https://orcid.org/0000-0002-9214-3409
Figures
Abstract
The electronic structures and absorption properties of Cs2BX6 halide compounds are investigated with first principle calculation and exchange correlation functional of GGA-PBE. Pressure and halogen ion doping are employed to regulate band gap. All materials suffer transition from indirect to direct band gap semiconductors but with different phase transition pressure. Structural and band structure calculating results show that the value of phase transition pressure is mainly determined by the volume of octahedron. When the volume of vacancy octahedron is much less than B-ion octahedron, the lowest band point of B-d orbitals transforms to Γ point, then the indirect semiconductors transform into direct band gap semiconductors. Calculating results of optical absorption implied that the systems have obvious blue shift, which result in the optical properties reduced. Based on suitable band gap and higher absorption coefficient, Cs2ZrI4Br2 can be an ideal candidate for perovskites solar cells.
Citation: Zhao Y-Y, Sheng S-Y (2023) The electronic and optical properties of Cs2BX6 (B = Zr, Hf) perovskites with first-principle method. PLoS ONE 18(12): e0292399. https://doi.org/10.1371/journal.pone.0292399
Editor: Mannix P. Balanay, Nazarbayev University, KAZAKHSTAN
Received: May 29, 2023; Accepted: September 19, 2023; Published: December 22, 2023
Copyright: © 2023 Zhao, Sheng. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting information files.
Funding: The work was supported by the Fundamental Research Funds for Technical Study of Ministry of Public Security with Grant No.2021JSYJC23; Scientific Research Project, Department of Education of Liaoning province, No.LJKZ0075; The Key Project Research of the Central Universities of Criminal Investigation Police University of China with Grant NO.D2021009; Fundamental Research Funds for the Central Universities of Criminal Investigation Police University of China, under Grant No.D2019018 These organizations only provide fund support. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
The lead-free halide perovskites have been widely studied for the last few years [1–4]. Compared with the traditional semiconductors, halide perovskites have attracted great attention owing to their high absorption coefficient, defect-tolerance, long diffusion length, appropriate band-gap [5–7]. They are widely used in photovoltaic solar cells, photoelectric detector, laser device, etc [8, 9]. However, many of these halide perovskites suffer two major issues of environmental stability [3, 10, 11] and low power conversion efficiency(PCE) [12]. These troubles currently preclude their widespread in commercial applications. Therefore, there is a strong desire to find environmentally stable and high efficiency perovskite materials. In order to resolve these problems, many groups have done a lot of theoretical and experimental researches.
The basic crystal structure of photovoltaics perovskite is ABX3. In inorganic perovskite A usually for Cs+, X represents halide ion, and B is divalent metal cation, whose volume is smaller than A. In the past few years, significant theoretical efforts and experiments have been made to understand properties of energy band and photovoltaic of these materials. Obviously, the most commonly used lead-free perovskite materials is set B with Sn2+ and Ge2+ [13–17]. But both of them suffer from much serious instability issues [18], and the lower PCE is also a troublesome problem [19]. Then the family of vacancy ordered double perovskites A2BX6 have been widely discussed as well [20, 21]. Results show that energy and optical properties are mostly determined by [BX6] octahedral, doping and pressure also have extraordinary effects on characteristics of lattice parameter, energy gap, optical absorption coefficient and so on. In 2017, group of Yao Cai completed the calculation of chemical trends and structural stability of A2BX6 (A = K, Rb, Cs; B = Pd, Pt, Sn, Te; X = Cl, Br, I) [22]. Their findings provide guidelines for the design of halide A2BX6 compounds. Muhammad Faizan et al. found Rb2PdBr6 and Cs2PtI6 were suitable for single-junction photovoltaic applications [23]. Some researchers have also shown that the band gap of materials could be regulated by doping alloying elements on B-site [24].
Judging from material stability, we prefer to choose Cs as A cation. In general, most theoretical and experimental results have indicated that Cs2TiX6 is an ideal photoelectric conversion material. Titanium, zirconium and hafnium belong to the same group, so they are some alike in nature stability and structural characters. In this context, through the first-principle calculation based on density functional theory (DFT), the energy and optical properties of Cs2HfI6−xXx and Cs2ZrI6−xXx with the influence of pressure are studied detailed. Firstly, the structural optimization and stability of the compound was discussed. Secondly, the energy band and density of states was calculated to study the phase transition from indirect to direct semiconductor with the influence of doping and pressure. Then the optical properties were studied. Finally, some conclusions were proposed in the last section of paper.
Calculating methods
First principle calculation was implemented by using Vienna ab initio simulation package (abinit) [25]. The exchange correlation function between electrons was described by generalized gradient approximation (GGA) with Perdew-Burker-Ernzerhof (PBE) [26]. The projector augmented wave (PAW) was employed to describe interactions between core and valence electrons [27]. Valence electron configuration-Cl (3s2 3p5), Br (3d10 4s2 4p5), I (4d10 5s2 5p5), Cs (6s1), Zr (4d2 5s2), Hf (4f14 5d2 6s2). The plane wave energy truncation for 20hartree. Structural relaxation using BFGS method [27]. The accuracy of relaxation convergence was set to 1.0 × 109hartree/atom, and interaction between atoms was less than 1.0 × 10−5hartree/Bohr. When using ab initio molecular dynamics (AIMD) [28] method to verify structure relaxation results, super lattice of 2 × 2 × 2 was adopted and k-point grid was Γ(0, 0, 0) only. In this work, the energy fluctuations accuracy converges to 0.25 hartree in 20 ps. When calculating the crystal energy and optical properties, 16× 16 × 16 k point grid was employed. In order to get more accurate absorption spectrum, the band number was set to triple of valence band.
Results and discussion
Structural properties and stability
Fig 1 represents the optimized geometric structures of Cs2BX6 (B = Hf,Zr) view along the (1 1 0) axis. Fig 1(a)–1(f) shows the structure of materials with doping concentration from x = 0 to x = 5. We can see that as for Cs2BX6 perovskites, the structure is a typical configuration of Fm − 3m cubic crystal. The BX6 form stable octahedron configuration, where halogen atoms locate at the vertices of octahedral, and B-site cation locate in the center of the octahedral structure. While A locates in the center of four neighboring octahedral structures. With the doping of halide atom, structures of materials are not standard cubic lattice any more. On the basis of existing results, the photoelectric characteristics of the material is mainly decided by the BX6 octahedron configuration [20, 21]. The radius of B and halogen atoms can directly affect the material structure, including lattice distortion, the bond length and bond angle. Besides, external pressure and temperature also have significant influence on lattice structure and optical properties [29–31].
(a)-(f) shows the optimized structure of materials with doping concentration from x = 0 to x = 5(balls color: green-Cs, yellow-Hf or Zr, purple-I, and blue means the doping halogen atom).
Then the structural optimized curves of total energy versus volume at P = 0 are shown in Fig 2 to describe the lattice distortion with the influence of doping. The differences between figures indicate that these compounds belong to different crystal systems at equilibrium with P = 0. Compared with the optimized structures shown in Fig 1, we can conclude that in a super cell Cs2ZrI6 is a cubic structure, Cs2ZrI4Br2 is the tetragonal body centered system, and Cs2ZrI2Cl4 is the orthorhombic body centered structure. The variation of structural optimized curves in this study is similar with that of Cs2TiBr6−xIx [30]. But for the compounds studied in this paper, there is little experimental and theoretical evidence to compare with our calculated results, so our data maybe a good reference for future work. The stability of compounds can be described by formation energy as the following equation:
(1)
where
, ECsI, and
are the total energies of Cs2BX6 system, CsI and BI4, respectively. With different pressure, all the formation energies of 26 kinds of perovskites with multiple doping concentration shown in Fig 3 are negative, which means that all the materials have excellent structural stability.
Different colours of curves in (a)-(d) stand for different doping concentration x of halogen elements. Triangular symbols represent transition point of indirect-direct gap semiconductors.
Band structure
To understand the electronic conductivity with different pressure, the band structure and density of states (DOS) were calculated. Take the pure lattice system Cs2ZrI6 and Cs2ZrCl6 for example, the results are shown in Figs 4 and 5. In Fig 4, we can see that with P = 0, Cs2ZrI6 is an indirect bandgap semiconductor with gap value of 1.83eV. The top of valence band(VBM) located at Γ(0, 0, 0) is mainly composed by I-4p orbital, and the bottom of conduction band(CBM) situated at X(0.5, 0.5, 0) is contributed by Zr-3d state. While P = 6.75 GPa, the material turn into direct bandgap semiconductor with gap value of 1.36eV. These results mean that with the increase of pressure, materials suffer from indirect-direct band gap transition. During this process, the VBM always stays at the same position, while the location of CBM moves from X-point to Γ-point, which accompanied with the decrease of energy value. The band structure of Cs2ZrCl6 in Fig 5 share the same feature with Cs2ZrI6, but the former has bigger band gap.
The bandgap is 1.83eV and 1.36eV, separately. P = 6.75GPa: there is a material transition from indirect to direct band gap semiconductor, and the CBM moves from X to Γ-point.
The bandgap is 3.69 eV and 3.53 eV, separately. Accompany with material transform from indirect to direct band gap semiconductor, the CBM moves from X to Γ.
The accuracy of density functional theory (DFT) predictions for ground state energies and density distributions can be improved by better hybrid functional for exchange correlation energy. According to Jacob’s ladder of approximate DFT methods, we know that GGA, meta-GGA(mGGA) and HSE06 belong to different level with functional complexity varies greatly. GGA takes density gradient into energy density functional to correct the error introduced by uneven distribution of electron density, and PBE pseudopotential is one of the most useful exchange-correlation functional. The mGGA is a most sophisticated semi-local functional, incorporating important exact conditions with respect to GGA functional. In general, mGGA functional with the kinetic energy density, which enters in the expansion of the angle-averaged exact exchange hole, thus being an important tool in the construction of exchange-correlation approximations. The most popular mGGA functional includes BR89, VSXC, TPSS and so on. The HSE06 functional is an outstanding representative of hybrid-GGA. It takes spin-orbit coupling into consideration so that usually gives bandgaps of heavy metals closer to experimental values than GGA results. This is because that spin-orbital coupling have an important effect on the bandgap by splitting the energy levels around Fermi level.
Fig 6 shows the band gaps of Cs2ZrI6−xBrx with P = 0(solid line) and phase transition pressure(dashed line) as a function of doping concentration, compared to three kinds of hybrid functional: GGA (circle), mGGA (triangle) and HSE06 (square). In this paper, the exchange-correlation energy of HSE06 is described as follows:
(2)
where
and
are the exchange and correlation energy functions of PBE, respectively. In general, the gap value of Cs2ZrI6−xBrx grows with the increase of Br doping. And the band gaps of materials calculated with GGA and mGGA method are basically consistent, while the results with HSE06 method are highly overvalued. These results agree well with previous theoretical values which indicate that the band gap of halide perovskites obtained by HSE06 is slightly larger than their experimental and other theoretical values [32]. The major reason may be that Zr is a so light element that it is unnecessary to consider electron coupling in band structure calculation. Therefore, in this paper we mainly use GGA hybrid functional method to study the properties of perovskites.
Both the structural change with doping and lattice distortion constructed by pressure can directly affect the electrical and optical properties. From now on, we discuss the competing effects of these two factors. Tables 1 and 2 are the calculated electronic bandgaps of perovskites. For all the 26 halide perovskites, halogen atoms can significantly regulate the material’s band gap. Unfortunately, all the materials are indirect band gap semiconductors. From the point of electronic transport, indirect bandgap semiconductors can also bring electrons from VBM to CBM, while in this process, part of the energy will lost in the form of phonons. This energy dissipation will greatly reduce the life of materials. Therefore, the direct band gap semiconductors are more popular in solar cells application. With the increase of pressure, all materials completed the transformation from indirect bandgap to direct bandgap semiconductor but with different phase transition pressure. Based on experimental data, solar battery materials band gap within the optimal range of 0.9–1.6 eV, and good photoelectric materials ideal band gap between 1.38 eV to 1.78 eV. Combined with our calculation data, materials of Cs2ZrI6, Cs2ZrI5Br, Cs2ZrI4Br2, Cs2ZrI3Br3, Cs2ZrI5Cl, Cs2ZrI4Cl2, Cs2ZrI3Cl3 can be used as solar cells, and Cs2ZrI2Cl4 is a better photoelectric material.
From Fig 3, we can clearly see that at phase transition point the pressure varies greatly for different materials. For Cs2HfI6−xBrx and Cs2ZrI6−xBrx, the difference of phase transition pressure caused by Br-doping is small. The former is mainly concentrated between 2.5GPa and 3GPa, while Cs2ZrI6−xBrx need more pressure about 4GPa. The transition pressure of Cs2ZrBr6 and Cs2ZrI6 are almost up to 5GPa and 6.75GPa separately. As to Cs2HfI6−xClx and Cs2ZrI6−xClx, the pressure fluctuates greatly near the phase transition point.
Considering the influence of pressure, we find that the trends of phase transition are the same for 26 kinds of perovskites. In general, Cs2BX6 compounds are considered as vacancy ordered double perovskites with B-periodic deficient of CsBX3. Due to the presence of vacancy ordered, double perovskite materials all possess so great elasticity coefficient that the volume of structure will decrease obviously with the increase of pressure. In our opinion, the volume declining rate of vacancy octahedron is higher than that of B-ion octahedron. When the volume of vacancy octahedron is much less than B-ion octahedron, the lowest band point of B-d orbitals transforms to Γ point. At the same time, materials were converted into direct band gap semiconductors. As to different halogen and B-site atoms, elastic coefficients of materials take different values, which lead to octahedral structures have various sensitivity to pressure. This is the reason why materials have different pressure values at the transition point.
Optical properties
In this section, the optical properties will be discussed in detail, and the optical absorption coefficients I(ω) defined through the linear response theory is calculated by the following equation:
(3)
where ω is the frequency of energy, I(ω) stands for the absorption coefficient, ϵ1(ω) and ϵ2(ω) are the real and imaginary parts of dielectric function, respectively. The absorption coefficients of 26 kinds halide perovskites with P = 0 and phase transition pressure are shown in Figs 7 and 8.
The optical spectrums of Cs2HfI6−xBrx with (a) P = 0 and (b) phase transition pressure. (c) and (d) are the same conditions of Cs2HfI6−xClx.
The optical spectrums of Cs2ZrI6−xBrx with (a) P = 0 and (b) phase transition pressure. (c) and (d) are the same conditions of Cs2ZrI6−xClx.
As can be seen from the spectrum diagram in Fig 7(a)–7(d), Cs2HfI6−xBrx has better optical absorption for high frequency light with wavelength between 300–450nm. With the increase of Br concentration, absorption region are mainly move to short-wave area and peak value of absorption coefficient has been reduced at the same time. Along with the phase transition of indirect-direct band gap semiconductor, the peak value of absorption coefficient was increased. Overall, absorption coefficient of Cs2HfI2Br4 is the largest, but the main absorption area is ultraviolet spectrum within 320–360nm. If the halogen doping replaced by Cl atom, the absorption peak increased while the spectrum has obvious blue shift among all the absorption wavelength. Which means the absorption properties greatly reduced in the visible light region.
Fig 8(a)–8(d) is the absorption coefficient of Cs2ZrI6−xXx compounds. Generally speaking, feature of spectral line has a similar trend with Cs2HfI6−xXx. But Cs2ZrI6−xXx has better optical absorption property with the visible light absorption wavelength about 300–600nm. As to direct band gap materials, the absorption width increase to 700nm (Fig 8(b) and 8(d)). From Fig 8(a)–8(b), it is clear that all the materials have good light absorption properties, especially for direct band gap semiconductors. While the light absorption property of Cs2ZrI6−xClx compounds is not well (Fig 8(c) and 8(d)). The absorption of visible light narrowed sharply with the increase of doping concentration, at the same time, peak value of absorption coefficient has decreased more than 40%. This may be caused by bigger radius of Cl- atom.
In general, Zr-based compounds Cs2ZrI6−xBrx are more suitable for solar cells. Considering with the band characters of materials, we can conclude that Cs2ZrI4Br2 is an excellent candidate for optoelectronic applications.
Conclusion
First principles calculation employing GGA-PBE method have been implemented to compute the electronic structures of 26 kinds of perovskites Cs2BI6−xXx, considering B = Hf and Zr cations, X as Cl and Br anion. The band gap can be regulated obviously by these ions. And all the materials suffer from indirect to direct band gap semiconductors under the impact of pressure. Calculated absorption coefficient trends identified that direct band gap materials of Cs2ZrI6−xBrx have good optical absorption properties, especially Cs2ZrI4Br2 is a perfect candidate for perovskite solar cells. In conclusion, the trends in band gaps and absorption characters with the influence of pressure and halide ion studied in the paper can be useful in guiding further work in halide perovskite solar cells.
References
- 1. Liang J, Liu J, Jin Z. All-Inorganic Halide Perovskites for Optoelectronics: Progress and Prospects. Solar RRL. 2017 Aug;1(10): 1700086.
- 2. Liang J, Wang C, Wang Y, Xu Z, Lu Z, Ma Y, et al. All-Inorganic Perovskite Solar Cells. Journal of the American Chemical Society. 2016 Nov;138(49): 15829–15832. pmid:27960305
- 3. Stoumpos CC, Malliakas CD, Kanatzidis MG. Semiconducting tin and lead iodide perovskites with organic cations: Phase transitions, high mobilities, and near-infrared photoluminescent properties. Inorganic Chemistry. 2013 Jul;52(15): 9019–9038. pmid:23834108
- 4. Wang Y, Zhang T, Xu F, Li Y, Zhao Y. A Facile Low Temperature Fabrication of High Performance CsPbI2Br All-Inorganic Perovskite Solar Cells. Solar RRL. 2018 Dec;2(1): 1700180.
- 5. Mao X, Sun L, Tao W, Chu T, Deng W, Han K. First-Principles Screening of All-Inorganic Lead-Free ABX3 Perovskites. The Journal of Physical Chemistry C. 2018 Mar;122(14): 7670–7675.
- 6. Correa-Baena JP, Abate A, Saliba M, Tress W, Jesper Jacobsson T, Gratzel M, et al. Advancements in perovskite solar cells: photophysics behind the photovoltaics. ENERGY AND ENVIRONMENTAL SCIENCE. 2014 May;7(8): 2518–2534.
- 7. Zhao C, Qiao X, Shao Q, Hassan M, Ma Z, Yao L. Synergistic effect of hydrogen peroxide and ammonia on lignin. Industrial Crops and Products. 2020 Apr;146: 112177.
- 8. Zhu T, Yang Y, Gong X. Recent Advancements and Challenges for Low-Toxicity Perovskite Materials. ACS Applied Materials and Interfaces. 2020 May;12(24): 26776–26811. pmid:32432455
- 9. Li N, Song L, Jia Y, Dong Y, Xie F, Wang L, et al. Stabilizing Perovskite Light-Emitting Diodes by Incorporation of Binary Alkali Cations. Advanced Materials. 2020 Mar;32(17): 1907786. pmid:32147854
- 10. Eames C, Frost JM, Barnes PRF, ORegan BC, Walsh A, Islam MS. Ionic transport in hybrid lead iodide perovskite solar cells. Nature Communications. 2015 Jun;6: 7497. pmid:26105623
- 11. Bass KK, McAnally RE, Zhou S, Djurovich PI, Thompsona ME, Melot BC. Influence of moisture on the preparation, crystal structure, and photophysical properties of organohalide perovskites. Chemical Communications. 2014 Oct;50: 15819–15822. pmid:25379572
- 12. Ni J, Wang W, Quintana M, Jia F, Song S. Adsorption of small gas molecules on strained monolayer WSe2 doped with Pd, Ag, Au, and Pt: A computational investigation. Applied Surface Science. 2020 Jun;514: 145911.
- 13. Noel NK, Stranks SD, Abate A, Wehrenfennig C, Guarnera S, Haghighirad AA,. Lead-free organic–inorganic tin halide perovskites for photovoltaic applications. Energy Environmental Science. 2014 May;7(27): 3061–3068.
- 14. Hao F, Stoumpos CC, Cao DH, Chang RPH, Kanatzidis MG. Lead-free solid-state organic–inorganic halide perovskite solar cells. Nature Photonics. 2014 May;8: 489–494.
- 15. Kumar MH, Dharani S, Leong WL, Boix PP, Prabhakar RR, Baikie T, et al. Lead-free Halide Perovskite Solar Cells with High Photocurrents Realized Through Vacancy Modulation. Advanced Materials. 2014 Sep;26(41): 7122–7127. pmid:25212785
- 16. Krishnamoorthy T, Ding H, Yan C, Leong WL, Baikie T, Zhang Z, et al. Lead-free germanium iodide perovskite materials for photovoltaic applications. Journal of Materials Chemistry A. 2015 Oct;3: 23829–23832.
- 17. Stoumpos CC, Frazer L, Clark DJ, Kim YS, Rhim SH, Freeman AJ, et al. Hybrid Germanium Iodide Perovskite Semiconductors: Active Lone Pairs, Structural Distortions, Direct and Indirect Energy Gaps and Strong Nonlinear Optical Properties. Journal of the American Chemical Society. 2015 May;137(21): 6804–6819. pmid:25950197
- 18. Ju MG, Sun G, Zhaob Y, Liang W. A computational view of the change in the geometric and electronic properties of perovskites caused by the partial substitution of Pb by Sn. Physical Chemistry Chemcal Physics. 2015 Jun;17: 17679–17687. pmid:26081196
- 19. Chen LJ. Synthesis and optical properties of lead-free cesium germanium halide perovskite quantum rods. RSC Advances. 2018 May;8: 18396–18399. pmid:35541141
- 20. Sheng SY, Zhao YY. First-principles study on the electronic and optical properties of strain-tuned mixed-halide double perovskites Cs2TiI6-xBrx. Physica B: Condensed Matter. 2022 Feb;626: 413522.
- 21. Zhao YY, Sheng SY. The electronic and optical properties of Cs2Ti1-xBxI6(B = Sn, Te, Se) with first principle method. Molecular Physics. 2022 Oct;120(22): e2129785.
- 22. Cai Y, Xie W, Ding H, Chen Y, Thirumal K, Wong LH, et al. Computational Study of Halide Perovskite-Derived A2BX6 Inorganic Compounds: Chemical Trends in Electronic Structure and Structural Stability. Chemistry of Materials. 2017 Aug;29(18): 7740–7749.
- 23.
M. Faizan, K. C. Bhamu, S. H. Khan, G. Murtaza, Xin He. Computational Study of Defect variant Perovskites A2BX6 for Photovoltaic Applications. arXiv. 2020 Apr;2002.07543.
- 24. Lin C, Zhao Y, Liu Y, Zhang W, Shao C, Yang Z. The bandgap regulation and optical properties of alloyed Cs2NaSbX6 (X = Cl, Br, I) systems with first principle method. Journal of Materials Research and Technology. 2021 Mar;11: 1645–1653.
- 25. Gonze X, Amadon B, Antonius G, Arnardi F, Baguet L, Beuken JM, et al. The Abinitproject: Impact, environment and recent developments. Computer Physics Communications. 2020 Mar;248: 107042.
- 26. Perdew J, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Physical Review Letters. 1998 Oct;77(18): 3865–3868.
- 27. Jollet F, Torrent M, Holzwarth N. Generation of Projector Augmented-Wave atomic data: A 71 element validated table in the XML format. Computer Physics Communications. 2014 Apr;185: 1246–1254.
- 28. Bernasconi M, Chiarotti GL, Focher P, Scandolo S, Tosatti E, Parrinello M. First-principle-constant pressure molecular dynamics. Journal of Physics and Chemistry of Solids. 1995 Mar;56(3): 501–505.
- 29. Li Y, Ullah S, Liu P, Chen Y, Wang L, Yang SE. Theoretical study on the electronic and optical properties of strain-tuned CsPb(I1-xBrx)3 and CsSn(I1-xBrx)3. Chemical Physics Letters. 2021 Jan;763: 138219.
- 30. Krarcha H, Bennecer B. Theoretical study of the structural, elastic, vibrational and thermal properties of perovskite halides Cs2TiBr6-xIx (x = 0, 2, 4, 6). Computational Condensed Matter. 2021 Dec;29: e00587.
- 31. Abutalib MM. Beryllium chloride monolayer as a direct semiconductor with a tunable band gap: First principles study. Optik. 2019 Jan;176: 579–585.
- 32. Liu D, Zha W, Yuan R, Chen J, Sa R. A first-principles study on the optoelectronic properties of mixed-halide double perovskites Cs2TiI6-xBrx. New J Chem. 2020 Jul;44(32): 13613–13618.