Surface reconstruction can generate effective attractive interactions between steps on vicinal surfaces, leading to the formation of step bunches. Modified repulsive interactions arise from the fluctuations of a step in the asymmetric environment at the edge of the step bunch. These are determined by a mapping to the ground state energy of a quantum particle between two rigid walls in an external field. This yields an edge energy term that controls the dynamics of faceting and causes wider step spacings at the edge of the bunch, in agreement with Monte Carlo simulations. [S0031-9007(97)03948-3] PACS numbers: 68.35.Md, 68.35.Rh Theories used to explain step morphology and dynamics on vicinal surfaces often relate the velocity of a step to changes in the local surface free energy expressed as a functional of the step positions [1,2]. Constraints on possible transverse step fluctuations arise because of the prohibitive energy cost arising from step overhangs. This gives rise to an effective entropic repulsive interaction between steps at nonzero temperature that tends to keep steps uniformly spaced [3]. The two-dimensional (2D) terracestep-kink (TSK) model [4], which can be mapped onto a 1D free-fermion model [5], provides a quantitative description of effects arising from the no-crossing constraint.A simpler 1D description may be adequate for many vicinal surface problems that exhibit quasi-onedimensional features. The 1D model can be obtained by averaging the transverse step fluctuations in the 2D TSK model over a mesoscopic distance L y along the step edge direction, expressing the effective step interactions in terms of the average positions of the steps. Rettori and Villain [6] proposed a 1D local free energy model for surfaces with nonuniform step spacings, summing separate contributions from each terrace, or equivalently, from individual steps with effective repulsive interactions between nearest-neighbor (NN) pairs of steps only. In the 1D NN approximation, the effective step pair interaction must vary as 1͞w 2 , with w the average width of the terrace separating them, so that the known results for the equilibrium free energy of a uniform vicinal surface [3,5,7] can be recovered. This model and various generalizations have proved very useful in a number of different applications [8][9][10][11][12].However, the simple NN description fails to describe some essential features of the physics in certain cases where competing interactions exist that favor very nonuniform step configurations. We study here one such example, the reconstruction induced "phase separation" into wide reconstructed facets and unreconstructed step bunches as seen on vicinal Si(111) and many other surfaces [13 -15].While reconstruction can lower the free energy of a flat terrace on which it occurs, it generally makes defects such as steps that disturb the reconstruction energetically more costly [3,16]. This suggests that reconstruction should occur on a stepped surface only for sufficiently wide terraces above some "critical" terrace w...