Abstract: An apparatus for processing materials includes a chamber within which frequency turbine plates rotate relative to a circumferential wall having diametrically opposed portions which are asymmetric relative to each other. The circumferential wall with asymmetric arrangement in this manner promotes the generation of pressure differentials and interference wave phenomena when plates are rotated relative to such asymmetric arrangements, and thereby facilitates materials being processed through the associated apparatus. One suitable form of the apparatus comprises a pressure interference wave mill suitable for processing materials, such as slag.