A Complete Picture of Cation Dynamics in Hybrid Perovskite Materials from Solid-State NMR Spectroscopy

Abstract

The organic cations in hybrid organic-inorganic perovskites rotate rapidly inside the cuboctahedral cavities formed by the inorganic lattice, influencing optoelectronic properties. Here, we provide a complete quantitative picture of cation dynamics for formamidinium-based perovskites and mixed-cation compositions, which are the most widely used and promising absorber layers for perovskite solar cells today. We use ²H and ¹⁴N quadrupolar solid-state NMR relaxometry under magic-angle spinning to determine the activation energy (E_a) and correlation time (τ_c) at room temperature for rotation about each principal axis of a series of organic cations. Specifically, we investigate methylammonium (MA⁺), formamidinium (FA⁺), and guanidinium (GUA⁺) cations in current state-of-the-art single- and multi-cation perovskite compositions. We find that MA⁺, FA⁺, and GUA⁺ all have at least one component of rotation that occurs on the picosecond timescale at room temperature, with MA⁺ and GUA⁺ also exhibiting faster and slower components, respectively. The cation dynamics depend on the symmetry of the inorganic lattice but are found to be insensitive to the degree of cation substitution. In particular, the FA⁺ rotation is invariant across all compositions studied here, when sufficiently above the phase transition temperature. We further identify an unusual relaxation mechanism for the ²H of MA⁺ in mechanosynthesized FA_xMA_1-xPbI₃, which was found to result from physical diffusion to paramagnetic defects. This precise picture of cation dynamics will enable better understanding of the relationship between the organic cations and the optoelectronic properties of perovskites, guiding the design principles for more efficient perovskite solar cells in the future.

Figure 1

Perovskite crystal structure (a) and principal axes of rotation for the most commonly employed cations: (b) methylammonium (MA⁺), (c) formamidinium (FA⁺), and (d) guanidinium (GUA⁺). H, C, and N atoms are represented by white, black, and blue balls, respectively.

Figure 2

Single pulse solid-state ²H MAS NMR spectra in the cubic phase of d-FAPbI₃ (a) and d₄-FAPbI₃ (b). The insets show a zoom of the isotropic resonances and the resolved peaks of the two ND₂ deuterons. ²H MAS NMR spectra in the tetragonal phase (at 260 K) of d-FAPbI₃ (c) and d₄-FAPbI₃ (d). Hahn-echo detected ¹⁴N MAS NMR spectra of d-FAPbI₃ (e). The inset shows a zoom of the central peak. All spectra were recorded at 5 kHz MAS; further experimental details are given in the Supporting Information.

Figure 3

Measured ²H and ¹⁴N longitudinal relaxation time constants (T₁) of black FAPbI₃ as a function of temperature. The discontinuities in the T₁ behavior are indicative of the crystallographic phase transition of the material. Experimental details are given in the Supporting Information.

Figure 4

d₅-FAPbI₃ NMR relaxometry and rotational diffusion rates. (a) Three ²H and one ¹⁴N T₁ constants measured as a function of temperature in the cubic phase. Dashed lines indicate the fit to the rotational diffusion model. (b) Arrhenius plot of the rotational diffusion constants derived from (a). Dashed lines indicate fits to the Arrhenius behavior. Only the five highest temperature points were considered in the Arrhenius fits as the phase transition at ∼285 K causes deviation from Arrhenius behavior.

Figure 5

FA⁺ dynamics in Cs-alloyed perovskite compositions. Experimentally measured (a) ²H and (b) ¹⁴N T₁ as a function of inverse temperature. Dashed lines represent fitted T₁ values using the rotational diffusion model.

Figure 6

FA⁺ dynamics in FA_xMA_1–xPbI₃ perovskite compositions. (a) Single pulse solid-state ²H MAS NMR spectra of the cubic phase of FA_0.70MA_0.30PbI₃. The MA⁺ peak shows J-coupling of ¹J(²H–¹⁴N) = 8.25 Hz. The deconvolution of all four sites is shown below the spectrum. Experimentally measured (b) ²H and (c) ¹⁴N T₁ as a function of inverse temperature and as a function of x in FA_xMA_1–xPbI₃.

Figure 7

²H relaxation times (T₁) of MA⁺ in FA_xMA_1–xPbI₃ prepared using either mechanosynthesis or a solution-based high-purity protocol as described in the text.

Figure 8

Experimentally measured (a) ²H and (b) ¹⁴N T₁ constants as a function of inverse temperature in MAPbI₃ and high-purity FA_0.78MA_0.22PbI₃. Dashed lines indicate fits to the rotational diffusion model.

Figure 9

²H and ¹⁴N T₁ constants of (a) MA⁺ and (b) GUA⁺ as a function of inverse temperature in MA_0.75GUA_0.25PbI₃ at 20 kHz MAS. Dashed lines indicate fits to the rotational diffusion model.

Figure 10

Comparison of experimentally measured rotational correlation times at room temperature for MA⁺, FA⁺, and GUA⁺ cations in the various iodoplumbate perovskite compositions studied in this work. The corresponding activation energies are shown in Figure S22.