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High entropy perovskite oxides (HEPOs) have been proposed to serve as improved cathode materials for solid oxide fuel cells (SOFCs); however, the larger compositional design space introduced by HEPOs urges for a better understanding of the correlation among the composition, phase stability and resulting properties of HEPO cathodes. In this work, a series of LaMnO3 based HEPOs (HEALMOs) were designed systematically to investigate the effect of the A site high entropy composition on the structure and thermochemical/electrical properties of HEALMO materials. The results show that the high entropy effect manifests itself on top of the conventional doping effect. First of all, neither the Goldschmidt tolerance factor nor the cation size difference can be used simply to predict the formation ability of single-phase HEALMOs. Meanwhile, HEALMOs may exhibit higher crystallographic symmetry with much higher cation size differences and at Goldschmidt tolerance factor values deviating more largely from 1. Secondly, while high-temperature stability including both resistance to elemental segregation and chemical compatibility with 8YSZ is affected by the A site cation size difference in a similar way to that of conventional perovskite oxides, HEALMOs show much enhanced stability at larger A site cation size differences. Finally, high entropy contributes to the maintenance of electrical conductivity in the high temperature range. The optimum HEALMO with the composition of (La0.2Nd0.2Sm0.2Ca0.2Sr0.2)MnO3 exhibits a combination of excellent high-temperature stability and good electrical conductivity, highlighting its great potential as a promising cathode material for SOFCs.

Following on the heels of the remarkable lead halide perovskite optoelectronic materials, interest in lead-free halide perovskites has grown rapidly in the past decade. Double perovskite halides with the general formula A₂MᴵMᴵᴵᴵX₆ (where A is a large monovalent cation in the perovskite A site, Mᴵ is a univalent metal, Mᴵᴵᴵ is a trivalent metal, and X is a halide) represent one of the promising classes of such materials, and of these, the iodides are particularly interesting since their band gaps are expected to be similar to those found in the iconic lead-containing phases, APbI₃. However, the successful synthesis of A₂MᴵMᴵᴵᴵI₆ iodides appears to have been elusive. In this work, we examine the likelihood that double perovskite halides will form using a combination of the Goldschmidt tolerance factor and the radius ratio of the trivalent metals, Mᴵᴵᴵ, and rationalize the rarity of double perovskite iodides in terms of these descriptors. Using this model as the formability criterion, we predict the possible existence of more than 300 hitherto unknown double perovskite iodides with organic and inorganic cations in the A site.

This review focuses on the advancements in stability of perovskite solar cells under stress from ambient moisture, high temperatures, and UV light exposure. Moisture stability has been improved by utilizing several polymeric encapsulation methods, moisture-resistant hole transport layers (HTLs), CF4 plasma treatments, and perovskite grain crosslinking. Fluorinated encapsulation methods have proven especially successful, producing cells that maintained their PCE after 75 days at 50% RH and 5 mW cm−2 of UV radiation. Temperature destabilization has been hypothesized to occur as a result of perovskite phase transitions and the HTL dopant migration to the mesoporous TiO2 surface. Temperature-sensitive perovskites have been stabilized by tuning the Goldschmidt tolerance factor and introducing thermally resistant HTLs embedded in a polymeric matrix with polycarbonate acting as an effective thermal insulating matrix. UV light instabilities have also been shown to occur due to the photocatalysis of TiO2 and the TiO2 perovskite interface. The introduction of a Sb2S3 buffer or CsBr clusters as interface modifiers can stabilize the interface of TiO2 perovskite. Herein, we aim at highlighting the main processes that prevent perovskite degradation using polymers and interfacial modifiers.

In alkyl ammonium lead halide based perovskites, the replacement of toxic Pb+2 with a suitable nontoxic divalent metal cation without losing the photovoltaic performance is one of the prime challenges to the researchers. The understanding of the effect of replacing Pb+2 on the structural and optical properties of alkyl ammonium lead halide based perovskites, and thereafter correlating their photovoltaic performances, comprise a fundamental study which is important towards developing efficient and non-toxic solar cells. In the present work, we used a wet chemical process to substitute Pb+2 with Sn+2 in different proportions into CH3NH3PbxSn(1−x)Cl3. The value of the Goldschmidt tolerance factor, which is a measure of structural stability of the perovskite lattice, was estimated theoretically. The theoretical calculations were correlated further with the experimentally obtained x-ray diffraction patterns of the original and substituted perovskites. The optical properties of CH3NH3Pb(1−x)SnxCl3 (0 ≤ x ≤ 1) perovskite thin-films were investigated by the ultraviolet–visible (UV–vis) absorption spectroscopy. The bandgap energy (Eg) for CH3NH3Pb(1−x)SnxCl3(0 ≤ x ≤ 1) were estimated from the optical absorption spectra. The Urbach energy (EU) which predicts defects, disorder and crystalline imperfections within semiconducting thin-films were estimated for the prepared perovskite thin films. The steepness parameter which apprises about strength of electron–phonon (Ee–p) interaction within perovskites were also estimated from the optical absorbance spectra to understand the effect of replacing Pb+2 with Sn+2. In addition, the variations in the surface morphologies of the prepared perovskites were studied using scanning electron microscopy. The I–V characteristics of the different cells were analysed and, finally, we attempted to correlate their photovoltaic performances with the opto-structural properties.

Two-dimensional Ruddlesden–Popper perovskites (2D RPPs) have been considered as promising building blocks for optoelectronic applications owing to optical properties comparable to the ones of 3D perovskites, together with superior stability. In addition, the more flexible structure adopted by such perovskites leads to a relaxation of the Goldschmidt tolerance factor (τ) requirement. Herein, we compare the crystalline and electronic structures, as well as the photophysics of two 2D perovskite single crystals (n-BA)2(MA)2Pb3I10 (BMAPI) and (n-BA)2(EA)2Pb3I10 (BEAPI) (n-BA = n-butylamine) containing small A-cations (MA, methylammonium) and large A-cations (EA, ethylammonium), respectively. The latter presents a relaxed τ (τEA > 1) compared with the requirement of a stable phase in 3D perovskites (τ < 1). Such relaxed τ is beneficial from the structural flexibility of the long organic cation bilayer and the pronounced lattice distortions in the 2D perovskite structures. We further elucidate how the greater lattice distortions concurrently modulate the electronic structure as well as trap densities in these 2D RPPs. The electronic band gap (Eg) of BEAPI (2.08 ± 0.03 eV) is ∼0.17 eV larger than the one of BMAPI (1.91 ± 0.03 eV). This is mainly because of a shift in the valence band maximum associated with the expansion of the Pb–I bond length in BEAPI. In addition, the overall trap state densities for BMAPI and BEAPI are calculated to be ∼2.18 × 1016 and ∼3.76 × 1016 cm–3, respectively, as extracted from the time-resolved photoluminescence studies. The larger trap density in BEAPI can be attributed to the stronger interfacial lattice distortion that sets in when large EA cations are contained into the inorganic crystal lattice. (Less)

Inorganic halide perovskites such as cesium lead iodide (CsPbI3) have drawn tremendous attention, as their tunable band gaps are desirable for solar cells as well as light emitting diodes. However, due to their low Goldschmidt tolerance factor, the cubic phase of bulk CsPbX3—the variant with desirable band gap—is not stable in ambient, especially in humid air. Besides, the low solubility of CsX in precursor makes it difficult to control the film thickness and morphology of CsPbX3, which becomes another obstacle for the practical application of inorganic perovskite. Here, we report a polymer assisted deposition of high-quality CsPbI2Br film by spin-coating a polymer-blended CsPbI2Br precursor. The long-chained polymer increases the viscosity of the solution, which enables us to achieve a ca. 700-nm thick film with a low solution concentration of CsPbI2Br. Moreover, the polymer network helps to regulate the crystallization process and provides more crystallization sites for perovskite film, reducing grain size and thus improving the film coverage. Perovskite solar cells with the polymer network exhibit improved efficiency and reproducibility (0.72% standard deviation). Moreover, the device demonstrates excellent robustness against moisture and oxygen, and maintains 90% of its initial power conversion efficiency (PCEs) after aging 4 months in ambient conditions. The conception of polymer incorporation into inorganic perovskite films paves a way to further increase the performance, stability and reproducibility of inorganic perovskite devices.

International audience; The Goldschmidt tolerance factor in halide perovskites limits the number of cations that can enter their cages without destabilizing their overall structure. Here we have explored the limits of this geometric factor and found that the ethylammonium (EA) cations which lie outside the tolerance factor range can still enter the cages of the 2D halide perovskites by stretching them. The new perovskites allow us to study how these large cations occupying the perovskite cages affect the structural, optical, and electronic properties. We report a series of cation engineered 2D Ruddlesden-Popper lead iodide perovskites (BA)2(EAxMA1-x)2Pb3I10 (x = 0-1, BA is n-butylammonium, MA is methylammonium) by incorporating large EA cation in the cage. Analysis of the single-crystal structures reveals that the incorporation of EA in the cage significantly stretches Pb-I bonds, expands the cage, and induces a large octahedral distortion in the inorganic framework. Spectroscopic and theoretical studies show that such structural deformation leads to a blue-shifted bandgap, sub-bandgap trap states with wider energetic distribution, and stronger photoluminescence quenching. These results enrich the family of 2D perovskites and provide new insights for understanding the structure-property relationship in perovskite materials.

Three-dimensional (3D) halide perovskites (HPs) are in the spotlight of materials science research due to their excellent photonic and electronic properties suitable for functional device applications. However, the intrinsic instability of these materials stands as a hurdle in the way to their commercialization. Recently, two-dimensional (2D) HPs have emerged as an alternative to 3D perovskites, thanks to their excellent stability and tunable optoelectronic properties. Unlike 3D HPs, a library of 2D perovskites could be prepared by utilizing the unlimited number of organic cations since their formation is not within the boundary of the Goldschmidt tolerance factor. These materials have already proved their potential for applications such as solar cells, light-emitting diodes, transistors, photodetectors, photocatalysis, etc. However, poor charge carrier separation and transport efficiencies of 2D HPs are the bottlenecks resulting in inferior device performances compared to their 3D analogs. This minireview focuses on how to address these issues through the adoption of different strategies and improve the optoelectronic properties of 2D perovskites.

The stability of organic–inorganic halide perovskite films plays an important role for their successful incorporation as absorber materials in solar cells under realistic operation conditions. While light-induced effects have been observed and traced to phase segregation, the impact of different stressors simultaneously is mostly unexplored. In this work, we investigate the combined influence of light and elevated temperature on the performance of mixed-cation mixed-halide perovskites. In particular, we compare the effect of different A-site cations on the photoluminescence (PL) properties and film stability when both stressors are used simultaneously. We find two pathways underlying the PL peak reduction and PL shift in the optical properties. For perovskite films composed of formamidinium and methylammonium as A-site cations, we can correlate the decrease in film performance to the formation of Pb(I,Br)2 and an increase in electron–phonon interactions. Similarly, Rb doping in the perovskite film exhibits comparable results. Contrary, using Cs as an additional A-site cation greatly enhances the overall performance and results in more stable film structures which indicates that Cs is effective in stiffening the perovskite lattice, which can be attributed to a better size match for the Pb(I,Br)3 sublattice as predicted by the Goldschmidt tolerance factor. These findings suggest that it is of importance to carefully select stressors when assessing performance related parameters of perovskite solar cells.

Lead free halide double perovskites have emerged as a stable alternative to lead based hybrid perovskites. Double perovskites involving cations like In3+, Sb3+ and Bi3+ are synthesized by varying the metal and halide composition and their optical properties are studied. The possibility of formation of double perovskites in terms of radius ratio, Goldschmidt tolerance factor and octahedral factor are discussed. Br–Cl mixed halide perovskites are synthesized via antisolvent precipitation reactions. XRD, EDAX, XPS and Raman spectroscopy studies confirmed the successful synthesis of the double perovskites, which have shown good stability under ambient conditions for months. Chlorine containing systems have shown better stability. Cs2AgInCl6, a direct bandgap material, has shown the highest stability and with addition of other halides the stability of the perovskites was observed to be decreased. The charge carrier relaxation observed from the photoluminescence (PL) spectra indicated the presence of trap states and disorder in the structures. Bi and Sb based double perovskites are indirect band gap materials, but have shown emission peaks at energy very close to the bandgap energy, which may be related to the pseudo-direct bandgap nature. This study has shown that the band gap and luminescence properties of the double perovskites can be easily tuned by varying halogens and by incorporating disorder in the structures and are suitable for optoelectronic applications.

Nonlinear nonradiative recombination processes are considered as a main obstacle to efficient lead halide perovskite light emitters as light emitting diodes and lasers. In this work, crystal structure ideality, described by the Goldschmidt tolerance factor, impact on Auger and bimolecular recombination rates in spin-coated mixed-cation CsxMA1–xPbBr3 and CsxFA1–xPbBr3 perovskite layers was investigated. The excitation-dependent carrier lifetime and diffusion coefficient were determined using optical pump–probe techniques: time-resolved photoluminescence and light-induced transient grating. Layers with a Goldschmidt tolerance factor closer to unity revealed Auger and bimolecular recombination rates smaller by up to an order of magnitude. The bimolecular coefficient (0.6–5 × 10–10 cm3/s) increased simultaneously with the Auger coefficient (0.05–2 × 10–27 cm6/s) upon increase of x and simultaneous decrease of tolerance factor, due to variation in the localized carrier population and Rashba splitting. A larger...

All-inorganic Br-rich perovskite photovoltaics with excellent stability have gained ever-increasing attention despite their slightly lower efficiency. Nowadays, trace heteroatom substitution has become a plausible approach to optimize perovskite properties as well as device performance. However, the substitution is limited by the Goldschmidt tolerance factor (t, 0.8

The properties of single-doped BaCe0.9Y0.1O3–δ and materials co-doped with 5 mol % of different cations (In3+, Zr4+ and Nb5+) with the general formula BaCe0.85Y0.1M0.05O3–δ were compared to examine the influence of dopants on the electrolyte properties. The samples were synthesized by the citric-nitric autocombustion method. BaCe0.85Y0.1In0.05O3–δ was successfully sintered at 1400 °C for 5 h in air, while a complete sintering of the other materials was carried out at 1550 °C. This makes the doping with In a preferable method since sintering temperatures below 1500 °C can limit BaO evaporation. The total conductivities (σ) calculated from the electrical measurements at 700 °C in wet hydrogen decreased in the following order: BaCe0.9Y0.1O3–δ > BaCe0.85Y0.1Zr0.05O3–δ > BaCe0.85Y0.1Nb0.05O3–δ > BaCe0.85Y0.1In0.05O3–δ. The stability of the ceramics exposed to a 100% CO2 atmosphere at 700 °C for 5 h was examined by X-ray analysis. It was observed that only BaCe0.85Y0.1In0.05O3–δ could sustain the aggressive environment containing traces of secondary phases, while the other samples were partially or significantly decomposed. By taking into account the values of the Goldschmidt tolerance factor (t) and dopant electronegativity (χ), it was found that the dopant electronegativity had a decisive role in inhibiting the carbonation of the ceramics.

Recent achievements, based on lead (Pb) halide perovskites, have prompted comprehensive research on low-cost photovoltaics, in order to avoid the major challenges that arise in this respect: Stability and toxicity. In this study, device modelling of lead (Pb)-free perovskite solar cells has been carried out considering methyl ammonium tin bromide (CH3NH3SnBr3) as perovskite absorber layer. The perovskite structure has been justified theoretically by Goldschmidt tolerance factor and the octahedral factor. Numerical modelling tools were used to investigate the effects of amphoteric defect and interface defect states on the photovoltaic parameters of CH3NH3SnBr3-based perovskite solar cell. The study identifies the density of defect tolerance in the absorber layer, and that both the interfaces are 1015 cm−3, and 1014 cm−3, respectively. Furthermore, the simulation evaluates the influences of metal work function, uniform donor density in the electron transport layer and the impact of series resistance on the photovoltaic parameters of proposed n-TiO2/i-CH3NH3SnBr3/p-NiO solar cell. Considering all the optimization parameters, CH3NH3SnBr3-based perovskite solar cell exhibits the highest efficiency of 21.66% with the Voc of 0.80 V, Jsc of 31.88 mA/cm2 and Fill Factor of 84.89%. These results divulge the development of environmentally friendly methyl ammonium tin bromide perovskite solar cell.

Using first-principles calculations, we show that $\mathrm{Cs}B{X}_{3}$ halides with $B=\text{Sn}$ or Pb undergo octahedral rotation distortions, while for $B=\text{Ge}$ and Si, they undergo a ferroelectric rhombohedral distortion accompanied by a rhombohedral stretching of the lattice. We show that these are mutually exclusive at their equilibrium volume although different distortions may occur as functions of lattice expansion. The choice between the two distortion modes is in part governed by the Goldschmidt tolerance factor. However, another factor explaining the difference between Sn and Pb compared with Ge and Si is the stronger lone-pair character of Ge and Si when forced to be divalent as is the case in these structures. The lone-pair chemistry is related to the off centering. While the Si-based compounds have not yet been synthesized, the Ge compounds have been established experimentally. As a final test of the importance of the tolerance factor we consider $\mathrm{RbGe}{X}_{3}$, which has smaller tolerance factor than the corresponding $\mathrm{CsGe}{X}_{3}$ because Rb is smaller than Cs. We find that it can lower its energy by both rotations or rhombohedral off-centering distortions but the latter lower the energy slightly more efficiently.

Perovskite lanthanum mangantites La0.825Sr0.175Mn0.9(Fe1-xNix)0.1O3 with x = 0; 0.5; 1 has been successfully prepared with the sol-gel method. The XRD pattern shows that all samples are single phase with no impurities. The result of refinement measurements using the Rietveld method showed that the samples formed rhombohedral with group space R-3c. the addition of doping concentration (x) does not change the crystal structure, but only causes a decrease in lattice parameter, unit cell volume, increases Mn – O – Mn bond angle, and changes the length of Mn – O bond. The Goldschmidt tolerance factor (τ) is calculated to define the stability of the crystal structure. It was found a little uniqueness of the calculation that the τ obtained for all samples has a slight difference with the reference of the τ. In the reference of τ, for the value of τ < 0.96 the material will have an orthorombic structure. Whereas for 0.89 < τ < 1, the material will have a rhombohedral structure. However, in the material La0.825Sr0.175Mn0.9(Fe1-xNix)0.1O3 it was found that the structure formed was rhombohedral with τ = 0.847 – 0.876. This is because the material is in the orthorhombic and rhombohedral phase transition regions.

This work shows that in the series of the Ruddlesden--Popper nickelate solid solution $A$${}_{4\ensuremath{-}x}$${B}_{x}$Ni${}_{3}$O${}_{10}$ ($A$ and $B$ = La, Pr and Nd; $x$ = 0, 1, 2 and 3) the transition temperatures as well as the room-temperature resistivities strongly correlate with the Goldschmidt tolerance factor t.

International audience; Organic-inorganic hybrid halide perovskites are promising semiconductors with tailorable optical and electronic properties. The choice of A-site cation to support a three-dimensional (3D) perovskite structure AMX3 (where M is a metal, and X is a halide) is limited by the geometric Goldschmidt tolerance factor. However, this geometric constraint can be relaxed in two-dimensional (2D) perovskites, providing us an opportunity to understand how various the A-site cations modulate the structural properties and thereby the optoelectronic properties. Here, we report the synthesis and structures of single-crystals (BA)2(A)Pb2I7 where BA = butylammonium, and A = methylammonium (MA), formamidinium (FA), dimethylammonium (DMA) or guanidinium (GA), a series of A-site cation varied in size. Single-crystal X-ray diffraction reveals that the MA, FA, and GA structures crystallize in the same Cmcm space group, while the DMA imposes the Ccmb space group. We observe that as the A-site cation becomes larger, the Pb−I bond continuously elongates, expanding the volume of the perovskite cage, equivalent to exerting “negative pressure” on the perovskite structures. Optical studies and DFT calculations show the Pb−I bond length elongation reduces overlap of the Pb s- and I p-orbitals and increases the optical bandgap, while Pb−I−Pb angles play a secondary role. Raman spectra show lattice softening with increasing size of the A-site cation. These structural changes with enlarged A cations result in significant decreases in photoluminescence intensity and lifetime, consistent with a more pronounced nonradiative decay. Transient absorption microscopy (TAM) results suggest that the PL drop may derive from a higher concentration of traps or phonon-assisted nonradiative recombination. The results highlight that extending the range of Goldschmidt tolerance factors for 2D perovskites is achievable, enabling further tuning of the structure-property relationships in 2D perovskites.

A linear relationship between the standard enthalpy of formation from binary oxides, Δ f H ox , and the Goldschmidt tolerance factor, t , for some A II B IV O 3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce, Pr, Tb, U, Pu, Am) perovskite oxides was used for estimation of Δ f H ox of Pr-substituted barium zirconates BaZr 1– x Pr x O 3 . A dependence of the relative change of the standard entropies, S 298 , on the relative change of the molar volumes in the reactions of formation of A II B IV O 3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce) from binary oxides was also found to be linear. Using this dependence, a relatively precise method of estimating S 298 was proposed, and S 298 of BaPrO 3 was calculated as (162.8 ± 2.8) J·mol -1 ·K -1 . Knowing S 298 of BaPrO 3 and using the literature data for S 298 of BaZrO 3 , the values of S 298 of BaZr 1– x Pr x O 3 were predicted on the assumption that BaZr 1– x Pr x O 3 is a regular or ideal solution of BaPrO 3 in BaZrO 3 as evidenced by the very small enthalpy of mixing calculated based on the estimated Δ f H ox . The values of standard entropy changes, Δ f S ox , and Gibbs energy changes, Δ f G ox , for the reactions of formation of BaZr 1– x Pr x O 3 from BaO, ZrO 2 and PrO 2 were also estimated. Substituting Pr for Zr in BaZr 1– x Pr x O 3 results in Δ f H ox and Δ f G ox becoming more positive, indicating the decrease of the relative stability with respect to the corresponding binary oxides. Expanded uncertainties of the estimated values of Δ f H ox and Δ f G ox are equal to 14 kJ∙mol -1 , and those of S 298 and Δ f S ox – less than 2.8 J∙mol -1 ·K -1 and 3.5 J∙mol -1 ·K -1 , respectively, for BaZr 1– x Pr x O 3 ( x = 0.0–1.0).

Orthorhombic V2O5 is a promising Mg battery cathode material, and reversible intercalation in the layered α-phase has been claimed experimentally. However, these results, based on electrochemistry and XRD, are controversial. Previous computational studies have predicted high activation barriers (∼1 eV) for ionic migration in α-V2O5, although improved Mg2+ mobility is expected in the δ-phase. Here, hybrid-exchange density functional theory is used to discuss structure, stability and intercalation in the α and δ phases, beginning with a model system with MV2O5 stoichiometry, and varying ionic radius of the M cations. The relative stability of the two phases upon intercalation of M is rationalised through a tolerance factor-like behavioural trend, providing a framework for phase selection using intercalants of different ionic size. This tolerance factor behaviour is due to the presence of ferroelectrically distorted (2 × 2 × 2) perovskite blocks within the α-V2O5 structure. The δ-phase is found to undergo a barrierless phase change to α in fully charged (de-intercalated) MgxV2O5 (x = 0), indicating that stabilisation of δ-MgxV2O5 is required at low x if the δ phase is to be retained for higher Mg mobility. By employing dispersion interactions to accurately reproduce the interlayer distance, activation barriers for ion migration are found to be higher than reported in previous studies, clarifying questions regarding the extent of Mg intercalation that can be achieved experimentally. Interlayer ions are found to lower activation barriers for Mg2+ mobility by up to ∼330 meV in the α phase by expanding the interlayer space. The results address open questions about the electrochemical performance of orthorhombic V2O5 as Mg battery cathode material, and indicate atomic level mechanisms that activate ionic mobility in layered V2O5.

Understanding the band alignment at oxide surfaces is of great importance for designing oxide-surface-based electronic, catalytic, and photocatalytic applications. We systematically investigate the band alignment of (001) surfaces of $A(\mathrm{II})B(\mathrm{IV}){\mathrm{O}}_{3}$ perovskites ($A=\mathrm{Ca}$, Sr, Ba, Pb; $B=\mathrm{Ti}$, Zr, Hf, Ge, Sn) through first-principles calculations using semilocal and hybrid functionals. The results are discussed with an emphasis on the effects of surface reconstruction on the band alignment. Reconstructed stoichiometric surfaces are generated by an evolutionary algorithm with surface energy minimization for various surface periodicity units by taking the orthorhombic phase of $\mathrm{CaTi}{\mathrm{O}}_{3}$, the tetragonal phase of $\mathrm{SrTi}{\mathrm{O}}_{3}$, and the cubic phases of $\mathrm{SrTi}{\mathrm{O}}_{3}$ and $\mathrm{BaSn}{\mathrm{O}}_{3}$ as representatives. Two types of reconstruction patterns are obtained as energetically favorable configurations common to these phases, which are composed of half-$A\mathrm{O}$ and -$B{\mathrm{O}}_{2}$ topmost layers, respectively. These reconstructed stoichiometric surfaces have energies comparable to those of nonstoichiometric surfaces, with full $A\mathrm{O}$ or $B{\mathrm{O}}_{2}$ termination under specific chemical potential conditions in $\mathrm{CaTi}{\mathrm{O}}_{3}$ and $\mathrm{SrTi}{\mathrm{O}}_{3}$. We systematically calculate the positions of the valence-band maxima and the conduction-band minima with respect to the vacuum level, namely, the ionization potentials and the electron affinities, for the reconstructed stoichiometric and the nonstoichiometric surfaces of $A(\mathrm{II})B(\mathrm{IV}){\mathrm{O}}_{3}$ perovskites. The ionization potentials and electron affinities at the reconstructed surfaces well describe the termination-plane dependencies of experimentally reported values. The surface band positions are found to show an approximately linear trend against the Goldschmidt tolerance factor, with the sign of slopes opposite to each other for the two types of reconstruction patterns. This tendency is explained by the tolerance-factor dependency of surface rumpling that significantly modifies the surface dipole, although the band positions of $A=\mathrm{Pb}$ systems exhibit a larger deviation from an expected trend due to Pb lone-pair states.

The two-dimensional (2D) hybrid perovskites, in particular the Ruddlesden-Popper (RP) phase, exhibit excellent optoelectronic properties, higher flexibility in the employed large organic cations, and an enhanced stability against the environmental agents compared to the three-dimensional (3D) perovskites. However, the small organic cations inserted into the octahedral voids have been limited so far to those three fulfilling the Goldschmidt tolerance factor (t) despite the relaxed structure of the 2D RP perovskites. In this work, the incorporation of the large guanidinium (Gua) cation into the octahedral sites of the "perovskite slabs"has been explored for the first time in 2D RP perovskites. Thus, the methylammonium (MA) cation in the PEA2MA2Pb3I10 perovskite (PEA = phenylethylammonium) has been gradually substituted by the Gua cation to synthesize thin films of the mixed-cation PEA2(MA1-xGuax)2Pb3I10 perovskite. X-ray diffraction (XRD) and grazing-incidence wide-angle X-ray scattering (GIWAXS) measurements have revealed a regular expansion of the unit cell when increasing the Gua content up to 90%, proving the sequential insertion into the lattice of the Gua having a larger ionic radius than that of the MA cation. Furthermore, the preferential orientation of the PEA2MA2Pb3I10 perovskite films with the (hk0) planes parallel to the substrate is maintained up to a limit value of 60% Gua content. Importantly, the combined analysis of the steady-state and time-resolved absorption and photoluminescence (PL) spectra has revealed a change in the distribution of the n-members of the 2D RP perovskites toward phases with lower n values upon increasing the Gua content. The position and intensity of the photoluminescence can be modulated within the low-dimensional perovskites (n = 2, 3, 4, and 5) at high Gua content (≥70%). We have fabricated solar cells based on the mixed-cation PEA2(MA1-xGuax)2Pb3I10 perovskites with power conversion efficiency (PCE) values similar to those of the reference cell (∼2.5%) up to percentages of Gua of 20%. The unencapsulated devices have shown a significant enhancement in the stability after 750 h, demonstrating the positive effect of the Gua cation on the degradation of the 2D RP perovskites., G.d.M. thanks the Ministry of Economy and Competitiveness for a “Ramón y Cajal” contract (RYC-2013-12772). S.R.-T. thanks the Ministry of Education, Culture and Sport for an FPU fellowship (FPU18/04452). This work was financially supported by the Ministerio de Economía y Competitividad (MINECO) through project CTQ2017-84221-R, cofinanced with the FEDER funds. We are grateful to Dr. Eduardo Espinosa Victor and Prof. Alejandro Rodríguez Pascual for their assistance with infrared spectroscopy. We also want to thank Prof. Juan Antonio Anta and Dr. Lidia Contreras-Bernal for their help in the fabrication of the solar devices and with the SEM measurements. Finally, we would like to appreciate the support from Dr. Eva García-Frutos in the realization of the NMR experiments

Antiperovskites have recently been attracting considerable attention because of their intriguing physical properties. We theoretically investigate polymorphism of mixed-anion antiperovskites ${M}_{3}^{2+}{X}^{3\ensuremath{-}}{\mathrm{N}}^{3\ensuremath{-}}\phantom{\rule{4pt}{0ex}}(M$ = Mg, Ca, Sr, Ba; $X$ = P, As, Sb, Bi) using the seven representative crystal-structure prototypes of $AB{Z}_{3}$ compounds. Stable crystal-structure exploration for four unreported compounds $({\mathrm{Mg}}_{3}\mathrm{PN},{\mathrm{Sr}}_{3}\mathrm{PN},{\mathrm{Ba}}_{3}\mathrm{PN}$, and ${\mathrm{Mg}}_{3}\mathrm{BiN})$ is also performed using ab initio evolutionary crystal-structure-search and lattice-dynamics calculations, which have consistently identified antiperovskite phases as their ground states. As a result of crystal-structure exploration, the orthorhombic perovskite $Pbnm$ phases of ${\mathrm{Mg}}_{3}\mathrm{PN},{\mathrm{Sr}}_{3}\mathrm{PN}$, and ${\mathrm{Ba}}_{3}\mathrm{PN}$ are obtained, while the cubic perovskite $Pm\overline{3}m$ phase is stable in ${\mathrm{Mg}}_{3}\mathrm{BiN}$. We show that the octahedral rotational distortions in ${M}_{3}\mathrm{PN}$ and ${M}_{3}\mathrm{AsN}$ reduce their Madelung energies, which is not common in conventional perovskites. Further, we estimate the ionic radii of anionic nitrogen ${\mathrm{N}}^{3\ensuremath{-}}$ and pnictogen ${X}^{3\ensuremath{-}}$ to explain the chemical trends for the phase stability, lattice distortion amplitude, total energies, valence bandwidths, and band gaps of ${M}_{3}X\mathrm{N}$ using the Goldschmidt tolerance factor. We also report the electronic structures of ${M}_{3}X\mathrm{N}$ with and without the rotational distortions and spin-orbit coupling. The valence bands of ${\mathrm{Mg}}_{3}X\mathrm{N}$ are created mainly from $p\text{\ensuremath{-}}p$ hybridization, whereas those of ${M}_{3}^{\ensuremath{'}}X\mathrm{N}\phantom{\rule{4pt}{0ex}}({M}^{\ensuremath{'}}$ = Ca, Sr, Ba) are constructed mainly from $d\text{\ensuremath{-}}p$ hybridization. We then explain the mechanism of the band-gap changes owing to the rotational distortions and spin-orbit coupling. The effective masses for the relevant ground-state phases of ${M}_{3}X\mathrm{N}$ are found to be comparable to preexisting compound semiconductors. Finally, we propose potential applications of earth-abundant semiconductors ${\mathrm{Mg}}_{3}\mathrm{PN}$ and ${\mathrm{Sr}}_{3}\mathrm{PN}$ as light absorbers and emitters utilizing their direct-type band structures and high optical absorption coefficients. The present study provides a clear picture and recipe for the understanding and design of mixed-anion antiperovskites.

International audience; Large organic A cations cannot stabilize the 3D perovskite AMX3 structure because they cannot be accommodated in the cubo-octhedral cage (do not follow the Goldschmidt tolerance factor rule), and they generally template low-dimensional structures. Here we report that the large di-cation aminomethylpyridinium (AMPY), can template novel 3D structures which resemble conventional perovskites. They have the formula (xAMPY)M2I6 (x = 3 or 4, M = Sn2+ or Pb2+) which is doubled the AMX3 formula. However, because of the steric requirement of the Goldschmidt tolerance factor rule, it is impossible for (xAMPY)M2I6 to form proper perovskite structures. Instead, a combination of corner-sharing and edge-sharing connectivity is adopted in these compounds leading to the new 3D structures. DFT calculations reveal that the compounds are indirect-bandgap semiconductors with direct bandgaps presenting at slightly higher energies and dispersive electronic bands. The bandgaps of the Sn and Pb compounds are ~ 1.7 eV and 2.0 eV, respectively, which is slightly higher than the corresponding AMI3 3D perovskites. The Raman spectra for the compounds are diffuse, with a broad rising central peak at very low frequencies around 0 cm-1, a feature that is characteristic of dynamical lattices, highly anharmonic, and dissipative vibrations very similar to the 3D AMX3 perovskites. Devices of (3AMPY)Pb2I6 crystals exhibit clear photoresponse under ambient light without applied bias, reflecting a high carrier mobility (μ) and long carrier lifetime (τ). The devices also exhibit sizable X-ray generated photocurrent with a high μτ product of ~1.2×10-4 cm2 /V and an X-ray sensitivity of 207 μC Gy-1 cm-2.

Sustainable energy supply is a crucial issue in times of climate change and receding fossil energy reserves. The emerging field of solar-driven thermochemical H2O and CO2 splitting cycles is a very promising approach to address this challenge. Providing low oxygen partial pressures is crucial in these processes. This issue is tackled by either high vacuum pumping or inert-gas sweeping. Both techniques come with a rather high energy penalty, leading to lower efficiencies of the whole process. Thermochemical oxygen pumping offers great potential to efficiently reduce oxygen partial pressures in these splitting cycles. In this work a material investigation campaign focusing on earth-abundant, cheap and non-toxic perovskites is presented. The experimental results are complemented with an approach to correlate this performance to inherent material properties, and in particular to the tolerance factor. In this framework, Ca-Mn-based perovskite compositions were demonstrated to function effectively as combined thermochemical oxygen-pumping and energy storage materials. Not only an almost two-fold increase of the reduction extent of ceria as a water splitting material was achieved due to the operation of perovskites as oxygen pumping materials, but this increase was rendered three-fold by applying a suitable temperature swing operation strategy. In parallel, the perovskites’ energy storage density can be significantly increased by exploiting specific phase transitions that can be rationally explained via the Goldschmidt tolerance factor. Hence, the work offers a novel approach to reach low oxygen partial pressures with minimal energy penalties and a derived model to evaluate occurring phase transitions and their corresponding heat effects.

Hybrid improper ferroelectricity, which utilizes nonpolar but ubiquitous rotational/tilting distortions to create polarization, offers an attractive route to the discovery of new ferroelectric and multiferroic materials because its activity derives from geometric rather than electronic origins. Design approaches blending group theory and first principles can be utilized to explore the crystal symmetries of ferroelectric ground states, but in general, they do not make accurate predictions for some important parameters of ferroelectrics, such as Curie temperature (TC). Here, we establish a predictive and quantitative relationship between TC and the Goldschmidt tolerance factor, t, by employing n = 2 Ruddlesden–Popper (RP) A3B2O7 as a prototypical example of hybrid improper ferroelectrics. The focus is placed on an RP system, (Sr1–xCax)3Sn2O7 (x = 0, 0.1, and 0.2), which allows for the investigation of the purely geometric (ionic size) effect on ferroelectric transitions, due to the absence of the second-ord...

Summary Cubic phase stabilization is extremely important for the application of cesium lead halide inorganic perovskite materials into fabrication of perovskite solar cells. Methods on how to stabilize inorganic perovskite phase have been discussed in this review. The increase of surface energy of perovskite grains can stabilize the cubic perovskite phase simply by decreasing the grain size or reducing the dimension of perovskite crystals. The substitution of cations or anions in the perovskite crystal lattice by different elements, followed by the rule of Goldschmidt tolerance factor, can also produce stable inorganic perovskites with enhanced electronic and optical properties. Meanwhile, an abundant choice of appropriate elements for the substitution can fundamentally enrich the library of stable inorganic perovskites.

The density functional theory based full-potential linear-augmented-plane-wave plus local-orbital method has been used to study the physical properties of PbSnO 3 in hypothetical cubic perovskite. An external pressure up to 40 GPa has been applied on PbSnO 3 to realize the variation in its electronic band structure and the subsequent optical properties. The stability of the PbSnO 3 has been investigated by the mechanical properties, the enthalpy of formation and Goldschmidt tolerance factor. Moreover, the Born criteria have been adopted to justify the mechanical stability of the PbSnO 3 perovskite. We show that the electronic bandgap of PbSnO 3 can be tailored from indirect to direct band gap at high symmetry (X-X) direction at an external pressure of magnitude ~ 26 GPa. The effect of pressure on the optical properties has been studied in terms of dielectric function, absorption, refraction, reflection, and optical loss factor. The application of hydrostatic pressure has shifted the maximum absorption toward the visible range, revealing that PbSnO 3 can be used for high- pressure optoelectronic applications.

In this study, we have developed a protocol for exploring the vast chemical space of possible perovskites and screening promising candidates. Furthermore, we examined the factors that affect the band gap energies of perovskites. The Goldschmidt tolerance factor and octahedral factor, which range from 0.98 to 1 and from 0.45 to 0.7, respectively, are used to filter only highly cubic perovskites that are stable at room temperature. After removing rare or radioactively unstable elements, quantum mechanical density functional theory calculations are performed on the remaining perovskites to assess whether their electronic properties such as band structure are suitable for solar cell applications. Similar calculations are performed on the Ruddlesden-Popper phase. Furthermore, machine learning was utilized to assess the significance of input parameters affecting the band gap of the perovskites.

Although significant progress has been made on the performance of inorganic–organic perovskite solar cells (PSCs), the commercialization of these PSCs is seriously hampered by their poor thermal/moisture stability. Inorganic cesium-based perovskites with relatively high phase stability are ideal alternatives although they still suffer from low photoelectrical conversion efficiency (PCE). Herein, for the first time, fluorine (F) was introduced into the X-site of ABX3 to modulate bulk-phase heterostructures and tolerance factors of inorganic CsPbBrI2−xFx with significantly enhanced PCE and stability. The α-/δ-phase heterojunction is beneficial for efficient dissociation of excitons and charge transport driven by the matched energy band offsets. The lifetime of charge carriers is prolonged due to the retarded charge recombination, which is evidenced by time resolved photoluminescence results; this results in improved short-circuit current density (JSC). In view of the Goldschmidt tolerance factor, partial substitution of iodine by fluorine (with a smaller ionic radius) in the ABX3 structure enlarges the inadequate index to stabilize the α-CsPbBrI2 structure. The CsPbBrI1.78F0.22 PSC with an optimized α-/δ-phase heterostructure displays a superior PCE of up to 10.26% and structural stability against moisture and time. This study sets up a new avenue for designing high-performance PSCs for potential industrial applications.

We have explored that the phase transition of colloidal perovskite CsPbI3 quantum dot (QD) during synthesis and purification processes are mainly induced by the increase of particle size (crystal growth). To stabilize the cubic structure, the metal cations Mn2+ and Zn2+ with smaller ion radius than that of Pb2+ were doped into the QD. These not only caused the lattice constriction and increased the Goldschmidt tolerance factor of perovskite structure, but also enhanced the Pb-I binding energy, all of which improve the tolerance of phase transition induced by the growth of crystal size during purification process. Besides, the doped QD solutions and films show fewer defects and lower trap density than those of the undoped samples, owing to the alleviation of lattice distortion. The results reveal that the Zn-doped and Mn-doped QD solar cells display power conversion efficiency of 13.5% and 12.0%, respectively, much higher than that of the control device.

Composition engineering plays an important role in generating novel properties and decreasing the lead (Pb) toxicity for halide perovskite materials. To find out the modulation effect introduced by the composition engineering, namely, B'-site co-metal ions, in (MA)2AgBi1-xSbxBr6 systems with various Bi/Sb ratios of x=0, 0.25, 0.75, 1.00, series of theoretical simulations and analyses are carried out. For the (MA)2AgBi1-xSbxBr6 systems, the Goldschmidt tolerance factor t and the octahedral factor μ indicate that all samples are in a standard double perovskite structure with alternating AgBr6 and Bi/SbBr6 octahedra. The calculated electronic structures show that the band gap of (MA)2AgBi1-xSbxBr6 decreases with the increase of Sb content, but the indirect band gaps are maintained for all samples. By analyses of the imaginary part ɛ2(ω) of dielectric function and the absorption spectra, we find that all (MA)2AgBi1-xSbxBr6 systems show absorption in the visible-light region. All these results indicate that the composition engineering adopted in this paper is an effective strategy to modulate the optical properties of (MA)2AgBi1-xSbxBr6 systems and may open a new way to put it into applications in the fields of solar cells and other optoelectronic devices.

Structural, electrical, and optical properties, as well as the thermal stability, of lead free mixed halide perovskites, Cs2InBr5-yXy·H2O (X = Cl, I; y = 0, 1, 2, 3, 4, 5) and Cs2InBr6-x·xH2O (x = 1, 2, 3, 4) were investigated using first principles calculation. The structural stability of all studied pervoskites has been estimated by the calculation of structural parameters, Goldschmidt tolerance factor, and the octahedral factor. The obtained band gap of I-doped Cs2InBr5-yIy·H2O systems are 2.049, 1.726, 1.581, 1.475 and 1.272 eV with y =1, 2, 3, 4, 5, lower than 2.391 eV of Cs2InBr5·H2O. The absorption spectra were also calculated to evaluate optical properties of Cs2InBr5-yXy·H2O, which presents an obvious red-shift for I-doped perovskites in the visible region, while a blue-shift for Cl-doped perovskites. The formation energies of Cs2InBr5-yXy·H2O were calculated and the obtained negative values determined their good thermodynamic stability, except Cs2InBrI4·H2O and Cs2InI5·H2O with the extremely small positive values. In addition, the influence of the amount of crystal water on the properties of Cs2InBr6-x·xH2O was also considered. The defect formation energies of Cs2InBr6-x·xH2O were calculated and the obtained negative values indicate their appropriate stability. In brief, Cs2InBr3I2·H2O and Cs2InBr4·2H2O are two optimal candidates among all the studied systems for the photovoltaic application. These results provide some ideas for understanding various properties of mixed halide perovskites.

A set of three dimensionally ordered (3-DOM) structure materials based on LaFe 1−x Ti x O 3 with different amount of titanium (from 0 to 20 mol %) were synthesized and investigated. It was found that titanium addition converts the LaFeO 3 structure from orthorhombic into cubic phase and those results stay in correlation with Goldschmidt tolerance factor calculations. To evaluate the chemical stability of synthesized materials the corrosion tests (720 h at ambient temperature in pure CO 2 and H 2 O 100% RH) were performed. Both FTIR and TGA-QMS techniques were used to characterize the samples prior and after the CO 2 /H 2 O exposition. It was found that during the test lanthanum carbonate is formed. Furthermore the intensity of carbonates vibrations correlate with the increase of titanium addition, which stays in agreement to TGA-QMS results. Additionally, average metal oxygen bond energy (ABE) calculations also substantiate that titanium addition leads to higher phase stability.

This Perspective outlines basic structural and optical properties of lead halide perovskite colloidal nanocrystals, highlighting differences and similarities between them and conventional II–VI and III–V semiconductor quantum dots. A detailed insight into two important issues inherent to lead halide perovskite nanocrystals then follows, namely, the advantages of defect tolerance and the necessity to improve their stability in environmental conditions. The defect tolerance of lead halide perovskites offers an impetus to search for similar attributes in other related heavy metal-free compounds. We discuss the origins of the significantly blue-shifted emission from CsPbBr3 nanocrystals and the synthetic strategies toward fabrication of stable perovskite nanocrystal materials with emission in the red and infrared parts of the optical spectrum, which are related to fabrication of mixed cation compounds guided by Goldschmidt tolerance factor considerations. We conclude with the view on perspectives of use of the colloidal perovskite nanocrystals for applications in backlighting of liquid-crystal TV displays.

A series of organic-inorganic hybrid perovskites ABX3 (A=diprotonated 1,4-diazabicyclo[2.2.2]octane or piperazine; B=Na+ or K+ ; X=ClO4- or BF4- ) has been synthesized. They feature a cubic cage-like host-guest structures of which A is the cationic guest residing in the anionic cage B8 X12 , B is the vertex of the cage with variable coordination numbers between six and twelve, and X is the bridging ligand with mono- and/or bidentate coordination modes. The extended Goldschmidt tolerance factor t is used to describe the phase stability of the compounds. Differential scanning calorimetry, variable-temperature structural analyses, and dielectric measurements reveal that order-disorder transitions of the A guest and/or X bridging ligand are supposed to be responsible for structural phase transitions and dielectric switching in the compounds.

In this review structural features, stability issues and physical properties of the eleven interlanthanide perovskites prepared at atmospheric pressure are surveyed and discussed. Due to the reduced size difference between cations, the structure of these oxides is strongly distorted with respect to the ideal cubic case. Therefore, in structure maps they are located close to the boundary of the perovskitic stability field; an interesting correlation between stability and the Goldschmidt tolerance factor t shows that the perovskitic temperature range narrows with decreasing t . Magnetic and optical properties are strictly related to the presence of 4 f electrons, that determine the existence of many discrete energy levels. Acceptor-doped LaYO 3 and LaYbO 3 are comparable in terms of protonic conductivity to the well known cerates, and thanks to their better chemical stability against CO 2 , they are a good alternative to the latter in solid oxide fuel cells. The high dielectric constant of some interlanthanide perovskites makes them interesting candidates as gate oxides in MOSFETs.

Rubidium lead halides (RbPbX3 ), an important class of all-inorganic metal halide perovskites, are attracting increasing attention for photovoltaic applications. However, limited by its lower Goldschmidt tolerance factor t≈0.78, all-inorganic RbPbBr3 has not been reported. Now, the crystal structure, X-ray diffraction (XRD) pattern, and band structure of perovskite-phase RbPbBr3 has now been investigated. Perovskite-phase RbPbBr3 is unstable at room temperature and transforms to photoluminescence (PL)-inactive non-perovskite. The structural evolution and mechanism of the perovskite-non-perovskite phase transition were clarified in RbPbBr3 . Experimentally, perovskite-phase RbPbBr3 was realized through a dual-source chemical vapor deposition and annealing process. These perovskite-phase microspheres showed strong PL emission at about 464 nm. This new perovskite can serve as a gain medium and microcavity to achieve broadband (475-540 nm) single-mode lasing with a high Q of about 2100.

We demonstrate inversion symmetry breaking induced by oxygen octahedral rotations in layered perovskite oxides $\mathrm{K}{A}_{R}{\mathrm{TiO}}_{4}$ (${A}_{R}$ = rare earth) using a combined experimental and theoretical approach including synchrotron x-ray diffraction, optical second harmonic generation, and first-principles lattice dynamics calculations. We experimentally find an interesting but counterintuitive phenomenon, i.e., the acentric-to-centric phase transition temperatures for K family are higher than those for previously reported Na family, in contrast to expectations based on the Goldschmidt tolerance factor, where the octahedral rotation instability toward the acentric phases would reduce with an increase in the radius of $A$-site alkali metal ions. Our detailed analysis of first-principles calculations for ${A}_{A}{A}_{R}{\mathrm{TiO}}_{4}$ (${A}_{A}=\mathrm{Na}$, K, Rb) reveals that the alkali metal and rare-earth ions play quite different roles in driving the octahedral rotations. Since rare-earth ions attract oxide ions more strongly than alkali metal ions due to the higher valence of the former in comparison with the latter (${A}_{R}^{3+}$ vs ${A}_{A}^{+}$), the optimization of coordination environment of rare-earth ions is the primary driving force of the octahedral rotations. Alkali metal ions serve to impose ``bond strains'' parallel to the layers, playing a secondary role in the octahedral rotations. Incorporation of large alkali metal ions generates a significant in-plane biaxial bond strain in ${A}_{R}\mathrm{O}$ and ${\mathrm{TiO}}_{2}$ layers through the expanded ${A}_{A}\mathrm{O}$ layers, and thereby facilitates the octahedral rotations because of the otherwise highly underbonding of rare-earth ions. Thus, the effect of $A$-site alkali metal size on the octahedral rotation instability can be explained in terms of the interlayer lattice mismatch. This understanding allows us to propose a geometric descriptor governing the structural instability in ${A}_{A}{A}_{R}{\mathrm{TiO}}_{4}$ layered perovskites. We believe that control over the interlayer lattice mismatch could be a useful strategy to tune the octahedral rotations in layered compounds.

The stability and formation of a perovskite structure is dictated by the Goldschmidt tolerance factor as a general geometric guideline. The tolerance factor has limited the choice of cations (A) in 3D lead iodide perovskites (APbI3), an intriguing class of semiconductors for high-performance photovoltaics and optoelectronics. Here, we show the tolerance factor requirement is relaxed in 2D Ruddlesden–Popper (RP) perovskites, enabling the incorporation of a variety of larger cations beyond the methylammonium (MA), formamidinium, and cesium ions in the lead iodide perovskite cages for the first time. This is unequivocally confirmed with the single-crystal X-ray structure of newly synthesized guanidinium (GA)-based (n-C6H13NH3)2(GA)Pb2I7, which exhibits significantly enlarged and distorted perovskite cage containing sterically constrained GA cation. Structural comparison with (n-C6H13NH3)2(MA)Pb2I7 reveals that the structural stabilization originates from the mitigation of strain accumulation and self-adjustable strain-balancing in 2D RP structures. Furthermore, spectroscopic studies show a large A cation significantly influences carrier dynamics and exciton–phonon interactions through modulating the inorganic sublattice. These results enrich the diverse families of perovskite materials, provide new insights into the mechanistic role of A-site cations on their physical properties, and have implications to solar device studies using engineered perovskite thin films incorporating such large organic cations., The Goldschmidt tolerance factor requirement is relaxed in 2D lead iodide perovskites, allowing various large organic cations to occupy the cuboctahedral cavity of perovskite cage.

The development of hybrid organic-inorganic perovskite solar cells is one of the most rapidly growing fields in the photovoltaic community and is on its way to challenge polycrystalline silicon and thin film technologies. High power conversion efficiencies can be achieved by simple processing with low cost. However, due to the limited long-term stability and environmental toxicity of lead in the prototypic CH3NH3PbI3, there is a need to find alternative ABX3 constitutional combinations in order to promote commercialization. The Goldschmidt tolerance factor and the octahedral factor were found to be necessary geometrical concepts to evaluate which perovskite compounds can be formed. It was figured out that the main challenge lies in estimating an effective ionic radius for the molecular cation. We calculated tolerance factors and octahedral factors for 486 ABX3 monoammonium-metal-halide combinations, where the steric size of the molecular cation in the A-position was estimated concerning the total charge density. A thorough inquiry about existing mixed organic-inorganic perovskites was undertaken. Our results are in excellent agreement with the reported hybrid compounds and indicate the potential existence of 106 ABX3 combinations hitherto not discussed in the literature, giving hints for more intense research on prospective individual candidates.