Structural dynamics of CH₃NH₃⁺ and PbBr₃⁻ in tetragonal and cubic phases of CH₃NH₃PbBr₃ hybrid perovskite by nuclear magnetic resonance

Abstract

Understanding the structural dynamics of lead-halide perovskites is essential for their advanced use as photovoltaics. Here, the structural dynamics of the CH₃NH₃ cation and PbBr₆ octahedra in the perovskite CH₃NH₃PbBr₃ were studied via nuclear magnetic resonance (NMR) to determine the mechanism of the transition from the tetragonal to cubic phase. The chemical shifts were obtained by ¹H, ¹³C, and ²⁰⁷Pb magic angle spinning NMR and ¹⁴N static NMR. The chemical shifts of the ¹H nuclei in CH₃ and NH₃ remained constant with increasing temperature, whereas those of the ¹³C and ²⁰⁷Pb nuclei varied near the phase transition temperature (T_C = 236 K), indicating that the structural environments of ¹³C and ²⁰⁷Pb change near T_C. The spin–lattice relaxation time T_1ρ values for ¹H, ¹³C, and ²⁰⁷Pb nuclei increased with increasing temperature and did not exhibit an abrupt change near T_C. In addition, the two lines in the ¹⁴N NMR spectra superposed into one line near T_C, indicating the occurrence of a phase transition to a cubic phase with higher symmetry than tetragonal. Consequently, the main factor causing the phase transition from the tetragonal to cubic phase near T_C is a change in the surroundings of the ²⁰⁷Pb nuclei in the PbBr₆ octahedra and of the C–N groups in the CH₃NH₃ cations.

Introduction

Lead-halide perovskites currently represent the most promising photovoltaic materials for the production of low-cost, high-performance solar cells^1,2. In recent years, researchers have succeeded in significantly improving the power conversion efficiency (PCE) of this hybrid perovskite, and rapid advances in this field led to a record-high PCE. The very important for optoelectronic heterostructures are solar cells, photodetectors, and laser diodes^3,4,5,6. For this class of materials, which has the general formula CH₃NH₃PbX₃ (X = Cl, Br, and I), an inorganic cage of PbX₆ octahedra encloses an organic cation at the CH₃NH₃⁺ site^{7,8,9,10,11,12}. The phase transition temperatures of CH₃NH₃PbBr₃, a representative perovskite, are 148.8, 154, and 236.3 K, corresponding to a total of four crystal phases^13,14; with decreasing temperature, the cubic phase (I) transforms to a tetragonal phase (II) at 236.3 K, to another tetragonal phase (III) at 154 K, and finally to an orthorhombic phase (IV) at 148.8 K. In tetragonal phase II, the CH₃NH₃⁺ ions undergo isotropic reorientation, whereas in the lower-temperature phases, the reorientation of C–N axes seems to be frozen¹⁵. All the phase transitions are first-order and order–disorder type, although the highest temperature transition is close to second-order. From the high-temperature cubic phase with freely rotating CH₃NH₃ cations, this compound enters lower-symmetry tetragonal phases and finally a low-temperature orthorhombic phase with the orientation of CH₃NH₃ cations fixed at ordered positions^{16,17,18,19,20}. At room temperature, the structure is cubic, the space group is Pm3m, and the lattice constant a = 5.93129 Å and Z = 1¹³. In this crystal structure, there exists a CH₃NH₃⁺ cation at the centre of a cube formed by corner-sharing PbBr₆ octahedra^18,21, as shown in Fig. 1. Below 236 K, the crystal structure has a tetragonal and belongs to the space group I4/mcm with lattice constants a = b = 8.32 Å, c = 11.83 Å, and Z = 4²². Throughout the transition from the tetragonal II phase to the tetragonal III phase at 154 K, the full width at half maximum of the Raman ν₆ band shows an abrupt increase⁸. At lower temperatures, CH₃NH₃PbBr₃ undergoes a first-order structural phase transition from the tetragonal III (I4/mmm) phase to the orthorhombic IV (Pnma) phase⁹.

Figure 1

Crystal structure of cubic phase CH₃NH₃PbBr₃. The software used to create the Fig. is CrystalMaker Software.

In a previous nuclear magnetic resonance (NMR) investigation, the temperature dependence of ⁸¹Br nuclear quadrupole resonance frequencies and ¹H spin–lattice relaxation times in the laboratory frame T₁ for CH₃NH₃PbBr₃ were discussed by Xu et al.²³ According to their results, the two ⁸¹Br NQR lines in phase II were reduced to one line in phase I. The discontinuity of the NQR line at this transition point implied a first-order transition. ¹H T₁ varied continuously, and no discernible change in the free induction decay was observed during the I–II transition. The phase transition had no significant effect on the motional state of the CH₃NH₃⁺ ions. Furthermore, Baikie et al.¹³ reported that the ¹H magic angle spinning (MAS) NMR spectra showed two clear peaks corresponding to the CH₃ and NH₃ environments in the high-temperature phase, and the ¹H and ¹³C NMR spectra of CH₃NH₃PbBr₃ showed that the CH₃NH₃⁺ units undergo dynamic reorientation.

Measuring the spin–lattice relaxation time in the rotating frame T_1ρ by MAS NMR allows for the probing of molecular motion in the kHz range, whereas the spin–lattice relaxation time in the laboratory frame T₁ measured by static NMR reflects motion in the MHz range. Although the ¹H T₁ of CH₃NH₃PbBr₃ has been examined by a few research groups, the corresponding phenomena by ¹H, ¹³C, and ²⁰⁷Pb MAS NMR spectra and T_1ρ have not been fully studied. In addition, information regarding ¹⁴N in the CH₃NH₃ cation has not yet been discussed.

In the present study, the structural dynamics of the CH₃NH₃ cation and PbBr₆ octahedra in CH₃NH₃PbBr₃ were studied in detail by NMR to resolve the phase transition mechanisms from the tetragonal phase to the higher-temperature cubic phase. The temperature dependences of the chemical shifts and spin–lattice relaxation time in the rotating frame T_1ρ were measured using ¹H MAS NMR, ¹³C cross-polarization (CP)/MAS NMR, and ²⁰⁷Pb MAS NMR with emphasis on the role of the CH₃NH₃ cation and PbBr₆ octahedra in CH₃NH₃PbBr₃. In addition, the ¹⁴N static NMR spectra of CH₃NH₃PbBr₃ in the laboratory frame were acquired near the phase transition temperature. The abovementioned results help in understanding the thermal stability and the structural dynamics based on the phase transition mechanism, towards the practical application of this material.

Experimental

CH₃NH₃Br and PbBr₂ were dissolved in a dimethylformamide solution and heated the mixed suspension on a hot plate to obtain a transparent solution. Detailed methods for the crystal growth are given elsewhere^21,24,25. The CH₃NH₃PbBr₃ single crystals obtained here were orange in colour with a square shape.

Differential scanning calorimetry (DSC) (TA, DSC 25) was conducted at a heating rate of 10 °C/min over a temperature range from 190 to 525 K under nitrogen gas. Thermogravimetric analysis (TGA) was performed on a thermogravimetric analyser (TA Instrument) in an interval from 300 to 780 K at a heating rate of 10 °C/min. Approximately 11.15 mg of CH₃NH₃PbBr₃ was used in each experiment.

NMR measurements were carried out at 9.4 T using a Bruker 400 MHz Avance II + spectrometer at the Korea Basic Science Institute, Western Seoul Center. The ¹H, ¹³C, and ²⁰⁷Pb NMR frequencies were 400.13, 100.61, and 83.75 MHz, respectively. Powdered samples were packed in zirconia MAS rotors with Macor caps, and the MAS rate was set to 10 kHz for the ¹H MAS, ¹³C MAS, and ²⁰⁷Pb MAS NMR measurements to minimise spinning sideband overlap. The spin–lattice relaxation time in the rotating frame T_1ρ was measured using an inversion recovery pulse sequence, which employs compensating pulses. The ¹³C T_1ρ values were measured by varying the duration of the ¹³C spin-locking pulse applied after the CP preparation period. The width of the π/2 pulse used for measuring T_1ρ of ¹H and ¹³C was 3.45 µs, and that for measuring T_1ρ of ²⁰⁷Pb was 3.5 µs. In addition, ¹⁴N NMR spectra of a CH₃NH₃PbBr₃ single crystal were measured with a Larmor frequency of 28.90 MHz in the laboratory frame.

Temperature-dependent NMR spectra were recorded over 180 to 430 K; the NMR spectra and relaxation times could not be measured outside this temperature range because of the limitations of the spectrometer. Sample temperatures were held constant within ± 0.5 K by controlling the nitrogen gas flow and heating current.

Experimental results

Figure 2 shows the DSC and TGA curves obtained under a nitrogen atmosphere. DSC analysis was used to determine the phase transition temperature; only one endothermic peak related to a phase transition was observed at 236 K, which is consistent with previously reported T_C values.^13,14 The thermal stability of CH₃NH₃PbBr₃ was examined by TGA. The first occurrence of mass loss began at approximately 530 K, which represents the onset of partial thermal decomposition. The mass sharply decreased between 550 and 650 K, with a corresponding mass loss of 22% near 650 K. Optical polarizing microscopy experiments were also conducted to further understand the thermal stability at high temperatures. The colour of the crystal was orange at room temperature, as shown in the inset in Fig. 2. As the temperature increased, the state of the crystal remained the same from 400 to 500 K. Above 550 K, a slight opacity occurred at the bottom of the crystal, and at approximately 600 K, the crystal was nearly opaque.

Figure 2

Differential scanning calorimetry (DSC) and thermogravi-metric analysis (TGA) of CH₃NH₃PbBr₃ (inset: color changes of CH₃NH₃PbBr₃ single crystal according to the temperature).

The ¹H NMR spectrum of CH₃NH₃PbBr₃ was recorded by MAS NMR at a frequency of 400.13 MHz. Figure 3 shows the ¹H MAS NMR spectrum at 300 K, where the spinning sidebands are marked with open circles and asterisks. The two peaks in the ¹H spectrum correspond to CH₃ and NH₃ environments, with the chemical shifts at δ = 3.27 and 6.36 ppm assigned to ¹H in CH₃ and NH₃, respectively. The chemical shifts remained quasi-constant with increasing temperature, indicating that the structural environments of ¹H in the CH₃ and NH₃ groups were unchanged (see the Supplementary Information). Additionally, the line width (full-width at half-maximum) of the ¹H MAS NMR signal at 300 K is approximately 1.62 ppm, which also remained nearly constant with temperature change.

Figure 3

¹H MAS NMR spectrum for CH₃ and NH₃ of CH₃NH₃PbBr₃ at 300 K, and the spinning sidebands are marked with open circles and asterisks.

The ¹H inversion-recovery curves for both CH₃ and NH₃ at each temperature were fitted to exponentials to extract T_1ρ. The data were well fitted a single exponential, indicating that there is one dominant relaxation mechanism acting per environment. Thus, T_1ρ was determined by fitting the decay plots with the equation below^26,27.

$${\text{P}}(t)/{\text{P}}_{0} = \exp \left( { - t/{\text{T}}_{{1\rho }} } \right),$$

(1)

where P(t) is the magnetisation, t is the spin-locking pulse duration, and P₀ is the total nuclear magnetisation of ¹H at thermal equilibrium. The recovery curves of ¹H in CH₃NH₃PbBr₃ were measured for various delay times at each temperature. Figure 4 (inset) shows the recovery traces for ¹H measured for delay times ranging from 1 to 200 ms at 300 K. The intensity of the recovery traces differed with delay time. The T_1ρ values obtained from the intensity versus delay time and shown in Fig. 4 reveal that T_1ρ increased with temperature because proton hopping was accelerated. This is in agreement with Xu et al.²³, who reported that the ¹H T₁ increased smoothly with increasing temperature through the high-temperature phase transition. The T_1ρ values of ¹H in CH₃ and NH₃ in the CH₃NH₃⁺ cation show similar trends with temperature and are nearly the same within the error range. The T_1ρ values show no change near the phase transition temperature (T_C = 236 K). T_1ρ increased with increasing temperature, reaching the maximum values of 592 ms and 456 ms for CH₃ and NH₃, respectively, near 330 K above the phase transition temperature, and then decreased with increasing temperature. Although the structural environment of ¹H in the CH₃NH₃ groups does not change with temperature, their molecular motion increases at high temperatures, as indicated by the T_1ρ values. Above T_C, the ¹H T_1ρ value for CH₃ slightly exceed that for NH₃.

Figure 4

¹H spin–lattice relaxation times T_1ρ for the CH₃ and NH₃ ions of CH₃NH₃PbBr₃ as a function of inverse temperature (inset: recovery plots of the ¹H MAS NMR spectrum by delay time at 300 K).

Structural analysis of the ¹³C and ²⁰⁷Pb nuclei in CH₃NH₃PbBr₃ was performed by MAS NMR, and the corresponding spectra at 300 K are shown as insets in Fig. 5. At room temperature, the ¹³C and ²⁰⁷Pb MAS NMR spectra show one signal each at chemical shifts of δ = 30.66 and 89 ppm with respect to tetramethylsilane and PbNO₃, respectively. Here, the line width for ¹³C at 300 K is narrow at 2.77 ppm, whereas that for ²⁰⁷Pb is quite broad at 206.24 ppm. Figure 5 shows the ¹³C and ²⁰⁷Pb chemical shifts of CH₃NH₃PbBr₃ measured as a function of temperature, illustrating that the ¹³C and ²⁰⁷Pb peak positions moved to higher chemical shifts upon heating. The chemical shifts near T_C changed, in contrast to the ¹H chemical shifts. The chemical shifts of the ¹³C and ²⁰⁷Pb signals relative to the reference signal are sensitive to the electronic environment of the nucleus. In particular, the ²⁰⁷Pb chemical shift changed more rapidly than that of ¹³C near T_C. From these results, the phase transition from the tetragonal to cubic phase is thought to arise from a change in the PbBr₆ octahedra.

Figure 5

¹³C and ²⁰⁷Pb chemical shifts in CH₃NH₃PbBr₃ as a function of temperature (inset: ¹³C and ²⁰⁷Pb MAS NMR spectrum of CH₃NH₃PbBr₃ at 300 K).

To determine the T_1ρ values of ¹³C and ²⁰⁷Pb in the rotating frame, the nuclear magnetisation was measured as a function of delay time. The signal intensities of the nuclear magnetisation recovery curves could be described by the single exponential function in Eq. (1), and the signal intensity followed this single exponential decay at all temperatures. From these results, the T_1ρ values were obtained for ¹³C and ²⁰⁷Pb in CH₃NH₃PbBr₃ as a function of inverse temperature, as shown in Fig. 6. The ¹³C and ²⁰⁷Pb T_1ρ values for CH₃ and PbBr₃ seem to follow a similar trend with temperature to that of the ¹H T_1ρ, where the values increase with increasing temperature and are approximately continuous near T_C. In addition, the ²⁰⁷Pb T_1ρ values are much lower than ¹³C T_1ρ.

Figure 6

¹³C and ²⁰⁷Pb spin–lattice relaxation times T_1ρ of CH₃NH₃PbBr₃ as a function of inverse temperature.

To obtain information concerning possible changes in the surroundings of the ¹⁴N ion, static NMR spectra of ¹⁴N (I = 1) in the laboratory frame were obtained. Temperature-dependent changes in the ¹⁴N resonance frequency are attributable to alterations in the structural geometry, indicating a change in the quadrupole coupling constant of the ¹⁴N nuclei. The spectra were obtained by the solid-state echo method using static NMR at a Larmor frequency of 28.90 MHz. Two resonance signals were expected from the quadrupole interactions of the ¹⁴N nucleus with spin I = 1. The ¹⁴N NMR spectra were shown at 225 and 270 K, and the resonance frequencies referenced with respect to NH₄NO₃ as a function of temperature are shown in Fig. 7. The line widths are very narrow at all temperatures. The two resonance signals for ¹⁴N, which are attributable to NH₃, superpose into one line at the transition point of 236 K. This single ¹⁴N resonance line indicates that a phase transition takes place to a new phase with a higher symmetry than tetragonal²⁸. In tetragonal phase below T_C, the electric field gradient tensors at the N sites vary, reflecting changes in the atomic configuration around the nitrogen. But, there is no electric field gradient tensor at the ¹⁴N site in the cubic structure because of the site symmetry of m3m.

Figure 7

The ¹⁴N resonance frequency of CH₃NH₃PbBr₃ single crystal as a function of temperature (inset: ¹⁴N NMR spectrum at tetragonal phase of 225 K and cubic phase of 270 K).

Conclusion

Using the information derived from NMR studies near T_C (= 236 K), we have probed the structural and dynamic features of CH₃NH₃PbBr₃ in detail and demonstrated its dynamic nature. The ionic dynamics of CH₃NH₃PbBr₃, with emphasis on the role of the CH₃NH₃ cation and PbBr₆ octahedra, were investigated by ¹H MAS NMR, ¹³C CP/MAS NMR, ²⁰⁷Pb MAS NMR, and ¹⁴N static NMR as a function of temperature. ¹H, ¹³C, and ²⁰⁷Pb NMR were used to identify the phase transition in CH₃NH₃PbBr₃ by detecting changes in the chemical shifts accompanying a change in crystallographic symmetry. Here, the CH₃ and NH₃ groups were distinguished based on the ¹H chemical shifts. The chemical shifts of the ¹H nuclei remained constant at all temperatures, whereas those of the ¹³C and ²⁰⁷Pb nuclei varied with temperature. The temperature dependence of the chemical shifts was sensitive to the rotation of the PbBr₆ octahedra. From these results, it is evident that the structural environments of ¹³C and ²⁰⁷Pb change near T_C. The change in ²⁰⁷Pb chemical shift near T_C can be explained by the rotation of PbBr₃. This is consistent with the established nature of the phase transition. Additionally, the NMR line widths of ¹H, ¹³C, and ²⁰⁷Pb were 1.62, 2.77, and 206.24 ppm, respectively, and the relaxation time is proportional to the inverse of the line width. Although the chemical shifts of ¹³C and ²⁰⁷Pb abruptly varied near T_C, the ¹H, ¹³C, and ²⁰⁷Pb T_1ρ values showed a similar trend with increasing temperature, and their T_1ρ values were continuous near T_C. These short relaxation times indicate ease of molecular motion. The TGA results also showed that CH₃NH₃PbBr₃ has a high thermal stability.

In addition, the abrupt change occurring in the resonance frequency of the ¹⁴N nuclei near T_C is attributable to a structural phase transition. The NH₃ groups in the structure are coordinated by PbBr₆, and thus atomic displacements in the environment of the ¹⁴N nuclei with temperature are correlated with PbBr₆. The electrostatic interactions governed by hydrogen-bonding interactions between the NH₃⁺ group in the CH₃NH₃ cation and the PbBr₆ octahedra play an important role in the dynamics of the CH₃NH₃ cations. Consequently, the main factor causing the phase transition from the tetragonal to cubic phase near T_C is a change in the surroundings of the ²⁰⁷Pb nuclei in the PbBr₆ octahedra and in the surroundings of C–N groups in the CH₃NH₃ cations. Based on these results, the structural dynamics within the CH₃NH₃PbBr₃ perovskite structure are expected to have a significant effect on the operation mechanism of perovskite solar cells.