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Stress and displacement fields of a two-dimensional solid under plane strain are solved subject to surface reconstruction boundary conditions. The alternating lateral Dirac-δ forces at steps owing to the reconstruction obtained by Alerhand et al (1988 Phys. Rev. Lett. 61 1973–6) are recovered from the gradient of the stress field solution. Sinusoidal vertical and lateral displacements on a terrace are obtained, in addition to the vertical force distribution, in the direction normal to the surface. Reconstructed periodic terraces reduce their elastic energy by increasing their average width, but the elastic energy density reaches a finite limit with an increased terrace width. A like-oriented step–step interaction with the force dipole from the surface reconstruction, using the Marchenko–Parshin model, is considered and found to be repulsive. Reconstructed terraces of a vicinal surface are thermodynamically stable when the surface has a large dangling bond energy and a large miscut angle. Small miscut angle or small surface tension tends to destabilize the surface, although our result suggests that a multilayer configuration will metastabilize the terraces owing to the interface elastic mismatch.

A concise formula expressing the entropy of adatoms as a divergence of their flow due to diffusion and deposition flux is presented. Adatom-elastic strain interaction is provided by a canonical coupling between the diffusion flow and the deformation gradient of the strained layer. It is found that the zero of the free energy of an adatom-strained layer continuum system should be that of a coherent unstrained layer, thus necessarily neglecting the cohesive energy contribution, while for the adatom-unstrained continuum layer the zero corresponds to an equilibrium between the adatoms and free atoms, which involves the cohesive energy.