The alums are what are known as double salts. They are formed from a sulfate of an alkali metal such as sodium or potassium or ammonium sulfate. The other salt is a sulfate of either aluminum or a transition metal such as chromium or iron. Once the two sulfates are dissolved in water in the correct proportion they will crystal as a single compound. So you have potassium aluminum sulfate known as common alum, ammonium aluminum sulfate (ammonium alum), potassium chromium sulfate (chrome alum) and two iron alums.
Chrome alum demonstrates what is known as dichroism. That is its solutions appear as a different color depending on whether they are viewed by transmitted light or reflected light.
