The mechanism of formation of a chessboard-like structure observed during coherent decomposition in alloys with several orientation variants of the precipitate phase is considered. It is based on the accommodation of coherency strain achieved by spatial rearrangement of orientation variants of the precipitate phase in an optimal pattern. The computational model of precipitation of the ordered tetragonal phase, based on the continuum stochastic field kinetic equations for the composition and lro parameters profiles, is formulated. Its numerical solution describes the spatial and temporal evolution of the microstructure, from nucleation to coarsening. It is shown that the chessboard-like microstructure is produced by strain-driven, self-assembling of orientation variants of the precipitate phase, faceted by the planes normal to the elastically soft directions. Coarsening of such microstructures occurs by consequent disappearance of entire rows of "tiles" in the pattern.
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