†These are used as crafting materials, but not in alchemy.
A Daedra Heart (or aortas daedrae)[1] is an ingredient that can be harvested from slain Daedra, primarily Dremora. In older times, they could be found on many other varieties of Daedra, including Clannfears, Daedroths, Golden Saints, Hungers, Ogrims, and Xivilai. These beings, to the extent that they can still be encountered, now produce other ingredients. But Dremora have consistently been a reliable source for Daedra Hearts.
†Diamonds in Oblivion are not alchemical ingredients, but only valuable as loot to be sold for gold. ‡Diamonds in Skyrim are also not used in alchemy, but can be used to craft jewelry. *In Elder Scrolls Online, Diamonds are used for crafting armor, and not in alchemy. ^In Blades, Diamonds are used for tempering gear or crafting jewelry, not in alchemy.
Diamonds are mined from volcanic regions such as Vvardenfell in Morrowind, and can also be found in mineral deposits in Skyrim. They are also commonly found in the ruins of the Dwemer, who presumably had industrial uses for them.
†Spoiled Dwemer Oil in Tribunal is a potion, rather than an ingredient. ‡This is used as a crafting material, but not for alchemy.
Dwarven Oil is extracted from Dwarven automatons, found in Dwemer ruins in Skyrim. Similar machines found around Vvardenfell were once used as a source of Scrap Metal.