An electrolytic cell for reducing a metal oxide, such as titania, in a solid state is disclosed. The electrolytic cell includes an anode formed from carbon and a cathode formed at least in part from the metal oxide. The electrolytic cell also includes a membrane that is permeable to oxygen anions and is impermeable to carbon in ionic and non-ionic forms positioned between the cathode and the anode to thereby prevent migration of carbon to the cathode.