Study on Paramagnetic Interactions of (CH₃NH₃)₂CoBr₄ Hybrid Perovskites Based on Nuclear Magnetic Resonance (NMR) Relaxation Time

Abstract

The thermal properties of organic–inorganic (CH₃NH₃)₂CoBr₄ crystals were investigated using differential scanning calorimetry and thermogravimetric analysis. The phase transition and partial decomposition temperatures were observed at 460 K and 572 K. Nuclear magnetic resonance (NMR) chemical shifts depend on the local field at the site of the resonating nucleus. In addition, temperature-dependent spin–lattice relaxation times (T_1ρ) were measured using ¹H and ¹³C magic angle spinning NMR to elucidate the paramagnetic interactions of the (CH₃NH₃)⁺ cations. The shortening of ¹H and ¹³C T_1ρ of the (CH₃NH₃)₂CoBr₄ crystals are due to the paramagnetic Co²⁺ effect. Moreover, the physical properties of (CH₃NH₃)₂CoBr₄ with paramagnetic ions and those of (CH₃NH₃)₂CdBr₄ without paramagnetic ions are reported and compared.

1. Introduction

Hybrid organic–inorganic compounds based on perovskite structures are currently attracting an increased amount of interest owing to their potential as substitutes for perovskite solar cells [1,2,3,4,5,6,7,8,9,10]. However, the toxicity and chemical instability of perovskites continue to be the major problems associated with their use in solar cells. Compounds in the (CH₃NH₃)₂MX₄ family (where M is the transition metal and X is halide) exhibit a variety of physical properties [1,11]. Ions of the transition metal M are located in the tetrahedral structure formed by the halogen ions X, and lie in the planes bridged by the (CH₃NH₃)⁺ cations [12]. These crystals have a layered structure and exhibit quasi-, two-dimensional magnetic properties. Most recently, electrochemical oxygen evolution of (CH₃NH₃)₂CoBr₄, a lead-free cobalt-based perovskite, has been reported by Babu et al. [13]. The (CH₃NH₃)₂CoBr₄ crystal belongs to the (CH₃NH₃)₂MX₄ series and the family of hybrid organic–inorganic compounds in which (CH₃NH₃)⁺ cations are connected via a bridge structure between the planes that contain the Co²⁺ ions. At room temperature, the (CH₃NH₃)₂CoBr₄ crystal structure has monoclinic symmetry and belongs to the space group P2₁/c, with lattice constants a = 7.9782 Å, b = 13.1673 Å, c = 11.2602 Å, and ß = 96.3260° [14]. The unit cell contains four formula units and four magnetic Co²⁺ ions. The (CoBr₄)²⁻ units are surrounded by seven (CH₃NH₃)⁺ cations, and two different crystallographic (CH₃NH₃)⁺ cations exist. Although the tetrahedral anion exhibits only C₁ symmetry, the deviation from an idealized tetrahedral symmetry is small. The NH₃⁺ polar heads of the chains connect the isolated (CoBr₄)²⁻ tetrahedral structure with weak N‒H···Br hydrogen bonds. On the other hand, (CH₃NH₃)₂CdBr₄ crystals at room temperature have a monoclinic structure and belong to the space group P2₁/c with lattice constants a = 8.1257 Å, b = 13.4317 Å, c = 11.4182 Å, ß = 96.1840°, and Z = 4 [15,16]. The structure of this crystal is very similar to that of the (CH₃NH₃)₂CoBr₄. Until now, the phase transition temperature, thermal property, and paramagnetic interactions of (CH₃NH₃)₂CoBr₄ have not been studied in full. The paramagnetic ions of the lead-free perovskite are eco-friendly, which is important for application to solar cells.

The present study was conducted to investigate the thermodynamic properties of the (CH₃NH₃)₂CoBr₄ crystal using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and optical polarizing microscopy. Additionally, the nuclear magnetic resonance (NMR) chemical shifts and spin–lattice relaxation times T_1ρ in the rotating frame of (CH₃NH₃)₂CoBr₄ were obtained using ¹H magic angle spinning (MAS) NMR and ¹³C cross-polarization (CP)/MAS NMR methods at several temperatures to probe the local environments and study the roles of the (CH₃NH₃)⁺ cations. Moreover, the physical properties of (CH₃NH₃)₂CoBr₄ including paramagnetic ions and (CH₃NH₃)₂CdBr₄ excluding paramagnetic ions were obtained from previous reports [17], and used as a comparison to understand the effects of Co²⁺ and Cd²⁺ ions.

2. Results and Discussion

TGA and DSC measurements were obtained to understand the thermal stability, structural phase transitions, and melting temperatures. The TGA and DSC curves of (CH₃NH₃)₂CoBr₄ are plotted within the temperature range of 300–770 K, as shown in Figure 1 and Figure 2. The transformation anomaly at 460 K (=T_C) in the DSC curve is related to the phase transition. The mass loss of 3.89% occurs at approximately 572 K (=T_d), and is ascribed to the onset of partial thermal decomposition. The compound (CH₃NH₃)₂CoBr₄ loses its crystallization at increased temperatures. When comparing the experimental TGA results and possible chemical reactions, the solid residue is calculated on the basis of Equations (1) and (2):

(CH₃NH₃)₂CoBr₄→(CH₃NH₂·HBr)₂CoBr₂→(CH₃NH₂)₂CoBr₂ (s) + 2HBr (g)

(1)

• Residue:
  [(CH₃NH₂)₂CoBr₂ (M = 280.857 g)]/[(CH₃NH₃)₂CoBr₄ (M = 442.681 g)] = 63.4%

  (CH₃NH₃)₂CoBr₄→(CH₃NH₂·HBr)₂CoBr₂→CoBr₂ (s) + 2(CH₃NH₂·HBr) (g)

  (2)
• Residue:
  [CoBr₂ (M = 218.741 g)]/[(CH₃NH₃)₂CoBr₄ (M = 442.681 g)] = 49.4 %

The mass loss of 37% near 669 K is likely attributable to the decomposition of the 2HBr moieties. Moreover, the mass loss near 700 K reaches 48.81%. These results are consistent with the TGA results reported by Babu et al. [13]. By the end, only CoBr₂ remains. The solid-state decomposition is essentially one of the chemical reactions that occur at the surface. The second stage is associated with the thermal decomposition of (CH₃NH₃)₂CoBr₄ to CoBr₂. Optical polarizing microscopy showed that the crystals have a seagrass color at room temperature. The color of the crystal does not vary as the temperature increases, and the crystal starts to melt at temperatures above T_d, as indicated at the surface. From the TGA and DSC results, the phase transition temperature is 460 K, and the partial decomposition temperature is at 572 K. The high-temperature phenomenon above T_d is not related to a physical change, such as structural phase transitions, but is instead related to chemical changes, such as thermal decomposition.

The temperature-dependent ¹H-NMR spectrum of (CH₃NH₃)₂CoBr₄ is obtained to understand and analyze its structure. All recorded spectra contain only one resonance line, and Figure 3 shows the spectrum at 410 K. The spinning sideband for ¹H in CH₃ is marked with open circles, and that for ¹H in NH₃ is marked with asterisks. The ¹H resonance line has an asymmetric shape, and the full-width at half maximum (FWHM) values on the left and right sides are not equal. The asymmetric line shape is attributed to the overlapping lines of the two ¹H in the (CH₃NH₃)⁺ cations. The ¹H-NMR chemical shift of δ = −0.3 ppm is due to the CH₃, while the ¹H-NMR chemical shift of δ = 4.2 ppm is due to the NH₃. The ¹H-NMR chemical shifts for the two ¹H in the (CH₃NH₃)⁺ cations are temperature-independent. They remain quasi-constant with increasing temperature, indicating that the structural environment of ¹H in the CH₃ and NH₃ groups does not change.

Figure 4 shows the recovery traces for the ¹H resonance lines for delay times that range from 1 μs to 20 ms at 300 K. Herein, the arrows mark the resonance lines at each delay time, while the other resonance lines are the sidebands. The T_1ρ values are obtained from the intensities of the magnetization recovery curves with respect to the delay time. The recovery traces are described by a simple mono-exponential function [18,19,20].

P(τ) = P(0) exp(−τ /T_1ρ)

(3)

where P(τ) is the NMR signal intensity measured after recovery time τ, and P(0) is the total nuclear magnetization of the protons at thermal equilibrium. This analysis method is used to obtain the T_1ρ values for the proton in the (CH₃NH₃)⁺ cations. However, the ¹H T_1ρ values for CH₃ and NH₃ are indistinguishable owing to the overlapping responses of the two protons. The ¹H T_1ρ values for (CH₃NH₃)₂CoBr₄ obtained herein and the corresponding values for (CH₃NH₃)₂CdBr₄ reported previously [17] are shown in Figure 5 as a function of the inverse temperature. In the case of (CH₃NH₃)₂CoBr₄, the ¹H T_1ρ values increased rapidly near 210 K, and those at high temperatures are almost continuous; the T_1ρ value at 180 K is 76 μs and that at 300 K is 10 times longer than that at 180 K. The T_1ρ value is very short at low temperatures, and thus indicates rapid energy transfer from the nuclear spin system to the surrounding environment. On the other hand, the ¹H T_1ρ values are obtained for each proton in CH₃ and NH₃ in the case of (CH₃NH₃)₂CdBr₄ as a function of reciprocal temperature. Herein, the T_1ρ values for the two protons of the (CH₃NH₃)⁺ cations are nearly the same within experimental error. The T_1ρ values of ¹H in the CH₃ and NH₃ ions abruptly decrease at approximately 360 K. The ¹H T_1ρ value of (CH₃NH₃)₂CoBr₄ including the paramagnetic ions is very short, whereas that of (CH₃NH₃)₂CdBr₄ excluding paramagnetic ions is very long.

The local environment of the carbons in (CH₃NH₃)₂CoBr₄ was studied by ¹³C MAS NMR, and the corresponding ¹³C-NMR chemical shifts are shown in Figure 6. Attention was paid to ¹³C-NMR, which should be a sensitive probe of the local environment and of the cation dynamics.

The ¹³C-NMR spectrum at 300 K in (CH₃NH₃)₂CoBr₄ shows two signals at the chemical shifts of δ = 68.3 ppm and δ = 117.9 ppm with respect to TMS [21]. The ¹³C-NMR spectrum consists of two lines that correspond to a-CH₃ and b-CH₃. The signals respectively represent the methyl carbons in the two crystallographically different a-CH₃ and b-CH₃. The ¹³C-NMR chemical shifts of the two compounds of (CH₃NH₃)₂CoBr₄ and (CH₃NH₃)₂CdBr₄ are shown in Figure 7 as a function of temperature. The ¹³C-NMR chemical shifts vary significantly with temperature. Specifically, the ¹³C-NMR chemical shifts in the case of (CH₃NH₃)₂CoBr₄ decrease slowly and monotonically as a function of temperature. Conversely, the ¹³C-NMR spectrum at 300 K in (CH₃NH₃)₂CdBr₄ shows two signals at chemical shifts of δ = 27.9 ppm and δ = 29.3 ppm. The ¹³C-NMR chemical shifts of the crystallographically different a-CH₃ and b-CH₃ slowly and monotonously increase as a function of temperature. The ¹³C chemical shifts of the CH₃ groups differ between the two compounds. Generally, the paramagnetic contribution to the NMR shift is responsible for the NMR spectra. The ¹³C chemical shift of (CH₃NH₃)₂CoBr₄, which contains paramagnetic ions, was significantly different to that of (CH₃NH₃)₂CdBr₄, which does not contain paramagnetic ions. The differences in the ¹³C chemical shifts could potentially be due to differences in the electron structures of the metal ions.

To determine the ¹³C T_1ρ, nuclear magnetization was measured as a function of the delay time. The signal intensities of the nuclear magnetization recovery curves are fitted by the mono-exponential function of Equation (3). From these results, T_1ρ values were obtained for the carbons in (CH₃NH₃)₂CoBr₄ and (CH₃NH₃)₂CdBr₄ as a function of the inverse temperature, as shown in Figure 8. In the case of (CH₃NH₃)₂CoBr₄, the T_1ρ values of ¹³C show a minimum value near 330 K, while the T_1ρ value abruptly decreases above 410 K. The T_1ρ values for a-CH₃ and b-CH₃ are also very similar and of the order of 10 ms. Conversely, the variation of T_1ρ with temperature in the case of (CH₃NH₃)₂CdBr₄ exhibits a minimum near 250 K for a-CH₃ and b-CH₃, respectively, and T_1ρ decreases abruptly above 360 K. The presence of these minima are attributed to the effects of the reorientation of (CH₃NH₃)⁺ cations. From the ¹³C T_1ρ curves, the relaxation processes of (CH₃NH₃)₂CdBr₄ are affected by molecular motion described by the Bloembergen–Purcell–Pound (BPP) theory [22]. The experimental values of T_1ρ are explained by the correlation time τ_C for molecular motion based on the BPP theory [22,23],

(1/T_1ρ) = 0.05(μ_o/4π)²[γ_H² γ_C² ħ²/r⁶][4F_a + F_b + 3F_c + 6F_d + 6F_e]

(4)

where

• F_a = τ_C/[1 + ω₁²τ_C²]
• F_b = τ_C/[1 + (ω_H ‒ ω_C)²τ_C²]
• F_c = τ_C/[1 + ω_C²τ_C²]
• F_d = τ_C/[1 + (ω_H + ω_C)²τ_C²]
• F_e = τ_C/[1 + ω_H²τ_C²].

where μ_o is the permeability, γ_H and γ_C are the respective gyromagnetic ratios for the ¹H and ¹³C nuclei, r is the distance of H–C, ħ = h/2π, and ω_H and ω_C are the respective Larmor frequencies of ¹H and ¹³C.

On the other hand, the relaxation processes of (CH₃NH₃)₂CoBr₄ with the paramagnetic Co²⁺ ions are affected by the molecular motion described by the Solomon equation [24]. When paramagnetic ions exist, the T_1ρ are represented by τ_C, as presented in [24]

(1/T_1ρ) = (1/15)(μ_o/4π)²[γ_I²γ_e²μ_B²S(S+1)/r⁶][4G_a + G_b + 3G_c + 6G_d + 6G_e]

(5)

where

• G_a = τ_C/[1 + ω₁²τ_C²]
• G_b = τ_C/[1 + (ω_C ‒ ω_e)²τ_C²]
• G_c = τ_C/[1 + ω_C²τ_C²]
• G_d = τ_C/[1 + (ω_C + ω_e)²τ_C²]
• G_e = τ_C/[1 + ω_e²τ_C²].

Here, γ_e is the gyromagnetic ratio of the electron, S is the total spin quantum number of the paramagnetic ion, and ω_e is the Larmor frequency of the electron. Additionally, ω₁ is the angular frequency at the spin-lock field; 59.52 kHz for (CH₃NH₃)₂CoBr₄ and 67.56 kHz for (CH₃NH₃)₂CdBr₄. The T_1ρ exhibits a minimum when ω₁τ_C = 1. Based on this condition, the coefficients of Equations (4) and (5) which are dependent on ω₁, ω_H, and ω_C, can be obtained. Furthermore, the value of τ_C can be calculated, and its temperature dependence follows a simple Arrhenius expression [22] according to,

τ_C = τ_oexp(−E_a/RT)

(6)

where τ_o is the preexponential factor, T is the temperature, R is the gas constant, and E_a is the activation energy. The activation energies for the tumbling motion of a-CH₃ and b-CH₃ in the case of (CH₃NH₃)₂CoBr₄ are obtained from the log τ_C vs. 1000/T curve, and are respectively equal to 24.51 ± 0.99 kJ/mol and 23.25 ± 1.30 kJ/mol, whereas the corresponding values in the case of (CH₃NH₃)₂CdBr₄ are 8.18 ± 0.37 kJ/mol and 7.65 ± 0.21 kJ/mol (see Figure 9). When paramagnetic Co²⁺ ions exist, 1/τ_C = 1/τ_r + 1/τ_M + 1/τ_e, where τ_r, τ_M, and τ_e, are the rotational correlation time, exchange correlation time, and electronic relaxation correlation time, respectively. The τ_r can represent molecular motion. For (CH₃NH₃)₂CdBr₄, there is no chemical exchange or paramagnetic terms, and so τ_C can directly reflect the molecular motion. In the case of (CH₃NH₃)₂CoBr₄, τ_e dominates the total correlation time, and thus, τ_C is not directly related to molecular motion.

3. Materials and Methods

The (CH₃NH₃)₂CoBr₄ single crystals were grown based on the slow evaporation of an aqueous solution with a 2:1 ratio of CH₃NH₂∙HBr and CoBr₂ at 300 K. Single crystals have a diamond shape and seagrass color.

The thermal properties and phase transition temperature were measured using a TGA (TA, DSC 25) instrument at a heating rate of 10 °C/min. The TGA and DSC curves were measured in an N₂ atmosphere, and the mass of the powder sample used in the experiment was 9.22 mg.

The solid-state MAS NMR spectra and the spin–lattice relaxation time T_1ρ in the rotating frame of (CH₃NH₃)₂CoBr₄ crystals were recorded on a Bruker 400 DSX NMR spectrometer (Bruker, Leipzig, Germany) at the Korean Basic Science Institute at the Western Seoul Center. Solid samples were inserted into 4 mm diameter zirconia rotors. The samples were spun at a sufficient speed to avoid spinning sidebands overlapping. The chemical shifts were defined with respect to tetramethylsilane (TMS). The ¹H T_1ρ values were measured using a π/2-τ pulse sequence by varying the duration of the spin-locking pulses. The ¹³C T_1ρ values were measured based on the variation of the duration of the ¹³C spin-locking pulse. The usual experimental approach assumes the use of cross-polarization from protons to enhance the ¹³C sensitivity. The widths of the π/2 pulses for ¹H and ¹³C were 4.1 μs and 4.2 μs, respectively. The T_1ρ values were measured in the temperature range of 180–430 K due to limitations of the experimental equipment associated with the measurements of the spectra and T_1ρ outside of this range. The sample temperatures were held constant by controlling the helium gas flow and the heater current [25,26].

4. Conclusions

The thermal properties and phase transition temperature of (CH₃NH₃)₂CoBr₄ crystals grown based on the slow evaporation method were investigated with TGA, DSC, and optical polarizing microscopy. The phase transition and partial decomposition temperatures were observed at 460 K and 572 K, respectively. The high-temperature phenomenon above 572 K was not related to a physical change like the structural phase transition. Instead, it was related to a chemical change, such as thermal decomposition.

The paramagnetic interactions of (CH₃NH₃)₂CoBr₄, associated with the role of the (CH₃NH₃)⁺ cations were studied by ¹H-NMR and ¹³C-NMR as a function of temperature. The ¹H and ¹³C MAS NMR were used to probe the dynamics of cations in (CH₃NH₃)₂CoBr₄ and (CH₃NH₃)₂CdBr₄. The chemical shift by the MAS NMR depended on the local field at the site of the resonating nucleus in crystals. The effect of these crystals on the ¹H and ¹³C-NMR chemical shifts was investigated using temperature-dependent NMR experiments. The contributions to the ¹³C-NMR chemical shifts are correlated with the distribution of spin density in the ligand moiety.

The temperature dependence of the T_1ρ values for ¹H reflect the modulation of the inter-NH₃ and inter-CH₃ dipolar interactions due to the (CH₃NH₃)⁺ cations. The variation of T_1ρ for ¹³C yielded a minimum, and it is apparent that the T_1ρ values for ¹³C are governed by tumbling motions. Moreover, the paramagnetic dopant led to the shortening of their T_1ρ values. Accordingly, it has been shown that the T_1ρ value is inversely proportional to the square of the magnetic moment of the paramagnetic ion [27]. The T_1ρ values of ¹H and ¹³C of the (CH₃NH₃)₂CoBr₄ crystals, which contain paramagnetic ions, are much shorter than those of the (CH₃NH₃)₂CdBr₄ crystals, which do not contain paramagnetic ions.

The (CH₃NH₃)₂CoBr₄ and (CH₃NH₃)₂CdBr₄ crystals are of the (CH₃NH₃)₂MX₄ type, whereas their individual dynamics differ significantly from the dynamic of the cations. The differences between the T_1ρ of the (CH₃NH₃)₂MBr₄ crystals (M = Co and Cd) are due to the differences between the electron structures of their Co²⁺ and Cd²⁺ ions. These ions screen the nuclear charge from the motion of the outer electrons. The Co²⁺ has unpaired d electrons, whereas Cd²⁺ has filled d shells. Their NMR properties stem from the differences between the chemical properties of paramagnetic Co²⁺ and non-paramagnetic Cd²⁺ ions. Furthermore, the NMR relaxation of diamagnetic Cd²⁺ ions is most probably driven by dipolar interactions, whereas the relaxation of paramagnetic Co²⁺ ions is mostly driven by interactions with the paramagnetic center.