In the examples we use a 2-dimensional primitive cubic structure. The individual crystals are rotated around the z-axis yet remain in plane. The left image shows the diffraction pattern obtained from 200 randomly oriented crystals. The right images shows the diffraction pattern of 200 crystals with preferred orientation. The sigma of the distribution was set to degrees.
Preferred orientation can suibstantially alter the appearence of the powder pattern.
It is a serious problem in experimental powder diffraction.