an oxide ceramic

This is the most common branch of the family. An oxide ceramic is a compound of a metal (or silicon) with oxygen: alumina Al2O3, zirconia ZrO2, magnesia MgO, titania TiO2, silica SiO2. Rust is iron's oxide; alumina is aluminium's; both are what you get when a metal has fully combined with the oxygen in air. In a sense, oxides are materials that have already burned, and so are content to be left alone.

Because oxygen is very electronegative, metal-oxygen bonds are strongly ionic, and the structures pack oxygen ions closely with metal cations tucked into the gaps (the structures field names them: rock-salt MgO, corundum Al2O3, fluorite-type zirconia, rutile TiO2). Practical consequences: oxides are already oxidised, so they are outstandingly stable in hot air (unlike carbides and nitrides, which can burn), they are hard and refractory, and most are excellent electrical insulators. Alumina alone is the workhorse of technical ceramics, spark-plug insulators, electronic substrates, wear parts, and 99.9 percent pure windows for lamps.

Oxides span the whole range from traditional to cutting-edge: clay and silica in a teapot, high-purity alumina in a hip implant, zirconia toughened for knife blades and dental crowns, barium titanate BaTiO3 in the billions of capacitors in your phone, YSZ carrying oxygen ions in a fuel cell. The one honest weakness: their air-stability does not extend to strongly reducing or acidic environments, and some (like plain zirconia) must be chemically stabilised to survive their own phase changes on heating and cooling.