Depiction and structural refinement of twinned crystals in multidimensional space

The structure of a simply twinned crystal can be described by a four- to six-dimensional twinned space group and refined using the multidimensional least-squares refinement technique for modulated structures and composite crystals. The twinned space group is obtained as an extension of the space group of the twin individual by adding the twinning operation to the latter. The proposed method of structure refinement has been tested based on the intensities of twinned beta-YbV4O8, P2(1)/n11, a = 9.030 Angstrom, b = 11.097 % c = 5.752 Angstrom, a = 104.94 degrees, beta = 90 degrees, gamma = 90 degrees.