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High resolution low-energy electron diffraction, scanning tunneling microscopy (STM), and transmission electron microscopy (TEM) have been used to study the temperature dependence of a vicinal (stepped) Si(111) surface with a polar angle of 6° from (111) along an azimuth rotated about 10° away from the high symmetry [112] direction. At the (1×1) to (7×7) reconstructive transition, the kinks at the step edges precipitate into a phase with high step density and increased rotation from the [112] direction, leaving behind a [112] oriented phase with triple-layer height steps and (7×7) reconstruction. The inclination and azimuth of the orientation of the kinked phase change continuously with temperature. When the surface is cooled to room temperature, STM images confirm a coexistence between the [112] oriented step-tripling phase and the kinked phase. In the step-tripling phase, the steps are very straight (kinks are rare) and oriented in the [112] direction. There is a small fraction of single-layer height steps between the predominant triple-layer height steps. All the terraces in this phase are (7×7) reconstructed. In the kinked phase, steps with a high density of kinks are bunched together and rotated to a direction about 45° away from [112]. TEM images of the surface topography also confirm the phase coexistence on a macroscopic scale. This phase separation (azimuthal faceting) is reversible, and can be understood thermodynamically by analogy with phase separation in a two-component fluid. [ABSTRACT FROM AUTHOR]