Brillouin Zones: Primitive Reciprocal Lattice Vectors

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In summary, the conversation discusses the properties of different lattice structures, specifically the FCC lattice and the zinc-blende lattice with GaAs. The FCC lattice has one atom per unit cell and a unique 3D shape for its first Brillouin zone, while the zinc-blende lattice has 2 atoms per unit cell. The primitive reciprocal lattice vectors and the Wigner-Seitz cell are defined for a unit cell with a basis. The change of the unit cell's content does not affect the lattice or its reciprocal space.
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Assaf Peled
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Hi fellows,

An FCC lattice has one atom per unit cell and a set of primitive vectors. Its 1st BZ has its distinctive 3D shape, set explicitly by the Wigner-seitz cell in the reciprocal space.

What if we have a zinc-blende (GaAs) lattice with 2 atoms per unit cell?
How are the primitive reciprocal lattice vectors defined for a unit cell with a basis? Consequently, how is the Wigner-Seitz cell defined in the reciprocal space ?

Thanks
 
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  • #2
The change of the content of the unit cell changes neither the direct nor the reciprocal lattice. Hence also the Wigner Seitz cell will remain unchanged.
 

What is a Brillouin Zone?

A Brillouin Zone is a region in reciprocal space that represents all possible wave vectors that can exist for a given crystal lattice. It is used to understand the electronic and vibrational properties of a crystalline material.

What are Primitive Reciprocal Lattice Vectors?

Primitive Reciprocal Lattice Vectors are the shortest vectors that span the reciprocal lattice. They are used to construct the Brillouin Zone and determine the symmetry of the crystal lattice.

How are Brillouin Zones related to the crystal lattice?

Brillouin Zones are related to the crystal lattice because they are constructed using the reciprocal lattice, which is a mathematical representation of the crystal lattice. The size and shape of the Brillouin Zone are determined by the symmetry of the crystal lattice.

Why are Brillouin Zones important in solid state physics?

Brillouin Zones are important in solid state physics because they provide a way to understand the electronic and vibrational properties of a crystalline material. They also help in the analysis and prediction of the material's behavior, such as its conductivity and optical properties.

How do you calculate the Primitive Reciprocal Lattice Vectors?

The Primitive Reciprocal Lattice Vectors can be calculated by taking the inverse of the real space lattice vectors. This is done using the Bravais-Miller-Brillouin (BMB) zone construction method, which involves constructing the reciprocal lattice and then finding the shortest lattice vectors that span it.

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