## 2 Materials and Methods
### Instruments  
X-ray powder diffraction (XRPD) measurements were performed using a Bruker D5005 diffractometer (Karlsruhe, Germany) with CuK\(\alpha\) radiation (40 kV, 40 mA), graphite monochromator, and scintillation detector. The patterns were collected in the angular range of 10-120\({}^{\circ}\), with a step size of 0.03\({}^{\circ}\) and a counting time of 12 s per step in a silicon sample holder with low background. Rietveld structural and profile refinement was carried out by means of TOPAS 3.0 Bruker software [22], on the basis of the known crystal structure models of the layered polymorphs. During the refinement, the background coefficients, scale factor, zero or displacement error, lattice parameters, crystallite sizes, isotropic thermal factors, and atomic positions were varied. The occupancies of sodium and dopant ions were fixed to stoichiometric values, due to the complexity of the samples and to the similar X-ray scattering factors of Mn, Cu, and Fe ions. To evaluate the structural stability, the patterns were also collected on all the samples in the 10-70\({}^{\circ}\) 20 range, step 0.03\({}^{\circ}\) and 2s/step of counting time after 7, 14, and 30 days of the maintenance in air. A Tescan Mira 3 (Tescan USA Inc., Warrendale, PA, USA) scanning electron microscope (SEM) was used for the morphological study on gold-sputtered powder samples. Energy-dispersive X-ray spectroscopy (EDS) analysis was also performed with the same instrument on non-sputtered powder samples. Element measurements were performed via inductively coupled plasma optical emission spectroscopy (ICP-OES iCAP 7400, Thermo Fisher Scientific, Waltham, MA USA) equipped with a concentric nebulizer, cyclonic spray chamber, and ceramic torch, according to the operating conditions suggested by the manufacturer. The linearity range of intensity vs. concentration was obtained using standard solutions (1-10 mg/L) prepared from a 1 mg/mL stock solution. Small amounts, exactly weighted, of each sample were treated with 0.5 mL of ultrapure 65% HNO\({}_{3}\) and 1.5 mL of ultrapure 37% HCl, refluxed for 10 min, evaporated to a small volume, and then diluted to 50 mL with ultrapure water. Clear solutions were obtained and analyzed for the determination of element content. The Mossbauer measurements were performed by means of a standard Mossbauer setup (home assembled) in transmission geometry. The spectra were collected by means of a Kr-CO\({}_{2}\) proportional counter, Fast\({}^{\text{TM}}\) (LND Inc., New York, USA) electronics for gamma-ray spectroscopy, and a Wissel\({}^{\text{TM}}\) spectrometer (Blieskastel, Germany), which wasrun in sinusoidal acceleration mode (\(\
u_{\rm max}=4.0\) mm/s) and calibrated using a standard metal iron foil. The \(\gamma\)-ray source was a 25-mCi \({}^{57}\)Co in rhodium matrix with the Lamb-Mossbauer factor \(f=0.63\), as measured by applying the method described by [PERSON] and [PERSON] [23]. Approximately 33 mg/cm\({}^{2}\) of each compound was used for the measurements. The Mossbauer spectra were interpreted by means of a fitting procedure, based on the evaluation of the transmission integral function, which takes into account the dependence of the Mossbauer spectra on the sample's effective thickness. The complete expression used to fit the spectra was:  
\[Y(v)=N_{b}(v)\bigg{\{}1-f_{S}^{r}\int_{-\infty}^{\infty}L_{S}(\omega-v,\Gamma_{ S})\Big{[}1-e^{(-t_{a}\sigma(\omega))}\Big{]}d\omega\bigg{\}}\]  
where \(Y(v)\) and \(N_{b}(v)\) are the detected counts and the spectrum baseline, respectively, as a function of the transducer velocity \(v\)[24]. Moreover, \(f_{S}^{r}\) is the reduced recoilless fraction of the source and \(L_{S}(\omega-v,\Gamma_{S})\) is the Voigt distribution (having \(v\) and \(\Gamma_{S}\) as center and FWHM, respectively) used to describe the source line shape. The Voigt profile has a Lorentzian component with natural line width, while that of the Gaussian one is suitable to reproduce the total linewidth of the source provided by the manufacturer (\(\Gamma_{S}=0.114\) mm/s).