Reflection-Solid State Physics-Lecture Slides, Slides of Solid State Physics

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Reflection

A system is said to possess reflection

symmetry if there exists a plane in the

lattice which divide it into two identical

halves which are mirrors images of each

other. Such a line or plane is represented by

m.

Figures of Reflection Symmetry

6/20/2012 4 Horizontal Line Symmetry Vertical Line Symmetry Horizontal and Vertical Line Symmetry docsity.com

Inversion

 Inversion is a point operation which is applicable

to 3D lattices only.

◦ Inversion symmetry implies that each point located at

r relative to a lattice point has an identical point

located at – r.

 The lattice possesses a center of inversion denoted

by I.

Bravais Lattice

 The crystal are classified on the basis of their

symmetry which is compared with the

symmetry of different point group. These

lattices consistent with the point group

operations are limited. Such lattices are

known as bravais lattices.

Types of Lattices

 It is stated that 10 and 32 point groups in

2 and 3 dimensions produce only 5 and 14

distinct bravais lattice respectively. These

bravais lattice further become parts of 4

and 7 distinct crystal system, respectively.

Three-Dimensional Lattice

Sr. No. Crystal System Lattice Parameters Bravais Lattice Common Abbreviation Lattice Symbol Examples 1 2 3 4 5 6 7 Cubic Tetragonal Orthorhombic Rhombohedral OR Trigonal Hexagonal Monoclinic Triclinic a = b = c α = β = γ = 90o a = b ≠ c α = β = γ = 90o a ≠ b ≠ c α = β = γ = 90o a = b = c α = β = γ ≠ 90o a = b ≠ c α = β = 90 o^ γ = 120o a ≠ b ≠ c α = γ = 90o^ ≠ β a ≠ b ≠ c α ≠ β ≠ γ ≠ 90o Simple Body-entered Face-centered Simple Body-entered Simple Body-entered End-centered Face-centered Simple Simple Simple End-centered Simple sc bcc fcc st bct so bco eco fco sr sh sm ecm Str

P I F P I P I C F P P P C P

Cu, Ag, Fe Na, NaCl, CsCl Β-Sn TiO 2 Ga, Fe 3 C, (cementite), As, Sb, Bi Mg, Zn, Cd, CaSO 4 K 2 Cr 2 O 7 6/20/2012 (^) docsity.com 10

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