Study of the structural, electronic, optical, and elastic properties of NaSrX3 (X = Br and I) perovskites using Density Functional Theory (DFT) with GGA formalism

 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 License 4.0. Study of the structural, electronic, optical, and elastic properties of NaSrX3 (X = Br and I) perovskites using Density Functional Theory (DFT) with GGA formalism Mona Hermann Charly YAPI 1, 2, *, Guy Müller Banquet OKRA 1, 2, Mélèdje C. Désiré 2, 3, Niaré Adama 2 and Kré N. Raymond 2 1 Laboratory of Environmental Sciences and Technologies (LSTE), University JEAN LOROUGNON GUÉDÉ (UJLoG), Daloa, BP 150 Daloa, Côte d’Ivoire. 2 Laboratory of Fundamental and Applied Physics (LPFA), University NANGUI ABROGOUA (UNA), Abidjan, BP 801 Abidjan 02, Côte d’Ivoire. 3 Institute for Research on New Energies (IREN), University NANGUI ABROGOUA (UNA), Abidjan, BP 801 Abidjan 02, Côte d’Ivoire. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 Publication history: Received on 27 August 2025; revised on 01 October 2025; accepted on 04 October 2025 Article DOI: https://doi.org/10.30574/wjarr.2025.28.1.3432 Abstract The electronic and optical properties of NaSrX3 (X = Br, I) perovskites using density functional theory (DFT) with GGA (Generalized Gradient Approximation) formalism. The lattice parameters obtained are 5.22 Å and 5.74 Å for NaSrBr3 and NaSrI3, respectively. NaSrBr3 and NaSrI3 have direct gaps of 2.51 eV and 1.49 eV, respectively. They all have a conduction band dominated by 3d statesof Sr, weakly mixed with 3s states of Na and 4s states of Sr. The valence band is dominated by the 2p states of the alkali metal and the 3d states of Sr. These perovskites also have very good optical properties: low reflectivity and high absorption in the ultraviolet. Observation of the different optical functions shows that the materials can slow down and deflect light in both the visible and ultraviolet ranges. Light can also be absorbed in energy ranges corresponding to the visible and UV spectrums. They are also transparent between 10 eV and 20 eV. These materials are suitable for various applications in both the visible and UV spectrums. The elastic properties of NaSrBr3 and NaSrI3 are also very interesting. The elastic constants found verify the criteria for mechanical stability. NaSrBr3 and NaSrI3 are ductile and likely to be ionic. They are anisotropic and stable materials. NaSrBr3 has a higher melting point than NaSrI3. This work confirms that NaSrBr3 and NaSrI3 have very good electronic, optoelectronic, elastic, and optical properties. Their use in a photovoltaic cell could increase its conversion efficiency. Keywords: DFT; Perovskites; Nasrx3; Electronic; Optical; Elastic 1. Introduction The world today faces serious energy challenges. Conventional energy sources are being depleted day by day. Added to this is the fact that the very exploitation of these energies poses a real environmental problem. It exacerbates global warming and causes considerable damage to the environment. Other energy sources are therefore needed. The only alternative is to turn to renewable energy sources. Renewable energy offers considerable advantages. The first advantage is that renewable energies have no harmful effects on the environment. Secondly, they are not difficult to exploit. And finally, these sources are inexhaustible. To ensure energy self-sufficiency for humanity, appropriate research in this field should be undertaken immediately. The most promising renewable energy source is photovoltaic energy based on solar cells. Most solar cells are made from silicon. This also has disadvantages: high production costs and the exploitation of silicon, which damages the environment. Other materials are also used. One example is multijunction solar cells consisting of several thin layers deposited by metal organic vapor phase epitaxy (MOVPE) or World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 161 molecular beam epitaxy. This type of solar cell achieves a record photo conversion efficiency. We can also mention tandem cells and CIGS cells. However, most of these solar cells have the same disadvantages as silicon cells. If we want to make photovoltaics the ideal candidate for alternative energy, we need to focus our research on other materials. This is why some researchers have turned their attention to perovskite materials. Perovskite cells have seen their efficiency increase to between 18% and 20% in 2015, which is close to that of silicon-based cells (25%) [1,2,3]. Most of these cells are made with organic perovskites. Perovskite solar cells have the advantage of good absorption of the solar spectrum, good flexibility and lightness, and low-temperature manufacturing, which can result in lower production costs. In addition, these materials are very abundant on earth. However, they pose stability problems. Research on these materials must therefore continue, not only to increase the efficiency of these cells, but also to resolve their instability issues. Inorganic perovskites, although they have low conversion efficiency, are nevertheless more stable than organic perovskites. Our work consisted of studying the structural, electronic, optical, and elastic properties of NaSrX3-type perovskites (X = Br and I) using density functional theory (DFT) with GGA formalism. 2. Materials and Methods 2.1. Materials This work was carried out using Quantum Expresso (qe-7.0) software [4,5,6] running on Ubuntu 25.04 Linux. Quantumespresso is a software suite consisting of several subprograms that perform specific tasks. We used a Core i7 computer (Lenovo series) with a frequency of 2.90 GHz. We also used other programs to process the data generated by Quantumespresso. These include Vesta, Gnuplot, and Xmgrace. Quantum Espresso itself contains several subprograms specific to very precise tasks. For this work, we used NaSrBr3 and NaSrI3 perovskites as materials. These materials are supposed to crystallize in a cubic crystal structure (Pm3m). Figure 1 shows a typical representation of the crystal structure of each material. We used five atoms per lattice. Figure 1 Cubic crystal structure of NaSrBr3 (left) and NaSrI3 (right) 2.2. Méthodes This work was carried out using density functional theory (DFT), a quantum calculation method. DFT is implemented by the Quantum Espresso code [4,5]. In this study, the DFT formalism used is the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE + GGA) [7,8,9]. We set the convergence level at 10-9 (1.0d-9 eV). The k points in the Brillouin zone were divided into 12×12×12. The kinetic cutoff energy was set at 80.0 Ry. However, it is important to note that the lattice parameter, kinetic cutoff energy, Monkhorst-Pack k-point sampling in the Brillouin zone, and other parameters of the perovskite material structures were obtained by relaxation. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 162 3. Results and discussion 3.1. Convergence test We performed convergence tests to determine the optimal equilibrium values for the NaSrBr3 and NaSrI3 perovskite structures under study. These optimized parameters are: lattice parameter, kinetic cutoff energy, and Monkhorst-Pack k-points in the Brillouin zone. The convergence level is 10-9 (1.0d-9 eV). This convergence test is performed using the vc_relax calculation. It consists of several iterations of the parameter values considered in order to obtain the most stable system. The most stable system is the one that corresponds to the parameter value that assigns the lowest energy to the material. 3.1.1. Lattice parameter Figure 2 shows the evolution of the total energy of the system as a function of the evolution of the lattice parameter of NaSrBr3 and NaSrI3. Figure 2 Convergence of Lattice Parameter acell. Table 1 shows the different lattice parameter values obtained for NaSrBr3 and NaSrI3. NaSrBr3 has a lattice parameter of 5.22 Å and NaSrI3 has a lattice parameter of 5.74 Å. Compared to other authors such as M T Hossain et al [10,11], our lattice parameters are lower. Table 1 Calculated mesh parameters Latice parameter acell in Å Materials Our results Literature results NaSrBr3 5.22 5.86 [10] NaSrI3 5.74 6.47 [11] 3.2. Convergence of Kinetic energy cut-off The cutoff kinetic energy (ecut) represents the kinetic energy of the electron wave function in the crystal that the latter cannot reach [4,5,12]. It is a limit that is set for each iteration. The relaxation of this quantity gave us 70 Ry, but for greater precision we chose a value above 70 Ry, i.e., 80 Ry. In fact, the higher this quantity, the more accurate the calculations will be. But in this case, the computing resources required will be enormous, as will the calculation time. In their work, M T Hossain et al used 67 Ry for NaSrBr3 [10] and 90 Ry for NaSrI3 [11]. 3.3. Convergence of k-point The k points of the Brillouin zone of the perovskites NaSrBr3 and NaSrI3 were sampled using the Monkhorst-Pack method [13]. The relaxation of the k points shows a convergence of 6×6×6. However, we chose to set our Monkhorst- World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 163 Pack grid to 12×12×12. We consider this sampling to be very relevant for these calculations. However, given that it is high, the computing resources and calculation time required will be enormous. It is well known in the literature that the k-point grid is very relevant from 8×8×8 onwards. 3.4. Electronic properties 3.4.1. Bands structure The electronic properties of the perovskite materials NaSrBr3 and NaSrI3 obtained are presented and discussed in this section. These electronic properties concern: the electronic band structure, the total density of states (TDOS) and partial densities of states (PDOS), and the charge density of the cubic perovskites NaSrBr3 and NaSrI3. The band structure is calculated according to the high symmetry direction of the first Brillouin zone on the path M-Γ-M-R-X-R-M. The band structure is crucial for describing the magnetic, electronic, optical, and thermal properties of a material [14]. Figure 3 shows the electronic band structure of NaSrBr3 and NaSrI3. Figure 3 Electronic band structure of NaSrBr3 and NaSrI3 The electronic band structure provides information on the nature of the material: whether it is a conductor, semiconductor, or insulator. It evaluates the energies at which electrons are present in the different energy bands. It also indicates the different regions where electrons are available. The band structure has two very important bands. The valence band (VB) and the conduction band (CB) are two neighboring bands but with different energy bands arranged one above the other. The conduction band is above and the valence band is below. Between these two is the Fermi energy level (EF). The gap is the distance between the minimum of the conduction band and the maximum of the valence band. It is this distance between the conduction band and the valence band, or gap, that determines whether a material is a conductor, semiconductor, or insulator. The wider the gap, the more insulating the material is. The material is conductive if the gap is zero. Sometimes the gap is very small, i.e., less than 5 eV, in which case the material is a semiconductor [14,15]. Table 2 shows the gap obtained for cubic NaSrX3 (X= Br and I) perovskite materials. Table 2 Gap values obtenir for pérovskites NaSrX3 (X= Br and I) Gap values in eV Materials Our results Literature results NaSrBr3 2.51 2.95 [10] NaSrI3 1.49 2.41 [11] NaSrBr3 and NaSrI3 have band gaps of 2.51 eV and 1.49 eV, respectively, which are less than 5 eV. NaSrBr3 and NaSrI3 are therefore semiconductors. M T Hossain et al [10] obtained a band gap of 2.95 eV for NaSrBr3, compared to 2.51 eV for us, and 2.41 eV for NaSrI3 [11], compared to 1.49 eV for us. The band gap values obtained for NaSrBr3 and NaSrI3 in our work are much lower than those obtained by M T Hossain et al [10, 11] in their work. The band gaps obtained in our work are all direct on the Γ-Γ path. These materials can therefore be used in electronic and optoelectronic applications. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 164 3.5. Partial and total densities of state The density of states (DOS) and total and partial densities of states (PDOS) provide insight into the contribution of different atomic orbitals to the density of states (DOS) and the nature of bonds in materials. Figure 4 shows the partial densities of states for NaSrX3-type perovskite materials (X = Br and I). In the NaSrBr3 material, the valence band is characterized by the 2p state of Br weakly mixed with the 5p states of Sr and 3d states of Sr. The conduction band is characterized by the 3d state of Sr, 4s of Sr, and 5p of Sr. In the NaSiI3 material, the valence band is characterized by the 2p state of I weakly mixed with the 3d state of Sr and 5p of Sr. The conduction band is characterized by the 3d state of Sr, 4s of Sr, and 4s of Sr. In this conduction band, the contribution of the 3d state of Sr is very strong. Based on the above, the valence band of NaSrX3-type perovskite materials (X = Br and I) is characterized by the 2p state of the halogen present weakly mixed with other states. Figure 4 Calculated total and partial densities of states for NaSrX3 (X = Br and I) The bottom of the conduction bands is dominated by the 3d states of Sr. Observing the boundaries of the valence band and conduction band of the materials studied, band overflows appear. These observations are presented in Figure 5. The graphs in figure 5 show the maximum valence band energy (EV), the minimum conduction band energy (EC), and the Fermi level (EF). The Fermi level EF of NaSrBr3 is located almost halfway between the conduction band and the valence band. In NaSrI3, the Fermi level EF is closer to the conduction band. Each graph shows band overlap in the band gap. These band overlaps are likely to reduce the gap in the event of doping. In NaSrBr3, it is the 2p of Br and the 4s of Sr that spill over into the band gap. In NaSrI3, the spillover is due to the 2p state of I. In the latter case, the 2p state completely crosses the band gap. NaSrI3 is therefore almost a conductor. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 165 Figure 5 The edges of bands of calculated state densities for NaSrBr3 ande NaSrI3 In order to better understand the nature of the bond between the different atoms contained in a material, its charge density must be observed. Figures 6 and 7 show the charge densities of NaSrBr3 and NaSrI3 in the crystallographic directions (110) and (100), respectively. Figure 6 Charge denssity of NaSrBr3 and NaSrI3 in crystallographic plane (110) The bonding behavior and charge distribution between atoms can be understood using the valence electron charge density derived from convergent wave functions. By observing the map of the variation in the electron charge density of a compound, information can be obtained about the type of bond between the constituents [16]. These charge density graphs show that the density is very high around the halogen atoms, i.e., Br and I. This is undoubtedly due to their high electronegativity compared to the other atoms present in these perovskites. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 166 Figure 7 Charge denssity of NaSrBr3 and NaSrI3 in crystallographic plane (100) The charge distribution is identical in each perovskite material. This charge distribution, as observed on each map, suggests a rather ionic or metallic bond between the Na atom and the alkali metals Br and I. In the (110) crystallographic plane, the distinctive charge distribution suggests a probable hybridization between Na and Br in NaSrBr3 and a hybridization between Na and I in NaSrI3. This therefore indicates a probable covalent Na-Br bond in NaSrBr3 and a probable covalent Na-I bond in NaSrI3. There is therefore a transfer of charges between Na and the alkali corresponding to these perovskites. However, according to the crystallographic plane (100), there will be no covalent bond between Sr and the corresponding alkali of the perovskite in question. 3.6. Optical properties 3.6.1. Real part and imaginary part of the complex dielectric function Optical properties provide insight into how the material reacts to light. These sought-after optical properties can be deduced from the complex dielectric function 𝜀. It represents the response of the material's electrons when it interacts with light and is written as : 𝜀(𝜔)= 𝜀𝑟(𝜔)+ 𝑖𝜀𝑖(𝜔). 𝜀𝑟 is real part and 𝜀𝑖, the imaginary. The imaginary part 𝜀𝑖 is responsible for the absorption of the material, and the real part 𝜀𝑟 is responsible for the polarization of the medium. In this work, the real and imaginary parts of the complex dielectric function of NaSrBr3 and NaSrI3 perovskites are shown in Figure 6. These curves have two parts : from 0 eV to 13 eV and then from 13 eV to 30 eV. Each part is characterized by different fluctuations. The maximum peak of the real part of the dielectric function of the NaSrBr3 and NaSrI3 compounds are positioned at energies of 4.32 eV and 3.28 eV, respectively. As for the imaginary part of the dielectric function of the NaSrBr3 and NaSrI3 compounds, they are positioned at energies of 4.44 eV and 3.64 eV, respectively. For each perovskite compound, the main imaginary peak and the main real peak almost coincide. These different peaks appear to converge at 3.0 eV when moving from the perovskite with the lightest halogen to that with the heaviest halogen. World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 167 Figure 8 Real part (in red) and imaginary part (in blue) of the dielectric function calculated 3.6.2. Optical functions Other optical functions can be deduced from the dielectric function. These are: refractive index n(ω), extinction coefficient k(ω), reflection coefficient or reflectivity R(ω), absorption coefficient α(ω), and optical conductivity σ(ω). These optical functions are represented respectively by Figures 7, 8, 9, 10, and 11. 3.7. Refractive index The complex refractive index is very important for understanding how photons affect the medium during propagation [15, 17]. The real part represents the real refractive index n(ω) in front of the phase velocity of the incident wave. The imaginary part is the extinction coefficient k(ω). The latter represents the reduction in incident light. A large real refractive index indicates slow light propagation and therefore greater deviation. A non-zero imaginary part of the complex refractive index means that light is absorbed by the medium. The wave will then weaken more and more as it propagates. A transparent material has a zero imaginary part and a zero and positive real part. Figure 7 shows the calculated real refractive index n(ω) of the perovskites NaSrBr3 and NaSrI3. Both compounds have positive refractive indices. Two parts can be distinguished: from 0 eV to 8 eV and from 8 eV to 30 eV. Figure 9 Refractive index for NaSrBr3 and NaSrI3 The refractive indices in these two materials are almost identical from 8 eV to 30 eV. In both materials, since the refractive index is non-zero, light passing through these materials is likely to propagate more slowly and will be more deflected in both the visible and UV ranges. The main peaks are 2.95 to 4.32 eV and 2.98 to 3.33 eV for NaSrBr3 and NaSrI3, respectively. These peaks are therefore almost identical. The static refractive index obtained for each is 1.63 and 3.16 for NaSrBr3 and NaSrI3, respectively. M T Hossain et al obtained 2.2 for NaSrBr3 and 1.57 for NaSrI3. This shows a very significant difference between our two studies. 3.8. Extinction coefficient K(ω) The extinction coefficient K(ω) is the imaginary part of the complex refractive index. Figure 8 shows the calculated extinction coefficient for the perovskites NaSrBr3 and NaSrI3. The extinction coefficient K(ω) characterizes the attenuation of electromagnetic radiation energy as it passes through the medium. The higher the value of K(ω), the stronger the interaction between the radiation and the material, resulting in greater attenuation of the beam intensity. A non-zero value of K(ω) means that light is absorbed by the medium. The wave will then weaken more and more as it propagates. A transparent material has a zero value of K(ω) and a positive real value of n(ω). World Journal of Advanced Research and Reviews, 2025, 28(01), 160-174 168 Figure 10 Extinction coefficient for NaSrX3 halide perovskites (X = F, Cl, Br and I) Looking at these graphs, two parts stand out, which are almost identical in both materials. These are: from 0 eV to 10 eV and from 20 eV to 25 eV. The main peak for NaSrBr3 and NaSrI3 is 4.52 eV. As the value of K(ω) is high between 2 eV and 8 eV, we can conclude that the interaction between radiation and matter is stronger. There is therefore greater attenuation of the light beam intensity. The same observation applies to both materials between 21 eV and 24 eV. Thus, in these two ranges, i.e., from 0 eV to 10 eV and from 20 eV to 25 eV, the value of K(ω) is not zero, meaning that light is absorbed by the material. The light will gradually weaken as it propagates through these materials. Between 10 eV and 20 eV, K(ω) is zero while n(ω) is non-zero. These two materials are therefore transparent between 10 eV and 20 eV. We note that no discussion has been made in the literature on this subject. 3.9. Reflectivity R(ω) Optical reflectivity characterizes the ability of a surface to reflect the light it receives. It is the ratio of the reflected intensity to that of the incident wave. Figure 9 shows the calculated optical reflectivity R(ω) of the perovskites NaSrBr3 and NaSrI3. Figure 11 Reflexivity for NaSrBr3 et NaSrI3 The same observation as before can be made. Two parts stand out in these two compounds. These two parts are almost identical in both compounds: from 0 eV to 10 eV and from 20 eV to 24 eV. The main peaks are 0.43 to 8.52 eV and 0.35 to 8.40 eV for NaSrBr3 and NaSrI3, respectively. The static reflectivity values (at 0 eV) are 0.058 and 0.462 for NaSrBr3 and NaSrI3, respectively. M T Hossain et al obtained main peaks at 8.2 eV for NaSrBr3 [10] and at 7.2 eV for NaSrI3 [11] and static reflectivity values at 0 eV of 0.07 for NaSrBr3 [10] and 0.05 for NaSrI3 [11]. 3.10. Absorption coefficient α(ω) The absorption coefficient α(ω) characterizes the decrease in intensity of an incident wave passing through a material. A high absorption coefficient indicates that the material strongly absorbs light, converting it into thermal energy. Such absorption results in low transmission or reflection. A low absorption coefficient indicates that the material is highly transparent. The absorption coefficient also characterizes whether the material is metallic, semiconducting, or insulating. Figure 10 shows the absorption coefficient α(ω) obtained for NaSrBr3 and NaSrI3. Absorption of the two materials begins at 1.50 eV and 1.0 eV for NaSrBr3 and NaSrI3, respectively. Absorption in these two compounds also has two parts: from 1 eV to 10 eV and from 20 eV to 25 eV. The two curves have the same shape and show the same similarity. The main peaks are located exactly at the same energy value, i.e., 4.52 eV for NaSrBr3 and NaSrI3. For these materials, there is absorption in both the visible and ultraviolet ranges.