vinod kumar (k11543) vaibhav ranjan (k11858) ms
TRANSCRIPT
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