Supporting Information The Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[hc(nh 2 ) 2 ]PbI 3, at 298 K Mark T. Weller, Oliver J Weber, Jarvist M. Frost, Aron Walsh Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Bath, BA2 7AY, UK Corresponding Author M.T.Weller@bath.ac.uk Experimental Synthesis 6.000 g (0.016 mol) of lead acetate trihydrate (Sigma) was added to a 3 neck round bottom flask equipped with reflux condenser containing 12.4 ml of HI (57 wt %, aq.) and 3.1 ml H 3 PO 2 (50 wt%, aq.). 1.647 g of formamidinium acetate (0.016 mol, Sigma) and the solution heated to 100 C, then immediately left to cool for crystals of black -FAPbI 3 to grow, which converted in solution to yellow crystals -FAPbI 3 at room temperature. The crystals were filtered, washed with dry diethyl ether and heated to 130 C in an oven for 2 hours. Final yield: 8.303 g, 83 %.
Powder X-ray diffraction patterns were collected on a Siemens / Bruker D5000 diffractometer using Cu K radiation ( = 0.15418 nm). Figure S1. Thermogravimetric analysis was carried out using a Polymer Laboratories PL-STA TGA with ISI Thermal Analysis software. Weight loss and heat flow of a 10 mg sample heated in air at 20 C / min was recorded up to 160 C. Neutron powder diffraction data collection and analysis. Approximately 10g of hydrogenous FAPI was loaded into a 5 mm vanadium slab can and neutron powder diffraction data were collected on the HRPD diffractometer at ISS at 298 K over a period of 10 hours. While a large incoherent background is obtained from hydrogen-containing samples in neutron diffraction over longer experimental times this is averaged and may, for crystallographically simple compounds, such as FAPI that give few well resolved diffraction peaks, be subtracted from the raw experimental data.
Figure S1 Comparison of reflection positions generated by the cubic unit cell of α-fapi used in this work ( upper) and the hexagonal cell of Stoumpos et al. 1 (lower) in the d-spacing region 1.30-2.0 Å.
Figure S2. Comparison of observed and calculated NPD profiles of α-fapi in the d-spacing range 2.3-2.0 Å using the model of Stoumpos. 1 Note the published model had no hydrogen atom position which would strongly affect reflection intensities Figure S3. Powder X-ray diffraction data collected on a Siemens / Bruker D5000 diffractometer using Cu K radiation ( = 0.15418 nm, no sample rotation to average peak intensities in a highly crystalline sample). Upper trace as prepared black -FAPbI 3. Lower trace - the same sample aged for 20 days in a dry ambient atmosphere showing a small level (~20%) conversion to the yellow δ-phase. Of note is that the pattern obtained after 20 days displays changes (in comparison to the freshly prepared material) in the relative intensities of diffraction peaks derived from the -FAPI still present; this may be interpreted as the result of rate of the phase transition to -FAPI occurring at dissimilar rates for different crystallographic growth directions.
Figure S4. Le Bail fits to PXRD data (Collected on Bruker D8 diffractometer with CuK α1 /K α2 radiation, phi rotation of sample at 60 rpm) of -FAPI. Upper pattern - cubic (Pm- 3m) model, χ 2 = 2.18. Lower pattern - trigonal (P-3m1) model, χ 2 = 3.04. 1 Note that fits to powder X-ray diffraction data would be expected to be of similar quality as diffraction is dominated by the heavy atom positions. No diffracted intensity was observed at additional reflection positions generated using the hexagonal model.
Figure S5. TGA of δ-fapbi 3 in the temperature range 25-160 C scanned at 5 C / min. Less than 1% observed weight loss from the sample of α-fapbi 3 over the temperature range scanned probably associated with the loss of surface adsorbed moisture, solvent. The initially yellow material had transformed fully to black -FAPbI 3 by visual inspection at the end of the experiment.
Computational Setup Calculations were performed on α-fapi within density functional theory with electron exchange and correlation described using the PBEsol functional form. Periodic boundary conditions with a plane wave basis set (500 ev cut- off with 2 2 2 k-points) were employed in the VASP codes. The projector augmented wave method was used to describe the frozen core electrons including scalar relativistic effects. Structure optimisation was performed until all internal atomic forces were within 0.001 ev/å. We undertook Born-Oppenheimer molecular dynamics at 300 K using a 2 2 2 supercell expansion of the fully optimised pseudo-cubic FAPI structure (see https://github.com/wmd-bath/hybrid-perovskites ). An integration timestep of 0.5 fs (sufficient to describe C-H and N-H vibrations) was combined with a reduced plane wave cut-off of 300 ev (at the gamma point for the supercell) to enable a sufficiently long production run of 200 ps. Trajectory frames were saved every 50 steps (0.025 ps). The first 10 ps (400 frames) of data were discarded, to provide time for equilibration. The typical 2 ps feature observed for the dynamics of interest suggest that this is sufficient time for decorrelation to occur (within the limit of our small system size), and is sufficient time for the ionic temperature to become well defined and stabilised at the thermostat setting of 300 K.
Figure S6. Density maps (two-dimensional hexagonal histograms in spherical coordinates) of FA alignment within the perovskite cage as determined by molecular dynamics at 300 K. (a) The data are centered on ϕ, θ = 0 being facial <100> orientation. (b) The symmetry folded data bounds the segment between <111> (bottom right), <110> (top right) and <100> (top left) orientations, showing the strong preference for <100> alignment at 300 K. Figure S7. Time correlation analysis of the alignment of the C-H bond in the FAPI system. The probability density (blue) is the autocorrelation time for the dot product of the bond vectors to have decayed to zero (i.e. the distribution of times by which the molecule has rotated by greater than 90 degrees). The cumulative probability (green) is the sum of this distribution. The point at which this cumulative probability is 0.5 defines where 50% of the molecules have had sufficient time to reorient by 90 degrees or more, and is the mean value that we take as the rolling over time constant of 2.0 ps. The standard autocorrelation is also presented (red).
Trajectory Analysis We have generalised our previously reported molecular dynamics analysis tools for MAPI (Frost, APL Materials 2014) to the FAPI system. The toolkit is freely available at https://github.com/jarvist/mapi-md-analysis. Taking the C-H bond as the reference vector, we build a histogram of the orientation distribution (in polar coordinates) of the eight FA ions in Figure S6(a). Basins are observed around the equivalent <100> directions. Asymmetry in these distributions is present due to the finite simulation length and the additional correlation imposed by the small simulation size; however, by exploiting the octahedral symmetry of the cube in which the molecule resides, the signal to noise ratio is greatly enhanced as shown in Figure S6(b). While a large fraction of orientational space is sampled at room temperature, there is an unambiguous preference for the molecular to align towards the face of a cube (<100>). Further analysis of the autocorrelation in molecular orientation revealed a time constant for the rolling over of the FA cation by 90 degrees to be 2.0 ps. Reference 1) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and near-infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019 9038.