image: 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 image, 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 image 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 image and image. The residual 10% are the image and image 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.