Now that the magnetic structure had been identified as well as the nuclear structure model, a complete combined Rietveld refinement was carried out using SXRD and ND data using Topas Academic v5.175. As the A-site contained three possible cations (Y, Ca and Sr), initially occupancies were refined using Y and Ca summed to a total of one on each A-site. This is because Y3+ and Sr2+ are indistinguishable by X-rays (both have 36 electrons) and have poor contrast in neutrons (bound coherent scattering lengths: Y 7.75 fm, Sr 7.02 fm).168 A small compositional restraint was given for the A-site, set as the EDX given composition of Y2.8Ca2.2, with Sr included in the Y total.
Combined refinements were carried out in the space group Pnma, as well as an alternative space group Pn21a, which was also identified for the reported YCa4Fe5O13 phase and has the
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same reflection conditions.222, 239 Though the best fit was obtained for the space group Pnma, during the refinement, it became obvious that the structure was not quite right due to differences in the fit and observations made from difference maps created from the observed − calculated fit. The Fourier difference maps showed that the Td sites contained a mismatch, indicating that the site should be split along the a-axis (see Figure 4.6) creating disordered Td Fe and O sites. This disordering is not possible using the Pnma space group with the YCa4Fe5O13 structure without adding additional atoms.
Figure 4.6 A) Using space group Pnma, left shows a Fourier map with Fe atoms (solid yellow), O atoms (solid red) and missing electron density (yellow pixels) for an ordered Td site shown right. B) Using space group Imma, right shows
disordered Td site with split Fe and O sites (half white) due to presence of a mirror plane, also represented in Fourier map on
left, which has no relative missing electron density. Difference Fourier maps generated from ND bank 5 data set.
It was decided to attempt to find an appropriate space group using the SXRD data rather than the ND data as this contained the additional complication of the presence of magnetic reflections. The lattice parameters and unit cell geometry were already identified, therefore the hkl reflections observed were listed where possible in order to obtain the reflection conditions. The reflection conditions are listed in Table 4.1 together with examples of reflections observed obeying the conditions. No reflections contradicting the conditions were observed and none were left without being indexed.
129 Reflection Conditions hkl 0kl h0l hk0 h00 0k0 00l h+k+l = 2n k+l = 2n ? h,k = 2n h = 2n k = 2n l = 2n Examples of observed reflections 1 4 1 0 3 1 2 6 0 6 0 0 0 2 0 002 1 6 1 0 7 1 2 10 0 0 4 0 1 1 2 0 9 1 2 12 0 0 6 0 1 3 2 0 6 2 2 14 0 0 12 0 2 5 1 0 8 2
Table 4.1 Showing the reflection conditions and examples of the conditions observed in SXRD data. The "?" signifies unknown conditions due to overlap of potential h0l reflections with known reflections.
Due to overlap with other allowed reflections, h0l conditions could not be assigned. Based on the observed reflection conditions, the highest symmetry space groups allowed are Imma, Immb, Im2a and I2mb for h + l = 2n, and Imcb and I2cb for h, l = 2n for h0l ambiguity. Combined refinements were carried out in all space groups, with the best fit obtained for the space group Imma, which also allowed for the modelling of the disordered Td site. Together with I2mb, which has ordered Td chains, they are not uncommon space groups to find for related structures. Brownmillerite phases such as Sr2Al1.07Mn0.93O5,240 Sr2Co2O5,241, and Ca2Fe2O5242 have been reported in Imma. The Brownmillerite structure Ca2Fe2O5 has also been reported to undergo a phase transition from Pnma at room temperature, to I2mb at ~ 700 °C,190, 219, 243 and Imma at ~ 1300 °C.244 The transition between the space groups occur due to changes in Td ordering along the a-axis, where the two Td in the unit cell point in opposite directions for Pnma, in the same direction for I2mb, and disordered in Imma.
As with the brownmillerite, the difference between the between the space groups Pnma, I2mb and Imma for the YCSFO structure is down to the Td ordering. For Pnma, the Td chains point right-right-left-left when looking down the c-axis, whereas in I2mb, the Td chains all point in the same direction. Finally, for Imma, the Td are disordered, as shown in Figure 4.7 along with the YCSFO structure represented in Pnma and I2mb. The Td have been highlighted within the black boxes for ease of comparison.
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Figure 4.7 Representation of the YCSFO structure in Pnma, I2mb and Imma space groups for comparison, with the main difference found in the ordering of Td chains (highlighted within black boxes). A-site atoms (green), O atoms (red) and B-site
polyhedra (brown).
For the combined Rietveld refinement, the ND time-of-flight diffractometer constants were all refined for the ND banks 2, 3, 4 and 5. The zero point was refined for the SXRD data giving a total of 13 refined diffractometer parameters. A total of 36 background parameters were refined; 6 for each ND histogram; 12 for SXRD histogram. Refined lattice parameters for YCSFO were constrained to the same value for ND and SXRD data. Structures for YCSFO (including the magnetic structure) were included in the Rietveld refinement.
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In order to improve the peak profile fitting, anisotropic strain broadening202 was refined for YCSFO in the SXRD data-set and the highest resolution (banks 4 and 5) ND data-sets to account for slight differences in peak shape for reflections corresponding to the long stacking axis. A total of 29 profile parameters were used in the refinement for all histograms; 3 for ND bank 2; 3 for ND bank 3; 8 for ND bank 4; 8 for ND bank 5; 7 for SXRD.
The relative occupancy of Y and Ca for each A-site were refined while the total occupancy of unity on each A-site was enforced. A soft chemical composition restraint was implemented to drive the refinement towards the EDX A-site composition of Y2.8Ca2.2, with Sr accounted for in Y total. A single isotropic displacement parameter was refined for each atom type; A-site (Y/Ca), B-site (Fe) and O. The atomic coordinates of each atom was refined within the symmetry allowed by each Wyckoff position.
Figure 4.8 below shows the fits from the combined Rietveld refinement of SXRD and ND data discussed above. A good fit was obtained for all data with an Rwp = 1.812, Rexp = 0.258.
A refinement was also carried out in Pnma, with the addition of a second O and Fe atom with 1/2 occupancy in order to model the disordered Td site. The additional atoms refined to the same positions as they appear using the space group Imma. The fit was not improved when compared to the refinement in Imma, despite the extra freedom of the atoms to move within Pnma. It was therefore decided to retain the higher symmetry space group Imma.
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Figure 4.8 Fit data from a combined refinement including only A-Site cations Y and Ca of A) SXRD data together with zoomed in regions of low and high angle, B) ND bank 2, C) ND bank 3, D) ND bank 4 E) ND bank 5 data.
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Before the anomalous scattering ASXRD data were added to the refinement, Sr was added to the three A-sites and refined. Each site had a large penalty, restraining the total occupancy to unity, as well as having a soft penalty to keep the total A-site cation ratio close to the EDX given ratio of YCa2.2Sr1.8. Simulated annealing was carried out with A-site occupancy, fractional coordinates, thermal parameters, lattice parameters and scale factors refined. This was to allow the refinement some freedom to change parameters that may affect the calculated intensities along with occupancy. This led to refined parameters with large errors, especially for Y and Sr occupancies, as well as very large errors for the refined composition. Ca occupancies refined with only small errors by comparison. This demonstrated the difficulty in distinguishing Y and Sr, and showed the need to use additional data for this purpose. These data are shown in Table 4.4. The next refinement to be set up was to contain the ASXRD data set.