Improving Resolution of Solid State NMR in Dense Molecular Hydrogen

TL;DR

This paper demonstrates the first application of homo-nuclear Lee-Goldburg decoupling in solid state NMR at pressures above 100 GPa, significantly improving spectral resolution in dense molecular hydrogen.

Contribution

It introduces a novel NMR decoupling technique under extreme conditions and employs Lenz lens resonators for homogeneous B1 fields in tiny sample cavities.

Findings

Achieved 1600-fold narrowing of 1H resonance line-widths

Demonstrated effective decoupling at pressures over 100 GPa

Used Lenz lens resonators for homogeneous excitation

Abstract

Recent advancements in radio-frequency resonator designs have led to the implementation of nuclear magnetic resonance in diamond anvil cells (DACs) at pressures well above 100 GPa. However, a relatively low resolution and the absence of decoupling sequences complicate the analysis of the results of solid state NMR in DACs. Here, we present the first application of homo-nuclear Lee-Goldburg (LG) decoupling at extreme conditions on high density molecular hydrogen. Lenz lens based two-dimensional resonator structures were found to generate a homogeneous B1 field across sample cavities as small as 12 picolitres, a prerequisite for optimal decoupling. At ideal LG conditions, the broad 1H resonance of molecular ortho-hydrogen was narrowed 1600-fold, resulting in line-widths of 3.1 ppm.

Full text

After the first prediction of a metallic phase under high compression by Wigner and HuntingtonWigner and Huntington (1935), and an estimation of the superconducting properties at room temperature by AshcroftAshcroft (1968), H2 became an archetypical test system in modern high pressure scienceMao and Hemley (1994). In 2017, experimentalDias and Silvera (2016) observations (although heavily disputedEremets and Drozdov (2017); Liu et al. (2017); Goncharov and Struzhkin (2017) suggested the transformation of hydrogen into a metallic state at around 500 GPa. Recent IR spectroscopic resultsLoubeyre et al. (2019) indicate a band gap closure at a pressure of 425 GPa, which may be interpreted as the onset of metallisation.

Molecular hydrogen remains an elusive “quantum solid”Van Kranendonk (1983) in high pressure research. Owing to the lack of core electrons, hydrogen nuclei are practically invisible to X-ray diffraction methodsStojilovic (2012). The equation of state of solid hydrogen was, however, determined up to 1 Mbar following three sets of diffraction peaks (100, 002 and 101)Loubeyre et al. (1996). Other structural probes, such as neutron diffraction, cannotbe applied at the necessary pressures in excess of 100 GPaBoehler et al. (2013), and complementary spectroscopic methods such as IR or Raman provide only limited information on the atomic or molecular arrangements of dense hydrogenMazin et al. (1997).

Nuclear Magnetic Resonance spectroscopy (NMR) is an alternative to the techniques mentioned above, and is widely regarded as one of the most versatile spectroscopic methods, probing local magnetic fields of single nuclei or whole molecular building blocks within inorganic compounds. A reason for the wide applicability of NMR lies in the development of Average-Hamiltonian-TheoryBrinkmann (2016) and subsequent decoupling pulse sequencesMehring and Waugh (1972); Vinogradov et al. (2001) as well as mechanical rotation methodsLowe (1959); ANDREW et al. (1958), leading to resonance line narrowing from formerly several hundred or thousands of ppm to often sub-ppm resolutionHennel and Klinowski (2005). While such high resolution techniques find widespread use in the fields of biochemistry, chemistry, or soft-matter physics, an application within diamond anvil cell research has never been pursued.

Recent developments of high pressure NMR techniques, using three-dimensional microcoilsMeier (2018a) or two-dimensional Lenz-lens based resonatorsMeier et al. (2017, 2018a, 2018b), enabled the detection of faint nuclear induction signals at pressures well into the megabar (1 Mbar = 100 GPa) regime with record pressures of up to 202 GPa, as reported recentlyMeier et al. (2019). Most of these high pressure NMR experiments have been focused on 1H nucleiMeier (2018b), owing to the large gyromagnetic ratio of protons, and subsequently high signal-to-noise ratiosLevitt (2000). At such pressures, a plethora of exotic physical phenomena can be observed, such as the elusive hydrogen-bond symmetrisation from ice VII to ice X governed by quantum-mechanical tunneling of protons within the H-bondsMeier et al. (2018a), or pressure induced hydrogen-hydrogen interactions in metal hydrides as a precursor of high temperature superconductivityMeier et al. (2019).

Monserrat et al.Monserrat et al. (2019) pointed out that NMR might be the only method available in diamond anvil cell based research to directly probe the atomic arrangement of hydrogen atoms at high densities. Using ab-initio calculations, theoretical 1H-NMR spectra at megabar pressures have been calculated, showing a surprisingly large dispersion of chemical shielding values, yielding the possibility to distinguish between theoretical high pressure phases of dense hydrogen.However, an attempt to identify crystallographic phases of H2 seemed unreasonable, as 1H-NMR linewidths in excess of $10^{3}$ ppm for ortho-hydrogen have been reported under cryogenic temperaturesHardy and Berlinsky (1973); Berlinsky and Hardy (1973); Washburn et al. (1983); Pedroni et al. (1976). Under decreasing H-H distances, this effect would certainly be more pronounced in high density phases of H2.

Here we present the first application of homo-nuclear Lee-Goldburg decouplingLee and Goldburg (1965) of molecular ortho-hydrogen in diamond anvil cells at pressures between 20 and 64 GPa.

Two DACs with 100 $\mu$m and 250 $\mu$m culeted diamonds have been prepared. Rhenium gaskets were pre-indented to about 15 and 25 $\mu$m thickness and the central hole has been laser drilled into the centre of the flat indented area, forming the sample cavity. Subsequently, the diamonds have been coated with a layer of 1 $\mu$m copper, and the rhenium gaskets with a 500 nm layer of electrically insulating Al2O3. Two dimensional Lenz lens NMR resonators have been cut out of the copper layers using focused ion beam milling.

All excitation coils were manufactured from 100 $\mu$m PTFE insulated copper wire, each consisting of 5 turns, and fixed around the diamond anvils. After loading, both coils were combined to form a Helmholtz-like excitation coil, providing a homogeneous inductive coupling into the respective Lenz lenses. Figure 1 shows three photographs of the set-up used: BX90Kantor et al. (2012) pressure cell mounted on a home-built NMR probe in the region of highest homogeneity of an ESR magnet (a); photograph of the inside of the DAC with both copper coated diamonds, the sealing rhenium gasket, as well as the Helmholtz excitation coil (b) and an SEM photograph of a prepared triple stage Lenz lens on the surface of a 100 $\mu$m culeted diamond.

Pressure cells were loaded with molecular hydrogen at the European Synchrotron Radiation Facility. Pressure was increased under cryogenic conditions by submerging the cells into liquid nitrogen, and Raman spectra were recorded at room temperature after every pressure increase, see figure 2. The pressure induced shift of the recorded vibron spectra at about 4250 cm*-1* are in accordance with previous studiesSharma et al. (1980); Hemley and Mao (1988).

All NMR experiments have been conducted at an external magnetic field of about 1063 mT, corresponding to a proton resonance frequency of 45.26 MHz. Chemical shift referencing has been performed, using a water sample as a reference standard in a BX90 pressure cell prepared in the same way as the hydrogen loaded cells.

Performing 1H-NMR nutation experiments at an average pulse power of 8 W has shown optimal 90*∘* pulse lengths of about 0.4 to 0.5 $\mu$s, corresponding to RF fields of $B_{1}=\pi/(2\gamma_{n}t_{\pi/2})=$ 11 to 15 mT. Supplementary figure 1 shows numerical simulations, using the $FEMM$ software package, of the B1 field distribution across a 40 $\mu$m x 15 $\mu$m sample cavity used when 100 $\mu$m culeted anvils are used. An average value of $\braket{B_{1}}=17mT$ (green iso-lines in supplementary figure 1) was found, in excellent agreement with the nutation experiments. Considering a standard deviation of about $\sigma$ = 3 mT (red isolines in supplementary figure 1), it was found that approximately 80 % of the sample volume lies within $\braket{B_{1}}\pm\sigma$. Thus, an effective volume $V_{eff}$, which is subject to a homogeneous $B_{1}$ field of $V_{eff}=0.8\cdot V_{0}$, has been defined.

According to the equation of state of molecular hydrogen in phase I, the molar volume at 20 GPa is 5.25 cm${}^{3}/mol$Loubeyre et al. (1996). Therefore, an upper limit of a total amount of 3 nmol of hydrogen loaded in the sample cavities could be estimated, corresponding to 1.7 $\cdot$ 1015 H2 molecules. Considering a normalised time domain signal-to-noise ratio of 8.8 and a limiting bandwidth of 1 MHz, a limit-of-detectionMeier et al. (2017) of 2$\cdot$1011 spins/Hz1/2 has been found.

Performing standard single pulse experiments, an intense and rapidly decaying 1H signal was detected, at the respective Larmor frequency of protons at 1063 mT, figure 3a. Fourier transform results in a dipolar broadened resonance spectrum of about 5000 ppm line width, figure 3b. Using inversion recovery experiments, spin lattice relaxation times between 15 to 21 ms have been found, in accordance with other NMR studies of Phase I of H2 at cryogenic temperaturesHardy and Berlinsky (1973); Washburn et al. (1983); Pedroni et al. (1976).

Lee-Goldburg decoupling experiments have been conducted at varying offset frequencies in steps of 10 kHz around the centre of gravity of the broad hydrogen spectrum shown in figure 3b. Figure 4 demonstrates the dependence of the linewidth after a Fourier transform of the free induction decay in the rotating frame (FIDRF). As can be seen, a resonance line-width minimum is observed at about foff = 20 kHz. In these first experiments, the saturating Lee-Goldburg pulses were incremented from initially 1 µs in steps of 500 ns for 8000 increments, resulting in a rotating frame time domain of 4 ms.

Figure 3a also shows the resulting FIDRF at 20 GPa. The free induction decay is stretched by a factor proportional to $|\lambda_{0}(\Theta)|^{-1}=|\frac{1}{2}(3cos^{2}\Theta-1|^{-1}$ where $\Theta$ denotes the angle between the direction of the irradiated LG-field and the external magnetic field B0 acting on the high pressure chamber. Comparison of the $1/e$ decay times, 900 ns for the FID (blue line in figure 3a) and about 2 ms for the FIDRF (orange trace in figure 3a) suggests an elongation of the FID by a factor of about 2000 and thus $|\frac{1}{2}(3cos^{2}\Theta-1|^{-1}\approx 4.5\cdot 10^{-4}$ or $\Theta=54.717^{\circ}$, close to the magic angle.

As the FIDRF is not fully decayed within the predefined time frame of 4 ms, the minimal line-width of its Fourier transform can be estimated to be $FWHM\approx 1/(4ms)=250~{}Hz\equiv 5.5~{}ppm$. Experimentally, we find a line width of about 6.4 ppm. By increasing the time scale of the LG-pulse to 16 ms (8000 increments in 2 $\mu$s steps), the FIDRF has been found to be almost completely decayed within the time frame of the LG-pulse, resulting in a spectral resolution of 3.1 ppm (see yellow spectrum in figure 3b).

Figure 5 shows a summary of the FWHM line widths of 1H-NMR spectra of molecular ortho-hydrogen in a pressure range of 20 to 64 GPa, after standard single pulse excitation and LG-decoupling. In almost all cases, line widths of about 3 to 5 ppm could be realised.

All resonance spectra were found to be almost fully represented by a Lorenzian line shape without any detectable signs of chemical shift anisotropy, evidencing the suitability of this approach for a purely dipolar broadened spin-1/2 systems. An interpretation of the chemical shift dependencies at increasing densities will be published elsewhere.

The aim of this study was to elucidate the possibility to achieve high spectral resolutions in diamond anvil cell based NMR. It was found that even one of the most basic homo-nuclear decoupling experiments, i.e. Lee-Goldburg irradiation, can be utilised to achieve resolutions as low as 3 ppm. While this value might still be considered too high when compared to magic angle spinning techniques, it represents a major improvement in spectral resolution in diamond anvil cells at extreme conditions.

The found resolution of 3 ppm may be improved in future experiments by extending the time domain in the rotating frame, or by achieving a higher SNR per increment by using a higher number of accumulations.

The applicability of homo-nuclear Lee-Goldburg decoupling is particularly powerful in systems governed by direct dipole-dipole interactions, such as H2, which are almost completely averaged out during the LG-experiments leaving only isotropic chemical shift interactions present. These results open the way for experiments at even higher pressures, and may eventually resolve the predicted structural models of Phases II and III of hydrogenFreiman and Crespo (2017).

I Acknowledgements

The authors thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG, projects DU 954/11-1, DU 393/13-1, DU 393/9-2, and ME 5206/3-1) and the Federal Ministry of Education and Research, Germany (BMBF, grant no. 05K19WC1) for financial support.

II Supplementary