  We measured the reduced partition function ratios for iron isotopes in
goethite FeO(OH), potassium-jarosite KFe3(SO4)2(OH)6, and hydronium-jarosite
(H3O)Fe3(SO4)2(OH)6, by Nuclear Resonant Inelastic X-Ray Scattering (NRIXS,
also known as Nuclear Resonance Vibrational Spectroscopy -NRVS- or Nuclear
Inelastic Scattering -NIS) at the Advanced Photon Source. These measurements
were made on synthetic minerals enriched in 57Fe. A new method (i.e., the
general moment approach) is presented to calculate {\beta}-factors from the
moments of the NRIXS spectrum S(E). The first term in the moment expansion
controls iron isotopic fractionation at high temperature and corresponds to the
mean force constant of the iron bonds, a quantity that is readily measured and
often reported in NRIXS studies.
