Local Electronic Structure in γ-LiAlO2 Studied by Single-Crystal 27Al NMR and DFT Calculations

Single-crystal NMR spectroscopy

Single-crystal (SC) NMR spectroscopy is a solid-state NMR method that has been used since the early days of NMR to study the magnitude and orientation of tensorial nuclear spin interactions in solids. This review first presents the field of SC NMR instrumentation, then provides a survey of software for analysis of SC NMR data, and finally it highlights selected applications of SC NMR in various fields of research. The aim of the last part is not to provide a complete review of all SC NMR literature but to provide examples that demonstrate interesting applications of SC NMR.

Local Electronic Structure in AlN Studied by Single-Crystal 27Al and 14N NMR and DFT Calculations

Both the chemical shift and quadrupole coupling tensors for 14N and 27Al in the wurtzite structure of aluminum nitride have been determined to high precision by single-crystal NMR spectroscopy. A homoepitaxially grown AlN single crystal with known morphology was used, which allowed for optical alignment of the crystal on the goniometer axis. From the analysis of the rotation patterns of 14N (I=1) and 27Al (I=5/2), the quadrupolar coupling constants were determined to χ(14N)=(8.19±0.02) kHz, and χ(27Al)=(1.914±0.001) MHz. The chemical shift parameters obtained from the data fit were δiso=−(292.6±0.6) ppm and δΔ=−(1.9±1.1) ppm for 14N, and (after correcting for the second-order quadrupolar shift) δiso=(113.6±0.3) ppm and δΔ=(12.7±0.6) ppm for 27Al. DFT calculations of the NMR parameters for non-optimized crystal geometries of AlN generally did not match the experimental values, whereas optimized geometries came close for 27Al with χ¯calc=(1.791±0.003) MHz, but not for 14N with χ¯calc=−(19.5±3.3) kHz.

Single-crystal 207Pb-NMR of wulfenite, PbMoO4, aided by simultaneous measurement of phosgenite, Pb2Cl2CO3

The effort for determining NMR interaction tensors from orientation-dependent spectra of single crystals may be greatly reduced by exploiting symmetry relations between atoms of the observed nuclide in the unit cell, as is well documented in the literature. In this work, we determined both the full chemical shift (CS) tensor of ²⁰⁷Pb and the unknown orientation of the rotation axis for the natural mineral phosgenite, Pb₂Cl₂CO₃, from a single rotation pattern, i.e. spectra of crystal orientations from 0 to 180°. In the tetragonal crystal structure of phosgenite, four symmetry-related, but magnetically inequivalent ²⁰⁷Pb are generated by the Wyckoff multiplicity. The mineral wulfenite, PbMoO₄, also crystallises in a tetragonal space group, but the site multiplicity for ²⁰⁷Pb generates only one magnetically inequivalent atom, thus not supplying sufficient experimental data to determine CS tensor and axis orientation from an arbitrary number of rotation patterns. One solution to this problem is to simultaneously acquire data of a known compound with high symmetry and Wyckoff multiplicity (here: phosgenite), which supplies additional constraints making the solution of the target compound (here: wulfenite) possible. The ²⁰⁷Pb CS tensors thus determined are characterised by the following eigenvalues in ppm: δ₁₁^PAS=(-2553±1), δ₂₂^PAS=(-1929±1), δ₃₃^PAS=(-1301±1) for phosgenite, and δ₁₁^PAS=(-2074±1), δ₂₂^PAS=(-2074±1), δ₃₃^PAS=(-1898±1) for wulfenite.

NMR interaction tensors of 51V and 207Pb in vanadinite, Pb5(VO4)3Cl, determined from DFT calculations and single-crystal NMR measurements, using only one general rotation axis

Orientation-dependent NMR spectra of a single crystal of the mineral vanadinite, Pb₅(VO₄)₃Cl, were acquired using only one rotation axis with a general orientation in the hexagonal crystal lattice (space group P6₃/m). The chemical shift (CS) tensors for the ²⁰⁷Pb on Wyckoff positions 6h and 4f, and both CS and quadrupole coupling tensor Q for ⁵¹V at the positions 6h were determined by including the NMR response of symmetry-related atoms in the unit cell (and in case of ²⁰⁷Pb at 4f, also the isotropic shift from MAS NMR spectra). This previously suggested 'single rotation method' greatly reduces the necessary amount of data acquisition and analysis. The precise orientation of the rotation axis could not be found by X-ray diffraction experiments because of the high linear absorption coefficient of vanadinite, which is chiefly due to its high lead content. The axis orientation was therefore included into the multi-parameter data fit routine. This NMR-based approach is widely applicable, and offers an alternative way of orienting single crystals. The NMR parameters derived from the tensor eigenvalues are δ_iso=(-1729±9) ppm, Δδ=(-1071±5) ppm, η_CS=0.362±0.008 for ²⁰⁷Pb at positions 6h, and δ_iso=(-1619±2) ppm, Δδ=(-780±58) ppm, η_CS=0.06±0.08 for positions 4f. For ⁵¹V, δ_iso=(-509±3) ppm, Δδ=(-37±2) ppm, η_CS=0.78±0.09, with the quadrupolar coupling described by χ=(2.52±0.01) MHz and η_Q=0.047±0.003. In contrast to the precisely determined tensor eigenvalues, the orientation of the eigenvectors in the crystal ab -plane of the vanadinite system could only be resolved by resorting to data obtained from density functional theory (DFT) calculations.