I would use natural slate tiles because I think they would look a lot nicer than glazed clay tiles. You can get 18 x 18 slate tiles pretty easily. It looks like 2 would cover the bottom of your tank. You could probably get the tile store you buy them from to cut them to the exact size for a couple of bucks.
There are a few ways you could go:
1) Just lay them in the bottom. You could then remove them easily for cleaning or if you want a change. They will collect gunk under the tiles which will break down and contribute to your nitrate levels.
2) You could put ~1/4" to ~1/2" spacers underneath them. Cut a hole or two for tubing/pipe. Plumb the tubing/pipe to a filter to suck all the water and gunk into the filter. Kind of a undergravel filter like application.
3) Use some silicone caulk and seal them into the bottom of the tank. This would make it very hard to change the tiles in the future and most likely affect the resale value of the tank.