Exploring the Multifaceted Nature of \(\mathbf{T}\mathbf{a}{\mathbf{C}\mathbf{u}}_{3}{\mathbf{\rm X}}_{4}\left(\mathbf{\rm X}=\mathbf{S},\mathbf{S}\mathbf{e},\mathbf{T}\mathbf{e}\right)\) Materials: A DFT Study Revealing Promising Structural, Optoelectronic, Thermodynamic and Thermoelectric Properties

The present study looks into the \({\text{TaCu}}_{3}{\text{\rm X}}_{4} (\text{\rm X}=\text{S},\text{ Se},\text{Te})\) compounds’ structural, mechanical, electronic, thermodynamic, optical, as well as thermoelectric attributes using a First-Principles computational method based on the Density-Functional theory (DFT) methodology. Initially, the implementation of the PBE-GGA approach was done to determine the lattice constants of the understudied compounds. A thorough analysis of the binding energy calculations has been performed to determine the structural stability of selected chemicals. Additionally, the study of elastic stiffness constants is utilized to evaluate the mechanical stability. It has been reported that the \({\text{TaCu}}_{3}{\text{\rm X}}_{4}(\text{\rm X}=\text{S},\text{ Se},\text{Te})\) compounds are mechanically stable due to fulfillment of Born-Stability criteria \(({C}_{44}<0)\). Through the determination of Pugh’s along with passion ratios as well as the Cauchy pressure, the ductile and the brittleness nature of the \({\text{TaCu}}_{3}{\text{\rm X}}_{4}(\text{\rm X}=\text{S},\text{ Se},\text{Te})\) compounds have been established. An analysis of the electronic band structure, total density of states, as well as partial density of states was performed in order to ascertain the electronic features. It has been shown that the compounds \({\text{TaCu}}_{3}{\text{\rm X}}_{4}(\text{\rm X}=\text{S},\text{ Se},\text{Te})\) exhibit indirect band gaps of 1.71, 1.65 and 0.14 eV, respectively. The thermodynamic stability of the materials under investigation was depicted by the computation of the Born-criteria along with binding energy. We have computed and evaluated a number of optical characteristics. In addition to presenting opacity at lower incoming photon energy levels, the selected compounds display considerable optical conductivity as well as absorption coefficients when subjected to energetic beams of photons. Moreover, \(\text{BoltzTraP}\) coding was utilized to evaluate the examined compounds \({\text{TaCu}}_{3}{\text{\rm X}}_{4}(\text{\rm X}=\text{S},\text{ Se},\text{Te})\) potential for thermoelectric uses. Based on an analysis of the Seebeck coefficient, electric and thermal conductivity, and power factor, it seems that the studied-compounds have potential to be effective candidates for applications in thermoelectric technology.