Investigation of Structural, Electronic, Magnetic and Thermoelectric Properties of Vacancy-Ordered Palladium-Based Perovskites A₂PdCl₆ (A = K, Rb, Cs) for Optoelectronic and Energy Applications

Investigation of Structural, Electronic, Magnetic and Thermoelectric Properties of Vacancy-Ordered Palladium-Based Perovskites A₂PdCl₆ (A = K, Rb, Cs) for Optoelectronic and Energy 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 Investigation of Structural, Electronic, Magnetic and Thermoelectric Properties of Vacancy-Ordered Palladium-Based Perovskites A₂PdCl₆ (A = K, Rb, Cs) for Optoelectronic and Energy Applications Zahid Ullah, Muhammad Amir khan, Sabaha Gul This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6028829/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Context and Methods Palladium-based vacancy-ordered perovskites A₂PdCl₆ (A = K, Rb, Cs) exhibit promising structural, electronic, magnetic, and thermoelectric properties. They crystallize in an Fm3̅m symmetry, with electronic transitions dominated by Pd d- and Cl p-orbitals. Their thermoelectric efficiency depends on electrical conductivity, Seebeck coefficients, and thermal conductivity. Density functional theory (DFT) calculations were performed using WIEN2k with the PBE functional, incorporating spin-orbit coupling where necessary. Electronic properties were analyzed via density of states (DOS) and band structure calculations. Thermoelectric properties were evaluated using Boltzmann transport theory via BoltzTraP. The figure of merit (ZT) was computed to assess thermoelectric efficiency. Magnetic properties were studied through spin-orbit coupling effects. These insights highlight the potential of A₂PdCl₆ for sustainable energy and electronic applications. Transport properties Magnetic Bandgap DFT WIEN2k Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction A₂PdCl₆, where A = K, Rb, and Cs, are palladium-based vacancy-ordered double perovskites that have attracted a lot of attention due to their many uses in gas sensing, data storage, energy conversion, optoelectronics, thermoelectrics, and spintronics. As an environmentally responsible substitute for lead-halide perovskites, these lead-free perovskites exhibit strong hydrogen affinity, variable electrical characteristics, and exceptional structural stability. The A-site cation (K, Rb, and Cs) affects lattice characteristics, band structures, thermoelectric efficiency, and magnetic behavior, while the Pd²⁺ cations in their cubic crystal structure are octahedrally coordinated by chloride anions [ 1 ]. Because of their remarkable affinity for hydrogen, A₂PdCl₆ perovskites are very useful for real-time gas sensing applications, especially for hydrogen detection in environmental and industrial monitoring [ 2 ]. Furthermore, they can be used in carbon dioxide reduction processes (CO₂RR), hydrogen evolution reactions (HER), and oxygen reduction reactions (ORR) due to their catalytic activity, which promotes sustainable energy conversion [ 3 ]. Optoelectronics holds promise for photodetectors, light-emitting diodes (LEDs), and solar cells due to their appropriate band gaps and effective carrier transport. A-site cation adjustment enables optimization in light-harvesting applications. Their strong ionic conductivity facilitates their application in supercapacitors and lithium/sodium-ion batteries, and their thermoelectric qualities also make them potential candidates for energy harvesting and waste heat recovery [ 4 ]. Additionally, according to current research, A₂PdCl₆ perovskites may have fascinating magnetic and spintronic characteristics that are fueled by spin-orbit coupling and possible magnetoresistive effects. This makes them useful for magnetic sensors, quantum computing, and non-volatile memory. Their structural adaptability increases their functional uses in next-generation electrical and energy storage devices by allowing for additional customization by external field control or substitutional doping [ 6 ]. All things considered, A₂PdCl₆ perovskites are unique materials with a broad range of applications in electrical, sensing, and renewable energy systems [ 7 ]. They are excellent contenders for upcoming sustainable energy solutions due to their lead-free nature, structural stability, and tunability [ 8 ]. To fully realize their potential, optimize their electrical, optical, catalytic, and magnetic properties for practical uses, and incorporate them into cutting-edge energy and electronic systems, more computational and experimental research will be necessary. 2. Method of Calculations Palladium-based vacancy-ordered double perovskites (A₂PdCl₆, where A = K, Rb, and Cs) were studied for their electrical and thermoelectric properties utilizing the full-potential Linearized Augmented Plane Wave (FP-LAPW) approach in conjunction with density functional theory (DFT) using the WIEN2k program [ 9 ]. The generalized gradient approximation (GGA) and local density approximation (LDA) of Perdew et al. [ 10 ] were used to assess the exchange-correlation energy. Modified functionals are required for more precise electronic structure predictions in semiconductors since conventional GGA + U (hybrid potential) and LDA approaches frequently overestimate band gaps [ 11 ]. The Seebeck effect, in which a temperature gradient (ΔT) causes a voltage (ΔV), was used to study the thermoelectric characteristics of A₂PdCl₆. The Seebeck coefficient (S) was used to quantify this effect. ZT = S²σT/κ, where σ is electrical conductivity and κ is thermal conductivity, is the dimensionless figure of merit that determines their thermoelectric efficiency [ 13 ]. Using the rigid band assumption and a constant relaxation time, the thermoelectric coefficients were calculated using Boltzmann transport theory [ 14 ]. The promise of A₂PdCl₆ for energy conversion applications is revealed by these first-principles calculations, which optimize its electronic structure and transport properties for thermoelectric and renewable energy technologies. 3. Results and Discussion 3.1 Structural Properties The compounds A₂PdCl₆ (A = K, Rb, and Cs) have a face-centered cubic (FCC) crystal structure and belong to the Fm3m space group. A-site cations (K, Rb, and Cs) are located at fractional coordinates (¼, ¼, ¼) in this structural configuration, as shown in Fig. 1 , and the central B-site cation (Pd) is located at the origin (0,0,0). At the same time, the X-site anions (Cl) are found at places of the form (x, 0, 0), where x is roughly 0.2 [[ 1 ],[ 3 ],[ 15 ]]. The high degree of symmetry suggested by this crystallographic framework may be very important in determining these materials' mechanical, optical, and electrical characteristics. Energy–volume relationships were calculated in order to perform structural modifications and obtain a better understanding of their basic characteristics, as shown in Fig. 2 . Key equilibrium parameters including lattice constants, bulk modulus, and total energy could be precisely determined by fitting these optimization curves with the Murnaghan equation of state. A thorough quantitative assessment of the ground-state stability of A₂PdCl₆ compounds is given by the data, which are methodically arranged in Table 1 . To evaluate the mechanical robustness and thermodynamic stability of these perovskites, it is crucial to comprehend these structural properties. One important factor in their possible incorporation into electrical and optoelectronic applications is their resistance to compression, which may be determined from the calculated bulk modulus. Further influencing their optoelectronic performance are the lattice characteristics, which also have an impact on the density of states and band structure. Their prospective application in cutting-edge technologies like photovoltaics and thermoelectrics is made possible by the careful optimization and study of A₂PdCl₆ perovskites. Their superior electrical properties and structural stability make them attractive options for useful materials of the future. Table 1 Ground-state parameters of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ compounds. Compoud Latticeconstant(Å) Volume(a.u) 3 Bulkmodulus(GPa) K2PdCl6 10.1734 1776.3473 33.0046 Rb2PdCl6 9.9634 (exp 9.990) 1668.6046 34.2689 Cs2PdCl6 10.6844 2057.7249 28.6101 3.2 Electron Charge Density A₂PdCl₆ (A = K, Rb, Cs) compounds have a mixed covalent and ionic bonding character, according to the electron density plots shown in Fig. 3 . The structural and electrical properties of these materials are mostly determined by the bonding qualities [[ 16 ],[ 17 ]]. The electron density distribution analysis shows that palladium (Pd) and chlorine (Cl) form covalent connections, which support the perovskite lattice's structural integrity and electronic structure. This covalent connection, which improves charge delocalization and affects the electronic band structure, results from the hybridization of Pd and Cl orbitals. The A-site cations (K, Rb, and Cs) on the other hand, mostly interact with Pd and Cl ionically. These interactions, which result in charge transfer and electrostatic stability of the structure, are caused by the notable difference in electronegativity between the halide perovskite lattice and the alkali metals. The size and polarizability of the A-site cation influence the kind of these ionic interactions, which in turn influences band gaps, lattice properties, and the stability of the material as a whole. The covalent and ionic bonding mixture is essential for adjusting the optoelectronic and thermoelectric characteristics of A₂PdCl₆ perovskites. The ionic interactions affect structural flexibility and defect tolerance, whereas the covalent Pd–Cl bonds contribute to the material's band structure and electrical conductivity. Optimizing these compounds for possible uses in gas sensing, thermoelectric, and solar technologies requires an understanding of these bonding properties. 3.3 Band Structure A qualitative depiction of the charge distribution is given by the electron density charts, which also indirectly reveal the size of the material's band gap. But by themselves, these plots cannot identify if the band gap is direct or indirect [[ 18 ],[ 19 ]]. Accurately characterizing the band gap value and its nature requires a thorough examination of the band structure, as shown in Figs. 4 and 5 . This was accomplished by utilizing three distinct exchange-correlation functionals: the Generalized Gradient Approximation (GGA), modified Becke-Johnson (mBJ), and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional approaches to calculate the electronic band structures of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆. It is generally known that because of its intrinsic delocalization inaccuracy, GGA consistently underestimates band gaps. As a result, the band gap computations were improved using the mBJ and HSE functionals, yielding more precise predictions for the electrical structure. All three compounds have a direct band gap, according to the band structure data, as their valence band maximum (VBM) and conduction band minimum (CBM) meet at the same high-symmetry point (X) in the Brillouin zone. A clear pattern emerges from a comparison of the calculated band gaps: K₂PdCl₆ has the smallest band gap of the three, while Cs₂PdCl₆ has the greatest, followed by Rb₂PdCl₆. Additionally, compared to mBJ and HSE, GGA regularly produces smaller band gap values, highlighting the need for sophisticated functionals for precise band structure predictions. These findings are essential for customizing the optoelectronic characteristics of A₂PdCl₆ perovskites since band gap engineering is a critical factor in material optimization for high-efficiency solar and optoelectronic applications. The trends that have been noticed offer a solid foundation for next experimental verifications and possible approaches to device integration. Table 2 Comparison of Band Gaps Calculated Using GGA, mB, and HSE Approximations No Compounds Bandgap(eV) GGA mBJ HSE 1 K2PdCl6 1.24 2.10 2.30 2 Rb2PdCl6 0.95 2.20 2.30 3 Cs2PdCl6 1.45 2.02 2.67 3.4 Density of States A₂PdCl₆'s electrical structure can be understood from the density of states (DoS) charts displayed in Fig. 7 (A = K, Rb, Cs). In these graphs, the conduction band is represented by the positive energy states, and the valence band by the negative energy states. The difference between the valence band maximum and the conduction band minimum identifies the bandgap, while the Fermi energy level (Ef) coincides with the valence band edge at zero energy [[ 19 ],[ 20 ],[ 21 ]]. This bandgap establishes whether a material is an insulator, semiconductor, or metal. K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ are clearly narrow-bandgap semiconductors, as shown in Fig. 7. Since Cl is the main contributor to the valence and conduction band edges, the electronic characteristics of these compounds are mostly determined by the features of chlorine's electronic structure. These materials may be appropriate for thermoelectric applications, as indicated by the high carrier concentration indicated by the high-intensity peaks seen close to the valence band edge. These compounds' electronic structure makes them attractive candidates for thermoelectric materials since thermoelectric efficiency relies on the capacity to minimize thermal conductivity while maintaining a sizable charge carrier concentration. Despite offering a broad overview of the electronic states, Fig. 8 's total DoS plots do not identify the precise atomic orbitals that contribute to the valence and conduction band boundaries. Plots of the partial density of states (PDoS) shown in Fig. 8 provide this information. These graphs show that in K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆, the p-orbitals of Cl are mostly responsible for the formation of the conduction and valence band edges. The substantial contribution of Cl p-states indicates that chlorine has a profound influence on the electronic transitions and charge transport characteristics in these materials. Furthermore, the presence of Cl p-orbitals at the band boundaries raises the prospect of these compounds having intriguing magnetic characteristics. Strong exchange interactions can result from partially filled p-orbitals in a variety of materials, which affects the magnetic behavior. Should comparable interactions take place in A₂PdCl₆ molecules, they would display beneficial magnetic properties, which would make them appropriate for spintronic applications. According to the DoS and pDoS investigations, K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ are semiconductors with narrow bandgaps and high carrier concentrations close to the valence band edge. Cl p-states dominate these materials' electrical characteristics, which may also play a role in their magnetic behavior in addition to influencing their semiconducting nature. They are therefore good options for spintronic and thermoelectric applications because of these characteristics. Additional research on their transport characteristics and possible magnetic interactions may shed more light on their applicability to cutting-edge electronic systems. 3.5 Thermoelectric Properties To evaluate a material's capacity to generate power, the thermoelectric property was computed [ 19 ]. The formula ZT = S2Tσ/κ, often known as the figure of merit, is used to measure the efficiency of thermoelectric materials [ 20 ]. By carefully selecting values for the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ), amplified thermoelectric materials can attain a high figure of merit (ZT) [[ 22 ],[ 23 ]]. The electrical voltage generated by the difference in thermal capacity of materials at a specific temperature gradient is known as the Seebeck coefficient, or "S." There is a positive correlation between a substance's electrical conductivity and the electrical voltage trend. A substance's ability to transfer heat energy within itself is known as its temperature conductivity. It is necessary to exceed the electrical conductivity values and Seebeck coefficient 'S' and simultaneously minimize the thermal conductivity 'κ' values in order to achieve improved thermoelectric power results. The present work aimed to explore the correlation between chemical capacity and several factors, such as ZT, thermal conductivity, electrical conductivity, and Seebeck coefficient. 3.6 Seebeck Coefficient The voltage produced per unit temperature gradient is measured by the Seebeck coefficient, also known as thermopower, which is a crucial factor in thermoelectric materials. shows a change in charge transport behavior in K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ as the temperature rises [ 24 ]. Although thermally activated carriers in conventional semiconductors cause their density to increase with temperature, the observed decrease points to a shift toward metallic conduction, where increased carrier density and electron scattering lessen energy-dependent asymmetry in transport. The alkali-metal cations' sizes account for the diversity among these compounds. K⁺ and Rb⁺ are examples of smaller cations that cause larger lattice distortions, which increase carrier localization at low temperatures and raise the Seebeck coefficient. On the other hand, as Fig. 9 (a) illustrates, the bigger Cs⁺ cation reduces localization and weakens lattice distortions, resulting in a lower. The Seebeck coefficients of all three compounds converge at increasing temperatures as thermal excitation overwhelms the effects of cations. Given that a large is essential for optimizing the thermoelectric figure of merit, the larger values found in K₂PdCl₆ and Rb₂PdCl₆ imply that they might provide superior thermoelectric efficiency. According to these results, A₂PdCl₆ perovskites have potential for energy conversion applications, especially in thermoelectric devices where high performance is enhanced. Additional research on electrical and thermal conductivity is required to assess their full thermoelectric potential, while Hall effect measurements may shed light on the kind and concentration of carriers and help to further elucidate their transport methods. By utilizing these materials' advantageous electrical properties for effective waste heat conversion and sustainable energy applications, an understanding of their qualities may facilitate their integration into next-generation thermoelectric systems. 3.7 Electrical Conductivity per Relaxation Time (σ/τ) By measuring electrical conductivity as a function of temperature, the electrical transport characteristics of are examined. It is necessary to clarify the electrical conductivity unit because it is not conventional [ 25 ]. In the case of thermally excited charge carriers, a diminishing trend with rising temperature would be interpreted as resistance and would suggest semiconductor-like behavior. In contrast to metallic conduction, where conductivity often falls because of increased electron-phonon scattering, the observed rise with temperature further supports semiconductor behavior if the unit is conductivity. Over the whole temperature range, the observed conductivity trends show that K₂PdCl₆ and Rb₂PdCl₆ have better electrical conductivity than Cs₂PdCl₆. Comparing K₂PdCl₆ and Rb₂PdCl₆ to Cs₂PdCl₆, this indicates either a lower density of scattering centers or higher charge carrier mobility as shown in Fig. 9 (b). Larger cations, like Cs⁺, widen the lattice and may lessen electron-phonon scattering at lower temperatures, which could be one explanation for the effect of cation size on the lattice structure. But more phonon activity could result in more charge carrier dispersion at higher temperatures, which would reduce Cs₂PdCl₆'s conductivity advantage over its equivalents. These findings are especially pertinent to thermoelectric applications, where maximizing power factor and total energy conversion efficiency requires high electrical conductivity. Because of their greater conductivity, K₂PdCl₆ and Rb₂PdCl₆ may be more suited for thermoelectric applications, where it's important to balance electrical and thermal transport qualities. The practicality of these compounds for thermoelectric and other electronic applications is strengthened by an understanding of their charge transport pathways, which offers important insights into their possible role in advanced energy materials. 3.8 Electronic Thermal Conductivity per Relaxation Time (κ/τ) By using their electronic thermal conductivity, which is obtained from the specified unit and most likely corresponds to thermal resistance, the thermal transport qualities are examined. A rising trend with temperature is then revealed by calculating thermal conductivity as [ 26 ]. In contrast to metals, where greater phonon scattering causes thermal conductivity to decrease with temperature, this behavior is different. Rather, the observed increase points to a pronounced electronic contribution to heat transfer, which is typical of semiconductors with small bandgaps. The enhancement of electronic heat transport by thermally activated charge carriers is responsible for the temperature-dependent rise in. The electronic thermal conductivity of K₂PdCl₆ and Rb₂PdCl₆ is comparatively higher than that of Cs₂PdCl₆, suggesting either a higher density of states or improved charge carrier mobility as shown in Fig. 9 (c). Cation size has a significant impact on how heat transport is modified; bigger cations, such as Cs⁺, may decrease phonon propagation because of increased lattice spacing, which lowers lattice thermal conductivity. Nevertheless, if electronic contributions predominate, this effect might be countered by an increase in electrical conductivity, preserving or even strengthening it. Optimizing the dimensionless figure of merit () for thermoelectric applications requires striking a balance between electrical and thermal conductivity. Excessive thermal dissipation can lessen the temperature gradient required for effective thermoelectric conversion, even though high enhances charge transport. Techniques like doping, alloying, or nanostructuring can be used to maintain high electrical conductivity while optimizing heat transfer characteristics. These results demonstrate the potential of K₂PdCl₆ and Rb₂PdCl₆ as thermoelectric materials, where their energy conversion efficiency may be improved by regulated heat and charge transport. 3.9 Figure of Merit The figure of merit, which is based on the correlation between heat conductivity, the Seebeck coefficient, and electrical conductivity, is used to assess the thermoelectric efficiency of [ 27 ]. According to the results, these materials' efficiency declines with increasing temperature, suggesting that heat transmission is a major factor limiting their functionality. The thermoelectric performance of K₂PdCl₆ and Rb₂PdCl₆ is comparable among the three compounds, although Cs₂PdCl₆ exhibits somewhat lower efficiency. An increase in electronic heat transmission, which results in increased energy loss, is the main cause of the efficiency decline at higher temperatures as shown in Fig. 9 (d). Because thermoelectric materials need to maintain a temperature differential in order to produce electricity, they are less able to do so when heat dissipation is high. Reducing heat transmission without sacrificing electrical conductivity should be the main goal of techniques to enhance thermoelectric performance. This is accomplished by enhancing phonon dispersion, which reduces the material's capacity to transfer heat by upsetting lattice vibrations. In order to suppress undesired heat transport and introduce scattering centers, methods like alloying, defect engineering, and nanostructuring can be employed. Furthermore, doping to alter the electrical structure can increase charge carrier mobility while reducing heat loss. These materials nevertheless show interesting thermoelectric capabilities, especially in lower temperature ranges, even though their efficiency decreases with increasing temperature. Their potential for energy conversion applications emphasizes how crucial it is to precisely balance thermal and electrical transport characteristics in order to optimize overall performance. 4. Magnetic properties Spin-polarized DFT with the GGA technique is used to computationally confirm that A₂PdCl₆ (A = K, Rb, and Cs) is non-magnetic. Cl⁻ ions octahedrally coordinate Pd(IV) (4d⁸) in these compounds, causing crystal field splitting in which the lower energy t₂g orbitals are totally occupied with 6 electrons while the higher energy eₓg orbitals are fully occupied with 2 electrons [[ 28 ],[ 29 ],[ 30 ],[ 31 ]]. An expected zero spin moment results from the fact that all d-electrons are coupled, meaning that there are no unpaired electrons to contribute to magnetism. Using GGA-PBE, a spin-polarized DFT calculation was carried out in WIEN2k to computationally confirm this. The total magnetic moment (:MMTOT) is roughly 0 µB, according to the self-consistent field (SCF) measurements, and the local moments (:MMI) for Pd, Cl, and A (K, Rb, and Cs) are likewise close to zero, indicating the absence of intrinsic magnetism. Furthermore, as is typical have no magnetism material, the spin-resolved density of states (DOS) analysis reveals no spin splitting, indicating that the spin-up and spin-down states are identical. With no spin polarization in the electronic states, the band structure calculation confirms this result. GGA alone is adequate for Pd(IV), as it is a weakly correlated ion; unless structural distortions or flaws are added, extra correlation effects from GGA + U are not required. Since A₂PdCl₆ has fully filled d-orbitals and no spin polarization, these computational results, which are based on electronic structure, magnetic moments, and DOS analysis, verify that the material is non-magnetic. The observed magnetism would therefore most likely result from external sources like flaws or doping, as no spontaneous magnetization is anticipated. 5. Conclusions Vacancy-ordered palladium-based perovskites A₂PdCl₆ (A = K, Rb, Cs) are investigated in this work using density functional theory (DFT) simulations to determine their structural, electronic, and thermoelectric characteristics. The A-site cation size affects the bulk modulus and lattice parameters, and structural optimization validates a stable face-centered cubic (Fm3̅m) symmetry. Cs₂PdCl₆ has the widest band gap among the three compounds, according to the electronic structure analysis, which suggests that it could be used in optoelectronic applications. Cl p-orbitals dominate the valence and conduction band edges, affecting the electronic transitions and charge transport properties, according to density of states (DoS) computations. In comparison to Cs₂PdCl₆, K₂PdCl₆ and Rb₂PdCl₆ exhibit greater Seebeck coefficients and electrical conductivity, indicating superior thermoelectric performance, according to thermoelectric study. However, overall thermoelectric efficiency decreases as temperature rises due to increased electronic heat conductivity. According to the determined figure of merit (ZT), these materials have potential for use in thermoelectric applications, especially at lower temperatures. Optimising electrical and thermal conductivity using techniques like doping, nanostructuring, or defect engineering could increase their effectiveness even further. The promise of A₂PdCl₆ perovskites as lead-free substitutes for sustainable energy applications is demonstrated by these findings. Future studies should concentrate on material changes and experimental validation to optimize their performance in practical thermoelectric and optoelectronic systems. Declarations Data Availability: All data supporting the findings of this study, including computational outputs, figures, and derived parameters, are provided within the manuscript and supplementary information files. Funding Declaration : This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. 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IOP Conf Ser Mater Sci Eng 1033:012080. https://doi.org/10.1088/1757-899X/1033/1/012080 Hasan N, Nishat SS, Sadman S, Shaown MR, Hoquee MA, Arifuzzaman M, Kabir A (2023) Magnetic, optoelectronic, and Rietveld refined structural properties of Al³⁺ substituted nanocrystalline Ni-Cu spinel ferrites: an experimental and DFT-based study. arXiv preprint arXiv:2301.11373 Marciniak J, Marciniak W, Werwiński M (2022) DFT calculation of intrinsic properties of magnetically hard phase L1₀ FePt. arXiv preprint arXiv:2204.05073 Rhone TD, Chen W, Desai S, Yacoby A, Kaxiras E (2018) Data-driven studies of magnetic two-dimensional materials. arXiv preprint arXiv:1806.07989 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-6028829","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":415814156,"identity":"ff6819cf-5e6c-42f2-afd1-3970f72b1351","order_by":0,"name":"Zahid Ullah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYJACZiBm7AexEgpI0TKzAaTFgBQtGw6AmMRokZ+R/vBxQY2d7ObzqxM/PDBgkOcXO4BfC+OMhGTjGceSjbfdeLtZAugww5mzEwg4SiLhmDQPG3PithtnN4C0JBjcJqCFTSKxTZrnX33i5hlnN/8gSguPRDKbNG/b4cQN/L3biLNFgucZszFv33HjGTd4t1kkGEgQ9ot8OzDEeL5Vy/b3n91880eFjTy/NAEtSPaBVUoQqxwE+A+QonoUjIJRMApGEgAA/2hCHXy74AEAAAAASUVORK5CYII=","orcid":"","institution":"Islamia College University","correspondingAuthor":true,"prefix":"","firstName":"Zahid","middleName":"","lastName":"Ullah","suffix":""},{"id":415814157,"identity":"a0442753-384a-451a-b469-6de91a9670d8","order_by":1,"name":"Muhammad Amir khan","email":"","orcid":"","institution":"Qurtuba University of Science and Information Technology","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"Amir","lastName":"khan","suffix":""},{"id":415814158,"identity":"08deaa7c-3ef6-479e-bea9-b3007317a8d1","order_by":2,"name":"Sabaha Gul","email":"","orcid":"","institution":"Islamia College University","correspondingAuthor":false,"prefix":"","firstName":"Sabaha","middleName":"","lastName":"Gul","suffix":""}],"badges":[],"createdAt":"2025-02-14 08:38:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6028829/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6028829/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":76731139,"identity":"06a88513-d8bd-4a06-a499-3e0548fda797","added_by":"auto","created_at":"2025-02-20 06:26:48","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":394988,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCrystal structure of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ compounds, illustrating their face-centered cubic (FCC) configuration.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/58f7ca7c184133b7dc08b4c3.png"},{"id":76729944,"identity":"b740b4b5-ec89-4abd-b0cf-6540341525e3","added_by":"auto","created_at":"2025-02-20 06:18:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":42868,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOptimization curves for K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ compounds.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/7eb52656464960e550e6ee6f.png"},{"id":76728609,"identity":"243b196a-659b-4a42-bff8-cbfde0121858","added_by":"auto","created_at":"2025-02-20 06:02:48","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":46539,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectron density plots of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆, illustrating the mixed covalent and ionic nature of their bonding.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/427167aecdd9c2ef535117cb.png"},{"id":76728608,"identity":"669071f6-9da2-4256-beb2-78f287e5bf06","added_by":"auto","created_at":"2025-02-20 06:02:48","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":42741,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGGA-calculated band gaps of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆, demonstrating that Cs₂PdCl₆ has the largest band gap among the three compounds.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/c8fa0a60ba4f185f39dccd4e.png"},{"id":76728612,"identity":"4356f4d8-c5e6-4a8c-8aee-7e361e406b54","added_by":"auto","created_at":"2025-02-20 06:02:48","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":30011,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003emBJ and HSE calculation of the band gaps of K2PdCl6, Rb2PdCl6 and Cs2PdCl6 compounds shown quitewider bandgapsascomparedtothose calculatedviaGGA.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/7de8d16148b5761f2cf4042d.png"},{"id":76729725,"identity":"15f1319d-7cd4-4087-af46-dc6363ffc85f","added_by":"auto","created_at":"2025-02-20 06:10:48","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":13993,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTotal Density of States (DoS) of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ Compounds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/130a4981a9afc83ae3bdc9e1.png"},{"id":76728621,"identity":"99fd54ea-8ead-4316-9129-1e1f9689fda6","added_by":"auto","created_at":"2025-02-20 06:02:48","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":4493,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not available with this version.\u003c/p\u003e","description":"","filename":"fig.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/b94fec65dce159e219d0ec9c.png"},{"id":76729723,"identity":"d7200771-a364-426e-90e6-cd86c36e0801","added_by":"auto","created_at":"2025-02-20 06:10:48","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":22723,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePartial Density of States (pDoS) Plots for K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆, Showing the Contribution of Cl p-States to the Conduction and Valence Band Edges.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/4201eb4f2d33f7107c5f1469.png"},{"id":76729726,"identity":"85bce8cc-0a4e-4c8b-9ebf-a3fb255dd6da","added_by":"auto","created_at":"2025-02-20 06:10:48","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":40635,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) Seebeck coefficient, (b) electrical conductivity, (c) thermal conductivity, and (d) figure of merit for K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ compounds.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/c9ac9198f0e194adecf2ec12.png"},{"id":76731242,"identity":"8c8a2b6b-37ae-4b6f-bac2-4f58b19a38d5","added_by":"auto","created_at":"2025-02-20 06:34:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1762114,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6028829/v1/38b78304-77c4-4a34-ad9c-811da642b499.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eInvestigation of Structural, Electronic, Magnetic and Thermoelectric Properties of Vacancy-Ordered Palladium-Based Perovskites A₂PdCl₆ (A = K, Rb, Cs) for Optoelectronic and Energy Applications\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eA₂PdCl₆, where A\u0026thinsp;=\u0026thinsp;K, Rb, and Cs, are palladium-based vacancy-ordered double perovskites that have attracted a lot of attention due to their many uses in gas sensing, data storage, energy conversion, optoelectronics, thermoelectrics, and spintronics. As an environmentally responsible substitute for lead-halide perovskites, these lead-free perovskites exhibit strong hydrogen affinity, variable electrical characteristics, and exceptional structural stability. The A-site cation (K, Rb, and Cs) affects lattice characteristics, band structures, thermoelectric efficiency, and magnetic behavior, while the Pd\u0026sup2;⁺ cations in their cubic crystal structure are octahedrally coordinated by chloride anions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Because of their remarkable affinity for hydrogen, A₂PdCl₆ perovskites are very useful for real-time gas sensing applications, especially for hydrogen detection in environmental and industrial monitoring [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Furthermore, they can be used in carbon dioxide reduction processes (CO₂RR), hydrogen evolution reactions (HER), and oxygen reduction reactions (ORR) due to their catalytic activity, which promotes sustainable energy conversion [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Optoelectronics holds promise for photodetectors, light-emitting diodes (LEDs), and solar cells due to their appropriate band gaps and effective carrier transport. A-site cation adjustment enables optimization in light-harvesting applications. Their strong ionic conductivity facilitates their application in supercapacitors and lithium/sodium-ion batteries, and their thermoelectric qualities also make them potential candidates for energy harvesting and waste heat recovery [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Additionally, according to current research, A₂PdCl₆ perovskites may have fascinating magnetic and spintronic characteristics that are fueled by spin-orbit coupling and possible magnetoresistive effects. This makes them useful for magnetic sensors, quantum computing, and non-volatile memory. Their structural adaptability increases their functional uses in next-generation electrical and energy storage devices by allowing for additional customization by external field control or substitutional doping [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. All things considered, A₂PdCl₆ perovskites are unique materials with a broad range of applications in electrical, sensing, and renewable energy systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. They are excellent contenders for upcoming sustainable energy solutions due to their lead-free nature, structural stability, and tunability [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. To fully realize their potential, optimize their electrical, optical, catalytic, and magnetic properties for practical uses, and incorporate them into cutting-edge energy and electronic systems, more computational and experimental research will be necessary.\u003c/p\u003e"},{"header":"2. Method of Calculations","content":"\u003cp\u003ePalladium-based vacancy-ordered double perovskites (A₂PdCl₆, where A\u0026thinsp;=\u0026thinsp;K, Rb, and Cs) were studied for their electrical and thermoelectric properties utilizing the full-potential Linearized Augmented Plane Wave (FP-LAPW) approach in conjunction with density functional theory (DFT) using the WIEN2k program [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The generalized gradient approximation (GGA) and local density approximation (LDA) of Perdew et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] were used to assess the exchange-correlation energy. Modified functionals are required for more precise electronic structure predictions in semiconductors since conventional GGA\u0026thinsp;+\u0026thinsp;U (hybrid potential) and LDA approaches frequently overestimate band gaps [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The Seebeck effect, in which a temperature gradient (ΔT) causes a voltage (ΔV), was used to study the thermoelectric characteristics of A₂PdCl₆. The Seebeck coefficient (S) was used to quantify this effect. ZT\u0026thinsp;=\u0026thinsp;S\u0026sup2;σT/κ, where σ is electrical conductivity and κ is thermal conductivity, is the dimensionless figure of merit that determines their thermoelectric efficiency [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Using the rigid band assumption and a constant relaxation time, the thermoelectric coefficients were calculated using Boltzmann transport theory [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The promise of A₂PdCl₆ for energy conversion applications is revealed by these first-principles calculations, which optimize its electronic structure and transport properties for thermoelectric and renewable energy technologies.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Structural Properties\u003c/h2\u003e \u003cp\u003eThe compounds A₂PdCl₆ (A\u0026thinsp;=\u0026thinsp;K, Rb, and Cs) have a face-centered cubic (FCC) crystal structure and belong to the Fm3m space group. A-site cations (K, Rb, and Cs) are located at fractional coordinates (\u0026frac14;, \u0026frac14;, \u0026frac14;) in this structural configuration, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and the central B-site cation (Pd) is located at the origin (0,0,0). At the same time, the X-site anions (Cl) are found at places of the form (x, 0, 0), where x is roughly 0.2 [[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e],[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e],[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]]. The high degree of symmetry suggested by this crystallographic framework may be very important in determining these materials' mechanical, optical, and electrical characteristics.\u003c/p\u003e \u003cp\u003eEnergy\u0026ndash;volume relationships were calculated in order to perform structural modifications and obtain a better understanding of their basic characteristics, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Key equilibrium parameters including lattice constants, bulk modulus, and total energy could be precisely determined by fitting these optimization curves with the Murnaghan equation of state. A thorough quantitative assessment of the ground-state stability of A₂PdCl₆ compounds is given by the data, which are methodically arranged in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. To evaluate the mechanical robustness and thermodynamic stability of these perovskites, it is crucial to comprehend these structural properties. One important factor in their possible incorporation into electrical and optoelectronic applications is their resistance to compression, which may be determined from the calculated bulk modulus. Further influencing their optoelectronic performance are the lattice characteristics, which also have an impact on the density of states and band structure. Their prospective application in cutting-edge technologies like photovoltaics and thermoelectrics is made possible by the careful optimization and study of A₂PdCl₆ perovskites. Their superior electrical properties and structural stability make them attractive options for useful materials of the future.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \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\u003eGround-state parameters of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ compounds.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\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=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompoud\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLatticeconstant(\u0026Aring;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVolume(a.u)\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBulkmodulus(GPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eK2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10.1734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1776.3473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e33.0046\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRb2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.9634 (exp 9.990)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1668.6046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e34.2689\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCs2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10.6844\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2057.7249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.6101\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Electron Charge Density\u003c/h2\u003e \u003cp\u003eA₂PdCl₆ (A\u0026thinsp;=\u0026thinsp;K, Rb, Cs) compounds have a mixed covalent and ionic bonding character, according to the electron density plots shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The structural and electrical properties of these materials are mostly determined by the bonding qualities [[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e],[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]]. The electron density distribution analysis shows that palladium (Pd) and chlorine (Cl) form covalent connections, which support the perovskite lattice's structural integrity and electronic structure. This covalent connection, which improves charge delocalization and affects the electronic band structure, results from the hybridization of Pd and Cl orbitals.\u003c/p\u003e \u003cp\u003eThe A-site cations (K, Rb, and Cs) on the other hand, mostly interact with Pd and Cl ionically. These interactions, which result in charge transfer and electrostatic stability of the structure, are caused by the notable difference in electronegativity between the halide perovskite lattice and the alkali metals. The size and polarizability of the A-site cation influence the kind of these ionic interactions, which in turn influences band gaps, lattice properties, and the stability of the material as a whole.\u003c/p\u003e \u003cp\u003eThe covalent and ionic bonding mixture is essential for adjusting the optoelectronic and thermoelectric characteristics of A₂PdCl₆ perovskites. The ionic interactions affect structural flexibility and defect tolerance, whereas the covalent Pd\u0026ndash;Cl bonds contribute to the material's band structure and electrical conductivity. Optimizing these compounds for possible uses in gas sensing, thermoelectric, and solar technologies requires an understanding of these bonding properties.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Band Structure\u003c/h2\u003e \u003cp\u003eA qualitative depiction of the charge distribution is given by the electron density charts, which also indirectly reveal the size of the material's band gap. But by themselves, these plots cannot identify if the band gap is direct or indirect [[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e],[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]]. Accurately characterizing the band gap value and its nature requires a thorough examination of the band structure, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. This was accomplished by utilizing three distinct exchange-correlation functionals: the Generalized Gradient Approximation (GGA), modified Becke-Johnson (mBJ), and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional approaches to calculate the electronic band structures of K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆.\u003c/p\u003e \u003cp\u003eIt is generally known that because of its intrinsic delocalization inaccuracy, GGA consistently underestimates band gaps. As a result, the band gap computations were improved using the mBJ and HSE functionals, yielding more precise predictions for the electrical structure. All three compounds have a direct band gap, according to the band structure data, as their valence band maximum (VBM) and conduction band minimum (CBM) meet at the same high-symmetry point (X) in the Brillouin zone.\u003c/p\u003e \u003cp\u003eA clear pattern emerges from a comparison of the calculated band gaps: K₂PdCl₆ has the smallest band gap of the three, while Cs₂PdCl₆ has the greatest, followed by Rb₂PdCl₆. Additionally, compared to mBJ and HSE, GGA regularly produces smaller band gap values, highlighting the need for sophisticated functionals for precise band structure predictions.\u003c/p\u003e \u003cp\u003eThese findings are essential for customizing the optoelectronic characteristics of A₂PdCl₆ perovskites since band gap engineering is a critical factor in material optimization for high-efficiency solar and optoelectronic applications. The trends that have been noticed offer a solid foundation for next experimental verifications and possible approaches to device integration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\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\u003eComparison of Band Gaps Calculated Using GGA, mB, and HSE Approximations\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=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCompounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eBandgap(eV)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGGA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003emBJ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eK2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRb2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCs2PdCl6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Density of States\u003c/h2\u003e \u003cp\u003eA₂PdCl₆'s electrical structure can be understood from the density of states (DoS) charts displayed in Fig.\u0026nbsp;7 (A\u0026thinsp;=\u0026thinsp;K, Rb, Cs). In these graphs, the conduction band is represented by the positive energy states, and the valence band by the negative energy states. The difference between the valence band maximum and the conduction band minimum identifies the bandgap, while the Fermi energy level (Ef) coincides with the valence band edge at zero energy [[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e],[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e],[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]]. This bandgap establishes whether a material is an insulator, semiconductor, or metal. K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ are clearly narrow-bandgap semiconductors, as shown in Fig.\u0026nbsp;7. Since Cl is the main contributor to the valence and conduction band edges, the electronic characteristics of these compounds are mostly determined by the features of chlorine's electronic structure. These materials may be appropriate for thermoelectric applications, as indicated by the high carrier concentration indicated by the high-intensity peaks seen close to the valence band edge. These compounds' electronic structure makes them attractive candidates for thermoelectric materials since thermoelectric efficiency relies on the capacity to minimize thermal conductivity while maintaining a sizable charge carrier concentration.\u003c/p\u003e \u003cp\u003eDespite offering a broad overview of the electronic states, Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e's total DoS plots do not identify the precise atomic orbitals that contribute to the valence and conduction band boundaries. Plots of the partial density of states (PDoS) shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e provide this information. These graphs show that in K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆, the p-orbitals of Cl are mostly responsible for the formation of the conduction and valence band edges. The substantial contribution of Cl p-states indicates that chlorine has a profound influence on the electronic transitions and charge transport characteristics in these materials.\u003c/p\u003e \u003cp\u003eFurthermore, the presence of Cl p-orbitals at the band boundaries raises the prospect of these compounds having intriguing magnetic characteristics. Strong exchange interactions can result from partially filled p-orbitals in a variety of materials, which affects the magnetic behavior. Should comparable interactions take place in A₂PdCl₆ molecules, they would display beneficial magnetic properties, which would make them appropriate for spintronic applications.\u003c/p\u003e \u003cp\u003eAccording to the DoS and pDoS investigations, K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ are semiconductors with narrow bandgaps and high carrier concentrations close to the valence band edge. Cl p-states dominate these materials' electrical characteristics, which may also play a role in their magnetic behavior in addition to influencing their semiconducting nature. They are therefore good options for spintronic and thermoelectric applications because of these characteristics. Additional research on their transport characteristics and possible magnetic interactions may shed more light on their applicability to cutting-edge electronic systems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Thermoelectric Properties\u003c/h2\u003e \u003cp\u003eTo evaluate a material's capacity to generate power, the thermoelectric property was computed [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The formula ZT\u0026thinsp;=\u0026thinsp;S2Tσ/κ, often known as the figure of merit, is used to measure the efficiency of thermoelectric materials [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. By carefully selecting values for the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ), amplified thermoelectric materials can attain a high figure of merit (ZT) [[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e],[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]]. The electrical voltage generated by the difference in thermal capacity of materials at a specific temperature gradient is known as the Seebeck coefficient, or \"S.\" There is a positive correlation between a substance's electrical conductivity and the electrical voltage trend. A substance's ability to transfer heat energy within itself is known as its temperature conductivity. It is necessary to exceed the electrical conductivity values and Seebeck coefficient 'S' and simultaneously minimize the thermal conductivity 'κ' values in order to achieve improved thermoelectric power results. The present work aimed to explore the correlation between chemical capacity and several factors, such as ZT, thermal conductivity, electrical conductivity, and Seebeck coefficient.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Seebeck Coefficient\u003c/h2\u003e \u003cp\u003eThe voltage produced per unit temperature gradient is measured by the Seebeck coefficient, also known as thermopower, which is a crucial factor in thermoelectric materials. shows a change in charge transport behavior in K₂PdCl₆, Rb₂PdCl₆, and Cs₂PdCl₆ as the temperature rises [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Although thermally activated carriers in conventional semiconductors cause their density to increase with temperature, the observed decrease points to a shift toward metallic conduction, where increased carrier density and electron scattering lessen energy-dependent asymmetry in transport. The alkali-metal cations' sizes account for the diversity among these compounds. K⁺ and Rb⁺ are examples of smaller cations that cause larger lattice distortions, which increase carrier localization at low temperatures and raise the Seebeck coefficient. On the other hand, as Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a) illustrates, the bigger Cs⁺ cation reduces localization and weakens lattice distortions, resulting in a lower. The Seebeck coefficients of all three compounds converge at increasing temperatures as thermal excitation overwhelms the effects of cations. Given that a large is essential for optimizing the thermoelectric figure of merit, the larger values found in K₂PdCl₆ and Rb₂PdCl₆ imply that they might provide superior thermoelectric efficiency. According to these results, A₂PdCl₆ perovskites have potential for energy conversion applications, especially in thermoelectric devices where high performance is enhanced.\u003c/p\u003e \u003cp\u003eAdditional research on electrical and thermal conductivity is required to assess their full thermoelectric potential, while Hall effect measurements may shed light on the kind and concentration of carriers and help to further elucidate their transport methods. By utilizing these materials' advantageous electrical properties for effective waste heat conversion and sustainable energy applications, an understanding of their qualities may facilitate their integration into next-generation thermoelectric systems.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Electrical Conductivity per Relaxation Time (σ/τ)\u003c/h2\u003e \u003cp\u003eBy measuring electrical conductivity as a function of temperature, the electrical transport characteristics of are examined. It is necessary to clarify the electrical conductivity unit because it is not conventional [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. In the case of thermally excited charge carriers, a diminishing trend with rising temperature would be interpreted as resistance and would suggest semiconductor-like behavior. In contrast to metallic conduction, where conductivity often falls because of increased electron-phonon scattering, the observed rise with temperature further supports semiconductor behavior if the unit is conductivity.\u003c/p\u003e \u003cp\u003eOver the whole temperature range, the observed conductivity trends show that K₂PdCl₆ and Rb₂PdCl₆ have better electrical conductivity than Cs₂PdCl₆. Comparing K₂PdCl₆ and Rb₂PdCl₆ to Cs₂PdCl₆, this indicates either a lower density of scattering centers or higher charge carrier mobility as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e(b). Larger cations, like Cs⁺, widen the lattice and may lessen electron-phonon scattering at lower temperatures, which could be one explanation for the effect of cation size on the lattice structure. But more phonon activity could result in more charge carrier dispersion at higher temperatures, which would reduce Cs₂PdCl₆'s conductivity advantage over its equivalents.\u003c/p\u003e \u003cp\u003eThese findings are especially pertinent to thermoelectric applications, where maximizing power factor and total energy conversion efficiency requires high electrical conductivity. Because of their greater conductivity, K₂PdCl₆ and Rb₂PdCl₆ may be more suited for thermoelectric applications, where it's important to balance electrical and thermal transport qualities. The practicality of these compounds for thermoelectric and other electronic applications is strengthened by an understanding of their charge transport pathways, which offers important insights into their possible role in advanced energy materials.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.8 Electronic Thermal Conductivity per Relaxation Time (κ/τ)\u003c/h2\u003e \u003cp\u003eBy using their electronic thermal conductivity, which is obtained from the specified unit and most likely corresponds to thermal resistance, the thermal transport qualities are examined. A rising trend with temperature is then revealed by calculating thermal conductivity as [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. In contrast to metals, where greater phonon scattering causes thermal conductivity to decrease with temperature, this behavior is different. Rather, the observed increase points to a pronounced electronic contribution to heat transfer, which is typical of semiconductors with small bandgaps.\u003c/p\u003e \u003cp\u003eThe enhancement of electronic heat transport by thermally activated charge carriers is responsible for the temperature-dependent rise in. The electronic thermal conductivity of K₂PdCl₆ and Rb₂PdCl₆ is comparatively higher than that of Cs₂PdCl₆, suggesting either a higher density of states or improved charge carrier mobility as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e(c). Cation size has a significant impact on how heat transport is modified; bigger cations, such as Cs⁺, may decrease phonon propagation because of increased lattice spacing, which lowers lattice thermal conductivity. Nevertheless, if electronic contributions predominate, this effect might be countered by an increase in electrical conductivity, preserving or even strengthening it.\u003c/p\u003e \u003cp\u003eOptimizing the dimensionless figure of merit () for thermoelectric applications requires striking a balance between electrical and thermal conductivity. Excessive thermal dissipation can lessen the temperature gradient required for effective thermoelectric conversion, even though high enhances charge transport. Techniques like doping, alloying, or nanostructuring can be used to maintain high electrical conductivity while optimizing heat transfer characteristics. These results demonstrate the potential of K₂PdCl₆ and Rb₂PdCl₆ as thermoelectric materials, where their energy conversion efficiency may be improved by regulated heat and charge transport.\u003c/p\u003e \u003cp\u003e \u003cb\u003e3.9 Figure of Merit\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe figure of merit, which is based on the correlation between heat conductivity, the Seebeck coefficient, and electrical conductivity, is used to assess the thermoelectric efficiency of [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. According to the results, these materials' efficiency declines with increasing temperature, suggesting that heat transmission is a major factor limiting their functionality.\u003c/p\u003e \u003cp\u003eThe thermoelectric performance of K₂PdCl₆ and Rb₂PdCl₆ is comparable among the three compounds, although Cs₂PdCl₆ exhibits somewhat lower efficiency. An increase in electronic heat transmission, which results in increased energy loss, is the main cause of the efficiency decline at higher temperatures as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e(d). Because thermoelectric materials need to maintain a temperature differential in order to produce electricity, they are less able to do so when heat dissipation is high.\u003c/p\u003e \u003cp\u003eReducing heat transmission without sacrificing electrical conductivity should be the main goal of techniques to enhance thermoelectric performance. This is accomplished by enhancing phonon dispersion, which reduces the material's capacity to transfer heat by upsetting lattice vibrations. In order to suppress undesired heat transport and introduce scattering centers, methods like alloying, defect engineering, and nanostructuring can be employed. Furthermore, doping to alter the electrical structure can increase charge carrier mobility while reducing heat loss.\u003c/p\u003e \u003cp\u003eThese materials nevertheless show interesting thermoelectric capabilities, especially in lower temperature ranges, even though their efficiency decreases with increasing temperature. Their potential for energy conversion applications emphasizes how crucial it is to precisely balance thermal and electrical transport characteristics in order to optimize overall performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Magnetic properties","content":"\u003cp\u003eSpin-polarized DFT with the GGA technique is used to computationally confirm that A₂PdCl₆ (A\u0026thinsp;=\u0026thinsp;K, Rb, and Cs) is non-magnetic. Cl⁻ ions octahedrally coordinate Pd(IV) (4d⁸) in these compounds, causing crystal field splitting in which the lower energy t₂g orbitals are totally occupied with 6 electrons while the higher energy eₓg orbitals are fully occupied with 2 electrons [[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e],[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e],[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e],[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]]. An expected zero spin moment results from the fact that all d-electrons are coupled, meaning that there are no unpaired electrons to contribute to magnetism.\u003c/p\u003e \u003cp\u003eUsing GGA-PBE, a spin-polarized DFT calculation was carried out in WIEN2k to computationally confirm this. The total magnetic moment (:MMTOT) is roughly 0 \u0026micro;B, according to the self-consistent field (SCF) measurements, and the local moments (:MMI) for Pd, Cl, and A (K, Rb, and Cs) are likewise close to zero, indicating the absence of intrinsic magnetism. Furthermore, as is typical have no magnetism material, the spin-resolved density of states (DOS) analysis reveals no spin splitting, indicating that the spin-up and spin-down states are identical. With no spin polarization in the electronic states, the band structure calculation confirms this result.\u003c/p\u003e \u003cp\u003eGGA alone is adequate for Pd(IV), as it is a weakly correlated ion; unless structural distortions or flaws are added, extra correlation effects from GGA\u0026thinsp;+\u0026thinsp;U are not required. Since A₂PdCl₆ has fully filled d-orbitals and no spin polarization, these computational results, which are based on electronic structure, magnetic moments, and DOS analysis, verify that the material is non-magnetic. The observed magnetism would therefore most likely result from external sources like flaws or doping, as no spontaneous magnetization is anticipated.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eVacancy-ordered palladium-based perovskites A₂PdCl₆ (A\u0026thinsp;=\u0026thinsp;K, Rb, Cs) are investigated in this work using density functional theory (DFT) simulations to determine their structural, electronic, and thermoelectric characteristics. The A-site cation size affects the bulk modulus and lattice parameters, and structural optimization validates a stable face-centered cubic (Fm3̅m) symmetry. Cs₂PdCl₆ has the widest band gap among the three compounds, according to the electronic structure analysis, which suggests that it could be used in optoelectronic applications.\u003c/p\u003e \u003cp\u003eCl p-orbitals dominate the valence and conduction band edges, affecting the electronic transitions and charge transport properties, according to density of states (DoS) computations. In comparison to Cs₂PdCl₆, K₂PdCl₆ and Rb₂PdCl₆ exhibit greater Seebeck coefficients and electrical conductivity, indicating superior thermoelectric performance, according to thermoelectric study. However, overall thermoelectric efficiency decreases as temperature rises due to increased electronic heat conductivity.\u003c/p\u003e \u003cp\u003eAccording to the determined figure of merit (ZT), these materials have potential for use in thermoelectric applications, especially at lower temperatures. Optimising electrical and thermal conductivity using techniques like doping, nanostructuring, or defect engineering could increase their effectiveness even further. The promise of A₂PdCl₆ perovskites as lead-free substitutes for sustainable energy applications is demonstrated by these findings. Future studies should concentrate on material changes and experimental validation to optimize their performance in practical thermoelectric and optoelectronic systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data supporting the findings of this study, including computational outputs, figures, and derived parameters, are provided within the manuscript and supplementary information files.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e :\u003c/p\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCai Y, Xie W, Ding H, Chen Y, Thirumal K, Wong LH, Mathews N, Mhaisalkar SG, Sherburne M, Asta M (2017) Computational study of halide perovskite-derived A₂BX₆ inorganic compounds: chemical trends in electronic structure and structural stability. 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IOP Conf Ser Mater Sci Eng 1033:012080. https://doi.org/10.1088/1757-899X/1033/1/012080\u003c/li\u003e\n\u003cli\u003eHasan N, Nishat SS, Sadman S, Shaown MR, Hoquee MA, Arifuzzaman M, Kabir A (2023) Magnetic, optoelectronic, and Rietveld refined structural properties of Al\u0026sup3;⁺ substituted nanocrystalline Ni-Cu spinel ferrites: an experimental and DFT-based study. arXiv preprint arXiv:2301.11373\u003c/li\u003e\n\u003cli\u003eMarciniak J, Marciniak W, Werwiński M (2022) DFT calculation of intrinsic properties of magnetically hard phase L1₀ FePt. arXiv preprint arXiv:2204.05073\u003c/li\u003e\n\u003cli\u003eRhone TD, Chen W, Desai S, Yacoby A, Kaxiras E (2018) Data-driven studies of magnetic two-dimensional materials. arXiv preprint arXiv:1806.07989\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Transport properties, Magnetic, Bandgap, DFT, WIEN2k","lastPublishedDoi":"10.21203/rs.3.rs-6028829/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6028829/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eContext and Methods\u003c/p\u003e \u003cp\u003ePalladium-based vacancy-ordered perovskites A₂PdCl₆ (A\u0026thinsp;=\u0026thinsp;K, Rb, Cs) exhibit promising structural, electronic, magnetic, and thermoelectric properties. They crystallize in an Fm3̅m symmetry, with electronic transitions dominated by Pd d- and Cl p-orbitals. Their thermoelectric efficiency depends on electrical conductivity, Seebeck coefficients, and thermal conductivity.\u003c/p\u003e \u003cp\u003eDensity functional theory (DFT) calculations were performed using WIEN2k with the PBE functional, incorporating spin-orbit coupling where necessary. Electronic properties were analyzed via density of states (DOS) and band structure calculations. Thermoelectric properties were evaluated using Boltzmann transport theory via BoltzTraP. The figure of merit (ZT) was computed to assess thermoelectric efficiency. Magnetic properties were studied through spin-orbit coupling effects. These insights highlight the potential of A₂PdCl₆ for sustainable energy and electronic applications.\u003c/p\u003e","manuscriptTitle":"Investigation of Structural, Electronic, Magnetic and Thermoelectric Properties of Vacancy-Ordered Palladium-Based Perovskites A₂PdCl₆ (A = K, Rb, Cs) for Optoelectronic and Energy Applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-20 06:02:41","doi":"10.21203/rs.3.rs-6028829/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7de4009a-9751-4523-a6ef-026267ba3447","owner":[],"postedDate":"February 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-02-20T06:02:43+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-20 06:02:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6028829","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6028829","identity":"rs-6028829","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}