Local and long-range atomic/magnetic structure of non-stoichiometric spinel iron oxide nanocrystallites

The atomic, magnetic and nano-structure of hydrothermally synthesized non-stoichiometric spinel iron oxide nanoparticles are examined in detail using a wide range of advanced structural characterization methods. The present study constitutes the first use of the recently developed magnetic pair-distribution-function analysis method to model the local magnetic structure in nanoparticles.


S5. Microstructural model -Considerations regarding refinement of microstrain
Attempts at implementing a microstrain contribution to the peak profile refinements were unsuccessful.
The refined parameters (Gaussian and/or Lorentzian) tend to zero causing either non-converging fits or unphysical negative peak widths. Refining the oxygen B-values (previously fixed to 0.5) allows physically meaningful strain values to be refined, however, at the cost of unphysical negative oxygen displacement factors. Ultimately, it is thus concluded that the effect of any microstrain on the observed diffraction peak profiles are negligible given the very minor difference in cell parameters, i.e. a(γ-Fe2O3)=8.33 Å and a(Fe3O4)=8.396 Å at ambient conditions, between the end-member structures and the relatively large/dominating Scherrer broadening due to the fine crystallite size. In any case, the effect, if any, of isotropic microstrain will not influence the obtained atomic structure or trend in extracted crystallite size.  The atomic structural model in tetragonal space group P43212 (as reported by Greaves,(Greaves, 1983)) employed in the refinement of the FL340C sample. Notes: The numbers in parentheses indicate the errors on the last significant digit of the refined parameters. The secondary hematite phase (space group R-3c) was found to constitute 0.9(5) wt%.

FL340C (FexO4)
IUCrJ (  The atomic structural model in tetragonal space group P43212 (as reported by Greaves, (Greaves, 1983) employed in the refinement of the FL390C sample.

FL390C (FexO4)
Space group: Notes: The numbers in parentheses indicate the errors on the last significant digit of the refined parameters. The secondary hematite phase (space group R-3c) was found to constitute 0.9(6) wt%.
IUCrJ (  The atomic structural model in tetragonal space group P43212 (as reported by Greaves, (Greaves, 1983)) employed in the refinement of the FL440C sample.

FL440C (FexO4)
Space group: Notes: The numbers in parentheses indicate the errors on the last significant digit of the refined parameters. The secondary hematite phase (space group R-3c) was found to constitute 0.7(5) wt%.

S9. PXRD -FL340C superstructure peak profile analysis
The peak profile analysis in the refinement of the whole pattern yielded a mean crystallite diameter of the FL340C sample of 8.71(8) nm. However, a moderate discrepancy between the fitted model and the superstructure reflections is observed. Applying Scherrer analysis to the (210) and (211) superstructure peaks alone indicates a vacancy-ordered domain size of 8(1) nm, while single-peak fitting of the (220) reflection indicates a spinel domain size of 9.4(3) nm.

Figure S8
Magnification of the 2θ-region containing the (210) and (211)  Supporting information, sup-13 S10. PXRD -FL390C superstructure peak profile analysis The peak profile analysis in the refinement of the whole pattern yielded a mean crystallite diameter of the FL390C sample of 15.6(2) nm. However, a moderate discrepancy between the fitted model and the superstructure reflections is observed. Applying Scherrer analysis to the (210) and (211) superstructure peaks alone indicates a vacancy-ordered domain size of 10(2) nm, while single-peak fitting of the (220) reflection indicates a spinel domain size of 18.6(10) nm.

Figure S9
Magnification of the 2θ-region containing the (210) and (211)  Supporting information, sup-14 S11. PXRD -FL440C superstructure peak profile analysis The peak profile analysis in the refinement of the whole pattern yielded a mean crystallite diameter of the FL440C sample of 17.0(2) nm. However, a moderate discrepancy between the fitted model and the superstructure reflections is observed. Applying Scherrer analysis to the (210) and (211) superstructure peaks alone indicates a vacancy-ordered domain size of 10(3) nm, while single-peak fitting of the (220) reflection indicates a spinel domain size of 20.5(6) nm.

Figure S10
Magnification of the 2θ-region containing the (210) and (211)  Quantitative analysis of the EDS spectrum from the mapped area was performed, however, an accurate determination of the exact FexO4 stoichiometry could not be obtained, due to the oxygen background signal, which cannot be discerned from the oxygen in the sample and thus leads to an underestimation

S18. Mössbauer analysis
The room temperature Mössbauer spectra of the three nanocrystalline spinel iron oxide powders are shown in Fig. S18 Table 2 and a compilation of the fitted parameters may be found below.

Figure S18
Room temperature Mössbauer spectra of samples synthesized at (a) 340 °C, (b) 390 °C and (C) 440 °C. The data has been modelled by three components; a superparamagnetic Fe 3+ doublet (red), a sextet from Fe 3+ below the superparamagnetic blocking temperature (TB) (yellow) and a general line-shape of magnetite (black).