DFT Calculation of the Structural, Electronic and Optical Properties of Sodium-Based Quaternary Heusler Alloys NaNbRhZ (Z= B, Al, Ga)

In this paper, we performed a comprehensive first-principles study based on density functional theory to investigate the structural, mechanical, dynamical, electronic, and optical properties of the quaternary Heusler compounds NaNbRhZ (Z[Formula: see text]B, Al, Ga). These materials crystallize in the cubic F-43m structure (space group No. 216), similar to the LiMgPdSn prototype. Among three considered atomic configurations, the most stable was the type 3 structure, where atoms X, X′, Y and Z occupy Wyckoff positions (0.75, 0.75, 0.75), (0, 0, 0), (0.25, 0.25, 0.25) and (0.5, 0.5, 0.5), respectively. Their nonmagnetic character is consistent with the Slater–Pauling rule, which predicts a zero total magnetic moment for systems with 18 valence electrons. Mechanical stability was confirmed via elastic constants that satisfy Borns stability criteria. Phonon dispersion calculations show no imaginary frequencies, confirming dynamic stability. Electronically, these compounds are nonmagnetic semiconductors with band gaps of 0.78[Formula: see text]eV (NaNbRhB), 0.46[Formula: see text]eV (NaNbRhAl) and 0.60[Formula: see text]eV (NaNbRhGa). Optical analyses reveal notable polarization effects in the infrared and ultraviolet regions. The refractive indices and absorption coefficients display typical semiconductor behavior, with absorption peaks at 2.45[Formula: see text]eV, 2.17[Formula: see text]eV and 2.21[Formula: see text]eV, respectively. Overall, NaNbRhZ (Z[Formula: see text] B, Al, Ga) alloys are stable, nonmagnetic semiconductors with promising mechanical and optical properties, making them strong candidates for various technological applications.