Chemistry and thermodynamics of the twin charge-ordering transitions in RBaFe2O5+w series

Thermal and volume parameters of the twin charge-ordering Verwey transitions in RBaFe₂O_5+w (R=a rare-earth element) are summarized as a function of R and w. Their determination is exemplified for case R = Dy, for which also synthesis conditions, phase relations, and refined crystal-structure data for the valence-mixed (Fe^2.5+) and charge-ordered (Fe²⁺ and Fe³⁺) phases are reported. Data for the R=Nd, Sm, Eu and Gd variants with wide ranges of oxygen non-stoichiometry suggest that increasing w decreases ΔS and the temperature of the transition in a manner that is similar to a behavior under increasing concentration of an ideal solution of RBaFe₂O₆ in RBaFe₂O₅. Thermal parameters of the transition for the ideal mixed-valence composition RBaFe₂O_5.000 are estimated from such compositional dependences, varying reasonably smoothly as a function of R (radius, electronegativity, polarizability). Parameter ΔV is the only one that follows the structural discontinuity between the charge-ordered R = Nd and variants with smaller trivalent R ions. The ordering of the d_xz orbitals of the Fe²⁺ ions is thus being achieved at a cost of lowering the symmetry when the R size becomes unfavorably large. A definition of the Verwey transition as a first-order orbital ordering of a valence-mixed phase is suggested.