1：Experimental Design and Method Selection:

The study used co-precipitation and hydrothermal synthesis to fabricate spinel black oxide nanoparticles doped with various metals (Mn, Ni, Co, Al, Zn, Sn). The optical properties were evaluated using UV-Vis-NIR and FT-IR spectroscopy, and structural analysis was done with XRD and SEM.

2：Sample Selection and Data Sources:

Samples were synthesized with different molar ratios of metals, specifically CuCr(2-x)MnxO4 for x values from

3：1 to Data on solar radiation intensity (ASTM G173) and blackbody emissivity were used for calculations. List of Experimental Equipment and Materials:

Equipment included autoclaves, furnaces, SEM (FEI Apreo, Quanta FEG 250), XRD (D8 ADVANCE), UV-Vis-NIR spectrometer (UV-3600), FT-IR spectrometer (IRTracer-100), integrating spheres (ISR-603, PN 048-10XX). Materials included metal chlorides (e.g., CuCl2-2H2O, CrCl3-6H2O, MnCl2-4H2O from Sigma Aldrich), sodium hydroxide, distilled water.

4：Experimental Procedures and Operational Workflow:

Metal precursors were dissolved in water, titrated with NaOH to precipitate hydroxides, hydrothermally treated at 200°C for 20 hours, rinsed, centrifuged, baked at 110°C, sintered at 550°C, and ground into nanoparticles. Reflectance and absorbance were measured with pressed powder samples.

5：Data Analysis Methods:

XRD data analyzed using Scherrer equation for crystal size, optical data used to calculate band gap via Kubelka-Munk method and Tauc plot, and Figure of Merit (FOM) calculated using integral equations based on reflectance profiles.