## 2 Materials and Methods
### Methods  
The study and characterization of La\({}_{2}\)Ti\({}_{2}\)O\({}_{7}\)-based oxide nanopowders obtained by the sol-gel method was approached according to the main factors influencing their structure and morphology. The following methods of characterization were used: infrared spectroscopy (FT-IR), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM) coupled with Energy Dispersive X-ray spectroscopy (EDX), transmission electron microscopy (TEM), X-ray diffraction (XRD), the determination of the BET-specific surface area and the pore distribution, and UV-Vis spectroscopy. FT-IR spectra of the thermally treated powders were recorded over the range of 4000-400 cm\({}^{-1}\) on a Jasco FT-IR-4700 spectrophotometer (Jasco, Tokyo, Japan) using the KBr disk method. The Renishaw inVia Qontor Spectrometer System (Renishaw PLC, Wotton-under-Edge, Gloucestershire, UK) for confocal Raman spectral imaging using the visible laser wavelength (532 nm) was used to examine the synthesized samples. The acquisition was performed in the spectral range 100 to 1000 cm\({}^{-1}\), using an exposure time of 10 s, a power lower than 10\(\%\) (5 mW) with different number of accumulations (usually 5 accumulations), and a grating of 1800 l/mm. The microscope objective was a Leica N PLAN X100 magnification (Leica Camera AG, Wetzlar, Germany) with a focal distance of 0.33 mm and numerical aperture of 0.85. The detector was a Master Renishaw Centrus (Renishaw, Wotton-under-Edge, UK). XPS measurements were performed using an XPS spectrometer (SPECS Surface Nano Analysis GmbH, Berlin, Germany) equipped with a PHOIBOS 150 mm hemispherical electron energy analyzer, a multichannel detector, and a monochromated Al K\(\alpha\) radiation (1486.7 eV) anode as the excitation source. The operating power was 250 W (12.5 kV \(\times\) 20 mA) and the spectra were recorded with 99 eV pass energy for general surveys and 30 eV pass energy for high-resolution, core-level measurements, with partial charge compensation provided by a neutralizer flood gun (1 eV \(\times\) 100 mA). The base pressure in the analysis chamber before measurements was 10\({}^{-10}\) mbar. The particle morphology and elemental composition of the samples were examined using a Verios G4 UC scanning electron microscope (Thermo Scientific, Brno, Czech Republic) equipped with an Energy Dispersive X-ray (EDX) spectroscopy analyzer (Octane Elect Super SDD detector, Octane, New York, NY, USA). For SEM analysis, the specimens were mounted on aluminum stubs using double-sided carbon adhesive tape and subsequently coated with a 6 nm platinum layer via a Leica EM ACE200 sputter coater (Leica, Vienna, Austria) to enhance electrical conductivity and mitigate charging effects under electron beam irradiation. Morphological characterization was performed utilizing a secondary electron detector (TLD--Through the Lens Detector) to accurately delineate particle shape and size. SEM micrographs were acquired at an accelerating voltage of 10 kV and a beam current of 0.4 nA. For EDX elemental analysis, the samples were examined at an accelerating voltage of 20 kV and a beam current of 6.4 nA. The TEM studies were performed using a transmission electron microscope Hitachi HT-7700 (Hitachi, Tokyo, Japan) at an accelerating voltage of 100 kV. For TEM analysis the nanoparticles were dispersed in ethanol, ultrasonicated, placed on carbon-coated copper grids with a 300-mesh size, and dried in an oven until the solvent was removed. The X-ray diffraction (XRD) patterns of the powders were obtained using a Rigaku Ultima IV diffractometer (Rigaku Corp., Tokyo, Japan). The instrument was configured in a parallel beam geometry with Cu K\(\alpha\) radiation (\(\lambda\) = 1.5406 A) and CBO optics, and operated at 40 kV and 30 mA. Data were collected with a step size of 0.02\({}^{\circ}\) and a scan speed of 2\({}^{\circ}\) min\({}^{-1}\). Phase identification was carried out with a Search-Match algorithm, connected to the PDF database.