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[Taku T. Suzuki](https://orcid.org/0000-0001-6041-4297), [Soshi Iimura](https://orcid.org/0000-0003-3270-155X)

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[Quench-condensed hydrogen films studied by cryogenic time-of-flight secondary ion mass spectrometry](https://mdr.nims.go.jp/datasets/6bcb9970-3af3-4b82-a170-bb8cfb8d483f)

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Quench-condensed hydrogen films studied by cryogenic ToF-SIMSTaku T. Suzuki∗ and Soshi IimuraNational Institute for Materials Science,1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan(Dated: August 2, 2024)AbstractSurface melting of solidified hydrogen has attracted attention in the field of superfluidity, but theexistence of surface melting of solid hydrogen itself is still controversial. In the present study, wedeveloped cryogenic time-of-flight secondary mass spectrometry (ToF-SIMS) capable of detectingsurface melting by selectively analyzing hydrogen on the outermost surface. Combined with low-energy ion scattering for well-defined film growth, we successfully investigated the surface structuraltransition of the quenched condensed hydrogen film grown on polycrystalline tungsten substratebelow the triple point. It was found that the ToF-SIMS intensity variation of H+ ions by increasingthe temperature of the solid hydrogen film at a constant ramp rate (temperature-programmed ToF-SIMS) shows two prominent features: the increase accompanied by sublimation and the decreasedue to the elimination of the hydrogen admolecule from the tungsten surface. Both features are wellexplained by the desorption of hydrogen molecules from the solid hydrogen surface. We observedno evidence of surface melting.PACS numbers:∗Corresponding author. E-mail: suzuki.taku@nims.go.jp1I. INTRODUCTIONCryogenic solid hydrogen has attracted attention due to its technological importance inthe storage and transportation of hydrogen as a clean energy source. It has been also animportant substance as a target in various experiments, such as nuclear reactions and laser-ion acceleration.Another interesting topic related to cryogenic solid hydrogen is the surface melting (or pre-melting, surface supercooling, etc) of solid hydrogen in the field of superfluidity. Since thefirst theoretical suggestion by Ginzburg and Sobyanin [1], a number of theoretical studieshave repeatedly pointed out the possible superfluid behavior of para H2 (pH2) like heliumthat is the only substance showing macroscopic superfluidity [2, 3, 5–11]. These predic-tions essentially arise from the quantum nature of pH2 with light mass and bosonic groundstate (J = 0 ). From the Bose condensation temperature of an ideal Bose gas given by3.31~2n2/3/kBmg2/3, the appearance of the superfluidity is naively expected at a highertemperature for pH2 than 4He, where kB is Boltzmann’s constant, m is the atomic mass,n is the number density, and g is the degeneracy of each single-particle state of a definitemomentum [1, 2]. The Bose temperature of pH2 is calculated to be about 6 K, which ishigher than the superfluid transition temperature of 4He (2.2 K).However, pH2 solidifies at a triple point temperature of 13.8 K, well above the predictedsuperfluid transition temperature, due to the stronger intermolecular attraction than he-lium based on the Van der Walls force. Therefore, the suppression of the intermolecularinteraction has been considered as a crucial factor for realizing superfluid pH2. The secondmacroscopic superfluidity following helium, if realized, should provide a deeper understand-ing of the quantum nature of matter; therefore, the control of intermolecular interaction ofhydrogen has been challenged by many researchers.The intermolecular interaction is often weakened at a surface due to the breaking of the bondat the terminated plane. The surface melting is a consequence of this intrinsic instability ofthe surface, which has been observed on various surfaces [12–14]. However, the appearanceof the surface melting seems to be still controversial for solid hydrogen as follows.2Several years ago, Makiuchi et al. claimed that anomalous diffusion appeared only at the topsurface of a solid hydrogen thin film grown on a glass substrate, which was further suggestedto be indicative of a superfluid state [15]. Before Makiuchi et al., there are also a number ofstudies suggesting the surface melting or similar phenomena of solid hydrogen. For exam-ple, it has been reported that the melting temperature is substantially lower than the triplepoint in a two-dimensional system of pH2 grown on a Li substrate [16]. The lower meltingtemperature of the surface than the bulk has also been reported for H2 clusters [17, 18] anda solid H2 film [19–22]. However, a more recent theoretical study by Boninsegni has claimedthat there is no evidence that the top layer of a pH2 film remains liquid [23]. Furthermore,experimental studies using surface plasmon resonance have reported that the surface moltenlayer of solid hydrogen does not exist [24].The striking contradiction between literature concerning the surface melting of solid hydro-gen may be partly due to the absence of analysis using a technique that is sensitive both to atopmost surface and hydrogen. A few available experimental data have been obtained usinghydrogen-sensitive techniques, such as neutron scattering, for powder samples to enhancethe surface volume ratio [22]. However, the melting of hydrogen in those powder experimentsmight be affected by the confinement effect [25].Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a well-established techniquefor selective analysis of surface hydrogen. Since the emitted secondary ion yield depends onthe density of the target molecules on the surface of which it is composed, surface meltingcan be detected from the intensity change of ToF-SIMS because the density of the targetmolecule generally changes significantly with the phase transition. Thus, the secondary ionyield drops with surface melting as the sample temperature is gradually increased if the melt-ing occurs (temperature-programmed ToF-SIMS). This technique has been demonstrated tobe useful for detecting the surface melting on various surfaces including ionic liquids [26].The ToF-SIMS intensity I is generally dependent on the surface density of the precursor ionCj asI = IpSKjηCj, (1)3where Ip the primary ion beam current, S the sputtering yield, Kj the ionization rate, andη the instrumental function. Assuming these parameters are constant except for Cj beforeand after the structural phase transition, the ToF-SIMS intensity drops at a phase transitionfrom solid to liquid because of the decrease of the constituent molecules density, that is Cjduring the phase transition. In other words, the ToF-SIMS intensity should decrease if themelting occurs, which has been confirmed for various samples including ionic liquids [26].To the best of our knowledge, this technique has not been applied to a solid hydrogen surface.A much lower temperature is required to solidify hydrogen compared to ionic liquids, andthis will be a challenge for ToF-SIMS analysis. The cryogenic technique combined withToF-SIMS is not trivial, because ToF-SIMS requires the incidence and exit of an ion beamfor measurements through apertures on the radiation shield, which remarkably reduces thecooling capability of the cryostat.It is noted that it has been reported that the hydrogen molecules on solid hydrogen surfacesare highly mobile even at much lower temperatures than the triple point. [15, 19] This hasbeen discussed in terms of surface diffusion of the hydrogen molecules with the activationenergy being substantially smaller than the thermal activation energy of a vacancy in thebulk solid hydrogen. These mobile hydrogen molecules on the surface are not necessarilyrelated to surface melting because the hydrogen molecules may move by hopping.There are also reports from previous studies concerning the annealing effect of a solid H2 film,which may closely related to the topic in the present study. It has been revealed that theelectrical conductivity of a quench condensed-H2 film increases by two orders of magnitudeby the increase of the temperature from 2 K to 4.2 K. [27–29] This observation has beendiscussed in terms of the surface roughness. It has been discussed that the annealing effectmay be caused by mobile uppermost surface layers.In the investigation regarding the surface melting of solid hydrogen, it is important tosolidify hydrogen on a clean substrate surface. This is especially the case for an ultra-thinfilm because the interaction of the adsorbed hydrogen with the underlying substrate surfacelargely affects the nature of the thin film. In fact, it has been indicated that the superfluid4properties of pH2 are influenced by impurities or intended dopants [3, 30]. Unfortunately,ToF-SIMS is not suitable for confirming the clean surface due to the lack of quantitationcaused by the matrix effect. For this reason, we combined ToF-SIMS with low-energy ionscattering spectroscopy (LEIS) in the present study. The area of the aperture placed at theradiation shield of the cryostat for entry and exit of the ion beam was minimized by sharingthe incident ion beam as well as the detector between ToF-SIMS and LEIS. This enabledsuccessful ToF-SIMS measurements on the surface of hydrogen films solidified by quenchcondensation.II. EXPERIMENTAL AND THEORETICAL METHODSExperiments were performed in an ultra-high vacuum (UHV) analysis chamber (7×10−9Pa) configured for home-built ToF-SIMS and LEIS. ToF-SIMS and LEIS shared the ionsource of electron impact type (ULVAC, FIG-5) as well as the detector that is an electro-static hemispherical energy analyzer (VSW, CL50), as shown in Fig. 1. A schematic drawingof the entire UHV chamber and evacuation system is shown in Fig. S1 [4]. Incident ionbeam was 2 keV He+ ion with the diameter of approximately 2 mm at the sample positionin both ToF-SIMS and LEIS. The ion beam was continuous in LEIS while it was pulsedin ToF-SIMS by the pulsed electric field, with a pulse width of 500 ns and a duty ratio of1.5%. The pulse signal for chopping and the output signal from the energy analyzer wererespectively used as a start and a stop signal of a time-to-digital converter (TDC) (FASTComTec, P7888) for obtaining ToF spectra. In ToF-SIMS, we set the pass energy and theanalysis energy of the energy analyzer to 90 eV and 10 eV, respectively. Thus, the secondaryions measured in ToF-SIMS have a kinetic energy of 10 eV, which, which were acceleratedto 90 eV inside the energy analyzer. The flight length corresponds to the distance betweenthe deflector for the ion beam chopping placed in the incident beam line and the detectorof the energy analyzer. In our ToF-SIMS measurement, the beam fluence was less than 1012ion·cm−2 that is the typical condition for static SIMS. In both ToF-SIMS and LEIS, the in-cident angle of the primary ion beam and the exit angle of the secondary ions measured fromthe surface normal of the sample were both 45◦. The hydrogen partial pressure in the UHVchamber during ToF-SIMS measurements was analyzed by quadrupole mass spectrometer(QMS, Pfeiffer Vacuum, Prisma).5We exposed a clean polycrystalline tungsten foil of thickness 0.1 mm (purity: 99.95%, Nilaco,Japan) cooled below 4 K to hydrogen gas (H2, HD, or D2) to prepare the quench condensed- hydrogen film. The surface of the tungsten foil was preferentially parallel to {100} dueto the rolling textures. The purity of the H2, HD, and D2 gases was 99.99999%, 97%, and99.995%, respectively (Suzuki Shokan Co., Ltd). Before the hydrogen film growth, the Wsubstrate surface was cleaned by a combination of flash heating to above 1800 K in UHVand 2 keV Ar+ ion sputtering. After repeated cycles of the surface cleaning procedure, wesuccessfully confirmed the clean W surface by LEIS (Fig. S2 [31]). The hydrogen partialpressure during the exposure was controlled to be 1.33×10−7 Pa for 0.1 L or less, 1.33×10−6Pa for over 0.1 L to 2 L, 1.33×10−5 Pa for over 2 L to less than 25 L, and 1.33×10−4 Pafor over 25 L, where 1 L = 1.33×10−4 Pa·s. The temperature-programmed ToF-SIMS mea-surements were started within 5 minutes of hydrogen exposure unless otherwise specified.Hydrogen gas for quench condensation was introduced into the analysis chamber througha variable leak valve. The H2 gas was supplied either directly from a cylinder or from ahomemade ortho-para converter that was constructed according to the literature. [32, 33]The ortho-para converter consisted of a copper tube (1/8 inch diameter, 1 m length) intowhich we put iron (III) hydroxide powder (Aldrich, catalyst grade, 30-50 mesh). It was at-tached to the cold head of the Gifford MacMahon (GM) closed-cycled He refrigerator (SHI,SRDK-205E). The flow rate of hydrogen gas was 50 Pa·L/s at temperatures below 40 K.After the pressure in the tube reached 1.5 atm, hydrogen in the copper tube was frozenwith the refrigerator cold head cooled below 4 K, and this temperature was maintained forseveral hours. Finally, the hydrogen gas that evaporated from the copper tube was used forthe film growth of solid hydrogen. The ortho-para conversion rate is estimated to be morethan 90%. [32, 33]We used a GM refrigerator (Iwatani, HE05) together with a homemade sample stage anda radiation shield to construct a UHV-compatible cryostat that allowed sample cooling tobelow 4 K during ToF-SIMS and LEIS measurements (Fig. 2). The thermal shield aroundthe sample, the shape of which is shown by the solid black line in Fig. 2, is retractableto allow the sample exchange through the load-lock chamber. The sample was electrically6floated for flash heating of the sample by electron bombardment and also to monitor theprimary ion beam current.The sample temperature was measured by a silicon diode sensor (Lake Shore, DT-670-SD-1.4H) placed near the sample, which was calibrated by the manufacturer from 1.4 K to 500K. The temperature deviation between the read temperature of the Si diode sensor andthe actual sample surface temperature is corrected by separate measurements on supercon-ducting transition of a polycrystalline Nb foil. The thickness of the Nb foil was 0.1 mm,which was the same as that of the W foil for the growth of the solid hydrogen film. Thenominal superconducting transition temperature of Nb (9.25 K) was confirmed beforehandby a SQUID magnetometer (Quantum Design, Inc., MPMS-XL) as shown in Fig. S3 [34]. Itwas observed that the read temperature of the silicon diode sensor at the superconductingtransition temperature of the Nb film (9.25 K) was 8.4 K (Fig. S4 [35]). In our tempera-ture calibration, this temperature difference (0.85 K) is added to the reading temperatureof the silicon diode sensor. Even after this temperature calibration, there should still be atemperature difference between the actual sample surface temperature and the calibratedtemperature. The effect of this temperature difference will be discussed in the Results andDiscussion section.Density functional theory (DFT) calculations were performed with VASP code [36–38] us-ing the PBEsol [39] exchange-correlation functional. We used cutoff energy of 550 eV anda k-point sampling of 9×9×1. In order to have an accurate description of the interac-tion between hydrogen and the tungsten surfaces, we considered Van der Waals-dispersionenergy-correction by S. Grimmes (DFT-D3 method) [40, 41]. The structure model of W(100)consists of six-layer slabs, where all short-bridge and three-fold sites on the surface are fullyoccupied by adsorbed hydrogen atoms and one a hydrogen molecule is ∼1.8Å above thehydrogen atom layer [42]. All of the atoms were relaxed during the geometry optimizationprocedure except the bottom two layers which were held fixed to the bulk geometry. 2×2supercell for the surface and a 30.0 Å vacuum in the c-direction are used. The resultant lat-tice constants of the model structure are a=b=6.37400 Å and c=38.06750 Å. The desorptionenergy of the hydrogen molecule on the hydrogen atom layer was estimated as energy differ-ence between the fully relaxed structure and the structure in which the hydrogen molecule7is ∼13 Å above the hydrogen atom layer (see the bottom of Fig. 8). The latter structurewas determined by placing the hydrogen molecule 1 Å away from the stable position in thec direction. The total energy was 1.5 meV lower than the sum of total energies of fullyhydrogen-atom-covered W(100) slab model and isolated hydrogen molecule, suggesting thatour calculations are accurate to this energy order.III. RESULTS AND DISCUSSIONFigure 3 shows ToF-SIMS spectra of a tungsten surface exposed to HD of 100 L. Duringthe exposure and the following ToF-SIMS measurement, the sample temperature was keptbelow 4 K. It has been indicated that the emission of H+ and D+ ions by keV energy He+ion impact is attributed to both the kinetic sputtering and the potential sputtering [43].The W-derived cation at a mass-to-charge ratio (m/z) of about 200 is composed of severalcomponents including hydrated tungsten (W − (H3O)+) and protonated tungsten (W − H+)in addition to tungsten mono-cation (W+).Figure 4 shows H+ intensity of ToF-SIMS in the temperature-programmed ToF-SIMS mea-surement. The sample was prepared by exposing it to a normal H2 atmosphere below 4 K.The measurement was performed by raising the sample temperature at the constant rate of2 K/min from the quench condensation temperature. We observed substantial enhancementof H+ ion emission by the increase of the sample temperature, as shown in Fig. 4. The peakposition with a small exposure of 0.3 L was about 25 K, which shifts to lower-temperatureside with larger exposure. Looking more closely, one notices that the onset position of thepeak (labeled (i) in Fig. 4) shifts to a lower temperature side with increasing exposure,while the decreasing slopes of the peak are shared among the different exposures resultingin the peak elimination at the identical temperature (labeled (ii) in Fig. 4). The shift of thepeak onset position (i) was almost complete at 25 L, where the peak onset position reachedbelow 5 K. Thus, the peak onset position (i) shows no shift with further exposure above 25L, which was confirmed upto 360 L (not shown).Desorption of hydrogen from the surface during ramping of the sample temperature occursnot only at the sample surface, but also at other parts of the cryostat, such as the second8stage of the refrigerator. It is noted that an overwhelming fraction of hydrogen moleculesadsorbs on the colder parts of the cryostat. However, the hydrogen molecules adsorbed onthe parts other than the sample surface are not detected by ToF-SIMS because the ionizationof the hydrogen molecule required for being detected takes place only at the impingementposition of the incident He+ ion beam. Note that the diameter of the incident He+ ion beam(about 2 mm) was much smaller than the sample size (10×10 mm2).We observed essentially no difference between normal H2 and para H2 in the temperature-programmed ToF-SIMS measurements (Fig. S5 [44]). Thus, the intensity variation of theH+ ion observed in Fig. 4 is not related to the nuclear spin isomer effect.The temperature-programmed ToF-SIMS result of the D2 film shown in Fig. 5 is quitesimilar to that of the H2 film in Fig. 4. The measurement conditions, such as quenchcondensation temperature and temperature ramping rate, were the same between the mea-surement for H2 (Fig. 4) and D2 (Fig. 5). Similar to H2, there are two prominent features inthe temperature-programmed ToF-SIMS result: the peak onset shift with exposure amountlabeled (i) and the peak elimination at the same temperature among the different exposureamounts labeled (ii).A closer look reveals a distinct isotope effect in the temperature of the peak onset position,which is summarized in Fig. 6 for the exposure amount of 100 L. The onset temperaturesof the hydrogen peak in Fig. 6 are, in order from lowest to highest, H2, HD, and D2, whichare 4.6 K, 5.2 K, and 5.9 K, respectively, for the half-maximum value. Since the increasein ToF-SIMS intensity from these onset temperatures is attributed to the densification ofthe hydrogen film as discussed below, the structural transition is discussed below using theonset temperature of the hydrogen peak.Those onset temperatures (4.6 K, 5.2 K, and 5.9 K for H2, HD, and D2, respectively) arecorrespond to the saturated vapor pressure of solid hydrogen for the pressure of 10−4 Paestimated from the following Eqs. (2)-(4). This saturated vapor pressure value is consistentwith the hydrogen partial pressure around those temperatures measured by QMS shown inFig. 7.9The solid-vapor saturation pressure of normal H2 (QH2) is shown to be approximately ex-pressed by [45]lnQH2 = 13.94− 97.88/T. (2)The expression is applied to the temperature range from 2.5 to 4.5 K in which the constantsublimation energy (813.8 J/mol) is assumed. It is noted that this value is close to thebinding energy of the hydrogen solid. Similarly, the solid-vapor saturation pressure of HD(QHD) and normal D2 (QD2) are approximately expressed bylnQHD = 14− 120/T (3)andlnQD2 = 15.91− 147.2/T, (4)respectively [45]. The applicable temperature ranges are 3.4-4.3 K and 3.8-5.3 K for thesame reason as H2, respectively. The temperatures for H2, HD, and D2 estimated for thepressure of 10−4 Pa are 4.2 K, 5.2 K, and 5.9 K using Eqs. (2)-(4), respectively. The factthat the onset temperatures of the hydrogen peak in Fig. 6 agree well with these values in-dicates that the onset of the hydrogen peak is due to the sublimation, although it is slightlyout of the applicable temperature range. Since the sublimation energy involved in Eqs.(2)-(4) corresponds to the binding energy of a solid, the desorption of hydrogen moleculesfrom the surface should take place on a solid surface (sublimation), not on a liquid surface(evaporation).Because a further elevation of the temperature enhances the sublimation of hydrogen fromthe surface, the falling edge of the hydrogen peak reflects the decrease of the surface hy-drogen concentration due to the desorption from the surface. Thus, the falling edge tem-perature is considered to reflect the hydrogen molecule - surface bond strength. To verifythis assumption, we estimated the desorption energy of the hydrogen molecule from a fullyhydrogen-atom-covered W(100) surface by DFT calculations. Figure 9 is a result of nudgeelastic band technique and plots the total energy against the location of a hydrogen moleculealong the path leading from the top of surface to vacuum. There is no activation barrier,and the energy difference between the initial and final states is calculated to be 78 meV.10The desorption energy of a molecule can also be estimated from the desorption temperatureof the molecule by using Readhead equation: [47]− dθdT=Aβθme(−EdRT), (5)where θ, T , A, β, m, Ed, R are surface coverage, temperature, pre-exponential factor, heat-ing rate, desorption order, desorption energy, and gas constant, respectively. By substitutingA = 1013 s−1, β=2 K/min, m=1, Ed=0.078 eV, R = 8.617×10−5 eV K−1 into the equation,the falling of the hydrogen peak is calculated to ∼30 K, which agrees well with the experi-mental value shown in Fig. 4. Therefore, it is evident that the falling of the hydrogen peakat ∼30 K reflects the desorption energy of hydrogen molecule from the fully hydrogen-atom-covered W(100) surface.The vapor pressure of hydrogen is not negligible at 3-4 K in UHV, which is the lowestachievable temperature in the present study. Therefore, it is crucial to discuss the ad-sorption/desorption balance at the sample surface during the film growth as well as themeasurement. From Eq. (2), it is estimated that the saturated vapor pressure of hydrogen(H2) is 1×10−5 Pa at 3.8 K, which is close to the exposure temperature in hydrogen filmgrowth. The hydrogen pressure introduced into the chamber (1×10−4 Pa) for hydrogenfilm growth of over 25 L was much higher than this pressure; therefore, the hydrogen filmthickness increases with the exposure time in the initial stage of film growth. As the filmthickness increases, the film growth rate is likely to decrease due to the limited thermalconductivity of the hydrogen film itself, because it is exposed to room temperature throughthe aperture of the thermal shield. Since the vapor pressure is exponentially dependenton the temperature, which is not negligible in our setup, the thermal radiation from theroom temperature part is considered to give an upper limit of the hydrogen film thickness.Indeed, we observed that the W-derived signal of ToF-SIMS still appears even after verylarge exposures such as 600 L (not shown). In our calculation for depth profiling of thedefect creation probability using the close-encounter probability method [48], it is estimatedthat the 2 keV He+ ion can create defects in the solid hydrogen film up to 200 nm depth.By considering the energy loss in the collisional cascade approaching the surface, the upperlimit of the hydrogen film thickness is estimated to be far below 200 nm.11In the initial stage of the temperature-programmed ToF-SIMS measurement, which wasstarted immediately after the hydrogen film growth by the exposure of 100 L, the hydrogenpartial pressure remains at about 1×10−4 Pa up to 6 K as shown in Fig. 7. This is a con-sequence of the balance between the evacuation rate and the desorption of hydrogen fromsome parts of the cryostat, whose area is much larger than the sample surface. Since thevapor pressure of hydrogen is estimated to be below 1×10−4 Pa up to the onset temperatureof the ToF-SIMS peak where sublimation is considered to start (about 4.2 K); hence thehydrogen film thickness is mostly maintained.Since the saturated vapor pressure of hydrogen in UHV is not negligible at the lowest achiev-able temperature (3-4 K) in our setup, the temperature-programmed ToF-SIMS result isassumed to depend on the pressure of hydrogen in the chamber. This point was investigatedby controlling the hydrogen partial pressure in the chamber. Figure 9 shows the comparisonbetween with and without the inlet of D2 gas (partial pressure: 1×10−4 Pa) during theToF-SIMS measurement. The actual D2 pressure during the measurement around the peaktemperature position (5-8 K) is estimated to be about 2×10−4 Pa and 1×10−4 Pa with andwithout the D2 gas inlet, respectively, by referring to the hydrogen partial pressure datashown in Fig. 7. It is observed that the onset temperature of the ToF-SIMS peak differseach other by about 0.6 K, which is consistent with the sublimation temperature differenceestimated by Eq. (4).It is observed in Fig. 9 that the D+ intensity with the D2 gas inlet is significantly largerthan that without the D2 gas inlet below the peak temperature. This is due to the densifi-cation of the film that occurs under the hydrogen atmosphere as discussed below. Since thedensification of the hydrogen film in the D2 atmosphere is continuous up to the sublimationtemperature, the ToF-SIMS peak is less pronounced with the D2 gas inlet.To summarize, the hydrogen intensity variation in the temperature-programmed ToF-SIMScurve shows two features: the intensity increase shifting to lower temperature with the ex-posure amount ((i) in Figs. 4 and 5) and the elimination of the peak at the identical positionamong different exposures ((ii) in Figs. 4 and 5). The former is due to the sublimation of12hydrogen and the latter is due to the desorption of hydrogen admolecules contacting to theatomic hydrogen layer grown on the tungsten surface. Since both phenomena take place ona solid surface and no indication suggesting liquid hydrogen is observed, the possibility ofsurface melting at the solid hydrogen surface is ruled out.There should be a deviation between the calibrated temperature and the actual sample sur-face temperature at temperatures lower than the superconducting transition temperatureof Nb that was used for the temperature calibration. We believe that this temperaturedeviation should not be so large enough to change the conclusion since the sublimationtemperature estimated using this temperature calibration is consistent with that estimatedfrom the hydrogen partial pressure measured by QMS shown in Fig. 7.The mechanism of the increase in hydrogen intensity by sublimation in temperature-programmed ToF-SIMS is discussed below. Figure 10 shows the ToF-SIMS intensity ofH+ and W-derived mono-cations as a function of exposure to normal H2 atmosphere below4 K. The intensity variation of H+ and W-derived mono-cation is similar in the exposurerange above 1 L. The similar behavior between H+ and W-derived mono-cation is attributedto the protonation of the sputtered tungsten atom that affects the intensity of the W-derivedmono-cations. On the other hand, the intensity variation is quite different in the initial stageof the exposure below 1 L: the intensity of the W-derived cations decreases while that ofH+ increases. This opposite behavior between the W-derived cations and H+ indicates thatthose ToF-SIMS intensities are governed by the surface coverage of hydrogen. Thus, theintensity variation of the W-derived cations is the consequence of two competing effects: thedecrease accompanied by the surface hydrogen coverage and the increase with the protona-tion of the sputtered tungsten atoms.It is observed in Fig.10 that the H+ intensity variation is saturated with an exposure of about5 L. This indicates that the tungsten surface is completely covered by exposure to hydrogenat this exposure level. Note that the change in the temperature-programmed ToF-SIMSprofile with the exposure to H2 in Fig. 4 saturates at a larger exposure level of 25 L. Thus,the amount of exposure to H2 needed for saturation of the change in the ToF-SIMS intensity(Fig. 10) and that in the temperature-programmed ToF-SIMS (Fig. 4) are substantially13different. The former is determined by the surface coverage by hydrogen, that is hydrogenadsorption, while the latter is determined by the sublimation as previously discussed. Thus,the discrepancy in the exposure amount dependence between these two results implies thatthe sublimation of the solidified hydrogen is not simply a reverse process of adsorption. Weconsider that the re-adsorption of sublimated hydrogen is the mechanism of densification ofthe quench-condensed film that is originally in a low-density state. The densification of theprecursor molecules in the film enhances the secondary ion emission intensity I as shown inEq. (1). It is reasonable to expect that the ionization rate Kj also changes by this densi-fication of the hydrogen film due to the matrix effect, but the relationship between Cj andKj is not clear in the present stage; hence the effect of the ionization rate is not discussedin this paper.The proposed mechanism of the densification of the quench-condensed hydrogen film by sub-limation is displayed in Fig. 11. It is well-known that the quench-condensed molecular filmhas generally a sherbet-like structure containing various voids, hence it is in a low-densitystate (Fig. 11 (a)). This is because the surface migration of a gas molecule is limited at thecryogenic temperature for the quench condensation. Thus, the hydrogen gas molecules aresticked at the firstly arrived position at the surface, which is the mechanism of the formationof the low-density film. It is noted that re-adsorption of the sublimated molecules smoothsthe rough surface, hence the density of the film increases (Fig. 11 (b)). Therefore, thequench-condensed molecular film is densified at the sublimation temperature while the totalnumber of molecules in the film decreases.Finally, the dissociative adsorption of hydrogen molecules is discussed. The hydrogen adsorp-tion on a tungsten surface has been investigated by numerous studies both from experimentand theory. If it is limited to the cryogenic temperature adsorption which can be directlycompared to the present study, however, the number of studies is limited. In the review byPtushinskii, it is stated that the adsorption of hydrogen is dissociative in the initial stageof the adsorption on a single crystalline tungsten surface at 5 K [46]. Dissociative adsorp-tion of hydrogen at cryogenic temperature (5 K) has been reported also by den Boer et alfor W(100) [49]. We also consider that adsorbed hydrogen contacting a tungsten surfacedecomposes at those cryogenic temperatures. This is because the desorption temperature14in the initial stage of the hydrogen exposure agrees well with our DFT calculation assum-ing dissociation of hydrogen contacting the tungsten surface. It is likely that the hydrogenadsorbs in the molecular form on this atomic hydrogen layer.IV. CONCLUSIONQuenched condensed hydrogen films grown on a polycrystalline tungsten substrate werestudied to investigate the existence of surface melting. For this purpose, we developedcryogenic ToF-SIMS combined with LEIS, sharing the incident He+ beamline as well as theenergy analyzer to minimize the entrance and exit apertures placed at the radiation shieldof the cryostat. We successfully demonstrated ToF-SIMS analysis of the solidified hydrogenfilm grown on the clean tungsten substrate surface as confirmed by LEIS. We found that thehydrogen ion intensity in temperature-programmed ToF-SIMS shows two prominent futuresdue to sublimation and elimination of hydrogen admolecules, both well explained by thedesorption of hydrogen molecules from the solid hydrogen surface, revealing no pre-meltinglayer on the surface.Data availabilityData will be made available on request.AcknowledgmentThis work was partly supported by JSPS KAKENHI Grant No. 19K12633 and theInnovative Science and Technology Initiative for Security, ATLA, Japan, Grant NumberJPJ004596. The authors appreciate the SQUID measurement by Dr. S. Arisawa.[1] V. L. Ginzburg, A. A. Sobyanin, Can liquid molecular hydrogen be superfluid?, ZhETFPis.Red. 15, 343 (1972).[2] H. J. Maris, G. M. Seidal, T. E. Huber, Supercooling of liquid H2 and the possible productionof superfluid H2, J. Low. Temp. Phys. 51, 471 (1983).15[3] M. C. Gordillo, D. M. Ceperley, Superfluidity in H2 films, Phys. Rev. Lett. 79, 3010 (1997).[4] See Supplemental Material at URL for schematic drawing of a UHV chamber and evacuationsystem used in this study.[5] M. C. Gordillo, J. Boronat, J. Casulleras, Zero-temperature equation of state of quasi-one-dimensional H2, Phys. Rev. Lett. 85, 2348 (2000).[6] V. S. Vorob’ev, S. P. Malyshenko, Superfluid molecular hydrogen, JETP Letters 71, 59 (2000).[7] Y. Kwon, K. B. Whaley, Nanoscale molecular superfluidity of hydrogen, Phys. Rev. Lett. 89,273401 (2002).[8] C. Cazorla, J. Boronat, Possible superfluidity of molecular hydrogen in a two-dimensionalcrystal phase of sodium, Phys. Rev. A 88, 224501 (2013).[9] T. Zeng, P. Roy, Microscopic molecular superfluid response: theory and simulations, Rep.Prog. Phys. 77, 046601 (2014).[10] M. Boninsegni, Superfluid response of parahydrogen clusters in superfluid 4He, J. Low. Temp.Phys. 201, 193 (2020).[11] M. C. Gordillo, J. Boronat, Supersolidity in the second layer of para-H2 adsorbed on graphite,Phys. Rev. B 105, 094501 (2022)[12] X. Fan, X. Chen, D. Pan, Y. Liu, P. Liu, M. Li, Localization and delocationzation of surfacedisordering in surface mediated melting, Phys. Rev. B 104, 134204 (2021).[13] K. Wang, H. Z. Wu, M. K. Ge, X. G. Hou, N. Liu, J. He, W. Xi, J. Luo, Multilayer-by-multilayer surface melting of Cu(200), Phys. Rev. B 98, 045425 (2018).[14] I. U. Vakarelski, D. Y. C. Chan, S. T. Thoroddsen, Drag moderation by the melting of an icesurface in contact with water, Phys. Rev. Lett. 115, 044501 (2015).[15] T. Makiuchi, K. Yamashita, M. Tagai, Y. Nago, K. Shirahama, Multiple diffusion-freezingmechanisms in molecular-hydrogen films, Phys. Rev. Lett. 123, 245301 (2019).[16] M. Boninsegni, Melting of a p-H2 monolayer on a lithium substrate, Phys. Rev. 70, 125405(2004).[17] K. Kuyanov-Prozument, A. F. Vilesov, Hydrogen clusters that remain fluid at low tempera-ture, Phys. Rev. Lett. 101, 205301 (2008).[18] M. C. Gordillo, D. M. Ceperley, Two-dimensional H2 clusters: A path-integral Monte Carlostudy, Phys. Rev. B 65, 174527 (2002).[19] E. Bloss, A. F. G. Wyatt, Surface diffusion of solid hydrogen, J. Low. Temp. Phys. 119, 74316(2000).[20] P. Leiderer, U. Albrecht, Investigation of quantum systems with surface plasmons and surfacestate electrons, J. Low. Temp. Phys. 89, 229 (1992).t[21] J. Classen, K. Eschenroder, G. Weiss, Structural relaxation and surface diffusion of quench-condensed hydrogen films, Physica B 219& 220, 678 (1996).[22] M. Maruyama, M. Bienfait, F. C. Liu, Y. M. Liu, O. E. Vilches, F. Rieutord, Quasi-liquidmolecular layer at solid hydrogen surfaces, Surf. Sci. 283, 333 (1993).[23] M. Boninsegni, Quasi2D H2 : on the verge of turning superfluid?, J. Low. Temp. Phys. 202,1 (2021)[24] U. Albrecht, R. Conradt, S. Heminghaus, P. Leiderer, Wetting phenomena in films of molecufarhydrogen isotopes, Low Temp. Phys. 22, 117 (1996).[25] H. K. Christenson, Confinement effects on freezing and melting, J. Phys.: Condens. Matter13, R95 (2001).[26] R. Souda, Matrix effects on secondary ion emission from a room-temperature ionic liquid,1-ethyl-3-methylimidazolium bis[trifluoromethanesulfonyl]imide, J. Chem. Phys. 130, 244707(2009).[27] K. Kono, U. Albrecht, P. Leiderer, Surface-state electrons on a hydrogen film. I. Annealing ofthe film, J. Low. Temp. Phys. 82, 279 (1991).[28] K. Kono, U. Albrecht, P. Leiderer, Surface state electrons on a hydrogen Film. 2. Influence ofadsorbed helium films, J. Low. Temp. Phys. 83, 423 (1991).[29] Y. P. Monarkha, U. Albrecht, K. Kono, P. Leiderer, Helium-film-induced retrapping transitionin the two-dimensional surface above an uneven solid-hydrogen, Phys. Rev.B47, 13812 (1993).[30] H. Li, X. Zhang, T. Zeng, R. J. Le Roy, P. Roy, Suppression of parahydrogen superfluidity ina doped nanoscale Bose fluid mixture, Phys. Rev. Lett. 123, 093001 (2019).[31] See Supplemental Material at URL for low-energy He+ ion scattering spectrum on the cleantungsten polycrystal surface.[32] T. Momose, T. Shida, Matrix-isolation spectroscopy using solid parahydrogen as the matrix:application to high-resolution spectroscopy, photochemistry, and cryochemistry, Bull. Chem.Soc. Jpn. 71, 1 (1998).[33] A. M. Juarez, D. Cubric, G. C. King, A compact catalytic converter for the production ofpara-hydrogen, Meas. Sci. Technolo. 13, N52 (2002).17[34] See Supplemental Material at URL for SQUID magnetometry data of the Nb film.[35] See Supplemental Material at URL for the electrical resistance of polycrystalline niobiumsubstrate as a function of the temperature measured with cooling the sample.[36] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals andsemiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).[37] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculationsusing a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).[38] P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).[39] J. P. Perdew et al., Restoring the density-gradient expansion for exchange in solids and sur-faces, Phys. Rev. Lett. 100, 136406 (2008).[40] S. Grimme, J. Antony, S. Ehrlich, S. Krieg, A consistent and accurate ab initio parametrizationof density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys.132, 154104 (2010).[41] S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion correcteddensity functional theory, J. Comput. Chem. 32, 1456 (2011).[42] Z. A. Piazza et al. Acta Materialia, Saturation of tungsten surfaces with hydrogen: A densityfunctional theory study complemented by low energy ion scattering and direct recoil spec-troscopy data, 145, 388 (2018).[43] J. Schou, B. Stenum, R. Pedrys, Sputtering of solid deuterium by He-ions, Nucl. Instrum.Meth. Phys. Res. B 182, 116 (2001).[44] See Supplemental Material at URL for temperature-programmed ToF-SIMS spectra on thenormal-H2 film and the para-H2 film grown by exposing the tungsten substrate to normal-H2and para-H2 atmosphere of 100 L, respectively.[45] P. C. Souers, Hdrogen Properties for Fusion Energy (University of California Press, LondonEngland, 1986) p. 49.[46] Y. G. Ptushinskii, Low-temperature adsorption of gases on metal surfaces (Review), LowTemp. Phys. 30, 1 (2004).[47] P. A. Redhead, Thermal desorption of gases, Vacuum 12, 203 (1962)[48] T. Fuse, O. Ishiyama, M. Shinohara, Y. Kido, Monte Carlo simulation of angular-scan spectrafor coaxial impact collision ion scattering spectroscopy (CAICISS), Surf. Sci. 372, 350 (1997).[49] D. den Boer, O. I. Shklyarevskii, J. A. A. W. Elemans, S. Speller, Low-temperature dissociative18adsorption of H on W, Mo, and Ta surfaces studied with mechanically controllable break-junctions, Phys. Rev. B 77, 165423 (2008).19FIG. 1: Schematic of ToF-SIMS combined with LEIS. The incident ion beam line (2 keV He+) andthe detector (electrostatic energy analyzer) are shared between ToF-SIMS and LEIS to minimizethe size of the aperture placed at the radiation shield for entry and exit of ions.20FIG. 2: (Color online) (a) Schematic of cryostat used for cryogenic ToF-SIMS. The heat-transferrod connecting the cold head of the GM refrigerator and the sample is displayed. The sapphireplate 5 mm thick is used for electrically insulating the sample, which is heated above 1800 K byelectron bombardment for surface cleaning. In temperature-programmed ToF-SIMS measurement,the heater placed in the heater block was used to raise the sample temperature at a constant rate.(b) Details around the sample station. The thermal shield made of aluminum around the sampleis removed in this picture to see the sample station.21FIG. 3: ToF-SIMS spectra of quench condensed HD film grown on a tungsten polycrystal substrateprepared by exposing to the HD atmosphere of 100 L below 4 K.22FIG. 4: Temperature-programmed ToF-SIMS spectra of H+ measured on the quench condensedhydrogen film on the tungsten substrate. The peak onset temperature and the temperature at whichthe peak disappears are indicated by solid and dashed arrows labeled (i) and (ii), respectively.23FIG. 5: Temperature-programmed ToF-SIMS spectra of D+ measured on the quench condensedhydrogen film grown on the tungsten substrate. The peak onset temperature and the tempera-ture at which the peak disappears are indicated by solid and dashed arrows labeled (i) and (ii),respectively.24FIG. 6: (Color online) Temperature-programmed ToF-SIMS spectra of H+ of the H2 film (solidblack curve), H+ of the HD film (dotted red curve), and D+ of the D2 film (blue chain curve). Theexposure amount is 100 L for all three measurements.25FIG. 7: The hydrogen partial pressure measured by QMS during the temperature-programmedToF-SIMS measurement for the H2 100 L/W sample. The ToF-SIMS measurement was startedimmediately after the hydrogen film growth was completed.26FIG. 8: (Color online) Temperature-programmed ToF-SIMS spectra of D+ of the D2 100L/Wsample with (solid black squares) and without (open red circles) introducing the D2 gas of 1×10−4Pa during the measurement.27FIG. 9: (Color online) Total energy change as a function of hydrogen molecule position alongthe path leading from the top of the hydrogen-atom-adsorbed W(100) surface to vacuum. In thebottom of the figure, the atomic positions of initial and final states are shown. Grey and pinkcircles denote W and hydrogen, respectively.28FIG. 10: (Color online) ToF-SIMS intensities of H+ (solid black squares) and W-derived cations(open red circles) as a function of exposure to H2 below 4 K.29FIG. 11: (Color online) Proposed densification mechanism of a quench-condensed hydrogen filmby annealing. The low-density hydrogen film grown by quench condensation (a) is densified bydesorption during sublimation followed by re-adsorption after annealing (b).30