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First-principles calculations of formation energies for 243 different configurations of the Cr-Ni-Re σ-phase were used to calculate a ternary phase diagram in the Bragg-Williams-Gorsky approximation (BWG) and to model finite-temperature thermodynamic properties. The binary and ternary phase diagrams were then calculated at different temperatures. Correct topology of the experimental ternary isothermal section of the phase diagram has been obtained with a relatively small difference in temperature between calculations and experiments.