Graphically oriented method for obtaining atomic displacement fields in crystals from irreducible representations of space groups

A method for obtaining distortion fields in a crystal from a given irreduci ble representation of the underlying space group is described. The method, based on projection operators of group theory, is graphically oriented and therefore calculation-free. For an example (space group P (4) over bar 2(1) m), complete sets of representation matrices are analytically calculated fo r all irreducible representations which correspond to all wave vectors of t he form k =(q,q,0). All 96 linear independent atomic displacement modes in the (3 x 3 x 1) supercell, which are induced by the two irreducible represe ntations with k =(1/3,1/3,0),are explicitly determined: the obtained atomic displacement fields are plane waves with wave vector k.