stability of mixed A-cation lead iodide perovskites †

The routes and kinetics of the degradation of thin films of methylammonium (MA)/formamidinium (FA) lead iodide perovskites (MA1 xFAxPbI3, 0# x# 1) under dry atmospheric conditions have been investigated. MA-rich phases decompose to the precursor iodide salts and PbI2, while FA-rich phases convert mainly to the yellow hexagonal phase. The reactivity is strongly inhibited for mixed cation phases of MA1 xFAxPbI3, for x 1⁄4 0.4 to 0.6, where the decomposition routes available to end member phases become less favourable. It is shown that for pristine films with x 1⁄4 0.6, PbI2 formation can be completely suppressed for up to 10 days. Kinetic analysis reveals that the rate of PbI2 formation decays exponentially with increasing FA content until x 1⁄4 0.7, beyond which the FA containing perovskite transforms rapidly to the hexagonal phase. Ab initio simulations of the decomposition reaction energies fully support the increased kinetic stability found experimentally for the mixed A-cation perovskites.

PbI 2 formation decays exponentially with increasing FA content until x ¼ 0.7, beyond which the FA containing perovskite transforms rapidly to the hexagonal phase.Ab initio simulations of the decomposition reaction energies fully support the increased kinetic stability found experimentally for the mixed A-cation perovskites.
2][3][4] They display near optimal band gap for solar light absorption, high absorption coefficients, steep absorption onsets and signicant charge carrier lifetimes (and thus diffusion lengths). 2,5These properties, combined with the processability of these materials, 6,7 have resulted in solar cell device efficiencies rising rapidly to over 22%. 8[14] The archetypal hybrid perovskite methylammonium (MA) lead iodide (CH 3 NH 3 PbI 3 ), MAPI, crystallises in the tetragonal space group I4/mcm at room temperature. 15][18][19] Such varying phase behaviour can be accounted for by the different sizes and hydrogen bonding mechanisms of these dissimilar organic cations, MA and FA.
Both MA and FA cations display directional hydrogen bonding, a factor of increasing importance in controlling phase behaviour as the system temperature is reduced and also for dening the relative stability of the two polymorphs of FAPI. 20tabilisation of mixed A site compounds relative to the end members of the series can be rationalised using geometrical arguments in which the perovskite tolerance factor is tuned using differently sized cations, as well as an entropic factor due to cation mixing. 213][24][25] We have previously shown that for compositions MA 1Àx FA x PbI 3 0 < x < 0.2 the structures are best described by a tetragonal unit cell from X-ray diffraction, while the rest of the composition range, 0.2 # x # 1, forms with a cubic cell, space group Pm 3m. 26 The compositional space for A site substitution between FA and MA has been explored in the literature. 27,28Huang et al. 23 studied the charge transport characteristics of single MA 1Àx FA x PbI 3 single crystals over the composition ranges 0 < x < 0.2 and 0.8 < x < 1 in increments of x ¼ 0.05.High carrier mobilities and lifetimes were obtained for x ¼ 0.1 and 0.15.Promising performance has also been demonstrated recently in photovoltaic devices, 22,29 where MA 0.9 FA 0.1 PbI 3 delivered an efficiency improvement to 20.2%, versus 18.6% for pure MAPI.Links between crystallinity, crystal phase stability, good optoelectronic properties and operational stability have been drawn, 24 indicating that highly crystalline compositions also suppress effects such as mixed halide phase segregation.
Furthermore, for the synthesis and efficient operation of devices the perovskite materials need to be stabilised with respect to the phase transition to the undesirable hexagonal 2Hperovskite polymorph, as occurs for FAPI and FA-rich solid solutions. 23,25The phase stability of MA 1Àx FA x PbI 3 has been studied for samples stored under a nitrogen atmosphere, indicating that for FA-rich compositions with x > 0.76, partial transition to the hexagonal phase is observed within days, while for compositions with more MA, the hexagonal phase is not observed by X-ray diffraction. 30The propensity for hybrid perovskites to react with water has also been reported. 31While high photovoltaic performance for MA 1Àx FA x PbI 3 has been demonstrated, the extended stability lifetime and decomposition of these compounds under moderately dry atmospheric conditions, likely to be similar to those used in device processing, have yet to be fully reported and are not completely understood.
In this work, for the rst time, the degradation of MA 1Àx FA x PbI 3 thin lms over the full compositional range 0 < x < 1, in increments of x ¼ 0.1, in air has been systematically investigated.The results provide a full understanding of the processes, thermodynamics and kinetics involved in the degradation of mixed A-cation lead perovskites.
Powder X-ray diffraction (PXD) data from MA 1Àx FA x PbI 3 were initially collected on as-made pristine lms (see ESI S1 and S2 †).Further diffraction patterns were subsequently obtained from the same samples aer 1, 3, 5, 7 and 10 days.The lms were stored below 30% relative humidity in the dark in order to control exposure to high levels of moisture and intense light, which are already known to cause degradation. 31Raw diffraction data were corrected for sample height displacement and analysed using the EVA diffraction suite.
PXD patterns for samples with 0 # x # 1 displayed the emergence of a peak centred at 2q ¼ 12.7 , representing the (001) reection for PbI 2 (Fig. 1).For 0 # x # 0.3, this reection grew in intensity over time, surpassing the relative intensity of the (100) perovskite reection centred at 2q ¼ 14 aer 10 days.However, consideration of PXD data from samples with x $ 0.4 showed that the presence of increasing levels of FA cation suppress the formation of PbI 2 , with the relative intensity of the (001) PbI 2 reection decreasing with increasing x, for the same time period of exposure to air.For the lm composition x ¼ 0.6, no PbI 2 is observed aer 7 days by PXD, with only trace amounts present aer 10 days.
For compositions x $ 0.7, the hexagonal d-phase is observed immediately aer lm fabrication.As previously observed for FAPI, increasing the annealing temperature to 180 C achieves full conversion to the perovskite a-phase for MA 1Àx FA x PbI 3 , x $ 0.8. 32However, these lms convert back to the hexagonal d-phase within 30 minutes of exposure to air.Suppression of d-phase formation was observed for x ¼ 0.7.
The presence of small amounts of PbI 2 in the as-made lms was found, for several values of x, to cause markedly increased rates of degradation.This was investigated further through the synthesis of x ¼ 0.6 lms that contained varying amounts of PbI 2 in the as-made thin lms.PXD analysis of these lms over a 10 day period following exposure to air showed the intensity of the PbI 2 (001) reection grew most rapidly for samples that contained observable levels of PbI 2 in the as-made sample (see ESI S3 †).It is apparent from the data that phase pure perovskite lms are required to suppress the growth rates of PbI 2 , as even trace amounts of PbI 2 present in as-made lms markedly catalyse the rate of further PbI 2 formation.At the low moisture level used in this study neither sunlight nor laboratory lighting had a discernible effect on the rate of material degradation.
The kinetics of the decomposition of thin lms of MA 1Àx FA x PbI 3 0.0 # x # 0.6 were investigated through analysis of the rate of PbI 2 phase formation.This was modelled through the following Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, where a is the phase fraction of the product, k is the rate constant, t is time and m is the Avrami exponent, the value of which depends on the crystallisation mechanism. 33Phase fractions in the degrading lms were initially estimated using Rietveld prole tting of the PXD data.However, renements for these highly textured orientated lms resulted in phase fraction values with large errors.Therefore, the peak area (A) of the (001) PbI 2 reection was used to approximate the extent of phase formation (a) as required for this analysis of the kinetics.
From the JMAK equation a linear relationship is expected when plotting ln(t) with ln ln(1/1 À A) (Fig. 2).For x ¼ 0.0-0.3 this linear relationship was observed up to 5 days.Aer this time, with very high levels of PbI 2 present, the change in the peak area of the (001) PbI 2 reection is unlikely to be representative of the true phase fraction of PbI 2 present in the surface of the lm.For x $ 0.4, with the lower levels of PbI 2 formed, the linearity was observed for the full duration of the 10 day study.Extracting the gradient and intercept of the linear model for each composition, x, a trend in rate constant modelled to a simple exponential decay can be observed (Fig. 3).It should be noted these results do not give absolute values for the rate constant of PbI 2 formation, due to the peak area approximation employed to yield the level of PbI 2 .Nevertheless, the exponential decay seen in Fig. 3  resistance in MA 1Àx FA x PbI 3 lm degradation to PbI 2 as x increases from 0.0 and approaches 0.6.

demonstrates a clear trend of increasing
The degradation routes observed for MA 1Àx FA x PbI 3 are summarised in Fig. 4. High rates of PbI 2 formation are found for x # 0.3, although increasing the FA content strongly suppresses this decomposition pathway.For x $ 0.7 this decomposition route competes with a phase transformation to the hexagonal d-phase.
Morphology and crystallite size within the thin lms are factors that might affect the degradation rate.Therefore SEM images were acquired for the as-prepared MA 1Àx FA x PbI 3 lms (ESI S5 †).For lms with x increasing from 0.0 to 0.6 the morphology was very similar and the average crystallite size (a few microns) only increased slightly with increasing FA content.For lms with x ¼ 0.7, which coincides with the appearance of a portion of the hexagonal d-phase, a very different crystallite morphology and much larger crystallite size was observed.Therefore it seems likely that thermodynamics, as opposed to lm morphology, is a major factor contributing to the decomposition kinetics.
To complement our experimental diffraction and kinetic measurements, we performed ab initio simulations on pure MAPI and a range of mixed MA/FA compositions to obtain insights into the trends in energetics of the degradation process.][36] Using direct calorimetric techniques, Navrotsky et al. 37 have shown MAPI to be thermodynamically unstable with respect to decomposition to PbI 2 and MAI.Here, the same intrinsic decomposition reaction was investigated involving the formation of PbI 2 and organic iodides as well as decomposition to the d-phase: Other decomposition routes and the effect of the cubic to tetragonal phase transition for MA-rich phases are discussed further in the ESI S4. † The reaction energies were calculated for a range of compositions (x) and the values are presented in Fig. 5.The results reveal three main features.
First, pure MAPI shows a highly exothermic energy indicating thermodynamic instability with respect to the reaction products PbI 2 and the organic iodide, which agrees well with experimental calorimetric measurements. 37Second, all the mixed MA 1Àx FA x PbI 3 compositions (0.0 # x # 0.6) show less favourable energetics, and hence a greater degree of stability, than pure MAPbI 3 .These results are consistent with our observation that formation of PbI 2 was suppressed for increasing FA content with only trace amounts of PbI 2 found aer 10 days for x ¼ 0.6.We note that Brivio et al. 38 nd very small entropy terms for halide ion mixing in MAPI-based perovskites, which would further increase the stability of Fig. 2 Example Avrami plot for MA 0.5 FA 0.5 PbI 3 .A linear relationship is observed when plotting ln(t) in hours and ln ln(1/1 À A), where the A is peak area under the PbI 2 (001) reflections in the X-ray diffraction patterns and t is time in hours.Similar plots were produced for each value of x.Fig. 3 Rate constant equivalents for PbI 2 growth fitted using an exponential decay function, calculated by extracting the intercept and gradient of linear models in the JMAK kinetic plots (Fig. 2), plotted using the peak area of the (001) PbI 2 reflection as an approximation for the phase fraction of PbI 2 transformed.mixed cation compositions.Third, when we consider the decomposition reaction energy for perovskite-structured alpha-FAPbI 3 we nd a highly exothermic energy suggesting a thermodynamically unstable structure.Indeed, it is known that in the preparation of compositions x $ 0.7 the yellow hexagonal (non-perovskite) d-phase is observed at room temperature.
The kinetic and thermodynamic stability results are further supported through the theoretical optimum A-cation size suggested by the Goldschmidt and octahedral tolerance factors.Fig. 6 shows the effect of A site mixing on the Goldschmidt tolerance factor and octahedral factor, indicating which compositions are geometrically likely to adopt a cubic perovskite unit cell.Other well-known hybrid/inorganic halide perovskite compounds substituted at the A, B, or X sites are plotted for comparison.The octahedral factor is dened as: And the Goldschmidt tolerance factor as: where r A , r B and r X are the ionic radii of the ABX 3 compound.Effective radii for organic cations taken from Kieslich et al. 39 and revised ionic radii for iodide and bromide compounds are taken from Travis et al. 40 Phases with the observed greatest stability towards decomposition, MA 1Àx FA x PbI 3 , 0.3 < x < 0.8, lie close to the centre of the cubic perovskite stability eld.
In conclusion, thin lms of the mixed organic cation perovskite system MA 1Àx FA x PbI 3 undergo degradation in air to non-perovskite phases at a much slower rate than the endmember MAPI and FAPI phases.For example, the composition MA 0.4 FA 0.6 PbI 3 synthesised with no contaminating PbI 2 phase is stable in air for up to 10 days.Ab initio simulations of the decomposition reaction energies fully support the observed increased stability of the mixed A-cation perovskites.The reduced reactivity of these phases is likely to be related to suppression of the two possible degradation mechanisms of (i) decomposition to PbI 2 and MAI, as found for MA-rich phases, and (ii) phase change as occurs for FA-rich phases.As FAPI does not degrade readily to FAI and PbI 2 , and MAPI adopts a single structure type, then any decomposition route of a mixed cation phase, such as MA 0.4 FA 0.6 PbI 3, requires the simultaneous formation of three new structure types, namely yellow FAPI, PbI 2 and MAI.We have shown that such a degradation route is less thermodynamically favourable and also has much slower kinetics.This combined experimental-computational study provides a greater understanding of the degradation routes of mixed A-cation perovskite halides, which is crucial for controlling and enhancing the long-term stability of perovskite solar cell materials.

Fig. 4
Fig. 4 Schematic of the experimentally determined degradation routes of MA 1Àx FA x PbI 3 (0 # x # 1).MA-rich phases decompose to PbI 2 and the precursor iodide salts, while FA-rich phases convert to the yellow d-phase.The routes are less favourable for the more stable x ¼ 0.4 to 0.6 mixed cation phases.PbI 6 octahedra are shown in yellow, with I represented as purple spheres.

Fig. 5
Fig. 5 Calculated energies for the decomposition reaction (2) for MA 1Àx FA x PbI 3 as a function of FA content (x).For consistent comparison, starting structural configurations based on pseudo-cubic, high order structures are presented here (with full data showing the same trends found in ESI S4 †).The shaded region indicates that in the preparation of compositions x > 0.7 the yellow hexagonal (nonperovskite) polymorph is observed.

Fig. 6
Fig.6Octahedral factor (m) versus tolerance factor (t) showing the range of compositions stabilised in the cubic perovskite structure for hybrid lead halide perovskites.Compositions MA 1Àx FA x PbI 3 , 0.3 < x < 0.8, which showed the greatest stability against degradation, are observed to lie close to the centre of the cubic perovskite structure stability field.