• “WEIGHT” OF THE OF RECIPROCAL LATTICE NODE IN THE CELL/ SUPER CELL OF THESE LATTICE

    Machines. Technologies. Materials., Vol. 12 (2018), Issue 12, pg(s) 506-509

    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.