Solid-State NMR and NQR Spectroscopy of Lead-Halide Perovskite Materials

Abstract

Two- and three-dimensional lead-halide perovskite (LHP) materials are novel semiconductors that have generated broad interest owing to their outstanding optical and electronic properties. Characterization and understanding of their atomic structure and structure–property relationships are often nontrivial as a result of the vast structural and compositional tunability of LHPs as well as the enhanced structure dynamics as compared with oxide perovskites or more conventional semiconductors. Nuclear magnetic resonance (NMR) spectroscopy contributes to this thrust through its unique capability of sampling chemical bonding element-specifically (^1/2H, ¹³C, ^14/15N, ^35/37Cl, ³⁹K, ^79/81Br, ⁸⁷Rb, ¹²⁷I, ¹³³Cs, and ²⁰⁷Pb nuclei) and locally and shedding light onto the connectivity, geometry, topology, and dynamics of bonding. NMR can therefore readily observe phase transitions, evaluate phase purity and compositional and structural disorder, and probe molecular dynamics and ionic motion in diverse forms of LHPs, in which they can be used practically, ranging from bulk single crystals (e.g., in gamma and X-ray detectors) to polycrystalline films (e.g., in photovoltaics, photodetectors, and light-emitting diodes) and colloidal nanocrystals (e.g., in liquid crystal displays and future quantum light sources). Herein we also outline the immense practical potential of nuclear quadrupolar resonance (NQR) spectroscopy for characterizing LHPs, owing to the strong quadrupole moments, good sensitivity, and high natural abundance of several halide nuclei (^79/81Br and ¹²⁷I) combined with the enhanced electric field gradients around these nuclei existing in LHPs as well as the instrumental simplicity. Strong quadrupole interactions, on one side, make ^79/81Br and ¹²⁷I NMR rather impractical but turn NQR into a high-resolution probe of the local structure around halide ions.

1. Introduction to Lead-Halide Perovskites

Lead-halide perovskites (LHPs) of an APbX₃ composition, where A is Cs, methylammonium (MA), or formamidinium (FA) and X = Cl, Br, I, or mixtures thereof, are compounds isostructural to diverse ABO₃-type oxide perovskites. LHPs have recently become a major class of optoelectronic materials owing to their exceptional electronic and optical characteristics.¹⁻⁴ These materials are intensely pursued for applications in photovoltaics,⁵⁻¹⁰ LCD technologies,¹¹⁻¹³ light-emitting diodes (LEDs),^4,14−16 lasers,¹⁷⁻²⁰ UV–vis–near-IR photodetectors,²¹⁻²⁸ direct conversion X-ray and gamma detectors,^9,29−36and scintillators^37,38 and as emerging quantum light sources.^39,40 In these applications, LHPs are used in their diverse forms, as single crystals, thick or thin films, and colloidal nanocrystals (NCs, Figure 1a–f), which are easy to produce by means of solution-phase chemistry or low-temperature melt-growth.^31,41−43 The remarkable characteristics of these materials include long carrier lifetime–mobility products and low densities of electronic traps (on par with GaAs and CdTe)⁴⁴⁻⁴⁶ despite the large concentrations of structural defects and the enhanced structure dynamics, a seeming paradox often referred to as defect tolerance.^4,47−52 Perovskite CsPbBr₃ gamma detectors exhibit energy resolution better than commercial CdTe-based detectors.^30,31,34,53 Perovskite X-ray detectors⁵⁴ and UV–vis detectors^21,55,56 exhibit high sensitivities on the order of 10³ μC Gy^1– cm^–2 and detectivities up to 10¹⁴ Jones, respectively, which compare favorably with respective commercial technologies. Thin-film solar cells with perovskites as light absorbers exhibit power conversion efficiencies (25.2%)^10,57 that surpass polycrystalline Si and essentially all emerging thin-film technologies and approach the single-crystalline Si world record (26.1%).^10,58 Colloidal ligand-capped LHP NCs (Figure 1b,c) are the first examples of colloidal quantum dots (QDs) exhibiting near-unity photoluminescence quantum yields (PL QYs) across the entire visible spectral range without the need for epitaxial overcoating for electronic passivation.^4,47 These NCs are also shown to exhibit long exciton coherence times and near-transform-limited emission line widths,^39,59 which, along with stable single photon emission,^60,61 makes them attractive for designing future sources of quantum light.^39,40,62

Figure 1.

LHP materials and the utility of NMR spectroscopy for their characterization. 3D and 2D LHPs are of practical interest in their various forms: (a) single crystals (Adapted with permission from ref (36). Copyright 2016 American Chemical Society) and (d) bulk powders, (b,c) colloidal NCs (Panel b Credit: Nadia Schwitz; Panel c Credit: Frank Krumeich), and (e,f) continuous films within optoelectronic devices (green and blue LEDs as examples) (Panel e Credit: Yevhen Shynkarenko; Panel f reprinted with permission from ref (83). Copyright 2019 American Chemical Society). (g) All elements of APbX₃ LHPs possess NMR-active isotopes, as exemplified for CsPbBr₃ using actual solid-state NMR spectra. (h) Modern NMR spectroscopy methods make for a versatile characterization toolbox. Depending on the probed spin interaction (Figure 2) and the structural aspect in question (Figure 3), a diverse range of pulse sequences and signal and resolution enhancing techniques are available (e.g., QCPMG, quadrupolar Carr–Purcell–Meiboom–Gill; REDOR, rotational-echo double resonance; DNP, dynamic nuclear polarization; EXSY, exchange spectroscopy; HMQC, heteronuclear multiple-quantum correlation; WURST, wideband, uniform rate, smooth truncation; MAS, magic-angle spinning). Image of Swiss Army Knife used with permission from Victorinox AG.

The crystal structure of APbX₃ perovskites is characterized by the 3D corner-interconnection of PbX₆ octahedra. Several polymorphs of such 3D LHPs exist as a result of the octahedral tilting and orientation of the A cation, thus reducing the symmetry from the archetypical cubic phase (to tetragonal, orthorhombic, or monoclinic) and deviating the Pb–X–Pb bond angles from the initial value of 180°. For instance, at room temperature (RT), the stable LHP polymorphs are cubic FAPbBr₃, MAPbCl₃, MAPbBr₃, and FAPbCl₃, tetragonal MAPbI₃, orthorhombic CsPbBr₃ (Figure 1d), and monoclinic CsPbCl₃, whereas CsPbI₃ and FAPbI₃ crystallize in nonperovskite 1D polymorphs (with edge- and face-sharing connectivity, respectively).⁶³⁻⁷⁶ The structural instability of the perovskite phases for CsPbI₃ and FAPbI₃ stems from Cs and FA cations being, respectively, too small and too large to optimally fill the A site.⁷⁷⁻⁸² Interestingly, stable perovskite phases can be obtained with mixed-ionic compositions (Cs/FA)PbI₃ or (Cs/FA)Pb(Br/I)₃.^8,84−88 The substitutional A-site doping by other monovalent cations, such as Rb⁺, K⁺, guanidinium (G), azetidinium, or dimethylammonium (DMA), reportedly results in improved device performance or higher material stability.⁸⁹⁻⁹⁷ The incorporation of a larger ethylendiammonium cation requires the concomitant formation of lead and halide vacancies, yielding so-called hollow LHPs.⁹⁸ The halides and the octahedral tilts define the band-gap energies of LHPs (ca. 1.5–3.0 eV).⁹⁹⁻¹⁰¹ Perovskite lattices also form upon the substitution of Pb²⁺ with Sn²⁺ or Ge^{2+76,102−109} or by a combination of monovalent and trivalent cations (e.g., Ag⁺, Cu⁺, Bi³⁺, In³⁺, and Sb³⁺ in so-called double perovskites).^109−114 These lead-free perovskites thus far fall behind in their optoelectronic quality due to both the different electronic structures (flat bands, indirect transitions in double perovskites, etc.)¹¹⁵ and the limited stability.^84,115

Recent years have seen a surge of activities beyond APbX₃, namely, in 2D LHPs, which are often reported to exhibit greater stability^116,117 and wherein structural variety can be realized by disrupting the connectivity in one dimension, for example, by cutting 3D perovskites into 2D slabs of adjustable thickness.^118−121 Most common are cuts along the <100> direction, as in Dion–Jacobson¹²² and Ruddlesden–Popper¹²³ types, or structures with alternating cations in the interlayer space.¹²⁴ 2D slab thicknesses n (number of octahedral layers within the slab) are typically in the range of n = 1–7.^{121,125−128} The interlayer region comprises bulky spacers, such as long-chain alkyl-, aryl-,¹²⁹ adamantantyl-,¹³⁰ alkylphenyl-¹²⁰ ammonium, and heterocyclic (e.g., benzimidazolium¹³¹ or quaterthiophene derivatives)¹³² cations. In general, owing to quantum and dielectric confinement, layered perovskites behave as multiple quantum-well structures,^133,134 with band-gap and exciton binding energies decreasing for larger n.^123,135,136 Larger exciton binding energies and cascade energy structures¹³⁷ favor fast radiative recombination, as required in, for instance, LEDs.^138,139 Smaller binding energies (n > 3) lead to efficient exciton dissociation into free carriers, as needed in photovoltaics^119,140 and photodetectors.^141,142 Octahedral distortions and tilts within 2D slabs give rise to piezo- and ferroelectric responses.^129,143,144 The chirality of the organic cations allows for the emission or detection of polarized light^145−148 and nonlinear optical responses.^149−152 Static and dynamic structural distortions and defects have a profound impact on the PL line widths and PL QYs (energetic disorder, exciton–phonon coupling, etc.).^{117,153−155} Because of their strong spin–orbit coupling, 3D LHPs have long been considered for spintronic applications, and whereas the Rashba effect has been observed experimentally,^156,157 its origin in these applications remains uncertain.^158,159 The reduced dimensionality of 2D perovskites favors symmetry reduction, resulting in larger Rashba splitting.^160,161 Moreover, the manipulation of spin polarization and spin funneling has been recently demonstrated in 2D perovskites.^162−164

The in situ formation of 2D perovskites at the interfaces or grain boundaries or as individual grains is often invoked in explaining the favorable effects of the addition of bulkier cations into standard protocols for the deposition of 3D perovksite films in optoelectronics.^165−170 Oftentimes, the exact structure of these concomitant phases remains unknown.

We also note that there exist nonperovskite lead halides with 1D corner-sharing or full disconnection of PbX₆ octahedra or those formed by face- and edge-sharing of PbX₆ octahedra as well as compounds with nonoctahedral coordination of Pb.^155,171 These compounds comprise electronically isolated states and hence bound or self-trapped excitons with the characteristic broadband emission and a steep temperature-dependent PL QY.^155,172 Such metal halides are also of great interest for optoelectronics and structural chemistry per se^171,173,174 and will benefit from the development of the magnetic resonance methods.

LHPs represent a transitional case in between rigid crystalline materials and soft, dynamic, and disordered matter. It remains counterintuitive how the defect tolerance emerges, that is, how highly intrinsic electronic and optical characteristics are retained and not hampered by the structural defectiveness and structural dynamics, both being greatly enhanced in comparison with the structurally more rigid, conventional semiconductors. In fact, soft lattices of these halides are increasingly considered to be a favorable factor.^178−181 In particular, the association of charge carriers with lattice vibrations—so-called polarons—may protect carriers from defect states and increase carrier lifetimes, can aid in exciton dissociation, and may slow carrier cooling. Polarons are also increasingly associated with the unusually high dielectric constants in LHPs. The broad compositional and structural engineerability of LHPs makes it possible to engineer their properties à la carte. There exists no perfect and universal structural characterization method for probing the atomic structure both statically and dynamically as well as locally and space-averaged. It is the entirety of observations from diverse methods that allows the complex structure–property relationships to be unveiled. Typically, detailed structural investigations into a new class of inorganic materials start with X-ray/electron/neutron diffraction methods and electron microscopy and may be complemented by vibrational spectroscopy. Time-resolved variants of these methods and their combinations with optical methods give an extra benefit of probing the structure dynamics or excited states.^182,183 This Perspective emphasizes and exemplifies the immense utility of magnetic resonance methods for characterizing LHPs and other metal halide materials and outlines future avenues in this field.

2. Utility of NMR and NQR for Lead-Halide Perovskites

Solid-state nuclear magnetic resonance (NMR) spectroscopy is a versatile tool for sampling the chemical nature, geometry, and topology of the surrounding of atomic nuclei as well as the structure dynamics in materials without prerequisites for the crystallinity, size, or composition of the sample. All elements constituting LHPs possess NMR-active isotopes (i.e., nuclei with a spin), such as ¹H, ¹³C, ^14/15N, ¹⁹F, ^35/37Cl, ^39/41K, ⁵⁵ Mn, ^63/65Cu, ⁷³Ge, ^79/81Br, ^85/87Rb, ^107/109Ag, ¹¹⁹Sn, ^121/123Sb, ^123/125Te, ¹²⁷I, ¹³³Cs, ²⁰⁷Pb, and ²⁰⁹Bi (Figure 1g,h). NMR spectroscopy is highly chemical-element-specific, as each isotope has a different Larmor frequency (ω₀) corresponding to the Zeeman splitting in the applied magnetic field and hence a very specific frequency range of the NMR signals. NMR spectroscopy is a high-resolution probe of the various interactions of the nuclear spin with other nuclear and electron spins or electromagnetic fields (Figure 2). Spin–spin interactions can provide, for instance, information about connectivity (J-coupling, H_J) or interatomic distance (dipolar coupling, H_DD), whereas spectral features produced by the surrounding magnetic field (chemical shift, H_CS) and electric field gradient (EFG, quadrupole interaction, H_Q) contain information about the nature and the geometry of the chemical species. Low crystallinity, static and dynamic structural disorder, concomitant phases, and impurities, all being recurring matters in LHP research (Figure 3), are seen very differently by NMR as compared with diffraction-based methods. This important complementarity of NMR methods for LHPs is evident from the surge of research articles containing solid-state multinuclear NMR data. Several recent review articles may serve as initial guidance to the present stake of NMR in LHPs. Franssen et al. reviewed the structural and dynamical aspects,¹⁸⁴ whereas Bernard et al. unified models and provided a perspective about the dynamics of MA in MAPbX₃.¹⁸⁵ In their perspective about the “ionics in hybrid halide perovskite”, Senocrate et al. summarized insights into the ion conduction in LHP obtained with NMR spectroscopy.¹⁸⁶

Figure 2.

Major interactions contributing to NMR spectra. In NMR spectroscopy, the spin energy transitions are studied. By applying an external magnetic field, the Zeeman interaction (H_Z) lifts the degeneracy between nuclear spin states. A spin of I = 5/2 is shown, in the absence of other spin interactions. Spin–spin interactions such as the dipolar coupling (H_DD) or the J-coupling (H_J) perturb the spin energies and so do deviations of the local magnetic field relative to the applied magnetic field by shielding and deshielding of neighboring spins (chemical shielding, H_CS). Also, nearby charges affect the spin energies through the coupling of the quadrupole moments of spins of I > 1/2 with the electric field gradient (EFG) generated by these charges (quadrupole interaction, H_Q). The NMR spectrum, which reflects the spin energy transitions, is affected by all of these interactions through the shift of the resonance frequency, signal broadening, shape distortion, generation of multiplets and tensor line shapes, and so on. Here a simulated ¹²⁷I NMR spectrum of MAPbI₃ at 16.4 T is shown as an illustration of the complexity that NMR spectra can exhibit. For a detailed discussion and mathematical descriptions of these interactions, the interested reader is referred to several NMR textbooks.^175−177

Figure 3.

Structural insights about LHPs accessible through NMR and NQR. The figure illustrates a nonexhaustive range of structural aspects that are within the reach of magnetic resonance methods. Besides these structural and chemistry insights, electronic effects of quantum size effects and dielectric confinement are addressable as well.

In this Perspective, we bring the reader’s attention to the vast insights that NMR spectroscopy yields about the structure and structure dynamics of diverse LHPs (2D and 3D compounds, from NCs to bulk single crystals). We then discuss prospects that highlight the complementarity of nuclear quadrupole resonance (NQR) for ^79/81Br and ¹²⁷I nuclei, possessing particularly large quadrupole moments and, in LHPs, exhibiting strong quadrupole interactions due to large EFGs. We also underline that a better understanding of the structure dynamics in LHPs should leverage rapid development in computational materials science (i.e., ab initio molecular dynamics (AIMD) and its combinations with classical molecular dynamics as well as density functional theory (DFT) calculations).^187−189

Diverse structural and dynamic aspects of LHP materials (Figure 3) can be studied by both NMR and NQR methods. Various lead-halide compounds and, for an individual compound, also different polymorphs (phase transitions, coexistence of polymorphs) can be readily resolved as signals with different resonance frequencies (usually different chemical shifts in NMR).^190−197 Static disorder in LHPs comprises (i) structural defects such as point defects (e.g., halide vacancies), interstitial atoms, stacking faults, and grain boundaries and (ii) compositional modulations such as the mixed-ionic occupation of lattice sites, ion segregation, and compositional gradients (typical for halide ions) as well as heteroatomic doping. Static disorder is seen as inhomogeneous broadening generated by the distribution of chemical surroundings, forming a continuum of resonance frequencies that define the signal shape. For certain types of defects (e.g., paramagnetic dopants), relaxation of the nuclear spins can be affected as well. The rich structural dynamics in LHPs ranges from the rotational and stretching freedom of the organic constituents or the various stretching and tilting modes of the lead-halide framework to rapid ionic motion. These dynamic processes can be probed through the temporal variation of spin interactions. Depending on the nature and the time scale of the dynamics, the relaxation behavior or the shape and position of the signal may be affected, oftentimes accompanied by significant homogeneous broadening of the respective signals. Surfaces become a chemically distinct feature in high-surface-area LHP materials, such as ligand-capped colloidal NCs or matrix-embedded NCs. NMR offers diverse handles to probe such surfaces by surface-selective excitation (e.g., through cross-polarization), signal enhancing methods (e.g., dynamic nuclear polarization (DNP)), as well as correlation and other types of 2D experiments. Finally, electronic effects of size quantization and dielectric confinement in colloidal LHP NCs or 2D LHPs are also within the reach of NMR spectroscopy. These can be investigated through, for instance, susceptibility effects or quadrupole and chemical shift interactions (paramagnetic shielding term).

3. A-Cations: Dynamics and Surfaces

There are only three monovalent cations known to form 3D APbX₃—MA⁺, FA⁺, and Cs⁺—owing to their geometric fitness into the 12-coordinate A-site.¹⁹⁸ Mixing these A-cations, concomitantly with mixing halides, is presently the most successful strategy for obtaining best-performing perovskite solar cells. For instance, the incorporation of MA or Cs stabilizes cubic FAPbI₃ against spontaneous transition into a nonperovskite lattice. Examples of such heavily substituted multinary perovskites include FA_0.83Cs_0.17Pb(I_0.6Br_0.4)₃,¹⁹⁹ (FA_0.3MA_0.7)_0.85Cs_0.15PbI₃,²⁰⁰ and FA_0.79MA_0.16Cs_0.05Pb(I_0.83Br_0.17)_2.97.²⁰¹ Further cations (e.g., G and DMA), which are not perovskite formers when used alone, readily incorporate themselves as A-site dopants.⁹²⁻⁹⁵ Interestingly, the analogous substitutional incorporation of the smaller Rb⁺ and K⁺ onto A-sites was not corroborated by NMR studies, as will be discussed further later. Important pertinent questions that may be addressable with NMR are (i) to what extent different A-cations mix within the perovskite phase, (ii) how they are distributed between different grains, and (iii) the possibility of segregation at the surfaces and interfaces. For instance, the high PL QYs (60–70%) and carrier mobilities (40 cm² V^–1 s^–1) of potassium-doped (Cs_0.06FA_0.79MA_0.15)Pb(I_0.85Br_0.15)₃ were attributed to surface and grain-boundary passivation with potassium halides.⁹⁶ In MA-free Cs-FA LHP films, the graded A-cation composition of the crystalline grains was rationalized as an inhibiting factor for the transfer of electrons across grain-boundaries.²⁰² NMR has been used to sample ^1/2H, ¹³C, ^14/15N, ³⁹K, ⁸⁷Rb, and ¹³³Cs spins and has permitted us to identify the structural environments of monovalent cations,^{192−194,203−219} their dynamics,^{185,194,196,206,215,216,219−225} the composition within phases,^{98,193,222,226−242} and the distribution between phases of LHPs.^{192,193,215,217,222}

Most of the early NMR studies on LHPs focused on MAPbX₃ compositions. Starting with the 1985 paper by Wasylishen et al.,²²⁰ the dynamics of the MA cations was assessed through ^1/2H, ¹³C, and ^14/15N nuclei.^{194,196,206,219,221,222,224,225} The MA cation motion can be categorized into two kinds: the fast cone-shaped, wobbling libration (∼300 fs in MAPbI₃) and the slower, jump-like rotation of the C–N axis of the MA molecule (∼3 ps in MAPbI₃).²⁴³ The great interest in MA dynamics is attributed to its association with long carrier lifetimes²⁴⁴ and its contribution to the stabilization of the perovskite electronic structure via hydrogen bonding.^244,245 In general, hydrogen bonding is little studied in LHPs, especially in 2D and lower dimensional derivatives.^246,247 Typical structural characterization methods, that is, X-ray diffraction, are challenging due to the low atomic number of hydrogen. NMR does not experience this limitation. For example, Baikie et al. found, using ¹H NMR, that only the amine moiety of MA interacts with the lead-halide framework and used their insights to refine their X-ray and neutron-diffraction data.²²¹

The fastest dynamics resolvable with NMR are those affecting the T₁ relaxation rates. Here the theoretical limit corresponds to the Larmor frequency range, which is several tens to hundreds of megahertz (depending on the gyromagnetic ratio of the nucleus and the applied magnetic field strength), corresponding to the time scale of a few picoseconds to several nanoseconds. Even faster dynamics is experienced by the nuclear spins as averaged electromagnetic fields, whereas slower dynamics from a few microseconds up to hundreds of milliseconds impacts T₂ relaxation rates. Slower dynamics (seconds and slower) may also be resolvable, for instance, by the sequential acquisition of spectra. Hence, because of the fast dynamics of MA compared with the NMR time scale, ¹H and ¹³C spectra of MAPbX₃ exhibit only narrow lines with a very similar chemical shifts across different halide compositions,^{206,209,221,222} but proton T₁ relaxation times change sharply at phase transitions.^{196,209,221,248} Quadrupolar couplings of the nuclear spins ¹⁴N and ²H (both spins of I = 1) were often used to investigate MA dynamics. ¹⁴N and ²H NMR spectra show no quadrupole splitting in the high-symmetry cubic phase due to isotropic spin surroundings and the fast reorientation of MA (Figure 4a).^{194,206,219,220,222,224,225} At lower temperatures, MAPbX₃ crystallizes in tetragonal and orthorhombic crystal systems, and small quadrupole couplings arise due to the loss of symmetry from the slower dynamics of the MA molecule.^{194,206,219,220,224,225} On the basis of the values and the temperature dependence of the line width, the relaxation constants, and the quadrupole coupling strengths, the contribution of the different rotations of MA (correlated and uncorrelated C₃ reorientation along the C–N axis, tunneling rotation, reorientation of the C–N axis, etc.) and their activation energies could be determined,^{194,196,206,219−222,224,225} as was comprehensively surveyed in ref (185). DFT calculations were used to determine the exact space group of MAPbI₃ at RT.²¹⁹¹⁴N quadrupole couplings constants (C_Q) were calculated for four symmetrically identical orientations of MA in the crystallographic ab plane predicted by Weller et al. (top of Figure 4a).²⁴⁹ The simulated spectra agreed well with the experimentally observed temperature behavior of the static ¹⁴N solid-state NMR spectra (Figure 4a). The temperature-dependent experimental and calculated C_Q values follow the ratio of the crystallographic c and a axes, thus permitting the space group of MAPbI₃ to be determined to be I4/mcm.

Figure 4.

NMR of A-cations in LHPs. (a) Top: Four MA orientations in the crystallographic ab plane predicted by Weller et al.²⁴⁹ Left: Experimental and simulated static ¹⁴N solid-state NMR spectra of MAPbI₃ spectra. Right: ¹⁴N quadrupole coupling constants from the experiment (filled black circles) follow the ratio of the crystallographic c and a axes with varying temperatures (red, solid line). The filled and empty diamonds represent the individual and the averaged values calculated with DFT for the four MA orientations. Adapted with permission from ref (219). Copyright 2017 American Chemical Society. (b) ²H MAS NMR spectra of G(d₆)_0.25MA_0.75PbI₃ multinary perovskite and 1D G(d₆)PbI₃ at 100 and 300 K. Insets are zoom-ins of the center band at higher sample spinning speeds. The dashed line indicates the expected shift of CH₃ND₃. Adapted with permission from ref (215). Copyright 2018 American Chemical Society. (c) Substantial integration of Rb inside the 3D perovskite structure was ruled out, whereas the formation of a 1D structured phase containing Rb could be observed with the help of the ⁸⁷Rb NMR spectra of APbX₃ (A = Cs, FA, MA, Rb; X = Br, I) materials.¹⁹² Reprinted with permission from ref (192). Copyright 2017 American Chemical Society.

There are further studies investigating the dynamics of organic cations in pure-phase (FAPbBr₃,²⁵⁰ FAPbI₃)^209,222 and increasingly mixed-ionic LHPs (FA_0.67MA_0.33PbI₃;²²² G_0.25MA_0.75PbI₃,²¹⁵Figure 4b; DMA_1–xMA_xPbI₃).²⁵¹ The capability to distinguish between dynamic and static disorder by separating homogeneous and inhomogeneous line width contributions is not unique to NMR spectroscopy, as, for instance, the PL line width as well as the PL QY and the radiative lifetime are also affected by temporal and spatial disorder.^153−155 However, NMR holds the advantage that the involved chemical structures can be traced because the NMR signals of the concerned structural moieties are the ones exhibiting homogeneous or inhomogeneous line broadening, respectively. By sampling organic and inorganic A-cations in mixed LHPs, insights into the dynamics, the A-cation distribution, and their incorporation are available for a vast range of compositions involving organic (MA⁺, FA⁺, DMA⁺, and G⁺) or inorganic (Cs⁺, Rb⁺, and K⁺) monovalent cations.^{192,193,215,217,222,250,252} For instance, Kubicki et al. showed that K⁺ and Rb⁺ ions do not substitutionally dope the lattice of 3D LHPs, as can be seen in the absence of a continuously shifting signal with gradual compositional change (Figure 4c). The results rather point to the formation of new, structurally unidentified phases.^192,193 The situation is different for the G-cation, which at low concentrations occupies the A-site positions.²¹⁵ Noticeably, ²H NMR indicated that the reorientation of G⁺ in 3D structures is accelerated compared with the dynamics in a nonperovskite 1D GPbI₃ (Figure 4b). The ²H quadrupole splitting of deuterated G⁺ reflects the reorientational dynamics of this cation within the structure. The broader splitting in nonperovskite G(d₆)PbI₃ indicates that the dynamics is restricted to rotations along the C–N axes, whereas isotropic reorientations on top of a fast C–N axial rotation are required to explain the narrow lines observed for G(d₆)_0.25MA_0.75PbI₃ perovskite materials. Kubicki et al. suggested that the reorientations of G-cations, which are faster than 10⁶ s^–1, could explain the improved performance of this material in solar cells,^215,229 in a similar way as the fast MA reorientation prolongs charge-carrier lifetimes in MAPbI₃.²⁴⁴ Grottel et al. have used ¹H NMR relaxation as a probe for the G-cation dynamics and activation energies of the latter as well as phase transitions in 1D GPbI₃ and 2D G₂PbI₄ structures.²⁵³

NMR spectroscopy is also increasingly instrumental for characterizing and elucidating the role of organic cations in 2D perovskites.^{130,253−257} For instance, the distinction between different molecules is straightforward, and their locations within slabs or interstitials can be clearly determined.^{130,253−255} Milić et al. could distinguish the FA cations in the slabs of 2D A₂FA_n–1Pb_nI_3n+1 (A: (adamantan-1-yl)methanammonium spacers) from those incorporated into a concomitant 3D FAPbI₃ using 2D ¹H–¹H spin-diffusion NMR spectra (Figure 5a).¹³⁰ The dynamics of organic cations extracted from ¹H relaxation times in different 2D LHP structures made it possible to draw conclusions about the crystal rigidity and, in turn, relate the softness of the lattice to the PL line width (exciton–phonon coupling) and other PL characteristics.²⁵⁷

Figure 5.

NMR of 2D LHPs. (a) Schematic of a 2D A₂FA₂Pb₃I₁₀ structure proposed by Milić et al., corroborated by ¹H–¹H spin-diffusion solid-state MAS NMR spectra recorded at different mixing times.¹³⁰ The cross peaks highlighted by the arrows in the spectra with longer mixing times indicate the proximity between some FA cations and the spacer cation (adamantan-1-yl)methanammonium (blue arrows in the scheme) and support the proposed structure. Reprinted with permission from ref (130). Copyright 2019 by John Wiley and Sons. (b) Relationship between the mean elongation of lead-halide octahedra in 2D A₂PbI₄ structures with various A cations (4NPEA, 4-nitrophenylethylammonium (two ²⁰⁷Pb NMR signals); PEA, phenylethylammonium; BA, butylammonium; PMA, phenylmethylammonium; EDBE, NH₃(CH₂)₂O(CH₂)₂O(CH₂)₂NH₃) and their ²⁰⁷Pb NMR isotropic chemical shifts. Reprinted with permission from ref (255). Copyright 2019 American Chemical Society.

The known NMR studies on inorganic A-cations are mainly focused on phase transitions in CsPbX₃ LHPs and the structural implications (tilting of lead-halide octahedra, symmetry loss/increase, increase in disorder, etc.) arising from temperature variations.^{203−205,258−260} In particular, ¹³³Cs spins were found to be valuable probes to study ferroelastic, twinned domain structures in CsPbCl₃.^{258,260−264}

4. ²⁰⁷Pb NMR Spectroscopy of Lead-Halide Perovskites

The large chemical shift range of ²⁰⁷Pb NMR (∼20 000 ppm) makes it a highly sensitive probe of major and subtle structural changes in the lead surroundings, including first, second, or third coordination shells. The ²⁰⁷Pb NMR signal of APbX₃ compounds is more deshielded for heavier halides: δ(APbCl₃) < δ(APbBr₃) < δ(APbI₃) (Figure 6a).^{206,265−270} In the mixed-halide perovskites APbCl_xBr_3–x and APbBr_xI_3–x (A = MA, FA; x = 0–3), seven distinct lead environments PbX_xX′_6–x (x = 0–6) were found with chemical shift spanning the range between two monohalide counterparts (Figure 6b), and the ²⁰⁷Pb NMR chemical shifts evolved linearly with the composition.^266−269 Any substantial dynamics of halide ions should manifest itself in ²⁰⁷Pb NMR, owing to the imparted changes in Pb–X bonding. 2D exchange spectroscopy (EXSY) captured the constantly changing Pb environment due to the exchange of halide atoms (Figure 6d),^268,269 in agreement with the known high diffusivity of halide ions in these materials.²⁷¹ The analysis of ²⁰⁷Pb NMR spectra from mixed-halide LHPs obtained with various synthetic procedures differentiates between solid solutions with different degrees of homogeneity and halide miscibility as well as crystallinity.^266−269 In the ²⁰⁷Pb NMR spectrum of solution-grown MAPbI_1.5Br_1.5, two phases were observed, assigned as MAPbIBr₂ and MAPbBr₃ based on their chemical shifts.²⁶⁷ However, the MAPbBr₃ phase was not seen in X-ray diffraction patterns, indicating its low crystallinity or localization as a thin layer around MAPbIBr₂ grains.

Figure 6.

²⁰⁷Pb NMR of LHPs. (a) ²⁰⁷Pb solid-state NMR spectra of APbX₃ compounds. Adapted with permission from ref (273) (Copyright 2020 by Wiley and Sons), ref (270) (Copyright 2019 Springer Nature), and ref (272) (Copyright 2018 American Chemical Society). (b) Gradual change of the halide composition, here from MAPbCl₃ to MAPbBr₃, results in lead environments with mixed-halide composition PbX_xX′_6–x (x = 0–6), whose positions in the spectra correspond almost exactly to the linear interpolation of the pure compounds APbX₃ and APbX′₃. Reprinted with permission from ref (269). Copyright 2018 American Chemical Society. (c) ²⁰⁷Pb LHP NMR of CsPbBr₃ at 100 K. The signal splitting is a 19-fold multiplet generated by the J-coupling to six bromine nuclei. The spikelet conforms with Pascal’s triangle. Reprinted with permission from ref (270). Copyright 2019 Springer Nature. (d) MAPbCl_1.5Br_1.5²⁰⁷Pb EXSY NMR spectra with increasing exchange times from left to right. The exchange between two of the seven lead environments (1: [PbCl₆]^4–, 2: [PbCl₅Br]^4–, 3: [PbCl₄Br₂]^4–, 4: [PbCl₃Br₃]^4–, 5: [PbCl₂Br₄]^4–, 6: [PbClBr₅]^4–, 7: [PbBr₆]^4–) produces a cross peak at their frequencies’ intersections, indicated by n,m for the exchange between environments n and m. With increasing mixing time, environments not only with one different halide atom (small squares) but also with two changing halides exchange (large squares). Adapted with permission from ref (269). Copyright 2018 American Chemical Society.

The influence of the composition of the halide coordination sphere of the lead atom on the lead isotropic chemical shifts (²⁰⁷Pb δ_iso) is stronger than the effect of connectivity between lead-halide octahedra or octahedral tilts. This is exemplified in Figure 6a, wherein different APbX₃ compounds are grouped by composition.^{191,270,272,273,191} Of these, nonperovskite lattices are δ-CsPbBr₃ and δ-CsPbI₃ (1D chains of edge-sharing octahedra) and δ-FAPbI₃ (face-sharing, 1D connectivity as well). A-cation substitution in 3D LHPs results in the ²⁰⁷Pb δ_iso trend CsPbX₃ < MAPbX₃ < FAPbX₃ in monohalide series (Figure 6a). Besides the structural effect of A-cations (octahedral tilts), the different magnetic properties of the A-cations (different gyromagnetic ratios, polarizabilities, spin multiplicities, etc.) may also contribute to the observed trend. Different octahedral tilts and hence a change in the symmetry also occur upon temperature-induced phase transitions. For instance, MAPbI₃ undergoes a transition from tetragonal to orthorhombic polymorphs upon cooling from 20 to −130 °C, seen as a reduction of ²⁰⁷Pb δ_iso from 1450 to ∼1100 ppm²¹⁹ and accompanied by the gradual appearance of spinning sidebands (i.e., a chemical shift anisotropy (CSA) tensor) due to reduced structure symmetry. Because of the strong temperature dependence of the ²⁰⁷Pb chemical shifts, Bernard et al. proposed the use of MAPbCl₃ as an internal thermometer for solid-state NMR experiments,²⁷⁴ alternative to the commonly used Pb(NO₃)₂ salt.²⁷⁵ In the ²⁰⁷Pb NMR spectra of MAPbCl₃, there is no apparent CSA, unlike Pb(NO₃)₂, which facilitates the temperature calibration in static solid-state NMR experiments. Furthermore, the ¹³C NMR signal from MA could serve as an internal standard.

In general, the line width of ²⁰⁷Pb NMR signals is large, from a few kilohertz up to tens of kilohertz, and arises from several line-broadening effects. These include the CSA, the positional disorder leading to a distribution of isotropic chemical shifts, the dipole–dipole coupling (at least for static spectra), and the dispersion of J-coupling values due to variations of the bond lengths and geometries. For MAPbCl₃, CsPbCl₃, MAPbBr₃, and CsPbBr₃, it was shown that the signal width is dominated by the lead-halide J-coupling, which is on the order of ca. 400 Hz (¹J_Pb–Cl) and 2.3 kHz (¹J_Pb–Br).^185,252,270 19-Fold multiplets were detected for these LHPs (only at low temperatures in the case of MAPbBr₃) due to the (almost) identical couplings of ²⁰⁷Pb nuclei with the six coordinating halide atoms, which all possess spins of I = 3/2 (Figure 6c). The signal width of other APbX₃ compounds is also likely to be defined by the lead-halide J-coupling patterns, but because of the increased inhomogeneous line width and lower structural symmetry, the lines of the pattern cannot be resolved.²⁷⁰ Although often overseen due to the inhomogeneous broadening of the signal or unsuited signal acquisition or processing, the lead-halide couplings had already been observed more than 20 years ago in the doctoral thesis of Holger Ulman (University Dortmund).²⁷⁶ A plethora of binary, ternary, and quaternary lead-halide materials were synthesized and characterized, and, for a large number of these compounds, the lead-halide coupling was recorded. ²⁰⁷Pb solid-state NMR can also be used to study decomposition products of MAPbI₃ when exposed to humidity or thermal stress²⁷⁷ or to unravel side reactions. For instance, in situ DMA formation was captured as a result of the dimethylformamide (solvent) reaction with MA⁺ during the preparation of MAPbI₃ thin films.²³⁶

The lower symmetry and the partially disrupted connectivity of the lead-halide octahedra in 2D LHPs affect the chemical shielding of ²⁰⁷Pb nuclei, leading to shifting of the isotropic value^255,272 and the appearance of spinning sidebands due to an increased CSA, which differ for lead atoms within and at the edges of the slabs.^255,278 Tremblay et al. delineated a linear dependence between the chemical shift and the elongation of the lead-halide octahedra produced by different slab-separating cations (Figure 5b).²⁵⁵ In 2D LHPs, the quantum confinement alters the energy levels of the conduction band (CB) and valence band (VB), resulting in different band-gap energies, whereas the dielectric effect does not alter the band -gap energy but equally shifts the CB and VB on an absolute energy scale. The isotropic and anisotropic chemical shifts may be highly potent probes of these confinement effects because changes in the electronic structure, affecting both the absolute energy values (isotropic chemical shift) as well as the electronic inhomogeneities (anisotropic chemical shift), impact the local magnetic field of ²⁰⁷Pb nuclei. The changes in the VB and CB energies might be compared with the HOMOs and LUMOs in Ramsey’s description of chemical shieldings in molecules,²⁷⁹ which was already applied to explain the observations in NMR spectra of quantized semiconductor materials (in particular, colloidal NCs and nanoplatelets).^280−283 However, one should expect that for the elucidation of the relationship of confinement effects with the chemical shift in 2D perovskites, computational approaches, considering many-body interactions and spin–orbit couplings, are required.

The broad signal width of APbX₃ materials, the modest gyromagnetic ratio (5.58 × 10⁷ rad s^–1 T^–1; about five times smaller than that of a proton), and the low natural abundance (22.1%) of ²⁰⁷Pb make it a relatively unreceptive nucleus. Accordingly, recording conventional ²⁰⁷Pb NMR spectra of LHPs usually requires measurement times of several hours. Hanrahan et al. have therefore investigated and quantitatively compared several experimental procedures, such as magic-angle spinning (MAS), low temperatures, dynamic nuclear polarization (DNP), and proton detection, which improve the signal intensity and reduce the acquisition time of ²⁰⁷Pb NMR spectra to a few minutes.²⁶⁵ They noted that the low-temperature spectra must be interpreted with care because phase transitions can occur, and the dynamics is influenced by the temperature change. Although their DNP enhancement factors were moderate for MAPbCl₃ (15–20) and MAPbBr₃ (3 to 4) at the applied magnetic field strength (9.4 T) and negligible for MAPbI₃, their results showcased a path to the efficient sampling of both LHP thin films and surface species in LHP NCs, which are morphologies with even lower lead concentrations than microcrystalline powders. Besides the experimentally demanding methods previously mentioned, another practically attractive avenue is the development of benchtop, low-magnetic field ²⁰⁷Pb NMR spectroscopy (with a permanent magnet) for the routine characterization of LHPs, as recently demonstrated for MAPbCl₃.²⁸⁴

5. Halide NMR and NQR

All heavier halides possess a quadrupole moment because they have spins of I > 1/2 (^35/37Cl I = 3/2, ^79/81Br I = 3/2, ¹²⁷I I = 5/2), whereas ¹⁹F has I = 1/2. Because fluorine is not a structure-former for LHPs, we focus on quadrupolar halide nuclei, yet we must note that ¹⁹F NMR is highly instrumental to the study of the fluorine-containing organic moieties of LHPs. For instance, Ruiz-Preciado et al. used it, in combination with DFT calculations, to probe halogen bonding at LHP surfaces.²⁸⁵ The occasional use of ¹⁹F NMR to characterize hybrid LHPs can also be found in refs (286 and 287). We also note that ¹⁹F solid-state NMR has been applied to numerous metal fluoride perovskites (ABF₃)^288−307 and 2D fluoride perovskites,³⁰⁸ where A = Li, Na, K, Cs, Rb, and ammonium (NH₄⁺) and B = Mg, Ca, Ba, Sr, Mn, Co, Zn, and Ho, to study diverse materials aspects, such as fluoride ion mobility³⁰⁹ or the material’s paramagnetism.^299,305

Quadrupolar halide nuclei are subject not only to the Zeeman interaction (H_Z, Figures 2 and 7) but also to the quadrupole interaction (H_Q) as their quadrupole moment couples to the EFG. The symmetry and the strength of the quadrupole interaction are described by, respectively, the asymmetry (η_Q) and the quadrupole coupling constant (C_Q). The latter scales with the quadrupole moment of the nuclear spin. Together, C_Q and η_Q parametrize the EFG, which contains structural, geometrical, and topological information about the nuclei’s surroundings, as they all reflect the charge distribution around the nuclear spin. With the continued advancements of higher magnetic fields, recently extending beyond 1 GHz for commercial devices, halide NMR spectroscopy of LHPs has a fruitful road ahead. For halide NMR to be feasible, the Zeeman interaction, which lifts the degeneracy of nuclear spin energies, must be at least of equal size as the quadrupole interaction. However, C_Q constants reported for LHP are all quite large. Table 1 is a survey of known halide NQR and NMR signals of APbX₃. The combination of the large quadrupole moments of the halide spins (Table 2) and the exceptionally large EFGs in LHPs leads to some of the largest C_Q values reported for halide nuclei.^310−312 Magnetic field strengths required to produce Larmor frequencies, ω₀, that are comparable to or larger in size than halide C_Q values in LHPs are at the limits of commercial spectrometers in the case of Cl and Br nuclei and are inaccessible for I nuclei. Therefore, NQR has been a method of choice for studying halide nuclear spin transitions (Figure 7). NQR is a zero-to-low-field sibling of NMR spectroscopy. In NQR, the EFG leads to the splitting of spin energy states, whose energy can be perturbed by a weak magnetic field, similarly to how NMR transitions are perturbed by the quadrupole interaction. A continuous transition from NQR to NMR is obtained with decreasing quadrupole coupling and by increasing the magnetic field strength (Figure 7). Theoretically, all of the material’s structure and dynamics aspects contained in the quadrupole interaction are equally accessible through NQR or NMR because the quadrupole parameters can be extracted either from the frequency of the NQR lines^313−317 or from the width and the shape of NMR signals.^318,319 Both kinds of nuclear resonance can be recorded on the same material; see, for instance, the chlorine and bromine NMR and NQR spectra of CsPbCl₃ and CsPbBr₃ in Figure 7. However, for very large quadrupole couplings, as in iodine-based LHPs, the presently available magnetic field strengths are low compared with the large C_Q, and the acquisition of the complex and broad ¹²⁷I NMR spectra (see the simulated spectrum in Figure 7) is impractical, whereas narrow-line ¹²⁷I NQR spectra can be rapidly recorded (Figure 7). Finding the resonance frequency of the signal is far more difficult in NQR than in NMR, as a frequency range from a few hertz up to several hundreds of megahertz must be screened because the NQR resonances scale with the quadrupole coupling.

Figure 7.

Halide NMR versus NQR, exemplified for CsPbX₃. Spins of I > 1/2 (I = 5/2 depicted example) possess a quadrupole moment, which interacts with the EFG generated by surrounding charges. This quadrupole interaction (H_Q) can, depending on its strength relative to the Zeeman interaction (H_Z), either perturb the NMR transitions (left part of the scheme) or, for strong quadrupole coupling strengths, be the dominant interaction. In the latter case, a perturbed NQR spectrum would be obtained, which would be further simplified by removing the magnetic field, producing a pure NQR spectrum, as shown on the right for CsPbBr₃ and CsPbI₃. For CsPbCl₃, only the resonance frequencies (ν) are shown (at various temperatures, T). Reprinted with permission from ref (190). Copyright 1983 by John Wiley and Sons. For halide quadrupole couplings (C_Q(³⁵Cl, CsPbCl₃) = 15.5 MHz, C_Q(⁷⁹Br, CsPbBr₃) = 133.6, 136.4 MHz), which are smaller than the Larmor frequencies (ω₀(³⁵Cl) = −58.8 MHz @ 14.1 T and ω₀(⁷⁹Br) = 175.4 MHz @ 16.4 T inhere), halide NMR spectra can be recorded, but with involved experimental conditions. Iodine C_Q values in LHPs are larger (ca. 500–600 MHz) than the ¹²⁷I Larmor frequencies (e.g., 140.1 MHz @ 16.4 T). Hence ¹²⁷I NMR is complex and too broad for practical acquisition. Only a simulation of the CsPbI₃¹²⁷I NMR spectrum at 16.4 T can be provided. Adapted with permission from ref (320). Copyright 2020 American Chemical Society.

Table 1. Summary of Reported Halide Quadrupole Parameters Obtained from Monohalide LHP NQR and NMR Spectra.

compound	nucleus	NQR lines (MHz)	CQ (MHz)	ηQ	temperature	source
CsPbCl3	35Cl	7.69–7.97			77–360 K	ref (190)
			15.48 (bulk)	0 (bulk)	100–273 K	ref (320)
			15.49–15.51 (NCs)	0 (NCs)	100–273 K	ref (320)
	37Cl	7.66–7.89			77–360 K	ref (190)
MAPbCl3	35Cl	8.128			298 K	ref (196)
CsPbBr3	79Br	70.43, 67.155, 38.42, 37.11			77 K	ref (195)
		68.068, 66.781, 37.28			300 K	ref (195)
			133.59, 136.36	0.006, 0.03	RT	ref (320)
	81Br	58.84, 56.14, 32.091, 30.975			77 K	ref (195)
		56.87, 55.782, 31.17			300 K	ref (195)
MAPbBr3	79Br	70.451			298 K	ref (196)
		69.701, 73.819			77.4 K	ref (196)
			141.0185	0.0099	RT	ref (320)
	81Br	58.842			298 K	ref (196)
		58.239, 61.678			77.4 K	ref (196)
FAPbBr3	79Br		149.1034	0.0642	RT	ref (320)
	79Br	74.6			RT	ref (250)
		73.2, 74.4			160 K	ref (250)
δ-CsPbI3	127I	56.55, 94.84; 71.07, 126.10	325.4; 428.6	0.397; 0.319	77 K	ref (195)
		56.2, 92.3; 70.15, 125.2	317.9; 425.1	0.423; 0.311	300 K	ref (195)
		56.1744, 92.9890; 70.0794, 124.9071	319.7; 424.3	0.415; 0.311	RT	ref (320)
γ-CsPbI3	127I		517.98; 537.36.7	0.025; 0.101	RT	ref (320)
MAPbI3	127I	83.430, 166.840; 82.062, 164.094	556.139; 573.063	0.010; 0.012	298 K	ref (196)
		85.973, 160.192; 84.895, 159.161	539.974; 536.132	0.241; 0.229	77.4 K	ref (196)
		82.057, 164.002; 83.449, 167.002	–528.1; −558.6	0.29; 0.34	298 K	ref (194)
		83.430, 166.846; 82.073, 164.114	556.16; 547.06	0.00; 0.01	297.3 K	ref (197)
		82.13, 164.28	547.59	0.00	350.8 K	ref (197)
α-FAPbI3	127I	87.294, 174.59; 85.205, 170.34	581.96; 567.84	0.00; 0.018	189.5 K	ref (197)
		86.61, 173.22	577.40	0.00	292.7 K	ref (197)
δ-FAPbI3	127I	57.315, 87.935	306.50	0.508	300.0 K	ref (197)

Table 2. NMR Properties of Quadrupolar Halide Nuclei.

nucleus	spin321	natural abundance (%)321	gyromagnetic ratio γ (106 rad s–1 T–1)321	quadrupole moment Q (e·fm–2)a 321
35Cl	3/2	75.76	26.241991	–8.165
37Cl	3/2	24.24	21.843688	–6.435
79Br	3/2	50.69	67.25619	30.5
81Br	3/2	49.31	72.49779	25.4
127I	5/2	100	53.8957	–71

^ae stands for the elementary charge 1.602·× 10^–19 C, with which the tabulated value Q must be multiplied to obtain the quadrupole moment in C/fm².

Unsurprisingly, halide NQR transitions in LHPs were investigated long before chloride and bromide NMR spectra, which were reported only recently.³²⁰ We have not found ¹²⁷I NMR spectra attributable to LHPs in the literature and have not succeeded in obtaining them ourselves. The first halide NQR of CsPbX₃ studies dates to the late 1960s and early 1970s,^195,322,323 a decade after Møller reported the determination of a perovskite lattice for CsPbX₃.^324,32535Cl NQR was used to explore the phase transitions and structural properties of CsPbCl₃.^{190,322,323,326} Possible crystal systems could be deduced from the number of NQR lines, their resonance frequencies, and their relaxation behavior. Furthermore, phase transitions and their order could be monitored and explained by the appearance of phonon vibrations. Some controversy existed about the temperatures of the phase transitions,³²⁷ possibly due to the various degrees of twinning in the CsPbCl₃ structure^{258,259,261,262} and the influence of the thermal history of the sample on the spectroscopic results.^323,326 Although fewer in number, similar ^79/81Br NQR studies on CsPbBr₃ were conducted in the past.^195,205

After Weber reported the synthesis of MAPbX₃ in 1978,³²⁸ the phase transitions in these materials were investigated using ³⁵Cl, ^79/81Br, and ¹²⁷I NQR.¹⁹⁶ Upon cooling, the signal from the single halide species in the cubic phase splits into two signals, corresponding to the inequivalent axial and equatorial halides of lead-halide octahedra in tetragonal and orthorhombic structures; see the ⁸¹Br NQR data of MAPbBr₃ in Figure 8a. The advent of efficient perovskite photovoltaics also fueled the interest in MAPbI₃ from the perspective of nuclear resonance studies. The recently reported ¹²⁷I NQR spectra of MAPbI₃^194,197,219 correlated the line width to the powder quality²¹⁹ as well as to the short-range dynamics (e.g., rotational/vibrational motion) of the iodine.¹⁹⁴ The reported ¹²⁷I quadrupole parameters of MAPbI₃ vary in publications, but the NQR resonance frequencies are comparable (Table 1). Discrepancies could originate from slightly different experimental temperatures (Figure 8b), diverse synthetic procedures, and different approaches to determining C_Q and η_Q.

Figure 8.

Halide NMR of organic–inorganic LHPs. (a) ⁸¹Br NQR frequencies of MAPbBr₃ recorded at various temperatures, evidencing the continuous structural changes and sharp phase transitions (dashed lines). Between 150 and 180 K, the signals were too weak to be detected. Reprinted with permission from ref (196). Copyright 1991 De Gruyter. (b) Temperature dependence of low-frequency ¹²⁷I NQR transitions of MAPbI₃ and FAPbI₃. Phase transitions are indicated by arrows. Upon cooling from the cubic (>333 K for MAPbI₃ and >283 K for FAPbI₃) to tetragonal crystal structure, the single ¹²⁷I NQR signal splits into two signals with an intensity ratio of 2:1, corresponding to the unequal equatorial and axial iodine atoms. Reprinted with permission from ref (197). Copyright 2018 Chemical Society of Japan. (c) High magnetic field strengths (here 16.4 T) make the acquisition of bromine NMR spectra of LHP possible. ⁷⁹Br NMR spectra of MAPbBr₃ and FAPbBr₃ are displayed, exhibiting the perfect axial symmetry of the bromine sites. Adapted with permission from ref (320). Copyright 2020 American Chemical Society. (d) ⁷⁹Br NQR spectra of Cs_xFA_1–xPbBr₃ (x = 0.0 to 0.35). The three signals observed at low Cs concentrations were attributed to Br with zero, one, and two Cs atoms as nearest neighbors. Adapted with permission from ref (250). Copyright 2020 American Chemical Society.

Meanwhile, NQR spectra of other iodine-based LHPs are rare. Yamada et al. found the ¹²⁷I NQR lines for two polymorphs of FAPbI₃ (cubic 3D and nonperovskite 1D phases). They also observed a phase transition from the cubic to tetragonal perovskite lattice at 283 K,¹⁹⁷ seen as the splitting of the single ¹²⁷I NQR line (only the low-frequency one is shown in Figure 8b) of the cubic phase into two lines corresponding to the inequivalent iodine atoms in the tetragonal phase. A similar study by Volkov et al. reported the ¹²⁷I NQR transitions and the corresponding quadrupole parameters of yellow nonperovskite δ-CsPbI₃ at 77 and 300 K.¹⁹⁵ Our group reproduced these findings recently and completed them with ¹²⁷I NQR spectra of γ-CsPbI₃ (Figure 7).³²⁰

The ³⁵Cl NMR spectrum of CsPbCl₃ and the ⁷⁹Br NMR spectra of CsPbBr₃, MAPbBr₃, and FAPbBr₃ are shown in Figures 7 and 8c. The large signal width requires the acquisition of multiple subspectra under static conditions with broadband excitation combined with the echo-train collection, as conventional signal averaging (e.g., MAS) brings no improvement. The acquisition of ¹²⁷I NMR spectra is impractical, as can be seen from the simulated ¹²⁷I NMR spectrum of orthorhombic γ-CsPbI₃ at 16.4 T in Figure 7. The spectrum is >300 MHz broad and exhibits a complex shape, whose spectral features are not trivial to interpret.

Very recently, the impact of Cs incorporation on the inorganic lattice of FAPbBr₃ was probed with ⁷⁹Br NQR, showing signal broadening with increasing Cs content. For low Cs concentrations (up to 10%), the signal splits into three lines, which the authors assigned to Br with zero, one, and two Cs atoms as nearest neighbors (Figure 8d).²⁵⁰

6. Lead-Halide Perovskite Colloidal Nanocrystals and Thin Films

LHP NCs are the latest generation of colloidal inorganic semiconductors.^69,329 Colloidal NCs comprise a crystalline core of typically 3–20 nm in diameter. When the NC size is comparable to or smaller than the Bohr diameter of a photogenerated electron–hole pair (exciton), the NC’s electronic structure is altered; in particular, the band-gap energy increases with decreasing NC size (quantum-size effect).^40,330 There exists an interface between the inorganic crystalline core and the long-hydrocarbon-chain capping ligands anchored to the surface via a suitable binding group. These ligands ensure the structural integrity of NCs and impart colloidal stability in apolar solvents. The surface state is also of paramount importance for the optical and electronic characteristics of semiconductor NCs.³³¹ Understanding and characterizing the NC surfaces has always been nontrivial. NMR spectroscopy is a rare analytical method that is (nearly) fully forgiving yet is highly sensitive to the degree and disruption of atomic order at the surface. For the investigation of the organic–inorganic interface, it is most desired to study the colloidal NCs in their native colloidal state. Ligands’ binding motifs and binding dynamics can be deduced from the line width and position of signals in 1D NMR spectra as well as from the information about internuclear distances and mobility from 2D NMR experiments (nuclear Overhauser effect spectroscopy (NOESY), diffusion ordered spectroscopy (DOSY), etc.). This suite of solution-state NMR methods for characterizing ligand shells has been well established for conventional colloidal semiconductor NCs^332,333 and recently extended to LHP NCs.^334−336 Also, solid-state NMR was used to probe the inorganic surface termination of CsPbBr₃ NCs.³³⁷ In ref (337), the distance dependence of the dipolar coupling (Figure 2) was utilized to probe the outmost Cs and Pb atoms by performing ¹H{¹³³Cs} RESPDOR (resonance-echo saturation-pulse double-resonance)and ¹H{²⁰⁷Pb} S-REDOR (symmetry-based resonance-echo double-resonance) experiments. These experiments probed the distance between the ammonium protons of the oleylammonium ligands and the closest ¹³³Cs and ²⁰⁷Pb nuclei. The dipolar coupling leads to a decrease in the intensity of the oleylammonium proton signal with increasing duration of the total recoupling time (the time during which the dipolar coupling is reintroduced). Strong couplings lead to a fast decrease in the signal intensity, and hence the behavior of the signal intensity over different recoupling times contains information about the number of, and the distance to, neighboring heteronuclei. The experimental initial rates were compared with the simulated curves obtained for four possible surface terminations. From this comparison, it was concluded that the studied CsPbBr₃ NCs exhibit Cs termination, and some of the surface Cs ions are replaced by oleylammonium ligands (Figure 9). In general, both the surface and the inorganic core of LHP NCs are addressable by NMR methods. The ²⁰⁷Pb NMR spectra of MAPbX₃ NCs^265,266 and CsPbBr₃ NCs^270,337 exhibit rather featureless signals at similar chemical shifts as their bulk counterparts (Figure 10a) but with much greater signal line width due to chemical and electronic disorder (inhomogeneous broadening). The ³⁵Cl NMR spectra of CsPbCl₃ NCs and the ⁷⁹Br and ¹²⁷I NQR lines of CsPbBr₃ and CsPbI₃ NCs are also closely matching those of the bulk counterparts in terms of the resonance frequencies and the spectral shape.³²⁰ However, the ⁷⁹Br NQR lines of CsPbBr₃ NCs are six times broader than those of the bulk due to inhomogeneous contributions. These NCs’ ⁷⁹Br NQR signals are also much less intense, such that the higher frequency line could not be detected (Figure 10a). A characteristic difference between the bulk and the NCs is the accelerated spin–spin relaxation (T₂) of halide nuclei in NCs.³²⁰ For instance, ³⁵Cl NMR signals relax faster in CsPbCl₃ NCs than in the bulk (Figure 10b), and the discrepancy between the T₁ and T₂ relaxation behaviors in the two sample morphologies is a strong indication of the accelerated structure dynamics in NCs, which was corroborated by AIMD calculations. These simulations indicated that surface and near-surface regions in NCs exhibit a much higher density of low-frequency phonon states (Figure 10c,d) and a larger distribution of lead-halide bond angles (Figure 10e). An alternative or complementary explanation to this anharmonic dynamics driven by low-energy modes could be the existence of a new pathway for ionic motion, for example, surface ionic mobility with extremely low activation energies, which could also account for the observed disparity in the T₂ behavior between NCs and bulk LHPs. A further computational analysis involving AIMD and DFT calculations would be needed to explore this and other structural hypotheses. We expect that embarking on the combination of magnetic resonance methods and increasingly powerful atomistic computational tools for materials is a strategy that will be indispensable for rationalizing the observed T₁ and T₂ behaviors in diverse solid-state materials.

Figure 9.

NMR of the NC surface. (a) Structural models of the orthorhombic (010) CsPbBr₃ surface. The position of an ammonium proton is indicated by an asterisk. Its simulated ¹H{¹³³Cs}/¹H{²⁰⁷Pb} multispin RESPDOR/S-REDOR curves in panel b (blue/orange lines) match the best experimental data of oleylamine- and oleic-acid-terminated CsPbBr₃ NCs. The curves correspond to the evolution of the ¹H signal intensity, ΔS/S₀ = (S – S₀)/S₀, where S is the signal at a given recoupling time and S₀ is the initial signal intensity over the exposure time (total recoupling time) of the ¹H spins to the dipolar coupling with ¹³³Cs/²⁰⁷Pb nuclei, respectively. Adapted with permission from ref (337). Copyright 2020 American Chemical Society.

Figure 10.

Structure disorder and dynamics in LHP NCs. (a) Both in bulk (black) and in NCs (blue), all atoms are accessible with magnetic resonance, as exemplified by CsPbBr₃ (A-cation: ¹³³Cs NMR spectra, unpublished; Pb(II) cation;²⁷⁰ halides: ⁷⁹Br NQR spectra at 90 K).³²⁰ (b) Temperature-dependent ³⁵Cl NMR T₂ relaxation times of bulk and nanocrystalline CsPbCl₃. (c) Regions 1–4 within a CsPbBr₃ NCs. (d) Plot of the partial phonon density of states in each of the four NC regions, normalized to the phonon frequency squared to accentuate the low-energy region. (e) Plots of the statistical distribution of Pb–Cl–Pb angles, α, within each NC region. Adapted from ref (270) (Copyright 2020 Springer Nature) and ref (320) (Copyright 2020 American Chemical Society).

Thin films of LHPs find use in LEDs (thicknesses down to few nanometers),¹⁴ photodetectors, and solar cells (hundreds of nanometers)^5,6 as well as in lasers.^17,338,339 Thicker films of up to and above 50 μm are required in X-ray and gamma detectors.²⁹ These films may greatly vary in their crystallinity^41,340 Furthermore, such films can be fully planar or may conformally coat diverse objects and shapes, such as in the case of LHP-coated microbeads for lasing.³⁴¹ Arguably, it is most desired to characterize such forms of LHPs intact, without, for instance, scraping the material of the film into a powder. Any such sample preparation is invasive by nature, especially for such soft materials as LHPs. There exist scarce examples of NMR measurements on thin films of LHPs.^192,215,342 Senocrate et al. have investigated the effect of light absorption on MAPbI₃ thin films by illuminating them in situ during the acquisition of NMR signals from MA cations (Figure 11a). They found no apparent difference between dark and illuminated samples, which corroborates the absence of the anticipated translational motion of MA cations.²²³ As discussed previously, the detection of ²⁰⁷Pb NMR LHP signals is time-demanding, and small sample quantities exacerbate the sensitivity issue. The sensitivity-enhancement experiments, however, have showcased the feasibility of the direct acquisition of the ²⁰⁷Pb NMR signal in thin films.²⁶⁵ As for halide nuclei, there have been no reports on NMR (or NQR) nuclear halide signals from LHP thin films. To this end, we would like to emphasize the practical feasibility of halide NQR studies of LHP thin films due to the high sensitivity of ^79/81Br and ¹²⁷I NQR. As an illustration, extrapolating from the ¹²⁷I NQR of the α-FAPbI₃ bulk signal, a thin film with a thickness of 10 nm and an area of 1 cm² (ca. 4 μg) should yield a detectable signal within several minutes (ca. 10 min for S/N > 3). The experimental simplicity and the low costs of the NQR setup as well as its noninvasive nature predispose the NQR for the direct probing of LHPs incorporated within the devices, possibly even in situ during device operation or upon external stimuli (Figure 11b). Most electron- or hole-conducting, metallic, or other layers will not affect the NQR experiment, and integrating simultaneous irradiation or optical spectroscopy is easier to implement compared with NMR spectroscopy. Such direct application of the NQR of devices eliminates the sample-altering manipulations for the removal of perovskite layers from the devices

Figure 11.

Magnetic resonance of LHP thin films and devices. (a) In situ NMR setup and ¹H and ¹³C NMR in situ spectra of a ¹³C-enriched MAPbI₃ thin film at various temperatures under irradiation (light) and under identical conditions in the dark. Adapted with permission from ref (223). Copyright 2018 American Chemical Society. (b) We outline NQR as a highly suitable method for acquiring spectra from LHP optoelectronic devices, including in situ and in operando measurements. “e-layer” and “h-layer” denote electron- and hole-conducting or injecting layer(s), respectively. The device structure may employ electron- and hole-blocking layers. Electrodes are commonly metallic or transparent conductive oxides of a suitable workfunction for injecting electrons and holes. Credit: Yevhen Shynkarenko.

7. Concluding Remarks

LHPs and other metal halides comprise chemical elements, most of which are easily accessible with magnetic resonance methods, and element specificity reduces the interference from other materials present in the sample. Magnetic resonance methods are applicable to crystalline and amorphous materials, including large single crystals, NCs, thin films, and so on. NMR and NQR probe both static and dynamic structural disorder, peculiarities of chemical bonding, and electronic effects. Highly porous materials, surfaces, and interfaces can be discriminatively probed with suitable adaptations of the methods. On top of reduced/disrupted crystallinity, as in LHP NCs and polycrystalline thin films, anomalous distributions and gradients of elements may emerge as well. NC surfaces and surface-bound ligands are structurally distinct regions, too. These effects are all within the reach of NMR and NQR techniques.

The strong quadrupole interaction imparts further potential to probe the material’s structure with accuracies comparable to those of synchrotron X-ray diffraction. For instance, the expansion of the crystal unit cell of CsPbBr₃ by just 0.001 Å produces, according to DFT calculations, a change of tens of kilohertz in the ⁷⁹Br C_Q.³²⁰ The effect on the ¹²⁷I C_Q values will be even more extreme due to the larger quadrupole moment of iodine nuclei (Table 2).

NQR spectra, while containing similar information on the structure and dynamics, can be easier to acquire for nuclei with stronger quadrupole coupling, such as those of halides. NQR also has a very useful practical twist—it does not require high-field magnets. Hence NQR can be more easily adapted for in situ and in operando studies. It does not require special sample preparation or separation from other components (e.g., conducting or protective layers). For instance, ¹⁴N and ³⁵Cl NQR are commonplace for drug, landmine, and explosive detection³⁴³ as well as for chemical quality and quantity control in the pharmaceutical industry.^344−346 In both cases, opening of containers or moving of the sample is either not desired or not possible (too heavy, consecutive degradation, explosion, destruction, etc.), a problem that is also faced with thin-film LHP devices. Hence, NQR spectroscopy has the potential to become a highly sensitive fingerprint quality-control tool for LHP devices or may give unique insight into the LHP material structure in relation to the operation conditions or the device fabrication methods.

Author Contributions

L.P., V.M., and M.K. prepared the manuscript.

The authors declare no competing financial interest.