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A novel approach is proposed for the description of possible reconstructive solid-state transformations, which is based on the analysis of topological properties of atomic periodic nets and relations between their subnets and supernets. The concept of a region of solid-state reaction that is the free space confined by a tile of the net tiling is introduced. These regions (tiles) form the reaction zone around a given atom A thus unambiguously determining the neighboring atoms that can interact with A during the transformation. The reaction zone is independent of the geometry of the crystal structure and is determined only by topological properties of the tiles. The proposed approach enables one to drastically decrease the number of trial structures when modeling phase transitions in solid state or generating new crystal substances. All crystal structures which are topologically similar to a given structure can be found by the analysis of its topological vicinity in the configuration space. Our approach predicts amorphization of the phase after the transition as well as possible single-crystal-to-single-crystal transformations. This approach is applied to generate 72 new carbon allotropes from the initial experimentally determined crystalline carbon structures and to reveal four allotropes, whose hardness is close to diamond. Using the tiling model it is shown that three of them are structurally similar to other superhard carbon allotropes, M-carbon and W-carbon.

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