Pre-defined k-point sets for Crystalline calculations: face-centered cubic lattices

The First Brillouin zone of a face-centered cubic lattice, with high symmetry k points marked. Note that this is also the Wigner-Seitz cell of a body-centered cubic lattice in real space.

The above k-point meshes were generated for face-centered cubic lattices, where the symmetry of the crystal is fully cubic, and the primitive lattice vectors are given by

• a₁ = ( 0 , ½ a , ½ a)
• a₂ = ( ½ a , 0 , ½ a)
• a₃ = ( ½ a , ½ a , 0)

with reciprocal lattice vectors

• b₁ = ( -2 pi/a , 2 pi/a , 2 pi/a )
• b₂ = ( 2 pi/a , -2 pi/a , 2 pi/a )
• b₃ = ( 2 pi/a , 2 pi/a , -2 pi/a )     (one hopes that some future version of HTML will be able to print pi = 3.1415926... in the original Greek)

these lattices include the space groups

• Fm(-3)m (#225) (fcc, NaCl, Fluorite and Heusler lattices)
• Fd(-3)m (#227) (diamond, NaTl, and Cu₂Mg lattices)

Both "regular" and "special" k-point meshes are listed, in lattice-coordinate format. The order of the mesh is the number of k-points which lie on the line between the origin and the point X (2 pi/a, 0, 0) in reciprocal space, or at X. (For "special k-points, this is the number of points on a line parallel to the origin-X line.) "Regular" and "Special" k-points on the same line have the same density of k-points in reciprocal space. Since the later meshes are "special", there are generally symmetrized special k-points than regular k-points.

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