Nuclear spin correlations and collective excitations in supercritical H . 2 Raina J. Olsen1,∗ Jon W. Taylor2, Cristian I. Contescu1, and James R. Morris1 1Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA and 2ISIS Spallation Neutron Source, STFC, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom A longstanding challenge in quantum computing is to find qubits that interact strongly with one another, but weakly with their environment to prevent decoherence, properties difficult to find in a single physical implementation.[1] Present technologies use strongly interacting qubits for two-qubit gates, [2, 3] while weakly interacting nuclear spins are useful for one-qubit gates [4] and coherent 6 memory.[5, 6] Nuclear spins are known to experience spontaneous long-range correlations only below 1 2.5 mili-Kelvin in superfluid 3He [7]. Here we present the first evidence of nuclear spin coupling in 0 molecular hydrogen (H ) at 74-92 Kelvin using neutron scattering, showing a fundamental change in 2 2 naturefromtheincoherentscatteringuniversallyexpectedfromhydrogen,whichreflectssingleparticle n properties of uncorrelated nuclear spins [8, 9], to coherent, with a peak materializing on the elastic line a [10, 11] indicating H -H nuclear spin correlations. In this novel phase, the dynamic response of the J 2 2 1 system also changes nature, and collective excitations with an effective mass of nine H2 are observed with inelastic scattering at momentum transfers up to 37 ˚A−1, corresponding to length scales smaller 2 than the H-H bond, where previous experiments have always found single atom excitations [12–19]. ] This novel behavior has only been observed from H2 within the subnanometer sized graphitic pores ci of a carbon material [20], marking the first demonstration that a confined materials environment can s be used to control nuclear spin correlations. As such, these results show that it may be possible to - engineer systems of interacting nuclear spin qubits for error correction and two-qubit gates. l r Figure 1 shows a novel phase change in H observed with inelastic neutron scattering (INS). Figs. 1(a) and 1(b) t 2 m show INS spectra collected at a series of temperatures between 52–96 Kelvin (K) from high pressure H adsorbed in 2 . two different nanoporous carbons: ‘3K’, the name of an activated carbon used here as a control, and ‘HS;0B-3’, a t a locallygraphiticcarbonwithporeshavingsub-nanometerwidths.[20]Materialscharacterizationdataonthesecarbons m are shown in the Extended Data (ED) Fig. 5. 1 - At the highest and lowest temperatures, the dynamic response of the H2 in these two carbon materials is nearly d identical. At any given value of the momentum transfer (Q) from the neutron to the system under study, the peak n energy transfer (¯hω) is equal to the kinetic energy (h¯Q)2/2M of a particle with mass M =1.2 amu, roughly equal to o themassofasinglehydrogenatomM =1.0amu. ThisresultisconsistentwithasystemofuncorrelatedH molecules, c 2 [ and fits to these spectra using an H2 molecular model [8, 14, 15, 17] are shown in the ED Fig. 8 and described in the Supplemental Information (SI). Fluid hydrogen has been extensively studied by INS, and this H recoil has always 1 beenobserved.[12–18]EvenwhentheHatomsarepartofalargermolecule, suchaswater(H O),[21–23]orwhenthe v 2 H forms a solid,[12, 17–19] recoil of single H atoms has always been observed. 1 2 The scattering from H adsorbed in the control sample, ‘3K’, changes only slightly with temperature. But for H 1 2 2 8 in ‘HS;0B-3’, the scattering shows an abrupt change, which occurs solely as a function of changes in temperature, 1 with the novel phase observed between 74–92 K. Two striking changes in the measured spectra are observed. Firstly, 0 the effective recoil mass changes from 1.2 amu to 18.1±0.6 amu. In addition, a new peak at 1.9 ˚A−1 appears on the 2. elastic line, shown in Fig 1(c). The novel elastic peak is large compared to the background elastic scattering in the 0 same range of Q collected from the system before the addition of H2, which includes scattering from the carbon and 6 thealuminumpressurecell. Inaddition, themaximumintensityofthehighmassrecoilis∼5timeslargerinintensity 1 than the background scattering in the same region (see ED Fig. 6 for a direct comparison). : v To understand the thermodynamic boundaries of the observed phase transition, we show scattering intensities as i a function of temperature, pressure, and carbon adsorbent in Figure 2. The high mass recoil and new elastic peak X are always observed together, and only at high H pressure in ‘HS;0B-3’. Their appearance strictly corresponds to 2 r a proportional decrease in the intensity of the ∼1 amu H recoil. In contrast, no high mass recoil or elastic peak is a observedatanytemperaturefromH inthecontrolsample‘3K’orin‘HS;0B-3’atlowpressure. Giventhisobservation 2 of several reversible transitions into and out of the novel phase and the large intensity of the novel features relative tothebackgroundscattering, wecomfortablyassociatetheappearanceofhighmassrecoilandsimultaneousdecrease in H recoil with a change in phase of the H in the system. 2 ∗ [email protected] 1 This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the UnitedStatesGovernmentretainsanon-exclusive,paid-up,irrevocable,world-widelicensetopublishorreproducethepublishedform of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public accesstotheseresultsoffederallysponsoredresearchinaccordancewiththeDOEPublicAccessPlan(http://energy.gov/downloads/doe- public-access-plan). 2 (a) (b) (c) 3K, 186 bar HS;0B, 187 bar 300 200 52 K bg. + H 2 200 100 bg. 100 0 0 200 61 K 200 100 100 0 0 200 78 K Al 200 V)100 H2 100 me 0 0 nsfer (120000 81 K 18.1 amu 200ensity y tra 0 1.2 amu 0100Int g r200 84 K e 200 n E100 100 0 0 200 88 K 200 100 100 0 0 200 96 K 200 100 100 0 0 5 10 15 20 5 10 15 20 1.52.02.5 Momentum transfer (Å−1) FIG. 1. Inelastic neutron scattering from adsorbed H showing a phase change as a function of sample and temperature. (a) 2 H adsorbed in control sample ‘3K’ at a nominal pressure of 186 bar. The background scattering from the system with no 2 H has been subtracted. (b) H adsorbed in sample of interest ‘HS;0B-3’ at a nominal pressure of 187 bar with background 2 2 subtracted. All spectra in panels (a) and (b) are shown using the same intensity color scale. (c) Data from the elastic line for H in ‘HS;0B-3’ summed over h¯ω=±10 meV, without background subtraction, shown in comparison to the background. 2 Observation of a strong elastic neutron scattering peak from a system of H is unprecedented because hydrogen 2 is a strong incoherent scatterer, with a ratio of incoherent to coherent scattering of σ /σ = 45.7, and so produces I C featurelessscatteringontheelasticline. Theexpectationoffeaturelessscatteringcanbederivedfromtheassumption that the measured incoherent scattering, S (Q(cid:126),ω), is equal to the time-dependent Fourier transform of the single I particle density correlation function, S (Q(cid:126),t)=(cid:104)eiQ(cid:126)·(cid:126)rˆje−iQ(cid:126)·(cid:126)rˆj(t)(cid:105), (1) I where(cid:126)rˆ (t) is the position operator of atom j at time t and (cid:104)...(cid:105) represents the thermal average. From Eq. 1, one j can derive the zeroth moment and first moment sum rules,[9, 24] (cid:90) ∞ S (Q(cid:126),ω)dω =1, (2) I −∞ (cid:90) ∞ ¯hQ2 S (Q(cid:126),ω)ωdω = , (3) I 2M −∞ The zeroth moment sum rule originates from the fact that Eq. 1 is a density self-correlation function and the particle must always be somewhere, and is an exact prediction of a featureless elastic line. The first moment sum rule means thattheaverageenergytransferisgivenbythekineticenergyofasingleatomatthegivenmomentumtransfer. Both of these rules are followed here in the normal phase of H , as well as in all previous neutron scattering studies of H 2 2 [12–19]. 3 (a) 1 ) s 0.5nit u H recoil b. (b) 0 ar 1 ( high M y recoil sit 0.5n e nt 0 ed i (c) 0.6z elastic ali peak 0.4m r o 0.2N 0 50 60 70 80 90 100 Temperature (K) FIG. 2. Intensity of inelastic neutron scattering spectra within different ranges of Q, ¯hω from adsorbed H as a function 2 of temperature, pressure, and carbon adsorbent. (a) Intensity of 1 amu hydrogen recoil, summed from h¯ω=14.3–58.8 meV, Q=2.5–6.8˚A−1. (b)Intensityofhighmassrecoil,fromh¯ω=14.3–73.7meV,Q=18.0–23.5˚A−1. (c)Areaundertheelasticpeak thatappearswiththehighmassrecoil,obtainedbyfittingalinearbackgroundplusaGuassiantotheelasticscattering. Data inpanels(a)and(b)arenormalizedtothesummedintensityofHrecoilatP=187barandT=52K,anderrorbarsareshown, butaresmallerthansymbolsizes. Legend: H in‘HS;0B-3’atP=187bar: Red (cid:50),P=123bar: Magenta ,P=30bar: Orange 2 (cid:51), and H2 in ‘3K’ at P=187 bar: Black +. (cid:35) But Eq. 1 is an approximation. The measured scattering is actually the Fourier transform of the nuclear spin pair correlation function, [9] SI(Q(cid:126),t)=(cid:88)i(i+1 1)(cid:104)eiQ(cid:126)·(cid:126)rˆj(cid:126)Iˆj ·(cid:126)Iˆj(cid:48)(t)e−iQ(cid:126)·(cid:126)rˆj(cid:48)(t)(cid:105), (4) j,j(cid:48) where(cid:126)Iˆis the nuclear spin operator. In most system nuclear spins of different atoms in the system are uncorrelated, in which case (cid:104)(cid:126)Iˆ(cid:126)Iˆ (t)(cid:105)=i(i+1)δ and Eq. 4 reduces to Eq. 1. j j(cid:48) jj(cid:48) It’s so rare for systems to have correlated nuclear spins, that S (Q(cid:126),ω) is simply called incoherent scattering, rather I thannuclearspindependentscattering. Butthestrongelasticpeakandhigheffectivemassoftheinelasticexcitations found in the present work defy both the zeroth and first moment sum rules in Eqs. 2–3, and thus indicate that the system must have some type of magnetic order with correlated nuclear spins in the novel phase. Since nuclear spins interact very weakly, the only other systems in which long-range correlated nuclear spins have been observed as they are here with ‘incoherent’ or spin-dependent elastic neutron scattering are those in which nuclear spin ordering is driven by a magnetic field through a hyperfine interaction with the electronic degrees of freedom at mili-Kelvin temperatures.[10, 11] It is well known that short-range nuclear spin correlations occur between the two identical H atoms in an H 2 molecule as a result of exchange symmetry. [8, 9] This results in two distinct forms of hydrogen: para-H with a net 2 nuclear spin S = 0, and ortho-H with a net nuclear spin S = 1. But the observed elastic peak is at Q∼1.9 ˚A−1, 2 corresponding to a spacing of 3.3 ˚A, a separation at which the H -H potential is strongly attractive,[25] and much 2 2 larger than the H–H bond distance of 0.71 ˚A. Thus the results indicate that there are H -H nuclear spin correlations 2 2 in the novel phase. While the momentum resolution of this experiment is not ideal, the resolution corrected width of the elastic peak is consistent with a correlation length of ∼35 ˚A, larger than the correlation length of ∼11 ˚A in bulk H ,[26] thus indicating that the spin correlations are not simply short-range. 2 Normally a phase transition that occurs as the temperature is lowered indicates passage of the system to a more ordered state, and we expect this order to persist as the temperature is lowered further. If the higher temperature bound of the observed phase at 92 K is associated with magnetic order of the H nuclear spins, then why do we see 2 this order dissapear at 74 K? While nuclear spins interact weakly, the net H spin is coupled to its orbital angular momentum, which has a 2 large energy dependence. Because the H protons are fermions and the wavefunction of identical fermions must be antisymmetric under exchange of the particles, the aligned proton spins of ortho-H must be combined with a 2 4 (a) −1 ) Å ( + = 0 on siti o 1 P −1 0 1 −1 0 1−1 0 1 Position (Å) (b) 300 ) V e m 200( r e sf n 100a r y t g r 0 e n E 5 10 15 Momentum transfer (Å−1) FIG.3. Understandingtheobservationof∼1amuHrecoilinDINSspectrafrom2amuH . (a)Cartoondepictingtheobserved 2 transitions. A combination of rotational motion of the molecule and translational motion of the center of mass results, on average, in a rolling type motion in which one H atom moves rapidly while the other is nearly fixed. The spins of the atoms, depictedbyredarrows,stayfixed. (b)RepresentativespectrumfromadsorbedH . AthinrecoillinewithM=2amuisplotted 2 for each observable rotational transition extending from the energy of the transition. Recoil lines are shown only in the region wheretherotationalformfactorFH2(Q)forthegiventransitionissignificant. AthickrecoillinewithM=1.2amurepresents JJ(cid:48) the sum result. wavefunction which is antisymmetric in space, J = 1,3,..., while anti-aligned spins of para-H must be combined 2 with a wavefunction which is symmetric in space, J =0,2,..., where J is the quantum number of the orbital angular momentum describing the orientation of the molecular axis. The J = 1 ortho state is 171 K above the J = 0 para state. Atroomtemperature,bulkequilibriumH is∼75%ortho,butpassesfrommostlyorthotomostlyparaat∼77 2 K,whichisquiteclosetothelowertemperatureboundoftheobservedphasetransitionat74K.Thuswehypothesize that the observed magnetic order occurs only in ortho-H with S = 1, and this magnetic ordering is broken by the 2 increasing concentration of para-H with S =0 as the temperature is lowered. 2 At the temperatures of this experiment, ortho-H occupies only the lowest J = 1 rotational state, with the J = 3 2 state at 1026 K. There are a total of 9 accessible states of ortho-H with J = 1,S = 1 , corresponding to the 2 combinations of nuclear spin states S =−1,0,1 and angular momentum states J =−1,0,1, where z is an arbitrary z z projection axis. Thus with antiferromagnetic ordering in a system of ortho-H we might expect formation of a nonet 2 (a group of 9) with a net spin S = 0. This interpretation is consistent with the observed recoil mass of 18.1 amu, which is equal to the mass of 9 H molecules. 2 We must emphasize that the observed transition in recoil mass cannot simply be explained by formation of any ∼18.1 amu H containing molecule, as the recoil mass derived in Eq. 3 is associated with nuclear mass rather than molecular mass. H recoil with mass ∼ 1 amu is observed in fluid[12–18] and solid H [12, 17–19] (molecular mass 2.0 2 amu) and even in H O[21–23] (molecular mass 18.0 amu). Given that the binding energies of these molecules, ∼5 2 eV, are much larger than the neutron incident energy used here, 400 meV, it is perhaps surprising that recoil of the H atom is observed. This occurs because the neutron tends to excite both rotational and translational excitations of the molecule at the same time. A given rotational excitation corresponding to a change in rotational velocity ∆v r is likely to be observed only at certain values of Q according to the form factor (or scattering probability) FH2(Q), JJ(cid:48) at which a given translational motion with a change in the velocity ∆v is also likely to be excited. On average, cm ∆v ∼∆v , with the net result a type of rolling motion in which only one atom is excited, as depicted in Figure 3. r cm Here, we observed M =1.2 amu, but M →1.0 as the neutron incident energy increases. This picture of a rolling motion in which only one atom is excited is valid only under the assumption that the H 2 spin, rotational, and translational degrees of freedom can be treated independently (except with the condition that J = 2n+S where n is an integer, as noted above), an assumption which is used to calculate the exact scattering probabilities FH2(Q) [8]. The highly novel collective recoil observed with a completely different FH2(Q) here means JJ(cid:48) JJ(cid:48) that the spin degrees of freedom must be coupled to the rotational and translational degrees of freedom in some way, as is depicted in Fig. 4(b). Until a quantitative theory is developed for this system this is all that can be definitively 5 (a) ) V e 600m ( r e 400sf n a r 200y t g r e 0 n E 5 10 15 20 25 30 35 Momentum transfer (Å−1) (b) −1 ) Å ( n 0 o siti o P 1 −2 −1 0 1 2 Position (Å) FIG. 4. Interpretation of the observed 18.1 amu recoil. (a) Spectrum collected in the novel phase with an incident neutron energy of 1000 meV. (b) Cartoon depicting two ortho-H molecules in a state in which their spins, orientations, and positions 2 arecoupledwithoneanother. Thespinsoftheatomsaredepictedbyredarrows,anddependontheorientationofthemolecular axis. concluded from the observation of high mass recoil. Butaqualitativeanalysismayofferinsightintopossibleexplanationsfortheobservedbehavior. AsshowninFigure 4(a), the high mass recoil persists as high as Q=37 ˚A−1. Because this corresponds to a length scale much smaller than the distance between atoms, the semi-classical impulse approximation normally applies, in which the neutron interacts over such small length and time scales that only one atom is excited over a short distance and the other atoms do not have time to respond to its change in motion. Observation of collective excitations in this regime seems to be consistent with the presence of long-range correlations in position, in which the motions of atoms in the system that are far apart are directly correlated and respond immediately. Longrangevelocitycorrelationsareafeatureofsuperfluidity,butthetemperaturesatwhichweobservedthisnovel phaseareanorderofmagnitudelargerthaninanyknownsuperfluid. Wehavepreviouslypredictedhightemperature superfluidityinasystemoflightstronglyinteractingspinlessparticles(4He, para-H )confinedinaperiodicpotential 2 with a lattice spacing equal to the interparticle spacing at which the intermolecular interaction is strongly attractive, consistentwiththe3.3˚Aspacingmeasuredhere.[27]Porescomposedoftwoparallellayersofgraphenewitha0.8–0.9 nm spacing provide the necessary environment, materials properties which are consistent with those of the sample of interest used in the present study. In superfluid 3He, in which the fermionic atoms forming a Cooper pair have ferromagnetically ordered nuclear spins, collective pair excitations with coupled spin and translational motion have beenpredicted[28]andobserved.[29,30]ThusthecorrelatednuclearspinsandcollectiverecoilwithamassofnineH , 2 consistent with antiferromagnetic ordering of the bosonic nuclear spins of ortho- H , observed here are qualitatively 2 consistent with known phenomena in superfluids. 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ExperimentsattheISISPulsedNeutronandMuonSourceweresupportedbyabeamtime allocation from the Science and Technology Facilities Council. Samples were provided by the ALL-CRAFT group at the University of Missouri. X-ray research was conducted at the Center for Nanophase Materials Sciences and microscopy research was conducted at the Oak Ridge National Laboratorys SHaRE User Facility, both of which are DOE-BESUserFacilities. JRMacknowledgessupportfromDOEsOfficeofScience, BasicEnergySciences, Materials Science and Engineering. The authors thank M. B. Stone and G. Siopsis for discussion. 8 I. METHODS Experiments were conducted using H adsorbed in powdered nanoporous carbons: ‘HS;0B-3,’ a carbon synthesized 2 by the pyrolysis of Saran (PVDC)[20] in which the high mass recoil is observed, and a material called ‘3K,’ a KOH activated carbon used here as a control. In general, Saran carbons are classified as non-graphitizable isotropic carbons,[31]meaningthatthereis,onaverage,nopreferreddirectionforgrapheneplanestolieandthecarbondonot become graphitic on heating to 2000 ◦C. Graphitic is defined as having the XRD lines of three-dimensional graphite. Published pore size distributions of ’HS;0B-#’ variants [20, 32] (where # refers to different batches synthesized by the same method[20]) have shown that the samples have a narrow distribution of pores under 1 nm in width while ‘3K’ has a broad range of pore sizes with an average size over 1 nm. Further characterization data are shown in the Extended Data (ED) Fig. 5. X-ray diffraction spectra were collected from powdered samples using Cu K-α X-rays. MicroscopyimageswerecollectedusinganaberrationcorrectedJEOL2200FS200keVscanningtransmission electron microscope. Pore size distributions were calculated from CO isotherms and N isotherms measured with 2 2 a Quantachrome Autosorb-1 instrument.[33] The TEM image in Fig 5(c) show regions where graphene stacks into nanoscale regions of graphite, resulting in the broad 002 graphite peak observed in the XRD spectrum in Fig. 5(a). But the other XRD lines of three-dimensional graphite are not observed, thus we refer to the ‘HS;0B’ as ‘locally graphitic,’ though it is a non-graphitizable carbon. We have previously shown inelastic neutron scattering data from H in variants of the same samples [32] at low 2 incident neutron energies, 30 meV and 90 meV, and at lower temperatures and pressures, T=23 K and P<50 mbar. The present measurements were conducted using similar methods for sample outgassing to remove oxygen and water, loading of carbon samples into cylindrical aluminum sample cans under 4He atmosphere with quartz wool between carbon powders and seals, loading of the sample can into the instrument and in situ leak checking with helium, flushing of helium and addition of hydrogen, and data collection. Here we describe in detail only methods that differ significantly, which primarily involve the different thermodynamic conditions. Neutron measurements were performed using the MARI spectrometer at the ISIS Neutron Source. Except where noted, the incident neutron energy was 400 meV. After outgassing and cooling, background spectra from the can+carbon+wool were collected at T = 15, 84, and 101 K. The volumes in the system consisted of 1.7 cc (cm3) in the sample can at the measurement T, 3.2 cc of capillary line with a gradient between T and room temperature, and 72 cc at room temperature where pressure was continually monitored with an accuracy of ±1 bar. After background measurements, the system was pressurized by connecting the system to a gas cylinder containing high purity room temperature normal-H (an equilibrium mixture of para-H and ortho-H ) at P>200 bar with the sample cell at 2 2 2 T=101 K, then the system was isolated from the gas cylinder and the sample cooled to 52 K. Reductions of pressure were conducted by venting the system to atmosphere for P >1.2, and to a vacuum system for P <1.2. As spectra were collected, the temperature was varied between T=52–101 K with a constant amount of H in 2 the system. We report here the pressure of these isochores at T=101 K as the nominal pressure. The system was allowed to equilibrate for 1.5 hours after addition of H , and 0.5 hours after temperature changes before spectra were 2 collected. Data was collected for approximately 2 hours at each T, P. The temporal order of the collected spectra was: ‘HS;0B-3’background,‘HS;0B-3’atnominalH pressuresof187barthen30barthen123bar,‘3K’background, 2 then ‘3K’ at 186 bar, always from low to high T when P>0. Given this temporal ordering, this means that we observed two transitions from a normal phase of H to the novel high mass recoil phase, and one transition in the 2 other direction, with all these transitions observed to occur solely in response to changes in the temperature of the sample T. Both transitions to the novel phase were observed within the same T range, but at quite different P, and the second transition into the novel phase was observed after 29 hours in the normal phase. After the second set of measurements in the novel phase, the sample was changed to the control ‘3K’, in which only the normal phase was observed. The pressure of the room temperature volume rose with temperature between every data point, and the final pressure at T=101 K after measurements was within ±2 bar of the loading pressure, thus there is no evidence of a leak in the system. This equilibriation with the room temperature volume also means that the amount of hydrogen in the sample can decreased slightly as its temperature increased. Besides the oxygen (M=16.0 amu) in the quartz wool, no significant amount of any element with a mass near 18.1 amu, including fluorine (M=19.0 amu) or neon (M=20.2 amu), was known to be present during synthesis[20] or preparation of the samples, or in the instrument vicinity. The sample mounting stick in the instrument was not adjusted during measurements, nor do we have any reasontosuspectthatnormaloperationoftheinstrumentwouldresultinsignificantmotionofthesampleintoorout of the beam. For each spectrum collected from the system containing hydrogen, the background spectrum collected at the closest temperature was used for background subtraction. Analysis of high Q aluminum Bragg peaks was used to estimate self-shielding factors f used for background subtraction. A minimum value of f =0.81 was found in the normal phase at P=187 bar and T=52 K, and a minimum of f =0.66 was found in the novel high mass recoil phase at P=187 bar and T=75 K. 9 II. EXTENDED DATA (a) MWCNT 3K HS;0B−4 (b) 10 e g)) 0.12 3K sity s) 5 al por3m/(A 0.08 HS;0B−3 ennit 0 nti (c XRD int(arb. u 105 Differe volume 0.04 0 0 10 20 30 40 50 5 10 15 20 25 30 35 2θ Pore width (Å) (c) (d) FIG.5. Materialscharacteristicsofcarbonadsorbents. (a)PowderX-raydiffractionspectrafromsampleofinterest,‘HS;0B-4’ and control ‘3K’, as well as a sample of multi-walled carbon nanotubes (MWCNTs). The MWCNTs and ‘HS;0B-4’ both show the002peakofgraphite. (b)PoresizedistributionscalculatedfromCO andN adsorptionisotherms. (c)BrightfieldSTEM 2 2 image of ‘HS;0B-2’, showing graphite in the material. Large pores formed where graphene layers split apart can be seen. (d) Dark field STEM image of ‘HS;0B-2’, showing a flakey grain of the material lying on the sample grid. 10 (a) (b) ) V e m 200 ( r e sf 100 n a y tr 0 g er 5 10 15 20 25 5 10 15 20 25 En Momentum transfer (Å−1) )300 Q=13.1−25.3 Å−1 H in HS;0B−4, 84 K (c) s 2 unit200 HS;0B−4 bg, 84 K b. ar100 ( y nsit 0 e −100 −50 0 50 100 150 200 250 300 nt Energy transfer (meV) I FIG. 6. Inelastic neutron scattering data (a) from H in HS;0B after background subtraction, shown in comparison to (b) the 2 backgroundscatteringfromthecarbon+samplecan+quartzwool,showingfreerecoilofthealuminum(M =26.98amu). Both spectra are shown with the same intensity color scale. (c) Sum over Q=13.1–25.3 ˚A−1 for the same spectra shown in panels (a)and(b). NotonlyisthescatteringfromthenovelphaseofH largerinintensitythanthebackground,butitalsopeaksat 2 a higher energy, corresponding to a smaller mass than the aluminum. 250 200 ) s nit u b. 150 new peak, area 889 r a ( y sit 100 n e nt I 50 bg., area 834 0 1.4 1.6 1.8 2 2.2 2.4 −1 Momentum transfer (Å ) FIG.7. DatafromtheelasticlineforH in‘HS;0B-3’summedoverh¯ω=±10meVatT =61K,P =187bar,withbackground 2 subtraction, shown in comparison to the background. Areas under the background and the novel elastic peak are shown, with the latter obtained by fitting a linear background plus a Guassian to the elastic scattering with the area under the Gaussian given.