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Lattice
• Regular , periodical arrangements of points in
three dimension.
• Lattice point : The points which presents in
the lattice
Basis
• Group of atom is called as basis
Crystal structure
• Lattice + basis = crystal structure
• Crystal structure is obtained by arranging the
basis in each and every lattice point
Unit cell
• Smallest geometric figure , by the repetition of
this we get complete crystal structure.
Crystal parameters
• The three mutual perpendicular lines OX,OY
and OZ.
• Inter axial lengths: OA = a , OB = b and OC = c
• Inter axial angles: α,β and γ
Crystal system
Cubic
Orthorhombic
Monoclinic
Triclinic
Hexagonal
Rhombohedral
Tetragonal
Bravais lattice
Lattice planes
Miller indices
d spacing in cubic lattice

d

a
h2  k 2  l 2
Calculation of number of atoms
per unit cell – Atomic radius –
Coordination number – Packing
factor for SC , BCC ,FCC and HCP
Simple Cubic structure
Atomic radius(r)

• r = a/2
Coordination number (N)
Body Centered Cubic
Number of atoms per unit cell
Coordination number
• For BCC the coordination number is 8
Face Centered Cubic
• Atomic radius = a √2 / 4
HCP
Na Cl structure
ZnS Structure
diamond and graphite Structure
Polymorphism and allotropy
• Polymorphism is a physical phenomenon where
a material may have more than one crystal
structure.
• A material that shows polymorphism exists in
more than one type of space lattice in the solid
state. If the change in structure is reversible,
then the polymorphic change is known as
allotropy.
• The prevailing crystal structure depends on both
the temperature and the external pressure.
• Allotropes of carbon
Diamond and graphite
Crystal defects
•
•
•
•

Point defect
line defect
surface defect
Burger vector
Point defect
Line defect
Burger vector
Dislocations
Surface defects
•
•
•
•

Grain boundary
Tilt boundary
Twin boundaries
Stacking fault
Thank you for your patience

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Physics unit 1