A process for making a solid electrolyte for an electrochemical cell. The process includes providing a multilayer material having a porous layer and a nonporous layer, the nonporous layer containing a first oxide selected from alpha-alumina, gamma-alumina, alpha-gallium oxide, and/or combinations thereof. In addition, an alkali-metal oxide vapor is provided and the nonporous layer is exposed to the alkali-metal oxide vapor at an elevated temperature such that the nonporous layer is converted to a solid second oxide electrolyte layer that is conductive to alkali metal ions. The second oxide is an alkali-metal-beta-alumina, alkali-metal-beta″-alumina, alkali-metal-beta-gallate, and/or alkali-metal-beta″-gallate.