EuBaFe₂O₅: Extent of charge ordering by Mössbauer spectroscopy and high-intensity high-resolution powder diffraction

¹⁵¹Eu and ⁵⁷Fe Mössbauer spectroscopy, differential scanning calorimetry, and high-intensity high-resolution synchrotron powder diffraction were used to determine the extent of long- and short-range charge ordering below the first-order Verwey-type transition in EuBaFe₂ O₅, the oxygen content of which was homogenized by annealing in sealed ampoule. The diffraction gives 0.68(5) valence unit of charge separation at 100 K. Interpretation of this value as 68% of iron being long-range charge ordered correlates with the total transition entropy per formula of about 0.7 of the theoretical value 2 R ln 2 that would be valid for all iron atoms being fully charge ordered. For long- and short-range order combined, ⁵⁷Fe Mössbauer spectroscopy suggests that about 90% of iron atoms occur as charge-ordered integer Fe^{2 +} and Fe^{3 +}. The residual 10% are the Fe^{2 +} and Fe^{3 +} that did not find the way to order. Local oxygen non-stoichiometry defects that revert the direction of the charge order are suggested as one of the origins of the short-range charge order. Accordingly, the long-range charge order seen by diffraction is highest in the portion of the sample that converts last upon heating, having the most ideal valence ratio.