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In the equilibrium states, the solid solubility between Fe and Cu is negligibly small. Using vapor deposition, however, we produced FexCu100-x solid solutions over the entire composition range. All the samples were crystalline: bcc structure at the Fe-rich side and fcc structure at the Cu-rich side. The transition from bcc to fcc occurred at around x=70, where the two phases were found to coexist. The fcc alloys exhibit a magnetic dilution leading to a magnetic percolation threshold at xc≃18, rarely seen in binary Fe alloys. Below xc, only spin-glass-like ordering is observed. Across the structure transition from fcc to bcc, there is a large discontinuity in Tc, and a very slight change in the atomic volume. Surprisingly, there are no noticeable discontinuities in the magnetic moment, hyperfine field, and isomer shift. The electronic structure of these alloys is discussed based upon x-ray photoemission spectroscopy measurement.