In this investigation, we undertake an ab initio exploration of the structural, mechanical, electronic, magnetic, optical, and thermoelectric characteristics of equiatomic quaternary Heusler compounds (EQH), specifically FeZrCrZ (Z = Si, Ge, Sn). Our investigation involves the utilization of the full-potential linearized augmented plane wave method (FP-LAPW) in density functional theory (DFT) framework, employing the generalized gradient approximation (GGA). The findings reveal that the Y-type-I arrangement, demonstrating ferromagnetic alignment, emerges as the most thermodynamically favored configuration among all FeZrCrZ (Z = Si, Ge, and Sn) compounds. Computed values for formation energy substantiate the feasibility of experimental synthesis.Furthermore, we meticulously determine elastic constants, confirming the structural robustness of the quaternary compounds. Dynamic stability analysis reinforces their stability. Electronic property assessments unveil the semi-metallic nature of FeZrCrZ (Z = Si, Ge, and Sn) alloys, showcasing complete spin polarization at the Fermi energy (100 %), a minimal energy gap, and magnetic moments of 2 μB when Z = Si, Ge, and 4 μB when Z = Sn. Optical property calculations encompass complex refractive index, dielectric function, reflectivity, absorption coefficient, and optical conductivity, indicating potential suitability of these compounds for optoelectronic applications. Employing Boltzmann transport theory, we investigate the thermoelectric performance of the compounds concerning temperature, and chemical potential. Evaluation of the thermoelectric response underscores their viability as thermoelectric materials, linked to a substantial figure of merit, increased Seebeck coefficient, and diminished thermal conductivity. This study provides crucial theoretical insights for experimental researchers, offering valuable information for the synthesis and application of these compounds in spintronics, thermoelasticity, and optoelectronics.
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