Using an ordered face-centered tetragonal alloy with the L10 superstructure, the effect of density of structural planar defects (antiphase boundaries, APBs) on the thermodynamic stability of alloys is investigated with respect to the structural-phase transformations in a low-stability state of the system. It is shown that the thermodynamic advantage of a long-period relaxational structure compared to the initial structure is ensured already at Т = 0 K by such relaxational effects as atomic displacements. The structure of the regions of atomic displacements near periodic APBs is the same as that of single APBs: the largest atomic displacements are localized in the vicinity of an APB and rapidly decrease with distance from it, while the size and structure of the regions of these distortions are maintained. It is established that in the ordered fcc tetragonal systems during structural-phase transformations the long-period state is a low-stability state of the system; it is therefore expected that an external action would not only result in a structural-phase transformation but also determine its pathway.