span a Bravais lattice, then
span the reciprocal lattice, which is also a bravais lattice.The reciprocal of the reciprocal lattice is the set of all vectors
for any recprocal lattice vector 
it is the original lattice.As we discussed above, a simple cubic lattice spanned by
Chapter 4: Broken Translational Invariance in the Solid State has the simple cubic reciprocal lattice spanned by:
An FCC lattice spanned by:
has a BCC reciprocal lattice spanned by:
Conversely, a BCC lattice has an FCC reciprocal lattice.
The Wigner-Seitz primitive unit cell of the reciprocal lattice is the first Brillouin
zone. In the problem set (Ashcroft and Mermin, problem 5.1), you will show that the
Brillouin zone has volumen
if the volume of the unit cell of the original lattice is 
. The first Brillouin zone is enclosed in the planes which are the perpendicularbisectors of the reciprocal lattice vectors. These planes are called Bragg planes forreasons which will become clear below.
Kevin M Contreras H
Electrónica del Estado Sólido
http://www.physics.ucla.edu/~nayak/solid_state.pdf
zone. In the problem set (Ashcroft and Mermin, problem 5.1), you will show that the
Brillouin zone has volumen
if the volume of the unit cell of the original lattice is 
. The first Brillouin zone is enclosed in the planes which are the perpendicularbisectors of the reciprocal lattice vectors. These planes are called Bragg planes forreasons which will become clear below.Kevin M Contreras H
Electrónica del Estado Sólido
http://www.physics.ucla.edu/~nayak/solid_state.pdf
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