Acceleration of hydrogen absorption by palladiumthrough surface alloying with goldKazuhiro Nambaa, Shohei Oguraa,1, Satoshi Ohnoa, Wen Dia, Koichi Katoa, Markus Wildea, Ivo Pletikosi�cb, Petar Pervanb,Milorad Milunb, and Katsuyuki Fukutania

aInstitute of Industrial Science, The University of Tokyo, 153-8505 Tokyo, Japan; and bInstitute of Physics, HR-10000 Zagreb, Croatia

Edited by Cynthia Friend, Harvard University, Cambridge, MA, and accepted by Editorial Board Member Richard Eisenberg June 15, 2018 (received for reviewJanuary 9, 2018)

Enhancement of hydrogen (H) absorption kinetics improves theperformance of hydrogen-purifying membranes and hydrogen-storage materials, which is necessary for utilizing hydrogen as acarbon-free energy carrier. Pd–Au alloys are known to showhigher hydrogen solubility than pure Pd. However, the effect ofAu on the hydrogen penetration from the surface into the sub-surface region has not been clarified so far. Here, we investigatethe hydrogen absorption at Pd–Au surface alloys on Pd(110) bymeans of thermal desorption spectroscopy (TDS) and hydrogendepth profiling with nuclear reaction analysis (NRA). We demon-strate that alloying the Pd(110) surface with submonolayeramounts of Au dramatically accelerates the hydrogen absorption.The degree of acceleration shows a volcano-shaped form against Aucoverage. This kinetic enhancement is explained by a reduced pen-etration barrier mainly caused by a destabilization of chemisorbedsurface hydrogen, which is supported by density-functional-theory(DFT) calculations. The destabilization of chemisorbed surface hy-drogen is attributed to the change of the surface electronic statesas observed by angle-resolved photoemission spectroscopy (ARPES).If generalized, these discoveries may lead to improving and control-ling the hydrogen transport across the surfaces of hydrogen-absorbing materials.

hydrogen | Pd–Au alloy | thermal desorption spectroscopy | nuclearreaction analysis | angle-resolved photoemission spectroscopy

Hydrogen (H) absorption in materials is crucially importantfor hydrogen-storage and hydrogen-purifying membranes.

Absorbed hydrogen also plays crucial roles in surface catalyticreactions such as hydrogenation and H-D exchange reactions ofhydrocarbons (1–4). Materials that efficiently absorb large quan-tities of hydrogen are required for these applications. Pd is knownas a hydrogen-absorbing material. In the hydrogen-absorptionprocess at Pd surfaces, the penetration process from the surfaceinto the subsurface region is recognized as the rate-limiting step(5, 6). Since the surface governs the penetration process, thepenetration kinetics are expected to be controllable by modifyingthe surface, such as its atomic structure (7) or by alloying withother materials.Although pure Au does not absorb hydrogen, the hydrogen

solubility in Pd alloyed with Au is enhanced compared with purePd (8–10) and reaches a maximum in Pd–Au alloys at Au con-centrations around 20–30%. We recently showed that a singlecrystalline Pd70Au30(110) alloy efficiently absorbs hydrogenthrough the surface Pd area and that H accumulates in the near-surface region at low temperatures of 120–180 K (11). However,the influence of Au on the kinetics of the hydrogen penetrationprocess has not yet been clarified. Addressing this issue in thepresent study, we investigate hydrogen absorption at Pd–Ausurface alloys prepared on Pd(110) by means of thermal de-sorption spectroscopy (TDS) and hydrogen depth profiling withnuclear reaction analysis (NRA). We demonstrate that alloyingwith submonolayer amounts of Au enhances the hydrogen ab-sorption kinetics by a factor of more than 40 compared with purePd(110). On the basis of the changes in the electronic surface

states as observed by angle-resolved photoemission spectroscopy(ARPES) and density-functional-theory (DFT) calculations, weattribute the origin of this drastic kinetic improvement by Au tothe decrease of the hydrogen chemisorption energy on the Pd–Au surface alloys.

Results and DiscussionFig. 1A shows the H2 TDS data taken from the clean Pd(110)surface and from the 0.3-monolayer (ML) and 1.8-ML Au/Pd(110)surfaces after exposure to 100-Langmuir (1 Langmuir = 1.33 ×10−4 Pa s) H2 at 120 K. The Au/Pd(110) surfaces wereannealed at 700 K for 5 min. This treatment leads to surfacealloying where Au atoms mainly stay in the surface layer (SIAppendix, Fig. S1). On the basis of previous studies on Pd–Ausurface alloys grown on Pd surfaces (12, 13), the surface Pdatoms are expected to form Pd monomers rather than Pd dimersand trimers at high surface Au concentrations. From cleanPd(110), three desorption peaks are observed at 153 (α1), 220 (α2),and 300 K (β). As reported previously, the α1 peak corresponds toabsorbed hydrogen (hydride phase) in a few nanometer deepsubsurface region, the α2 peak is related to the lifting of a hy-drogen adsorption-induced surface reconstruction of Pd(110), andthe β peak can be attributed to chemisorbed surface hydrogen (6,14, 15). On the 0.3-ML Au/Pd(110) surface, the intensity of the α1peak increases significantly, the intensity of the β peak is almostthe same compared with Pd(110), and the α2 peak disappears.The peak temperature of the α1 feature shifts to 173 K and thatof the β peak shifts to 295 K. On the 1.8-ML Au/Pd(110) surface,

Significance

Surfaces are gates to control the transport of energy and mate-rials between the gas phase and bulk. For the hydrogen storage,the transport of hydrogen across the surface is recognized as thebottleneck, e.g., 1 H2 in 1,000 impinging a Pd surface penetratesthe surface. Here, we demonstrate that alloying the Pd(110)surface with submonolayer amounts of Au dramatically acceler-ates the hydrogen absorption, by a factor of more than 40. Thisdiscovery will lead to enhancement of hydrogen absorption ki-netics, thereby improving the performance of hydrogen-purifying membranes and hydrogen-storage materials, whichis a key for utilizing hydrogen as a carbon-free energy carrier.

Author contributions: S. Ogura and K.F. designed research; K.N., S. Ogura, S. Ohno, W.D.,and I.P. performed research; K.N., S. Ogura, K.K., M.W., I.P., P.P., M.M., and K.F. analyzeddata; K.K. performed theoretical calculations; and S. Ogura and K.F. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. C.F. is a guest editor invited by theEditorial Board.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).1To whom correspondence should be addressed. Email: ogura@iis.u-tokyo.ac.jp.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1800412115/-/DCSupplemental.

Published online July 13, 2018.

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the intensity of the α1 peak is higher than that for clean Pd(110),while the β-peak intensity is about 35% of that from pure Pd(110).The peak temperature of the β feature is 272 K here, but shifts tolower temperature when the Au amount is increased as shownin Fig. 1B. The peak temperature of the α1 peak shifts to highertemperature as the peak intensity increases and the peak shape isasymmetric with a sharp high-temperature edge, which are typicalfeatures of zero-order desorption and characteristic for near-surface absorbed hydrogen in Pd (14, 16, 17).To support the above assignment of the α1 TDS peak to

absorbed H, hydrogen concentration depth profiles were mea-sured by NRA. Fig. 2 shows the NRA profiles from the cleanPd(110) surface and the 0.3-ML Au/Pd(110) surface after 1,000-Langmuir H2 exposure at 120 K. The NRA profile from theclean Pd(110) surface shows a Gaussian-like feature centeredaround depth 0 and a low-intensity decaying feature up to 10 nm.The Gaussian-like feature corresponds to the chemisorbed sur-face hydrogen and the decaying feature corresponds to theabsorbed hydrogen into the near-surface region (6). The NRAprofile from Au/Pd(110) shows a high γ-ray yield near the surfacethat decays into the depth up to 10 nm, which indicates sub-stantial H incorporation into the near-surface region as well aschemisorption of H on the surface. The area of the profile takenfrom Au/Pd(110) is about 4.5× larger than that from barePd(110) in this depth region. Since the γ-ray yield at 10 nm is stillhigher than in pure Pd(110), hydrogen is expected to be absor-bed in the deeper region than in pure Pd(110). The H concen-trations at 5 nm for pure Pd(110) and the Pd–Au surface alloy

are 4.2 and 13 at %, respectively. Since the β peak is alreadysaturated on pure Pd(110), the increased amount corresponds tothe hydrogen absorbed in the near-surface region. The NRAdata support the conclusion that the α1 peak in the TDS spectra,which increased significantly by addition of Au, originates fromthe absorbed hydrogen. Since the Au atoms mainly stay in thesurface layer, Au only modifies the hydrogen solubility in a fewsubsurface layers and the hydrogen solubility below these layersshould be nearly the same as in pure Pd(110). The NRA data onthe other hand show that the H-containing region of Au/Pd(110)with a higher H concentration than Pd(110) extends beyond10 nm. Therefore, the effect of Au is to modify the kinetics ofpenetration from surface to subsurface rather than to signifi-cantly influence the hydrogen solubility.Fig. 3 shows the area of the α1 and β peaks from the Au/Pd(110)

surfaces normalized by those from Pd(110) as a function of theAu coverage. To determine individual peak areas, we separated theα1 and β peaks by fitting the TDS spectra to two asymmetricGaussian functions. The α1-peak area of the Au/Pd(110) surfacesshows a volcano-shaped form (18) against Au coverage with amaximum around 0.4-ML Au, from where it gradually decreaseswith increasing amount of Au. The α1-peak area is about 42×larger at 0.4 ML and notably 2.3× larger at 2.2 ML compared withthat from clean Pd(110). This result shows that the surface alloyingwith submonolayer amounts of Au significantly enhances the hy-drogen absorption. Fig. 3 (Inset) shows the β-peak area normalizedby that from Pd(110). The intensity of the β peak monotonouslydecreases with increasing Au coverage.It is recognized that the rate-limiting step for hydrogen ab-

sorption is the penetration from the surface to the subsurfaceregion. Hydrogen atoms have to overcome the penetration barrierto diffuse from the surface into the subsurface region. The pen-etration barrier is determined by the energy levels at the adsorp-tion state and the transition state to the first subsurface octahedralsite. To clarify the origin of the accelerated hydrogen absorption,the adiabatic potential for a single H to penetrate the surface wascalculated for the clean Pd(110) and 0.5-ML Au/Pd(110) surfacesby DFT calculations. Fig. 4A shows the atomic structure of the0.5-ML Au/Pd(110) surface assumed for the calculation, wherehalf of the surface Pd atoms of Pd(110) were periodically replacedby Au atoms. Fig. 4B shows the calculated energy diagrams fromthe surface site (surface octahedral site, O1) through the sub-surface tetrahedral (T1, T2) and octahedral (O2, O3) sites. Thecalculated energy levels are shown with reference to the metal and

α1

α2

β

A

B

Fig. 1. (A) H2 TDS spectra taken from the 0.3- and 1.8-ML Au/Pd(110) sur-faces and Pd(110) after 100-Langmuir H2 exposure at 120 K. (B) H2 TDSspectra taken from the Au/Pd(110) surfaces with various Au coverages. En-larged spectra around the β peak are also shown.

Fig. 2. NRA profiles taken from the clean Pd(110) and the 0.3-ML Au/Pd(110)after exposure to 1,000-Langmuir H2 at 120 K.

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1/2 H2 at infinite separation. On Pd(110), the penetration barrierfrom the surface to the first octahedral site (O2) is 0.49 eV, whichis given by the energy difference between the O1 site and thetransition state from the T1 to O2 sites. On the Au/Pd(110) sur-face, on the other hand, the hydrogen adsorption on the surface isdestabilized by 0.16 eV and the transition state from the surface tothe T1 site is also destabilized by 0.28 eV compared with Pd(110).However, the energy level at the transition state from the T1 to O2sites is hardly changed, and hence the highest energy level forpenetration is the transition state from the surface to the T1 site.The penetration barrier is 0.39 eV, which is smaller than that ofPd(110) by 0.10 eV. The DFT results support the experimentalobservation that the hydrogen absorption is considerably acceleratedby alloying with submonolayer amounts of Au. If we estimatethe penetration barrier required for the enhancement factor of 42 asobserved in the experiment on the basis of the simple Arrheniusrelation, the decrease of the penetration barrier is calculated to be0.04 eV, which is in agreement with the DFT calculations.The decrease of the hydrogen adsorption energy revealed by

the DFT calculations also explains the behavior of the β peak inthe TDS spectra. The peak temperature of the β peak shifts tolower temperature with increasing Au amount (Fig. 1B), in-dicating a decrease of the hydrogen adsorption energy with in-creasing Au amount if the H2 dissociation barrier on the Pd–Ausurface alloys is assumed to be negligible as on pure Pd. Thisassumption is justified by the fact that H2 dissociative adsorptionstill takes place on the Au/Pd(110) surface alloys with the sub-monolayer amounts of Au and by a theoretical calculation forPd–Ag alloy surfaces where H2 dissociatively adsorbs on surfacePd sites without any dissociation barrier (19). The present DFTcalculations also show that the absorption in the O2 site is morestable for Au/Pd(110) than Pd(110). This result is consistent withprevious data that the hydrogen solubility in bulk Pd–Au alloyswith Au concentrations less than 50% is higher than in the purePd (8–10).With increasing surface Au concentration, the chemisorbed

surface hydrogen is expected to be accordingly destabilized. Thisdestabilization also enhances H2 desorption, which is a com-petitive process to the H penetration process. The transitionstate from the surface to the O2 site will be also accordinglydestabilized, which increases the penetration barrier. In addition,

the number of surface Pd sites decreases and the H2 dissociationbarrier may appear, resulting in the lower adsorption rate. Allthese effects lower the absorption rate at higher surface Auconcentrations. As a result, the enhancement factor of hydrogenabsorption shows a volcano-shaped form with a maximum at acertain amount of Au as seen from the α1 TDS peak area inFig. 3.It should be noted that Fig. 4 shows the energy diagram for the

direct penetration process where a H atom diffuses fromthe surface to the subsurface sites. However, it is reported thatthe hydrogen absorption might proceed in a concerted motion oftwo H atoms involving a chemisorbed H and an excess H atomsupplied by dissociation of H2 on the nearly fully H-coveredsurface (5, 6). In that case, a more detailed analysis includingthe interaction of these H atoms with the surface is required,which will be a future subject to be solved.The adsorption energy of a molecule on a metal surface de-

pends on the surface electronic structure. Fig. 5 shows plots ofthe ARPES intensity as a function of the electron momentum kyand electron energy E with respect to the Fermi level EF (E −EF) from Pd(110) and Au/Pd(110) surfaces measured along thesurface Brillouin zone Γ–Y line. For the clean Pd(110) surface, asharp band is observed around 0.3 eV below EF as seen in Fig.5A. The band shows a nearly flat feature near ky = 0 and bendsdownward at ky > 0.4 Å−1. This band corresponds to the surfacestate or the quantum well state of Pd(110) as reported previously(20–23). An additional feature around 2–3 eV appears at ky >0.6 Å−1. Fig. 5B shows the ARPES intensity taken from 0.48-MLAu/Pd(110). The intensity of the Pd-related band around 0.3 eVdecreases while the intensity of the band around 2–3 eV at ky =0 increases. Fig. 5C shows the ARPES data from the as-grown2.4-ML Au/Pd(110). The 0.3-eV band is completely absent and abroad band around 2–5 eV appears. There is also intensity

-0.04-0.16

-0.25

O1

T1O2

O3T2

Au

Pd

E

O1

T1 O2 T2 O3-0.31

0.08

-0.47

0

-0.20 -0.22 -0.16

-0.12

-0.19-0.19

0.040.040.02-0.02

0.02 0.04

Au/Pd(110) Pd(110)

H212

[110]

[110][001]

A

B

Fig. 4. (A) Schematic model of the 0.5-ML Au/Pd(110) used for DFT calcu-lations. (B) Potential energy diagrams for a single H atom across the (solidline) 0.5-ML Au/Pd(110) and (dotted line) Pd(110) surfaces. The energies areshown in electron volts.

Fig. 3. Au coverage dependence of the α1-peak area from the Au/Pd(110)surfaces normalized by that from Pd(110) as a function of Au coverage.(Inset) β-peak area from the Au/Pd(110) surfaces normalized by that fromPd(110) as a function of Au coverage. Lines through the data points areguides to the eye.

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around 6–7 eV. These bands around 2–5 and 6–7 eV correspondto the Au d bands and the flat region with a low intensity from EFto 2 eV corresponds to the Au s-p band as observed on Ausurfaces and Au-rich Pd–Au surface alloys (24–26), indicatingthat the as-grown 2.4-ML Au/Pd(110) surface is similar to the Ausurface. Therefore, the band around 2–3 eV near ky = 0 observedin Fig. 5B is assigned to the Au band. The Au band around 2–3 eVshown in Fig. 5B is narrower and its position is shallower with re-spect to EF compared with that on the as-grown 2.4-MLAu/Pd(110)(SI Appendix, Fig. S2). The features of the 0.48-ML Au/Pd(110),which is an example of the Au/Pd(110) surface with submonolayeramounts of Au, look like a mixture of the bands from Pd(110) andAu(110) and resemble the features of the Pd70Au30(110) alloysurface with a surface Au concentration of 45–58% (11) shown inFig. 5D.It has been shown that the position of the metal d-band center

with respect to EF is a good indicator of the adsorption energy of amolecule on a surface (27, 28). As the d-band center shiftsdownward away from EF, the d-band center theory (27, 28) pre-dicts that the surface becomes less reactive, resulting in a loweradsorption energy. As the d-band center shifts closer to EF, on theother hand, the surface becomes more reactive, resulting in ahigher adsorption energy. The ARPES data for the Au/Pd(110)surfaces with various amounts of Au show that the intensity of thePd band decreases and its position shifts downward (SI Appendix,Fig. S2). On the basis of the d-band center model, this leads todestabilization of hydrogen adsorption on the surface Pd site. Thisexplains the observed monotonous decrease in the peak temper-ature of the β peak with increasing amount of Au (Fig. 1B).Whereas the energies of O1, T1, and the transition state from

O1 to T1 are destabilized on Au/Pd(110), which is well explainedby the surface electronic structure, the energy level at the tran-sition state from T1 to O2 is hardly changed and the energies ofO2, T2, and the transition state from O2 to T2 are stabilized asrevealed by the DFT calculations. This stabilization can be partlyattributed to the expansion of the Pd lattice by Au that reducesthe energy loss accompanied by the lattice distortion upon hy-drogen absorption, which is used to explain the higher H solu-bility in Pd–Au alloys than in pure Pd.In summary, we have investigated the hydrogen absorption by

Au-alloyed Pd(110) surfaces, and found that the addition ofsubmonolayer Au significantly accelerates hydrogen absorption.The enhancement factor shows a volcano-shaped form against Aucoverage. This enhancement is explained by the destabilization ofthe chemisorbed surface hydrogen and the smaller increase of theenergy level at the transition state of the penetration process

compared with the surface, resulting in the decrease of the pen-etration barrier from the surface into the subsurface. Our resultsclearly show that the addition of only a small amount of Au canenhance the hydrogen absorption kinetics, which is important forthe hydrogen storage and hydrogen purification. This finding willlead to improving and controlling the hydrogen transport acrosssurfaces of Pd-related alloys and hydrogen-absorbing materialsand also to controlling catalytic activities and selectivities of thesesurfaces for surface reactions where absorbed hydrogen playsimportant roles.

MethodsThe experiments were performed in ultrahigh vacuum (UHV) chambers with abase pressure below 1 × 10−8 Pa. A Pd single-crystal rod was Laue-oriented tothe (110) direction, cut within 0.5° precision, and mechanically polished tosubmicrometer roughness with a suspension of Al2O3 powder (0.05-μm grainsize). The Pd(110) sample was set in each UHV chamber and cleaned by re-peated cycles of Ar ion sputtering at 300 K with an ion energy of 800 eV for5 min, annealing at 1000 K in UHV, oxidation at 700–750 K in 5 × 10−5 Pa O2 for4 min, reduction at 300 K in 5 × 10−5 Pa H2 for 1–4 min, and final flashing to 600 Kin UHV. The surface of Pd(110) was characterized by Auger electron spectroscopy(AES) and low-energy electron diffraction (LEED) (SI Appendix, Fig. S1).

The TDS measurements were performed at a heating rate of about 2 K s−1

using a shielded and differentially pumped quadrupole mass spectrometerafter exposure to H2 by backfilling the chamber through a leak valve. Thedosage is given in the Langmuir unit (1 Langmuir = 1.33 × 10−4 Pa s).

The NRA measurements were performed in another UHV chamber withthe 1H(15N, α γ)12C nuclear reaction using 15N ion beams (29, 30) provided bythe van de Graaff tandem accelerator at The University of Tokyo. Bydetecting the 4.43-MeV γ-ray emitted by the reaction, the hydrogen con-centration can be measured. This nuclear reaction has a resonance at anenergy of 6.385 MeV with a narrow width of 1.8 keV. When 15N beams withthe resonance energy are incident on the sample, they react with only sur-face H atoms. When 15N ions with an energy higher than the resonanceenergy are incident on the sample, on the other hand, the ions lose a part oftheir energy in the bulk and then they react with H atoms at the depthwhere the 15N energy has reduced to 6.385 MeV. Thus, by counting thenumber of the emitted γ-ray as a function of the 15N beam energy, one canmeasure hydrogen depth profiles. The absolute hydrogen concentrationcan be obtained by comparing with an NRA depth profile for a standardpolystyrene sample (31). The ion beam current was about 15 nA in the2 × 2 mm2-beam spot on the sample.

The ARPES spectra were taken at 300 K in another UHV chamber by ahemispherical electron analyzer (Scienta SES-100) with an energy resolution ofabout 40 meV using 21.22-eV photons from a helium discharge source with abeam-spot diameter of about 2 mm. For the parallel momentum scan the polaranglewas changed from 0 to 24° at an interval of 2° from the normal direction.

Deposition of Au was conducted using heated tungsten coils loaded withAu wire at a sample temperature of 300 K and at rates of about 1.0 ML min−1

in the LEED, AES, and TDS measurements, 0.9 ML min−1 in the NRA

ky (A-1)

E - E

F (e

V)

A B C D

Fig. 5. Plots of ARPES intensity as a function of ky and E − EF measured along the Γ–Y line for (A) clean Pd(110), (B) annealed 0.48-ML Au/Pd(110), (C) as-grown 2.4-ML Au/Pd(110), and (D) Pd70Au30(110) annealed at 600 K.

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measurements, and 0.015 ML min−1 in the ARPES measurements. Onemonolayer is defined as 9.35 × 1014 atoms cm−2 for Pd(110). The amount ofdeposited Au atoms was monitored by a quartz oscillator placed near thesample. In the ARPES measurement, the amount of deposited Au was de-termined from the ARPES spectra on the basis of a previous study where theAu-derived band almost saturates in intensity at 1-ML Au (24). In the TDSexperiments shown in Fig. 1, each Au layer was deposited after cleaning thesample. In the TDS experiments shown in Fig. 2, the amount of deposited Auwas incrementally increased with cycles of Au deposition of 0.1 ML followedby annealing at 700 K for 5 min. In the ARPES experiment shown in Fig. 5, Auwas additionally deposited after cycles of Au deposition and annealing at700 K for 5 min. The as-grown 2.4-ML Au/Pd(110) surface in Fig. 5 wasprepared by the deposition of 1.67-ML Au on the 0.73-ML Au/Pd(110) sur-face and this surface corresponds to a thick Au layer grown on Au/Pd(110).

Adiabatic potentials for a single H atom in the (110) surface structureswere evaluated by theoretical calculations based on DFTwith the generalizedgradient approximation within Perdew, Burke, and Ernzerhof formalism (32).We applied the PHASE code (33). The calculations were performed usingprojector-augmented wave potentials (34) for hydrogen, palladium, andgold atoms with equally spaced 16 k points for Brillouin-zone samplings. Thecutoff energies are 25 Ry for the wave functions and 196 Ry for the aug-mented electron densities. The (110) surface structures are represented by a

repeated slab of a (2 × 3 × 6) unit cell with periodic boundary conditions.Inversion symmetry with respect to the slab center is implemented to in-crease the computational efficiency. Reaction rates can be determined byexamining the activated H atoms near the saddle points on potential energysurfaces as predicted by transition-state theory. First, the surface structuresincluding the H atom at octahedral or tetrahedral sites are relaxed accord-ingly to be in equilibrium positions to find initial and final metastable statesduring the H-atom migration. At each point on the H migration path, the Hatom is relaxed into equilibrium positions on the plane normal to the mi-grating direction, while the other atoms are relaxed into equilibrium posi-tions. Thus, the H atom can be moved through the saddle points onpotential energy surfaces between the octahedral and tetrahedral sites fromthe bulk toward the (110) surface, leading to the most plausible path for theH-atom migration.

ACKNOWLEDGMENTS. The authors thank Prof. Hiroyuki Matsuzaki andChuichiro Nakano (The University of Tokyo) for assistance in the acceleratoroperation and Prof. Michio Okada (Osaka University) for providing the sam-ple and for helpful discussions. This work was supported by Grants-in-Aid forScientific Research from Japan Society for the Promotion of Sciences (JSPSKAKENHI) Grants JP16K04957, JP17K19048, and JP18H05518.

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