Jain College of Engineering.
Ruby Garnet
17. Crystal Directions and Planes
• The Directions are described by
giving the co-ordinates of the
point
of the
first whole numbered
through which each
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
•
•
•
•
x = 1
x
y = 2
y
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
z z = 3
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.
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