Reaction kinetics of the thermal decomposition of MAPbI3 thin films

Reaction Kinetics of the Thermal Decomposition of MAPbI3Thin Films Thomas Burwig∗and Paul Pistor† Martin Luther University Halle-Wittenberg, Von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany (Dated: May 17, 2021) Despite their outstanding optoelectronic properties, metal halide perovskites have not yet seen widespread use in commercial applications. This is mostly due to their lack of stability with respect to several external factors, e.g. humidity, heat, light and oxygen. Even though extensive studies have been carried out over the last decade a lot of questions regarding their thermal stability still remain and various publications have put forth different approaches for measuring and quantifying the conditions of their decomposition. However, differences in the experimental setups and in the reported values make comparisons of the reported results challenging. We show an approach, where MAPbI3thin films are thermally decomposed in high vacuum within a temperature range from 220 ◦C to 250 ◦C, while monitoring changes in the crystal structure using an in situ X-ray diffraction setup. This process reveals the complete phase evolution of the thin films from MAPbI3 into PbI2. The time resolved data was then evaluated in view of the reaction kinetics using three different approaches. First, an Arrhenius fit was applied to ln kover 1/T, where the rate constant kwas determined by fitting a first order exponential decay onto the decreasing peak area of the most prominent diffraction peaks. Secondly, a model fitting approach was used, where the data was tested against a set of different reaction models. Lastly, a model free isoconversional approach was applied. By doing this, we succeed to characterize the decomposition and determine the kinetic triplet, consisting of the activation energy E, the frequency factor Aand the reaction model f(α). With the help of the kinetic triplet the decomposition reaction can be expressed in a physically meaningful way and allows to predict the decomposition dynamics of MAPbI3thin films for varying sets of temperatures. INTRODUCTION Metal-halide perovskites (MHPs) have garnered interest in the photovoltaic research community in 2009 and have seen very noteworthy achievements in regard to their power conversion efficiencies when used as absorber layers in solar cells.[1] Due to their remarkable opto-electronic properties they are also being researched for the use in LEDs,[2–5] lasers[6] and high-energy photo detectors.[7, 8] The strongest remaining concern in view of their industrial application is their long term stability. MHPs have been reported to decompose when exposed to environmental influences such as humidity, oxygen, light and heat.[9, 10] There are also certain phenomena pertaining to their stability that are not yet well understood, like self-healing effects observed in certain metal-halide perovskites that would allow for a regeneration of lost performance when stored in the dark.[8, 11–14] Another important factor in the stability of perovskite solar cells (PSCs) are their contact layers: Commonly used hole transport layers, such as spiroOMeTAD, can significantly exacerbate the gradual decline of a PSCs power conversion efficiency.[15, 16] Despite this, there are reports of PSCs that have successfully been tested against some of the protocols in the IEC 61215 norm[17, 18], but specific testing protocols need to be developed in order to realistically ascertain the real-world long-term performance of PSCs. Now that the knowledge of metal-halide perovskites and their vulnerabilities has grown significantly over the past few years, there have been recent proposals for standardization in testing for research purposes, that take the mentioned phenomena into account.[19] Significant advancements in understanding the perovskites’ decomposition pathways and in improving their stability have been made recently. For MAPbI3, the organic methyl-ammonium (MA) molecule has proven to be a major factor in its instability. Exchanging this molecule, partially or fully, with Cs or formamidinium (FA) has been found to greatly increase the resulting perovskite’s durability.[20–29] Our experiments on CsPbI3and CsPbBr3have also shown a major increase in thermal stability, when MA is exchanged for Cs.[30] 2D perovskites and quasi-2D perovskites have also been shown to exhibit increased stability towards humidity and heat[15, 31, 32] while showing great promise for applications as LEDs.[2, 4, 5] While the impact of humidity or photo-induced degradation can be mitigated by encapsulation or the choice of improved contact layers,[33–36] the exposure to thermal loads is intrinsic to certain applications such as solar cells. Therefore, resistance to heat is a major factor for perovskite solar cells absorbers. Yet, up to this day, the results on the thermal stability of perovskites exhibit a large spread and a lot of questions remain open. Notably, there is no consensus on the intrinsic stability of MAPbI3. The Gibbs free energy for its decomposition into PbI2and MAI at room temperature has been calculated to be positive by some groups and negative by others, while it is more definitely positive for MAPbBr3 and MAPbCl3, which renders the latter two intrinsically stable.[10] It is well supported by now, that the stability limiting component in MAPbI3is the organic 2 MAI, which might itself decompose into either HI and CH3NH2or CH3I and NH3[10] Akbulatov et al. found that MAPbI3first decomposes into PbI2and MAI, with the latter one further decomposing into CH3I and NH3, while they also observed CH4, C2H4and HI as additional gaseous species.[29] Other groups disagree on the gaseous species that form from the decomposition of the MA molecule, as they found primarily HI and CH3NH2as decomposition products.[37] The preparation of the perovskite also plays a significant role in the species of gas released. MAPbI3thin films prepared by Song et al. have been shown to release NH3and CH3I above 100 ◦C and HI and CH3NH3above 180 ◦C.[38] In contrast to that, a MAPbI3powder by Juarez-Perez et al. released all four gaseous species at temperatures above 50 ◦C.[33] These discrepancies are discussed in detail by Juarez-Perez in reference [39]. Wet chemically processed MAPbI3can also release solvent residues, for example DMF, which might influence stability.[10] We chose co-evaporation as the preparation method, because it is industrially attractive, scalable and results in more stable films as compared to wet-chemical processing.[40] Dewi et al. compared the stability of PSCs prepared with co-evaporated MAPbI3 absorber layers to PSCs with solution processed MAPbI3 layers. The former ones retained around 80 % of their initial power conversion efficiency when stored for 3,600 h at 85 ◦C and 10 % RH, while the latter ones had their efficiency drop to almost 0 % after only 1,000 h.[40] Despite the consensus on the relatively low thermal stability of MAPbI3, only few attempts have been made to consistently obtain the kinetic parameters of the decomposition reaction, and, to our knowledge, no attempts have been made so far to derive these directly for MAPbI3thin films. In this work, we study the thermal decomposition of absorber-grade, co-evaporated MAPbI3 thin films in high vacuum. The choice of the preparation method and the absence of atmospheric exposure of these films allow us to exclude any solvent or moisture related impact on the decomposition reaction and to study the intrinsic thermal stability of the MAPbI3 absorber. In previous works, we used our in situ XRD setup to monitor the phase evolution of MHP thin films during a temperature ramp and extracted the onset temperature of decomposition. To do this, thin films were prepared on glass substrates in high vacuum and then, without vacuum break, heated with a ramp of 3 K/min. By observing the phase evolution via the XRD peaks we could observe, depending on the perovskite under investigation, recrystallization, phase changes and complete decomposition for temperatures from room temperature up to approximately 400 ◦C. Using the same method and setup for each experiment, we were able to compare the thermal decomposition onset of different perovskites (MAPbI3, MAPbBr3, MAPbCl3, CsPbI3, CsPbBr3, and Cs2AgBiBr6).[30, 41, 42] As long as the experimental conditions are carefully controlled and kept the same from trial to trial, the results allow for a meaningful comparison of the thermal stability between these materials. However, thermal decomposition experiments that take their data from a single temperature ramp make it difficult to pinpoint the moment of decomposition. Whether TGA or XRD is used, the onset of the decomposition will be a minute and gradual change in signal that is spread over a long time and the onset of decomposition is difficult to specify and relatively imprecise. Additionally, it will depend on the ramping speed and decomposition dynamics, i.e. the slower the decomposition progresses, the higher the reported temperature will be. In reference [41] we found that 50 % of the MAPbI3was decomposed when the temperature ramp had reached around 230 ◦C. This lies in good agreement with the results of Dualeh et al. who found the onset of decomposition of MAPbI3at 234 ◦C using TGA measurements of powder samples.[43] However, as has been rightly pointed out by Zhang et al., the observed decomposition temperature depends strongly on the temperature regime and ramp that is used, as some isothermal experiments show decomposition of MAPbI3at much lower temperatures.[10] Using isothermal experiments, multiple groups found a beginning decomposition at the surface of MAPbI3already at approximately 80 ◦C after exposure times of around 1 h.[10, 44] There is an obvious disagreement in the onset of decomposition and kinetic parameters between various sets of studies, which calls for clarification. The ambiguity in the thermal decomposition temperatures and mechanisms in this temperature regime is especially critical, as solar cells can reach operating temperatures of up to 85 ◦C[17]. Here we provide further analysis of the thermal decomposition of MAPbI3, the prototypical metal-halide perovskite, in a thin film configuration. As simple decomposition measurements based on one temperature do not suffice to determine the reaction kinetics, we observe the decomposition at four different temperatures close to the decomposition onset temperature established in the previous ramping experiments, and aim to obtain the temperature-dependent kinetic parameters of the reaction. Similarly motivated, Yu et al. extracted an activation energy Eof 120 kJ/mol from isothermal decomposition experiments of powder mixtures of MAPbI3diluted in KBr, but did not state the corresponding frequency factor.[45] Brunetti et al. and Juarez-Perez et al. calculated activation energies E of 76 kJ/mol and 93 kJ/mol, respectively, for the thermal decomposition of MAPbI3powders and included the corresponding frequency factors A, together with data for other perovskites.[37, 46] This way, the thermal decomposition reaction of a material is quantified in a physically more rigorous way and is also easier to compare than the disparate and isolated results that are often reported. It also allows for predictions about the progress of decomposition for any given combination of time and temperature, with the limitation that the predictions lose 3 accuracy for temperatures that are far away from the values that were used to determine the parameters. In this work we determine the kinetic triplet of the thermal decomposition of MAPbI3thin films, consisting of the activation energy E, the pre-exponential factor Aand the reaction model f(α), where αis the extent of conversion, a value between 0 (beginning of reaction) and 1 (end of reaction). We will first give a short overview over the necessary theory. Afterwards, we explain our experimental process in more detail. For the evaluation of the results we will employ three established methods: Firstly, we assume a first order process and calculate the rate constant kfor each experiment through fits to the exponentially decaying XRD peak areas. We then fit an Arrhenius function to ln kover 1/T to determine Eand A. Secondly, we use a model fitting approach to determine E,Aand f(α) and evaluate how well the different decomposition models fit to our data. Lastly, we use a model free isoconversional method, where the αdependence of the reaction speed is expressed not with a separate factor f(α), but is instead expressed through α dependent values for Eand A. The latter two methods, among others, were presented in detail by Vyazovkin et al.[47] THEORY The activation energy Eand the frequency factor A determine the rate constant kaccording to the formula [47] k=A·exp −E RT (1) where Ris the universal gas constant and Tis the absolute temperature. By using a reaction model f(α) and k, the change in αover the time tcan be expressed via the differential equation [47] dα dt=k(T)·f(α) (2) The reaction model f(α) – for examples see table I – describes how the overall reaction speed depends on α. Different assumptions about the rate limiting factors of a reaction, e.g. geometrical constraints, diffusion or density of nucleation sites lead to the formulation of different reaction models. A good introduction into the different kinds of reaction models and their underlying physical assumptions is given in the references [48] and [49]. A kinetic triplet, consisting of E,Aand f(α), completely defines the progression of a given single-step reaction as a function of temperature and time. Two groups have determined kinetic parameters for the thermal decomposition of MAPbI3powders: Juarez-Perez et al. found an E= 93 ±8 kJ/mol and gave a value for the turnover ratio ktthat was ln kt= 5.6±0.8 s−1with the data being fitted with an nth-order Prout–Tompkins auto-catalytic model.[46] Brunetti et al. found an activation energy of 80 ±20 kJ/mol and determined this reaction to be of the first order via DTA measurements.[37] Both groups used MAPbI3powder within a He atmosphere for their experiments, while Juarez-Perez made additional experiments in vacuum. To obtain our data, we conducted isothermal decomposition experiments at four different temperatures and monitored the decomposition by in situ X-ray diffraction (XRD). For the analysis, we take the XRD peak area as a measure for the progress of the decomposition. Motivated by the results of Brunetti et al., our first approach was to fit a simple first order exponential decay onto the declining peak area for every experiment: a(t) = a0·exp (−k t) (3) with tas the time, aas the peak area (with a0being the area at t= 0) and kas the reaction rate. An exponential fit of the data yields a value for kfor each isothermal experiment. Then ln kcan be plotted against 1/T to obtain an Arrhenius plot of the form: ln k= ln A−E RT (4) where Ris the universal gas constant and Tis the absolute temperature. A linear fit of the data points then gives a value for Efrom the slope and a value for Afrom the intersection with the y-Axis. While this approach is a reasonable starting point, it has a significant drawback: Even if the model fits the data well mathematically, the first order reaction model was assumed a priori and alternative decomposition mechanisms are not considered. Generally, a given set of experimental data can be reasonably well fitted to a variety of different reaction model, and the obtained values for Eand Amay then differ accordingly in order to compensate for the different model. These considerations were elaborated on in more detail by Vyazovkin et al.[47]. In the next stage of analysis, we therefore tested a large set of models against the experimental data simultaneously, as suggested by Vyazovkin et al. This is commonly referred to as the model fitting approach. The selection of reaction models that our data has been tested against is listed in table I, which displays f(α) and the integrated reaction model g(α), which is calculated as follows: g(α) = Zα 0 [f(α)]−1(5) To gain an intuition on what g(α) signifies, one can think about it in the following way: g(α) gives a value that, when divided by the rate constant k, gives the time t after which the conversion αis reached. This can be expressed in the following relation: g(α) = k(T)·t(6) 4 TABLE I. The selection of models that were used for the calculations presented here. This selection was taken from Khawam et al.[48], who also go into detail on how to derive these relations. g(α) denotes the integrated reaction model as calculated by equation 5. Symbol Model Name f(α)g(α) F0 Zeroth Order 1 α F1 First Order; Mampel 1 −α−ln(1 −α) F2 Second Order (1 −α)2(1 −α)−1−1 F3 Third Order (1 −α)3(1/2)[(1 −α)−2−1] R2 Contracting Area 2(1 −α)1/21−(1 −α)1/2 R3 Contracting Volume 3(1 −α)2/31−(1 −α)1/3 D1 1D Diffusion 1/2α−1α2 D2 2D Diffusion −1/ln(1 −α) ((1 −α) ln(1 −α)) + α D3 3D Diffusion 2(1 −α)2/3(1 −(1 −α)1/3)−1[1 −(1 −α)1/3]2 D4 Ginstling-Brounshtein 3/[2((1 −α)−1/3−1)] 1 −(2/3)α−(1 −α)2/3 P2 Power Law 2α1/2α1/2 P3 Power Law 3α2/3α1/3 P4 Power Law 4α3/4α1/4 P2/3 Power Law 2/3α−1/2α3/2 A2 Avrami-Erofeev 2(1 −α)[−ln(1 −α)]1/2[−ln(1 −α)]1/2 A3 Avrami-Erofeev 3(1 −α)[−ln(1 −α)]2/3[−ln(1 −α)]1/3 A4 Avrami-Erofeev 4(1 −α)[−ln(1 −α)]3/4[−ln(1 −α)]1/4 B1 Prout-Tompkins α(1 −α) ln[α/(1 −α)] + c This also means, that when plotting g(α) over tfor a set of experimental data at a temperature T, the slope of that plot gives a value for kfor that temperature. To reduce the uncertainty that is often seen at the very beginning and at the very end of a process, one can restrict the range of the g(α) over tplot to values between, for example, α= 0.1 and α= 0.9, which has been done for the evaluations presented here. The results of these fits can then be used to construct a classic Arrhenius plot, where ln kis plotted over 1/T and Eand Aare calculated in the conventional way. The quality of the linear fit onto the Arrhenius graph gives a good indication of how well the respective model describes the process. Another way to address the question which reaction model fits best to the experimental data, is to use the following method: The data is first transferred into a reduced time relation. For this, an arbitrary extent of conversion close to the end is chosen, e.g. α= 0.9. The time at which this conversion was reached is taken as tα and then the reduced time tris calculated by tr=t/tαfor all data points. A given model results in a very specific shape of the α(tr) curve and so this approach can be used to determine how well a particular model fits the experimental data. It is also possible to choose two values for αand normalize between them, so that tr= 0 is at α1and tr= 1 is at α2. This is especially useful, if the exact starting point of the decomposition is difficult to determine. Since this is the case for our data, we chose an approach with α1= 0.1 and α2= 0.9. To quantify how well the experimental data fits the calculated curves, one can compute the residual sum of squares S2: S2 j=1 n−1 n X i=1 (texp,i −tcalc,j(αi))2(7) where texp,i are the times of the experimental data points and tcalc,j(αi) are the times predicted by model jfor the corresponding value of α. To help with ordering the results, the minimum value for S2 jis determined and the normalized residual Fjis calculated:[47] Fj=S2 j S2 min (8) This value will be 1 for the best fitting model and >1 for all others. It gives an easy to read indication of how much larger S2 jis for every model when compared to the best fitting one. Finally, we test a model free approach, the so called isoconversional method. The previous approaches assumed a fixed activation energy Eand a fixed rate constant A. The αdependence of the reaction speed was found in f(α). In contrast to this, the isoconversional method delivers values for Eand Athat directly depend on αand thus change over the course of the process. The values for E(α) do not depend on the choice of a reaction model, while the obtained values for A(α) do. This method is especially useful when analyzing multi step reactions but it can also be applied to single step reactions. To calculate the values of E(α) and A(α) for a given α, first 5 −ln(tα,i) is plotted over 1/Tifor every temperature Ti. This gives an Arrhenius plot of the following form:[47] −ln(tα,i) = ln Aα g(α)−Eα RTi (9) Again, the values for E(α) and A(α) can be calculated from a linear fit. To obtain the proper dependence of E and Aon αthis is then done for a selection of values for α. EXPERIMENTAL DETAILS We prepared and decomposed the MAPbI3thin films in a high vacuum chamber under an operating pressure of approximately 10−5mbar. The high vacuum offers a reproducible atmosphere, specifically removing the impact from oxygen and water exposure. The MAPbI3was synthesized via co-evaporation of the precursors MAI (evaporated at 110 ◦C) and PbI2(evaporated at 317 ◦C) onto a soda lime glass substrate that was at room temperature at the time of deposition. The average rate of perovskite growth was 0.6˚ A/s and the finished films had a thickness of around 600 nm. During the co-evaporation the chamber pressure rose to around 10−4mbar, mostly due to the partial pressure of the evaporated MAI. The time-resolved in situ XRD signature of an exemplary growth process can be found in the supporting information. The MAPbI3perovskite undergoes a tetragonal to cubic structural phase change at approximately 60 ◦C.[41, 50] Furthermore, we observed a recrystallization of our thin films in previous experiments. This manifested in a variation of the relative Bragg peak intensities corresponding to the MAPbI3phase, indicating a change in the preferential orientation of the thin film. In order to separate these effects from actual decomposition, the samples have been preheated to 150 ◦C for 1.5 h in the isothermal decomposition experiments. A sample from a process that was stopped after this preannealing was used to confirm that the resulting film still consisted of black perovskite. For the decomposition the samples were subjected to a constant temperature at 220 ◦C, 230 ◦C, 240 ◦C or 250 ◦C. This choice of temperatures was informed by our previous temperature ramp experiments. This previous work also contains more information on the growth of the perovskite layers.[41] The supporting information include a scanning electron microscopic image of a MAPbI3layer before annealing as well as an image of a fully decomposed sample. During the processes the samples were monitored using an in situ XRD system that took one scan every minute with a fixed source-detector-geometry. The system uses a Cu X-ray source, whose radiation is filtered through a Ni window. The detector array consists of three Dectris Mythen 1 K modules covering a 2θrange of 28 ◦. The chamber’s windows are made of Kapton. Further details on the in situ XRD system can be found in reference [41]. Exemplary XRD scans of the as deposited films and of the films annealed to 150 ◦C – taken during the in situ XRD analysis – can be found in the supporting information. One central assumption of these evaluations is the correspondence of the extent of conversion to the intensity of the XRD peaks. Therefore, other factors influencing the peak intensity need to be addressed and, if possible, suppressed. The following paragraphs give an overview over other factors potentially influencing the XRD peak area and how we addressed them: Recrystallization of the perovskite during the annealing phase: We noticed a recrystallization of the perovskite above 120 ◦C, that lead to a change in the relative peak intensities. Because of this we included a pre-annealing to 150 ◦C that was held for 1.5 h before setting the final temperature that lead to the decomposition. While during this pre-annealing step the (100) and (200) loose intensity, the increase in peak intensity of the (222) peak at roughly 24.2◦and the (210) peak at roughly 31.3◦ confirm that, at this temperature, we observe a recrystallization and not the start of the decomposition. For the decomposition at the set temperatures, we then observe a simultaneous and parallel decrease of all XRD peak associated with the perovskite phase, indicating the decomposition as less and less scattering material is available. A transition into another distinct crystal phase upon heating: The highest temperature phase that is known of MAPbI3exhibits a cubic crystal structure with space group Pm-3m which forms at roughly 60 ◦C.[41, 50] The pre-annealing to 150 ◦C should ensure that the film is completely transformed into this high temperature phase. A melting of the crystal without an actual decomposition: For conventional 3D metal halide perovskites no melting point is known because the perovskites decompose before a melting point is reached.[51] A layer of educts (specifically PbI2) that forms on top of the film and thus reduces the XRD intensity: The decomposition of a 600 nm thick MAPbI3layer would result in an approximately 300 nm thick PbI2layer, due to the molar volume of PbI2being roughly half that of MAPbI3. The intensity of a beam I0will fall to intensity Iby going through a film of thickness xas expressed by the relation I=I0exp(−µ x), where µis the linear attenuation coefficient of the permeated material. For PbI2, with an X-ray beam energy of 8.04 keV, the value for µis 1.557 cm−1.[52] This would result in a worst-case decrease of the beam intensity by roughly 4.6 %, which can be considered negligible. A deposition of educts on the evaporation chamber windows, which will also reduce the XRD intensity: A deposition of material on the chamber windows would reduce the overall signal strength, thus a few experiments were conducted without exchanging the chamber windows in 6 between trials. The resulting relative decrease in signal strength per experiment was roughly 1 %, thus this factor can also be seen as having a negligible influence. The windows were always freshly replaced for the trials presented in this work before each experiment. Presence of an amorphous phase: Any amorphous material would not provide sharp XRD peaks. However, the perovskite is not expected to form an amorphous phase upon heating, and any crystallization of an initially present amorphous phase would lead to an increase in peak intensity, and not to the observed decrease. Finally, the most clear indication that the reaction at the final temperature is indeed the thermal decomposition reaction, is the increasing XRD peak intensity of the decomposition product PbI2. RESULTS AND EVALUATION After reaching the respective decomposition temperature, the evolution of the XRD peaks indicates a complete decomposition of the MAPbI3perovskite into PbI2. As an example, figure 1 shows the complete decomposition at a temperature of 230 ◦C. In this graph, the set of in situ XRD scans is depicted in a colormap, where each row corresponds to one XRD scan, the x-axis represents the time scale and the XRD intensity is color-coded. The most intense XRD peak of the MAPbI3perovskite in this presentation is the (100) peak at 28.0◦. All MAPbI3 peaks showed a parallel decline, while the PbI2peaks arose directly afterwards. The films after the completed decomposition all had the characteristic yellow color of PbI2. Figure 2 compares the evolution of the (100) peak of the MAPbI3thin films during the isothermal decomposition for the 4 decomposition temperatures of 220 ◦C, 230 ◦C, 240 ◦C and 250 ◦C. For the following evaluation, the area of this peak was chosen as the main indicator for the decomposition of the perovskite, with the peak area before the heating corresponding to a conversion ratio of α= 0 and the complete disappearance of the peak corresponding to α= 1. In addition to the MAPbI3(100) peak, the growing (001) peak of PbI2, the decomposition product, is visible. It is of note, that the MAPbI3layer in the 250 ◦C process contained slightly more lead iodide from the beginning than the other films, according to its XRD signature. A small amount of initial PbI2would not make a difference for a first order reaction model, as that would simply equate an already partially reacted film, while the reaction rate stays constant over the course of a first order reaction. The impact on other reaction models, however, would depend strongly on the reaction mechanism. For example, the PbI2particles could act as reaction nuclei. In this case, an absolute absence of PbI2 could lead to a delayed reaction, where even as a temperature is reached, where the reaction would be thermodyFIG. 1. XRD colormap of the decomposition process at 230 ◦C. The X-ray intensity is color coded, with the y-axis displaying the detected diffraction angle range and the x-axis the evolution in time. The depiction includes the final part of the pre-annealing step at 150 ◦C and the complete decomposition process. The box at the left of the colormap shows the XRD references for MAPbI3and PbI2. The reference for PbI2was taken from the PDF database under ID 00-0070235, the MAPbI3reference was calculated using a lattice constant of 6.33 ˚ A ([41], at 150 ◦C) and assuming the space group Pm¯ 3m.[53] namically likely, the absence of any reaction nuclei would hinder the reaction until either a critical temperature is reached, or other small defects or disturbances provide enough of an energetic perturbation for the reaction to occur. In that case, a very small initial amount of PbI2 might actually be beneficial for the sake of a thermodynamic analysis. However, since the exact mechanism of this reaction is, as of yet, unknown, it is difficult to exactly predict the influence of excess PbI2. In any case, its influence is likely greatest at the very start of the reaction and becomes smaller as the reaction, which itself leads to the formation of PbI2, progresses. Galwey and Brown pointed out in the Handbook of Thermal Analysis and Calorimetry (Vol. 1, Chapter 3) that some smoothing of the data can be necessary for certain experimental 7 FIG. 2. Overview of the decomposition processes at different temperatures. The colormaps show a selected diffraction angle range around the most prominent MAPbI3peak ((100) at 14.0◦). The bottom graph shows the substrate temperatures for the different processes. The graphs are scaled so that the reaching of the final temperature is at point t= 0. Notably, the (100) MAPbI3peak at 14.0◦and its kβpeak at 12.7◦decay with increasing speed as the temperature increases, which indicates an increase in the rate of the decomposition of the MAPbI3. This decomposition coincides with the growth of the (100) PbI2peak at 12.7◦. techniques.[49] So, to reduce the impact of measurement noise, each data point has been put through a moving average with the two preceding and the two following data points. First Order Approach For the first part of the evaluation we assume a first order model, where the decays of the peak areas are fitted exponentially according to equation 3. For a pure decomposition reaction, the peak intensity of all XRD peaks should decline simultaneously, because the amount of scattering material diminishes, i.e. the relative peak intensities should stay constant. Furthermore, the amount of the reaction product (PbI2) should increase accordingly. In order to verify this, the evolution of four different XRD peaks is evaluated: The declining normalized peak areas aof the (100), (200) and (210) peaks of MAPbI3are plotted in logarithmic scale in figure 3. Simultaneously to the decaying of the MAPbI3peaks, the area of the PbI2(001) peak is rising. It is of note that the kβpeak of the MAPbI3(100) reflex overlaps this PbI2 (001) peak, which leads to some uncertainty in the exact determination of the progress of the PbI2’s growth. For better comparability, figure 3 dshows (1 −a) for this latter peak. All 3 MAPbI3peaks decay in parallel, which increases the confidence that the observed behavior is in fact a decomposition and not a recrystallization as observed at lower temperatures. The decays show a 8 FIG. 3. Logarithmic plots for the time evolution of the peak intensities. a-c: Normalized peak area afor different peaks of MAPbI3for all isothermal decomposition experiments. a: (100) MAPbI3;b: (200) MAPbI3;c: (210) MAPbI3;d: (001) PbI2. In the latter case, one minus the normalized peak area, (1 −a), is plotted for better comparability. clear exponential character at the beginning, so these first parts were used for the exponential fits. The reaction rate kwas taken from the fits according to equation 3. Then ln kwas plotted against 1/T which is shown in figure 4. A linear fit of this data resulted in the activation energies and frequency factors shown in table II. The results settle around a value for Eof roughly 110± 20 kJ/mol and a value for ln Aof around 19 ±5. The evaluations of the four different peaks agree well with each other, demonstrating the consistent behavior of the peaks. TABLE II. Results of the first order approach for the analyzed peaks. Peak E[kJ/mol] ln A[s−1] (100) MAPbI3110.5±17.4 19.3±4.1 (200) MAPbI3105.5±23.3 17.9±5.5 (210) MAPbI3108.7±32.2 18.7±7.6 (001) PbI2114.2±26.7 19.4±6.3 9 FIG. 4. Arrhenius plots showing the relation of ln kover 1/T for the isothermal experiments and different XRD peaks. The colors represent the different processes and the sub-figures represent different XRD peaks. The dotted lines indicate the linear fits. a: (100) MAPbI3;b: (200) MAPbI3;c: (210) MAPbI3;d: (001) PbI2. Model Fitting Approach In continuation, different reaction models will be considered and compared in detail for the (100) MAPbI3 peak, as this peak was the most prominent one. For this model fitting approach the experimental data in the reduced time depiction will be compared to the predictions from the different models listed in table I. In the isothermal experiments, the decomposition temperature was not reached instantaneously, but rather ramped up from the 150 ◦C preheating step to the temperature of isothermal decomposition during 5 min, to avoid overshooting. The actual decomposition begins slightly before the end temperature is reached and so we chose an initial peak intensity before the decline as the starting value for α= 0, not the intensity when the decomposition temperature is reached. This way we accept an uncertainty for the first 2 to 3 data points while assuring that the initial peak area correctly corresponds to α= 0. Figure 5 shows the averaged αfor the (100) peak from α= 0.1 to α= 0.9 in comparison to the different models. The residual sum of squares for all models can be found in the supporting information. According to these calculations, the best fitting models are the one dimensional diffusion (D1), contracting volume (R3), contracting area (R2), the 2/3 Power law (P2/3) and the first order (Mampel) model.