Hi VTsteam, When you put iron ore in a blast furnace with coke and limestone, what you get running out of the bottom, is pure iron, but because it has been smelted with coke, it has picked up a high content of carbon. When the run off is allowed to cool it is known as cast iron. Cast iron is very strong under compression, but also very brittle. The process for producing wrought iron from cast was to remelt the cast iron in a reverbatory furnace (where the iron is heated by indirect heat, so it cannot absorb any more carbon) the furnace, known as a puddlers hearth is also charged with iron oxide, and when the iron melts the carbon reacts with the oxygen in the oxide, and boils out of the iron as carbon dioxide. This reduces the carbon content, and after a process of removing from the furnace and power hammering (and repeating) it becomes almost pure iron with fibres of slag running through it, which can be seen on a piece of fractured wrought iron. Take pure iron, minus the slag, and add to it a small amount of carbon, and you have mild steel, useful, but not hardenable other than case hardening. Add slightly more carbon, and you have a tool steel that can be worked and shaped hot in its soft state, and then hardened through and tempered so it is tough, and will also hold a sharp edge. All these metals are Iron/carbon alloys, and this is a gross simplification of metallurgy as learned in the school metalwork shop and from the excellent Hardening, tempering and heat treating by Tubal Cain, No1 in the workshop practice series. hope this helps,
Phil