We report a surface X-ray diffraction study of the crystalline structure changes and critical behavior across the (3 root 2 x root 2)R45 degrees -> (root 2 x root 2)R45 degrees surface phase transition at 360 K for 0.5 monolayers of Sn on Cu(100). The phase transition is of the orderdisorder type and is due to the disordering of the Cu atomic vacancies present in the low temperature phase. Two different atomic sites for Sn atoms, characterized by two different heights, are maintained across the surface phase transition.