We present a comprehensive study on the interfacial molecular ordering of an n-alkane, triacontane, at the SiO2/air interface, for submonolayer and excess coverage. The molecular ordering was studied by X-ray diffraction and reflectivity at temperatures from far below bulk melting to above the surface freezing temperature. It is found that the phase behavior of bulk and that of interfacial triacontane are quite different. From the literature it is known that bulk triacontane has three solid phases: one crystalline phase (monoclinic) and two rotator phases (RIII and RIV) with solid/solid transitions at, approximate to61degreesC and close to the melting point into the liquid phase (approximate to67degreesC), respectively. All solid bulk phases have inclined molecules. We show that interfacial triacontane has only two ordered solid phases: a crystalline phase (orthorhombic) and a rotator phase. In both phases the molecules are oriented normal to the interface. At the interface, the temperature of the transition from the crystalline phase to the rotator phase can be as low as 40degreesC. For both submonolayer and excess coverage, the interfacial rotator phase can persist up to 70degreesC. This means that above 67degreesC, for excess coverage, the solid rotator phase coexists with liquid bulk triacontane ("surface freezing"). The different phase behavior in bulk and at the interface is explained with different interlayer interactions. We also find that, directly after solidification, the interfacial layer is usually in a highly amorphous, nonequilibrium state. This we attribute to rapid solidification because of the efficient cooling at the interface. Depending on thermal treatment and time, the interfacial layer can anneal to various degrees of molecular ordering, which is reflected in the phase behavior.