## 3 Results  
### Xrd  
The diffractograms measured for the three kinds of sample are shown in Figure 1. The diffraction peaks are indexed on the basis of the structure of magnetite. The lattice parameters derived from these measurements are the same within the experimental accuracy for all the samples (Table 1). Magnetic and maghemite (\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)) have the same structure (cubic inverse spinel) and very similar lattice parameters (0.8397 nm and 0.8315 nm, respectively). Hence, it is not possible to discriminate between these two iron oxides, in particular for a core-shell structure with a magnetite core covered by a thin shell of maghemite (which is probably the present case). Figure 1: Diffractograms measured for sample A (bare Fe\({}_{3}\)O\({}_{4}\) NPs), sample B (citrate-coated NPs, ex situ) and sample C (citrate-coated NPs, in situ). The curves are offset to improve the clarity of the plot. The main peaks in the diffractograms are indexed on the basis of the structure of magnetite. From the visual comparison of these curves we can see that the peaks of samples A and B have almost the same width whereas those of sample C are broader. The average sizes of the single NPs were estimated by using three different methods in order to be more confident on the obtained results. The basic assumption of the analysis is that each NP consists of a single coherence domain and that the size of the domains is smaller than the coherence length of experimental set-up. When the NPs form aggregates (such as in the present case) a reliable determination of the average size of the individual (primary) NPs is awkward by analysing TEM images (Figure S2, Supplementary Materials) [30]. The results of the analysis are summarized in Table 1. The Scherrer method allows one to estimate the average size of the particles from the width of the diffraction peaks. NPs can be considered spherical (see Figure S2, Supplementary Materials) and the size of the NPs identified with their diameter. The average diameter reported in Table 1 for each kind of sample is the average of the values calculated for the peaks in the diffractogram. In this way it is possible to compensate for possible errors in the measurement of the peak width and to the direction dependence of the size of the crystallites. The results of the analysis by the Scherrer method confirm that the NPs in sample C have a smaller size than those in samples A and B. The Scherrer method attributes entirely the width of a diffraction peak to the limited size of the crystal grains. However, an additional contribution to the broadness of a peak may come from the microstrain induced by crystal defects (dislocations, for instance). This contribution was estimated by analysing the data on the basis of the Williamson-Hall method. The data for all the three kinds of sample follow only approximately the linear behaviour predicted by the Williamson-Hall method (Figure S3 Supplementary Materials) [31]. This may be due to deviations from the uniform strain model assumed in this version of Williamson-Hall method [32]. However, the analysis indicates that the main contribution to the width of the diffraction peaks comes from the nanometric size of the crystals. Hence, the results of the Williamson-Hall approach for the size of the particles are fully consistent with those of Scherrer analysis (see Table 1). In addition to the average diameter also the PSD curves were determined by analysing the diffraction peak profiles. The average diameters of the NPs and the standard deviations, \(\sigma\), for the three kinds of sample calculated by using the Pielaszek and the Rietveld methods are reported in Table 1. The PSD curves of samples A, B and C are shown in Figure 2. The PSD function used in the Pielaszek method is the gamma distribution function. This function,