First-principles Study of the Structural Properties of RbSnI2Br Perovskites Under Pressure

As a member of lead-free perovskite, tetragonal phase perovskite RbSnI2Br has a long-term development prospect. Due to the effect of structural changes on physical properties, we have explored the pressure-induced phase transition of RbSnI2Br perovskite. For this project, the structural properties of the tetragonal phase perovskite RbSnI2Br are studied by using the Perdew-Burke-Ernzerhof (PBE) functional for the generalized gradient approximation (GGA) under pressure conditions of 0 GPa–1 GPa. The calculation results of structural factors were in excellent agreement with those obtained from previous studies at the ground state, which ensures the accuracy of the study. The results show phase transitions occur with increasing pressure. The structural space group of β-RbSnI2Br changes from P4/MMM (tetragonal system) to P1 (triclinic system) under pressure in the range of 0 GPa–1 GPa. All these provide a relative theoretical basis for our further understanding of α-RbSnI2Br perovskite.


Introduction
In recent years, perovskite solar cells (PSCs) have undergone a rapid and steady development due to their simple preparation techniques, excellent photovoltaic (PV) performances, and low manufacturing cost, and are considered to be one of the most promising photovoltaic cells [1].The organic-inorganic mixture of halide perovskite ABX 3 [A + =MA + , FA + (organic cation); B + =Pb 2+ , Sn 2+ ; X − =Cl − , Br − , I − (halogen anion)] has drawn a lot of attention on account of its excellent carriers mobilities, long carriers diffusion length and high light absorption coefficient [2].In 2009, CH 3 NH 3 PbX 3 (X=I, Br, Cl) perovskite material was first applied to solar cells as a PV absorber and had a photoelectric conversion efficiency (PCE) rate of 3.8% [3].With the rapid development and process optimization of organic-inorganic hybrid PSCs, unprecedented achievements have been made in a brief period, evidenced by the increase of PCE to 25.2% [4].Therefore, the material has been widely used in solar cells, photonic emitters, photodetectors, and other photovoltaic devices [2].However, the exposed organic cationic methylammonium cation (MA + ) and the formamide cations (FA + ) exposed to the air are easily decomposed by sunlight and rain.What's more, poor thermal stability has hindered their development.In contrast, all-inorganic halide perovskites, with excellent thermal stability and good PEC, are what researchers are interested in and have gradually become a new research highlight.In 2015, the Snaith group has successfully prepared inorganic CsPbI 3 PSCs by adding an appropriate amount of hydroiodic acid to the CsPbI 3 precursors liquid and lowering the perovskite crystallization temperature, which was the first appearance of inorganic halide PSCs [5].
Common perovskites with all-inorganic halides include all-inorganic lead-based perovskites (CsPbI 3 , CsPbBr 3 , CsPbCl 3 , etc.) and all-inorganic tin-based ones (CsSnI 3 , CsSnBr 3 , CsSnCl 3 , etc.).Lead-based PSCs have such advantages as tunable band gap, strong light absorbance coefficient, high electronic mobility, and long carriers diffusion length [4].However, lead, a toxic metal, may result in environmental contamination and health problems [6], hindering the long-term development of lead-based PSCs.There is a great need to seek a lead-free perovskite material to replace lead-based ones so as to embrace green and sustainable development.Tin-based perovskites show similar crystal structure and electronic properties to lead-based counterparts.Moreover, the former has received considerable focus in the area of PSCs due to its advantageous semiconductor characteristics [7].Recent years have witnessed the improved PCE of eco-friendly tin-based perovskites through in-depth studies [8].In 2020, based on experiments and theoretical calculations, the PCE of tin-based PSCs reached 13.4% with striking long-term durability [9].Research shows that tin-based perovskites generally have four phasors, α phase (cubic phase), β phase (tetragonal phase), γ phase (orthogonal phase), and Y phase (triangular phase) [10].CsSnI 3 is in the mixed crystal state at room temperature.A γ-Y phase transition can be observed, showing an oxidation instability in CsSnI 3 [11].The A site of CsSnI 3 perovskite material is doped with Rb element, and its orthogonal γ phase and triangular Y phase tend to evolve stably in the process of gradually replacing Cs element with Rb element [12].Walsh and Son's team studied perovskite (Rb, Cs) SnI 3 by exploring the stoichiometry of Rb to Cs, revealing that its stability enhances as the Rb doping ratio increases, especially for the orthogonal phase [13].In 2021, Rahman and Roknuzzaman's group evaluated the photovoltaic and optoelectronic features of RbSnX 3 (X=Cl, Br, I), Rb-based Perovskites.RbSnI 3 , with excellent ductility, absorbance coefficient, and photoinductivity, has great prospects for next-generation ultraviolet photodetectors [14].Inhibiting phase separation can be achieved by C-site doping in addition to A-site doping.Tao's team replaced the I element in the CsSnI 3 perovskite material with the Br element to realize C site doping.The formation energy analysis of the doping structure showed that substituting I with Br could prevent the phase transition from gamma to Y [15].Meanwhile, such kind of substitution could adjust the optical band gap and carrier concentration of CsSnI 3 PSCs [16].CsSnI 3 is prone to phase separation either at room temperature or under constantly changing conditions such as temperature and pressure.The phase separation can be inhibited by selecting the Rb element at position A and I 2 Br at position X.
The structure of perovskites can be changed by chemical additives, interface engineering, element doping, and pressure to adjust photoelectric properties and improve PCE [17].The structural changes of the PSC material with pressure applied will influence its properties consequently [18].The suitability of pressure-induced CsGeI 3 for PSCs was found through the comparative analysis of photoelectric properties [17].Some studies have used first principles to calculate the structural, electronic, optical as well as mechanical performances of nontoxic halide perovskite RbSnX 3 (X=Cl, Br) in hydrostatic pressure [19].To date, there have been relevant studies on the structure, electronic as well as thermodynamic properties of γ-phase RbSnI 2 Br perovskites by using first principles [15], but the relevant properties are lacking, especially under pressure-induced conditions.Under these circumstances, this paper uses the density general functional based on theory first-principles to explore structural features for β-RbSnI 2 Br perovskites under the static pressure of 0 GPa-1 GPa.

Computational methods
The calculations were performed by using the CASTEP module, which depends on a first-principle plane waves pseudopotential method on the basis of density functional theory [20].The Perdew-Burke-Ernzerhof (PBE) function for generalized gradient approximation (GGA) had been used as a way to describe the relevance of exchanges between electrons [21].This monkhorst-pack scheme [21] was adopted for the integral calculations of the system in the Brillouin district, in which a 4×4×4 k grid points and 400 eV plane waves cutoff energy were employed to assure well convergence in the system energy along with the configuration at the quasi-complete plane wave basis level.The total energy for the structural optimization was 10 −5 eV when the lattice geometry was completely relaxed till this Hellmann Feynman force that acts upon every atom would be lower than 0.01 eV/Å.

Results and discussions
Correct and stable crystal structures are important prerequisites for studying their electronic and optical properties.Based on the Pauli exclusion principle and the principle of eight-electron stability, the constructed α-RbSnI 3 perovskite is to be a body-centered cubic structure in the space cluster PM-3M [7].In detail, the Rb atom occupies the 8c site, and the B atom Sn occupies the 4a site, while the iodide anion is at the 24e Wyckoff site, as illustrated in Figure 1.The structures of β-RbSnI 2 Br perovskite are the X-doped α-RbSnI 3 with Br element instead of I element.The doped β-RbSnI 2 Br perovskite is cubic with a P4/MMM space group.The crystal structure optimization is evidenced in Figure 2.
In accordance with the calculation, the lattice constant settlement results are shown in Table 1, from which we can observe that the α-RbSnI 3 results calculated in this paper are consistent with the published theory calculations and experimental studies.Compared with the cubic structure of α-RbSnI 3 perovskite, the β-RbSnI 2 Br perovskite is a cubic crystal system after X-site doping, which changes the crystal system and spatial structure.After structural optimization, the energy volume (E-V) curve is simulated, as illustrated in Figure 3.When the volume is 227.808Å 3 , the lowest energy is -4810.856eV.After optimization of energy and volume, the greater the value of negative energy displayed, the smaller the lattice energies, and the better the stabilization of the structure is [13].
Table 1 Cell Parameters, Volume (Å 3 ) and Space Group of α-RbSnI    2. The phase transition of β-RbSnI 2 Br perovskite occurs when pressure is applied.The structural space group of β-RbSnI 2 Br changes from P4/MMM (tetragonal system) to P1 (triclinic system) under pressure, ranging from 0 to 1 GPa.The crystal cell parameters such as lattice constant, angle, and volume change obviously compared with the ground state without pressure, but the cell parameters change less under different pressures.The space group will change its lattice parameters, and the intensity of the change also reflects the change of the group itself.4 describes the change of cell parameters under pressure.After applying the pressure, the crystal energy, volume, bond length, and bond angle all change significantly.In detail, the energy increases slightly after applying the pressure, indicating that its stability decreases correspondingly (Figure 4a).The volume change declines with increasing pressure values, representing a closer distance between the atoms (Figure 4b). Figure 4c shows the change in the bond length with the pressure of Rb-Br and the bond length gets shorter as the pressure increases.As illustrated in Figure 4d, the overall trend of the Sn-Rb-Sn bond angle increases from 66.64 • to 78 • at the left and right sides.The volume, bond length, and bond angle after applying the pressure all satisfy the linear equation.

Figure 3
Figure 3 Energy Volume (E-V) curve of β-RbSnI 2 Br perovskite Cell parameters and spatial groups change owing to the effects of pressures as reflected in Table2.The phase transition of β-RbSnI 2 Br perovskite occurs when pressure is applied.The structural space group of β-RbSnI 2 Br changes from P4/MMM (tetragonal system) to P1 (triclinic system) under pressure, ranging from 0 to 1 GPa.The crystal cell parameters such as lattice constant, angle, and volume change obviously compared with the ground state without pressure, but the cell parameters change less under different pressures.The space group will change its lattice parameters, and the intensity of the change also reflects the change of the group itself.
-RbSnI 2 Br perovskite at a pressure of 0 GPa-1 GPa (a) Energy change curve, (b) Volume change curve, (c) Rb-Br bond length change curve, (d) Sn-Rb-Sn bond angle change curve 4. Conclusions In this work, β-RbSnI 2 Br perovskite has been studied under the pressure of 0 GPa-1 GPa by utilizing density functional theory based on first principles with Perdew-Burke-Ernzerhof (PBE) function for generalized gradient approximation (GGA).This thesis has investigated the structural properties of β-RbSnI 2 Br perovskite at a static pressure interval of 0.1 GPa.Its phase transformation is induced by increasing pressure.The tetragonal phase β-RbSnI 2 Br with space group P4/MMM transformed the triclinic phase β-RbSnI 2 Br with space group P1 under the above pressure range.Besides, the results show the volume, bond length, and bond angle satisfy the linear equation after applying the pressure.Angle and volume change remarkably in comparison with the ground state without pressure, but the cell parameters change less under different pressures.With respect to the consequences of structural changes upon physical characteristics, it behooves us to investigate the electronic properties of β-RbSnI 2 Br perovskite under different pressures.

Table 2
Cell Parameters, Volume, and Space Groups of β-RbSnI 2 Br Perovskite Under the Pressures Ranging from 0 GPa to 1 GPa.