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Temperature-dependent EXAFS measurements of the Pb L3-edge allow quantification of the anharmonicity of the lead-halide bond of chlorine-substituted methylammonium (MA) lead triiodide

This article reports on studies of chlorine-substituted MAPbI3 using combined temperature-dependent XRD synchrotron and Pb-L3 edge EXAFS to analyze the anharmonicity of the lead halide bond. The EXAFS parameters were described in the orthorhombic phase by an Einstein or T2 type behavior, which was then compared with the experimental EXAFS parameters of the tetragonal/cubic phase. In the orthorhombic phase, it was observed that the asymmetry of the pair distribution function (cumulant C3) in MAPbCl3 is much lower than in MAPbI3. Compared with the behavior in the orthorhombic phase, the anharmonicity changed after the phase transition to the room temperature phase, with MAPbCl3 showing an increased anharmonicity and MAPbI3 a decrease. The differences between MAPbI3 and 2% chlorine substitution were small, both in the orthorhombic and tetragonal phases. By determining the structural parameters required to convert the effective force constants k0 and k3 resulting from the EXAFS analysis into the Morse potential parameters {\alpha} and D, we could establish that our results agree with other experimental findings. Moreover, by using XRD we found that the [PbX6] octahedra shrink slightly in the tetragonal phase of MAPbI3 and MAPbI2.94Cl0.06, towards increasing temperatures. This behavior in the tetragonal phase is related to the dominant negative tension effects observed by EXAFS.


INTRODUCTION
The evolution of halide perovskite photovoltaics 1 from their early beginnings 2 to advanced tandem solar cells with 30% efficiency 3 is very impressive. However, despite this extraordinary development, many fundamental questions still need to be answered in this research area. 4,5 We have made it our task to understand the fundamental properties of chlorine substituted MAPbI3 perovskites as much as possible since chlorine substitution in methylammonium ([CH3NH3] + , MA) lead trihalide (X3; X = I, Cl) hybrid perovskites leads to an improvement of material stability and also to an improvement of electronic properties. 6,7 In doing so, we rely on basic crystallographic knowledge that was recently gained in our research group on hybrid perovskites. [8][9][10][11] This includes the realization that the solubility of chlorine in MAPbI3 is limited, so that a maximum of 3 mol% chlorine can be incorporated in MAPbI3 and a maximum of 1 mol% iodine in MAPbCl3. 11 12,13 where the MA molecule rotates freely, changes into a tetragonal structure (most commonly used I4/mcm) at 330 K, 8,10 in which rotation of the MA molecule is much more restricted (there is still a disorder in the crystal structure), and then changes into the ordered orthorhombic structure (Pnma) at 161 K, [14][15][16] in which the crystal structure is fully ordered. A similar phase transformation evolution is observed for MAPbI2.94Cl0.06, where slightly lower phase transformation temperatures were found compared to MAPbI3 (326 K, cubic → tetragonal, and 155 K, tetragonal → orthorhombic). 17 For the chlorine halide, the cubic Pm3 � m crystal structure was observed down to a temperature of 177 K. 18 For lower temperatures, however, there are ambiguous observations in the literature. The intermediate structure of MAPbCl3 (temperature range from 177 K to 172 K), has been described as tetragonal and eventually modulated 19 , but could not be observed by others. 20 The low temperature modification is described as orthorhombic, space group Pnma. 21 Although this is the same space group symmetry as in the low temperature phase of MAPbI3, the crystal structure differs because in MAPbCl3, compared to the cubic structure, all three axes are doubled. FTIR investigations showed that, in the orthorhombic phase (T < 161 K for MAPbI3 and T < 172 K for MAPbCl3), the iodide is more strongly influenced by hydrogen bonding than the chloride. 22 Our QENS results on MAPbI3, MAPbCl3, and MAPbI2.94Cl0.06 showed that chlorine substitution in the orthorhombic phase leads to a weakening of the hydrogen bridge bonds since the characteristic relaxation times of the threefold MA molecule jump rotation around the C-N axis at 70 K in MAPbCl3 (135 ps) and MAPbI2.94Cl0.06 (485 ps) are much shorter than in MAPbI3 (1635 ps). 17 The structural counterpart of the changes in the dynamics of MA molecules caused by chlorine substitution is the influence of chlorine substitution on the tilting and distortion of the [PbX6] octahedra, especially in the temperature range of the orthorhombic-tetragonal phase transformation. In fact, phase transitions in lead-halide perovskites are rather directly linked to the flexibility of the overall inorganic framework, i.e. the anharmonicity of the octahedral tilting, which may be for example quantified with the Pb-X-Pb or X-Pb-X in plane angle. [23][24][25][26] Further important aspects of the anharmonicity of the inorganic framework in lead halide perovskites are the asymmetries in the Pb-X pair distribution function observed in the analysis of the local structure. [27][28][29] The different entropy contributions (stochastic structural fluctuations, anharmonicity and lattice softness) in hybrid perovskites are now considered to have a bigger influence on the optoelectronic properties than the dynamics of the MA molecule. 5 This finding is crucial since the optoelectronic properties are of greatest importance for the application as photovoltaic material. Many of the optoelectronic properties are, in turn, strongly influenced by the ordering processes of the orthorhombic/tetragonal phase transformation. The prominent importance of the anharmonicity of the halide motion becomes clear when one considers that, for example, an iodine shift of 0.4 Å leads to a considerable decrease in the maximum allowed charge carrier mobility (about 160 cm 2 V -1 s -1 ), 30 which can be interpreted as dipolar fluctuations of the charges. 5 Since the short-range order of the central lead atom is modified by the change of the octahedron geometry, one way to examine the anharmonicity of the lead-halide bond is X-ray absorption fine structure (XAFS). XAFS investigations of MAPbX3 perovskites have so far been mostly applied to thin film samples, mainly to investigate the formation of precursors [31][32][33] or to study degrading processes. 34 To this end, the X-ray absorption near edge structure (XANES) region of the Pb L3-edge was mainly investigated, but more and more publications have been investigating the extended X-ray absorption fine structure (EXAFS) region to better understand the lead-halide bonds. 35,36 Because the interatomic distance, in our case the lead-halide distance, is the fundamental physical quantity, EXAFS is particularly sensitive (for details on the EXAFS methodology see section 2.3.2). It should be mentioned that Pb L3-edge EXAFS studies were available before interest in hydride perovskites increased in recent years. 37 Although there are some publications dealing with the EXAFS edges of the anion, with the work being confined to bromine, 38 we want to limit ourselves to the Pb L-3 edge for better comparability.
Besides the consideration of the temperature dependence of the EXAFS Debye-Waller factor, 39 the framework of the temperature-dependent EXAFS cumulant analysis developed in the last decades [40][41][42][43][44][45] allows further statements about the properties of the investigated atomic pairs since statements about the anharmonicity can also be made. 46 Through a combination of temperature-dependent EXAFS Pb L3-edge-investigations and temperature-dependent synchrotron XRD studies, the influence of the chlorine substitution on the EXAFS Debye-Waller factor, the distortions of the [PbX6] octahedra and thus the anharmonicity of the Pb-X bonds was investigated in three different samples: MAPbI3, MAPbCl3, and MAPbI2.94Cl0.06. The experimental determination of the effective force constants that govern the anharmonicity of the lead-halide bond enables the corresponding Morse parameters to be obtained, which allows comparison with other experimental results and theoretical calculations, such as DFT calculations.

Synthesis and sample handling
Small single crystals of MAPbI3, MAPbCl3, and MAPbI2.94Cl0.06, which were further ground in an agate mortar and used in powder form, were synthesized as described previously. 9,11,22 After synthesis, the powder was tested for phase purity using X-ray diffraction (XRD) (Bruker D8 powder diffractometer with sample spinner with Bragg-Brentano geometry, and Cu Ka1 radiation) and no impurity phases were detected. The samples were handled in the glove box or under an inert gas atmosphere (argon).

Synchrotron XRD and EXAFS measurements
The temperature-dependent Pb L3-edge (13.035 keV) EXAFS and the synchrotron XRD measurements were both performed on the KMC-2 beam line 47 at BESSY II, Helmholtz-Zentrum, Berlin, Germany. This beam line operates a graded SiGe monochromator constructed of two independent crystals (energy resolution of E/ΔE = 4000). The beam intensity at the KMC-2 is stabilized to an accuracy of 0.3%. The two experiments, EXAFS and XRD, could be conducted because the KMC-2 beam line comprises two end stations: "XANES" and "Diffraction". X-ray powder diffraction data in the range of 4°< 2Θ< 94.4° were collected at the "Diffraction" end station of KMC-2 beam line using a radiation energy of 8048 eV (λ = 1.5406(1) Å). A modified Gifford-McMahon (GM) closed-cycle cryocooler, in-house label TMP-CCR-HXR, configured with a double Kapton cupola and helium exchange gas, was used. The samples were placed in a flat sample holder, and mounted in symmetric reflection geometry. Diffraction and EXAFS measurements were carried out in BESSY II TopUp mode at 298 mA.
For the EXAFS experiments, the cryostat was mounted at the Cryo-EXAFS stage (Fig. S1)  Each temperature step of the synchrotron XRD measurements took 2-5 minutes to heat up (or to cool down for the low temperature structure of MAPbCl3), followed by 15 minutes equilibration and 37 minutes data collection, for a total of 54 minutes.

Synchrotron XRD
Structural analysis of the data was done using F.O.X. for simulated annealing, 48 and Fullprof for Rietveld refinement (Fullprof.2k. version 5.30 & 7.20). 49 The MA cation was treated throughout the analysis as a rigid body, with geometry taken from previous DFT optimization. 22 The refinement of anisotropic temperature factors for the halide atoms could not be done consistently for all data sets (for details, see supplement (section MSRD and MSD), so that in most cases isotropic temperature factors were refined with the Rietveld method. Details of the analysis of the orthorhombic MAPbCl3 phase and individual results are given in supporting information.

EXAFS
EXAFS covers an energy range from 30 to 1000 eV above the absorption edge. This allows the local structural environment of the absorber atom to be investigated. In this context, the coordination numbers N, the interatomic distances and the variation or distribution of these distances are important. The interatomic distance to the nearest neighbor atoms REXAFS is the basic physical quantity to which the EXAFS is sensitive. The mean square relative displacement (MSRD) -i.e. the EXAFS Debye-Waller factor 2 -is important. The EXAFS Debye-Waller factor corresponds to the variation of the atomic distances. The relationship (also called "EXAFS formula") 50 of N, REXAFS and 2 will be discussed later in this section. First, we want to show the way from the measured absorbance spectra to the EXAFS analysis (Fig. 1). The goal here is to Fourier transform the absorption "fine structure" χ(k) data after data normalization and background subtraction to obtain the radial distance distribution. The Athena software from the Demeter 0.9.26 8 software suite 51 was used for standardization and energy calibration of the EXAFS data. 50 Starting point of the EXAFS data treatment was the determination of the respective E0 values of the temperature-dependent EXAFS spectra for the three analyzed samples. The first derivatives of the normalized sample spectra, and the corresponding normalized reference spectra (Pb foil) were exported from Athena, and the E0 positions (first maximum) were determined by fitting a Gaussian function with fityk 52 .

Fig. 1
Simplified EXAFS "Workflow" overview, EXAFS data processing with Demeter 0.9.26 software suite, fitting the paths calculated from IFEFFIT with the EXAFS formula (as described in this section) in Artemis. Crystallographic Information File (CIF).
We chose this way because in Athena no error values for the energy calibration are available, with   the way we chose beam damage or effects due to phase transitions could be excluded because E0   remained constant within the E0 variance of about 0.1 eV over the whole temperature range for all three samples. For the energy calibration, 13035 eV was used for the Pb reference. The following averaged E0 values were determined for MAPbI3: E 0 = 13035.39(9) eV, for MAPbI2.94Cl0.06: E 0 = 13036.17(6) eV and for MAPbCl3: E 0 = 13036.53(8) eV (Fig. S2). After the E0 calibration ( Fig.   S3), the data for the respective temperature could be merged and a background correction (Rbkg = 1.5 for all three samples) 53 was applied in Athena (Fig. 1). The actual EXAFS fits in Artemis were then performed in radial space (R range: 2 -4 Å for MAPbI3 and MAPbI2.94Cl0.06; and for MAPbCl3 with an of R range: 1.5 -3.0 Å) with multiple k weights (k = 1, 2, and 3) on the Fourier transformed data (k range: 3 -14 Å −1 for MAPbI3 and MAPbI2.94Cl0.06; for MAPbCl3 the k range is 3 -12 Å −1 ).
In Artemis, the parameter 0 2 (amplitude reduction factor), REXAFS (distance from the absorbing atom to the scattering atom), N (degeneracy), 2 (mean square radial displacement), C3 (asymmetry parameter) and C4 (symmetrical flattening or sharpening) of the EXAFS formula are used as fit parameters and thus the paths i (absorbing atom / scattering atom), calculated with the software framework IFEFFIT 51 (within Artemis, Fig. 1), are fitted individually. The EXAFS formula is: 41  2, S10a, and S11). 15 MAPbCl3 at temperatures above 170 K shows a cubic crystal structure, space group Pm3 � m, which was refined using the structure model of Baikie. 13 Upon further cooling, at 170 K the appearance of a non-cubic phase is evident from beginning peak splitting and additional weak reflections and at 172 K the cubic phase had vanished completely. In order to describe this phase an orthorhombic lattice of a ≈ 8.0 Å, b ≈ 11.3 Å, c ≈ 7.9 Å (orthorhombic phase O2) was necessary (Fig. S4, S7, S10c, S11 and Table S1). This is in contrast to older descriptions, but in agreement with recent observations. 20,57 The intermediate, tetragonal phase is absent, and the observed orthorhombic phase is different. A satisfactory description of the peak intensities was only possible in space group Pnma. It should be noted that this fully-ordered structure is the same as observed for the lowtemperature phases of MAPbI3 and MAPbBr3. At 150 K and below ( Fig. S5 and S6) a second phase appears as a minor fraction, which can be described with good agreement by the known lowtemperature structure of MAPbCl3, which also has space group Pnma, but a larger unit cell of a ≈ 11.2 Å, b ≈ 11.3 Å, c ≈ 11.3 Å (orthorhombic phase O1). 21 However, this fraction only reached about 20% even at the lowest temperature of 30 K; the major part of the sample remained in the O2 structure with the smaller unit cell. We did not test it extensively, but from the comparison of a number of experiments with different samples it is probable that the formation of the large-cell structure is hindered in finely ground samples (Fig. S8). Measurements with coarser samples seem to form larger fractions of this phase, up to close to 100% with a very coarse sample. However, due to extremely bad particle statistics, no structure refinement was possible from these data. We wish to point out in particular that samples prepared for EXAFS experiments are very finely ground and thus have to be assumed to form nearly exclusively the small-cell form O2 at low temperatures.
All attempts to describe all peaks with one phase failed. A few extra peaks appearing at 150 K and below remained unexplained. This could indicate a third fraction or unidentified structural variations in one of the two phases.

EXAFS
In the k 3 -weighted Pb L3-edge EXAFS data in k-space shown in Fig. 3 and in the Fourier transforms of the EXAFS signal in Fig. 4  MAPbCl3, this effect cannot be observed in this manner. However, we can also observe clearly that at higher temperatures above the tetragonal-orthorhombic phase transformation, only minor changes occur ( Fig. 3 and 4). Based on our results from the Rietveld analysis of the synchrotron XRD data we conclude that only one lead-halide distance has to be considered for the development of a theoretical model to describe our temperature-dependent Pb L3-edge EXAFS data in the orthorhombic low temperature phase for MAPbI3, MAPbI2.94Cl0.06 and MAPbCl3. This is because that the distance resolution Δr is limited by the observable k-space Δk of our EXAFS measurements since the following applies: 62,63 In our case this means that with a usable k-space of Δk = 11 Å -1 (interval k = 3 -14 Å −1 ), Δr of less than 0.143 Å can no longer be resolved unambiguously. The standard deviation σr from averaging the three different lead-iodine distances in MAPbI3 (Fig. S14) and MAPbI2.94Cl0.06 determined in the Rietveld analysis is a maximum of 0.022 Å in the orthorhombic phase and is even smaller by an order of magnitude in the tetragonal phase.

Fig. 3
The temperature-dependent measured k 3 -weighted Pb L3-edge EXAFS data in k-space (black squares) and the respective best fits for MAPbI3 (red lines), for MAPbI2.94Cl0.06 (blue lines) and for MAPbCl3 (green lines). For the six temperatures presented, an offset was chosen for ease of presentation, but this is the same for all measured samples. Note that the values of the ordinate are the same in all three figures.
Also, from crystal structure analyzes of MAPbCl3 in the orthorhombic phase O1 known from literature, 21,59 we can conclude that the six different lead-chlorine distances (σr = 0.095 Å) ( Fig.   S15) cannot be resolved with our EXAFS data, since it is even more difficult here that only a k range from 3 to 12 Å -1 can be used due to the weaker oscillations (Δr < 0.174 Å). The orthorhombic phase observed here (phase O2) has an even smaller averaged lead-chlorine bond length splitting of σr = 0.05 Å, so that it is justified to assume only one averaged distance. These considerations contrast with the investigations of Ishida et al. 37 where two lead-iodine distances were assumed for the orthorhombic phase of MAPbI3 and four lead-chlorine distances for the orthorhombic phase of MAPbCl3. However, when we look at the results of this investigation we quickly see that this analysis leads to a lead-halide distance that is way too small (for example, a value of 3.140(2) Å is given for 11 K results of MAPbI3) 37 . It is significantly smaller than the smallest Pb-I distance of MAPbI3 of 3.177(2) Å (20 K; Pb-I3 orthogonal symmetry equivalent in  distances that were too small, even when using 4 paths (2 with N = 2 and 2 with N = 1, with N = degeneracy of the path). These much too small (non-physical) distances observed by Ishida et al., 37 (especially for MAPbCl3) were only obtained because it was assumed that a separation of the leadhalide distances should be possible with the k-range used at the time, which is obviously not the case. Because of this observation we examined the temperature-dependent EXAFS data of our three samples with only one lead-halide distance REXAFS (one path of the first path Pb-X with N = 6) and accordingly with only one EXAFS Debye Waller value (σ 2 ). Thereby, we investigated Pb L3-edge EXAFS data in the orthorhombic phase (between 20 K and 155 K) but also in tetragonal/cubic phases for comparison (up to 300 K). The range in R space (R: 2 -4 Å for MAPbI3 and MAPbI2.94Cl0.06, and R: 1.5 -3.0 Å for MAPbCl3) of the Fourier transformed EXAFS spectra that was used for the analysis ensured that only the lead-halide distance of the first path Pb-X(1) in the fitted region was considered (in the case of MAPbI3 the second nearest neighbor of the central lead atom is too far away to contribute significantly, around 4.87 Å for the C atom and around 4.92 Å for the N atom of the MA molecule, but also for the chlorine compound (O2 phase at 35 K) the next neighbors were sufficiently distant, 4.38 Å for the N atom and 4.39 Å for the C atom).
Visualization of the scattering amplitudes (calculated by Artemis via IFEFFIT) and fits of the 20 K EXAFS data using the next paths ( Fig. S12 and S13) showed the following: The intensity ratios for MAPbI3 in the R range 2 -4 Å are such that 99.0% of the scattering come from the first path Pb-I(1) (98.2% for MAPbCl3 in the R range of 1.55 -3 Å) and only 1% from all other paths (1.8% for MAPbCl3). For Pb-I(1) (resp. Pb-Cl(1)) the fit results were identical and showed that the first FT peak (Pb-X(1)) is not influenced by the next paths. Alternatively, an EXAFS analysis with the software EDA instead of Artemis could have been considered as it was carried out for ReO3, 64 but we limited our work to the chosen procedure since an additional EXAFS analysis would have gone beyond the scope of this work. All fits were performed in R space. The third and fourth cumulants (C3 and C4) also had to be used to describe the EXAFS data, as they improved both the Chi2 values and the R-factors of the fits (Fig. S16).  To determine the temperature-dependent behavior of C2, the temperature-dependence of the relative ΔC2 is fitted with an Einstein behavior as described by Dalba and Fornasini. 69,70 According to Bunker, 63 the Einstein model is given by the following relation: where µ = m1m2/(m1+m2) [g/mol] is the reduced mass of the absorber/scatterer pair, ΘE is the Einstein temperature and 2 is the static component which, however, does not have to be considered here, as we have proceeded from the relative MSRD. The resulting temperaturedependent behavior of C2 is shown in Fig. 6a Table   1). The effective force constant k0 is not to be confused with the force constant of lattice dynamic models. 39 For the three components we obtained the k0 values given in Table 1. The difference of the temperature-dependent behavior of C2 (and thus also νE and k0) between MAPbI3 and MAPbCl3 was significant (Fig. 6a). MAPbI2.94Cl0.06 caused only small differences compared to MAPbI3, thus νE and k0 hardly differed (within the observed errors) for these two components. In general, it could be seen that the Einstein model determined for the orthorhombic phase also describes the temperature-dependent behavior of C2 for the tetragonal/cubic phase well (Fig. 6a). In principle, the temperature-dependent behavior of C2 (parallel mean square relative displacement: "parallel MSRD") could be compared directly with the parallel MSD (parallel mean square displacement) determined from diffraction experiments. 64, 71 The parallel MSD corresponded to the averaged principal direction of the anisotropic temperature ellipsoids that were aligned parallel to the leadhalide bond. 71 However, since anisotropic temperature factors (ADP) 72 must be considered for the investigated halide atoms in the hybrid perovskites, but these could not be determined for all temperatures and components from the carried out Rietveld refinements (and are also not usable and consistent in the literature), we reference here to a summary of the present results in the supplement (section MSRD and MSD) and also refer to later investigations with a parameterized Rietveld refinement 73 approach. From the temperature-dependent comparison of the relative interatomic distances ΔREXAFS and the averaged relative interatomic distances ΔRXRD resulting from synchrotron XRD, however, it was also possible to infer the relative "perpendicular MSRD" (Δ<Δu 2 >), which corresponded to the vibrations perpendicular to the lead-halide bond direction (in-plane vibrations). The following relationship applied: 67 which can be calculated from the experimental data shown in Fig. 2 However, the static component does not need to be considered here, as we have proceeded from the relative perpendicular MSRD. Analogous to k0, the corresponding perpendicular effective force constant ┴ from the correlated Einstein model could be calculated.
The determined Einstein temperatures ΘE(perp) ( Table 1) described the behavior of the perpendicular MSRD in the orthorhombic phase well (Fig. 6b), whereby the differences between MAPbI3 and MAPbI2.94Cl0.06 are somewhat larger than for the parallel MSRD (Fig. 6a). Again, the temperaturedependent behavior of MAPbCl3 was clearly different from that of MAPbI3. For all three components, after the phase transition to the tetragonal/cubic phase, significantly larger values were observed for the perpendicular MSRD than predicted by the determined Einstein behavior.
This effect was particularly large in the case of MAPbCl3 since a jump-like change in the perpendicular MSRD was observed here.  For the relationship between perpendicular MSRD and the perpendicular MSD obtained from diffraction measurements, please refer to the comments in the supplement (section MSRD and MSD).
The ratio γ = perpendicular MSRD / parallel MSRD describes the degree of anisotropy of the relative vibrations. 67 The ratio γ was usually not constant as a function of temperature since different correlated Einstein relations were determined for the parallel MSRD and the perpendicular MSRD. For purely isotropic vibrations in an ideal Debye crystal, the ratio γ = 2, 66,67,74 but since our samples showed very clear anisotropy, larger γ ratios were obtained (Fig. 7). Here, MAPbI3 and MAPbI2.94Cl0.06 already showed very clear anisotropy in the orthorhombic phases, whereas an almost isotropic behavior (γ only slightly greater than 2) was observed for MAPbCl3. While the ratio γ is temperature-dependent, the ratio ξ = k0/ ┴ provides a temperatureindependent description of the degree of anisotropy of the relative vibrations, 67 which is valid for the whole temperature range of the orthorhombic phase (     77 ) and perpendicular MSRD.
The two ratios│k3│/k0 (potential anharmonicity) 77 and ξ = k║/k ┴ (degree of anisotropy of the relative vibrations) 76 (9) 3.76 (2) k║ [eV/Å 2 ] 1.315 (3) 1.324 (6) 1.751 (9) k3 (5) 1.38 (9) For the analysis of the Artemis Fit results, we used the relative values ΔC3 with respect to the lowest temperature for the temperature-dependent C3 cumulants, as we did for REXAFS and C2. ΔC3 was fitted 67 by a simplified version of the classical approximation for cumulants valid for higher temperatures: 65,77  so that we can assume that an adjustment of ΔC3 in the orthorhombic phases (up to 160 K) is also meaningful. As a result of our analysis, we obtained the temperature dependence of C3 shown in Fig. 9 and the force constants k3 in Table 1. We observe a positive C3 for all three components, which corresponds to an asymmetric Gaussian behavior with more weight to the longer Pb-X bonds of the pair distribution function. Since C3 in the orthorhombic phase is larger for MAPbI3 and MAPbI2.94Cl0.06 than for MAPbCl3, we also observe that MAPbI3 and MAPbI2.94Cl0.06 exhibit a more asymmetric form of the pair distribution function, i.e. more weight to the longer Pb-X bonds, than MAPbCl3. In general, the assumed T 2 -like behavior described the experimental values of all three components in the orthorhombic phase quite well. In relation to this, we note that the determined k3 also described the relative thermal expansion Δa very well, because of the asymmetry of the effective potential (a = -3k3C2/k0) 67 as shown in Fig. 8 where x = r -r0 is the deviation of the interatomic distance from the position of the potential minimum. The effective potentials for the orthorhombic phase shown in Fig. 10a could each be compared with the corresponding harmonic potentials, in which case only k0 was considered: The potential anharmonicity, 77 measured by the ratio | 3 |/k 0, was indeed quite similar for all three components (MAPbI3: 0.67(2), MAPbI2.94Cl0.06: 0.68 (2), and for MAPbCl3: 0.65 (3)). Yet, the three components differed in the various effects of anharmonicity (thermal expansion of the bond C1 (REXAFS) and the asymmetry of the distribution of the distances C3, Fig. 8 and Fig. 9) as already seen. It is worth mentioning that the deviation of ΔC1 (bond expansion) and Δa (relative thermal expansion because of to the asymmetry of the effective potential) in our study was very small (Fig.  8), which to our knowledge has not been observed in the literature before. On the contrary, it is usually observed that Δa is always smaller than ΔC1. 77 The difference rv between ΔC1 and Δa is then regarded as a shift of the effective potential minimum. We now want to go one step further and make the connections between our results and an experimental Morse potential determined for MAPbI3. The experimental results we will refer to here were obtained from temperature-dependent neutron total scattering experiments to elucidate the local structure of MAPbI3. 28 S2 and S3 are structure parameters that depend on the environment of the central atom of the local structure under investigation. In our case, we needed these structure parameters for an octahedral environment. To do this, we used the method described by Hung et al. to derive S2 and S3: 81  where Mi is the ith atomic mass, � is the bond unit vector, the sum i is over absorbers (i=1) and backscatters (i=2), the sum j is over their first nearest neighbors, excluding absorbers and backscatterers themselves, whose contributions are described by the term V(x) (see the Supplement for details on the calculation of the structure parameters S2 and S3). As a result, S2 = 1.1322 and S3 = -0.9633 were obtained for MAPbI3 for the octahedral environment of the lead (S2=9/8; S3= -31/32 with M1=M2. In Table S4, the structure parameters for MAPbI2.94Cl0.06 and MAPbCl3 are given). Thus, we obtained D = 0.235(6) eV and α = 1.57(4) Å -1 for MAPbI3, resulting in the Morse potential shown in Fig. 10b and 11 with a good agreement with the experimental values of Liu 28 .  calculations as available in the literature 82 (Fig. 11, S24). More generally, it can also be said that EXAFS results can be used as a benchmark for theoretical calculations. 70

CONCLUSIONS
The       The newly build Cryo-EXAFS environment at KMC-2 "XANES" end station at BESSY II has been developed for in situ gas adsorption combined with X-ray powder diffraction experiments 1 and has been modified for use on the XANES end station. With multiple Kapton windows and a variable sample holder system, measurements in transmission and fluorescence geometries are possible.

Rietveld refinement of MAPbCl3
The two-phase nature of the low-temperature samples was established by comparing the difference between two diffraction patterns taken at the same temperature, but from samples that had formed different fractions of the two phases (samples 1 & 2 in Fig. S8). Rietveld refinement was done cation were kept at fixed values. For the low temperature phase with the large 11 Å x 11 Å x 11 Å unit cell, the published structure of Chi was used. 3 As this phase only reaches a fraction of 22% the maximum, structural parameters were not refined. The structure of the intermediary phase in space group Pnma and medium sized 8 Å x 11 Å x 8 Å unit cell was refined using isotropic thermal displacement parameters for the chlorine atom on the 4c site. The chlorine on the 8d site was refined with anisotropic displacement, however with the off-diagonal parameters fixed to ensure a displacement ellipsoid orientation normal to the Pb-Pb line. Correlation between thermal displacement parameters and the atom positions are too high, so that independent refinement would lead to unphysical results. This is most likely caused by the high pseudo-symmetry of the structure.
Position and orientation of the NH3CH3 cation were refined using a rigid-body approach based on a DFT-optimization of the molecule geometry used previously. 4 Thermal displacement parameters were kept fixed. The orientation of C-N direction and hydrogen positions were not experimentally determined, but assumed based on symmetry restrictions and geometry. Refined parameters for the single-phase structure at 160 K are given in Table S1.    Fig. S5. The trifold splitting of the cubic 100 peak at 15.6° at first glance looks like it might be explained by the orthorhombic unit cell of low-temperature phase described in the literature alone (lower row of Bragg peaks). However, the relative intensities are in strong conflict with this interpretation, as are the positions of strong peaks at high diffraction angles. Relative intensities vary strongly between differently prepared samples in a manner that can only be explained by a mixture of phases with varying fractions. The group of peaks at 22.2°, resulting from the cubic 110 peak shows two additional weak peaks, which remain unexplained. Their origin is unknown, but they reliably appear in all low-temperature synchrotron XRPD measurements of MAPbCl3.     Fig. S5, which was heavily ground and consists mostly of orthorhombic phase O2, containing only 17 % of the phase described in the literature as low-temperature phase (phase O1). Sample 2 is the same batch, but only lightly ground, and contains about 30 % of O1 phase. Sample 3 is a different batch and very lightly ground only, to the degree typically used in laboratory XRD. This sample consists entirely of the literature lowtemperature phase O1. However, low divergence of synchrotron radiation leads to bad particle statistics, preventing Rietveld refinement. EXAFS experiments discussed in this paper were done on samples ground even harder than sample 1; pure phase O2 was present in the powders used for EXAFS measurements. For MAPbI3 no such effect was observed.     (12)

MSRD and MSD
In general, the comparison of mean square relative displacement (MSRD) from cumulant analysis of temperature-dependent EXAFS data and mean square displacement (MSD) from diffraction allows deeper insights into the vibrational anisotropy of the bonds under consideration. 11 For our case, this means that we have to consider the sum of the temperature factors of the lead and the halide atom for the MSD from the diffraction, and the parallel MSRD and the perpendicular MSRD for the MSRD from the EXAFS data. For our investigated hybrid perovskites, however, an isotropic temperature factor is present for the lead atom in the diffraction and a discus-shaped atomic displacement ellipsoid is present for the halide atoms (Fig. S19a). It should be noted here that the comparison of partially anisotropic temperature factors for the MSDs and MSRD from EXAFS were already carried out for a very similar system, namely ReO3. 12 However, the atomic displacement ellipsoid was parameterized in the Rietveld refinement by the six anisotropic displacement parameters (ADP  Fig. S18). In a subsequent Rietveld refinement on the synchrotron data of MAPbI2.94Cl0.06, ADPs for the halide atoms could be refined. Here, the isotropic temperature factors of the lead atoms were no longer free parameters, but the parameters given by Einstein's behavior were used (Fig. S21). For the synchrotron data of MAPbI3, this approach did not allow refinement of the ADPs for the iodine atoms, so that we could only draw a comparison with the literature data available to us (Table S3 and Fig. S20). Furthermore, the analysis of ADPs is only possible to a limited extent for MAPbCl3.
For example, although a refinement of the anisotropic temperature factors for the chlorine atom on the Wyckoff position 8d is possible for the synchrotron data at 160 K (Table S1 and Fig. S7), only isotropic temperature factors can be refined for the chlorine atom on 4c (Fig. S22). The analysis of the isotropic temperature factors for the lead atom is also difficult. In some cases, lower temperatures result in negative temperature factors, so that we refrain from a detailed discussion for the time being. From our preliminary compilation (Fig. S20-S22), however, we can already note for MAPbI3 and MAPbI2.94Cl0.06 (probably also for MAPbCl3) that parallel MSD = Pb Uiso + halide U � 3 (Fig. S19) is larger than parallel MSRD (the difference then corresponds to the displacement correlation function (DCF) 13,14 ). The DCF is similar to that for ReO3. 15 The differences between perpendicular MSD = Pb Uiso + halide U � 1 (Fig. S18) and the perpendicular MSRD seem to be smaller for MAPbI3 and MAPbI2.94Cl0.06. Overall, however, it can be stated that there is not yet sufficient information regarding the ADPs from the diffraction, especially in the orthorhombic phase. One possibility would be to carry out a parameterized Rietveld refinement. 16 This is beyond the scope of this work and could be a future approach to this issue.  (Franz et al. 2016. Note that the orientation of I2 is not drawn correctly in Fig. 3 of the original work). 5 Orientation of the CH3NH3 + cation in the pseudo-cubic [PbI3] cage. The discus-shaped atomic displacement ellipsoids of the iodine atoms (in violet) are represented at 50 % probability. b) Enlargement of the atomic displacement ellipsoid of I2 from a) with principal axes of the anisotropic atomic displacement parameters. c) Principle representation of the discus-shaped atomic displacement ellipsoids of the iodine atom I2. The atomic displacement ellipsoid can be represented by the mean square displacement (MSD) parameters U1, U2 and U3 (principal axes of the anisotropic atomic displacement parameters). 10 The averaged mean square displacement (MSD) U � 1 (perpendicular MSD) was determined from averaging the U1 and U2 values of the corresponding atom positions. U � 3 (parallel MSD) was determined from the averaged value from U3.  [5][6][7][8] From the ADP's, the principal axes of the ADP (U1, U2, and U3) were calculated with Vesta. 9 The eigenvectors of Ucart (ADP's with Cartesian basis) define the principal directions of the anisotropic displacement ellipsoid. 10 The averaged mean square displacement (MSD) U � 1 (perpendicular MSD) was then determined from the U1 and U2 values of the corresponding atom positions. For U � 3 (parallel MSD), the averaged value from U3 was determined. The last column shows the isotropic displacement parameters for lead.  (2) 0.172(2) 0.0225 (7) (Table S3). b) solid red circles: perpendicular MSRD/2; open symbols: the sum of the averaged mean square displacement U � 1 (perpendicular MSD), and the isotropic temperature factor Uiso of the lead atom derived from diffraction literature values (Table S3). Red lines: a) parallel MSRD, b) perpendicular MSRD/2 Einstein behavior; grey lines: a) perpendicular MSRD/2, and b) parallel MSRD Einstein behavior; dashed and dotted lines: extrapolations of the low-temperature, Einstein model fits to higher temperatures.  (Table S1) and Baikie et al. 2 is shown. In b), the perpendicular MSRD is shown, which was calculated based on ΔRXRD and ΔREXAFS. In addition, the sum of the averaged mean square displacement U � 1 (parallel MSD) and Pb Uiso derived from diffraction (Table S1)