A method for producing a usable by-product in a cyclone reactor. The method comprises introducing a reactant into a housing of the reactor through an inlet; using a burner to combust a first portion of the reactant in an exothermic reaction provided in a flame zone near a center of the housing; consuming a second portion of the reactant in an endothermic reaction near an outer wall of the housing to produce the by-product as part of a slag layer; and removing the slag layer including the by-product though an outlet in the housing; wherein the endothermic reaction takes place at a temperature of at least 1600° C.