Optical and theoretical study of NaCr(P 2 O 7 ): a look through the Neuhauser model and Racah theory.

A sample of NaCr(P 2 O 7 ) was synthesized using the solid-state reaction method. X-ray diffraction and Rietveld refinement confirmed the formation of a monoclinic structure with the P 2 1 / a space group. Scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis identified the morphology and homogeneity of the chemical composition. The optical absorption spectrum revealed a direct optical band gap of 2.9 eV and an Urbach energy of 0.44 eV. Notably, the absorption spectrum showed an interference dip on the lowest energy band 4 T 2g ( 4 F), attributed to spin-orbit coupling between states 2 E g ( 2 G) and 4 T 2g ( 4 F). This phenomenon was analyzed using the Neuhauser model based on coupled potential energy surfaces. From this analysis, the electronic structure of Cr 3+ (3d 3 ) ions in the NaCr(P 2 O 7 ) sample was determined, enabling a reliable calculation of Racah and crystal-field parameters. The results showed good agreement between experimental and theoretical energy levels. The study demonstrates the impact of spin-orbit interactions using the coupled potential energy surface model.