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 "title": "Solid-state NMR spectroscopy",
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 "excerpt": "Solid-state NMR spectroscopy applies nuclear magnetic resonance to solid samples, determining chemical structure, three-dimensional structure, and dynamics at the atomic level, reporting on local atomic environments.",
 "snippet": "Solid-state NMR spectroscopy applies nuclear magnetic resonance to solid samples, determining chemical structure, three-dimensional structure, and dynamics at the atomic level, reporting on local atomic environments.",
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 "markdown": "# Solid-state NMR spectroscopy\n\nSolid-state NMR spectroscopy applies nuclear magnetic resonance to solid samples to determine their chemical structure, three-dimensional structure, and dynamics at the atomic level. It reports on local atomic environments rather than on the long-range order that diffraction methods require.<sup>[1](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)</sup><sup> • </sup><sup>[2](https://journals.iucr.org/m/issues/2017/04/00/lt5004/)</sup>\n\n| Key fact | Value |\n|---|---|\n| What it determines | Chemical structure, 3D structure, and dynamics of solids and semi-solids at the atomic level<sup>[1](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)</sup> |\n| Magic angle | \\( \\arccos(1/\\sqrt{3}) = 54.7356^{\\circ} \\) from the static field \\( B_{0} \\)<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup> |\n| Typical MAS rates and rotors | 5–100 kHz typical; ultrafast MAS reaches about 200 kHz at the laboratory level, with commercial CPMAS probes up to 160 kHz using 0.4 mm rotors<sup>[1](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)</sup> |\n| Cross-polarization gain | Up to a factor of 4 for ¹³C and 5 for ²⁹Si from protons; natural abundances 1% and 5%<sup>[4](https://www.mdpi.com/2673-6497/2/2/9)</sup> |\n| ¹H and ¹³C shift ranges | ~20 ppm for ¹H in diamagnetic solids versus ~200 ppm for ¹³C; static ¹H dipolar linewidths reach tens of kHz<sup>[5](https://www.sciencedirect.com/science/article/abs/pii/S0926204011001202)</sup> |\n| DNP sensitivity boost | Factors of 10 to 10⁴ from transferring electron polarization to nuclei<sup>[6](https://www.annualreviews.org/content/journals/10.1146/annurev-matsci-081720-085634)</sup> |\n\n## How it works\n\nIn a solid, molecules do not tumble, so anisotropic interactions that average to zero in solution NMR survive and broaden the lines. The chemical shift is a tensor with principal components \\( \\delta_{11} \\ge \\delta_{22} \\ge \\delta_{33} \\); in solution, molecular tumbling reduces the observed shift to the isotropic value, while in a powder the observed shift depends on each crystallite's orientation.<sup>[4](https://www.mdpi.com/2673-6497/2/2/9)</sup> Direct through-space dipolar couplings and, for nuclei with spin greater than 1/2, quadrupolar interactions add further broadening.\n\nMagic-angle spinning (MAS) removes most of this broadening mechanically. The anisotropic Hamiltonian contains a spatial factor proportional to \\( 3\\cos^{2}\\theta - 1 \\), which vanishes when the sample spins about an axis at 54.7° to the field; the anisotropic part then averages to zero while the isotropic shift is retained.<sup>[7](http://www.solidstatenmr.org.uk/lectures_files/pdfs/EssentialTechniques.pdf)</sup> Rapid rotation at this angle averages the first-order anisotropic parts of the chemical-shift and dipolar interactions, and the first-order quadrupolar interaction, leaving isotropic shifts and J couplings as in fluids; second-order quadrupolar effects remain in the central transition, and the removed anisotropy reappears as spinning sidebands spaced at the rotation frequency \\( \\nu_{\\mathrm{R}} \\).<sup>[8](https://royalsocietypublishing.org/doi/10.1098/rsta.1981.0032)</sup>\n\nQuadrupolar broadening is the main exception. More than 70% of stable nuclides are quadrupolar, so this interaction dominates many solid spectra.<sup>[2](https://journals.iucr.org/m/issues/2017/04/00/lt5004/)</sup> MAS removes quadrupolar broadening only to first order, and can reduce the central-transition width by only about a factor of three, which motivates the dedicated two-dimensional experiments described below.<sup>[9](https://www.sciencedirect.com/science/article/abs/pii/S0926204097000271)</sup><sup> • </sup><sup>[1](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)</sup>\n\n## How it is done\n\nPowder samples are packed in rotors, typically made of zirconia or silicon nitride, with outer diameters from 2.5 to 14.0 mm; two separate gas streams, bearing gas to support the sample and drive gas to spin it, set the rotation.<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup> High-resolution spectra of dilute spin-1/2 nuclei combine three techniques: cross-polarization (CP) from abundant spins, MAS, and high-power heteronuclear decoupling.<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup>\n\nCP lets dilute spins borrow magnetization from protons, with a theoretical enhancement of \\( \\gamma_{I}/\\gamma_{S} \\), the ratio of magnetogyric ratios; setting it up requires satisfying the Hartmann–Hahn match condition, in which the nutation rates of the two coupled spins are equal.<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup><sup> • </sup><sup>[10](http://xuv.scs.illinois.edu/chem540/GroupProjects/Piehl_Torres_SourcePaper.pdf)</sup> CP also shortens recycle delays to the proton \\( T_{1} \\).<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup> During detection, ¹H decoupling fields of at least 60–100 kHz are applied, with sequences such as TPPM and its derivatives SPINAL, XiX, and SW-TPPM being the methods of choice in contemporary MAS experiments.<sup>[3](https://www.pascal-man.com/book/practical.pdf)</sup><sup> • </sup><sup>[11](https://pmc.ncbi.nlm.nih.gov/articles/PMC12117474/)</sup>\n\n## Origin\n\nRotating a solid sample for NMR was first demonstrated by E. R. Andrew, A. Bradbury, and R. G. Eades, who reported spectra from a crystal rotated at high speed in Nature in 1958<sup>[13](https://preview-www.nature.com/articles/1821659a0)</sup>, and I. J. Lowe independently reported free induction decays of rotating solids in [Physical Review Letters](https://www.edgepedia.org/physical-review-letters) in 1959.<sup>[12](https://doi.org/10.1103/physrevlett.2.285)</sup> The theory of NMR in rotating solids, which underlies the interpretation of MAS spectra and sidebands, was published by M. Matti Maricq and J. S. Waugh in 1979.<sup>[14](https://doi.org/10.1063/1.437915)</sup> High-resolution ¹³C spectra of solid glassy polymers, an early demonstration of CP combined with MAS, were reported by Jacob Schaefer, E. O. Stejskal, and R. Buchdahl in Macromolecules in 1975<sup>[15](https://doi.org/10.1021/ma60045a010)</sup>; such work was enabled by the combination of dipolar decoupling, cross-polarization, and magic-angle rotation.<sup>[16](https://onlinelibrary.wiley.com/doi/10.1002/anie.198814681)</sup>\n\n## Variants\n\nMethods for improving resolution of quadrupolar spectra form a family. A double-rotor experiment averaging second-order quadrupolar effects was reported by A. Samoson, E. Lippmaa, and A. Pines in 1988, and double-angle spinning with a time-dependent spinner axis angle by A. Llor and J. Virlet, also in 1988.<sup>[17](https://doi.org/10.1016/0009-2614%2888%2987362-7)</sup> Multiple-quantum MAS (MQMAS) was introduced by Ales Medek, John S. Harwood, and [Lucio Frydman](https://www.edgepedia.org/lucio-frydman) in 1995 as a two-dimensional method for quadrupolar nuclei in solids.<sup>[18](https://doi.org/10.1021/ja00156a015)</sup> A quantitative MQMAS scheme followed from Gang Wu, David Rovnyak, and [Robert G. Griffin](https://www.edgepedia.org/robert-g-griffin) in 1996<sup>[19](https://doi.org/10.1021/ja9614676)</sup>, and a review of the method by Amir Goldbourt and P. K. Madhu appeared in 2004.<sup>[20](https://doi.org/10.1016/s0066-4103%2804%2954003-6)</sup> The satellite-transition MAS (STMAS) experiment was reported by Sharon E. Ashbrook and Stephen Wimperis in 2004.<sup>[21](https://doi.org/10.1016/j.pnmrs.2004.04.002)</sup> MQMAS resolves inequivalent sites, separates isotropic chemical from quadrupolar shifts, and yields each site's quadrupolar coupling parameters.<sup>[22](https://nationalmaglab.org/library/publications/NHMFL_Publication-6905.pdf)</sup>\n\nDipolar recoupling experiments deliberately reintroduce couplings under MAS to measure distances and connectivities; named methods include rotational resonance, RFDR, REDOR, TEDOR, PDSD, and DARR.<sup>[11](https://pmc.ncbi.nlm.nih.gov/articles/PMC12117474/)</sup> TOSS suppresses spinning sidebands with five timed π pulses synchronized with the rotor, though its centerband is not quantitative.<sup>[7](http://www.solidstatenmr.org.uk/lectures_files/pdfs/EssentialTechniques.pdf)</sup>\n\n**²⁹Si MAS NMR** deserves special mention for silicates, zeolites, and glasses. ²⁹Si is spin-1/2, so its spectra are intrinsically better resolved than those of quadrupolar nuclei such as ²⁷Al; distinct ²⁹Si shift ranges for different silicate structural units were observed, as noted in the later [American Mineralogist](https://www.edgepedia.org/american-mineralogist) study, with silicon deshielded as the number of attached Si–O–Si bridging oxygens decreases.<sup>[23](http://www.minsocam.org/ammin/AM70/AM70_332.pdf)</sup> The Q(n) notation counts bridging oxygens per SiO₄ tetrahedron, n = 0–4. In CaSiO₃ glass, a 2D ²⁹Si experiment correlating isotropic MAS with anisotropic line shapes resolved and quantified all five Q(n) species even though the 1D MAS spectrum was completely unresolved.<sup>[24](https://pubs.acs.org/doi/full/10.1021/jp9700342)</sup>\n\n## Applications\n\nIn zeolites and catalysts, symmetry-based ²⁹Si dipolar recoupling MAS NMR probing distance-dependent interactions between naturally abundant ²⁹Si nuclei was applied to three-dimensional zeolite framework structures by Darren H. Brouwer and colleagues in 2004<sup>[25](https://doi.org/10.1021/ja043228l)</sup>; combining such NMR data with powder XRD yielded structural models for purely siliceous zeolites, and zeolite ITQ-4 was solved from PXRD plus a single ²⁹Si double-quantum correlation spectrum.<sup>[26](https://doi.org/10.1021/ja052306h)</sup><sup> • </sup><sup>[2](https://journals.iucr.org/m/issues/2017/04/00/lt5004/)</sup>\n\nIn energy storage, solid-state NMR tracks decomposition products, electrode and electrolyte changes, and capacity fade over charge–discharge cycles using nuclei such as ⁶,⁷Li, ²³Na, ¹⁹F, and ¹H, and in situ NMR with imaging visualizes lithium-front displacement inside electrodes during operation.<sup>[27](https://www.technologynetworks.com/tn/articles/solid-state-nmr-finds-its-place-in-energy-storage-research-understanding-paramagnetic-materials-408250)</sup> DNP-enhanced ¹³C [CPMAS](https://www.edgepedia.org/cross-polarization-magic-angle-spinning) has been used to characterize the solid electrolyte interphase in batteries, and battery cells have been assembled inside the NMR rotor for in situ MAS measurements.<sup>[6](https://www.annualreviews.org/content/journals/10.1146/annurev-matsci-081720-085634)</sup><sup> • </sup><sup>[28](https://weizmann.elsevierpure.com/ws/files/111307144/ml_Solid-State-Nuclear-Magnetic-Resonance_Dynamic-Nuclear_AM_2022.pdf)</sup> Ultra-fast MAS above 100 kHz enables site-specific assignments in complex paramagnetic solids, including air-sensitive Fe(II) catalysts and mixed Fe²⁺/Mn²⁺/Mg²⁺ olivine-type cathode materials.<sup>[29](https://pmc.ncbi.nlm.nih.gov/articles/PMC11701365/)</sup> The same rate regime has transformed biomolecular solid-state NMR, where protein structure determination requires typically at least 10 spatial restraints per residue from recoupling experiments.<sup>[29](https://pmc.ncbi.nlm.nih.gov/articles/PMC11701365/)</sup><sup> • </sup><sup>[11](https://pmc.ncbi.nlm.nih.gov/articles/PMC12117474/)</sup>\n\n## Limitations and alternatives\n\nSensitivity is the principal constraint for rare nuclei at natural abundance. CP helps but is nonuniform in heterogeneous samples, for example preferentially enhancing surface siloxane groups in MCM-41 silica, so CP spectra must be interpreted critically.<sup>[4](https://www.mdpi.com/2673-6497/2/2/9)</sup> Quadrupolar second-order broadening persists under MAS and requires MQMAS or STMAS.<sup>[1](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)</sup><sup> • </sup><sup>[21](https://doi.org/10.1016/j.pnmrs.2004.04.002)</sup> Rotor design trades sample volume against speed: a 1.3 mm rotor reaches about 67 kHz and a 0.7 mm rotor about 110 kHz, with linear velocity held near 250 m/s; solution-like ¹H spectra of rigid solids require spinning faster than ¹H–¹H dipolar couplings, about 70 kHz at least.<sup>[30](https://pmc.ncbi.nlm.nih.gov/articles/PMC10319395/)</sup> Distance measurements from dipolar couplings are quantitative only for isolated spin pairs, and NMR, as a short-range technique, gives no direct evidence for unit-cell size.<sup>[31](https://www.degruyter.com/document/doi/10.1524/9783486992540-007/pdf?licenseType=free)</sup>\n\nAgainst these limits stand real strengths. In one zeolite study, REDOR and variable-contact-time CP gave a true Si–F distance of about 1.75 Å where XRD indicated an overlong ~1.9 Å.<sup>[31](https://www.degruyter.com/document/doi/10.1524/9783486992540-007/pdf?licenseType=free)</sup> Solid-state NMR and powder XRD are complementary: NMR contributes phase purity, disorder, tautomeric form, and intermolecular interactions, and NMR shifts calculated by periodic DFT (GIPAW) can validate powder-XRD structures.<sup>[32](https://www.mdpi.com/2073-4352/12/9/1277)</sup>\n\nRecent developments attack sensitivity and resolution together. DNP transfers polarization from unpaired electrons via microwave irradiation; the prevalent materials formulation uses about 16 mM TEKPol biradicals in tetrachloroethane at typically 100 K, with gains up to four orders of magnitude for surface layers<sup>[28](https://weizmann.elsevierpure.com/ws/files/111307144/ml_Solid-State-Nuclear-Magnetic-Resonance_Dynamic-Nuclear_AM_2022.pdf)</sup>, and rational design of dinitroxide polarizing agents continues, with a 2024 study by Amrit Venkatesh and colleagues.<sup>[33](https://doi.org/10.1002/anie.202317337)</sup> Reduced-field instruments around 200 MHz are increasingly used for paramagnetic battery materials, where lower fields reduce broadening<sup>[27](https://www.technologynetworks.com/tn/articles/solid-state-nmr-finds-its-place-in-energy-storage-research-understanding-paramagnetic-materials-408250)</sup>, and small coils in ultrafast probes generate RF fields of about 500 kHz and above.<sup>[30](https://pmc.ncbi.nlm.nih.gov/articles/PMC10319395/)</sup>\n\n## References\n\n1. [Solid-state NMR spectroscopy (Reif, Ashbrook, Emsley, Hong, Nature Reviews Methods Primers, 2021)](https://portal.fis.tum.de/en/publications/solid-state-nmr-spectroscopy/)\n2. [NMR crystallography: structure and properties of materials from solid-state NMR observables (IUCrJ)](https://journals.iucr.org/m/issues/2017/04/00/lt5004/)\n3. [Practical Aspects of Modern Routine Solid-State Multinuclear Magnetic Resonance Spectroscopy: One-Dimensional Experiments](https://www.pascal-man.com/book/practical.pdf)\n4. [Solid State NMR for Nonexperts: An Overview of Simple but General Practical Methods (Solids/Magnetochemistry, MDPI)](https://www.mdpi.com/2673-6497/2/2/9)\n5. [Applications of high-resolution 1H solid-state NMR (Solid State Nuclear Magnetic Resonance)](https://www.sciencedirect.com/science/article/abs/pii/S0926204011001202)\n6. [Dynamic Nuclear Polarization Solid-State NMR Spectroscopy for Materials Research (Annual Review of Materials Research)](https://www.annualreviews.org/content/journals/10.1146/annurev-matsci-081720-085634)\n7. [Essential Techniques in Solid-state NMR (UK solid-state NMR facility lecture notes)](http://www.solidstatenmr.org.uk/lectures_files/pdfs/EssentialTechniques.pdf)\n8. [Magic angle spinning in solid state n.m.r. spectroscopy (E. R. Andrew, Phil. Trans. R. Soc. A, 1981)](https://royalsocietypublishing.org/doi/10.1098/rsta.1981.0032)\n9. [Triple, quintuple and higher order multiple quantum MAS NMR of quadrupolar nuclei (Amoureux & Fernández, Solid State Nucl. Magn. Reson.)](https://www.sciencedirect.com/science/article/abs/pii/S0926204097000271)\n10. [Tutorial on analytic theory for cross-polarization in solid state NMR (Concepts Magn. Reson. Part A, 2008)](http://xuv.scs.illinois.edu/chem540/GroupProjects/Piehl_Torres_SourcePaper.pdf)\n11. [Dipolar Recoupling in Rotating Solids](https://pmc.ncbi.nlm.nih.gov/articles/PMC12117474/)\n12. [I. J. Lowe (1959). Free Induction Decays of Rotating Solids. Physical Review Letters.](https://doi.org/10.1103/physrevlett.2.285)\n13. [Nuclear Magnetic Resonance Spectra from a Crystal rotated at High Speed | Nature](https://preview-www.nature.com/articles/1821659a0)\n14. [M.Matti Maricq, J. S. Waugh (1979). NMR in rotating solids. The Journal of Chemical Physics.](https://doi.org/10.1063/1.437915)\n15. [Jacob Schaefer, E. O. Stejskal, R. Buchdahl (1975). High-Resolution Carbon-13 Nuclear Magnetic Resonance Study of Some Solid, Glassy Polymers. Macromolecules.](https://doi.org/10.1021/ma60045a010)\n16. [High-Resolution Solid-State 13C-NMR Spectroscopy of Polymers (Voelkel, Angew. Chem. Int. Ed., 1988)](https://onlinelibrary.wiley.com/doi/10.1002/anie.198814681)\n17. [Towards high-resolution NMR of more nuclei in solids: Sample spinning with time-dependent spinner axis angle (Chemical Physics Letters, 1988)](https://doi.org/10.1016/0009-2614%2888%2987362-7)\n18. [Ales Medek, John S. Harwood, Lucio Frydman (1995). Multiple-Quantum Magic-Angle Spinning NMR: A New Method for the Study of Quadrupolar Nuclei in Solids. Journal of the American Chemical Society.](https://doi.org/10.1021/ja00156a015)\n19. [Gang Wu, David Rovnyak, Robert G. Griffin (1996). Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids. Journal of the American Chemical Society.](https://doi.org/10.1021/ja9614676)\n20. [Multiple-Quantum Magic-Angle Spinning: High-Resolution Solid-State NMR of Half-Integer Spin Quadrupolar Nuclei (Annual reports on NMR spectroscopy, 2004)](https://doi.org/10.1016/s0066-4103%2804%2954003-6)\n21. [Sharon E. Ashbrook, Stephen Wimperis (2004). High-resolution NMR of quadrupolar nuclei in solids: the satellite-transition magic angle spinning (STMAS) experiment. Progress in Nuclear Magnetic Resonance Spectroscopy.](https://doi.org/10.1016/j.pnmrs.2004.04.002)\n22. [Multiple-Quantum Magic-Angle Spinning NMR: A New Technique for Probing Quadrupolar Nuclei in Solids (National MagLab, Frydman group)](https://nationalmaglab.org/library/publications/NHMFL_Publication-6905.pdf)\n23. [High-resolution 29Si NMR study of silicate and aluminosilicate glasses: the effect of network-modifying cations (American Mineralogist, 1985)](http://www.minsocam.org/ammin/AM70/AM70_332.pdf)\n24. [Anionic Species Determination in CaSiO3 Glass Using Two-Dimensional 29Si NMR (J. Phys. Chem. B)](https://pubs.acs.org/doi/full/10.1021/jp9700342)\n25. [Darren H. Brouwer and colleagues (2004). Symmetry-Based 29Si Dipolar Recoupling Magic Angle Spinning NMR Spectroscopy: A New Method for Investigating Three-Dimensional Structures of Zeolite Frameworks. Journal of the American Chemical Society.](https://doi.org/10.1021/ja043228l)\n26. [A Solid-State NMR Method for Solution of Zeolite Crystal Structures (Brouwer, Darton, Morris, Levitt, JACS 2005)](https://doi.org/10.1021/ja052306h)\n27. [Solid-State NMR Finds Its Place in Energy Storage Research: Understanding Paramagnetic Materials (Technology Networks)](https://www.technologynetworks.com/tn/articles/solid-state-nmr-finds-its-place-in-energy-storage-research-understanding-paramagnetic-materials-408250)\n28. [Dynamic Nuclear Polarization in battery materials (Solid-State Nuclear Magnetic Resonance, repository copy)](https://weizmann.elsevierpure.com/ws/files/111307144/ml_Solid-State-Nuclear-Magnetic-Resonance_Dynamic-Nuclear_AM_2022.pdf)\n29. [Resolving Structures of Paramagnetic Systems by Solid-State NMR: The Revolving Power of Ultra-Fast MAS](https://pmc.ncbi.nlm.nih.gov/articles/PMC11701365/)\n30. [Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications (Chemical Reviews; PMC)](https://pmc.ncbi.nlm.nih.gov/articles/PMC10319395/)\n31. [The complementary use of solid state NMR and powder diffraction for structure determination (Z. Kristallogr. Suppl. 26, 2007)](https://www.degruyter.com/document/doi/10.1524/9783486992540-007/pdf?licenseType=free)\n32. [NMR Crystallography as a Vital Tool in Assisting Crystal Structure Determination from Powder XRD Data (Crystals, 2022)](https://www.mdpi.com/2073-4352/12/9/1277)\n33. [Amrit Venkatesh and colleagues (2024). Rational Design of Dinitroxide Polarizing Agents for Dynamic Nuclear Polarization to Enhance Overall NMR Sensitivity. Angewandte Chemie International Edition.](https://doi.org/10.1002/anie.202317337)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Chemistry › Chemical principles and methods › Analytical chemistry › Nuclear magnetic resonance spectroscopy*\n\n*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Sep 30, 2026 · Last review: Sep 30, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n",
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 "speakable": "Solid-state NMR spectroscopy applies nuclear magnetic resonance to solid samples, determining chemical structure, three-dimensional structure, and dynamics at the atomic level, reporting on local atomic environments."
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