Interplay between organic cations and inorganic framework and incommensurability in hybrid lead-halide perovskite ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$

Organic-inorganic coupling in the hybrid lead-halide perovskite is a central issue in rationalizing the outstanding photovoltaic performance of these emerging materials. Here, we compare and contrast the evolution of the structure and dynamics of hybrid ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ and inorganic ${\mathrm{CsPbBr}}_3$ lead-halide perovskites with temperature, using Raman spectroscopy and single-crystal x-ray diffraction. Results reveal a stark contrast between their order-disorder transitions, which are abrupt for the hybrid whereas smooth for the inorganic perovskite. X-ray diffraction observes an intermediate incommensurate phase between the ordered and the disordered phases in ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$. Low-frequency Raman scattering captures the appearance of a sharp soft mode in the incommensurate phase, ascribed to the theoretically predicted amplitudon mode. Our work highlights the interaction between the structural dynamics of organic cation ${\mathrm{CH}}_3{\mathrm{NH}}_3{}^{+}$ and the lead-halide framework, and unravels the competition between tendencies for the organic and inorganic moieties to minimize energy in the incommensurate phase of the hybrid perovskite structure.

Figure 1

Temperature-dependent Raman spectra of hybrid and inorganic lead-halide perovskite crystals. (a) Color plot and (b) line plot of low-frequency Raman spectra of ${\mathrm{CsPbBr}}_3$. (c) Color plot and (d) line plot of low-frequency Raman spectra of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$. (e) Color plot and (f) line plot of mid- and high-frequency Raman spectra of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$, including ${\mathrm{CH}}_3{\mathrm{NH}}_3{}^{+}$ internal modes such as ${\mathrm{NH}}_3$ wagging at $910{\mathrm{cm}}^{-1}$, C-N stretching at $969{\mathrm{cm}}^{-1}$, C-H stretching at 2890–$2970{\mathrm{cm}}^{-1}$, and N-H stretching around $3100{\mathrm{cm}}^{-1}$. Horizontal white lines in (a) and (c) indicate commensurate phase transition temperatures reported in previous studies [11, 12, 18, 19]. Raman spectra are normalized at each temperature, except for (e) to show the intensity drop of ${\mathrm{CH}}_3{\mathrm{NH}}_3{}^{+}$ internal modes across the orthorhombic-tetragonal phase transition.

Figure 2

Temperature-dependent low-frequency Raman spectra of the orthorhombic, incommensurate, and tetragonal phases of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$. (a) Color plot of spectra above, in, and below the incommensurate phase. (b) Line plot of spectra at each temperature.

Figure 3

Single-crystal x-ray diffraction of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ crystals. Reciprocal lattice reconstructions for ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ at (a) 160, (b) 150, and (c) 140 K. The views are along a principal direction of the parent (cubic) structure and are labeled for the conventional settings of $I4/mcm,Imma$, and $Pnma$, respectively. (d) and (e) Splitting of reflections by twinning and modulation. Reflection points are taken from marked boxes in (b), and are magnified by the same scale. Green squares are main reflections $\left(m=0\right)$ for two twin-related domains. Blue dots are satellite reflections $\left(m=00\pm 1\right)$. The unindexed spot marked by a purple square is a reflection from a further minor twin domain. The incommensurate modulation wave vectors $q_{\text{inc}}$ are defined by the blue dot–green square pairs, whose angle and magnitude are identical in (d) and (e). (f) Evolution of the incommensurate modulation wave vector $q_{\text{inc}}$ with temperature. Red dots and green squares represent data from two different measurements.

Figure 4

Characteristics of the soft amplitudon mode within the incommensurate phase of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$. (a) Schematic phonon dispersion curves of the amplitudon and phason branches. Adapted from Ref. [28]. (b) Temperature-dependent line shift (upper panel) and linewidth (lower panel) of the amplitudon mode in the incommensurate phase. (c) Soft mode shifting behavior. LFR: Red circles plot the low-frequency Raman measurement results. INS: Green squares plot lowest-energy data points from the inelastic neutron scattering measurement [25].