The steel skull cap is called a cervelliere. In the 12th Century, it would have been a Crusader's only head protection. But, by the early 14th Century, a soldier would add a great helm over it before battle.
During the 14th Century, the back of these caps would grow longer, into what is called a bascinet. Then, the bascinet would grow heavier and acquire a visor, eliminating the need for a great helm.
This is a picture of 14th Century cervellieres
taken from the Manesse manuscript, which is dated around 1330.
I bought my cervelliere from Albion Armorers. They carry a lot of hard-to-find designs, and their Web site is very informative.