First-Principles Insights into the Electronic Structure, Optoelectronic, and Thermoelectric Properties of X₂SrS₄ (X = Y, La) Chalcogenides for Energy Generation Applications

First-Principles Insights into the Electronic Structure, Optoelectronic, and Thermoelectric Properties of X₂SrS₄ (X = Y, La) Chalcogenides for Energy Generation Applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article First-Principles Insights into the Electronic Structure, Optoelectronic, and Thermoelectric Properties of X₂SrS₄ (X = Y, La) Chalcogenides for Energy Generation Applications Haris Haider, Banat gul, ahmad ali, Gulzar Khan, Tahirzeb khan, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8687783/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 4 You are reading this latest preprint version Abstract A first-principles investigation of the chalcogenide compounds Y₂SrS₄ and La₂SrS₄ is carried out to explore their structural, electronic, optical, and thermoelectric properties with a view toward photovoltaic and energy-conversion applications. Density functional theory (DFT) calculations are performed using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The electronic band structures are evaluated using both the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) and the Tran–Blaha modified Becke–Johnson (TB-mBJ) potential to obtain reliable band-gap estimates. The calculated band gaps for Y₂SrS₄ are 1.744 eV (GGA) and 2.481 eV (TB-mBJ), while those for La₂SrS₄ are 1.861 eV and 2.479 eV, respectively. In both compounds, the band gaps are direct in nature and fall within the visible energy range, confirming their semiconducting behavior with dominant p-type conduction. The density of states analysis reveals that the primary electronic transitions originate from S- p states in the valence band to Y- d states in the conduction band for Y₂SrS₄, and from S- p to La- d states for La₂SrS₄. Optical properties, including the complex dielectric function, refractive index, absorption coefficient, energy-loss function, and reflectivity, are systematically examined. The static reflectivity at zero photon energy is found to be approximately 20% for Y₂SrS₄ and 21% for La₂SrS₄, indicating moderate surface reflection and favorable light-harvesting characteristics. Strong optical absorption in the visible and ultraviolet regions further supports their suitability for optoelectronic and photovoltaic applications. In addition, thermoelectric transport calculations reveal promising performance at elevated temperatures, with the dimensionless figure of merit (ZT) reaching 0.74 for Y₂SrS₄ and 0.70 for La₂SrS₄ at 300 K, and increasing to 0.79 and 0.82, respectively, at 800 K. Overall, the combined electronic, optical, and thermoelectric characteristics identify X₂SrS₄ (X = Y, La) compounds as attractive multifunctional materials for photovoltaic solar cells, optoelectronic devices, and high-temperature thermoelectric applications. Chalcogenide Compounds Structural Properties DFT Wien2k First-principles Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction The chemicals that are represented by the A 2 BX 4 type are ternary chalcogenide materials or compounds, which are essentially rare earth-alkaline earth chalcogenide/chalcogen compounds. Every element in group 16 or VI-A of the periodic table is categorized as a chalcogen; the term "chalcogenides" is more commonly used to refer to sulfides, selenides, and tellurides other than oxides. Scientists from all over the world have been concentrating on chalcogenides in recent years [ 1 , 2 ]. The word "chalcogen" is formed by combining the Greek and Greek-Latin words "khalkos" (copper) and "genes" (made or born). Some individuals refer to these chalcogenides as members of the oxygen family, which also includes tellurides, sulfides, and selenides. Chalcogenides are chemical compounds that are either amorphous or crystalline and contain at least one chalcogen anion, such as sulfur (S), selenium (Se), or tellurium (Te), as well as at least one additional electropositive element covalently bonded to the chalcogen [ 3 ]. Materials made up of three elements; typically metals or metalloids plus one or more chalcogens, such S, Se, and Te, are known as ternary semiconducting chalcogenides [ 4 , 5 ]. Alkali metal chalcogenide compounds are now recognized for their consistent physiochemical and physical properties, which makes them crucial for the development of new technologies and materials. Researchers are looking into chalcogenide perovskites for use in solar cells and other optoelectronic devices [ 6 ]. International scientists have recently become fascinated by chalcogenides, particularly ternary ones [ 2 ]. The urgent need for renewable energy, with a focus on increasing solar efficiency, has raised interest in solar energy research. This search led to the investigation of substitute parts for traditional photovoltaic (PV) absorbers [ 7 , 8 ]. Banat et al. conducted a first principles study on the novel ternary chalcogenides Ga 2 TeM 2 (M = S, Se) to investigate their structural, optical, electronic, and thermoelectric properties. The findings demonstrated that both materials had a direct band gap in the visible region of light, making them suitable for PVs and optoelectronics [ 9 ]. Although they belong to a family of materials, chalcogenides' diverse properties allow them to be used in a wide range of technologies, including solar cells, light-emitting diodes (LEDs) [ 10 , 11 ], magneto-resistive devices (MRDs), superconductors, and topological insulators [ 12 ]. Because of their unusual optical, electrical, and sometimes magnetic properties, they have attracted a lot of attention and are therefore great prospects for a wide range of technical applications [ 13 – 15 ]. Gilani et al. reported that gold or aurum (Au) decorated transition metal dichalcogenides like WTe2 nano-sensors provide an affordable and non-invasive method for detecting and diagnosing voltaic organic compounds (VOCs) linked lung cancer in the early stages [ 17 ]. Thin films based on chalcogenide materials (S, Se) are also used in photodetectors, Salah et al. [ 19 ] reported that the A 2 BX 4 type chalcogenide, where A = Ga, B = Hg and X = S, Se, can be used as absorber materials in PV devices with high efficiency. The high capacitance characteristics of certain chalcogenides have garnered significant attention, as the electrodes are the most important component of supercapacitors (SCs) [ 20 , 21 ]. Materials such as CaPr2S 4 and CaPr2Se4 have been shown to have a number of properties that make them excellent candidates for spintronic and energy harvesting applications [ 22 ], while the spinel materials CaCe2S 4 and CaCe2Se4 have the same potential applications [ 23 ]. By using various exchange-correlation functions, an ab-initio study of TCs compounds XCo 2 S 4 (X = Mg, Zn) was conducted. The electronic characteristics showed that the materials displayed the indirect band gaps within the range of 0.2 eV to 1.4 eV [ 24 ]. The band gap nature of the ternary chalcogenide materials Rb 2 SiS 3 , Rb 2 GeS 3 , and Rb 2 SnS 3 was revealed, with values of 2.806 eV, 2.206 eV, and 2.156 eV, respectively, demonstrating their semiconducting nature. A trend of decreasing band gap values was observed [ 25 ]. Using DFT, the computational thermoelectric (TE) characteristics, lattice, and band structure of LiSbX 2 (X = S, Se, Te) ternary chalcogenide materials were investigated. The band gap calculation indicated an indirect nature, with values of 0.13 eV, 0.52 eV, and 0.96 eV for LiSbTe 2 , LiSbSe 2 , and LiSbS 2 respectively [ 26 ]. The ternary chalcogenide compounds Y 2 ZnX 4 (Y = In, Ga and X = S, Se) were computationally analyzed. The results showed that, while the band gaps in the visible range ranged from 1.47 eV for Ga 2 SnSe 4 to 2.55 eV for In 2 ZnS 4 , the compound exhibited a favorable optical absorption value of 105 cm − 1 in the ultraviolet (UV) spectrum [ 27 ]. Using DFT, the optical, structural, thermoelectric, and electronic properties of LiInX 2 (X = Se, Te) were examined. The band gap was computed using the mBJ-GGA potential approximation, yielding direct band gap values of 3.61 eV for LiInSe 2 and 2.33 eV for LiInTe 2 , which are comparable to experimental values. The results also demonstrated that both materials had strong optical absorption in the ultraviolet and visible ranges, and the phonon dispersion analysis confirmed that the compounds were dynamically stable [ 28 ]. A DFT analysis was performed for BaCuMF (M = S, Se) using the TB-mBJ and the PBE-GGA approximations for band-gap analysis. The band gap values in PBE-GGA were determined to be 1.28 eV and 1.62 eV for BaCuSF and BaCuSeF, respectively, whereas in TB-mBJ they were 2.69 eV and 2.64 eV, the quaternary semiconductors based on copper (Cu) offered unique optical response and thermoelectric properties [ 29 ]. The band gap was proposed to be direct and equal to 1.812 eV for CaZrS 3 and 1.117 eV for CaZrSe 3 after the metal chalcogenide perovskites materials, such as CaZrX 3 (X = S, Se), which were promising absorber materials based on their optical features, were investigated for photovoltaic absorbing [ 30 ]. Many of the researchers carried out their work on examining the band gaps, density of states, optical properties and many other physical as well as chemical properties of chalcogenide materials. In this study we are carrying out the DFT of ternary chalcogenide materials Y 2 SrS 4 and La 2 SrS 4 for examining their structural features, band gaps, density of states and optical properties in order to contribute to the research on chalcogenides an effort is made to do so. As, these materials are selected especially because there was no DFT work found on these materials. Computational Details We used the FP-LAPW technique for our computations, simulating different aspects of the chosen materials Y2SrS4 and La2SrS4 using a DFT code called WIEN2k [ 31 ]. The thermoelectric transport properties are calculated by a code named as BoltzTraP [ 32 ]. First-Principles Calculations is another name for the simulations we ran for this investigation. To compare their band gaps, we investigated the band gaps in this study using PBE-GGA [ 33 ] and TB-mBJ [ 34 , 35 ]. The DOS and optical properties were solely investigated using TB-mBJ. For a fair energy convergence, we used RMT x K max = 8 in our computation. In La 2 SrS 4 , the RMT values are 2.00, Sr = 2.00, and S = 2.00, whereas in Y 2 SrS 4 , they are 2.50, Sr = 2.39, and S = 2.23. For SCF calculations, the charge converged up to 0.001 e, and the energy convergence value was assumed to be 0.0001 Ry. In the atomic sphere, the L max was set to 7 and the G max to 12. For precise and superior energy convergence, the k-points were set at 1000 in the first irreducible Brillouin zone. Now, -6.0 Ry was chosen as the cut-off energy for the separation of the core and valence states. A detailed computation is then performed for both Y 2 SrS 4 and La 2 SrS 4 materials to assess their potential for optoelectronic properties. The relationship known as Ehrenreich and Cohen's Relation [ 36 ] determines the real and imaginary parts of the dielectric's frequency-dependent complex function, \(\:\epsilon\:\left(\omega\:\right)\) . $$\:{\epsilon\:}\:\left({\omega\:}\right)\:=\:{{\epsilon\:}}_{1}\:\left({\omega\:}\right)\:+\:\text{i}{{\epsilon\:}}_{2}\:\left({\omega\:}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$ The dielectric function's real and imaginary parts can be found using; $$\:{{\epsilon\:}}_{1}\left({\omega\:}\right)=1+\frac{2}{{\pi\:}}\text{P}{\int\:}_{0}^{{\infty\:}}\frac{{{\omega\:}}^{{\prime\:}}{{\epsilon\:}}_{2}\left({{\omega\:}}^{{\prime\:}}\right)}{{{\omega\:}}^{{\prime\:}2}-{{\omega\:}}^{2}}\text{d}{{\omega\:}}^{{\prime\:}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(2\right)$$ And $$\:{{\epsilon\:}}_{2}\left({\omega\:}\right)=\frac{4{{\pi\:}}^{2}{\text{e}}^{2}}{{\Omega\:}}\sum\:_{\text{k},\:\text{v},\text{c}}{{\omega\:}}_{\text{k}}{\left|⟨{{\Psi\:}}_{\text{c}\text{k}}|{\text{p}}_{{\alpha\:}}|{{\Psi\:}}_{\text{v}\text{k}}⟩\right|}^{2}{\delta\:}\left({\text{E}}_{\text{c}\text{k}}-{\text{E}}_{\text{v}\text{k}}-\text{ħ}{\omega\:}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(3\right)$$ The \(\:{\epsilon\:}_{1}\left(\omega\:\right)\) real part of the dielectric function and the \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) imaginary part of the dielectric function of the complex dielectric function \(\:\epsilon\:\left(\omega\:\right)\) can be used to calculate the other optical parameters, such as \(\:n\left(\omega\:\right)\) refractive index, \(\:R\left(\omega\:\right)\) reflectivity function, \(\:I\left(\omega\:\right)\) function of absorption coefficient, \(\:L\left(\omega\:\right)\) the energy loss function. The following formulae provide these parameters: $$\:n\left(\omega\:\right)={\left(\frac{1}{2}\sqrt{\left({\epsilon\:}_{1}^{2}\left(\omega\:\right)+{\epsilon\:}_{2}^{2}\left(\omega\:\right)\right)}+{\epsilon\:}_{1}\left(\omega\:\right)\right)}^{\frac{1}{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$ $$\:I\left(\omega\:\right)=\alpha\:\left(\omega\:\right)\:=\frac{\sqrt{\:2\:}\omega\:}{c}{\left(\:\sqrt{\left({\:\epsilon\:}_{1}^{2}\left(\omega\:\right)\:+\:{\epsilon\:}_{2}^{2}\left(\omega\:\right)\:\right)}\:+\:{\epsilon\:}_{1}\left(\omega\:\right)\right)}^{\frac{1}{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$ $$\:R\left(\omega\:\right)={\left|\frac{\sqrt{\epsilon\:\left(\omega\:\right)-1}}{\sqrt{\epsilon\:\left(\omega\:\right)+1}}\right|}^{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$ $$\:L\left(\omega\:\right)=\frac{{\epsilon\:}_{2}\left(\omega\:\right)}{{\epsilon\:}_{1}^{2}\left(\omega\:\right)+{\epsilon\:}_{2}^{2}\left(\omega\:\right)}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(7\right)$$ Results and Discussion Structural Properties The crystal is located in space group No. 122, which is the tetragonal I-42d space group. The Fig. 1 (a, b) shows the ground state energies of the crystal structure and optimization energy vs. crystal volume for eight data points. To determine the equilibrium volume, the structure was first allowed to relax through volume fluctuation. The equilibrium volume is located at the place with the lowest energy. During the optimization phase, the ground state energy values or total energy values were simulated for different unit cell volumes. For Y 2 SrS 4 , the equilibrium or stable volume was determined to be 2132.7952 (a.u) 3 at the lowest energy of -46194.357944 R y . The bulk modulus and its derivative were 4.4440 GPa and 74.1772 GPa, respectively. At the lowest total or ground state energy value, -87090.019491 R y , the equilibrium volume for La 2 SrS 4 is 2402.7657 (a.u) 3 , and the bulk modulus is 67.1630 GPa, with a derivative of the bulk modulus of 4.1058 GPa. In Y 2 SrS 4 , the atomic radius of Y is 1.82 A 0 , that of Sr is 2.15 A 0 , and that of S is 1.08 A 0 . Likewise, in La 2 SrS 4 , the atomic radius is 1.88 A 0 for La, 2.15 A 0 for Sr, and 1.08 A 0 for S. The crystal structure of Y 2 SrS 4 and La 2 SrS 4 is shown in Fig. 2 . In Y 2 SrS4, Sr + 2 is bonded to eight analogous S − 2 atoms in eight coordination geometry. The bond lengths and bonding of the materials are described here. The Sr-S bond lengths are four longer and two shorter. The value of Sr-S's shorter bond lengths is 2.61 A 0 , while the value of its longer bond lengths is 3.16 A 0 . The bond length distance of Y-S has a dispersion between 2.7 A 0 and 3.0 A 0 . The Y + 3 is attached to six equivalent S − 2 atoms in six coordination geometry. Two Y-S bonds are shorter, measuring 2.70 A 0 ; two are moderate, measuring 2.76 A 0 ; and two are longer, measuring 2.98 A 0 . Likewise, three S − 2 are bonded to three equivalent Y + 3 atoms, two S − 2 are bonded to two equivalent Sr − 2 atoms, and S − 1 is bonded in five coordination geometry. For S-Y, there are three bond lengths: one is small (2.70 A 0 ), one is moderate (2.76 A 0 ), and one is long (2.98 A 0 ). The bond lengths for S-Sr are 2.61 A 0 for short bonds and 3.160 A 0 for long bonds. The bond lengths and bonding of La 2 SrS 4 material are also covered here. In La 2 SrS 4 , Sr + 2 is bound to 8 analogous S − 2 atoms in 8 coordination geometry. The Sr-S bond lengths are two; 4 longer and two; 4 shorter. The value of Sr-S's shorter bond lengths is 2.61 A 0 , while the value of its longer bond lengths is 3.16 A 0 . The bond length distance of La-S has a spread between 2.7 A 0 and 3.2 A 0 . The La + 3 is attached to 8 equivalent S − 2 atoms in 8 coordination geometry. Two La-S bond lengths of 2.70 A 0 , two 2.76 A 0 , two 2.98 A 0 larger bond lengths, and two 3.13 A 0 bond lengths may be found. Likewise, S − 1 is joined to La + 3 and S − 2 in 5 coordination geometry, three S − 2 is joined to 3 comparable La + 3 atoms, and two S − 2 is joined to two equivalent Sr − 2 atoms. For S-La, there are three different bond lengths: one is short (2.70 A 0 ), one is moderate (2.98 A 0 ), and one is long (3.13 A 0 ). The bond lengths for S-Sr are 2.61 A 0 for short bonds and 3.160 A 0 for long bonds. Table 1 The ground state energies, equilibrium volume, bulk modulus and its derivatives Materials Energy in the Ground State Equilibrium Volume Bulk Modulus Derivative of Bulk Modulus Y 2 SrS 4 -46194.357944 R y 2132.7952 (a.u) 3 74.1772 GPa 4.4440 GPa La 2 SrS 4 -87090.019491 R y 2402.7657 (a.u) 3 67.1630 GPa 4.1058 GPa Table 2 Atomic radii and space group symbols and numbers of Y 2 SrS 4 and La 2 SrS 4 materials Name of the Compounds Space Group Number Space Group Symbol Atomic Radii (A 0 ) Y/La Sr S Y 2 SrS 4 122 I-42d 1.82 2.15 1.08 La 2 SrS 4 122 I-42d 1.88 2.15 1.08 Table 3 Lattice Parameters of Chalcogenide materials Y 2 SrS 4 and La 2 SrS 4 Name of the Compounds Lattice Parameters a (A 0 ) b (A 0 ) c (A 0 ) α β γ Y 2 SrS 4 8.20 8.20 8.53 90 0 90 0 90 0 La 2 SrS 4 8.20 8.20 8.53 90 0 90 0 90 0 Band Structure The Figs. 3 and 4 depict the band structure of Y 2 SrS 4 and La 2 SrS 4 ; the band gap is represented by the band diagram with the energy axis (y-axis) and wave vector axis or k-points (x-axis). For both materials in two exchange correlation functionals (PBE-GGA and TB-mBJ), the range of energy is taken in from − 4 eV to 0 eV in the valence band (VB), while in the conduction band (CB) it is taken in the range of 0 eV to 7 eV. The most accurate value of the band gap over PBE-GGA is predicted by the TB-mBJ. The path to the electron flow is represented by the high symmetry k-points on the y-axis. For every band structure, the "Γ-H-N-Γ-P" path represents the k-point path. "E F " stands for the Fermi-level of energy at 0 eV. The Fig. 3 displays the material Y 2 SrS 4 , and we used TB-mBJ and PBE-GGA to calculate the band gap. With a direct semi-conducting nature, the band gap value for PBE-GGA is 1.744 eV, whereas the energy band gap value calculated by the TB-mBJ is 2.481 eV at the "Γ" points, respectively. The TB-mBJ exhibits a high energy band gap, while the PBE-GGA displays a reduced energy band gap. The visible energy range [ 36 ] spans from 1.59 eV (780 nm of wavelength) to 3.26 eV (380 nm of wavelength), and both the band gap values calculated by PBE-GGA and TB-mBJ fall within this range. Therefore, the material simulated by PBE-GGA has a band gap of 1.744 eV (711.01 nm), meaning that when it absorbs visible light with a wavelength of 711.01 nm, it will exhibit an electron/hole transition. The transition will occur at the visible light wavelength of 499.73 nm since the band gap in TB-mBJ is 2.481 eV (499.73 nm). Since holes make up the majority of the carriers in both PBE-GGA and TB-mBJ, the band lines in CB lie close to the EF (Fermi-level of energy) at 0 eV, indicating that the material is a p-type semiconductor. Similarly, Fig. 4 illustrates the La 2 SrS 4 material. At the "Γ" point, the band gap for PBE-GGA is 1.861 eV (666.22 nm), whereas for TB-mBJ it is 2.479 eV (500.14 nm). The visible energy and wavelength range include several band gaps. It is predicted that the visible energy region will exhibit electronic/hole transitions in this material (La 2 SrS 4 ). The band gap diagram indicates that the material is a p-type (most carriers are holes) semiconductor in both exchange correlation (XC) potentials since the band lines in the VB are close to the Fermi-level. This indicates that the holes are the majority carriers. Both materials have the potential to be used in diodes, transistors, photovoltaic solar cells, and optoelectronics since they are p-type semi-conductors with a band gap that falls inside the visible spectrum of light. Table 4 The summary of band gaps and their nature Compound Name Band Gaps Nature of Band Gaps Type of Semi-Conductor PBE-GGA TB-mBJ Y 2 SrS 4 1.744 eV 2.481 eV Direct Band Gap p-type La 2 SrS 4 1.861 eV 2.479 eV Direct Band Gap p-type Density of States While PDOS shows the electrical transition of electrons/holes from one state in VB to another state in CB, DOS, particularly TDOS, discloses the nature of the material to be p-type or n-type in semiconductors and band gaps. The Fig. 5 and Fig. 6 are indicating the TDOS and PDOS of the materials Y 2 SrS 4 and La 2 SrS 4 respectively. The energy range in CB was chosen from 0 eV to 7 eV, but in DOS, the VB is taken within the range of -4 eV to 0 eV. Only the sophisticated XC potential TB-mBJ evaluates the DOS, either TDOS or PDOS. The TDOS of Y 2 SrS 4 is displayed in Fig. 5 (a), which indicates that the electronic transition from S-atom to Y-atom in CB is prominent in VB. The p-type nature is revealed by the significant peaks in the total atom TDOS that are located close to the Fermi level. Figure 5 (b, c, d) shows that the material Y 2 SrS 4 has PDOS. The p-orbital of S (S-p state) in VB, as seen in Fig. 5 (d), and the d-orbital of Y (Y-d state) in CB, as seen in Fig. 5 (b), are the dominating transitions in PDOS. Although they are not at all dominating, the other states are also playing a role in the transformations. Comparably, Fig. 6 (a) depicts the TDOS of La 2 SrS 4 , which shows that the transition of electrons/holes from VB to CB is primarily between S-atom and La-atom and that the semi-conducting nature of the material with p-type is due to the peak of the states in the VB close to the Fermi-level. The material's PDOS is displayed in Fig. 6 (b, c, d), where the transitions from the p-orbital of the S-atom in VB to the d-orbital of the La-atom in the CB are primarily occurring. Optical Properties When photons strike a substance, its optical characteristics show how it behaves. Examining a material's optical characteristics is crucial to determining its suitability for use in solar cells, diodes, transistors, and other devices. Figure 7 displays the Y 2 SrS 4 and La 2 SrS 4 optical characteristics, respectively. The Fig. 7 shows the optical characteristics of Y 2 SrS 4 and La 2 SrS 4 respectively. The Fig. 7 (a) shows the dielectric function \(\:{\epsilon\:}_{1}\left(\omega\:\right)\) , and for Y 2 SrS 4 and La 2 SrS 4 , the real component, the static real function \(\:{\epsilon\:}_{1}\left(0\right)\) , is 6.90 and 7.17, respectively. Since the TB-mBJ potential was used to analyze the optical characteristics of these materials, the band gap values for Y 2 SrS 4 and La 2 SrS 4 were determined to be 2.481 eV ( \(\:\epsilon\:\left(0\right)=\) 6.90) and 2.479 eV ( \(\:\epsilon\:\left(0\right)=\) 7.17), respectively. The materials with small band gaps have high values of real static dielectric functions, and vice versa. These values of static dielectric functions \(\:{\epsilon\:}_{1}\left(0\right)\) indicate that the materials can act as better dielectric media and can be used as a capacitor for the storage of charges, among many other applications. The imaginary component of the dielectric function \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) , as shown in Fig. 7 (b), is examined to determine the material's absorptive character. The plots of \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) indicate that their threshold values are consistent with the band gap values, with the maximum value \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) for Y 2 SrS 4 lying at 4.7 eV and for La 2 SrS 4 at 5.7 eV. Following the specified energy ranges, both materials exhibit a drop in the \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) function. The materials in the visible area exhibit a linear increase in \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) , which continues in the ultraviolet area of light close to the visible region. The efficiency of materials' incident photons, light, or radiation is connected to the \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) function. The material's capacity to absorb and release energy is measured by the imaginary dielectric function, \(\:{\epsilon\:}_{2}\left(\omega\:\right)\) . The refractive index \(\:n\left(\omega\:\right)\) , which indicates the type of photon or light transmission in the materials, is displayed in Fig. 7 (c). For Y 2 SrS 4 and La 2 SrS 4 , the static function refractive index \(\:n\left(0\right)\) is 2.62 and 2.67, respectively. For Y 2 SrS 4 and La 2 SrS 4 , the dynamic refractive index, denoted as \(\:n\left(\omega\:\right)\) , began to rise at 0.6 eV and 0.7 eV, reaching its maximum value at 5.5 eV and 6.5 eV, respectively. The material begins to absorb incident photons when their energy equals the band gap energies of the materials. This is represented by the coefficient of absorption function \(\:I\left(\omega\:\right)\) in Fig. 7 (d). La 2 SrS 4 will begin to absorb photons at 2.479 eV, while Y 2 SrS 4 will begin at 2.481 eV. For Y 2 SrS 4 and La 2 SrS 4 , the greatest absorption peaks are located at 13.2 eV and 18.2 eV, respectively. The material's electron/hole transition from VBM to CBM will be shown by the greatest absorptions. The absorption indicates the exact amount of energy that the substance absorbs. The Fig. 7 (e) displays the reflectivity \(\:R\left(\omega\:\right)\) . The reflectivity function \(\:R\left(\omega\:\right)\) can be used to forecast the material's surface shape. Generally speaking, smooth, orderly surface morphologies are linked to high reflectivity. At 0 eV, Y 2 SrS 4 has a static reflectivity \(\:R\left(0\right)\) of 0.20 (20%) while La 2 SrS 4 has a \(\:R\left(0\right)\) of 0.21 (21%). Therefore, we can anticipate that Y 2 SrS 4 will have an absorptivity or absorptance of 0.80 (80%) and La 2 SrS 4 will have an absorptivity or absorptance of 0.79 (79%). An indication of how quickly electrons will lose energy while moving through a substance is provided by the energy loss function (ELF) in Fig. 7 (f). There is very little energy loss in both the visible and infrared regions of photon energy. The ultraviolet area of energy is where the energy loss begins to rise. At 17.81 eV, where L(ω) is 1.98, the ELF reaches its greatest peak; for Y 2 SrS 4 and La 2 SrS 4 , the \(\:L\left(\omega\:\right)\) is 0.98 at 16.3 eV. These ELF peaks show the loss of resonant energy. Thermoelectric Properties The thermoelectric performance of Y₂SrS₄ and La₂SrS₄ over the temperature range of 50–800 K is illustrated in Fig. 8 (a–f), highlighting their potential as high-temperature thermoelectric materials. Both compounds exhibit a monotonic increase in electrical conductivity (σ/τ) with temperature, indicating thermally activated charge carrier transport. As shown in Fig. 8 (a), σ/τ reaches approximately 1.5 × 10¹¹ Ω⁻¹ m⁻¹ s⁻¹ for Y₂SrS₄ and 1.3 × 10¹¹ Ω⁻¹ m⁻¹ s⁻¹ for La₂SrS₄ at 800 K. Across the entire temperature range, Y₂SrS₄ consistently demonstrates slightly higher electrical conductivity than La₂SrS₄, suggesting enhanced carrier mobility or a lower effective mass. The Seebeck coefficients of both compounds remain positive throughout the studied temperature range, confirming dominant p-type conduction with good thermopower retention at elevated temperatures. As depicted in Fig. 8 (b), the Seebeck coefficients at 300 K are approximately 235 µV K⁻¹ for Y₂SrS₄ and 220 µV K⁻¹ for La₂SrS₄. With increasing temperature, the Seebeck coefficient gradually increases and tends to saturate, reaching about 245 µV K⁻¹ for Y₂SrS₄ and 255 µV K⁻¹ for La₂SrS₄ at 800 K. The slightly higher Seebeck coefficient of La₂SrS₄ at elevated temperatures indicates stronger energy-dependent carrier transport, which is beneficial for high-temperature thermoelectric efficiency. Figure 8 (c) shows the temperature dependence of the electronic specific heat (C v ), which increases rapidly with temperature for both materials due to the progressive thermal population of electronic states near the Fermi level. At 300 K, C v is approximately 0.9 J mol⁻¹ K⁻¹ for Y₂SrS₄ and 0.8 J mol⁻¹ K⁻¹ for La₂SrS₄, rising to about 4.6 and 4.2 J mol⁻¹ K⁻¹, respectively, at 800 K. The consistently higher C v of Y₂SrS₄ correlates well with its superior electrical conductivity. The electronic thermal conductivity (κₑ/τ), presented in Fig. 8 (d), follows a similar increasing trend with temperature. At 300 K, κₑ/τ is approximately 0.6 × 10¹¹ W m⁻¹ K⁻¹ s⁻¹ for Y₂SrS₄ and 0.5 × 10¹¹ W m⁻¹ K⁻¹ s⁻¹ for La₂SrS₄, with further increases observed at higher temperatures. Despite this rise, the magnitude of κₑ remains moderate, allowing for a net enhancement in thermoelectric performance. As a consequence of the simultaneous increase in electrical conductivity and sustained high Seebeck coefficients, the power factor (PF) increases significantly with temperature, as shown in Fig. 8 (e). At 300 K, the PF is approximately 1.0 × 10¹¹ W K⁻² m⁻¹ s⁻¹ for Y₂SrS₄ and 0.8 × 10¹¹ W K⁻² m⁻¹ s⁻¹ for La₂SrS₄. These values increase to about 4.3 × 10¹¹ and 4.0 × 10¹¹ W K⁻² m⁻¹ s⁻¹, respectively, at 800 K. Consequently, the dimensionless figure of merit (ZT), shown in Fig. 8 (f), increases steadily with temperature. ZT values of approximately 0.74 for Y₂SrS₄ and 0.70 for La₂SrS₄ are obtained at 300 K, rising to about 0.79 and 0.82, respectively, at 800 K. Overall, Y₂SrS₄ exhibits superior performance at low to intermediate temperatures due to its higher electrical conductivity and power factor, whereas La₂SrS₄ slightly outperforms Y₂SrS₄ at higher temperatures owing to its enhanced Seebeck coefficient and balanced thermal transport. These results indicate that both compounds are promising candidates for mid- to high-temperature thermoelectric applications. Conclusion In this work, a comprehensive density functional theory (DFT) investigation of the ternary chalcogenide compounds Y₂SrS₄ and La₂SrS₄ is presented. All calculations were performed using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The ground-state properties were first determined through structural optimization, revealing that both compounds crystallize in the tetragonal I -42 d space group. Subsequently, the structural, electronic, optical, and thermoelectric properties were systematically evaluated using two exchange–correlation (XC) functionals, namely the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) and the Tran–Blaha modified Becke–Johnson (TB-mBJ) potential. At equilibrium, the calculated ground-state energies of Y₂SrS₄ and La₂SrS₄ were − 46,194.357944 Ry and − 87,090.019491 Ry, corresponding to equilibrium volumes of 2132.7952 (a.u.)³ and 2402.7657 (a.u.)³, respectively. The bulk modulus and its pressure derivative were found to be 74.18 GPa and 4.44 for Y₂SrS₄, and 67.16 GPa and 4.11 for La₂SrS₄, indicating moderate mechanical rigidity for both compounds. The electronic band structures were calculated using both PBE-GGA and TB-mBJ functionals. The PBE-GGA approach yielded band gaps of 1.744 eV for Y₂SrS₄ and 1.861 eV for La₂SrS₄, whereas the TB-mBJ potential, known for its improved accuracy in band-gap estimation, predicted wider band gaps of 2.481 eV and 2.479 eV, respectively. Owing to its superior predictive capability, only the TB-mBJ results were considered for the density of states (DOS) and optical properties analysis. The DOS analysis reveals that the dominant electronic transitions occur from S- p states in the valence band to Y- d states in the conduction band for Y₂SrS₄, and from S- p to La- d states for La₂SrS₄. The optical response of both materials was analyzed based on the complex dielectric function. The static dielectric constants ε(0) were found to be 6.90 for Y₂SrS₄ and 7.17 for La₂SrS₄. Correspondingly, the static refractive indices n (0) were calculated to be 2.61 and 2.67, while the static reflectivities R (0) were approximately 0.20 (20%) and 0.21 (21%) for Y₂SrS₄ and La₂SrS₄, respectively. The optical absorption spectra indicate absorption onsets at 2.481 eV for Y₂SrS₄ and 2.479 eV for La₂SrS₄, consistent with their TB-mBJ band gaps. The maximum absorption peaks were observed at photon energies of approximately 13.2 eV and 18.2 eV for Y₂SrS₄ and La₂SrS₄, respectively. These results suggest that both compounds possess strong optical absorption characteristics, making them promising candidates for optoelectronic applications, including photovoltaic solar cells. Furthermore, the calculated thermoelectric transport properties confirm the p-type semiconducting behavior of both Y₂SrS₄ and La₂SrS₄. The favorable Seebeck coefficients, electrical conductivity trends, and resulting power factors highlight the potential applicability of these materials in thermoelectric energy conversion, particularly in the mid- to high-temperature regime. Declarations Conflict of Interest The authors declare that they have no competing interests. Author Contribution Haris Haider wrote the original draft, Gulzar Khan, provided overall guidance, and supervised all stages of the research.. Banat Gul and Ahmad Ali contributed to data analysis and interpretation. Tahir Zeb Khan and S. Zulfiqar assisted in experimental setup and methodology. Shaukat Ali Khattak and Irfan Ullah supported data acquisition and technical validation. Muhammad Adil and Muhammad Salman Khan contributed to figure preparation and formatting Data Availability The data supporting the findings of this study are available from the corresponding author upon reasonable request. 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Johnson, A simple effective potential for exchange, 124 (2006) Ehrenreich, H., Cohen, M.H.: Self-Consistent Field Approach to the Many-Electron Problem. Phys. Rev. 115 , 786–790 (1959) Sliney, D.H.: What is light? The visible spectrum and beyond. Eye. 30 , 222–229 (2016) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 29 Jan, 2026 Editor assigned by journal 28 Jan, 2026 Submission checks completed at journal 28 Jan, 2026 First submitted to journal 24 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8687783","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":582257187,"identity":"9df8bac9-3a7f-487a-8462-13d182d6b21b","order_by":0,"name":"Haris Haider","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Haris","middleName":"","lastName":"Haider","suffix":""},{"id":582257188,"identity":"90995dbc-54ba-41d0-8faf-047f4e4458e2","order_by":1,"name":"Banat gul","email":"","orcid":"","institution":"National University of Sciences and Technology","correspondingAuthor":false,"prefix":"","firstName":"Banat","middleName":"","lastName":"gul","suffix":""},{"id":582257189,"identity":"f2ecf64a-63a4-4e89-8d03-495f9339b0d2","order_by":2,"name":"ahmad ali","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"ahmad","middleName":"","lastName":"ali","suffix":""},{"id":582257190,"identity":"85c2b34e-216e-491d-94f3-5a125a9985ad","order_by":3,"name":"Gulzar Khan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYFAC5gYgkZAAZBxgYDgAFjIAieDRwgjTwpZAshYeA+K0yEckNn/4uSctj392z8fPPGcORzOwN2+TYNyRhlOL4Y3EBsOeZznFEnfObpbmuXE4t4HnWJkE45kc3FpmJDYk8ByoSGy4kbtBOucDUItEjpkEY1sFXi0H/wC1zL+R8/g3WIv8G/xa5CUSG5t5DuQkbriRwyadA3KYBA9IC26HGfA8bGaWOZCWuPFGmpn1nzPpuW08acUWiWdwe1++PfnwxzcHkhPn3Uh+fHPGMevcfvbDG2983JGM25YD6CJsICKxAacOBnnscox4tIyCUTAKRsGIAwAcy2KnoXryxwAAAABJRU5ErkJggg==","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":true,"prefix":"","firstName":"Gulzar","middleName":"","lastName":"Khan","suffix":""},{"id":582257191,"identity":"12deaeeb-c92e-4c21-b2e9-a6277e7a02b1","order_by":4,"name":"Tahirzeb khan","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Tahirzeb","middleName":"","lastName":"khan","suffix":""},{"id":582257192,"identity":"35a31576-4def-4813-b9a8-101d88c11ef6","order_by":5,"name":"Syed Zulfiqar","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Syed","middleName":"","lastName":"Zulfiqar","suffix":""},{"id":582257193,"identity":"d7852bea-ccb7-451d-bf8d-0c4bf6783cf3","order_by":6,"name":"shaukat ali khattak","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"shaukat","middleName":"ali","lastName":"khattak","suffix":""},{"id":582257194,"identity":"511ce8fd-1926-4c0d-b972-c0e902fc23b4","order_by":7,"name":"irfan Ullah","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"irfan","middleName":"","lastName":"Ullah","suffix":""},{"id":582257195,"identity":"73f722de-13f2-4688-b038-dad68a241d1f","order_by":8,"name":"Muhammad Adil","email":"","orcid":"","institution":"Islamia College University","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Adil","suffix":""}],"badges":[],"createdAt":"2026-01-24 15:23:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8687783/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8687783/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103821993,"identity":"df4b3f78-2252-48b6-98bb-3fd8bc4961bc","added_by":"auto","created_at":"2026-03-03 10:30:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":286691,"visible":true,"origin":"","legend":"\u003cp\u003eVolume Optimization (Energy Vs. Volume) Curves of (a) Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and (b) La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/23e08330bdf162cfd8172557.png"},{"id":103821990,"identity":"c2a96f71-dbf9-4251-8c57-7aa872b73b18","added_by":"auto","created_at":"2026-03-03 10:30:20","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":531892,"visible":true,"origin":"","legend":"\u003cp\u003eCrystallographic Structure of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4 \u003c/sub\u003eand 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4","display":"","copyAsset":false,"role":"figure","size":327356,"visible":true,"origin":"","legend":"\u003cp\u003eThe Energy Band Structure Diagram of La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/203ed12a225a665deec536e2.png"},{"id":103821989,"identity":"a3cf0550-ce04-41ef-85ff-885c940ce2cb","added_by":"auto","created_at":"2026-03-03 10:30:20","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":99354,"visible":true,"origin":"","legend":"\u003cp\u003eThe TDOS and PDOS of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/7d869a79d41451d2895c6959.png"},{"id":103821988,"identity":"891d74dc-c516-4a51-b993-8cd6514c3b08","added_by":"auto","created_at":"2026-03-03 10:30:20","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":93542,"visible":true,"origin":"","legend":"\u003cp\u003eThe TDOS and PDOS of Chalcogenide Compound La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/994d686d9f72345e8620f955.png"},{"id":104401063,"identity":"23e9dd76-21e8-4467-a10f-aab3a3bfc745","added_by":"auto","created_at":"2026-03-11 12:11:45","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":325729,"visible":true,"origin":"","legend":"\u003cp\u003eOptical Properties (a) Real Dielectric Function (b) Imaginary Dielectric Function (c) Refractive Index (d) Absorption (e) Reflectivity (f) Energy Loss Function of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/8b791db67078875c5bba199f.png"},{"id":103821991,"identity":"942dab6d-4bf1-44eb-ad34-41f410d6d612","added_by":"auto","created_at":"2026-03-03 10:30:20","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":416689,"visible":true,"origin":"","legend":"\u003cp\u003eThe Thermoelectric Parameters of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e Chalcogenides\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/a9fa24541158404a2d32948b.jpg"},{"id":105032839,"identity":"4f3d6e96-30c9-41eb-bf6e-d40dfa5bc00b","added_by":"auto","created_at":"2026-03-20 07:05:52","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3170676,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8687783/v1/976a83ea-9728-48bf-94da-948be841a2b5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"First-Principles Insights into the Electronic Structure, Optoelectronic, and Thermoelectric Properties of X₂SrS₄ (X = Y, La) Chalcogenides for Energy Generation Applications","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe chemicals that are represented by the A\u003csub\u003e2\u003c/sub\u003eBX\u003csub\u003e4\u003c/sub\u003e type are ternary chalcogenide materials or compounds, which are essentially rare earth-alkaline earth chalcogenide/chalcogen compounds. Every element in group 16 or VI-A of the periodic table is categorized as a chalcogen; the term \"chalcogenides\" is more commonly used to refer to sulfides, selenides, and tellurides other than oxides. Scientists from all over the world have been concentrating on chalcogenides in recent years [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The word \"chalcogen\" is formed by combining the Greek and Greek-Latin words \"khalkos\" (copper) and \"genes\" (made or born). Some individuals refer to these chalcogenides as members of the oxygen family, which also includes tellurides, sulfides, and selenides. Chalcogenides are chemical compounds that are either amorphous or crystalline and contain at least one chalcogen anion, such as sulfur (S), selenium (Se), or tellurium (Te), as well as at least one additional electropositive element covalently bonded to the chalcogen [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Materials made up of three elements; typically metals or metalloids plus one or more chalcogens, such S, Se, and Te, are known as ternary semiconducting chalcogenides [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Alkali metal chalcogenide compounds are now recognized for their consistent physiochemical and physical properties, which makes them crucial for the development of new technologies and materials. Researchers are looking into chalcogenide perovskites for use in solar cells and other optoelectronic devices [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eInternational scientists have recently become fascinated by chalcogenides, particularly ternary ones [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The urgent need for renewable energy, with a focus on increasing solar efficiency, has raised interest in solar energy research. This search led to the investigation of substitute parts for traditional photovoltaic (PV) absorbers [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Banat et al. conducted a first principles study on the novel ternary chalcogenides Ga\u003csub\u003e2\u003c/sub\u003eTeM\u003csub\u003e2\u003c/sub\u003e (M\u0026thinsp;=\u0026thinsp;S, Se) to investigate their structural, optical, electronic, and thermoelectric properties. The findings demonstrated that both materials had a direct band gap in the visible region of light, making them suitable for PVs and optoelectronics [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Although they belong to a family of materials, chalcogenides' diverse properties allow them to be used in a wide range of technologies, including solar cells, light-emitting diodes (LEDs) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], magneto-resistive devices (MRDs), superconductors, and topological insulators [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Because of their unusual optical, electrical, and sometimes magnetic properties, they have attracted a lot of attention and are therefore great prospects for a wide range of technical applications [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Gilani et al. reported that gold or aurum (Au) decorated transition metal dichalcogenides like WTe2 nano-sensors provide an affordable and non-invasive method for detecting and diagnosing voltaic organic compounds (VOCs) linked lung cancer in the early stages [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Thin films based on chalcogenide materials (S, Se) are also used in photodetectors, Salah et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] reported that the A\u003csub\u003e2\u003c/sub\u003eBX\u003csub\u003e4\u003c/sub\u003e type chalcogenide, where A\u0026thinsp;=\u0026thinsp;Ga, B\u0026thinsp;=\u0026thinsp;Hg and X\u0026thinsp;=\u0026thinsp;S, Se, can be used as absorber materials in PV devices with high efficiency. The high capacitance characteristics of certain chalcogenides have garnered significant attention, as the electrodes are the most important component of supercapacitors (SCs) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Materials such as CaPr2S\u003csub\u003e4\u003c/sub\u003e and CaPr2Se4 have been shown to have a number of properties that make them excellent candidates for spintronic and energy harvesting applications [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], while the spinel materials CaCe2S\u003csub\u003e4\u003c/sub\u003e and CaCe2Se4 have the same potential applications [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBy using various exchange-correlation functions, an ab-initio study of TCs compounds XCo\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;Mg, Zn) was conducted. The electronic characteristics showed that the materials displayed the indirect band gaps within the range of 0.2 eV to 1.4 eV [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The band gap nature of the ternary chalcogenide materials Rb\u003csub\u003e2\u003c/sub\u003eSiS\u003csub\u003e3\u003c/sub\u003e, Rb\u003csub\u003e2\u003c/sub\u003eGeS\u003csub\u003e3\u003c/sub\u003e, and Rb\u003csub\u003e2\u003c/sub\u003eSnS\u003csub\u003e3\u003c/sub\u003e was revealed, with values of 2.806 eV, 2.206 eV, and 2.156 eV, respectively, demonstrating their semiconducting nature. A trend of decreasing band gap values was observed [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Using DFT, the computational thermoelectric (TE) characteristics, lattice, and band structure of LiSbX\u003csub\u003e2\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;S, Se, Te) ternary chalcogenide materials were investigated. The band gap calculation indicated an indirect nature, with values of 0.13 eV, 0.52 eV, and 0.96 eV for LiSbTe\u003csub\u003e2\u003c/sub\u003e, LiSbSe\u003csub\u003e2\u003c/sub\u003e, and LiSbS\u003csub\u003e2\u003c/sub\u003e respectively [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The ternary chalcogenide compounds Y\u003csub\u003e2\u003c/sub\u003eZnX\u003csub\u003e4\u003c/sub\u003e (Y\u0026thinsp;=\u0026thinsp;In, Ga and X\u0026thinsp;=\u0026thinsp;S, Se) were computationally analyzed. The results showed that, while the band gaps in the visible range ranged from 1.47 eV for Ga\u003csub\u003e2\u003c/sub\u003eSnSe\u003csub\u003e4\u003c/sub\u003e to 2.55 eV for In\u003csub\u003e2\u003c/sub\u003eZnS\u003csub\u003e4\u003c/sub\u003e, the compound exhibited a favorable optical absorption value of 105 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in the ultraviolet (UV) spectrum [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Using DFT, the optical, structural, thermoelectric, and electronic properties of LiInX\u003csub\u003e2\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;Se, Te) were examined. The band gap was computed using the mBJ-GGA potential approximation, yielding direct band gap values of 3.61 eV for LiInSe\u003csub\u003e2\u003c/sub\u003e and 2.33 eV for LiInTe\u003csub\u003e2\u003c/sub\u003e, which are comparable to experimental values. The results also demonstrated that both materials had strong optical absorption in the ultraviolet and visible ranges, and the phonon dispersion analysis confirmed that the compounds were dynamically stable [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. A DFT analysis was performed for BaCuMF (M\u0026thinsp;=\u0026thinsp;S, Se) using the TB-mBJ and the PBE-GGA approximations for band-gap analysis. The band gap values in PBE-GGA were determined to be 1.28 eV and 1.62 eV for BaCuSF and BaCuSeF, respectively, whereas in TB-mBJ they were 2.69 eV and 2.64 eV, the quaternary semiconductors based on copper (Cu) offered unique optical response and thermoelectric properties [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The band gap was proposed to be direct and equal to 1.812 eV for CaZrS\u003csub\u003e3\u003c/sub\u003e and 1.117 eV for CaZrSe\u003csub\u003e3\u003c/sub\u003e after the metal chalcogenide perovskites materials, such as CaZrX\u003csub\u003e3\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;S, Se), which were promising absorber materials based on their optical features, were investigated for photovoltaic absorbing [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMany of the researchers carried out their work on examining the band gaps, density of states, optical properties and many other physical as well as chemical properties of chalcogenide materials. In this study we are carrying out the DFT of ternary chalcogenide materials Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e for examining their structural features, band gaps, density of states and optical properties in order to contribute to the research on chalcogenides an effort is made to do so. As, these materials are selected especially because there was no DFT work found on these materials.\u003c/p\u003e"},{"header":"Computational Details","content":"\u003cp\u003eWe used the FP-LAPW technique for our computations, simulating different aspects of the chosen materials Y2SrS4 and La2SrS4 using a DFT code called WIEN2k [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The thermoelectric transport properties are calculated by a code named as BoltzTraP [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. First-Principles Calculations is another name for the simulations we ran for this investigation. To compare their band gaps, we investigated the band gaps in this study using PBE-GGA [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] and TB-mBJ [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The DOS and optical properties were solely investigated using TB-mBJ. For a fair energy convergence, we used RMT x K\u003csub\u003emax\u003c/sub\u003e = 8 in our computation. In La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the RMT values are 2.00, Sr\u0026thinsp;=\u0026thinsp;2.00, and S\u0026thinsp;=\u0026thinsp;2.00, whereas in Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, they are 2.50, Sr\u0026thinsp;=\u0026thinsp;2.39, and S\u0026thinsp;=\u0026thinsp;2.23. For SCF calculations, the charge converged up to 0.001 e, and the energy convergence value was assumed to be 0.0001 Ry. In the atomic sphere, the L\u003csub\u003emax\u003c/sub\u003e was set to 7 and the G\u003csub\u003emax\u003c/sub\u003e to 12. For precise and superior energy convergence, the k-points were set at 1000 in the first irreducible Brillouin zone. Now, -6.0 Ry was chosen as the cut-off energy for the separation of the core and valence states. A detailed computation is then performed for both Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e materials to assess their potential for optoelectronic properties.\u003c/p\u003e \u003cp\u003eThe relationship known as Ehrenreich and Cohen's Relation [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] determines the real and imaginary parts of the dielectric's frequency-dependent complex function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\epsilon\\:}\\:\\left({\\omega\\:}\\right)\\:=\\:{{\\epsilon\\:}}_{1}\\:\\left({\\omega\\:}\\right)\\:+\\:\\text{i}{{\\epsilon\\:}}_{2}\\:\\left({\\omega\\:}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe dielectric function's real and imaginary parts can be found using;\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{{\\epsilon\\:}}_{1}\\left({\\omega\\:}\\right)=1+\\frac{2}{{\\pi\\:}}\\text{P}{\\int\\:}_{0}^{{\\infty\\:}}\\frac{{{\\omega\\:}}^{{\\prime\\:}}{{\\epsilon\\:}}_{2}\\left({{\\omega\\:}}^{{\\prime\\:}}\\right)}{{{\\omega\\:}}^{{\\prime\\:}2}-{{\\omega\\:}}^{2}}\\text{d}{{\\omega\\:}}^{{\\prime\\:}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAnd\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{{\\epsilon\\:}}_{2}\\left({\\omega\\:}\\right)=\\frac{4{{\\pi\\:}}^{2}{\\text{e}}^{2}}{{\\Omega\\:}}\\sum\\:_{\\text{k},\\:\\text{v},\\text{c}}{{\\omega\\:}}_{\\text{k}}{\\left|⟨{{\\Psi\\:}}_{\\text{c}\\text{k}}|{\\text{p}}_{{\\alpha\\:}}|{{\\Psi\\:}}_{\\text{v}\\text{k}}⟩\\right|}^{2}{\\delta\\:}\\left({\\text{E}}_{\\text{c}\\text{k}}-{\\text{E}}_{\\text{v}\\text{k}}-\\text{ħ}{\\omega\\:}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{1}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e real part of the dielectric function and the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e imaginary part of the dielectric function of the complex dielectric function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e can be used to calculate the other optical parameters, such as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e refractive index, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e reflectivity function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:I\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e function of absorption coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e the energy loss function. The following formulae provide these parameters:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:n\\left(\\omega\\:\\right)={\\left(\\frac{1}{2}\\sqrt{\\left({\\epsilon\\:}_{1}^{2}\\left(\\omega\\:\\right)+{\\epsilon\\:}_{2}^{2}\\left(\\omega\\:\\right)\\right)}+{\\epsilon\\:}_{1}\\left(\\omega\\:\\right)\\right)}^{\\frac{1}{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:I\\left(\\omega\\:\\right)=\\alpha\\:\\left(\\omega\\:\\right)\\:=\\frac{\\sqrt{\\:2\\:}\\omega\\:}{c}{\\left(\\:\\sqrt{\\left({\\:\\epsilon\\:}_{1}^{2}\\left(\\omega\\:\\right)\\:+\\:{\\epsilon\\:}_{2}^{2}\\left(\\omega\\:\\right)\\:\\right)}\\:+\\:{\\epsilon\\:}_{1}\\left(\\omega\\:\\right)\\right)}^{\\frac{1}{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:R\\left(\\omega\\:\\right)={\\left|\\frac{\\sqrt{\\epsilon\\:\\left(\\omega\\:\\right)-1}}{\\sqrt{\\epsilon\\:\\left(\\omega\\:\\right)+1}}\\right|}^{2}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:L\\left(\\omega\\:\\right)=\\frac{{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)}{{\\epsilon\\:}_{1}^{2}\\left(\\omega\\:\\right)+{\\epsilon\\:}_{2}^{2}\\left(\\omega\\:\\right)}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eStructural Properties\u003c/h2\u003e \u003cp\u003eThe crystal is located in space group No. 122, which is the tetragonal I-42d space group. The Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (a, b) shows the ground state energies of the crystal structure and optimization energy vs. crystal volume for eight data points. To determine the equilibrium volume, the structure was first allowed to relax through volume fluctuation. The equilibrium volume is located at the place with the lowest energy. During the optimization phase, the ground state energy values or total energy values were simulated for different unit cell volumes. For Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the equilibrium or stable volume was determined to be 2132.7952 (a.u)\u003csup\u003e3\u003c/sup\u003e at the lowest energy of -46194.357944 R\u003csub\u003ey\u003c/sub\u003e. The bulk modulus and its derivative were 4.4440 GPa and 74.1772 GPa, respectively. At the lowest total or ground state energy value, -87090.019491 R\u003csub\u003ey\u003c/sub\u003e, the equilibrium volume for La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e is 2402.7657 (a.u)\u003csup\u003e3\u003c/sup\u003e, and the bulk modulus is 67.1630 GPa, with a derivative of the bulk modulus of 4.1058 GPa. In Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the atomic radius of Y is 1.82 A\u003csup\u003e0\u003c/sup\u003e, that of Sr is 2.15 A\u003csup\u003e0\u003c/sup\u003e, and that of S is 1.08 A\u003csup\u003e0\u003c/sup\u003e. Likewise, in La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the atomic radius is 1.88 A\u003csup\u003e0\u003c/sup\u003e for La, 2.15 A\u003csup\u003e0\u003c/sup\u003e for Sr, and 1.08 A\u003csup\u003e0\u003c/sup\u003e for S. The crystal structure of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In Y\u003csub\u003e2\u003c/sub\u003eSrS4, Sr\u003csup\u003e+\u0026thinsp;2\u003c/sup\u003e is bonded to eight analogous S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms in eight coordination geometry. The bond lengths and bonding of the materials are described here. The Sr-S bond lengths are four longer and two shorter. The value of Sr-S's shorter bond lengths is 2.61 A\u003csup\u003e0\u003c/sup\u003e, while the value of its longer bond lengths is 3.16 A\u003csup\u003e0\u003c/sup\u003e. The bond length distance of Y-S has a dispersion between 2.7 A\u003csup\u003e0\u003c/sup\u003e and 3.0 A\u003csup\u003e0\u003c/sup\u003e. The Y\u003csup\u003e+\u0026thinsp;3\u003c/sup\u003e is attached to six equivalent S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms in six coordination geometry. Two Y-S bonds are shorter, measuring 2.70 A\u003csup\u003e0\u003c/sup\u003e; two are moderate, measuring 2.76 A\u003csup\u003e0\u003c/sup\u003e; and two are longer, measuring 2.98 A\u003csup\u003e0\u003c/sup\u003e. Likewise, three S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e are bonded to three equivalent Y\u003csup\u003e+\u0026thinsp;3\u003c/sup\u003e atoms, two S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e are bonded to two equivalent Sr\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms, and S\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e is bonded in five coordination geometry. For S-Y, there are three bond lengths: one is small (2.70 A\u003csup\u003e0\u003c/sup\u003e), one is moderate (2.76 A\u003csup\u003e0\u003c/sup\u003e), and one is long (2.98 A\u003csup\u003e0\u003c/sup\u003e). The bond lengths for S-Sr are 2.61 A\u003csup\u003e0\u003c/sup\u003e for short bonds and 3.160 A\u003csup\u003e0\u003c/sup\u003e for long bonds. The bond lengths and bonding of La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e material are also covered here. In La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, Sr\u003csup\u003e+\u0026thinsp;2\u003c/sup\u003e is bound to 8 analogous S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms in 8 coordination geometry. The Sr-S bond lengths are two; 4 longer and two; 4 shorter. The value of Sr-S's shorter bond lengths is 2.61 A\u003csup\u003e0\u003c/sup\u003e, while the value of its longer bond lengths is 3.16 A\u003csup\u003e0\u003c/sup\u003e. The bond length distance of La-S has a spread between 2.7 A\u003csup\u003e0\u003c/sup\u003e and 3.2 A\u003csup\u003e0\u003c/sup\u003e. The La\u003csup\u003e+\u0026thinsp;3\u003c/sup\u003e is attached to 8 equivalent S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms in 8 coordination geometry. Two La-S bond lengths of 2.70 A\u003csup\u003e0\u003c/sup\u003e, two 2.76 A\u003csup\u003e0\u003c/sup\u003e, two 2.98 A\u003csup\u003e0\u003c/sup\u003e larger bond lengths, and two 3.13 A\u003csup\u003e0\u003c/sup\u003e bond lengths may be found. Likewise, S\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e is joined to La\u003csup\u003e+\u0026thinsp;3\u003c/sup\u003e and S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e in 5 coordination geometry, three S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e is joined to 3 comparable La\u003csup\u003e+\u0026thinsp;3\u003c/sup\u003e atoms, and two S\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e is joined to two equivalent Sr\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e atoms. For S-La, there are three different bond lengths: one is short (2.70 A\u003csup\u003e0\u003c/sup\u003e), one is moderate (2.98 A\u003csup\u003e0\u003c/sup\u003e), and one is long (3.13 A\u003csup\u003e0\u003c/sup\u003e). The bond lengths for S-Sr are 2.61 A\u003csup\u003e0\u003c/sup\u003e for short bonds and 3.160 A\u003csup\u003e0\u003c/sup\u003e for long bonds.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe ground state energies, equilibrium volume, bulk modulus and its derivatives\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterials\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnergy in the Ground State\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEquilibrium Volume\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBulk Modulus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDerivative of Bulk Modulus\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-46194.357944 R\u003csub\u003ey\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2132.7952 (a.u)\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e74.1772 GPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.4440 GPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLa\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-87090.019491 R\u003csub\u003ey\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2402.7657 (a.u)\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67.1630 GPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.1058 GPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAtomic radii and space group symbols and numbers of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e materials\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eName of the Compounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSpace Group Number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSpace Group Symbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003eAtomic Radii (A\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eY/La\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSr\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eI-42d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLa\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eI-42d\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLattice Parameters of Chalcogenide materials Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eName of the Compounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e \u003cp\u003eLattice Parameters\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ea (A\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eb (A\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ec (A\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eα\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eγ\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLa\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e90\u003csup\u003e0\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Band Structure","content":"\u003cp\u003eThe Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e depict the band structure of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e; the band gap is represented by the band diagram with the energy axis (y-axis) and wave vector axis or k-points (x-axis). For both materials in two exchange correlation functionals (PBE-GGA and TB-mBJ), the range of energy is taken in from \u0026minus;\u0026thinsp;4 eV to 0 eV in the valence band (VB), while in the conduction band (CB) it is taken in the range of 0 eV to 7 eV. The most accurate value of the band gap over PBE-GGA is predicted by the TB-mBJ. The path to the electron flow is represented by the high symmetry k-points on the y-axis. For every band structure, the \"Γ-H-N-Γ-P\" path represents the k-point path. \"E\u003csub\u003eF\u003c/sub\u003e\" stands for the Fermi-level of energy at 0 eV. The Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the material Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, and we used TB-mBJ and PBE-GGA to calculate the band gap. With a direct semi-conducting nature, the band gap value for PBE-GGA is 1.744 eV, whereas the energy band gap value calculated by the TB-mBJ is 2.481 eV at the \"Γ\" points, respectively. The TB-mBJ exhibits a high energy band gap, while the PBE-GGA displays a reduced energy band gap. The visible energy range [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] spans from 1.59 eV (780 nm of wavelength) to 3.26 eV (380 nm of wavelength), and both the band gap values calculated by PBE-GGA and TB-mBJ fall within this range. Therefore, the material simulated by PBE-GGA has a band gap of 1.744 eV (711.01 nm), meaning that when it absorbs visible light with a wavelength of 711.01 nm, it will exhibit an electron/hole transition. The transition will occur at the visible light wavelength of 499.73 nm since the band gap in TB-mBJ is 2.481 eV (499.73 nm). Since holes make up the majority of the carriers in both PBE-GGA and TB-mBJ, the band lines in CB lie close to the EF (Fermi-level of energy) at 0 eV, indicating that the material is a p-type semiconductor. Similarly, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e material. At the \"Γ\" point, the band gap for PBE-GGA is 1.861 eV (666.22 nm), whereas for TB-mBJ it is 2.479 eV (500.14 nm). The visible energy and wavelength range include several band gaps. It is predicted that the visible energy region will exhibit electronic/hole transitions in this material (La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e). The band gap diagram indicates that the material is a p-type (most carriers are holes) semiconductor in both exchange correlation (XC) potentials since the band lines in the VB are close to the Fermi-level. This indicates that the holes are the majority carriers. Both materials have the potential to be used in diodes, transistors, photovoltaic solar cells, and optoelectronics since they are p-type semi-conductors with a band gap that falls inside the visible spectrum of light.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe summary of band gaps and their nature\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCompound Name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eBand Gaps\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNature of Band Gaps\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eType of Semi-Conductor\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePBE-GGA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTB-mBJ\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.744 eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.481 eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDirect Band Gap\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep-type\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLa\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.861 eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.479 eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDirect Band Gap\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep-type\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Density of States","content":"\u003cp\u003eWhile PDOS shows the electrical transition of electrons/holes from one state in VB to another state in CB, DOS, particularly TDOS, discloses the nature of the material to be p-type or n-type in semiconductors and band gaps. The Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e are indicating the TDOS and PDOS of the materials Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e respectively. The energy range in CB was chosen from 0 eV to 7 eV, but in DOS, the VB is taken within the range of -4 eV to 0 eV. Only the sophisticated XC potential TB-mBJ evaluates the DOS, either TDOS or PDOS. The TDOS of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e is displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a), which indicates that the electronic transition from S-atom to Y-atom in CB is prominent in VB. The p-type nature is revealed by the significant peaks in the total atom TDOS that are located close to the Fermi level. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b, c, d) shows that the material Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e has PDOS. The p-orbital of S (S-p state) in VB, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d), and the d-orbital of Y (Y-d state) in CB, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b), are the dominating transitions in PDOS. Although they are not at all dominating, the other states are also playing a role in the transformations. Comparably, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) depicts the TDOS of La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, which shows that the transition of electrons/holes from VB to CB is primarily between S-atom and La-atom and that the semi-conducting nature of the material with p-type is due to the peak of the states in the VB close to the Fermi-level. The material's PDOS is displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b, c, d), where the transitions from the p-orbital of the S-atom in VB to the d-orbital of the La-atom in the CB are primarily occurring.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Optical Properties","content":"\u003cp\u003eWhen photons strike a substance, its optical characteristics show how it behaves. Examining a material's optical characteristics is crucial to determining its suitability for use in solar cells, diodes, transistors, and other devices. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e displays the Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e optical characteristics, respectively. The Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the optical characteristics of Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e respectively. The Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) shows the dielectric function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{1}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, and for Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the real component, the static real function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{1}\\left(0\\right)\\)\u003c/span\u003e\u003c/span\u003e, is 6.90 and 7.17, respectively. Since the TB-mBJ potential was used to analyze the optical characteristics of these materials, the band gap values for Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e were determined to be 2.481 eV (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\left(0\\right)=\\)\u003c/span\u003e\u003c/span\u003e 6.90) and 2.479 eV (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\left(0\\right)=\\)\u003c/span\u003e\u003c/span\u003e 7.17), respectively. The materials with small band gaps have high values of real static dielectric functions, and vice versa. These values of static dielectric functions \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{1}\\left(0\\right)\\)\u003c/span\u003e\u003c/span\u003e indicate that the materials can act as better dielectric media and can be used as a capacitor for the storage of charges, among many other applications. The imaginary component of the dielectric function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b), is examined to determine the material's absorptive character. The plots of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e indicate that their threshold values are consistent with the band gap values, with the maximum value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e for Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e lying at 4.7 eV and for La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e at 5.7 eV. Following the specified energy ranges, both materials exhibit a drop in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e function. The materials in the visible area exhibit a linear increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, which continues in the ultraviolet area of light close to the visible region. The efficiency of materials' incident photons, light, or radiation is connected to the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e function. The material's capacity to absorb and release energy is measured by the imaginary dielectric function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{2}\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e. The refractive index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, which indicates the type of photon or light transmission in the materials, is displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(c). For Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the static function refractive index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\left(0\\right)\\)\u003c/span\u003e\u003c/span\u003e is 2.62 and 2.67, respectively. For Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the dynamic refractive index, denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, began to rise at 0.6 eV and 0.7 eV, reaching its maximum value at 5.5 eV and 6.5 eV, respectively. The material begins to absorb incident photons when their energy equals the band gap energies of the materials. This is represented by the coefficient of absorption function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:I\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(d). La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e will begin to absorb photons at 2.479 eV, while Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e will begin at 2.481 eV. For Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the greatest absorption peaks are located at 13.2 eV and 18.2 eV, respectively. The material's electron/hole transition from VBM to CBM will be shown by the greatest absorptions. The absorption indicates the exact amount of energy that the substance absorbs. The Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(e) displays the reflectivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e. The reflectivity function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e can be used to forecast the material's surface shape. Generally speaking, smooth, orderly surface morphologies are linked to high reflectivity. At 0 eV, Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e has a static reflectivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\left(0\\right)\\)\u003c/span\u003e\u003c/span\u003e of 0.20 (20%) while La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e has a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\left(0\\right)\\)\u003c/span\u003e\u003c/span\u003e of 0.21 (21%). Therefore, we can anticipate that Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e will have an absorptivity or absorptance of 0.80 (80%) and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e will have an absorptivity or absorptance of 0.79 (79%). An indication of how quickly electrons will lose energy while moving through a substance is provided by the energy loss function (ELF) in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(f). There is very little energy loss in both the visible and infrared regions of photon energy. The ultraviolet area of energy is where the energy loss begins to rise. At 17.81 eV, where L(ω) is 1.98, the ELF reaches its greatest peak; for Y\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e and La\u003csub\u003e2\u003c/sub\u003eSrS\u003csub\u003e4\u003c/sub\u003e, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\left(\\omega\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e is 0.98 at 16.3 eV. These ELF peaks show the loss of resonant energy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eThermoelectric Properties\u003c/h2\u003e \u003cp\u003eThe thermoelectric performance of Y₂SrS₄ and La₂SrS₄ over the temperature range of 50\u0026ndash;800 K is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a\u0026ndash;f), highlighting their potential as high-temperature thermoelectric materials. Both compounds exhibit a monotonic increase in electrical conductivity (σ/τ) with temperature, indicating thermally activated charge carrier transport. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a), σ/τ reaches approximately 1.5 \u0026times; 10\u0026sup1;\u0026sup1; Ω⁻\u0026sup1; m⁻\u0026sup1; s⁻\u0026sup1; for Y₂SrS₄ and 1.3 \u0026times; 10\u0026sup1;\u0026sup1; Ω⁻\u0026sup1; m⁻\u0026sup1; s⁻\u0026sup1; for La₂SrS₄ at 800 K. Across the entire temperature range, Y₂SrS₄ consistently demonstrates slightly higher electrical conductivity than La₂SrS₄, suggesting enhanced carrier mobility or a lower effective mass. The Seebeck coefficients of both compounds remain positive throughout the studied temperature range, confirming dominant p-type conduction with good thermopower retention at elevated temperatures. As depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(b), the Seebeck coefficients at 300 K are approximately 235 \u0026micro;V K⁻\u0026sup1; for Y₂SrS₄ and 220 \u0026micro;V K⁻\u0026sup1; for La₂SrS₄. With increasing temperature, the Seebeck coefficient gradually increases and tends to saturate, reaching about 245 \u0026micro;V K⁻\u0026sup1; for Y₂SrS₄ and 255 \u0026micro;V K⁻\u0026sup1; for La₂SrS₄ at 800 K. The slightly higher Seebeck coefficient of La₂SrS₄ at elevated temperatures indicates stronger energy-dependent carrier transport, which is beneficial for high-temperature thermoelectric efficiency. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(c) shows the temperature dependence of the electronic specific heat (C\u003csub\u003ev\u003c/sub\u003e), which increases rapidly with temperature for both materials due to the progressive thermal population of electronic states near the Fermi level. At 300 K, C\u003csub\u003ev\u003c/sub\u003e is approximately 0.9 J mol⁻\u0026sup1; K⁻\u0026sup1; for Y₂SrS₄ and 0.8 J mol⁻\u0026sup1; K⁻\u0026sup1; for La₂SrS₄, rising to about 4.6 and 4.2 J mol⁻\u0026sup1; K⁻\u0026sup1;, respectively, at 800 K. The consistently higher C\u003csub\u003ev\u003c/sub\u003e of Y₂SrS₄ correlates well with its superior electrical conductivity.\u003c/p\u003e \u003cp\u003eThe electronic thermal conductivity (κₑ/τ), presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(d), follows a similar increasing trend with temperature. At 300 K, κₑ/τ is approximately 0.6 \u0026times; 10\u0026sup1;\u0026sup1; W m⁻\u0026sup1; K⁻\u0026sup1; s⁻\u0026sup1; for Y₂SrS₄ and 0.5 \u0026times; 10\u0026sup1;\u0026sup1; W m⁻\u0026sup1; K⁻\u0026sup1; s⁻\u0026sup1; for La₂SrS₄, with further increases observed at higher temperatures. Despite this rise, the magnitude of κₑ remains moderate, allowing for a net enhancement in thermoelectric performance. As a consequence of the simultaneous increase in electrical conductivity and sustained high Seebeck coefficients, the power factor (PF) increases significantly with temperature, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(e). At 300 K, the PF is approximately 1.0 \u0026times; 10\u0026sup1;\u0026sup1; W K⁻\u0026sup2; m⁻\u0026sup1; s⁻\u0026sup1; for Y₂SrS₄ and 0.8 \u0026times; 10\u0026sup1;\u0026sup1; W K⁻\u0026sup2; m⁻\u0026sup1; s⁻\u0026sup1; for La₂SrS₄. These values increase to about 4.3 \u0026times; 10\u0026sup1;\u0026sup1; and 4.0 \u0026times; 10\u0026sup1;\u0026sup1; W K⁻\u0026sup2; m⁻\u0026sup1; s⁻\u0026sup1;, respectively, at 800 K.\u003c/p\u003e \u003cp\u003eConsequently, the dimensionless figure of merit (ZT), shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(f), increases steadily with temperature. ZT values of approximately 0.74 for Y₂SrS₄ and 0.70 for La₂SrS₄ are obtained at 300 K, rising to about 0.79 and 0.82, respectively, at 800 K. Overall, Y₂SrS₄ exhibits superior performance at low to intermediate temperatures due to its higher electrical conductivity and power factor, whereas La₂SrS₄ slightly outperforms Y₂SrS₄ at higher temperatures owing to its enhanced Seebeck coefficient and balanced thermal transport. These results indicate that both compounds are promising candidates for mid- to high-temperature thermoelectric applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work, a comprehensive density functional theory (DFT) investigation of the ternary chalcogenide compounds Y₂SrS₄ and La₂SrS₄ is presented. All calculations were performed using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The ground-state properties were first determined through structural optimization, revealing that both compounds crystallize in the tetragonal \u003cem\u003eI\u003c/em\u003e-42\u003cem\u003ed\u003c/em\u003e space group. Subsequently, the structural, electronic, optical, and thermoelectric properties were systematically evaluated using two exchange\u0026ndash;correlation (XC) functionals, namely the Perdew\u0026ndash;Burke\u0026ndash;Ernzerhof generalized gradient approximation (PBE-GGA) and the Tran\u0026ndash;Blaha modified Becke\u0026ndash;Johnson (TB-mBJ) potential. At equilibrium, the calculated ground-state energies of Y₂SrS₄ and La₂SrS₄ were \u0026minus;\u0026thinsp;46,194.357944 Ry and \u0026minus;\u0026thinsp;87,090.019491 Ry, corresponding to equilibrium volumes of 2132.7952 (a.u.)\u0026sup3; and 2402.7657 (a.u.)\u0026sup3;, respectively. The bulk modulus and its pressure derivative were found to be 74.18 GPa and 4.44 for Y₂SrS₄, and 67.16 GPa and 4.11 for La₂SrS₄, indicating moderate mechanical rigidity for both compounds. The electronic band structures were calculated using both PBE-GGA and TB-mBJ functionals. The PBE-GGA approach yielded band gaps of 1.744 eV for Y₂SrS₄ and 1.861 eV for La₂SrS₄, whereas the TB-mBJ potential, known for its improved accuracy in band-gap estimation, predicted wider band gaps of 2.481 eV and 2.479 eV, respectively. Owing to its superior predictive capability, only the TB-mBJ results were considered for the density of states (DOS) and optical properties analysis. The DOS analysis reveals that the dominant electronic transitions occur from S-\u003cem\u003ep\u003c/em\u003e states in the valence band to Y-\u003cem\u003ed\u003c/em\u003e states in the conduction band for Y₂SrS₄, and from S-\u003cem\u003ep\u003c/em\u003e to La-\u003cem\u003ed\u003c/em\u003e states for La₂SrS₄. The optical response of both materials was analyzed based on the complex dielectric function. The static dielectric constants ε(0) were found to be 6.90 for Y₂SrS₄ and 7.17 for La₂SrS₄. Correspondingly, the static refractive indices \u003cem\u003en\u003c/em\u003e(0) were calculated to be 2.61 and 2.67, while the static reflectivities \u003cem\u003eR\u003c/em\u003e(0) were approximately 0.20 (20%) and 0.21 (21%) for Y₂SrS₄ and La₂SrS₄, respectively. The optical absorption spectra indicate absorption onsets at 2.481 eV for Y₂SrS₄ and 2.479 eV for La₂SrS₄, consistent with their TB-mBJ band gaps. The maximum absorption peaks were observed at photon energies of approximately 13.2 eV and 18.2 eV for Y₂SrS₄ and La₂SrS₄, respectively. These results suggest that both compounds possess strong optical absorption characteristics, making them promising candidates for optoelectronic applications, including photovoltaic solar cells.\u003c/p\u003e \u003cp\u003eFurthermore, the calculated thermoelectric transport properties confirm the p-type semiconducting behavior of both Y₂SrS₄ and La₂SrS₄. The favorable Seebeck coefficients, electrical conductivity trends, and resulting power factors highlight the potential applicability of these materials in thermoelectric energy conversion, particularly in the mid- to high-temperature regime.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of Interest\u003c/strong\u003e \u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eHaris Haider wrote the original draft, Gulzar Khan, provided overall guidance, and supervised all stages of the research.. Banat Gul and Ahmad Ali contributed to data analysis and interpretation. Tahir Zeb Khan and S. Zulfiqar assisted in experimental setup and methodology. Shaukat Ali Khattak and Irfan Ullah supported data acquisition and technical validation. Muhammad Adil and Muhammad Salman Khan contributed to figure preparation and formatting\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data supporting the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDevika, R., Vengatesh, P., Shyju, T.J.M.T.P.: Review on ternary chalcogenides: potential photoabsorbers, (2023)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhan, M.M.: Chalcogenides for visible light-induced photocatalysis, Nanostructured Materials for Visible Light Photocatalysis, Elsevier2022, pp. 185\u0026ndash;195\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEnamala, M.K., Chavali, M., Tangellapally, A., Pasumarthy, D., Murthy, M.K., Kuppam, C., Chaudhary, V., Mishra, R., Naradasu, D.: Use of chalcogenides-based nanomaterials for wastewater treatment including bacterial disinfection and organic contaminants degradation, Chalcogenide-Based Nanomaterials as Photocatalysts, Elsevier2021, pp. 243\u0026ndash;259\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSujith, C., Joseph, S., Mathew, T., Mathew, V.J.S.S.S.: Exploring the electronic and optical anisotropy of quasi-one-dimensional ternary chalcogenide CrSbSe3: A DFT study, \u003cb\u003e130\u003c/b\u003e 106926. 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Johnson, A simple effective potential for exchange, 124 (2006)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEhrenreich, H., Cohen, M.H.: Self-Consistent Field Approach to the Many-Electron Problem. Phys. Rev. \u003cb\u003e115\u003c/b\u003e, 786\u0026ndash;790 (1959)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSliney, D.H.: What is light? The visible spectrum and beyond. Eye. \u003cb\u003e30\u003c/b\u003e, 222\u0026ndash;229 (2016)\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Chalcogenide Compounds, Structural Properties, DFT, Wien2k, First-principles","lastPublishedDoi":"10.21203/rs.3.rs-8687783/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8687783/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA first-principles investigation of the chalcogenide compounds Y₂SrS₄ and La₂SrS₄ is carried out to explore their structural, electronic, optical, and thermoelectric properties with a view toward photovoltaic and energy-conversion applications. Density functional theory (DFT) calculations are performed using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The electronic band structures are evaluated using both the Perdew\u0026ndash;Burke\u0026ndash;Ernzerhof generalized gradient approximation (PBE-GGA) and the Tran\u0026ndash;Blaha modified Becke\u0026ndash;Johnson (TB-mBJ) potential to obtain reliable band-gap estimates. The calculated band gaps for Y₂SrS₄ are 1.744 eV (GGA) and 2.481 eV (TB-mBJ), while those for La₂SrS₄ are 1.861 eV and 2.479 eV, respectively. In both compounds, the band gaps are direct in nature and fall within the visible energy range, confirming their semiconducting behavior with dominant p-type conduction. The density of states analysis reveals that the primary electronic transitions originate from S-\u003cem\u003ep\u003c/em\u003e states in the valence band to Y-\u003cem\u003ed\u003c/em\u003e states in the conduction band for Y₂SrS₄, and from S-\u003cem\u003ep\u003c/em\u003e to La-\u003cem\u003ed\u003c/em\u003e states for La₂SrS₄. Optical properties, including the complex dielectric function, refractive index, absorption coefficient, energy-loss function, and reflectivity, are systematically examined. The static reflectivity at zero photon energy is found to be approximately 20% for Y₂SrS₄ and 21% for La₂SrS₄, indicating moderate surface reflection and favorable light-harvesting characteristics. Strong optical absorption in the visible and ultraviolet regions further supports their suitability for optoelectronic and photovoltaic applications. In addition, thermoelectric transport calculations reveal promising performance at elevated temperatures, with the dimensionless figure of merit (ZT) reaching 0.74 for Y₂SrS₄ and 0.70 for La₂SrS₄ at 300 K, and increasing to 0.79 and 0.82, respectively, at 800 K. Overall, the combined electronic, optical, and thermoelectric characteristics identify X₂SrS₄ (X\u0026thinsp;=\u0026thinsp;Y, La) compounds as attractive multifunctional materials for photovoltaic solar cells, optoelectronic devices, and high-temperature thermoelectric applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"First-Principles Insights into the Electronic Structure, Optoelectronic, and Thermoelectric Properties of X₂SrS₄ (X = Y, La) Chalcogenides for Energy Generation Applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 10:30:15","doi":"10.21203/rs.3.rs-8687783/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-29T07:35:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-29T04:14:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-29T03:47:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Optical and Quantum Electronics","date":"2026-01-24T15:08:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5f87c0da-1d37-4cc2-8ca7-4341315023ac","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-04-05T13:38:44+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-03 10:30:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8687783","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8687783","identity":"rs-8687783","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}