Brillouin Zones: Primitive Reciprocal Lattice Vectors

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SUMMARY

The discussion focuses on the definition of primitive reciprocal lattice vectors and the Wigner-Seitz cell in the context of different crystal structures, specifically comparing face-centered cubic (FCC) lattices and zinc-blende (GaAs) lattices. It is established that an FCC lattice has one atom per unit cell, while a zinc-blende lattice contains two atoms per unit cell. Importantly, the change in the content of the unit cell does not affect the direct or reciprocal lattice, nor does it alter the Wigner-Seitz cell in reciprocal space.

PREREQUISITES
  • Understanding of FCC lattice structures
  • Knowledge of zinc-blende (GaAs) crystal structure
  • Familiarity with primitive vectors in crystallography
  • Concept of Wigner-Seitz cells in reciprocal space
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  • Study the properties of face-centered cubic (FCC) lattices
  • Explore the characteristics of zinc-blende (GaAs) lattices
  • Learn about the calculation of primitive reciprocal lattice vectors
  • Investigate the implications of Wigner-Seitz cells in solid-state physics
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Physicists, materials scientists, and crystallographers interested in solid-state physics and the analysis of crystal structures.

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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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.
 

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