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Alloys of FexHf100-x (20 ≤ x ≤ 100) were fabricated by a vapor-quench method. The amorphous state, as verified by x-ray diffraction, is realized over a wide composition range of 20 ≤ x ≤ 94. The magnetic phase diagram was determined. The variation with Fe content of the magnetic ordering temperature (Tc) in Fe-Hf amorphous alloys shows a maximum at xp≈87. In contrast, the effective magnetic hyperfine field and therefore the Fe moment increases monotonically with x. Amorphous pure Fe is likely to be magnetic (Tc ~200 K) with a large magnetic moment. At higher Fe concentrations (x>95), the samples are crystalline alloys and strongly ferromagnetic. These sharp changes of the magnetic properties are consequences of structural differences, a fact which has been observed in every Fe-early transition metal alloy system reported thus far. In general, the magnetic properties and hyperfine interactions of amorphous Fe-Hf alloys are very similar to those of amorphous Fe-Zr alloys.