ABSTRACT: The series BaIn1-x Fe x O2.5+?, x = 0.25, 0.50, and 0.75, has been prepared under air-fired and argon-fired conditions and studied using X-ray diffraction, d.c. and a.c. susceptibility, Mössbauer spectroscopy, neutron diffraction, X-ray near edge absorption spectroscopy (XANES), and X-ray pair distribution (PDF) methods. While Ba2In2O5 (BaInO2.5) crystallizes in an ordered brownmillerite structure, Ibm2, and Ba2Fe2O5 (BaFeO2.5) crystallizes in a complex monoclinic structure, P21/c, showing seven Fe3+ sites with tetrahedral, square planar, and octahedral environments, all phases studied here crystallize in the cubic perovskite structure, Pm3?m, with long-range disorder on the small cation and oxygen sites. 57Fe Mössbauer studies indicate a mixed valency, Fe4+/Fe3+, for both the air-fired and argon-fired samples. The increased Fe3+ content for the argon-fired samples is reflected in increased cubic cell constants and in the increased Mössbauer fraction. It appears that the Pm3?m phases are only metastable when fired in argon. From a slightly modified percolation theory for a primitive cubic lattice (taking into account the presence of random O atom vacancies), long-range spin order is permitted for the x = 0.50 and 0.75 phases. Instead, the d.c. susceptibility shows only zero-field-cooled (ZFC) and field-cooled (FC) divergences at ?6 K [5 K] for x = 0.50 and at ?22 K [21 K] for x = 0.75, with values for the argon-fired samples in [ ]. Neutron diffraction data for the air-fired samples confirm the absence of long-range magnetic order at any studied temperature. For the air-fired x = 0.50, a.c. susceptibility data show a frequency-dependent ?'(max) and spin glass behavior, while for x = 0.75, ?'(max) is invariant with frequency, ruling out either a spin glass or a superparamagnetic ground state. These behaviors are discussed in terms of competing Fe3+-Fe3+ antiferromagnetic exchange and ferromagnetic Fe3+-Fe4+ exchange. The PDF and 57Fe Mössbauer data indicate a local structure at short interatomic distances, which deviates strongly from the average Pm3?m model. Fe Mössbauer, PDF, and XANES data show a systematic dependence on x and indicate that the Fe3+ sites are largely fourfold-coordinated and Fe4+ sites are fivefold- or sixfold-coordinated.