Not that it really matters, since the word is what it is, but "carbon iron" doesn't specify very much, since almost all iron contains carbon. As I understand the process, carbon is used in the extraction of iron from its ore. But then the carbon has to be removed from the metal, because carbon percentages above around 3% make irons like cast iron, which is too brittle to hammer into shape or to form into an edge, although it can be poured and cast. Steel results when you reduce the carbon percentage, so that the metal becomes soft enough to work on an anvil. The Bessemer smelter was such a game-changer because it used simple compressed air to blow through molten iron and bind the excess carbon. So it seems odd to me that the name "carbon iron" is applied to a material whose main feature is the removal of carbon.