Abstract: A process and apparatus for polishing diamond or carbon nitride. A reaction and polishing take place at the interface between an oxygen superionic conductor (yittria-stabilized zirconia) and the diamond or carbon nitride. Oxygen anions are transported to the interface under the influence of a chemical gradient and react with the diamond or carbon nitride. Other mechanisms, such as an electric field and/or heat, that increase the partial pressure of oxygen on the opposing side of the interface of reaction can be used to accelerate the reaction time. The process may be undertaken at low temperatures and without mechanical motion, making it an attractive and useful polishing method. In addition, there is no residue of the polishing process which needs to be removed and polishing can be accomplished in ambient air.