Abstract: The disclosure refers to the art of remarkably increasing the hardness of alumina materials, such as alumina abrasives, alumina ceramics or aluminum oxide single crystal (sapphire), containing aluminum oxide (Al.sub.2 O.sub.3) as the main component, or the hardness of products using the same.The alumina material is partially or wholly hardened to have a micro-Vickers hardness of no less than 2600 kgf/mm2 (under a test load of 300.times.9.807 mN) by inclusion of an oxide or fluoride additive which is solid-soluble in aluminum oxide. Preferable examples of the additive include TiO.sub.2 and/or Y.sub.2 O.sub.3.