Multinuclear solid-state NMR investigation of structurally diverse low-dimensional hybrid metal halide perovskites

Abstract

Owing to their synthetic versatility and optoelectronic tunability, low-dimensional hybrid metal halide perovskites (MHPs) provide a key avenue for the design of future optoelectronic materials. Nuclear magnetic resonance (NMR) spectroscopy has emerged as a powerful tool for structural characterisation and molecular dynamics elucidation in MHPs, which are known to control the materials' optoelectronic properties. In this work, we utilise solid state NMR to study structurally diverse hybrid MHPs containing 2D, 1D and 0D inorganic motifs that are templated by a series of xylylenediammonium cations and compare their characteristics with those of archetype 3D perovskites. The highly resolved scalar coupling pattern (J¹(²⁰⁷Pb–^79/81Br) = 1.98 kHz) in the ²⁰⁷Pb NMR spectrum of 0D meta-xylylenediammonium lead bromide ((mXDA)₂PbBr₆), reveals that ²⁰⁷Pb NMR of methylammonium lead bromide (MAPbBr₃) and formadinium lead bromide (FAPbBr₃) is sensitive to local Br positional disorder, associated with the fast reorientation of the MA/FA cations. Variable temperature ¹H spin–lattice relaxation quantifies the correlation time of the reorientation of the MA/FA cations at picosecond timescales, in contrast to the slower motion of the bulky cations in the low-dimensional perovskites. Additionally, the study of meta-xylylenediammonium tin halides ((mXDA)₂SnX₆) provides the first direct detection of tin-halide scalar coupling patterns (J¹(¹¹⁹Sn–^79/81Br) = 1.51 kHz; J¹(¹¹⁹Sn–^35/37Cl) = 260 Hz).

---

Introduction

Metal halide perovskites (MHPs) have been the subject of fervent research over the last ten years due to their exceptional optoelectronic properties and flexible structural characteristics.^1,2 The typical three-dimensional (3D) crystal structure of MHPs is given by the chemical formula ABX₃, where the metal centre B²⁺ is surrounded by six halide X⁻ anions (chlorine, bromine or iodine) forming the octahedral repeat unit. Lead halide perovskites have, in particular, garnered the most interest due to their capability to yield high efficiency optoelectronic devices, however less-toxic alternatives have also been actively researched with tin emerging as the most promising non-lead metal centre.^3,4 The A⁺ cations are typically small organic molecules, such as methylammonium (MA) and formadinium (FA), in organic–inorganic “hybrid” perovskites or small inorganic ions (Cs⁺) in all-inorganic perovskites, all of which act as structural templating and charge balancing agents.

In the typical ABX₃ perovskite structures, the halometallate octahedral units are connected through corner sharing in three directions, creating 3D inorganic lattices. However, the versatile structural flexibility of the metal halide perovskite system allows different dimensional frameworks to be realised through the use of suitable larger organic cations. In contrast to morphologically controlled species (e.g. 2D nanoplates and 0D quantum dots), the corresponding hybrid materials feature inorganic frameworks that are of reduced dimensionality (i.e. limited connectivity) at the molecular level. 2D perovskites, such as butylammonium lead bromide ((BA)₂PbBr₄),⁵ contain sheets, or layers, of typically corner sharing [BX₆]⁴⁻ octahedra, while 1D and 0D congeners contain chains of [BX₆]⁴⁻ octahedra and isolated octahedral [BX₆]⁴⁻ units, respectively. The latter generally follows the chemical formula A₄BX₆, which is identical to the 0D caesium lead bromide phase Cs₄PbBr₆.⁶ Physically, the reduced dimensionality at molecular level leads to various quantum-confinement induced effects, such as tunable band gaps and improved photoluminescence, while also resulting in higher stability than their nanosized analogues. In this article, the use of 0D, 1D, and 2D terminologies shall refer to such low-dimensional hybrid perovskites.

Solid state nuclear magnetic resonance (NMR) spectroscopy has been shown to be a powerful, non-destructive technique in the structural characterisation of perovskites.^7–9 It can analyse both amorphous (surface or nanocrystal MHP) and crystalline (bulk MHP) materials, unlike traditional diffraction techniques. In addition to structural information, NMR can probe molecular dynamics and chemical bonding via relaxometry and correlation NMR, respectively. Furthermore, its element-specific nature allows focused investigation on the desired component (metal, ion, ligand, or dopant). The majority of NMR perovskite reports have focused on the study of cation phases, dynamics and molecular rotations in hybrid perovskites using ¹H, ²H, ¹³C, ¹⁴N and ¹³³Cs NMR experiments.^7,10–44 In addition, ²⁰⁷Pb NMR has been proven to be useful in determining the structure and phase composition of lead halide perovskites with new or mixed cations/anions;^{31,32,36,44–68} high resolution ²⁰⁷Pb NMR spectra of some perovskites have also revealed scalar coupling patterns.^{24,31,46,47,69}

Scalar coupling (also called J-coupling) refers to the perturbation of the observed nuclei's energy levels due to the polarisation of the covalent bond electron pairs by a secondary nuclei. This creates a splitting in the NMR resonance, with a frequency difference equal to the scalar coupling parameter J¹. The energy level is raised or lowered depending on the orientation of the second nucleus's spin sub-level (m) with the external magnetic field. Hence, a bond to a spin S which has 2S + 1 possible spin sub-levels, results in 2S + 1 degenerate energy levels. The splitting of the energy levels is compounded when the observed nucleus is bonded to multiple magnetically equivalent nuclei. The final number of degenerate energy levels is given by 2nS + 1, where n is the number of such bonds. In the NMR spectrum this manifests as a splitting of the resonance into a multiplet of 2nS + 1 resonances, whose intensities follow a binomial distribution. The strength of the scalar coupling, quantified by J¹, is dependent on multiple factors including the degree of covalence of the bonds and the degree of orbital overlap. Hence, ²⁰⁷Pb scalar coupling can provide information on the haloplumbate bond lengths, angles and rigidity in perovskite materials.

Recently, Aebli et al. measured the ²⁰⁷Pb NMR of MAPbX₃, FAPbX₃, CsPbX₃ and Cs₄PbBr₆ (X = Br and Cl) and confirmed an absence of resolved scalar coupling for MAPbBr₃ and FAPbBr₃ at room temperature. This absence is intriguing as the predicted perfect cubic symmetry of the PbBr₆ octahedra in these perovskites rules out merging of the scalar coupling pattern due to structural asymmetry. Conversely, greater structural symmetry explains the more resolved scalar coupling pattern in Cs₄PbBr₆ than CsPbBr₃, which has been observed in several reports.^46,47,69 Aebli et al.⁶⁹ postulated that the lack of scalar coupling resolution at room temperature in MAPbBr₃ and FAPbBr₃ was result of the fast cation dynamics in both systems. Hence, ²⁰⁷Pb NMR could prove to also be a probe of the fast organic cation dynamics in hybrid perovskites, which, outside of NMR techniques, has relied upon neutron scattering or molecular dynamic simulations for study.^18,70,71 For their hypothesis to be proven, Aebli et al. called for comparison with 0D hybrid perovskites. Such materials could provide a symmetric PbX₆ octahedral configuration, without the rapid cation dynamics environment, due to the significant steric effect provided by the relatively bulkier organic molecules required to template a 0D perovskite structure.

Therefore, the lead–bromide hybrid perovskite based on the meta-xylylenediammonium cation ((mXDA)₄PbBr₆) was chosen for this work because it has been shown to feature relatively symmetrical [PbBr₆]⁴⁻ octahedra in an isolated 0D structure.^72–74 We further found that by simply changing the position of the methylammonium chain, the resulting inorganic frameworks within the materials crystal lattice can be modulated. In particular, para-xylylenediammonium induces the formation of monolayered 2D lead bromide structure in (pXDA)PbBr₄, while ortho-xylylenediammonium templates 1D bromoplumbate chain motifs in (oXDA)₂Pb₂Br₈. As such, the XDA cation series acts as a perfect platform to study not only the scalar coupling properties and how it is related to the cation dynamics, but also to gain insight over how such properties would vary as a function of inorganic structural dimensionality.

This work presents the first ²⁰⁷Pb MAS NMR of the xylylenediammonium lead bromides which, alongside structural data via single crystal X-ray diffractometry (SCXRD), is compared to well-known lead halide perovskites: MAPbBr₃, FAPbBr₃, CsPbBr₃, Cs₄PbBr₆ and (BA)₂PbBr₄. The results are corroborated with cation dynamics via ¹H/¹³³Cs spin–lattice nuclear relaxation measurements. In addition, we provide the first synthesis and structural characterisations of: ortho-xylylenediammonium lead bromide, (oXDA)₂Pb₂Br₈; meta-xylylenediammonium lead chloride, (mXDA)₂PbCl₆; meta-xylylenediammonium tin bromide, (mXDA)₂SnBr₆; and meta-xylylenediammonium tin chloride, (mXDA)₂SnCl₆. The 0D tin perovskites are also examined via ¹¹⁹Sn MAS NMR experiments.

Methodology

Synthetic procedures

Growth of single crystals of MAPbBr₃, FAPbBr₃, CsPbBr₃, Cs₄PbBr₆, and (BA)₂PbBr₄. MAPbBr₃ and FAPbBr₃ samples were grown using inverse temperature crystallization.⁷⁵ Briefly, MABr (0.112 g) and PbBr₂ (0.367 g) were dissolved in DMF (1 mL) while FABr (0.125 g) and PbBr₂ (0.367 g) were dissolved in DMF–GBL (1 : 1 volume ratio total 1 mL) to create 1 M perovskite solutions. The solutions were then slowly heated to 100 °C. The resulting single crystals grown thereof were then harvested, washed and dried under reduced pressure accordingly. Meanwhile, CsPbBr₃, Cs₄PbBr₆ and (BA)₂PbBr₄ were synthesized through the normal temperature crystallization method with concentrated HBr (48%; 1 mL)) being used as the solvent. Therein, a stochiometric amount of PbO (0.223 g) was dissolved in HBr before CsBr (0.213 g or 0.852 g)) or butylamine (0.200 mL) were added to create 1 M perovskite solutions. The solution was then heated gently to 100 °C with vigorous stirring (50 °C for Cs₄PbBr₆ with 12 hours of stirring). The solutions were then slowly cooled to room temperature to obtain crystals. The crystals were then washed and dried under reduced pressure, before being ground to fine powder for solid state NMR measurement.

General procedure for preparation of xylylenediammonium halide (XDABr/XDACl) salts. To a round bottom flask containing ethanol (∼10 mL) and the requisite xylylenediamine (3.7 mmol; ca. 0.5 g scale), cooled to 0 °C, was added a stoichiometric amount of concentrated HBr (48%)/HCl (37%) (415/301 μL). After stirring the solution for 1 hour, all volatiles were then removed using a rotary evaporator. The solids, thereby, obtained were washed with copious amounts of diethyl ether and dried under vacuum at 50 °C overnight. (oXDA)Br was synthesised in inert conditions via the Schlenk line technique due to instability in ambient air.

Growth of single crystals of 0D (mXDA)₂BX₆ perovskites. Previously synthesized organic halide salts (in excess) were dissolved in DMF with halide salts PbBr₂/PbCl₂/SnBr₂/SnCl₂ at 100 °C (to produce a 1 M perovskite solution. Then, following the antisolvent vapour-assisted recrystallisation method, antisolvent vapour dietheylether was allowed to diffuse into the perovskite solution under inert conditions, which afforded single crystals suitable for X-ray crystallography. The same crystals were stored in inert conditions before being quickly ground to fine powder and packed for solid state NMR measurement.

Growth of single crystals of (pXDA)PbBr₄ and (oXDA)₂Pb₂Br₈. The prior synthesis did not produce (pXDA)PbBr₄ and (oXDA)₂Pb₂Br₈; instead the following alternative procedure was used. Mixtures of stoichiometric amounts of organic bromide salt (synthesized previously) and PbBr₂ (0.25 mmol scale) in concentrated HBr (48%; 1 mL) (to produce concentrations of 0.25–0.30 M relative to Pb²⁺) were prepared in a two-necked round bottom flask and heated, with stirring, at ∼135 °C for around 1 hour. The clear solutions that resulted were then allowed to cool slowly to room temperature, which afforded single crystals suitable for X-ray crystallography. The same crystals were stored in inert conditions before being quickly ground to fine powder and packed for solid state NMR measurement.

Analytical techniques

For single crystal X-ray measurement and study, a Bruker X8 CCD area detector diffractometer was used and the data was collected using graphite monochromated Mo-Kα radiation (λ = 0.71073 Å) at particular temperatures. Data reduction and absorption corrections were performed using the SAINT and SADABS software packages, respectively.⁷⁶ All structures were solved by direct methods and refined by full-matrix least squares procedures on F2, using the Bruker SHELXTL-2014 software package.^77,78 Non-hydrogen atoms were anisotropically refined before hydrogen atoms were introduced at calculated positions for further refinement of data. The graphical illustrations of crystal structures used throughout were mainly created using the program VESTA.⁷⁹ Full crystallographic and refinement data can be found in the ESI Tables S1 and S2.†

The photoluminescence (PL) spectra were acquired using a WITec alpha 300RAS confocal Raman microscope. The UV line of a linearly polarized CW solid laser (He–Cd, 325 nm) was chosen and the excitation power was kept below 10 μW on sample to avoid photo degradation and saturation of the detector.

Solid-state NMR experiments were completed on a 14.1 T Bruker Advance III HD 600 MHz spectrometer using a 1.9 mm Bruker HXY probe. Single crystal samples were manually ground before packing. The ²⁰⁷Pb NMR (ν₀(²⁰⁷Pb) = 125.60 MHz) Hahn-echo experiments utilised an MAS frequency of 12 kHz, a π/2 pulse of 5 μs (determined on Pb(NO₃)_2(s)), a recycle delay of 5 s, and a rotor synchronised echo delay. The ¹H NMR saturation recovery experiments utilised MAS frequencies of 12–40 kHz, a ¹H π/2 pulse length of 2.5 μs, and a 200 pulse saturation block. The ¹¹⁹Sn[¹H] and ¹³C[¹H] NMR CP experiments utilised an MAS frequency of 12 kHz, a 5000 μs contact pulse length, a ¹H π/2 pulse length of 2.5 μs, high power proton decoupling and recycle delays dependent on the ¹H saturation recovery results. All spectra were processed using the Topspin software package and referenced to the unified scale using IUPAC recommended frequency ratios relative to the ¹³C adamantane_(s) methylene resonance (δ = 37.77 ppm).^80,81 Spectral deconvolution was performed with dmfit.⁸²

Results and discussion

Each of the XDA-based materials crystallize in monoclinic space group P2₁/c, as determined via SCXRD, and the refined structures are shown in Fig. 1. Fig. 1(a–c) demonstrates how varying the position of the methylammonium functional groups on the phenyl ring of the cations results in lead bromide perovskites of different dimensionalities. In particular, mXDA leads to (mXDA)₂PbBr₆, a 0D perovskite with isolated octahedral units (Fig. 1(a)), while the isomeric pXDA templates the formation of (pXDA)PbBr₄, a 2D perovskite with isolated monolayers of corner-sharing octahedral units expanding in the b–c plane (Fig. 1(c)). The oXDA cation, on the other hand, produces (oXDA)₂Pb₂Br₈, which has a more complex structure, with 1-D chains of edge-sharing octahedral units along the c-axis with additional branches of singular corner-sharing units (Fig. 1(b)). Isovalent substitution of the metal halide components does not typically alter the resulting inorganic framework configuration. This is illustrated by examples shown in Fig. 1(d–f) where hybrid materials (mXDA)₂PbCl₆, (mXDA)₂SnBr₆, and (mXDA)₂SnCl₆ were found to exhibit the same isolated 0D structure as (mXDA)₂PbBr₆. To confirm the organic cation integrity in the series of low-dimensional hybrid perovskites investigated in this work, ¹³C CPMAS NMR experiments were conducted and the corresponding spectra can be seen in ESI Fig. S1.†

Fig. 1 The SCXRD determined structures of (a) (mXDA)₂PbBr₆, (b) (oXDA)₂Pb₂Br₈, (c) (pXDA)PbBr₄, (d) (mXDA)₂PbCl₆, (e) (mXDA)₂SnBr₆, and (f) (mXDA)₂SnCl₆ with molecular drawings of the respective organic cations inset.

Hybrid materials with isolated [PbBr₆]⁴⁻ ions, such as 0D (mXDA)₂PbBr₆, are relatively rare in occurrence with less than ten compounds being reported so far in the literature.^83–89 The organic species responsible for directing such molecular lead-bromide octahedra are diverse in structure, but some similarities can still be drawn. This includes the presence of both dicationic ammonium groups and a bulky core. The former is needed to not only satisfy the charge balancing requirements to the [PbBr₆]⁴⁻ units, but also to drive the lattice formation through H bonding with Br⁻ ions. The relative position of the ammonium groups in the organic molecule dictates the formation of isolated [PbBr₆]⁴⁻ octahedra. For example, a 1D chain was obtained in the case of (oXDA)₂Pb₂Br₈ because the proximity of the methylammonium functionality in oXDA prevents the formation of separate octahedra. On the other hand, the ammonium groups in pXDA are far enough apart to allow one bromoplumbate octahedron to corner-share with four octahedral neighbors along an equatorial plane. Propagation in two directions eventually leads to layered [PbBr₄]²⁻ architectures in (pXDA)PbBr₄. The bulky core of the organic cation enforces the physical separation between each bromoplumbate octahedron as a result of steric hindering and in the case of XDA, this role is fulfilled by the phenyl ring. In all the investigated mXDA templated perovskites, the phenyl rings are arranged in parallel displaced stacks with centroid–centroid distances of 4.2–4.3 Å and centroid normal-centroid vector angles of 33–38°. The phenyl rings in (pXDA)PbBr₄ and (oXDA)₂Pb₂Br₈ are T-stacked and parallel displaced respectively (centroid–centroid distance of 5.8 and 5.4 Å). A more detailed discussion on the specificity of isomeric XDA cations in templating low-dimensional perovskite with different inorganic architectures, in comparison to other reported 0D templating cations, can be found in the ESI.†

Low-dimensional lead halide perovskites tend to demonstrate broadband photoluminescence. Such behaviour has been documented by several studies and the origin is ascribed to the self-trapped excitons formed in the disordered crystal lattice.^90–92 Structurally, the broadband emission has also been correlated with different parameters of inorganic lattice distortion within the materials, such as inter-octahedral tilting and intra-octahedral (coordination) deformation.^93–95 As expected from the octahedral distortion of the XDA lead bromide perovskites, they produce broadband emission across the visible light region (Fig. S5†).

The ²⁰⁷Pb solid state NMR spectra of each lead bromide perovskite are presented in Fig. 2. Scalar coupling patterns have been resolved in the spectra of (mXDA)₂PbBr₆, Cs₄PbBr₆, and CsPbBr₃, where coupling of ²⁰⁷Pb nuclei (spin ½) with six ^79/81Br nuclei (spin [/]) results in 19 degenerate resonances with a binomial intensity distribution. Such phenomena have previously been observed for Cs₄PbBr₆, CsPbBr₃, CsPbCl₃, MAPbBr₃, and MAPbCl₃. Our results did not resolve the pattern for the MA perovskites, however previous reports of scalar coupling in the ²⁰⁷Pb spectra of the MA-based perovskites were taken at much lower temperatures and/or lower magnetic fields, which explains the discrepancy.⁶⁹

Fig. 2 The ²⁰⁷Pb NMR spectra of the lead bromide perovskites. Experimental and simulated spectra are displayed in blue and red respectively.

The ²⁰⁷Pb NMR fitting parameters are detailed in Table 1. The isotropic chemical shift (δ_iso) varies between 600 and −600 ppm, and has a general dependency on the structure of the PbBr₆ octahedra. Fig. 3(a) shows a negative correlation between δ_iso and the mean Pb–Br bond length, giving a coefficient of determination (R²) of 0.78. As the bond length increases the negative paramagnetic shielding contribution decreases (i.e. the total shielding of the ²⁰⁷Pb nucleus increases), resulting in a decrease in chemical shift frequency. This correlates with the findings of Dimitrenko et al. who utilised density functional theory (DFT) calculations to show that the ²⁰⁷Pb paramagnetic contribution is the dominant variable affecting the ²⁰⁷Pb chemical shielding when varying the electronegativity of the halide bond, achieved by swapping the X halide in Pb(II)X₂ compounds.¹⁰⁰ In addition, Lee et al. reported a negative correlation between δ_iso(²⁰⁷Pb) and mean Pb–I bond lengths across a series of 3D/2D lead iodide perovskites.⁶¹ Values for the two (oXDA)₂Pb₂Br₈ Pb sites were not included in the linear fit due to the large site disorder. Both sites have effective coordination numbers (n_e) below 5.7 (while sites from all other lead bromides have n_e > 5.99) which would strongly effect their ²⁰⁷Pb chemical shift. Variations from the predicted trend can be explained by cation differences and distances between octahedral layers. For example, (pXDA)PbBr₄ and (BA)₂PbBr₄ have very similar structures and cations but fall on either side of the trendline. This is due to the greater inter-octahedral Pb–Pb distance in the latter (between both adjacent Pb and Pb in separate layers) resulting in a reduced magnetic shielding and hence a relatively higher chemical shift. Fig. 3(a) demonstrates how ²⁰⁷Pb NMR can differentiate between the structural dimensionalities of the perovskites due to its sensitivity to Pb–Br bond lengths and greater structure.

Table 1 ²⁰⁷Pb NMR parameters of the lead bromide perovskites in comparison with their ¹H or ¹³³Cs longitudinal relaxation times T₁, determined at 14.1 T and at room temperature. Uncertainties are represented in italic parentheses

Perovskites	Dimensionalities	^207Pb NMR			Cation NMR relaxation
		δiso (ppm)	Scalar coupling		^1H T1 s	^133Cs T1 s
			J^1(^207Pb–^79/81Br) (kHz)	FWHM^a (kHz)
a Full-width half maximum (FWHM) of observable scalar coupling resonances.
(mXDA)2PbBr6	0D	−595.0(6)	1.98(7)	1.17(7)	1.5	—
(oXDA)2Pb2Br8	1D	215(40), −142(47)	—	—	0.7	—
(pXDA)PbBr4	2D	53(7)	—	—	0.7	—
(BA)2PbBr4	2D	83(15)	—	—	2
MAPbBr3	3D	358(7)	—	—	24	—
FAPbBr3	3D	502(7)	—	—	32	—
Cs4PbBr6	0D	−361.1(7)	2.02(8)	1.26(8)	—	159
CsPbBr3	3D	265(1)	2.38(14)	2.12(14)	—	200

---

Fig. 3 Plots of (a) ²⁰⁷Pb isotropic chemical shift and (b) ²⁰⁷Pb–^79/81Br scalar coupling constants vs. octahedral Pb–Br mean atomic distance for the lead bromide perovskite series. Linear fits are presented with R² values of 0.776 and 0.997 for the isotropic chemical shift and scalar coupling constants respectively. Values taken from the report of Aebli et al.⁶⁹ are marked with blue triangles. (oXDA)PbBr₄ values are considered as anomalous (red squares) and hence are left out of the linear fits.

The scalar coupling parameter J¹(²⁰⁷Pb–^79/81Br) is the frequency difference between each resonance in the pattern, and is a measure of the intensity of the local magnetic field perturbation created by the shared electrons. It follows that the J¹ value for a set pair of nuclei is negatively proportional to the bond length l. Fig. 3(b) confirms the trend for J¹(²⁰⁷Pb–^79/81Br) in lead bromide perovskites providing the correlation:

The lead bromide perovskites investigated in this study only provided 3 data points for analysing the scalar coupling, however the J¹ value for MAPbBr₃ at 100 K by Aebli et al. also fits the trend.⁶⁹ Furthermore, the same trend can be observed for lead chloride scalar couplings, as seen in ESI Fig. S2.†

For the perovskites whose scalar coupling is not resolved, other interactions must be broadening the individual resonances sufficiently to “smear” the scalar coupling pattern. The most obvious culprit would be distortion in the [PbBr₆]⁴⁻ octahedral units, where asymmetry would result in large ²⁰⁷Pb chemical shift anisotropy broadening. In more symmetrical cases differing bond-lengths and angles could result in mismatched scalar couplings for each bond and smearing of the pattern. Table 2 details the structural parameters of each of the lead bromides investigated here, with several metrics defining distortion of the [PbBr₆]⁴⁻ octahedra.

Table 2 Structural parameters of the lead bromide perovskites determined via SCXRD. Uncertainties are represented in italic parentheses

Perovskites	Dimensionality	Space group	Pb–Br length		Br–Pb–Br angle variance (°)	[PbBr6]^4− ne^a	Ref.
			Mean (Å)	σ (Å)
a Effective coordination number.b Determined in this work.
(mXDA)2PbBr6	0D	Pm21/c	3.0290(4)	0.0148	36.72	5.996	^b
(oXDA)2Pb2Br8	1D	Pm21/c	3.0259(1), 3.0013(1)	0.1145, 0.1056	99.56, 27.56	5.671, 5.688	^b
(pXDA)PbBr4	2D	Pm21/c	2.9966(3)	0.0132	6.14	5.996	^b
(BA)2PbBr4	2D	Pbca	3.0040(3)	0.0078	9.42	5.999	93
MAPbBr3	3D	Pm3̄m	2.9664(3)	0.0000	0.00	6.000	96
FAPbBr3	3D	Pm3̄m	2.9849(1)	0.0000	0.00	6.000	97
Cs4PbBr6	0D	R3̄c	3.0284(4)	0.000	0.06	6.000	98
CsPbBr3	3D	Pbnm	2.9677(1)	0.0120	34.84	5.997	99

---

The 2D and 1D perovskites have ²⁰⁷Pb patterns defined by chemical shift anisotropy (CSA) broadening due to the low symmetry about the [PbBr₆]⁴⁻ octahedral units, which hides any underlying scalar coupling. The large Pb–Br length/angle distortion present in the two distinct lead sites in (oXDA)₂Pb₂Br₈ (see Table 2) results in two very broad overlapping resonances. The ²⁰⁷Pb NMR spectrum is of poor quality as the (oXDA)₂Pb₂Br₈ perovskite was not stable and samples degraded, despite synthesizing under inert conditions and packing quickly. During the long acquisition time necessary for wide-line ²⁰⁷Pb NMR experiments the ²⁰⁷Pb resonance was lost and the sample had changed colour to black. The “step-like” 2D perovskite architecture reported by Hoffman et al., has a similar arrangement of corner sharing [PbX₆]⁴⁻ in shorter chains (2–4 octahedral units) which are linked by edge sharing [PbX₆]⁴⁻ into a larger 2D network.¹⁰¹ The edge sharing octahedral units in these step-like perovskites are similarly distorted as in (oXDA)₂Pb₂Br₈, due to the asymmetrical positioning of neighbouring [PbX₆]⁴⁻ octahedra. They reported no such problems with stability. Instead the organic molecule itself seems to be the source of the instability as the synthesized organic bromide salt degraded when left in open atmosphere. As this study was most interested in comparing the ²⁰⁷Pb NMR of different hybrid perovskite architectures with symmetrical octahedral units, higher quality ²⁰⁷Pb NMR of (oXDA)₂Pb₂Br₈ was not pursued further.

The 2D perovskites (pXDA)PbBr₄ and (BA)₂PbBr₄ have relatively symmetrical [PbBr₆]⁴⁻ units (n_e > 5.99) so the source of the asymmetry is less obvious. In contrast, other well-known 2D lead bromide perovskites such as phenylethyl ammonium lead bromide, (PEA)₂PbBr₄, have more distorted octahedra (n_e = 5.76)¹⁰² resulting in broad CSA patterns in the ²⁰⁷Pb spectrum (see ESI Fig. S3†), which is why this perovskite was not chosen for further comparison. Instead the ²⁰⁷Pb NMR of (pXDA)PbBr₄ and (BA)₂PbBr₄ is sensitive to the asymmetry beyond their octahedral units, due to their planar arrangement of octahedra. The resulting CSA broadening is evident from the asymmetrical line-shape of the ²⁰⁷Pb resonances, most obvious in the static spectra of (BA)₂PbBr₄. Their CSA fitting and parameters can be seen in ESI Fig. S3.†

The scalar coupling of CsPbBr₃ and Cs₄PbBr₆ have been reported several times,^14,46,69 and the poorer resolution of the pattern in CsPbBr₃ is due to its Pb–Br bond length variation, in contrast to the perfect symmetry of the Cs₄PbBr₆ units. The 0D and 3D hybrid perovskites are more intriguing, as a very well defined scalar coupling pattern is present in the ²⁰⁷Pb NMR spectrum of (mXDA)₂PbBr₆ but not present in MAPbBr₃ or FAPbBr₃ (at room temperature). This is despite the perfect symmetry in the [PbBr₆]⁴⁻ units of the cubic 3D perovskites reported by SCXRD. By utilising the linear trend from the resolved scalar coupling patterns we can predict J¹ values for the cubic lead bromides as ∼2.3 kHz, which is in agreement with the J¹ observed by Aebli et al. for MAPbBr₃ at 100 K.⁶⁹ By simulating the ²⁰⁷Pb NMR line shapes with these J¹ values, a minimum scalar coupling resonance broadening required to obscure their patterns is determined as > 3.0 kHz. This broadening is almost triple the width of the (mXDA)₂PbBr₆ scalar coupling resonances, despite the larger Pb–Br bond length/angle variance (see Table 2) present in the 0D perovskite.

Aebli et al. postulated that the lack of scalar coupling resolution in MAPbBr₃ and FAPbBr₃ at room temperature was result of the fast cation dynamics in both systems.⁶⁹ The organic cations in MAPbX₃ and FAPbX₃ are known to undergo rapid reorientation within the cuboctahedral cage. The MA and FA cation reorientation time have been thoroughly examined in the literature, providing values ranging between 0.2–5 ps for MAPbBr₃,^{16,19,31,70,71,103,104} 6 ps for FAPbBr₃,⁷⁰ 0.4–14 ps for MAPbI₃,^{16,19,34,103–107} and 2–8 ps for FAPbI_3.^{18,34,108,109}

Evidence for Aebli and coworker's hypothesis includes the observation of a scalar coupling pattern in the ²⁰⁷Pb NMR of MAPbBr₃ at 100 K, where the fast reorientation of the MA cation is reportedly much reduced.^69,70 Here, we utilised variable temperature ¹H NMR spin–lattice relaxation measurements to probe the cation dynamics, as reported previously for MA and FA perovskites.^16,18,110 Spin–lattice NMR relaxation (measured by the characteristic relaxation time T₁) is the return of the nuclear magnetisation to equilibrium parallel with the applied static magnetic field. In solids where the dominant relaxation occurs through the dipole–dipole interaction mediated by molecular motions,¹¹¹ the relaxation is dependent on the corelation time via eqn (2):

where τ_c is the correlation time of molecular reorientation and r is the inter-moment distance. This relationship is demonstrated in Fig. 4(a). The relaxation is most efficient when the molecular dynamics are at a rate close to the nuclear magnetic precession frequency (ω₀τ_c ≈ 1); for ¹H nuclei at 14.1 T this corresponds to a τ_c around 10⁻¹⁰ s. Faster and slower molecular dynamics both result in slower relaxation. However, by observing the trend in relaxation time with temperature, which acts to increase the frequency of the molecular motion, we can determine whether the motion is in a fast (ω₀τ_c ≪ 1) or slow (ω₀τ_c ≫ 1) timescale regime.^18,112

Fig. 4 (a) Schematic of the ideal ¹H T₁-correlation time relationship for dipolar mediated relaxation following eqn (2) at 14.1 T, using a representative inter-moment distance r = 2 Å, to demonstrate the different timescale regimes. (b) Plot of ¹H T₁ versus inverse temperature for FAPbBr₃, MAPbBr₃, (mXDA)₂PbBr₆, and (pXDA)PbBr₄.

Fig. 4(b) shows the ¹H spin–lattice relaxation times at varying temperatures for the organic cation lead bromides. MAPbBr₃ and FAPbBr₃ have high ¹H T₁ relaxation times, which increase with temperature and therefore are in the fast-timescale regime at room temperature, as expected from the reported picosecond reorientation times. In the fast time scale regime (ω₀τ_c ≪ 1) eqn (2) can be simplified to:

Hence, by utilising the inter-moment distances determined by Fabini et al. for the cations in MAPbI₃ and FAPbI₃,¹⁸ we can determine the MA and FA correlation times as 2 ps and 7 ps respectively in MAPbBr₃ and FAPbBr₃. These values are based on many assumptions and therefore should be used to judge the scale of the rate of motion, however they are in good agreement with the reported values for MAPbBr₃ and FAPbBr₃ which utilised a variety of techniques including: ²H and ¹⁴N quadrupolar relaxation;^19,31 quasi-elastic neutron scattering;⁷⁰ GHz spectroscopy;¹⁰³ 2D infrared spectroscopy;¹⁰⁴ molecular dynamics;⁷¹ and ¹H nuclear relaxation.¹⁰⁶

Conversely, the 0D perovskite (mXDA)₂PbBr₆ demonstrates ¹H T₁ relaxation times that become shorter with increasing temperature, putting it within the slow timescale regime (τ_c ≫ 100 ps). By observing the perovskites ¹H relaxation over a wide enough temperature range to cover the entire behaviour shown in Fig. 4(a) and fitting the data with eqn (2), a more exact correlation time could be acquired. Unfortunately, we could not access a large enough temperature range for this study. However, we can confirm the intuitive hypothesis that the bulky cations forming the low dimensional perovskites are much less mobile than the rapidly reorientating cations in the 3D perovskite.

Aebli et al. postulated that the rapid reorientation of the cations, causes a local variation of Pb–Br bond lengths/angles in MAPbBr₃ and FAPbBr₃, due to the H-bonding between the cation NH₃⁺ groups and the surrounding Br atoms. The resulting distribution of scalar coupling strengths, J, would smear the scalar coupling pattern.⁶⁹ Our examination of a 0D hybrid lead bromide gives us a lower bound on the necessary Pb–Br distortion, as (mXDA)₂PbBr₆ presents a well-resolved scalar coupling pattern despite a permanent Pb–Br bond length standard deviation of 0.015 Å. Additionally, the distortion cannot be only present at the picosecond timescales of the cation dynamics, otherwise the ²⁰⁷Pb nucleus would observe an averaged Br position. Two discrete NMR resonances separated by a frequency of Δν will merge when the exchange rate between the two sites becomes proportional to the reciprocal of the frequency difference. Much faster site exchange will result in the detection of a single resonance, as the NMR detection is observing the average of the two sites.¹¹² The necessary broadening to merge the ²⁰⁷Pb scalar coupling patterns is ∼3.0 kHz, hence dynamic disorder would need to occur at slow dynamics (>10⁻⁴ s timescales) to cause the required NMR line shape coalescence.

Hence, we believe the ²⁰⁷Pb NMR scalar coupling provides further evidence of permanent short-range disorder in the local structures of MAPbBr₃ and FAPbBr₃, despite the long-range periodic cubic structure observed by SCXRD. This corroborates previous studies of MAPbBr₃ and FAPbBr₃ at room temperature showing non-cubic refinements of pair distribution function (PDF) data at <10 Å and large atomic displacement parameters (ADP) for Br perpendicular to the Pb–Br bond.^113–118 Worhatch et al. used X-ray PDF refinement to show improved fits in cubic 2 × 2 × 2 supercells of MAPbBr₃ and FAPbBr₃ with Br atoms displaced transversely to the Pb–Pb line, resulting in a distribution of Br–Pb–Br bond angles below 180°.¹¹⁶ This transverse Br distortion is corroborated by the ab initio molecular dynamics studies of Maity et al. who showed that MA cation dynamics were correlated with Br–Pb–Br scissoring distortions.⁷¹ Alternatively, X-ray PDF refinements by Page et al. and extended absorption fine structure (EXAFS) refinements by Nandi et al. both found improved fitting of the local structure of MAPbBr₃ via pseudo-cubic orthorhombic structures, with Pb–Br bond length standard deviations of 0.0624 and 0.164 Å respectively.^113,115 Clearly the exact local structure of the PbX₆ octahedra in hybrid 3D perovskites is still uncertain, but there is agreement on the presence of local disorder in these structures. Hence, our ²⁰⁷Pb NMR comparison with low-dimensional hybrid perovskites confirms the presence of significant local disorder at slow timescales in MAPbBr₃ and FAPbBr₃, and corroborates the linkage between this disorder and the fast dynamics of their organic cations.

Other possible causes of the ²⁰⁷Pb NMR broadening in MAPbBr₃ and FAPbBr₃ were investigated. Ionic diffusion in MAPbX₃ and FAPbX₃ is known to be prevalent and dominated by anion vacancy diffusion with large reported diffusion coefficients.^119–121 Despite this, the concentration of halide vacancies and mobile halides, reported to be between 10¹⁴–10¹⁷ cm⁻³,^121–123 is too low to distort the environment of sufficient Pb nuclei to smear the bulk ²⁰⁷Pb NMR pattern. Additionally, the halide positional exchange in MHPs is predicted to occur at the frequency of the ionic lattice vibrations (ps timescales),^120,121,124 which are too fast be the cause of the scalar coupling smearing. Dominant broadening via dipolar or CSA interactions can be ruled out with comparison of ²⁰⁷Pb NMR spectra performed at variable MAS frequencies, which showed no difference in the MAPbBr₃ line shape between 24 kHz and static conditions (see ESI Fig. S4†). Previous reports by Rosales et al. and Bernard et al. proposed scalar relaxation due to the fast quadrupolar relaxation of the halides as the source of the ²⁰⁷Pb NMR broadening in the lead bromides.^31,125 A spin ½ nuclei I coupled to a fast relaxing quadrupolar nuclei S, will gain a contribution to its relaxation if the relaxation of S is at an equivalent or higher rate than the frequency of the scalar coupling parameter. This relaxation is termed scalar relaxation of the second kind (SC2) by Abragam et al.¹²⁶ To test this hypothesis, the ²⁰⁷Pb T₂ relaxation of MAPbBr₃ was measured via CPMG pulse sequence. The T₂ of 0.23(3) ms correlates to a transverse relaxation broadening of 1400 Hz, close to the measured FWHM of the scalar coupling resonances in (mXDA)₂PbBr₆ and Cs₄PbBr₆. Hence, the SC2 broadening, and other components refocused by a CPMG pulse sequence, cannot be the dominant component of the width of the ²⁰⁷Pb resonances of MAPbBr₃.

Fig. 5 compares the ²⁰⁷Pb and ¹¹⁹Sn NMR spectra for the Br and Cl analogues of (mXDA)₂PbX₆ and (mXDA)₂SnX₆; the NMR parameters are presented in Table 3. The replacement of Br with Cl in (mXDA)₂PbX₆ shifts the ²⁰⁷Pb chemical shift by −763 ppm due to a less negative paramagnetic contribution to the chemical shielding and hence a lower chemical shift.¹⁰⁰ This mirrors the effect of increasing the Pb–X bond length, which was discussed previously. The same trend in ²⁰⁷Pb δ_iso when changing from Br to Cl can be seen in previous reports of MAPbX₃, FAPbX₃, CsPbX₃, Cs₄PbX₆, and (BA)₂PbX₄.^45,56,58,63 Interestingly, the Δδ_iso is larger in the 3D/2D perovskites (−950 to −1000 ppm), than for the 0D perovskites (mXDA)₂PbX₆ and Cs₄PbX₆ (−754 ppm). The difference in the scale of the trend for the 0D perovskites may be due to the longer Pb–X bond lengths, which could dampen the influence of changing the halide on the paramagnetic shielding at the Pb nucleus. This could be explored further via DFT calculations. The ¹¹⁹Sn δ_iso of (mXDA)₂SnCl₆ is also shifted negatively from that of (mXDA)₂SnBr₆ (Fig. 5). Corroborating the ²⁰⁷Pb NMR results, the ¹¹⁹Sn Δδ_iso for the 0D mXDA perovskites is larger (−228 ppm) than that seen in the literature for 3D MASnX₃ perovskites (Br to Cl shift of −82 ppm).¹²⁷

Fig. 5 The ²⁰⁷Pb MAS NMR spectra of (mXDA)₂PbBr₆ and (mXDA)₂PbCl₆ and the ¹¹⁹Sn CPMAS NMR spectra of (mXDA)₂SnBr₆ and (mXDA)₂SnCl₆. Experimental spectra, simulated spectra and deconvoluted resonances are displayed in blue, red and grey respectively.

Table 3 ²⁰⁷Pb/¹¹⁹Sn NMR parameters for (mXDA)₂BX₆ perovskites, determined at 14.1 T and at room temperature

Perovskites	^207Pb/^119Sn NMR
	δiso (ppm)	Scalar coupling
		J^1(B–X) (kHz)	FWHM^a (kHz)
a Full-width half maximum (FWHM) of observable scalar coupling resonances.
(mXDA)2PbBr6	−595.0	1.98	1.17
(mXDA)2PbCl6	−1357.2/−1359.3	0.38/0.38	0.33/0.34
(mXDA)2SnBr6	−723.8	1.50	0.80
(mXDA)2SnCl6	−951.5	0.26	0.36

---

The ²⁰⁷Pb NMR of (mXDA)₂PbCl₆ presents with a resolved scalar coupling pattern. The ^35/37Cl anions have spin [/] like ^79/81Br, resulting in the same pattern as for the lead bromides; however, the scalar coupling constant is smaller at 380 Hz (see Table 3). Furthermore, the ²⁰⁷Pb NMR of (mXDA)₂PbCl₆ is sufficiently resolved that it may be possible to distinguish slight differences in the resonances of ²⁰⁷Pb coupled to ³⁵Cl and ³⁷Cl isotopes. Fig. 5 shows the two deconvoluted resonances with relative integrals equal to the natural abundance population difference between ³⁵Cl and ³⁷Cl (0.76 : 0.24); the difference in fitting quality with just one scalar coupling pattern is shown in ESI Fig. S6.† The ¹¹⁹Sn CPMAS NMR of (mXDA)₂SnBr₆ and (mXDA)₂SnCl₆ (Fig. 5) demonstrates similar scalar coupling patterns to the lead bromides as ¹¹⁹Sn is also a spin ½ nucleus. The scalar coupling constants are reduced compared to Pb with J¹(¹¹⁹Sn–^79/81Br) = 1.51 kHz and J¹(¹¹⁹Sn–^35/37Cl) = 260 Hz. To the authors knowledge this is the first direct experimental observation of J¹(¹¹⁹Sn–^35/37Cl) and J¹(¹¹⁹Sn–^79/81Br) coupling, with previous reports providing only indirectly determined or computed values.^128,129 The resolution of scalar coupling patterns in all of the 0D perovskites despite B site metal and halide choice, corroborates the relation of the scalar coupling pattern to the rigidity of the perovskite structure. The metal halide octahedra templated by the mXDA cation are all relatively symmetrical with similar metrics of octahedral distortion as (mXDA)₂PbBr₆ (see ESI Table S3†).

Conclusions

This work presents an SCXRD and solid state NMR structural characterisation of the xylylenediammonium hybrid perovskite series, which form low-dimensional 0D, 1D and 2D perovskites, due to the varying position of the NH₃ functional groups about the cations phenyl ring. Improved understanding of these structures is anticipated to assist in the design of future low-dimensional perovskites for optoelectronic perovskite applications. The mXDA cation is shown to form a 0D perovskite structure (mXDA)₂BX₆ for B = Pb, Sn and X = Br, Cl. Examination of the highly resolved scalar coupling pattern present in the ²⁰⁷Pb NMR of (mXDA)₂PbBr₆, provides insight into the ²⁰⁷Pb NMR of 3D perovskites MAPbBr₃ and FAPbBr₃, confirming significant local Br positional disorder coupled to the fast cation reorientation, which is not observed in the long-range averaged model provided by traditional crystallography. The local halide flexibility likely plays a role in the phenomena of halide ion migration and carrier dynamics, which are of importance to the optimal optoelectronic performance of these hybrid materials. Lastly, we further demonstrate the sensitivity of the solid state NMR toolkit to local structure and dynamics in metal halide perovskite material with diverse inorganic architectures and dimensionalities.

Data availability

Additional data supporting this article have been included as part of the ESI.† Raw NMR data for this article (Topspin data file format) are available at KU Leuven Research Data Repository at https://doi.org/10.48804/RVHL2D. CIF data for associated crystal structures have been deposited in the Cambridge Crystallographic Data Centre under deposition numbers CCDC 1545198, 2300668–2300671, 2350304.

Author contributions

TJNH: conception, drafting, acquisition, analysis, interpretation. BF: conception, revision, acquisition, analysis, interpretation. TK, WPDW, KX: revision, acquisition. JWA: revision. NM: conception, revision.

Conflicts of interest

The authors declare the following competing financial interest(s): N. M. is a director of Prominence Photovoltaics Pte Ltd, a perovskite solar cell commercialization company. There are no other conflicts of interest.

Acknowledgements

We thank the Singapore Ministry of Education (Academic Research Fund MOE2019-T2-2-032), the Singapore National Research Foundation (Competitive Research Program NRF-CRP14-2014-03; Intra-CREATE Collaborative Grant NRF2018-ITC001-001; Energy Innovation Research Program NRF2015EWT-EIRP003-004; Solar CRP S18-1176-SCRP), and Fonds Wetenschappelijk Onderzoek (Senior Postdoctoral Fellowship 1253824N) for funding this research. We would like to acknowledge the Center of High Field NMR Spectroscopy and Imaging at Nanyang Technological University for the use of their facilities. In addition, TJNH is grateful for valuable discussions about the possible sources of ²⁰⁷Pb NMR broadening with: J. V. Hanna and S. Morris, while at NTU; and D. Sakellariou and R. de Oliveira-Silva, while at KU Leuven.

Notes and references

1. S. D. Stranks and H. J. Snaith, Nat. Nanotechnol., 2015, 10, 391–402.
2. B. Saparov and D. B. Mitzi, Chem. Rev., 2016, 116, 4558–4596.
3. R. Chiara, M. Morana and L. Malavasi, ChemPlusChem, 2021, 86, 879–888.
4. E. Aktas, N. Rajamanickam, J. Pascual, S. Hu, M. H. Aldamasy, D. Di Girolamo, W. Li, G. Nasti, E. Martínez-Ferrero, A. Wakamiya, E. Palomares and A. Abate, Commun. Mater., 2022, 3, 1–14.
5. D. B. Mitzi, Chem. Mater., 1996, 8, 791–800.
6. H. Lin, C. Zhou, Y. Tian, T. Siegrist and B. Ma, ACS Energy Lett., 2018, 3, 54–62.
7. L. Piveteau, V. Morad and M. V. Kovalenko, J. Am. Chem. Soc., 2020, 142, 19413–19437.
8. D. J. Kubicki, S. D. Stranks, C. P. Grey and L. Emsley, Nat. Rev. Chem, 2021, 5, 624–645.
9. C. J. Dahlman, D. J. Kubicki and G. N. M. Reddy, J. Mater. Chem. A, 2021, 9, 19206–19244.
10. D. J. Kubicki, D. Prochowicz, A. Hofstetter, M. Saski, P. Yadav, D. Bi, N. Pellet, J. Lewiński, S. M. Zakeeruddin, M. Grätzel and L. Emsley, J. Am. Chem. Soc., 2018, 140, 3345–3351.
11. D. J. Kubicki, D. Prochowicz, A. Hofstetter, P. Péchy, S. M. Zakeeruddin, M. Grätzel and L. Emsley, J. Am. Chem. Soc., 2017, 139, 10055–10061.
12. T. Baikie, N. S. Barrow, Y. Fang, P. J. Keenan, P. R. Slater, R. O. Piltz, M. Gutmann, S. G. Mhaisalkar and T. J. White, J. Mater. Chem. A, 2015, 3, 9298–9307.
13. W. M. J. Franssen and A. P. M. Kentgens, Solid State Nucl. Magn. Reson., 2019, 100, 36–44.
14. A. Kanwat, B. Ghosh, S. E. Ng, P. J. S. Rana, Y. Lekina, T. J. N. Hooper, N. Yantara, M. Kovalev, B. Chaudhary, P. Kajal, B. Febriansyah, Q. Y. Tan, M. Klein, Z. X. Shen, J. W. Ager, S. G. Mhaisalkar and N. Mathews, ACS Nano, 2022, 16, 2942–2952.
15. W. M. J. Franssen, S. G. D. van Es, R. Dervişoğlu, G. A. de Wijs and A. P. M. Kentgens, J. Phys. Chem. Lett., 2017, 8, 61–66.
16. Q. Xu, T. Eguchi, H. Nakayama, N. Nakamura and M. Kishita, Z. Naturforsch. A, 1991, 46, 240–246.
17. Q. Xu, T. Eguchi and H. Nakayama, Bull. Chem. Soc. Jpn., 1992, 65, 2264–2266.
18. D. H. Fabini, T. A. Siaw, C. C. Stoumpos, G. Laurita, D. Olds, K. Page, J. G. Hu, M. G. Kanatzidis, S. Han and R. Seshadri, J. Am. Chem. Soc., 2017, 139, 16875–16884.
19. R. E. Wasylishen, O. Knop and J. B. Macdonald, Solid State Commun., 1985, 56, 581–582.
20. W. T. M. Van Gompel, R. Herckens, G. Reekmans, B. Ruttens, J. D'Haen, P. Adriaensens, L. Lutsen and D. Vanderzande, J. Phys. Chem. C, 2018, 122, 4117–4124.
21. W. M. J. Franssen, B. J. Bruijnaers, V. H. L. Portengen and A. P. M. Kentgens, ChemPhysChem, 2018, 19, 3107–3115.
22. C. Anelli, M. R. Chierotti, S. Bordignon, P. Quadrelli, D. Marongiu, G. Bongiovanni and L. Malavasi, Inorg. Chem., 2019, 58, 944–949.
23. D. J. Kubicki, D. Prochowicz, A. Hofstetter, S. M. Zakeeruddin, M. Grätzel and L. Emsley, J. Am. Chem. Soc., 2017, 139, 14173–14180.
24. T. J. N. Hooper, Y. Fang, A. A. M. Brown, S. H. Pu and T. J. White, Nanoscale, 2021, 13, 15770–15780.
25. L. Xie, P. Vashishtha, T. M. Koh, P. C. Harikesh, N. F. Jamaludin, A. Bruno, T. J. N. Hooper, J. Li, Y. F. Ng, S. G. Mhaisalkar and N. Mathews, Adv. Mater., 2020, 32, 2003296.
26. D. Prochowicz, P. Yadav, M. Saliba, D. J. Kubicki, M. M. Tavakoli, S. M. Zakeeruddin, J. Lewiński, L. Emsley and M. Grätzel, Nano Energy, 2018, 49, 523–528.
27. D. J. Kubicki, D. Prochowicz, A. Hofstetter, S. M. Zakeeruddin, M. Grätzel and L. Emsley, J. Am. Chem. Soc., 2018, 140, 7232–7238.
28. W. Xiang, Z. Wang, D. J. Kubicki, W. Tress, J. Luo, D. Prochowicz, S. Akin, L. Emsley, J. Zhou, G. Dietler, M. Grätzel and A. Hagfeldt, Joule, 2019, 3, 205–214.
29. D. J. Kubicki, D. Prochowicz, A. Pinon, G. Stevanato, A. Hofstetter, S. M. Zakeeruddin, M. Grätzel and L. Emsley, J. Mater. Chem. A, 2019, 7, 2326–2333.
30. O. Knop, R. E. Wasylishen, M. A. White, T. S. Cameron and M. J. M. V. Oort, Can. J. Chem., 1990, 68, 412–422.
31. G. M. Bernard, R. E. Wasylishen, C. I. Ratcliffe, V. Terskikh, Q. Wu, J. M. Buriak and T. Hauger, J. Phys. Chem. A, 2018, 122, 1560–1573.
32. A. Senocrate, I. Moudrakovski and J. Maier, Phys. Chem. Chem. Phys., 2018, 20, 20043–20055.
33. A. Scarperi, N. Landi, A. Gabbani, N. Jarmouni, S. Borsacchi, L. Calucci, A. Pucci, E. Carignani, F. Pineider and M. Geppi, Pure Appl. Chem., 2023, 95, 1031–1042.
34. A. Mishra, M. A. Hope, M. Grätzel and L. Emsley, J. Am. Chem. Soc., 2023, 145, 978–990.
35. A. Mishra, D. J. Kubicki, A. Boziki, R. D. Chavan, M. Dankl, M. Mladenović, D. Prochowicz, C. P. Grey, U. Rothlisberger and L. Emsley, ACS Energy Lett., 2022, 7, 2745–2752.
36. A. Senocrate, I. Moudrakovski, G. Y. Kim, T.-Y. Yang, G. Gregori, M. Grätzel and J. Maier, Angew. Chem., Int. Ed., 2017, 56, 7755–7759.
37. P. Raval, R. M. Kennard, E. S. Vasileiadou, C. J. Dahlman, I. Spanopoulos, M. L. Chabinyc, M. Kanatzidis and G. N. Manjunatha Reddy, ACS Energy Lett., 2022, 7, 1534–1543.
38. M. A. A. Kazemi, N. Folastre, P. Raval, M. Sliwa, J. M. V. Nsanzimana, S. Golonu, A. Demortiere, J. Rousset, O. Lafon, L. Delevoye, G. N. M. Reddy and F. Sauvage, Energy Environ. Mater., 2023, 6, e12335.
39. I. Spanopoulos, I. Hadar, W. Ke, P. Guo, E. M. Mozur, E. Morgan, S. Wang, D. Zheng, S. Padgaonkar, G. N. Manjunatha Reddy, E. A. Weiss, M. C. Hersam, R. Seshadri, R. D. Schaller and M. G. Kanatzidis, J. Am. Chem. Soc., 2021, 143, 7069–7080.
40. C. J. Dahlman, R. M. Kennard, P. Paluch, N. R. Venkatesan, M. L. Chabinyc and G. N. Manjunatha Reddy, Chem. Mater., 2021, 33, 642–656.
41. A. Krishna, M. A. Akhavan Kazemi, M. Sliwa, G. N. M. Reddy, L. Delevoye, O. Lafon, A. Felten, M. T. Do, S. Gottis and F. Sauvage, Adv. Funct. Mater., 2020, 30, 1909737.
42. P. Fu, M. A. Quintero, C. Welton, X. Li, B. Cucco, M. C. De Siena, J. Even, G. Volonakis, M. Kepenekian, R. Liu, C. C. Laing, V. Klepov, Y. Liu, V. P. Dravid, G. N. Manjunatha Reddy, C. Li and M. G. Kanatzidis, Chem. Mater., 2022, 34, 9685–9698.
43. P. Raval, M. A. Akhavan Kazemi, J. Ruellou, J. Trébosc, O. Lafon, L. Delevoye, F. Sauvage and G. N. Manjunatha Reddy, Chem. Mater., 2023, 35, 2904–2917.
44. L. Pan, Z. Liu, C. Welton, V. V. Klepov, J. A. Peters, M. C. De Siena, A. Benadia, I. Pandey, A. Miceli, D. Y. Chung, G. N. M. Reddy, B. W. Wessels and M. G. Kanatzidis, Adv. Mater., 2023, 35, 2211840.
45. A. Karmakar, A. M. Askar, G. M. Bernard, V. V. Terskikh, M. Ha, S. Patel, K. Shankar and V. K. Michaelis, Chem. Mater., 2018, 30, 2309–2321.
46. A. Ray, D. Maggioni, D. Baranov, Z. Dang, M. Prato, Q. A. Akkerman, L. Goldoni, E. Caneva, L. Manna and A. L. Abdelhady, Chem. Mater., 2019, 31, 7761–7769.
47. A. Kanwat, N. Yantara, Y. F. Ng, T. J. N. Hooper, P. J. S. Rana, B. Febriansyah, P. C. Harikesh, T. Salim, P. Vashishtha, S. G. Mhaisalkar and N. Mathews, ACS Energy Lett., 2020, 5, 1804–1813.
48. M. Jagadeeswararao, P. Vashishtha, T. J. N. Hooper, A. Kanwat, J. W. M. Lim, S. K. Vishwanath, N. Yantara, T. Park, T. C. Sum, D. S. Chung, S. G. Mhaisalkar and N. Mathews, J. Phys. Chem. Lett., 2021, 12, 9569–9578.
49. B. Febriansyah, T. M. Koh, P. J. S. Rana, T. J. N. Hooper, Z. Z. Ang, Y. Li, A. Bruno, M. Grätzel, J. England, S. G. Mhaisalkar and N. Mathews, ACS Energy Lett., 2020, 5, 2305–2312.
50. B. Febriansyah, Y. Lekina, J. Kaur, T. J. N. Hooper, P. C. Harikesh, T. Salim, M. H. Lim, T. M. Koh, S. Chakraborty, Z. X. Shen, N. Mathews and J. England, ACS Nano, 2021, 15, 6395–6409.
51. B. Febriansyah, Y. Li, D. Giovanni, T. Salim, T. J. N. Hooper, Y. Sim, D. Ma, S. Laxmi, Y. Lekina, T. M. Koh, Z. X. Shen, S. A. Pullarkat, T. C. Sum, S. G. Mhaisalkar, J. W. Ager and N. Mathews, Mater. Horiz., 2023, 10, 536–546.
52. P. J. S. Rana, B. Febriansyah, T. M. Koh, B. T. Muhammad, T. Salim, T. J. N. Hooper, A. Kanwat, B. Ghosh, P. Kajal, J. H. Lew, Y. C. Aw, N. Yantara, A. Bruno, S. A. Pullarkat, J. W. Ager, W. L. Leong, S. G. Mhaisalkar and N. Mathews, Adv. Funct. Mater., 2022, 2113026.
53. K. Fykouras, J. Lahnsteiner, N. Leupold, P. Tinnemans, R. Moos, F. Panzer, G. A. de Wijs, M. Bokdam, H. Grüninger and A. P. M. Kentgens, J. Mater. Chem. A, 2023, 11, 4587–4597.
54. B. A. Rosales, L. Men, S. D. Cady, M. P. Hanrahan, A. J. Rossini and J. Vela, Chem. Mater., 2016, 28, 6848–6859.
55. C. Roiland, G. Trippé-Allard, K. Jemli, B. Alonso, J.-C. Ameline, R. Gautier, T. Bataille, L. L. Pollès, E. Deleporte, J. Even and C. Katan, Phys. Chem. Chem. Phys., 2016, 18, 27133–27142.
56. A. Karmakar, M. S. Dodd, X. Zhang, M. S. Oakley, M. Klobukowski and V. K. Michaelis, Chem. Commun., 2019, 55, 5079–5082.
57. A. Karmakar, A. Bhattacharya, G. M. Bernard, A. Mar and V. K. Michaelis, ACS Mater. Lett., 2021, 261–267.
58. A. M. Askar, A. Karmakar, G. M. Bernard, M. Ha, V. V. Terskikh, B. D. Wiltshire, S. Patel, J. Fleet, K. Shankar and V. K. Michaelis, J. Phys. Chem. Lett., 2018, 9, 2671–2677.
59. S. Brochard-Garnier, M. Paris, R. Génois, Q. Han, Y. Liu, F. Massuyeau and R. Gautier, Adv. Funct. Mater., 2019, 29, 1806728.
60. M. Aebli, B. M. Benin, K. M. McCall, V. Morad, D. Thöny, H. Grützmacher and M. V. Kovalenko, Helv. Chim. Acta, 2020, 103, e2000080.
61. J. Lee, W. Lee, K. Kang, T. Lee and S. K. Lee, Chem. Mater., 2021, 33, 370–377.
62. N. Landi, E. Maurina, D. Marongiu, A. Simbula, S. Borsacchi, L. Calucci, M. Saba, E. Carignani and M. Geppi, J. Phys. Chem. Lett., 2022, 13, 9517–9525.
63. M. A. Hope, M. Cordova, A. Mishra, U. Gunes, A. Caiazzo, K. Datta, R. A. J. Janssen and L. Emsley, Angew. Chem., 2024, 136, e202314856.
64. M.-H. Tremblay, F. Thouin, J. Leisen, J. Bacsa, A. R. Srimath Kandada, J. M. Hoffman, M. G. Kanatzidis, A. D. Mohite, C. Silva, S. Barlow and S. R. Marder, J. Am. Chem. Soc., 2019, 141, 4521–4525.
65. O. Nazarenko, M. R. Kotyrba, S. Yakunin, M. Aebli, G. Rainò, B. M. Benin, M. Wörle and M. V. Kovalenko, J. Am. Chem. Soc., 2018, 140, 3850–3853.
66. P. Fu, M. A. Quintero, E. S. Vasileiadou, P. Raval, C. Welton, M. Kepenekian, G. Volonakis, J. Even, Y. Liu, C. Malliakas, Y. Yang, C. Laing, V. P. Dravid, G. N. M. Reddy, C. Li, E. H. Sargent and M. G. Kanatzidis, J. Am. Chem. Soc., 2023, 145, 15997–16014.
67. A. Krishna, V. Škorjanc, M. Dankl, J. Hieulle, H. Phirke, A. Singh, E. A. Alharbi, H. Zhang, F. Eickemeyer, S. M. Zakeeruddin, G. N. M. Reddy, A. Redinger, U. Rothlisberger, M. Grätzel and A. Hagfeldt, ACS Energy Lett., 2023, 8, 3604–3613.
68. R. Ji, Z. Zhang, M. Deconinck, Y. J. Hofstetter, J. Shi, F. Paulus, P. Raval, G. N. M. Reddy and Y. Vaynzof, Adv. Energy Mater., 2024, 2304126.
69. M. Aebli, L. Piveteau, O. Nazarenko, B. M. Benin, F. Krieg, R. Verel and M. V. Kovalenko, Sci. Rep., 2020, 10, 8229.
70. V. K. Sharma, R. Mukhopadhyay, A. Mohanty, M. Tyagi, J. P. Embs and D. D. Sarma, J. Phys. Chem. Lett., 2020, 11, 9669–9679.
71. S. Maity, S. Verma, L. M. Ramaniah and V. Srinivasan, Chem. Mater., 2022, 34, 10459–10469.
72. P. S. Klee, Y. Hirano, D. B. Cordes, A. M. Z. Slawin and J. L. Payne, Cryst. Growth Des., 2022, 22, 3815–3823.
73. T. Krishnamoorthy, Low-dimensional metal halide perovskite phosphors for solid-state lighting, Nanyang Technological University, 2019.
74. R. Chiara, M. Morana, G. Folpini, A. Olivati, B. Albini, P. Galinetto, L. Chelazzi, S. Ciattini, E. Fantechi, S. A. Serapian, A. Petrozza and L. Malavasi, J. Mater. Chem. C, 2022, 10, 12367–12376.
75. M. I. Saidaminov, A. L. Abdelhady, G. Maculan and O. M. Bakr, Chem. Commun., 2015, 51, 17658–17661.
76. SAINT and SADABS, Bruker AXS Inc., 2007.
77. G. M. Sheldrick, Acta Crystallogr., Sect. A, 2015, 71, 3–8.
78. G. M. Sheldrick, Acta Crystallogr., Sect. C, 2015, 71, 3–8.
79. K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
80. R. K. Harris, E. D. Becker, S. M. Cabral De Menezes, R. Goodfellow and P. Granger, Concepts Magn. Reson., 2002, 14, 326–346.
81. R. K. Harris, E. D. Becker, S. M. Cabral de Menezes, P. Granger, R. E. Hoffman and K. W. Zilm, Pure Appl. Chem., 2008, 80, 59–84.
82. D. Massiot, F. Fayon, M. Capron, I. King, S. Le Calvé, B. Alonso, J.-O. Durand, B. Bujoli, Z. Gan and G. Hoatson, Magn. Reson. Chem., 2002, 40, 70–76.
83. Y. Takeoka, K. Asai, M. Rikukawa and K. Sanui, Chem. Lett., 2005, 34, 602–603.
84. Y. Wei, C. Li, Y. Li, Z. Luo, X. Wu, Y. Liu, L. Zhang, X. He, W. Wang and Z. Quan, Angew. Chem., Int. Ed., 2022, 61, e202212685.
85. J.-L. Song, W.-J. Chen, K.-B. Chu and Y.-H. Zhou, Dalton Trans., 2018, 47, 14497–14502.
86. B.-B. Cui, Y. Han, B. Huang, Y. Zhao, X. Wu, L. Liu, G. Cao, Q. Du, N. Liu, W. Zou, M. Sun, L. Wang, X. Liu, J. Wang, H. Zhou and Q. Chen, Nat. Commun., 2019, 10, 5190.
87. Y. Li, G. Zheng, C. Lin and J. Lin, Solid State Sci., 2007, 9, 855–861.
88. Y. Chen, Y.-Y. Zheng, G. Wu, M. Wang, H.-Z. Chen and H. Yang, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2010, 66, m417.
89. M.-H. Jung, K. C. Ko and W. R. Lee, Dalton Trans., 2019, 48, 15074–15090.
90. T. Hu, M. D. Smith, E. R. Dohner, M.-J. Sher, X. Wu, M. T. Trinh, A. Fisher, J. Corbett, X.-Y. Zhu, H. I. Karunadasa and A. M. Lindenberg, J. Phys. Chem. Lett., 2016, 7, 2258–2263.
91. A. Yangui, D. Garrot, J. S. Lauret, A. Lusson, G. Bouchez, E. Deleporte, S. Pillet, E. E. Bendeif, M. Castro, S. Triki, Y. Abid and K. Boukheddaden, J. Phys. Chem. C, 2015, 119, 23638–23647.
92. X. Wang, W. Meng, W. Liao, J. Wang, R.-G. Xiong and Y. Yan, J. Phys. Chem. Lett., 2019, 10, 501–506.
93. M. D. Smith, A. Jaffe, E. R. Dohner, A. M. Lindenberg and H. I. Karunadasa, Chem. Sci., 2017, 8, 4497–4504.
94. B. Febriansyah, T. Borzda, D. Cortecchia, S. Neutzner, G. Folpini, T. M. Koh, Y. Li, N. Mathews, A. Petrozza and J. England, Angew. Chem., Int. Ed., 2020, 59, 10791–10796.
95. L. Mao, Y. Wu, C. C. Stoumpos, M. R. Wasielewski and M. G. Kanatzidis, J. Am. Chem. Soc., 2017, 139, 5210–5215.
96. A. Jaffe, Y. Lin, C. M. Beavers, J. Voss, W. L. Mao and H. I. Karunadasa, ACS Cent. Sci., 2016, 2, 201–209.
97. C. Li, E. J. Juarez-Perez and A. Mayoral, Chem. Commun., 2022, 58, 12164–12167.
98. M. De Bastiani, I. Dursun, Y. Zhang, B. A. Alshankiti, X.-H. Miao, J. Yin, E. Yengel, E. Alarousu, B. Turedi, J. M. Almutlaq, M. I. Saidaminov, S. Mitra, I. Gereige, A. AlSaggaf, Y. Zhu, Y. Han, I. S. Roqan, J.-L. Bredas, O. F. Mohammed and O. M. Bakr, Chem. Mater., 2017, 29, 7108–7113.
99. M. Rodová, J. Brožek, K. Knížek and K. Nitsch, J. Therm. Anal. Calorim., 2003, 71, 667–673.
100. O. Dmitrenko, S. Bai and C. Dybowski, Solid State Nucl. Magn. Reson., 2008, 34, 186–190.
101. J. M. Hoffman, X. Che, S. Sidhik, X. Li, I. Hadar, J.-C. Blancon, H. Yamaguchi, M. Kepenekian, C. Katan, J. Even, C. C. Stoumpos, A. D. Mohite and M. G. Kanatzidis, J. Am. Chem. Soc., 2019, 141, 10661–10676.
102. K. Shibuya, M. Koshimizu, F. Nishikido, H. Saito and S. Kishimoto, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2009, 65, m1323–m1324.
103. A. Poglitsch and D. Weber, J. Chem. Phys., 1987, 87, 6373–6378.
104. O. Selig, A. Sadhanala, C. Müller, R. Lovrincic, Z. Chen, Y. L. A. Rezus, J. M. Frost, T. L. C. Jansen and A. A. Bakulin, J. Am. Chem. Soc., 2017, 139, 4068–4074.
105. A. A. Bakulin, O. Selig, H. J. Bakker, Y. L. A. Rezus, C. Müller, T. Glaser, R. Lovrincic, Z. Sun, Z. Chen, A. Walsh, J. M. Frost and T. L. C. Jansen, J. Phys. Chem. Lett., 2015, 6, 3663–3669.
106. T. Chen, B. J. Foley, B. Ipek, M. Tyagi, J. R. D. Copley, C. M. Brown, J. J. Choi and S.-H. Lee, Phys. Chem. Chem. Phys., 2015, 17, 31278–31286.
107. A. M. A. Leguy, J. M. Frost, A. P. McMahon, V. G. Sakai, W. Kockelmann, C. Law, X. Li, F. Foglia, A. Walsh, B. C. O'Regan, J. Nelson, J. T. Cabral and P. R. F. Barnes, Nat. Commun., 2015, 6, 7124.
108. M. T. Weller, O. J. Weber, J. M. Frost and A. Walsh, J. Phys. Chem. Lett., 2015, 6, 3209–3212.
109. M. A. Carignano, Y. Saeed, S. A. Aravindh, I. S. Roqan, J. Even and C. Katan, Phys. Chem. Chem. Phys., 2016, 18, 27109–27118.
110. E. M. Mozur, M. A. Hope, J. C. Trowbridge, D. M. Halat, L. L. Daemen, A. E. Maughan, T. R. Prisk, C. P. Grey and J. R. Neilson, Chem. Mater., 2020, 32, 6266–6277.
111. N. Bloembergen, E. M. Purcell and R. V. Pound, Phys. Rev., 1948, 73, 679–712.
112. R. G. Bryant, J. Chem. Educ., 1983, 60, 933.
113. K. Page, J. E. Siewenie, P. Quadrelli and L. Malavasi, Angew. Chem., 2016, 128, 14532–14536.
114. A. Bernasconi and L. Malavasi, ACS Energy Lett., 2017, 2, 863–868.
115. P. Nandi, S. Mahana, E. Welter and D. Topwal, J. Phys. Chem. C, 2021, 125, 24655–24662.
116. R. J. Worhatch, H. Kim, I. P. Swainson, A. L. Yonkeu and S. J. L. Billinge, Chem. Mater., 2008, 20, 1272–1277.
117. G. Reuveni, Y. Diskin-Posner, C. Gehrmann, S. Godse, G. G. Gkikas, I. Buchine, S. Aharon, R. Korobko, C. C. Stoumpos, D. A. Egger and O. Yaffe, J. Phys. Chem. Lett., 2023, 14, 1288–1293.
118. J.-W. Lee, S. Seo, P. Nandi, H. S. Jung, N.-G. Park and H. Shin, iScience, 2021, 24, 101959.
119. A. Osherov, Y. Feldman, I. Kaplan-Ashiri, D. Cahen and G. Hodes, Chem. Mater., 2020, 32, 4223–4231.
120. J. M. Frost and A. Walsh, Acc. Chem. Res., 2016, 49, 528–535.
121. L. McGovern, M. H. Futscher, L. A. Muscarella and B. Ehrler, J. Phys. Chem. Lett., 2020, 11, 7127–7132.
122. L. Bertoluzzi, C. C. Boyd, N. Rolston, J. Xu, R. Prasanna, B. C. O'Regan and M. D. McGehee, Joule, 2020, 4, 109–127.
123. H. Xue, G. Brocks and S. Tao, Phys. Rev. Mater., 2022, 6, 055402.
124. A. M. A. Leguy, A. R. Goñi, J. M. Frost, J. Skelton, F. Brivio, X. Rodríguez-Martínez, O. J. Weber, A. Pallipurath, M. I. Alonso, M. Campoy-Quiles, M. T. Weller, J. Nelson, A. Walsh and P. R. F. Barnes, Phys. Chem. Chem. Phys., 2016, 18, 27051–27066.
125. B. A. Rosales, M. P. Hanrahan, B. W. Boote, A. J. Rossini, E. A. Smith and J. Vela, ACS Energy Lett., 2017, 2, 906–914.
126. A. Abragam and A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, Oxford, New York, 1983.
127. D. J. Kubicki, D. Prochowicz, E. Salager, A. Rakhmatullin, C. P. Grey, L. Emsley and S. D. Stranks, J. Am. Chem. Soc., 2020, 142, 7813–7826.
128. R. R. Sharp, J. Chem. Phys., 1974, 60, 1149–1157.
129. A. Bagno, G. Casella and G. Saielli, J. Chem. Theory Comput., 2006, 2, 37–46.

---

Footnote

† Electronic supplementary information (ESI) available. CCDC 2300670, 2300671, 2300669, 2350304, 2300668 and 1545198. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4ta02833c

---