Introduction

INS spectroscopy is a technique that can be used to study the dynamics of atoms and molecules in the solid state [1]. Neutrons’ penetration depth is of the order of millimeters and passes readily through the walls of metal containment vessels. This makes neutron scattering particularly amenable to complex sample environments, making gas handling and pressure cells relatively straightforward. INS has excellent sensitivity to hydrogen, distinguishing between molecular and atomic hydrogen. Thermal neutrons, with energies below 1000 meV, as is the case of INS, are very gentle; they do not cause radiation damage or heating of the sample in most cases.

INS spectra can also be rigorously calculated from the output of theoretical calculations, like molecular dynamics and lattice dynamics [2, 3]. The modeling includes fundamental and higher-order excitations. In the case of lattice dynamics calculations, the calculated spectra results are rigorous within the harmonic approximation. In the case of molecular dynamics calculations, the software can convert the calculated molecular dynamics trajectories into a simulated spectrum.

The VISION spectrometer is located on beamline 16b (BL 16b) at the Spallation Neutron Source (SNS) in Oak Ridge, Tennessee. VISION is an indirect geometry inelastic neutron scattering spectrometer that boasts the highest flux and resolution for instruments of its kind. VISION also has medium-resolution neutron diffraction capabilities, allowing simultaneous dynamics and structure characterization of materials.

In this paper, we present the basics of the technique and recent examples of the power of INS and the unique capabilities of VISION. The first example is the use of INS and computing modeling applied to structural inference in metal hydrides, as is the case of ZrV\(_2\)H\(_{x}\) with \(x \sim 4\) [4]. The second example is a demonstration and characterization of the facile formation of hydrogen water clathrates in confined nanospace, clearly illustrating the power of the multimodal capabilities of VISION and advanced sample environment, i.e., neutron spectroscopy and diffraction combined with high-pressure hydrogen gas-handling capabilities available at ORNL [5].

INS spectroscopy in a nutshell

The neutron is an elementary particle with no electric charge, with a rest mass close to the proton mass. The neutron displays wave-particle duality; how we treat the neutron as a wave or particle depends on the observed phenomenon. When dealing with incoherent INS, it is convenient to regard it as a particle. However, the scattered neutron is treated theoretically as a spherical wave [1]. When looking at neutron diffraction, or coherent inelastic scattering, the wave properties of neutrons manifest themselves as interference that determines the manner of propagation.

As a spectroscopic technique, INS can study molecular and crystal vibrations in solids. The technique is conceptually similar to Raman and infrared spectroscopies.

During an INS experiment, the intensity in the signal represents the strength of neutron scattering from the sample at a given energy transfer from the neutron to the sample. Because of its mass, the neutron can transfer both energy and momentum to the sample. The spectra obtained from INS spectrometers vary due to the design. In the particular case of the VISION spectrometer, the spectrum is measured at a fixed “trajectory” in energy transfer \(\omega\) and momentum transfer \(\varvec{Q}\). Albeit the spectra look similar to IR and Raman, there are some significant differences.

  • There are no selection rules. In principle, all vibrations are visible

  • The vibrational intensities are proportional to the amplitude on the vibration and the cross section of the elements involved in the vibration

  • In solids, the INS intensity corresponds to the integrated intensity over the first Brillouin zone. As a consequence, line shapes have meaning. Effectively it includes phonon dispersion effects

  • Rigorous calculations of INS spectra are possible from models that determine vibrational frequencies and eigenvectors (also known as displacements [2, 6, 7])

  • Neutrons are a penetrating probe of matter; neutrons can penetrate millimeters of sample material and many centimeters of adequate containment vessels (sample containers)

Figure 1
figure 1

Photo of the VISION secondary spectrometer.

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The VISION spectrometer

VISION is an indirect geometry INS spectrometer; it has the highest flux and resolution for instruments of its kind. VISION is located at 16 m from the coupled water moderator, at room temperature, in beamline 16b [8]. Figure 1 shows a photo of the VISION spectrometer.

A sample in VISION receives a white (polychromatic) beam of pulsed neutrons. The instrument has choppers that allow the operation of the instrument at 30 Hz. After scattering, the neutrons are analyzed by a curved parametric array of pyrolytic graphite crystals (PG 002) of 1 cm\(^2\) each in the secondary spectrometer. The analyzer selects the scattered neutrons that have around 3.55 meV of energy. A Beryllium filter (at 25K) removes higher orders reflections, and the neutrons finally hit a \(^3\)He pixelated detector. The design of the secondary spectrometer is such that each pixel has a well-characterized distance from the sample. By measuring the time of flight (ToF) from the moderator to the detector and subtracting the ToF from the sample to the detector (determined by construction and calibration), it is possible to obtain the initial energy of the neutron; the final energy is known by design and can be calibrated. There are two banks, one in backscattering ( high \(\textbf{Q}\), \(2 \theta = 135^o\)), and the other in forward scattering (low \(\textbf{Q}\), \(2 \theta = 45^o\)).

Figure 2
figure 2

Spectral capabilities of VISION. Top panel) the diffraction capabilities of VISION on the 90 \(^o\) bank on a CuBe alloy sample. Bottom panel left) the quasielastic (QENS) signal from ammonia as measured by VISION (note that the x-axis is linear and the vertical scale is logarithmic. Bottom panel right) the INS spectrum of ammonia (note the energy axis is logarithmic, while the vertical axis is linear).

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VISION measures the vibrational spectrum, from -2 meV to 1000 meV (-16 cm\(^{-1}\) to 4,000 cm\(^{-1}\)). Because it measures over the elastic line, it also measures the quasielastic neutron scattering signal (QENS) along two different trajectories in \(\varvec{Q}\). The QENS signal does not have enough \(\varvec{Q}\) information for detailed analysis, but it can be used to track the mobility of species when doing a temperature scan; for example, see refs. [9, 10].

The instrumental resolution of the VISION is given by \(\Delta \omega / \omega \approx 1.5 \%\) (\(\omega < 2\) meV), while around the elastic line, “QENS resolution,” the resolution is 120 \(\mu\)eV FWHM (-1 meV \(< \omega <\) 2 meV) [7].

The instrument also has two diffraction banks, one in backscattering geometry (\({\textbf {Q}}\) range 1.5–30 Å\(^{-1}\)) and another at 90 \(^o\) (\(\varvec{Q}\) range 1.3–14 Å\(^{-1}\)). The resolution of the diffraction banks is \(\Delta d / d \approx 10^{-2}\).

VISION is a multimodal neutron spectrometer, Fig. 2 shows the diffraction, INS, and QENS capabilities of VISION.

Molecular hydrogen spectral characteristics

In the case of a diatomic molecule, the rotational energy levels in free space are given by \(E_J = J \times (J+1) B_{Rot}\), where J is the rotational quantum number and \(B_{Rot}\) is the rotational constant. \(B_{Rot} = \frac{\hbar ^2}{2 I_{H{-}H}}\). For \(H{-}H\), it has a value of \(B_{Rot} = 14.7\) meV. The rotational wavefunctions are the spherical harmonics [1, 11, 12]. For each value of J, there are \(2 \times J + 1\) possible spin states described by the quantum number \(m = -J, -J+1, 0, J-1, J\).

Figure 3
figure 3

The spectra of hydrogen species in VISION in the -1 to 1000 meV energy transfer range, the insert zooms in the area of interest around the elastic and rotational line of \(p{-}H_2\). Blue trace) almost pure solid \(p{-}H_2\) ( 97%) at 10K. Orange trace) solid \(n{-}H_2\) ( 25% \(p{-}H_2\), 275% \(o{-}H_2\)) at 10K. Green trace) liquid \(p{-}H_2\). Note that the sharp rotational features are no longer present in the liquid. The arrows represent the major transitions observed.

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As a consequence of quantum mechanical restrictions on the symmetry of the rotational wavefunction, there are two species of molecular hydrogen, para-hydrogen (\(p{-}H_2\)) and ortho-hydrogen (\(o{-}H_2\)) [12]. For \(^1\)H, with spin \(\tfrac{1}{2}\) is a fermion. As such, it has to obey Fermi statistics, also called the Pauli principle. For \(^1\)H\(_2\), the even values of \(J = 0, 2, 4, \cdots\) are called para-hydrogen, while the odd values of \(J = 1, 3, 5, \cdots\) are ortho-hydrogen. Di-hydrogen gas at room temperature is a mixture of 25 % para-hydrogen and 75 % ortho-hydrogen. In the case of the gas, there is little to no conversion between species; the hydrogen species are spin trapped. The transition can be induced by adsorbing hydrogen at liquid hydrogen temperatures \(\sim 20K\) onto a paramagnetic material that acts as a catalyst; conversion can be achieved in a few minutes [12].

For pure solid \(p{-}H_2\), the first transition observable appears at 14.7 meV and corresponds to the \(p{-}H_2 \rightarrow o{-}H_2\) usually represented \(J_{0 \rightarrow 1}\). This transition is allowed in INS because the neutron can exchange its spin with one of the atoms in the molecule, consequently converting \(p{-}H_2\) into \(o{-}H_2\) and vice-versa.

Figure 3 shows the spectra of \(p{-}H_2\) and \(n{-}H_2\) in the solid phase; the spectra of liquid \(p{-}H_2\) at 17K are also shown. All spectra are measured in backscattering. In the case of \(o{-}H_2\), the first transition is a phonon that has a maximum around 5 meV, \(\omega _{1 1}\). The phonon has almost no cross section for \(p{-}H_2\) [11]. For \(p{-}H_2\), the first transition is \(J_{0 \rightarrow 1}\), and the second transition is \(J_{0 \rightarrow 1} + \omega _{1 1}\) corresponding to the rotational transition plus the phonon of \(o{-}H_2\). The third observed transition is the \(J_{1 \rightarrow 2}\), with a contribution from \(2 \times J_{0 \rightarrow 1}\).

The hydrogen molecule has a low mass (2 amu); most of the energy transfer is recoil from the molecule. In the case of liquid hydrogen, there is no sharp transition at the rotational energy because all the energy transfer is recoil, Fig. 3. The presence of the rotational line at high \(\varvec{Q}\) can only happen when the hydrogen molecule is immobile. This is the case in solid hydrogen or when hydrogen is strongly adsorbed, under extreme pressures, trapped in a cage, etc. [9, 10].

Formation hydrogen clathrate hydrate in confined nanospace

Clathrate hydrates are formed by water molecules arranged in a 3D hydrogen-bonded network with void spaces or cages that trap gas molecules. Natural clathrates contain methane or carbon dioxide as guest molecules. We found that wet Petroleum Pitch Activated Carbon (PPAC) readily forms synthetic methane hydrates that grow under mild conditions (3.5 MPa and 2 \(^{\circ }\)C), with faster kinetics (within minutes) than nature, it is fully reversible and has a nominal stoichiometry that mimics nature [13].

Figure 4
figure 4

Inelastic neutron scattering for increasing H\(_2\) pressures. (Top panel) Background subtracted INS patterns at 5 K of (a) D2O-PPAC pressurized with hydrogen at 100, 135, and 200 MPa. INS patterns show the appearance of new peaks at hydrogen pressures of 135 MPa and above attributed unambiguously to the formation of hydrogen hydrates. (Bottom panel) INS patterns at 5 K of normal H2 at atmospheric pressure, 180 MPa, and (h) 310 MPa. INS patterns show that solid hydrogen exhibits a characteristic contribution at low energy transfer (ca. 10 meV under high-pressure conditions). Interestingly, the doublet observed for enclathrated hydrogen fits with the signal of solid hydrogen under pressure (circle on top panel) and arrow in the bottom panel.

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Hydrogen molecules (H\(_2\)) can also be the guest molecule in a clathrate. Hydrogen clathrates could be potential hydrogen storage reservoirs with a maximum capacity of ca. 5.0 w% and 4.6 g/L [14].

Hydrogen clathrate has not been found in nature. Previous studies demonstrated that hydrogen clathrate can be synthesized with an SII structure [15] at pressures of 200 MPa. The main obstacles to the formation are i) high pressures are necessary, due to the small kinetic radius of H\(_2\), to form the H\(_2\) clathrate; ii) the nucleation kinetics is very slow due to the limited liquid–gas interface.

Figure 5
figure 5

Neutron diffraction (ND) analysis at increasing nH\(_2\) pressures. All neutron diffraction patterns were obtained at 5 K for the D2O-PPAC pressurized with normal hydrogen at 100, 135, and 200 MPa. Theoretical patterns for hexagonal ice (Ih) and sII structure in gas hydrates are included for comparison. The patterns confirm the formation of hydrogen hydrates with the traditional sII structure at hydrogen pressures of 135 MPa and above.

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By analogy, we studied specially designed activated carbon materials that can surpass these obstacles by acting as nanoreactors promoting the nucleation and growth of hydrogen clathrate hydrates [5]. The confinement effects in the inner cavities promote the massive growth of hydrogen hydrates at moderate temperatures, using pure water, with extremely fast kinetics and much lower pressures than the bulk system.

Using the multimodal capabilities of VISION to operate simultaneously as an INS spectrometer and a neutron diffractometer, it was demonstrated that it is possible to form hydrogen clathrate on wet PPAC at pressures that are 30 % lower, and the reaction takes place in a matter of minutes for samples of the size of a few cc.

A CuBe high-pressure cell, with an internal volume of 4 cc, was used with a manual piston compressor to deliver gas pressure in the range 0–200 MPa [5]. Figure 4 shows the INS of the D\(_2\)O-loaded PPAC at different pressures. The cell is loaded with PPAC, and D\(_2\)O is added to wet the PPAC in the cell. The cell is connected to the gas pressure system.

Initially, the sample is heated to 350K at atmospheric pressure of H\(_2\) gas. Once the temperature is reached, the cell is pressurized with hydrogen (100, 135, 200 MPa), and the system is submitted to a cooling ramp down to 5K. Once the temperature reaches 160K, the sample cell is evacuated to 0.1 MPa. The temperature profile shows that the cooling between 280K and 273K is extremely fast (ca. 5 min), i.e., complete water-to-hydrate formation occurs in less than 10 min.

We observed the formation of hydrogen clathrates at lower pressures than expected. We can see that H\(_2\) is trapped inside the clathrate by the spectroscopic signature, the broad rotational line at 14.7 meV, and the low energy feature around 10 meV, top panel in Fig. 4. This is similar to the results observed in [16]. The nature of the doublet is the rattling mode of the ortho-hydrogen molecule inside the cavity. To quantify the effective pressure of the trapped molecules, we compare it with the bottom panel in Fig. 4. We used the values to estimate the internal pressure of the trapped ortho-hydrogen to be around 140 MPa, which coincides with the pressure necessary to form this clathrate in the first place.

Further, we use the diffraction data from VISION to verify the formed structure. Figure 5 shows the data from VISION diffraction banks. The top panel is the experimental data, while the bottom panel shows the calculated spectra for the sII clathrate and ice 1 h. The combined information allows the unequivocal determination of the formation of a hydrogen clathrate at 1.35 MPa ( around 30% lower than without the PPAC).

Anomalous H–H distances in metal hydrides

The number of hydrogen atoms in a metal hydride depends on the interaction of the hydrogen atoms with the metal and the hydrogen–hydrogen interactions.

Figure 6
figure 6

Top panel) Inelastic neutron scattering at various temperatures as measured by the high-resolution neutron spectrometer VISION. The intensity was corrected by the Bose–Einstein statistics to account for the temperature dependence of the scattering process, and the background signal was subtracted. Top left) ZrV\(_2\)H\(_{2.0}\). Top right) ZrV\(_2\)H\(_{3.7}\). Bottom panel) Configurational energy per 8 formula units of ZrV\(_2\)H\(_{4}\), with hydrogen atoms occupying different sites. The color code visualizes the number of hydrogen atoms with distances around 1.6 Å. If only the \(H_O\) site is occupied (\(x = 0\)), Switendick’s criterion will not be violated and is thus the most stable configuration. The average number of violations increases to one with x = 0.125 and increases further as additional neighboring interstitials with H–H distances around 1.6 Å are found. Figures were redrawn from [4].

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Switendick [17] suggested that the minimum distance between hydrogen atoms in transition metals is 2.1 Å. In \(ZrV_2H_x\), two sites are available for hydrogen atoms, octahedral (\(H_O\)) and tetrahedral (\(H_T\)) sites. Occupancy of neighboring octahedral sites violates the Switendick criterion.

Figure 7
figure 7

Simulated INS spectra for different representative configurations in a supercell containing 8 units cells for Zr\(_8\)V\(_{16}\)H\(_{T_{(32-n)}}\)H\(_{O_{n}}\), for \(n = 0, 1, 2 \dots , 12\). A gap between acoustic and optical phonons is observed at low hydrogen content and reproduced by DFT calculations. The gap happens when there are no occupation of interstices with H–H distances below 2.1 Å. The thick lines (\(n=0, 2\), and 10) show structures that contain no criterion violations after the geometry optimization. There are no vibrational modes in the gap. The thick blue trace shows the spectra for hydrogen atoms only in the tetrahedral site (ZrV\(_2\)H\(_{T_{(4-x)}}\)H\(_{O_{x}}\) for x = 0). The peaks arising in the gap need the consideration of hydrogen violating the Switendick criterion. When \(n>0\), some hydrogen atoms may violate the criterion.

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Inelastic neutron scattering is used as a local probe of the hydrogen interactions combined with electronic structure modeling of a well-studied and prototypical metal hydride ZrV\(_2\)H\(_x\). The results provide evidence for anomalous hydrogen–hydrogen distances as short as 1.6 Å. The findings offer insights into new materials with novel properties, such as very high Tc superconductivity and other quantum behaviors [4].

Density functional theory (DFT) calculations were performed to understand the origin of the low energy peak. The simulated INS spectra of ZrV\(_2\)H\(_2\) match those measured experimentally, including acoustic and optical phonons branches. The calculated peaks are slightly higher in energy for the high energy excitations than the experimental data (few meV). We attribute this to the effects of anharmonicity, which also gives rise to the broadening of the high energy peaks. On the other hand, the agreement breaks down for higher H concentrations. Most notably, no excitations in the spectral region around 50 meV are calculated by DFT if the hydrogen occupation of the interstices is constrained such that no H–H distances are less than 2.1 Å.

The expected gap between acoustic and optical phonons is observed at low hydrogen content and reproduced by DFT calculations omitting the occupation of interstices with H–H distances below 2.1 Å, irrespective of the hydrogen content. At higher hydrogen loading, the peak arising in the gap needs the consideration of hydrogen violating the Switendick criterion.

The Switendick limit arises due to the interaction between the two protons and their associated electrons. Molecular hydrogen has a \(H-H\) distance of 0.74 Å; in this case, the strongly repulsive Coulomb force of the protons is outweighed by the strong covalent interaction. In metal hydrides, the locally increased electron density between H atoms is smaller since electrons from hydrogen distribute among other bonds in the material. Resulting in a minimum possible distance between hydrogen atoms in conventional metal hydrides around 2.1 Å under ambient conditions [18].

To determine the nature of these short H–H distances, we performed a large number of full structure minimizations for 3201, distinct initial configurations of a supercell containing 8 formula units of ZrV\(_2\)H\(_{T_{(4-x)}}\)H\(_{O_x}\) as shown in the bottom panel of Fig. 6. There is one configuration for Zr\(_8\)V\(_{16}\)H\(_{T_{32}}\); while we randomly created 100 different initial configurations for each Zr\(_8\)V\(_{16}\)H\(_{T_{(32-N)}}\)H\(_{O_{N}}\) (\(N=1, \ldots , 32\)). After the structure minimization, we plotted the configurational energy as a function of composition, and we determine the number of H–H violations of the Switendick criterion, i.e., H–H pairs that have interatomic distances around 1.6 Å. In many cases, even when some of the atoms initially have short H–H distances, the relaxed structure accommodates these atoms in positions within the lattice where the distances satisfy the criterion, see Fig. 7. However, after relaxing their position, some atoms are entropically trapped in configurations that violate the criterion. These atoms are responsible for the peak observed at 50 meV. From the results of our calculations, we estimate that the total number of atoms violating the Switendick criterion is of the order of \(\sim 4 \%\) in this material.

The existence of short H–H distances could have implications in a variety of areas. Superconductivity near room temperature has been proposed for dense group metal hydrides [19]. AlH\(_3\) has 2.54 Å H–H distances at ambient pressure that are reduced to 1.54 Å at 110 GPa [20]. LaH\(_{10}\) has comparable H–H distances and is a room temperature at megabar pressures [21, 22]. For more details on the methods and conclusions, see [4].

Conclusion

This paper illustrates the use of INS and VISION to study hydrogen-containing materials. It is essential to highlight that these experiments cannot be effectively done using other, more common techniques.

In the case of ZrV\(_2\)H\(_x\), with \(x>3.7\), we found that the spectroscopic signature is compatible with a short H–H distance in the material. The H–H distance is of the order of the distances necessary for other metal hydrides to facilitate superconductivity at high temperatures. These short distances result from the configurational entropy of the hydrogen atoms in the metal, the H atoms are trapped when the hydrogen gets in and as the system cools down, they remain in these high energy configurations. To achieve that conclusion, it is necessary to run a large number of high-level DFT calculations. The number of hydrogen atoms violating the Switendick criterion is small, of the order of a few percent [4]. This effect is unlikely to be measured with neutron diffraction. Other techniques like X-ray diffraction are unsuitable for finding hydrogen positions in metal hydrides.

The second example shows the use of VISION’s multimodal capabilities to demonstrate the facile formation of hydrogen clathrates at lower temperatures than before. Also, the reaction is proceeding at a fast pace. The low energy peak, which is due to the rattling of the ortho-hydrogen molecule inside the cages is consistent with a molecule trapped at high pressure. The clathrate stability was also studied and is stable up to 240K. The use of high-pressure CuBe cells, with cell walls of 5 mm thickness, means that the system cannot be studied with X-rays.

Methods

Computer modeling of INS spectra

Computer models are part of the toolkit required to interpret and analyze experimental data. Atoms in solids and molecules experience motion around their equilibrium positions, called vibrations. In the case of a crystal, this motion is described as a phonon. It represents the collective motions of the atoms in a crystal at the same frequency.

Using VISION, the sampling of momentum transfer is almost uniform within the first Brillouin zone. One consequence of the effective averaging of the vibrational intensities in the Brillouin zone is that the shape of the spectral features conveys information about the phonon dispersion of the atoms in the material. In this particular case, there are no strong sharp lines in the spectra.

The spectral intensity of INS spectra is also called the scattering law. For an atom i that is vibrating in mode \(\nu\) with frequency \(\omega _{\nu }\), with an amplitude of motion \({}^i\varvec{U}_{\nu }\), the corresponding intensity is

$$\begin{aligned} S \left( \varvec{Q}, \omega _{\nu } \right) ^n_i \propto \sigma _i \frac{(\varvec{Q} \cdot {}^i\varvec{U}_{\nu })^{2n}}{n!} \exp {\left( \left( \varvec{Q} \cdot \sum _{\nu } {}^i \varvec{U}_{\nu } \right) ^2 \right) } \end{aligned}$$
(1)

with \(\sigma _i\) is the cross section of atom i, \(\varvec{Q}\) is the momentum transfer, and n is the order of the final state of the mode. [23]

For the harmonic oscillator, the amplitude of the vibration (also called displacement) is given by

$$\begin{aligned} \left\langle {}^i\varvec{U}_{\nu } \right\rangle ^2 = \frac{\hbar }{2 \mu _{\nu } \omega _{\nu }} \coth { \left( \frac{\hbar \omega _{\nu }}{k_B T}\right) }, \end{aligned}$$
(2)

where \(\mu _{\nu }\) is the reduced mass of the mode, T is the temperature, and \(K_B\) is Boltzmann constant [1].

Equations 1 and 2 are simplified versions of the equations required for a more robust and rigorous calculation of \(S \left( \varvec{Q}, \omega \right)\). In practice, available software can use lattice dynamics calculations and the harmonic approximation to calculate the scattering law more precisely [2, 3, 6, 7, 24,25,26].