Crystal structures and rotational dynamics of a two-dimensional metal halide perovskite (OA)₂PbI₄

Metal halide perovskites (MHPs), such as CH₃NH₃PbI₃, have been intensively studied in recent years for their attractive electronic, optical, and optoelectronic properties. The high device performances of MHPs result from their unique properties such as changeable bandgap, extended charge carrier lifetime, and high light absorption.^1–11 Some microscopic mechanisms have been reported to account for these special properties, such as polaronic features dominant in three-dimensional (3D) MHPs with organic molecules,^6,12–23 excitonic features dominant in MHPs with lower dimensionality such as two-dimensional (2D) MHPs,^24,25 and coexistence in other cases.^26–28 Recent investigations^{21,22,29–32} and our previous studies have illuminated the role of organic molecules in the phonon melting and charge screening in 3D MHPs.^6,33

In this work, we investigate the structural phase transitions and rotational dynamics of organic cations in the two-dimensional hybrid perovskite, octyl-ammonium lead iodide³⁴ [(OA)₂PbI₄, where OA⁺ = C₈H₁₇NH₃⁺], by performing neutron diffraction measurements and quasielastic neutron scattering as a function of temperature, 100 K < T < 370 K, covering the three different structural phases of (OA)₂PbI₄. Our quasielastic neutron data enabled us to apply a group theoretical analysis based on the crystal structure to understand the nature of the rotation motion of the OA⁺ cation, and the resulting model includes the symmetry and relaxation times as a function of temperature. Our analysis shows that, in the high temperature (HT) phase (T > 310 K), the OA⁺ cation presents a combination of a twofold rotation (C₂) of the head group NH₃–CH₂, around the crystallographic c-axis, threefold rotations (C₃) of terminal CH₃ and NH₃ groups, and slow librations of the remaining CH₂ groups. While in the intermediate temperature (IT) and low temperature (LT) phases, only the C₃ rotations exist. Upon further cooling in the LT phase (T < 170 K), the C₃ rotation is difficult to detect within the instrument resolution. On the other hand, our diffraction data show that upon heating the thermal factor associated with atomic thermal fluctuations increases dramatically as the system enters the IT phase.

To study the structural phase transitions of (OA)₂PbI₄, we performed elastic neutron scattering on an ∼5g nondeuterated (OA)₂PbI₄ powder sample as a function of temperature, with the Spin Polarized Inelastic Neutron Spectrometer (SPINS, NG-5) located at the NCNR. Manifested by the peak appearance or disappearance, Fig. 1(a) shows that the system undergoes two structural phase transitions upon cooling at 210(5) K and 305(5) K. Upon heating, however, the transitions occur at 245(5) K and 310(5) K, as shown in Fig. 1(b). This thermal hysteresis, which is also reported in the differential scanning calorimetry (DSC) experiment (Fig. S1), indicates that there are energy barriers between the structural phases.

In order to refine the crystal structures of the three different phases, we have performed neutron diffraction measurements on an ∼1g deuterated powder sample of (OA)₂PbI₄ using the powder diffractometer (POWGEN, BL-11A) at the Oak Ridge National Laboratory (ORNL) located in Oak Ridge, Tennessee, USA. Figure 2 shows the neutron diffraction data obtained in the three different phases. As shown in Fig. 2(a), at 350 K in the high temperature (HT) phase, the data can be reproduced by the orthorhombic structure with Acam symmetry and lattice constants of a_H = 8.7615 Å, b_H = 8.7634 Å, and c_H = 41.0560 Å. The overlaid images in Fig. 2 show the refined structural configuration in which the long-chain molecule is curled beyond the edge of the PbI₃ sublattice. The bending of the molecule greatly suppresses its possible rotation modes in the HT phase. In principle, the whole-molecular rotation of the OA⁺ cation is forbidden due to this configuration, during which the OA⁺ cation would collide with adjacent OA⁺ cations.

Figure 2(b) shows the diffraction data obtained at 270 K in the intermediate temperature (IT) phase. Additional Bragg peaks that cannot be indexed by the HT Acam symmetry appear, such as the orthorhombic (102). These additional peaks can be indexed by an orthorhombic structure with the Pbca space group and lattice constants of a_I = 8.9660 Å, b_I = 8.6873 Å, and c_I = 37.5264 Å. The bending cation reshapes into a straight chain oriented along the c-axis of the unit cell, as shown in Fig. 2(b). Upon further cooling into the low temperature (LT) phase, the diffraction data show the appearance of even more peaks, such as a monoclinic (011) shown in Fig. 2(c), indicating the further reduction in symmetry. The LT phase Bragg peaks can be indexed by the monoclinic structure with P2₁/a space group and lattice constants of a_L = 8.4289 Å, b_L = 8.9497 Å, c_L = 18.5813 Å, and β = 96.0328°. Detailed structural parameters for all three phases are listed in the supplementary material.

Note that the diffraction pattern at 20 K has sharp Bragg peaks at high Qs, while at 270 K and 350 K, those high Q Bragg peaks become very weak. This indicates that at 270 K and 350 K the atoms thermally fluctuate very severely from their equilibrium positions. Figure 3 shows that the average refined isotropic thermal factors U_iso associated with the thermal fluctuations of each type of atom are plotted as a function of temperature with the error bar describing the standard deviations. At low temperatures, the ions are tightly bounded through the Coulomb interactions due to the ionic character of this crystal. When the temperature increases, thermodynamics plays a more important role and loosens the ionic bonds. As the temperature increases, the ions vibrate around more to yield large U_iso values (Fig. 3), which is proportional to the root-mean-square atomic displacements from their equilibrium positions.

To understand the mechanism of the two structural transitions, we identify one possible transition pathway for each transition and perform first-principles density functional theory (DFT) calculations on the structures with constrained optimization to estimate the configurations and energies along the pathway. Figure 4(a) shows some of the intermediate structures along the transition pathway from the LT phase to the IT phase. This pathway involves an in-plane shift of the inorganic layers in the a-direction of the LT phase along with a torsion in the head group NH₃–CH₂ of the organic molecule. The black and red lines illustrate the deformation of the crystallographic unit cell. The LT and IT states are separated by an energy barrier with an order of hundreds of millielectron volts in height, as shown in Fig. 4(b). With the increasing temperature, the increase in the isotropic thermal factor at the LT-to-IT structural transition, shown in Fig. 3, indicates that the LT–IT transition could be driven by the increase in the entropy term associated with the atomic thermal fluctuations, such as the jiggling of the Pb–I octahedron, in the Helmholtz free energy.

The transition pathway from the IT phase to HT phase is identified by a lattice elongation in the c-direction and a slight contraction in the ab plane, along with a bending of the organic cation away from the c-axis across the center of the inorganic lattice. Some of the possible intermediate structures are shown in Fig. 4(c) with the calculated system energies [Fig. 4(d)]. It is a puzzle how the organic cation bends dramatically in the HT phase (T > 310 K), when compared to the IT and LT phases below 310 K. We will show below that the HT phase has very different rotational dynamics than in the IT and LT phases, which might be the reason for the bending of the organic cation only in the HT phase.

In order to evaluate the rotational dynamics of the OA cation, we performed quasielastic neutron scattering on a powder sample of nondeuterated (OA)₂PbI₄, using the Cold Neutron Chopper Spectrometer (CNCS) at the ORNL. Figure 5 shows 3D quasielastic scattering data from (OA)₂PbI₄, measured at six different temperatures with the CNCS upon cooling.

At 370 K, in the high-temperature (HT) orthorhombic phase, there is a broad peak centered at ℏω = 0 meV. Upon cooling into the intermediate-temperature (IT) orthorhombic phase, as shown at 280 K, this elastic peak becomes narrower in energy. Upon further cooling to 210 K in the low-temperature (LT) monoclinic phase, the quasielastic signal moves to even lower energies and becomes unresolved from the elastic signal due to the instrumental energy resolution of 0.1 meV. We chose to do fittings in the negative-energy region because it is free from phonon effects at low temperatures and has less noise than the positive-energy region at high temperatures.

To better visualize the quasielastic and elastic signals, we integrated the data over three different energy windows, −0.1 < ℏω < 0.1 meV, −0.4 < ℏω < −0.2 meV, and −1.0 < ℏω < −0.8 meV and plotted their Q-dependence, S(Q).

In the energy range −0.1 < ℏω < 0.1 meV [Fig. 6(a)], at each temperature, the intensity decreases with increasing Q due to the Debye-Waller factor. As the temperature decreases, the elastic intensity becomes higher while the quasielastic intensity goes lower due to the inhibition of the rotational motion of the organic cation.

For the −0.4 < ℏω < −0.2 meV energy window [Fig. 6(b)], at 370 K, S(Q) is peaked at Q ∼ 1.5 Å⁻¹. Upon cooling down to 260 K, the intensity peak gradually shifts to higher Q ∼ 2.0 Å⁻¹ and the magnitude greatly decreases. Upon further cooling, more prominent changes occur; at 210 K and 170 K, the intensity peak is not observed. S(Q) becomes much weaker for −1.0 < ℏω < −0.8 meV [Fig. 6(c)]. The weak intensity at 170 K over these energy windows is consistent with the strong enhancement of the intensity in the energy window −0.1 < ℏω < 0.1 meV [Fig. 6(a)].

Because of the strong incoherent neutron scattering amplitude of hydrogen atoms, neutron scattering measurements provide a superb sensitivity toward the probing dynamics of the OA⁺ cation. By analyzing the Q and ℏω dependent scattering intensity, the nature of hydrogen motion can be determined.

The rotation model that accounts for the preferential molecular orientation is called the jump model. The rotational motion of the OA⁺ cation is restricted by its own symmetry as well as the local crystal symmetry. In principle, it is almost impossible for the long OA⁺ to obtain an isotropic rotation due to limitations based on its size, shape, and local energy landscape. Here, we only consider proper rotations instead of improper rotations such as inversion and mirror reflections. Group theory has been discussed thoroughly, and we simply repeat the basic formalism as in the following. The scattering function for rotational motions of molecules in a crystal can be written as^33,35

where $e−u2Q2$ is the Debye-Waller factor, $u2$ is the mean squared atomic displacement, and the sum over γ runs over all the irreducible representations Γ_γ of Γ. The structure factor A_γ(Q) is given by^33,35

where g is the order of group Γ and l_γ is the dimensionality of Γ_γ. The sums $∑α⋯$ and $∑β⋯$ run over all the classes of C and M, respectively. The sums over $∑Cα⋯$ and $∑Mβ⋯$ run over all the rotation operations belonging to the crystal class, α, and to the molecule class, β, respectively. The characters of Γ_γ, $χγαβ$⁠, are the products of the characters of C_γC and M_γM, $χγαβ=χγCαχγMβ$⁠. Here, j₀(x) is the zeroth spherical Bessel function and $R−CαMβR$ represents the distance between the initial atom position R and final atom position C_αM_βR, called the jump distance. The relaxation time for the Γ_γ mode, τ_γ, is calculated as^33,35

where n_α and n_β are the number of symmetry rotations of the classes α and β, respectively. E and e represent the identity operations of C and M.

Here, we provide the simplest jump models that reproduce our CNCS data. For the HT phase, we divided the cation rotation into three parts as follows:

1. NH₃-CH₂ rotation:

For one head part of the cation, two modes are expected: C₂ rotation of the NH₃-CH₂ group around the c-axis across the center of the inorganic cage and C₃ rotation of the NH₃ head group, as shown in Figs. 7(a) and 7(b).

1. CH₃ rotation:

For the other end of the cation, CH₃, we used Γ = C₃, where C₃ represents the threefold symmetry of the CH₃ group, as shown in Fig. 7(c).

1. Librations of other CH₂:

Theoretically, other CH₂ groups would not stay static during the complex rotation motion of the cation. Thus, we introduce a libration model to simulate the behavior of other CH₂ groups on average [Fig. 7(a)]. During the slow libration, the cation body consisting of six CH₂ groups will deform accordingly.

According to a recent X-ray diffraction study³⁴ and our neutron diffraction data, the long-chain OA⁺ cation lies along the c-axis and bends beyond the edge of the inorganic cage in the HT phase, with the unique axis chosen to be the c-axis (c > a, b). This configuration prohibits the whole-molecular rotation around the c-direction due to steric hindrance from neighboring OA⁺ cations. As summarized in detail in the supplementary material, the point group of C₂ has two irreducible representations: two one-dimensional (A and B). The point group C₃ has two irreducible representations: one one-dimensional (A) and one two-dimensional (E). Thus, for the NH₃ group, $ΓNH3=C2⊗C3$⁠, there are four irreducible representations: $ΓNH3={A⊗A,A⊗E,B⊗A,B⊗E}$⁠. For the adjacent CH₂, $ΓCH2=C2$⁠, there two irreducible representations. For the CH₃ group at another end of the molecule, $ΓCH3=C3$⁠, there are two irreducible representations. The libration behavior is modeled as a pseudo-C₂ rotation with an average jump distance of ∼1.6 Å. There are then three different relaxation times, $τC2$⁠, $τC3$⁠, and τ_libration, that are related to the corresponding rotation operations. The fitted parameters are listed in Table I as a function of temperature. The Q-dependence of A_γ(Q) is obtained from the jump distance |R − C_αM_βR|, which is calculated based upon the crystal structures. For all our analyses, the average jump distance was used in C₃ rotations of NH₃ and CH₃ groups (for details, see the supplementary material).

Apart from the rotational signal, the incoherent phonons in the interested energy region cannot be ignored. Thus, we add a phonon contribution term,³⁵ which is approximated as $Q2e−<u2>Q2$⁠, into our neutron data fitting. The fitted U_iso is consistent with the refined root-mean-square cation atomic displacements (Fig. 3). Before using this combination model, we tried other models, but these other models could not reproduce the Q-dependence of the data. As shown in Figs. 5 and 6, the combination of the models presented in this section can reproduce the data decently well over 310 K ≤ T ≤ 370 K in the HT phase. The corresponding fitting parameters are plotted in Fig. 8 and listed in Table I.

In the IT and LT phases, the partial-molecular rotation is abandoned mainly because of the great mismatch in Q-dependence fitting. Due to the same reason, the librations are ruled out. Only C₃ rotations of the NH₃ and CH₃ groups are applied. Details are discussed in the supplementary material.

Our results on the rotational dynamics and the structures suggest us that the major difference among 350 K, 270 K, and 20 K is the difference in the rotational dynamics: as shown in Figs. 5–7 and as discussed in the text, at both 20 K and 270 K, only the C₃ rotations of the two terminal CH₃ and NH₃ groups are active and the rest part of the cation is frozen [see Fig. 7(c)]. We believe that this is the reason for the shape of the organic cation being more or less the same for both temperatures. On the other hand, at 350 K in the high-temperature orthorhombic phase, the rotational dynamics is much more complex, involving a C₂ rotation of the NH₃-CH₂ head group and librations of the other CH₂ groups in addition to the C₃ rotations of CH₃ and NH₃. The different rotational dynamics in the HT phase might be the reason for the bending of the organic cation in the phase.

In this paper, we have characterized the structural phase transitions and rotational dynamics of the organic cation in a two-dimensional MHP, (OA)₂PbI₄, as a function of temperature. We have shown that the two structural phase transitions have thermal hysteresis, resulting from the existence of the potential barriers between the structural phases, and the transitions are due to the changes in the vibrational and rotational entropy. As for the rotational dynamics, our results show that in the high-temperature phase, the OA cation exhibits a combination of a twofold rotation of the NH₃–CH₂ head group around the c-axis of the crystallographic unit cell, threefold rotations of the NH₃ and CH₃ groups, and slow librations of the other CH₂ groups, while in the intermediate-temperature and low-temperature phases, only the threefold rotations remain. There is a consensus that excitonic features dominate in 2D MHPs, while in 3D MHPs, more polaronic features dominate. It remains to be seen whether or not rotational dynamics affects the optoelectronic properties in 2D MHPs.

See the supplementary material for the sample preparation procedures, the refined crystal structures at different temperatures, and the detailed calculations and discussions involved in the rotational dynamic analysis.

This work at the University of Virginia was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0016144. The research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences. This research used resources at Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The computational work was performed by utilizing the resources at the National Energy Research Scientific Computing (NERSC) Center, which is supported by the Office of Science of the U.S. Department of Energy (Contract No. DE-AC02-05CH11231). We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work.