vinod kumar (k11543) vaibhav ranjan (k11858) ms

Assignment of Material science Topic- “Brillouin zone ”

SUBMITTED TO:- Mr.Amardeep sir ASSISTANT PROFESSOR

MECHANICALDEPARTMENT

SUBMITTED BY:-VINOD KUMAR(k11543) VAIBHAV

RANJAN(K11858)BRANCH-

MECHANICAL

TABLE OF CONTENTS Introduction Construction of brillouin zone Reciprocal Lattice in 1D Reciprocal Lattice in 2D application Conclusions

Introduction A Brillouin zone is defined as a Wigner-Seitz primitive

cell in the reciprocal lattice. What is primitive cell ?The primitive cell is defined as unit cell which contains

lattice points at corner only

Construction of brillouin zonesThe brillouin zones are constructed from

the planes which are the perpendicular or bisectors of all reciprocal lattice vectors

The first zones is the smallest volume about the origin enclosed by these planes

The second zone is the volume between the first zone and next set of planes

Reciprocal Lattice in 1DReciprocal lattice in 1 D

The 1st Brillouin zone: Weigner-Seitz primitive cell in the reciprocal lattice

k

0 2/a 4/a-2/a-4/a-6/a

-/a /a

Reciprocal Lattice of a 2D Lattice

Industrial application:

The industrial application of brillouin zones in use to Carbon nanotubes

What is carbon nanotubes: Carbon nanotubes are unique tubular

structures of nanometer diameter and large length/diameter ratio. The nanotubes may consist of one up to tens and hundreds of concentric shells of carbons with adjacent shells separation of 0.34 nm.

conclusion In the brilliouin zones the major

developments in both the basic research and the industrial application of the carbon nanotubes are reviewed. The theoretical efforts are directed to the understanding the amazing mechanical, electronic, transport, vibrational,thermal, application of brilliouin zones and carbon zone etc