The only material we pray on is mud that is pure and clean. We don't pray on clay to "worship it", haply we pray on it because it is considered as a pure material, and as all Muslims — Shi'a and Sunni — believe that one must be clean and in a clean environment to pray.
I once asked my Sunni friend: "Why do you Sunni people pray with your shoes on in the mosque? Isn't the mosque an untainted and a holy place? What if you get mud on shoes, can you still pray with them?" She replied with: "Yes we can pray with our shoes if there's mud on it because mud is 'taher' (clean), so it doesn't really matter" I told her that "Us Shi'a Muslims pray on mud merely because its 'taher' (طاهر) and Sunni Muslims object that and believed that we are worshiping them as idols"
The point is that Shi'a Muslims pray on a 'turbah (تربه)' (which comes from the word tarab that means mud) because it is taher and pure. And the Prophet (pbuh) used to pray on pure flat GROUND because in the Prophet's time they did not have a sijadah (prayer carpet) as there was no technology back then to produce them.
