Orientational alignment in a dilute dispersion of kaolinite particles has been investigated in a flow pattern that combines both shear and elongational stress, namely flow at a jet created by a 2 mm diameter nozzle inserted in a 6 mm diameter pipe. Spatially-resolved X-ray diffraction with synchrotron radiation permits detailed maps of the alignment to be deduced and compared with fluid mechanics calculations of the flow. The angular distribution of diffracted intensity from a given position in the pipe provides information about the orientation distribution of the particles. This is quantified and presented in terms of order parameters. The cone-shaped nozzle provides a jet of liquid giving a high degree of alignment of the particles that is uniform along lines across the conical section and constant in the small straight-sided region at the exit of the nozzle. The vortex motion that arises from the flow with a modest Reynolds number could be determined as well as the tendency for some particles to align with their large faces perpendicular to the overall flow direction at the flat surface of the nozzle outlet.