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Density functional theory calculations have been used to study the mixing behavior of Fe-Cr alloys. The heats of formation ΔE_f of 65 Fe-Cr structures in their magnetic ground states have been determined. A positive ΔE_f is found over most of the concentration range. From 0-12 % Cr a small negative ΔE_f down to -8 meV/atom is found. The origin of the negative Δ E_f in Fe-rich structures is traced to the solution energy of single Cr atoms. At low concentration, Cr atoms in Fe repel each other, causing ordering. The Cr-Cr interactions are well reproduced even without the self-consistent relaxation of the electron density and the positions of atoms. Multi-ion (or concentration-dependent) interactions are indispensable in order to describe the whole phase diagram. The interesting magnetic situation that arises when ferromagnetic and antiferromagnetic metals are mixed in different ratios is discussed with reference to nearest- and next-nearest-neighbor clusters of Cr in Fe. Magnetic frustration leads to a strong dependence of the Cr moment on the number of Cr neighbors. The "normal" chemical-mixing energy and the influence of magnetism are distinguished by comparing magnetic and nonmagnetic calculations for similar systems.