Structural analysis at room temperature (Single Crystal ND)
The room temperature crystal structure analysis carried out from single-crystal ND data confirms the cubic Pm\(\stackrel{-}{3}\)m space group. The three possibilities of MA delocalization, i.e. [100], [110] and [111] were tested, and the best fit was achieved when the MA unit is aligned along [110] direction. This fact is in agreement with our previous results from neutron powder refinements21. Furthermore, the single-crystal data allow us to refine the C–N displacement in the inorganic lattice in addition to the anisotropic displacement factors. The crystallographic results and the main Br∙∙∙H distances and angles are listed in Table 1 and Table 2, respectively.
Theoretical studies of MAPbBr3 differ regarding the MA alignment in cubic symmetry. Varadwaj et al.36 found that the [100] and [111] orientations are the most energetically favourable. However, Yin et al.37 reported that the MA is aligned along [110] from ab initio calculations and Raman spectroscopy. They also observed that MA only interacts with the inorganic lattice by H-bonds through –NH3, and these distances are in agreement with our results. However, the values in Table 2 reveal an additional H-bond through –CH3 by H22 atoms. Figure 1 illustrates a unique MA in the PbBr3 cage where the deduced H-bond interactions are highlighted and labelled with the numbers listed in Table 2. On the other hand, additional information on the MA behaviour can be obtained from the anisotropic atomic displacement factors. The H12 is slightly flattened in the N–H12∙∙∙Br direction (label 6); in contrast, H11 is slightly stretched in the H-bond labelled as 1, while it is very stretched in the H-bond labelled 2 (see Table 2 and Fig. 1). This last behaviour is in agreement with the hardness of H-bond interaction, as can be deduced from the distance and angles. Finally, the anisotropic displacement of N and C atoms suggests that the MA unit could rotate in the [100] direction; this movement implies that the MA units move over the [100] configurations. This fact suggests an energetic similarity between [110] and [100] positions in this phase. Besides DFT evidences, this behaviour was also observed by us from synchrotron X-ray diffraction, where the MA evolved from [110] to [100] directions below room temperature21.
Table 1 : Crystallographic data for MAPbBr3 phase in cubic system (Pmm) from single crystal ND at 298 K.
a = 5.9259(1) Å, and V = 208.10(1) Å3
|
x
|
y
|
z
|
Ueq
|
focc
|
Pb
|
0
|
0
|
0
|
0.0306(2)
|
1
|
Br
|
0.5
|
0
|
0
|
0.1027(3)
|
1
|
N1
|
0
|
0.6084(3)
|
0.6084(3)
|
0.0667(5)
|
0.0833
|
C2
|
0
|
0.4416(2)
|
0.4416(2)
|
0.0667(5)
|
0.0833
|
H11
|
0.5
|
0.557(3)
|
0.739(2)
|
0.13(3)
|
0.0417
|
H12
|
0.648(1)
|
0.711(1)
|
0.584(2)
|
0.11(2)
|
0.0417
|
H21
|
0.5
|
0.527(3)
|
0.278(2)
|
0.13(3)
|
0.0417
|
H22
|
0.352(1)
|
0.335(2)
|
0.454(3)
|
0.11(2)
|
0.0417
|
wRF2 = 5.83%, χ2 = 1.7, RBragg = 4.04%
|
Atomic displacement parameters (Å2)
|
|
U11
|
U22
|
U33
|
U12
|
U13
|
U23
|
Pb
|
0.0306(2)
|
0.0306(2)
|
0.0306(2)
|
0
|
0
|
0
|
Br
|
0.0200(2)
|
0.1440(4)
|
0.1440(4)
|
0
|
0
|
0
|
N1
|
0.0548(4)
|
0.0726(5)
|
0.0726(5)
|
0
|
0
|
-0.0548(5)
|
C2
|
0.0548(4)
|
0.0726(5)
|
0.0726(5)
|
0
|
0
|
-0.0548(5)
|
H11
|
0.27(6)
|
0.03(3)
|
0.10(1)
|
0
|
0
|
-0.03(3)
|
H12
|
0.103(9)
|
0.103(9)
|
0.13(3)
|
-0.05(1)
|
-0.03(2)
|
0.005(2)
|
H21
|
0.27(6)
|
0.03(3)
|
0.10(1)
|
0
|
0
|
-0.03(3)
|
H22
|
0.103(9)
|
0.103(9)
|
0.13(3)
|
-0.05(1)
|
-0.03(2)
|
0.005(2)
|
Table 2: Possible H-bond distances of MA at 300 K.
|
Label
|
Distance (Å)
|
Angle (°)
|
–NH3
|
|
|
|
NH11∙∙∙Br1
|
1
|
3.05(1)
|
99.0(7)
|
NH11∙∙∙Br1
|
2
|
3.36(1)
|
117.7(1)
|
NH12∙∙∙Br1
|
3
|
2.74(1)
|
174.8(4)
|
–CH3
|
|
|
|
CH21∙∙∙Br1
|
4
|
3.53(1)
|
90.2(5)
|
CH21∙∙∙Br1
|
5
|
3.39(1)
|
114.1(3)
|
CH22∙∙∙Br1
|
6
|
2.89(1)
|
172.0(4)
|
Structural analysis at 2 K
The structural investigation performed at very low temperature, where the methylammonium’s mobility is minimized, allows making a detailed analysis of H-bond interactions between the MA and the PbBr6 inorganic framework. For this purpose, a high statistics NPD pattern was collected at 2 K at D20 powder diffractometer. Taking into account the previous results at low temperatures, MAPbBr3 should be at the orthorhombic symmetry in the Pnma space group19,21. The initial Le Bail refinements confirmed this symmetry; therefore, according to this model, the lead atoms are allocated in 4b (0,1/2,0) Wyckoff site and the bromides in 4c (x,1/4,z) and 8d (x,y,z) sites. This space group presents anti-phase octahedral tilts along a and c-axis and an in-phase octahedral tilt along b-axis, typified as a−b+a− in the Glazer’s notation38. A subsequent analysis, taking into account this inorganic framework, is used to obtain the missing nuclear density (scattering length density) in the lattice from Difference Fourier Maps. Figure 2 illustrates the positive (yellow) and negative (light blue) isosurfaces corresponding to the carbon/nitrogen and hydrogen atoms, respectively. These densities match the methylammonium cation and they allow to locate the atoms: C and N are at 4c (x,1/4,z) and H atoms distributed in 4c (x,1/4,z) and 8d (x,y,z) sites. The NPD pattern was successfully fitted with this model, as illustrated in Fig. 3. The main crystallographic data are shown in Table 3. The structure is similar to the one reported by Swainson et al.19 in a deuterated sample at 11 K and by Yang et al.22 at 95 K. It is important to remark that, in contrast with previous reports, no constraints were used in the refinements of the atomic position of the MA group, e.g. with no rigid body considerations.
Table 3 Crystallographic data for MAPbBr3 phase in orthorhombic system (Pnma) from NPD at 2 K.
a = 7.9335(4) Å, b = 11.8301(5) Å, c = 8.5743(3) Å and V = 804.74(5) Å3
|
x
|
y
|
Z
|
Uiso
|
focc
|
Pb1
|
0
|
0
|
0.5
|
0.002(1)
|
1
|
Br1
|
0.9689(8)
|
0.25
|
0.4839(8)
|
0.002(1)
|
1
|
Br2
|
0.2981(5)
|
0.0277(3)
|
0.7106(5)
|
0.002(1)
|
1
|
N1
|
0.5500(7)
|
0.25
|
0.5971(7)
|
0.005(1)
|
1
|
H11
|
0.682(2)
|
0.25
|
0.596(2)
|
0.032(2)
|
1
|
H12
|
0.512(2)
|
0.1795(5)
|
0.652(1)
|
0.032(2)
|
1
|
C2
|
0.481(1)
|
0.25
|
0.4336(8)
|
0.005(1)
|
1
|
H21
|
0.348(2)
|
0.25
|
0.431(2)
|
0.032(1)
|
1
|
H22
|
0.523(2)
|
0.1795(5)
|
0.378(1)
|
0.032(1)
|
1
|
Rp = 0.83%, Rwp = 1.09%, χ2 = 3.64, RBragg = 6.81%
|
The H∙∙∙Br distances and Br∙∙∙H–N (and C) angles are listed in Table 4. From these distances and angles, it is possible to deduce that the H-bonds exist only in the H11∙∙∙Br1 and H12∙∙∙Br2 atom pairs for –NH3 and in H21∙∙∙Br1 and H22∙∙∙Br2 for –CH3 group, labelled as 1, 4, 5 y 8 respectively. Figure 4 illustrates the MA unit in the PbBr3 perovskite cage, where these four H-bonds are highlighted and numbered. These distances show that the MA unit is shifted, such that the (N)H∙∙∙X distances are shorter than (C)H∙∙∙X ones, which is expected considering the greater electronegativity of N respect to C. This displacement is 0.17 Å, considering the difference between the centres of MA and the PbBr3 perovskite cage. Additionally, these distances can be compared with those obtained by from DFT calculations. Varadwaj et al.36 found theoretically the same four H-bonds interactions with the following values: 2.501 Å and 2.446 Å for (N)H∙∙∙Br and 3.005 Å and 2.916 Å for (C)H∙∙∙Br. These distances and the angles reported from DFT are in agreement with those experimentally obtained in the present work.
Table 4 : Possible H-bond distances of MA at 2 K.
|
Label
|
Distance (Å)
|
Angle (°)
|
–NH3
|
|
|
|
NH11∙∙∙Br1
|
1
|
2.47(2)
|
157.6(7)
|
NH11∙∙∙Br2
|
2
|
3.24(1)
|
106.2(4)
|
NH12∙∙∙Br1
|
3
|
3.25(1)
|
105.5(4)
|
NH12∙∙∙Br2
|
4
|
2.52(1)
|
152.4(6)
|
–CH3
|
|
|
|
CH21∙∙∙Br1
|
5
|
3.04(2)
|
170.1(7)
|
CH21∙∙∙Br2
|
6
|
3.96(1)
|
107.5(3)
|
CH22∙∙∙Br1
|
7
|
3.24(1)
|
101.3(5)
|
CH22∙∙∙Br2
|
8
|
2.93(9)
|
164.8(6)
|
Sequential analysis from 2 to 250 K (ΔT ≈ 4.5 K)
As mentioned in the Introduction Section, there are at least three phases confirmed in this temperature range: Pnma, I4/mcm and Pm\(\stackrel{-}{3}\)m. To analyse this and the role of MA in the transitions, several ND patterns were sequentially collected during the warming process from 2 K to 250 K with a temperature interval of ≈ 4.5 K. A first analysis of all patterns was made from the 2D plots shown in Fig. 5, where the phase transitions are observed. The tetragonal to cubic transition occurs abruptly between the patterns collected at 228.5 and 233.1 K. This temperature transition is in agreement with previous results from DSC, Vibrational Spectroscopy and crystallographic studies19,24,27,37. Otherwise, the transition from orthorhombic to tetragonal is diffuse and it is spread in a wide temperature range (from 146.6 to 155.6 K); moreover, the pattern collected at 151.1 K shows an intermediate situation but it was not possible to index it. This is highlighted in Fig. 5 for different reflections. This situation is similar to that found by us from synchrotron x-ray diffraction data at 150 K21.
The remaining patterns were correctly fitted with the previously reported space groups. The results are plotted in Fig. 6, where the thermal evolution of normalized unit-cell parameters and volume/Z are illustrated. Up to 146.6 K, the patterns were successfully fitted within an orthorhombic symmetry in the Pnma space group, based on the model presented in Table 2 and with no need of establishing any rigid body’s constrains. In this symmetry, the three unit-cell parameters remain in a plateau up to 40 K; then, while a parameter increases, the c axis undergoes a subtle reduction; conversely, the b parameter remains virtually constant. See Fig. 6a.
This particular thermal evolution of the unit-cell parameters is certainly unexpected; however, it can be well related to the MA position and its interactions with the inorganic framework. For instance, as shown in Fig. 4, the MA unit is lying on the a-c plane and it can be only shifted within this plane; hence, it is not surprising that the b parameter hardly changes in this temperature range. On the other hand, the opposite evolution of a and c parameters are due to the movement of MA in this plane; as temperature decreases the MA alignment comes near to the c axis with the consequent increase of c parameter and, simultaneously, the decrease of a parameter. This effect also can be observed in the octahedral tilts, as illustrated in Fig. 7, where the Pb–Br–Pb angles are shown. It is possible to observe that the Pb–Br2–Pb angle presents greater changes than Pb–Br1–Pb; this fact is also in agreement with the unit-cell parameters evolution.
The unit-cell volume evolution (Fig. 6b) remains constant up to 40 K and then this increase is the result of as a compromise between the unit-cell parameters behaviour.
After an abrupt phase transition, which will be analysed later on, the tetragonal phase is observed above 155.6 K, which is described in the I4/mcm space group. In this case, the MA unit was better modelled using the rigid body formalism, unveiling four possible positions of the organic cation. This refinement strategy was needed due to the delocalization of MA in this tetragonal phase. Thereby, it is possible to obtain a more realistic description of the MA situation within the inorganic framework. This organic unit was refined in both position and direction. As representative of this temperature range, Fig. 8 shows the Rietveld pattern refinement at 155.6 K together with a schematic view of the tetragonal crystal structure. Figure 9 shows a single MA unit in the inorganic framework where the main H-bond interactions are highlighted.
In the I4/mcm space group, Pb atoms are placed in 4c (0, 0, 0), whereas Br1 and Br2 atoms are located at 4c (0, 0, 1/4) and 8h (x, x + 1/2, 0) Wyckoff sites, respectively. The C, N and H atoms forming the organic unit are in 32m (x, y, z). The transition to the I4/mcm space group involves an in-phase octahedral tilt along the c-axis, typified as a0a0c+ in Glazer’s notation38. The complete crystallographic parameters are included in Table 5.
Table 5
Crystallographic data for MAPbBr3 phase in the tetragonal system (I4/mcm) from NPD at 155.6 K.
a = 8.2815(5) Å, c = 11.8508(8) Å and V = 812.77(8) Å3
|
x
|
y
|
z
|
Uiso
|
focc
|
Pb1
|
0
|
0
|
0
|
0.0053(6)
|
1
|
Br1
|
0
|
0
|
0.25
|
0.0584(19)
|
1
|
Br2
|
0.28909(6)
|
0.78910(6)
|
0
|
0.059(4)
|
1
|
C1
|
-0.0401
|
0.53029
|
0.21642
|
0.001(4)
|
0.125
|
N1
|
0.08945
|
0.45138
|
0.28560
|
0.001(4)
|
0.125
|
H1
|
0.11534
|
0.52114
|
0.35206
|
0.101(5)
|
0.125
|
H2
|
-0.0660
|
0.46053
|
0.14997
|
0.101(5)
|
0.125
|
H3
|
-0.1391
|
0.54472
|
0.26369
|
0.101(5)
|
0.125
|
H4
|
-0.0013
|
0.63802
|
0.18966
|
0.101(5)
|
0.125
|
H5
|
0.18843
|
0.43695
|
0.23833
|
0.101(5)
|
0.125
|
H6
|
0.05064
|
0.34365
|
0.31237
|
0.101(5)
|
0.125
|
Atomic Displacement Parameters (Å2)
|
|
U11
|
U22
|
U33
|
U12
|
Pb
|
0.0076(9)
|
0.0076(9)
|
0.00071
|
0
|
Br1
|
0.087(3)
|
0.087(3)
|
0.00071
|
0
|
Br2
|
0.036(3)
|
0.036(3)
|
0.104(7)
|
0.024(3)
|
Rp = 0.657%, Rwp = 0.891%, χ2 = 3.41, RBragg = 4.38%
|
This tetragonal phase is retained from 155.6 K up to 228.5 K, where a sequential refinement reveals the evolution of MAPbBr3 with temperature. Figure 6 shows the variation of the unit-cell parameters, a and c, and the unit-cell volume. The a parameter increases with temperature, while the c parameter slightly decreases. As a consequence, the unit-cell volume evolution increases with temperature.
Finally, the NPD patterns collected from 233.1 K to 250.0 K exhibit a cubic crystal structure. Figure 6 shows the unit-cell parameter and volume variation. All parameters regularly increase upon warming up, as is expected by the thermal expansion.
In addition, this sequential analysis also reveals some aspects of these phase transitions. While the T-C transition is smooth, the O-T one is abrupt, displaying a break in the unit-cell parameter and volume cell evolution, see Fig. 6. This behaviour is known and can be related to the change from fixed to delocalized MA cation. However, as mentioned in the Introduction section, several crystallographic aspects of this transition remain unknown. In our previous report on the structural evolution of MAPbBr3 from high-angular resolution SXRD, the pattern collected at 150 K was not compatible with the Pnma or I4/mcm space groups21. This was also observed in our sequentially acquired NPD data, at 151.5 K, as highlighted in Fig. 5. This fact prompted a more detailed inspection in this narrow temperature range, in order to unveil certain features regarding this transition.
Sequential analysis from 145 to 157 K (ΔT ≈ 0.5 K)
An additional sequential analysis was performed with a shorter temperature interval (≈ 0.5 K) around the orthorhombic/tetragonal transition. Figure 10 displays the 2D plot of the same three angular ranges shown in Fig. 5, exhibiting the evolution of several diffraction peaks within this temperature region. These additional measurements unveil the existence of an additional crystallographic phase in the 148.5–155.2 K temperature range.
Several works report on a possible coexistence of the orthorhombic and tetragonal phases in this interval22,26; we therefore considered the cited possibility. However, it was not possible to accomplish an accurate refinement using this two-phase approach. In other cases, different structural proposals (orthorhombic or tetragonal)23–25 described for this short temperature range did not allow fitting the ND patterns.
On the other hand, the more recent analyses over this issue were made for Gou and Wiedemann et al., who proposed an incommensurate structure27,28. This last work reports an incommensurately modulated structure in the (3 + 1)D superspace group Imma(00γ)s00 at 150 K from single crystal X ray diffraction data28.
Based on this report, we managed to fit the patterns with a derived commensurate Imma model, reaching a satisfactory result. A careful inspection of the patterns showed no evidence of an incommensurate structure. Indeed, no additional peaks of a modulated phase are observed in our data set. Thus, we concluded that our perovskite, according to NPD data, exhibits a low-temperature phase (2-148.3 K) defined in a Pnma orthorhombic symmetry, a novel orthorhombic Imma phase (148.8-153.8 K), a tetragonal structure defined in the I4/mcm space group (154.5-228.5 K) and a high-temperature phase (233.1–300 K) in a cubic Pm\(\stackrel{-}{3}\)m symmetry. The evolution of some selected reflections across the three space groups is displayed in the 2D plots of Fig. 10, illustrating the complexity of the MAPbBr3 crystallographic behaviour in this narrow temperature region.
Within this framework, we assembled a Imma model based upon the reported orthorhombic structure28. In this space group, Pb atoms are placed in 4a (0, 0, 0), whereas Br1 and Br2 atoms are located at 4e (0, 1/4, z) and 8g (1/4, y, 1/4) Wyckoff sites, respectively. The MA group is delocalized around (0, 1/4, 1/5) position. The transition to the Imma space group involves an in-phase octahedral tilt along c-axis, typified as a0b−c− in Glazer’s notation38.
Additionally, by means of Difference Fourier Maps (DFM) from NPD data, we were able to discern the organic cation, revealing the existence of two distinct delocalized MA groups, in two different positions. The elucidated organic units were refined using the rigid body approach, giving satisfactory results; see Fig. 11a for a Rietveld refinement at 150.5 K and Fig. 11b for the illustrated crystallographic model. The corresponding crystallographic information is listed in Table S1.
Thus, from a trial and error analysis of the MA position and subsequent DFM calculations, it was possible to find two MA units with different delocalization. As shown in Fig. 12a, one of the MA units is twofold delocalized along the b axis, with the H atoms directed towards each of the four Br atoms. The other MA molecule is also twofold delocalized along the a-axis, with a small tilt of about 10°, see Fig. 12b. This MA tilt explains the possible formation of H-bonds and the distortion of the PbBr6 structure. The shortest Br···H distance is highlighted in Fig. 11b, showing the correlation between the MA position and the inorganic PbBr3 distortion.
Figure 13 shows three plots that compare structural details of the low-temperature crystallographic phases, illustrating the behaviour of the novel orthorhombic Imma phase, compared to the already known Pnma and I/4mcm phases. The thermal evolutions of these parameters completes that previously shown in Figs. 6 and 7. Figure 13a displays the variation of the mean unit-cell volume/Z; there is a general expansion as temperature increases, with some fluctuations around the phase transition due to the rearrangement of the unit cell. Figure 13b illustrates the dependence of the unit-cell parameters with temperature; they are displayed in a pseudocubic form for a better comparison. Within the narrow temperature region for this intermediate Imma phase, the a parameter decreases with temperature whilst b and c increase. Figure 13c shows the evolution of the Pb-Br1-Pb and Pb-Br2-Pb angles.
H-Bond thermal evolution
It is well known that the H-bond interactions in hybrid perovskite materials play a paramount role in the stability of the crystal structures and their phase transitions. Hence, considering the H-bond interactions above described (2 K, 155.6 and 300 K), we now analyse the thermal evolution of these parameters in the 2–250 K temperature range. Figure 14 shows the H∙∙∙Br as a function of temperature. The label numbers in this Figure match those used in Figs. 1, 4 and 9 for RT, 155.5 and 2 K, respectively, and the number in parenthesis indicates if the H-bonds are single or twofold. It is possible to observe a progressive splitting in the NH∙∙∙Br and CH∙∙∙Br distances. While at high temperature there are not substantial differences when the H is bonded to a nitrogen or a carbon, at lower temperatures this difference takes relevance. This difference is moderate in the tetragonal symmetry, but it increases in the orthorhombic phase. This behaviour joins two aspects of the crystal structure at lower temperatures. First, the MA delocalization, presented in the cubic and tetragonal symmetry, avoids the formation of strong H-bond interactions. Then, in the orthorhombic phase the delocalization disappears, enabling the interaction between the MA unit and the PbBr6 lattice. The second aspect is the distortion of the inorganic framework, evidenced in the octahedral tilting or in the Br–Pb–Br angles (Fig. 7). Contrasting both parameters (Figs. 7 and 14) it is possible to confirm that the H-bond formation is enabled by the PbBr6 lattice distortion or vice versa. Anyway, this aspect reveals the structural complexity of these technological attractive hybrid perovskites.