2.1. Synthesis of FAPbBr₃

Powder samples were synthesized using different routes [after Saidaminov et al. (2015) and Baikie et al. (2013)] for the D₄ and hydrogenous samples. Hydrogenous FAPbBr₃ powder was synthesized from stoichiometric mixtures of FABr (99.99% from Ossila) and PbBr₂ (98+%, extra pure, from Arcos Organics) in di­methyl­formamide (DMF, 99.8%, Roth) and homogenized overnight at room temperature, followed by evaporation of the solvent at 75°C, yielding 100% FAPbBr₃.

2.2. Synthesis of (D₄)-FAPbBr₃

16.7 g (0.160 mol, 1 equiv.) of formamidinium acetate was dissolved in 25 ml milliQ water (18.2 MΩ) in a 100 ml two-neck flask equipped with reflux condenser, dropping funnel and magnetic stirring bar. The reaction mixture was cooled in an ice bath. Subsequently, 4.5 ml hydro­bromide acid (HBr in 47% water, 0.176 mol, 1.1 equiv.) in 10 ml milliQ water was added under constant stirring. Then, HBr was added to the reaction mixture. This mixture was heated to reflux for around one hour. Afterwards water and acetic acid were distilled in a rotary evaporator until a white powder occurred. Subsequently, another 4.5 ml of hydro­bromic acid in 10 ml milliQ water was added and distilled in the rotary evaporator until 19.87 g (99.35%) formamidinium bromide, as a white crystalline powder resulted.

In a 50 ml flask with stirring bar and a stopper, 8 g of formamidinium bromide was dissolved in ca 25 ml of deuterium oxide. Additionally 1–2 ml (0.064 mol) of deuterium bromide in D₂O were added. After one hour of stirring, the deuterium oxide was removed by rotary evaporation. This procedure was repeated three times, yielding 7.95 g formamidinium bromide D₄. Afterwards the dry product was used in the following steps without further purification. The final reaction step was similar to the aforementioned synthesis procedure for the hydrogenous FAPbBr₃ only exchanging FABr with (D₄)-FABr. The samples were stored under N₂ to avoid potential degradation by oxygen and humidity.

2.3. Neutron powder diffraction and synchrotron X-ray powder diffraction

For a reliable detection of hydrogen/deuterium positions and to distinguish between C and N, neutron powder diffractograms were collected at the fine-resolution powder diffractometer E9 (FIREPOD) at the BER II neutron source at Helmholtz-Zentrum Berlin (HZB) (Franz & Hoser, 2017). A deuterated (D₄) and a hydrogenated FAPbBr₃ sample were placed in 6 mm diameter vanadium cans and measured in a temperature range of 3–300 K using a dry cryostat (TROK). A wavelength of λ = 1.7982 (1) Å (511-Ge) was applied.

X-ray powder diffraction data in the range of 5°< 2θ < 134° were collected for FAPbBr₃ at the diffraction end station of KMC-2 beamline (BESSY II, HZB; Többens & Zander, 2016) using a radiation energy of 8048 eV [λ = 1.5406 (1) Å]. Additionally, for low-temperature experiments a modified Gifford–McMahon (GM) closed-cycle cryocooler, in-house label CCR-XRD, configured with a double Kapton cupola and helium exchange gas was used (HZB, 2018). For an exact determination of the phase transition temperatures selected-region powder diffractograms (25°< 2θ < 35°) in the range from 20 to 285 K in 1 K steps were additionally taken.

2.4. Analysis

3.1. The cubic Pmm structure at 300 K

The overall room-temperature structures of (D₄)-FAPbBr₃ and FAPbBr₃ were found to be similar to studies performed by Schueller et al. (2018) and show the Glazer notation a⁰a⁰a⁰. No octahedral tilting is present.

In a refinement from laboratory X-ray powder diffraction data, Hanusch et al. (2014) placed the central carbon of the FA molecule as the rotational centre at the 1b Wyckoff position at (½, ½, ½) in the centre of the cuboctahedral cage. Nitro­gen was placed twelvefold disordered at (y, y, ½) with y = 0.3363 (5), with both nitro­gen atoms in the molecule represented by the same Wyckoff position. This simplifying approach restricts the N—C—N angle to a reasonable value of 120°.

From single-crystal X-ray diffraction data, Govinda et al. (2018) refined this model by allowing both atoms to deviate from their high-symmetry site, with C at 6f (x, ½, ½) and N at 24l (x, y, ½). This refinement places the carbon 0.42 (1) Å away from the centre of the cage, but does not fundamentally change the model. In both cases, the high site symmetry of 1b results in a sphere of disordered nitro­gen atoms around a carbon atom or a small sphere of disordered carbon atoms. Hydrogen atoms are not included in either model.

Our approach, using rigid-body modelling to restrict the number of free parameters, as a matter of principle places every atom of the molecule on a low symmetry, general Wyckoff site 48n (x, y, z). This of course results again in embedded spheres of carbon, nitro­gen and hydrogen. However, in contrast to previously published models the distribution of scattering power density within the spheres must be consistent with intramolecular geometry. This, together with the non-negligible scattering power of hydrogen, allows for a determination of the real positioning of the individual molecules underlying the disordered distribution.

Our results for FAPbBr₃ are in good agreement with the above-mentioned results. Carbon is located almost in the middle of the cubic unit cell, at 0.49 Å from the centre, and very close to the positions found by Govinda et al. (2018). However, where the older models restrict the nitro­gen to a single sphere, we found the two independent nitro­gen atoms to occupy very different positions. One, 1.03 Å from the centre approximately at (y, y, ½), conforms to the position found in the previous studies. The other, 1.36 Å from the centre and approximately at (x, ½, ½), is a newly identified position. Both positions place nitro­gen at approximately 3.2 Å from the bromine anion, in positions to form hydrogen bonds. Overall, this structure is not significantly different from the published structures, but described by a more detailed model.

The situation is different for (D₄)-FAPbBr₃ (see Fig. 2). In the deuterated compound the FA cation is found to be heavily decentred, with the central carbon atom at more than 2 Å distance from the 2b site and one of the nitro­gen atoms close to it. This displacement is accompanied by very high Debye–Waller factors in particular of the FA cation. Pb and Br also have higher Debye–Waller factors than in the hydrogenated compound. A possible reason for this high displacive disorder might be that the higher mass of the deuterium hinders the rotation of the cation and thus the breaking of the hydrogen bonds necessary for this rotation. The resulting stronger average hydrogen bond might pull the cation out of its average position in the centre of the cage. A problematic aspect of the observed structure is that it places one deuterium too close to Br⁻, at a distance of only 1.73 Å. This, however, can be explained by geometric effects that make the distance between the average atom positions obtained by diffraction appear shorter than the real local distances. The low-temperature structure refinement shows that the displacement of Br from its high-symmetry position in the cubic structure can be more than 0.4 Å; this is in agreement with the r.m.s. displacement from the Debye–Waller factor. In addition the strong displacement of the cation in the direction lateral to the Br⋯D—N hydrogen bond also means that real local Br⋯D distances are much higher. In the following discussion of the low-temperature structures we will see that this motif of a highly displaced FA⁺ cation is present in all modifications of the deuterated compound.

Figure 2 Octahedral network of FAPbBr3 and (D4)-FAPbBr3 at 300 K (space group ). Displayed here is one FA position out of 48; left: FAPbBr3 unit cell with PbBr6 octahedra and the inclined FA molecule in the centre; Right: (D4)-FAPbBr3 with its FA molecule strongly dislocated from the unit-cell centre; the atoms are number and colour coded as follows: hydrogen – 1, yellow; deuterium – 2, red; nitro­gen – 3, light blue; carbon – 4, light grey, lead (octahedra) – grey; bromine – brown (edges of octahedra).

3.2. The tetragonal P4/mbm structure at 240 and 180K

The neutron data refinement of FAPbBr₃ at 240 K and 180 K, and (D₄)-FAPbBr₃ at 240 K yield the tetragonal space group P4/mbm () in which the octahedral network tilts in-plane around the c axis (a⁰a⁰c⁺) (see Fig. 3). In this space group, the centre of the cage at site 2c has local symmetry mmm. As this symmetry is higher than the molecule symmetry of mm2, at least twofold disorder is inevitable. However, a significant tilt of the molecule breaks symmetry even further, resulting in a fourfold disorder with formamidinium on site 8j with site symmetry m. The placement of the molecule at this special site, where the mirror plane of the molecule coincides with the mirror plane of the space group, was not purported by the structural model, it resulted from the Rietveld refinement without significant deviations. While the preceding is valid regardless of deuteration state, the structures differ in the placement of the molecule. In the hydrogenated form, displacement from the centre of the cage is again small. This results in the formation of nearly symmetric, but weak N—H⋯Br hydrogen bonds with two opposing edges of the cage. In (D₄)-FAPbBr₃, the molecular centre atom carbon is strongly shifted out of the centre position. Consequently, only one N—D⋯Br hydrogen bond is formed, which is shorter. The position and orientation of the formamidinium cation in the hydrogenated form is very similar to the one underlying the disordered distribution in the cubic phase.

Figure 3 Octahedral network of FAPbBr3 at 180 and 240 K (left and middle) and (D4)-FAPbBr3 (right) shown along [001] (top) and [] (bottom); the crystal structures adopt space group P4/mbm with in-plane tilted octahedra around the c axis with the molecular distribution at 240 K and 180 K in [110]; in (D4)-FAPbBr3, the FA molecule is dislocated from its central position in the cuboctahedral void; the atoms are number and colour coded as follows: hydrogen – 1, yellow; deuterium – 2, red; nitro­gen – 3, light blue; carbon – 4, light grey, lead (octahedra) – grey; bromine – brown (edges of octahedra).

3.3. The orthorhombic Pnma structure at 140, 10 and 3 K

The measurements taken at the BERII neutron source were at 10 K for FAPbBr₃, and at 140, 10 and 3 K for (D₄)-FAPbBr₃. Due to the extensively long measurement times for the hydrogenous sample (to reach satisfying neutron counts statistics of the powder pattern) only one measurement in the stability region of the orthorhombic phase could be performed.

The low-temperature phases (see Figs. 4, 5 and 6) of FAPbBr₃ adopt the orthorhombic crystal system with space group Pnma (). The local symmetry at the centre of the cage is m_b, a mirror plane perpendicular to b. This would allow for a fully ordered structure with the planar FA molecule inside the mirror plane. This is not realized. In the hydrogenated forms the planar FA molecule is oriented nearly exactly perpendicular to m_b (see Fig. 5, left). This results in twofold disorder, with 0.5:0.5 partial occupation of symmetrically equivalent orientations. The placement of the FA cation close to the centre of the cage and its orientation are very similar to the positioning underlying the distribution in the tetragonal form of the compound.

Figure 4 Visualization of the (D4)-FAPbBr3 in which the refinement resulted in two symmetry-independent molecular positions: molecule 1 (left) is diagonally located in the Br-lozenge with the molecular centre atom C in the middle; molecule 2 (right) is strongly off-centred towards the PbBr6 network. The atoms are number and colour coded as follows: hydrogen – 1, yellow; deuterium – 2, red; nitro­gen – 3, light blue; carbon – 4, light grey, lead (octahedra) – grey; bromine – brown (edges of octahedra).

Figure 5 Visualization of octahedral networks of FAPbBr3 (left) and (D4)-FAPbBr3 (middle and right) at 10 K. (D4)-FAPbBr3 shows two symmetry-independent molecular positions in which the second molecule is strongly off-centred from the Br-lozenge centre. The atoms are number and colour coded as follows: hydrogen – 1, yellow; deuterium – 2, red; nitro­gen – 3, light blue; carbon – 4, light grey, lead (octahedra) – grey; bromine – brown (edges of octahedra).

Figure 6 (D4)-FAPbBr3 network at 3 K with visualization of the two symmetry-independent molecular positions and their different inclination angles. The atoms are number and colour coded as follows: hydrogen – 1, yellow; deuterium – 2, red; nitro­gen – 3, light blue; carbon – 4, light grey, lead (octahedra) – grey; bromine – brown (edges of octahedra).

The structures of deuterated (D₄)-FAPbBr₃ could not be described satisfactory with only one independent FA molecule. It was necessary to split it into two independent ones, resulting in an overall fourfold disorder (see Fig. 5, middle and right; Fig. 6). The distribution of the cation over these two independent sites is stable, refining to occupation ratios of 0.58 (1): 0.42 (1) without any significant change over the whole temperature range (see Fig. 6). The higher occupied position is once again similar to the one observed in the respective, D₄ in this case, tetragonal form. The cation is in an orientation lateral to the m_b plane, but shifted out of the centre of the cage and tilted, so that a single N—D⋯Br hydrogen bond can form. The cations at the lower occupied site, on the other hand, are shifted so far from the centre that one ND₂ group extends into the lozenge spanned by bromine that forms the window between adjacent cages.

3.4. Temperature-dependent phase transitions

In the synchrotron diffraction pattern overview (see Fig. 7) it can be clearly seen that the difference in the powder pattern is fairly small and the evidence-giving region is between 25° < 2θ < 35°. Thus, regions of interest scans were taken in 1 K steps and the phase transition temperatures could be determined. The 220/022 superlattice reflections show the orthorhombic–tetragonal phase transition at 157 K. The orthorhombic 221/122 superlattice reflections vanish at 264 K and as a consequence, mark the tetragonal–cubic phase transition (see Fig. 8).

Figure 7 Overview of synchrotron powder diffraction data of FAPbBr3 taken from 20 K to 300 K in 30–60 K steps.

Figure 8 Synchrotron X-ray diffraction contour colour plot of a selected 2θ region, collected using a ramp rate of 1 K and showing the temperature-dependent phase transition of FAPbBr3 from Pnma to P4/mbm at 157 K (lower dashed black line) and from P4/mbm to at 264 K (upper dashed black line).

Fig. 9 shows the temperature dependence of the lattice parameters of both hydrogenous FAPbBr₃ and (D₄)-FAPbBr₃ as determined by the refinement of the neutron diffraction data. For a better comparability all lattice parameters are shown as pseudocubic (indexed as psc) with a, c_psc = and b_psc = b/2. The orthorhombic, tetragonal and cubic lattice parameters are shown in Table S1. The thermal expansion of the pseudocubic lattice parameters of the hydrogenous sample follow – as expected – a clear trend up to 300 K. In contrast, the lattice parameter a of (D₄)-FAPbBr₃ shows an unusual behaviour shortly before the phase transition from Pnma to P4/mbm (Fig. 9, bottom view).

Figure 9 Evolution of the lattice parameters in terms of increasing temperature of hydrogenous (upper view) and deuterated (lower view) FAPbBr3. The inset in the bottom figure displays the zoomed region between 0 and 10 K. For a better comparability the pseudocubic lattice parameters are displayed. The error bars are smaller than the symbol sizes and the dashed lines are only a guide for the eye. The pseudocubic a lattice parameter (black squares) in (D4)-FAPbBr3 shows an unusual thermal behaviour shortly before the phase transition from Pnma to P4/mbm.

The connected PbBr₆ octahedra are defined by the Pb—Br1—Pb and Pb—Br2—Pb angles (see Fig. 10, left-hand-side; the FA molecule is not displayed for clarity). With increasing temperature, these angles increase and converge to reach 180° at room temperature, leading to an arrangement of the octahedra as shown in Fig. 2 for FAPbBr₃ and (D₄)-FAPbBr₃.

Figure 10 Comparison of the tilt angle Pb—Br2—Pb in FAPbBr3 and (D4)-FaPbBr3. The spatial extent caused by the two molecular positions leads to an increased tilting of the octahedral network. The dashed lines are only a guide for the eye.

Glazer notation of octahedral tilting in Pnma is a⁻b⁺a⁻ with an out-of-phase tilting around the cubic a axes and an in-phase tilting around the cubic b axis ([001]_cub = [101]_orth, [010]_cub = [010]_orth and [100]_cub = [10]_orth). The latter is shown in Fig. 10 (right) as Pb—Br2—Pb angle. In contrast to hydrogenous FAPbBr₃, the tilt angle in (D₄)-FAPbBr₃ in the range from 3 to 240 K is lower and, furthermore, does not show a significant increase up to 240 K. The two symmetry-independent molecular sites which are present in all deuterated low-temperature modifications crystallizing in space group Pnma require more space in the voids between the octahedra. To compensate for this, the octahedral network is forced to tilt further. Since the FA molecule is located in the ac plane the lattice parameters are influenced by this as well.

Fig. 11 displays the mean unit-cell volumes of hydrogenous and deuterated FAPbBr₃ from 3 to 300 K (calculated from the pseudocubic lattice parameters and chosen due to the enhanced comparability of the values). The graph shows the increased unit-cell volume of (D₄)-FAPbBr₃ due to deuteration. The unusual thermal behaviour of the a lattice parameters at 140 K (see Fig. 9) is reflected in the value for the volume of (D₄)-FAPbBr₃ and is in the range of the value of the hydrogen-containing samples.

Figure 11 Comparison of mean unit-cell volumes of FAPbBr3 (black squares) and (D4)-FAPbBr3 (blue open circles). (D4)-FAPbBr3 shows the larger unit cell, compared to the FAPbBr3. The dashed lines are only a guide for the eye.