Index

Core dictionary version 3.3.0

_space_group_generator.xyz

Definition:

   
    A parsable string giving one of the symmetry generators of the
    space group in algebraic form.  If W is a matrix representation
    of the rotational part of the generator defined by the positions
    and signs of x, y and z, and w is a column of translations
    defined by the fractions, an equivalent position X' is
    generated from a given position X by

          X' = WX + w.

    (Note: X is used to represent the bold italic x in International
    Tables for Crystallography Volume A, Chapter 1.5.)

    When a list of symmetry generators is given, it is assumed
    that the complete list of symmetry operations of the space
    group (including the identity operation) can be generated
    through repeated multiplication of the generators, that is,
    (W3, w3) is an operation of the space group if (W2,w2) and
    (W1,w1) [where (W1,w1) is applied first] are either operations
    or generators and:

        W3 = W2 x W1
        w3 = W2 x w1 + w2.

    Reference: International Tables for Crystallography (2016). Volume A,
     Space-group symmetry, edited by M. I. Aroyo, 6th ed.
     Chichester: John Wiley & Sons.

Type: Code

Category:
space_group_generator