Exercise 2: Calculate the reciprocal lattice of a single sheet of graphite (graphene) and construct its first Brillouin zone. b₁ = b2 b3 = = 2п а2 х аз a1 (a2 x aз 2п аз ха1 a1 (a2 x aз) 2п а1 х а2 a₁ (a2 x a3) L Fig. 2.2 Structure of a graphite sheet. Left: The unit cell (gray) of this hexagonal lattice is spanned by the lattice vectors |a1| and |a2|, with a lattice constant of |a1|=|a2| = 0.246 nm. It contains a basis of two carbon atoms (full circles) occupying non-equivalent sites. The distance between two neighboring atoms is 0.142 nm. Right: The first Brillouin zone of the graphite sheet with points of high symmetry.
Exercise 2: Calculate the reciprocal lattice of a single sheet of graphite (graphene) and construct its first Brillouin zone. b₁ = b2 b3 = = 2п а2 х аз a1 (a2 x aз 2п аз ха1 a1 (a2 x aз) 2п а1 х а2 a₁ (a2 x a3) L Fig. 2.2 Structure of a graphite sheet. Left: The unit cell (gray) of this hexagonal lattice is spanned by the lattice vectors |a1| and |a2|, with a lattice constant of |a1|=|a2| = 0.246 nm. It contains a basis of two carbon atoms (full circles) occupying non-equivalent sites. The distance between two neighboring atoms is 0.142 nm. Right: The first Brillouin zone of the graphite sheet with points of high symmetry.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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Transcribed Image Text:Exercise 2:
Calculate the reciprocal lattice
of a single sheet of graphite
(graphene) and construct its
first Brillouin zone.
b₁
=
b2
b3
=
=
2п а2 х аз
a1 (a2 x aз
2п аз ха1
a1 (a2 x aз)
2п а1 х а2
a₁ (a2 x a3)
L
Fig. 2.2 Structure of a graphite sheet. Left: The unit cell (gray) of this
hexagonal lattice is spanned by the lattice vectors |a1| and |a2|, with
a lattice constant of |a1|=|a2| = 0.246 nm. It contains a basis of
two carbon atoms (full circles) occupying non-equivalent sites. The
distance between two neighboring atoms is 0.142 nm. Right: The first
Brillouin zone of the graphite sheet with points of high symmetry.
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