*3.1. XRD and Rietveld Analysis*

From the Rietveld refinement of the XRD and neutron diffraction powder (NPD) patterns measured at RT and 2 K, respectively, the results suggested for all samples the presence of only an orthorhombic Pnma (No. 62) crystal structure [11], i.e., no secondary phase was observed. In addition, both experiments showed similar behavior for the lattice parameters a, b, and c within their uncertainties. Thus, the refined values of the cell parameters are plotted in Figure 1a,b, which suggested: (i) a linear evolution of the cell parameters (Figure 1a) at RT and 2 K as a function of iron concentration (x), (ii) the c parameter changed more rapidly than the a or b parameters, and (iii) a continuous increase in cell volume with Fe concentration (Figure 1b) at both temperatures. For the size estimation of YFeO3 crystallites (RS7 sample) (see refined diffractogram in Figure 1c), we used the modified Scherrer's formula that expresses the anisotropic size broadening as a linear combination of spherical harmonics (SHP) if the anisotropic size contribution

belongs only to the Lorentzian component of the total Voigt function [10]. Therefore, the explicit formula for the SPH approach of size broadening is given by Equation (1) [12]:

$$\beta\_{\rm h} = \frac{\lambda}{D\_{\rm h} \cos \theta} = \frac{\lambda}{\cos \theta} \sum\_{d \neq p} a\_{l \, imp} y\_{l \, imp} (\Theta\_{\rm h}, \Phi\_{\rm h}) \tag{1}$$

where *h* is assigned to the (hkl) indices, *β<sup>h</sup>* is the size contribution to the integral width of reflection (hkl), *ylmp*(Θh, Φh) are the real components of spherical harmonics (arguments Θ<sup>h</sup> and Φ<sup>h</sup> are the polar and azimuthal angles of vector (hkl) with respect to a Cartesian crystallographic frame), and *almp* are the refined coefficients, related to the Laue class [13]. For the RS7 sample, a -1 Laue class was used.

**Figure 1.** Cell parameter (**a**) and volume (**b**) variation with the x (Fe concentration) and Rietveld refinement XRD diffractogram (**c**) for the RS7 sample. The inset in (**c**) is the simulated structure obtained after refinement using VESTA (red spheres are oxygen atoms, white and blue are yttrium atoms, and green spheres are iron atoms). While blue, red, and green arrows indicate the a, b, and c crystallographic axes, respectively. Miller indexes are given between parentheses, black dots are the experimental data, the red line is the calculated diffractogram, and the vertical green lines are the Bragg's diffraction position. Solid lines in (**a**,**b**) are guides for visualization.

The obtained profile refinement gave acceptable statistical parameters for the reliability factor, Rp (%); weighted profile residual, Rwp (%); expected profile residual, Rexp(%); and goodness of fit, χ2; having quantitative values as follows: Rp = 16.2%, Rwp = 10.4%, Rexp = 26.19%, and χ<sup>2</sup> = 0.94, while the refined harmonic coefficients were found equal to Y00 <sup>=</sup> −0.00574, Y20 = 0.01395, Y21<sup>+</sup> <sup>=</sup> −0.06448, Y21<sup>−</sup> = 0.01518, Y22<sup>+</sup> = 0.07557, and Y22<sup>−</sup> = −0.03690, respectively. With these values, the anisotropic Lorentzian size broadening gave a mean crystallite value of 84 (8) nm. Hence, combining all above data, it can be

inferred that the autocombustion method allowed nanocrystalline Fe-substituted YCrO3 powders with a single phase, orthorhombic-like structure to be obtained.
