Study of the structural, electronic, optical and elastic properties of NaSrX3 (X = F, Cl) perovskite materials using the ab-initio method

 Corresponding author: Mona Hermann Charly YAPI Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Study of the structural, electronic, optical and elastic properties of NaSrX3 (X = F, Cl) perovskite materials using the ab-initio method Mona Hermann Charly YAPI 1, 2, *, Bakary Coulibaly ABOU 3, Guy Müller Banquet OKRA 1, 2 and Womblegnon Stephane GUIA 1 1 Department of Mathematics Physics Chemistry, Physics Teaching Unit, Laboratory of Environmental Sciences and Technologies, JEAN LOROUGNON GUÉDÉ University, BP 150 Daloa, Côte d’Ivoire. 2 Laboratory of Fundamental and Applied Physics (LFAP), University Nangui Abrogoua, BP 801 Abidjan 02, Côte d’Ivoire. 3 Institute for Research on New Energies, (IRNE), University Nangui Abrogoua, BP 801 Abidjan 02, Côte d’Ivoire. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 Publication history: Received on 10 August 2025; revised on 16 September 2025; accepted on 19 September 2025 Article DOI: https://doi.org/10.30574/gscarr.2025.24.3.0287 Abstract In this work, we studied the structural, electronic, optical, and elastic properties of NaSrX3 type perovskites (X: halogen F and Cl) using density functional theory (DFT) implemented in Quantum-expresso by GGA. The lattice parameters of NaSrF3 and NaSrCl3 are 4.01 Å and 4.65 Å, respectively. We discovered that NaSrF3 behaves as an insulator, while NaSrCl3 behaves as a semiconductor. They have direct gaps. The gap for NaSrF3 is 6.02 eV and that for NaSrCl3 is 4.09 eV. They all have a conduction band dominated by Sr 3d states, weakly mixed with Na 3s and Sr 4s states. The valence band is dominated by alkali 2p and Sr 3d states. These perovskites also have very good optical properties: low reflectivity and high absorption in the ultraviolet range. These materials are elastically stable. They have good rigidity and show greater resistance to bond bending and bond angle distortion. However, NaSrF3 is ductile and NaSrCl3 is brittle. NaSrCl3 will withstand higher temperatures than NaSrF3. This study shows that these materials are suitable for various applications in both the visible and UV ranges. They have very interesting properties for optoelectronics. Keywords: NaSrX3 perovskites; Solar cell; DFT; Electronic properties; Optical properties 1. Introduction The world today is experiencing a significant decline in energy resources. Conventional energy sources are becoming increasingly scarce. This phenomenon has been further exacerbated by global population growth. In addition, the exploitation of conventional energy sources has a negative impact on the environment and is changing our planet's climate. It is therefore essential to turn to new energy sources if we want to ensure a sustainable lifestyle for humanity and preserve the environmental balance. The alternative energy source should therefore be respectful of the environment and the human living environment. There is no better candidate than renewable energies. Renewable energy such as photovoltaic energy represents an alternative to this energy deficit. Electricity can be produced using solar cells that convert solar energy. The conversion takes place in the active layer of the cell. Silicon is the material used as the active layer in these solar cells. However, solar cells made from silicon are very expensive. Furthermore, the extraction of silicon damages the environment. It is therefore necessary to use other materials that are less expensive to produce and do not harm the environment, such as perovskites [1,2,3,4]. Perovskites are very easy to handle and therefore easier to integrate into solar cells than silicon. Their use does not pose a significant threat to the environment. The most commonly used perovskites are organic perovskites such as methylammonium lead iodide (MAPI) perovskite [5]. Although this type of perovskite has a good conversion rate, it does have stability issues due to its structure. Inorganic perovskites, on the other hand, have very low conversion efficiency but are more stable than the former. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 211 Research on them has increased in recent decades. In this work, we studied the structural, electronic, optical, and elastic properties of NaSrX3 (X: halogen) perovskites [2] using density functional theory (DFT) implemented in Quantumexpresso by GGA [6,7]. We determined the electronic properties of these materials as well as their optical properties. 2. Materials and Methods 2.1. Materials To perform this work, we used Quantum Expresso (qe-7.0) software, which allows ab initio calculations to be performed [6,7,8]. This software suite ran on Linux Ubuntu 25.04. The Ubuntu 25.04 operating system is installed on a computer with a 2.90 GHz Core i7 processor (Lenovo series). Other programs (besides Quantum Espresso) were also used to process the data generated by Quantum Espresso, namely Vesta, Gnuplot, and Xmgrace. Quantum Espresso itself contains several subprograms designed for very specific tasks. The materials used are perovskite materials of the NaSrX3 type (X = F and Cl). These materials are assumed to crystallize in a cubic crystal structure (Pm3m). Figure 1 shows a typical representation of the crystal structure of each material. Figure 1 Cubic crystal structure of NaSrF3 (left) and NaSrCl3 (right) 2.2. Methods This work was carried out using the density functional theory (DFT) method. The density functional theory method is implemented in the Quantum Espresso code [9,10]. Several DFT approximations exist, and we used the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE + GGA) [11]. The advantage of the GGA method is that it takes into account the local electron density and its firstand second-order gradients included in the enhancement factor. The convergence level of our calculations is set appropriately at 10-9 eV (1.0-9 eV). The kinetic energy cutoff is 80.0 Ry. The k-point grid in the Brillouin zone is 12×12×12. The lattice parameter, kinetic energy cutoff, Monkhorst-Pack k-point sampling in the Brillouin zone, and other structural parameters of cubic perovskite materials of the NaSrX3 type (X = F and Cl) were relaxed to obtain equilibrium parameters. 3. Results and discussion 3.1. Convergence test Convergence tests were performed on several parameters in order to determine the equilibrium parameters of of cubic perovskite materials of the NaSrX3 type (X = F and Cl). The parameters on which these convergence tests were performed are: the lattice parameter, the cutoff kinetic energy, and the Monkhorst-Pack k-points in the Brillouin zone. The convergence level used is 10−10 eV. The convergence test is possible thanks to the vc_relax calculation. To do this, several values of the parameter under consideration are tested by a vc_relax calculation around these parameter values in order to obtain the most stable system. The most stable system corresponds to the parameter value that minimizes the energy of the structure. This value is then chosen as the parameter value to be sought. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 212 3.1.1. Lattice parameter In the various graphs in Figure 2, we show the evolution of the total energy as a function of the mesh parameter for each structure. Figure 2 Convergence of Lattice Parameter acell. The lattice parameters of the different perovskite materials are shown in Table 1. The lattice parameters obtained are 4.01 Å and 4.65 Å for NaSrF3 and NaSrCl3, respectively. We compared them with those found by M.H. Benkaboua et al [12], Jalil ur Rehman et al [13], Mohammad Reda Kablia et al [14], and Aiman Jehana et al [15]. Our results are lower than those obtained in their papers. Table 1 Calculated mesh parameters Latice parameter acell in Å Materials Our results Literature results NaSrF3 4.01 4.64 [12], 4.78 [13, 14] NaSrCl3 4.65 5.73 [15] 3.1.2. Convergence of Kinetic energy cut-off The cutoff kinetic energy (ecut) represents the maximum value of the kinetic energy of the electron wave function in the crystal [16,17,18]. It is the limit that is set in the calculation at each iteration. In our work, the calculation begins to converge at 70 Ry. However, we chose to set this cutoff energy ecut at 80 Ry. It should be noted that the higher the kinetic cutoff energy (ecut), the more accurate the calculations are, which is preferable. However, it should also be noted that a high value for this parameter makes the calculation very complex and therefore very slow. In their work, Jalil ur Rehman et al [13] and Mohammad Reda Kablia et al [14] used 40 Ry for NaSrF3, while Aiman Jehana et al [15] used 60 Ry for NaSrCl3. 3.1.3. Convergence of k-point We sampled the Brillouin zone of cubic NaSrX3 perovskite structures using the Monkhorst-Pack method [19]. For each structure, convergence is observed from the Monkhorst-Pack points (k_points) 6×6×6. However, we chose to set our Monkhorst-Pack mesh to 12×12×12. This sampling is considered more relevant to the work we have done. The results will be very accurate, but they will be heavier and therefore require more computing time than a 6×6×6 k-point grid. Greater computing resources were therefore necessary. It is worth noting those used by other authors. These include: 17×17×17 for M.H. Benkaboua et al [12], 6×6×6 for Jalil ur Rehman et al [13], 2×2×2 for Mohammad Reda Kablia et al [14], and Aiman Jehana et al [15] did not mention their point_k used. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 213 3.2. Electronic properties 3.2.1. Bands structure This section presents the different electronic properties of NaSrX3 (X=F and Cl) perovskite materials obtained using the DFT method through GGA formalism. We determined: the electronic band structure, the total density of states (TDOS) and the partial densities of states (PDOS) of cubic NaSrX3 (X= F and Cl) perovskites in the high symmetry directions of the first Brillouin zone. We also determined the band gap energy of NaSrX3 (X= F and Cl) perovskite materials. The magnetic, electronic, optical, and thermal properties of a material depend greatly on its band structure [15]. This is why it is very important to determine the band structure of the material in question in order to study these different properties. The electronic band structures of NaSrX3 perovskite structures (X= F and Cl) are shown in Figure 3. They are calculated in the high-symmetry direction of the first Brillouin zone following the path of high-symmetry points MΓ-M-R-X-R-M. The electronic band structure of a material is one of the characteristics that differentiates it from other materials. It provides explicit information about the energy values that electrons can have in order to be present in the energy bands. It also indicates the regions where electrons are not available. The valence band (VB) and the conduction band (CB) are different energy bands arranged one above the other. Figure 3 Electronic band structure of NaSrX3 (X= F et Cl) The valence band is below the Fermi energy level (EF) and the conduction band is above it. The distance between the minimum of the conduction band and the maximum of the valence band is the gap or band gap. This band gap is very important for materials. If it is very wide, the material is an insulator. However, if it is zero, the material is conductive. There is a third type of material with a gap of less than 6 eV, which are semiconductors. The gaps obtained for cubic NaSrX3 (X= F and Cl) perovskite materials are shown in Table 2. We find that NaSrF3 and NaSrCl3 have gaps of 6.02 eV and 4.09 eV, respectively. NaSrCl3 has a very high gap of close to 6 eV. However, it is known that materials with a band gap greater than 5 eV are insulators and those with a gap below 5 eV are semiconductors [20]. We can conclude that NaSrF3 is an insulator, whereas NaSrCl3 is a semiconductor. Other authors have also obtained gap values in their work. For the perovskite NaSrF3, M.J. Mehl et al [21] obtained 5.11 eV and M.H. Benkaboua et al [12] obtained a gap of 4.48 eV, which is significantly lower than ours. For NaSrCl3, Aiman Jehana et al [15] obtained 3.62 eV. The calculated gaps of cubic NaSrX3 (X=F and Cl) perovskite materials are all direct gaps on the Γ-Γ path. These materials are well suited for electronic and optoelectronic applications. Table 2 Gap values obtained for perovskites NaSrX3 (X= F et Cl) Gap values in eV Materials Our results Literature results NaSrF3 6.02 4.48 [12], 4.78 [13], 5.11 [21] NaSrCl3 4.09 3.62 [15] GSC Advanced Research and Reviews, 2025, 24(03), 210-224 214 3.2.2. Partial and total densities of state To understand the contribution of different atomic levels to the density of states (DOS) and the nature of the bonds for these compounds, we determined the total and partial densities of states using the GGA formalism implemented in DFT. The partial density of states for NaSrX3 type perovskite materials (X=F and Cl) are shown in Figure 4. As mentioned for the band structure, here too two bands are very important, namely the conduction band and the valence band. Figure 4 4 Calculated total and partial densities of states for NaSrF3 and NaSrCl3 In NaSrF3 material, the valence band is characterized by the 2p state of F weakly mixed with the 3d state of Sr. The conduction band is characterized by the 3d state of Sr, 4s of Sr, 5p of Sr, and 3s of Na. In this conduction band, the contribution of the 3d state of Sr is very strong. In NaSrCl3 material, the valence band is characterized by the 2p state of Cl weakly mixed with the 3d state of Sr. The conduction band is characterized by the 3d state of Sr weakly mixed with the 4s states of Sr and 5p states of Sr. After this analysis, it appears that the valence bands of NaSrF3 and NaSrCl3 are characterized by the 2p state of the halogen weakly mixed with other states. The bottoms of their conduction bands are all mainly dominated by the 3d states of Sr. These two bands are therefore very important for understanding the properties and applications of these materials. Now let's look at what happens at the boundaries of the valence band and conduction band of the materials studied. Figure 5 shows these situations. Each figure shows three very important values. These are the maximum valence band (EV), the minimum conduction band (EC), and the Fermi level (EF). The Fermi level of each material is well located within the valence band. The Fermi level is closer to the valence band than to the conduction band in NaSrF3. The opposite is true in NaSrCl3. The concentration of free carriers (electrons and holes) is therefore equal. In NaSrCl3, electrons at absolute zero temperature are closer to the conduction band than those in NaSrF3. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 215 Figure 5 Bands observed at the band gap boundary for NaSrF3 and NaSrCl3 Analysis of each graph shows that there is band overflow in each band gap. These band overflows could lead to a possible reduction in the gap if, for example, doping is carried out. In NaSrF3, it is the 2p states of F and 3d states of Sr that overflow the band gap. In NaSrCl3, the band overflows are due to the 2p states of Cl, 3d states of Sr, and 4s states of Sr. We have represented in Figures 6 and 7 the charge densities of the two compounds in the (110) and (100) crystallographic planes, respectively, to better understand the nature of the bond between the different atoms contained therein. Figure 6 Charge denssity of NaSrF3 and NaSrCl3 in crystallographic plane (110) The binding and charge distribution behavior between atoms can be understood using the valence electron charge density derived from convergent wave functions. The valence electron charge densities are calculated for the (110) crystallographic plane and the results obtained for NaSrF3 and NaSrCl3 are summarized in figure 6. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 216 Figure 7 Charge denssity of NaSrF3 and NaSrCl3 in crystallographic plane (100) The charge density graphs show a maximum density near the fluorine and chlorine atom, certainly due to their high electronegativity compared to the other atoms present in these perovskites. We also notice that the charge distribution is almost identical in these two compounds. The charge distribution is strongly localized around the center of halogen atoms. The charge density map of these compounds assumes an ionic bond or a metal bond between these atoms. It should be remembered that to our knowledge no author has discussed the charge density of these compounds. 3.3. Optical properties 3.3.1. Real part and imaginary part of the complex dielectric function To design electronic and optoelectronic devices using materials, it is necessary to understand how these materials interact with light. It is therefore necessary to study their optical properties. If their optical properties are known, their future applications can be predicted. The optical characteristics sought in a material are: low refractive index, high absorption coefficient in a certain wavelength range, etc. To achieve this, the optical parameters of the material must be correctly estimated. This will enable the emergence of innovative electronic components. The dielectric function is the basic quantity for determining the optical properties of any material. The complex dielectric function 𝜀 is the response of the electrons in a compound when it receives electromagnetic radiation. It is written as : 𝜀(𝜔)= 𝜀𝑟(𝜔)+ 𝑖𝜀𝑖(𝜔), where 𝜀𝑟 and 𝜀𝑖 are the real part and the imaginary part, respectively. They are obtained using the Kramers Kronig relation [22]. The imaginary part 𝜀𝑖 is responsible for the absorption of the material, while the real part 𝜀𝑟 is related to the polarization of the medium. In our work, the real and imaginary parts of the complex dielectric function of NaSrF3 and NaSrCl3 perovskites are shown in figure 8. All these curves have two very significant parts. The first part ranges from 0 eV to 10 eV and the second from 20 eV to 30 eV. The first part is characterized by various fluctuations. These fluctuations are more or less significant. The second part also includes fluctuations, but they are less significant than the previous ones. The maximum peak of the real part of the dielectric function of the NaSrF3 and NaSrCl3 compounds are positioned at energies of 6.24 eV and 5.44 eV, respectively. As for the imaginary part of the dielectric function of the NaSrF3 and NaSrCl3 compounds, they are located at energies of 8.24 eV and 5.84 eV, respectively. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 217 Figure 8 Real part (red) and imaginary part (blue) of the dielectric function calculated 3.3.2. Optical functions The dielectric function is used to deduce optical functions such as: the refractive index n(ω), the extinction coefficient k(ω), the reflection coefficient or reflectivity R(ω), the absorption coefficient α(ω), and the optical conductivity σ(ω). Refractive index n(ω) The complex refractive index helps us understand how photons affect the medium as they propagate [22]. It has two significant parts: the real part and the imaginary part. The real part is the real refractive index n(ω), which describes the phase velocity of the incident wave. The imaginary part is the extinction coefficient k(ω). It represents the reduction in incident light. When the real refractive index of the medium is high, the wave travels more slowly and is therefore more likely to be deflected. If the imaginary part is non-zero, the medium absorbs light at the wavelength at which it is non-zero. This wave then weakens more and more as it propagates. A transparent material has a zero imaginary part and a non-zero, positive real part. Figure 9 shows the refractive index of NaSrF3 and NaSrCl3. Figure 9 Refractive index for NaSrX3 halide perovskites (X = F and Cl) Each compound studied has a positive refractive index. The refractive index is zero and is high at certain points. We can therefore say that light passing through these materials is likely to be slower and more deflected in the visible and UV ranges. NaSrF3 and NaSrCl3 have main peaks of 2.63 to 8.15 eV and 2.89 to 5.76 eV, respectively. However, Jalil ur Rehman [13], in their work, obtained a main peak for NaSrF3 at 9.36 eV. Mohammad Reda Kabli et al obtained a maximum peak of 1.50 to 9.53 eV [14]. For NaSrCl3, Aiman Jehan et al obtained 2.1 to 6.6 eV [15]. Our refractive indices at frequency 0, i.e., n(0), are 1.47 and 1.59 for NaSrF3 and NaSrCl3, respectively. Aiman Jehan et al. obtained 1.5 for NaSrCl3 [15]. M.H. Benkabou et al obtained 1.4 for NaSrF3 [12]. Extinction coefficient K(ω) Figure 10 shows the extinction coefficient K(ω) for each calculated perovskite material NaSrF3 and NaSrCl3. The main peaks in the NaSrF3 and NaSrCl3 materials are 1.69 to 8.44 eV and 1.74 to 5.84 eV, respectively. From 3.85 eV to 15 eV and from 18.5 eV to 31 eV, the extinction coefficient K is non-zero in both materials. It should be noted that for these energy ranges, these materials absorb the light they receive. The wave will therefore weaken more and more as it propagates. On the other hand, in the energy regions where the extinction coefficient is zero, these materials will be transparent, which is confirmed by the non-zero value of the refractive index in these regions. We can therefore deduce that NaSrF3 and NaSrCl3 are transparent from 0 to 4 eV and from 0 to 3 eV, respectively. No author has discussed the extinction coefficient in the literature for NaSrF3 and NaSrCl3. GSC Advanced Research and Reviews, 2025, 24(03), 210-224 218 Figure 10 Extinction coefficient for NaSrX3 halide perovskites (X = F and Cl) Reflexivity R(ω) Figure 11 shows the calculated optical reflectivity R(ω) of the perovskites NaSrF3 and NaSrCl3. Optical reflectivity describes the ability of a surface to reflect light. It represents the ratio of the reflected light intensity to the incident light intensity. High reflection peaks are observed at energies of 6.30 eV, 9.13 eV, 10.30 eV, 11.74 eV, 12.51 eV, 24.00 eV, and 24.85 eV for NaSrF3, and 5.80 eV, 8.39 eV, 10.95 eV, and 23.85 eV for NaSrCl3. The reflection coefficient values in NaSrF3 are lower than those observed in NaSrCl3. M.H. Benkabou et al obtained peaks at 10.78 eV, 25.02 eV, and 28.94 eV for NaSrF3 [12]. Jalil ur Rehman et al obtained their main peak at 6.03 eV [15]. At zero frequency, the reflectivity values observed are 0.036 and 0.037 for NaSrF3 and NaSrCl3, respectively. Figure 11 Reflexivity for NaSrX3 halide perovskites (X = F and Cl) Absorption coefficient α(ω) Figure 12 shows the absorption coefficient α(ω) calculated for the perovskites NaSrF3 and NaSrCl3. The optical absorption coefficient reflects the decrease in the intensity of light radiation as it passes through a material. The material strongly absorbs light if the absorption coefficient is high. It then converts it into thermal energy. This results in low transmission or reflection. If the absorption coefficient is low, the material has high transparency. The absorption coefficient also reveals the metallic, semiconductor, or insulating nature of the material. In our work, the absorption of both materials starts at 2.82 eV. The curves show two coinciding energy absorption zones. These are 2.82 eV to 13.78 eV and 18.40 eV to 30 eV. The main absorption peak for each material is in the first part. It is 5.9 eV for NaSrF3 and 8.44 eV for NaSrCl3. Figure 12 Absorption coefficient for NaSrX3 halide perovskites (X = F and Cl) Optical conductivity σ(ω) Figure 13 shows the optical conductivity σ(ω) calculated for NaSrF3 and NaSrCl3. The transport of electrons when the material reacts to incident light is explained by the optical conductivity σ(ω) [23]. For each compound, σ(ω) initially behaves as almost zero, then increases. The imaginary value of the conductivity (real part) at 0 eV is zero for NaSrF3 and NaSrCl3. The imaginary value of the conductivity is not zero for NaSrF3 and NaSrCl3 at 0 eV. This function then adopts more or less decreasing fluctuations as the energy increases. The main peak of conductivity (real) for NaSrF3 is located at 8.41 eV and 5.80 eV for NaSrCl3. The main peak of conductivity (imaginary) for NaSrF3 appears at 23.87 eV, while that of NaSrCl3 appears at 10.87 eV.