“Weight” of the of reciprocal lattice node in the cell/ super cell of these lattice

  • 1 Grodno, Belarus, Faculty of physics and technology – Yanka Kupala State University of Grodno, Belarus,
  • 2 Faculty of Innovative Technologies of Mechanical Engineering – Yanka Kupala State University of Grodno, Belarus,


Geometrically, the reciprocal lattice is built on the basis of the lattice of the crystal according to the rule
a j ak jk , where
the vectors
a j , ak are the periods of the crystal and reciprocal lattices corresponding  jk  0 at j  k and jk  1 at j  k (j, k = 1,2,3). The “weight” of the reciprocal lattice node, determined by the structural amplitude of the crystallographic plane corresponding to it, should not be zero, since in this case the reciprocal lattice node will be homologous to any point of the reciprocal space outside the lattice. Crystals with Bravais I, F, C – type cells in the reciprocal lattice are characterized by super cells, periods of which are n – times larger than ∗ = −1, where a is the period of the lattice cell. With respect to complex structures, even if they are single-element, the period of the super cell of the reciprocal lattice can exceed ∗ several times. For a diamond crystal ∗ = 4∗under the super cell of the reciprocal lattice it is necessary to use the smallest parallelepiped, the “weight” of all vertex nodes of which is not equal to zero.



  1. Vainshtein, B. Sovremennaja kristallografija, Moscow, Nauka, 1979. Vol.1. 384 p.
  2. Katsnelson, M. Dinamika i termodinamika kristallicheskoĭ reshetki, Moscow, IzdAT, 2002. 384 p.
  3. Ladd M., Palmer R. Structure Determination by X-ray Crystallography, Berlin, Springer, 2013. 756 p.

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