Phase transition pathway of hybrid halide perovskites under compression: Insights from first-principles calculations

Lead halide perovskites undergo pressure-induced phase transition, facilitated by bond compressions and different tilt patterns of the ${\mathrm{PbI}}_6$ octahedra. Utilizing first-principles calculations we investigated 14 possible tilt systems of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ under compression, derived from the high-symmetry $Pm\overline{3}m$ structure. Fr substitution is adopted to mimic the rotational disorder effect of the ${\mathrm{CH}}_3{\mathrm{NH}}_3$ cation with the similar size (at room temperature or higher). Analyses of these phases reveal an interplay between tilting and distortion of the ${\mathrm{PbI}}_6$ octahedra. Dynamical fluctuations at finite temperature provide additional insight into the phases' stability. Drawing from the trends observed in $\mathrm{Fr}\mathrm{Pb}{\mathrm{I}}_3$ and additional calculations for perovskites involving differently ordered organic cations, we propose that phase transition in ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ occurs from tetragonal at ambient pressure to orthorhombic under high pressure via the pathway I4/mcm$\to$P4/mbm$\to$Imm2. The distinct discontinuity in the calculated volume-pressure curve of I4/mcm and band-gap evolution of the proposed phases are consistent with photoluminescence shifts observed in ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ under pressure.

Figure 1

(a)–(d) The four typical crystal structures observed in lead halide peorvskites with space group of $Pm\overline{3}m$, I4/mcm, P4/mbm, and Imm2.

Figure 2

(a) Calculated $\mathrm{\Delta }H$ between distorted system and cubic ($Pm\overline{3}m$) phase of $\mathrm{Fr}\mathrm{Pb}{\mathrm{I}}_3$ as a function of pressure. (b) Symbols corresponding to Cmcm, $P{4}_2$/nmc, Immm, $P\overline{1}$ structures overlap with that of I4/mcm and P4/mbm and thus shown separately. (c) $\mathrm{\Delta }H$ between tetragonal (I4/mcm) and cubic ${\mathrm{MAPbI}}_3$ with different MA orientations under changing pressure. All enthalpies are calculated by DFT-PBE method.

Figure 3

The calculated phonon dispersion of tetragonal P4/mbm structure using DFT-PBE method for $\mathrm{Fr}\mathrm{Pb}{\mathrm{I}}_3$ at (a) 0 K and (b) at 300 K,respectively. The coordinates of high-symmetry $K$ points are $\mathrm{\Gamma }$ (0, 0, 0), $X$ (0, 0.5, 0), $M$ (0.5, 0.5, 0), $Z$ (0, 0, 0.5), $R$ (0, 0.5, 0.5), $A$ (0.5, 0.5, 0.5) [53].

Figure 4

Calculated transition barrier of $\mathrm{Fr}\mathrm{Pb}{\mathrm{I}}_3$ from I4/mcm to P4/mbm (blue line) and I4/mcm to Imm2 (red line) structure as a function of pressure using NEB method.

Figure 5

Enthalpy difference of tetragonal P4/mbm, orthorhombic Imm2, and triclinic structure relative to tetragonal I4/mcm structure of ${\mathrm{MAPbI}}_3$ (a) without SOC (b) with SOC as a function of pressure. The enthalpies are calculated by DFT-PBE method. The principal axes of MA molecule oriented to the [111] direction.

Figure 6

(a)–(d) The volume variation, Pb-I-Pb bending angle of adjacent octahedral layer, Pb-I bond length, calculated and experimental band gaps of tetragonal (I4/mcm, P4/mbm) structure and orthorhombic Imm2 structure of ${\mathrm{MAPbI}}_3$ as a function of pressure [28]. (e), (f) The calculated band structures and density of states of orthorhombic Imm2 structure of ${\mathrm{MAPbI}}_3$ at 0.5 GPa using the DFT-PBE method. The coordinates of high-symmetry $K$ points are $\mathrm{\Gamma }$ (0, 0, 0), $X$ (0.5, 0, 0), $S$ (0.5, 0.5, 0), $Y$ (0, 0.5, 0), $Z$ (0, 0, 0.5), $U$ (0.5, 0, 0.5), $R$ (0.5, 0.5, 0.5), $T$ (0, 0.5, 0.5).