A solid electrolyte having high electrical conductivity even in a low-temperature region is provided. A solid electrolyte containing a hexagonal perovskite-related compound, in which the compound is a compound represented by the following general formula (1), and an electrolyte layer and a battery using the solid electrolyte are disclosed. Ba.sub.7-αNb.sub.(4−x-y)Mo.sub.(1+x)M.sub.yO.sub.(20+z) (1), in the formula (1), M is a cation of at least one element; a represents a Ba deficiency amount and represents a value of 0 or more and 0.5 or less, x represents a value of −1.1 or more and 1.1 or less, y represents a value of 0 or more and 1.1 or less, and z represents an oxygen non-stoichiometry and represents a value of −2.0 or more and 2.0 or less, provided that in the formula (1), |x|+y≥0.01 is satisfied.

One-step solution combustion synthesis (SCS) methods for fabricating durable crystalline transuranic-doped rare earth zirconium pyrochlores are described. Methods are fast, amenable to upscaling, and present a simple strategy for producing crystalline ceramic materials that meet the minimum attractiveness criteria for special nuclear material. The methods include analysis of reactants and reaction conditions to select proper fuel as well as proper fuel content so as to encourage formation of the crystalline product in a single-step synthesis procedure.

One-step solution combustion synthesis (SCS) methods for fabricating durable crystalline transuranic-doped rare earth zirconium pyrochlores are described. Methods are fast, amenable to upscaling, and present a simple strategy for producing crystalline ceramic materials that meet the minimum attractiveness criteria for special nuclear material. The methods include analysis of reactants and reaction conditions to select proper fuel as well as proper fuel content so as to encourage formation of the crystalline product in a single-step synthesis procedure.