Sure. Cubic zirconiums are composed of zirconium and oxygen and other elements are added to produce different colored gems.
Diamonds (pure diamonds) are composed solely of carbon. The carbon in a diamond is arranged in a 3-dimensional lattice (i don't remember what exact shape). Each carbon atom is covalently bonded to each carbon atom around it, making the structure of the diamond incredibly strong (this is one of the reasons it's one of the hardest substances known to man). Natural diamonds take thousands of years or more to form. The carbon usually comes from decayed organic matter (trees, cows, anything that was once living) and is then subjected to intense pressure and heat which causes the carbon atoms to arrange into diamond structure.
You're probably familiar with pencil "lead", it's actually graphite. Graphite is carbon atoms arranged in 2-dimensional sheets that are layered on top of one another and held together with weak inter-molecular forces. This gives graphite a very weak structure which allows it to be used in pencils and such. Amazing how the 2-d structure is incredibly weaker than the 3-d struture.
Does this help?