Lab corundum is where it's at. Almost as hard as diamond (Mohs 9), but much less prone to cracking than diamond. It's available in tons of colors (most famous are blue and red -- sapphires and rubies). Lab-grown is so much better than natural that the way they identify natural is by looking for imperfections that lab versions don't have.

Oh, and diamonds burn while aluminum oxide does not.

There's no need to go broke when you can buy a superior product for less money.