Crystal Physics

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

CubicOrthorhombicMonoclinicTriclinicHexagonalRhombohedralTetragonal

Bravais lattice

Lattice planes

Miller indices

d spacing in cubic lattice

222 lkh

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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 carbonDiamond 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

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