Research ArticleMATERIALS SCIENCE

Entropy-driven structural transition and kinetic trapping in formamidinium lead iodide perovskite

See allHide authors and affiliations

Science Advances  21 Oct 2016:
Vol. 2, no. 10, e1601650
DOI: 10.1126/sciadv.1601650
  • Fig. 1 Neutron diffraction patterns of HC(ND2)2PbI3.

    Measured at (A) 390 K, (B) 220 K, and (C) 15 K. Refined structures with the symmetry of (D) cubic PmEmbedded Imagem for 390 K, (E) hexagonal P63/mmc for 220 K, and (F) hexagonal P63/m for 15 K. The neutron intensities are plotted in arbitrary units (arb. units). The spheres in dark gray, violet, pink, and light blue represent Pb, I, H/D, and N atoms, respectively. The view of the C atoms is blocked by the N atoms in this projection angle. The insets in (A) and (B) compare the two different models (see the main text for details). The inset of (C) shows an extra (111)h peak at 15 K that is absent at 220 K.

  • Fig. 2 Structural thermal hysteresis.

    Elastic neutron scattering data obtained from FAPbI3 at SPINS, NCNR, upon heating (A and C) and upon cooling (B and D). (A) and (B) are contour maps of the scattering intensity as a function of momentum transfer, Q, and temperature, T. Q range of 1.65 to 1.76 Å−1 was covered to probe the distinctive nuclear Bragg peaks—(1,1,1)c, (0,2,0)h, and (1,1,1)h—associated with the cubic, Hex-IT, and Hex-LT phases, respectively. (C) and (D) are integrated intensities of the three peaks—(1,1,1)c (black circle), (0,2,0)h (red square), and (1,1,1)h (blue triangle)—as a function of temperature. The light gray line indicates the temperature-dependent diffuse scattering intensity, as explained in the text.

  • Fig. 3 Quenching and energy landscape.

    (A) The elastic neutron scattering data were taken during rapid thermal quenching. (B) The kinetically trapped cubic phase indicates the existence of a potential energy barrier between the cubic and hexagonal phases. In (B), the red dashed line represents a schematic energy landscape, the details of which are shown in Fig. 4. The blue solid line represents the free energy landscape that accounts for the entropy contribution.

  • Fig. 4 Transition pathway and energy barrier.

    (A) Illustration of a possible transition pathway from the cubic to the hexagonal structure. The colored polygons represent the cages formed by iodine atoms located at the corners. The purple lines connecting iodine atoms, such as the hexagonal and triangle lines in the initial cubic structure, are drawn at each step to show how the iodine atoms move and the cages distort along the pathway. The eight spheres inside each polygon represent the HC(ND2)2+ (FA+) cation. The dark gray spheres represent lead atoms. Each lead atom is surrounded by six iodine atoms. The dark gray, green, and red solid lines connecting the lead atoms represent a pair of neighboring lead atoms that share one iodine (corner-sharing PbI3 octahedra), two iodine atoms (edge-sharing), and three iodine atoms (face-sharing), respectively. The dark gray lines in the initial cubic structure show the cube of a unit cell. The dashed blue lines in the final hexagonal structure are connecting the lead atoms in different unit cells in the hexagonal ab plane. (B) Calculated energy of the optimized structures along the pathway. (C) Number of corner-sharing (dark gray symbol), edge-sharing (green symbol), and face-sharing (red symbol) PbI3 octahedra and single-bonded iodine atoms (blue symbol) per six cubic unit cells along the pathway.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/10/e1601650/DC1

    Tables of atomic parameters for the three structural phases

    Preferred orientation of FA+ cation in the hexagonal phase

    Synchrotron x-ray diffraction measurements

    Confirmation of thermal equilibrium during neutron measurement

    Kinetic trapping of the cubic structure by thermal quenching

    Details on DFT calculations

    table S1. Refined structural parameters of FAPbI3 for 390 K.

    table S2. Refined structural parameters of FAPbI3 for 220 K.

    table S3. Refined structural parameters of FAPbI3 for 15 K.

    fig. S1. Orientation of FA+ cation.

    fig. S2. Refined crystal structure.

    fig. S3. Synchrotron x-ray powder diffraction data for FAPbI3.

    fig. S4. Check for thermal equilibrium during elastic neutron scattering measurements.

    fig. S5. Temporal monitoring of the stability of the cubic phase at 8.2 K after thermal quenching.

    References (2731)

  • Supplementary Materials

    This PDF file includes:

    • Tables of atomic parameters for the three structural phases
    • Preferred orientation of FA+ cation in the hexagonal phase
    • Synchrotron x-ray diffraction measurements
    • Confirmation of thermal equilibrium during neutron measurement
    • Kinetic trapping of the cubic structure by thermal quenching
    • Details on DFT calculations
    • table S1. Refined structural parameters of FAPbI3 for 390 K.
    • table S2. Refined structural parameters of FAPbI3 for 220 K.
    • table S3. Refined structural parameters of FAPbI3 for 15 K.
    • fig. S1. Orientation of FA+ cation.
    • fig. S2. Refined crystal structure.
    • fig. S3. Synchrotron x-ray powder diffraction data for FAPbI3.
    • fig. S4. Check for thermal equilibrium during elastic neutron scattering measurements.
    • fig. S5. Temporal monitoring of the stability of the cubic phase at 8.2 K after thermal quenching.
    • References (2731)

    Download PDF

    Files in this Data Supplement: