The structure of the fully relaxed phases of a Langmuir monolayer of tetracosanoic acid is determined by x-ray diffraction and reflection along an isotherm at approximately 20.5-degrees-C. Isotherms taken by allowing the surface pressure to stabilize between incremental compressions are seen to be qualitatively different from the constant-rate nonrelaxed isotherms typically seen in the literature. At low densities the monolayer consists of an inhomogeneous film of islands of a crystalline (or hexatic) phase with molecular tilt ordering that is analogous to that of the smectic I liquid crystal. Small amounts of impurities (approximately 0.5% of the monolayer) account for the change in surface pressure with area in this region. Upon compression to the point that the free space between islands becomes negligible the film appears homogeneous. On further compression the time required for full relaxation becomes long (i.e., approximately hours), the tilt angle of the molecular axis decreases and the x-ray unit cell is compressed. Including this homogeneous I phase the phase sequence observed by diffraction upon compression is I-U-I-U, where U refers to an untilted orthorhombic phase. The outer two phases of this sequence are pure phases which form homogeneous monolayers, but the inner two are inhomogeneous phases each coexisting with an amorphous phase that does not have an observable diffraction signal. At the boundaries demarcating the I and U phases, a phase whose tilt ordering is analogous to that of a smectic F phase is seen to coexist. The preceding phase sequence is sensitive to the degree of relaxation permitted the monolayer after an incremental compression. In particular, if the monolayer is not allowed to relax completely after each compression, the untilted U phase may never appear. The U <--> I transition is shown to be reversible for a relaxed monolayer.
