Atomistic Mechanism from Vacancy Trapped H/He Atoms to Initiation of Bubble in W under Low Energy Ions Irradiation
Yu-Wei You, Xiang-Shan Kong, Q. F. Fang, Jun-Ling Chen, G.-N. Luo, C. S. Liu, B. C. Pan, Y. Daid
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a y Atomistic Mechanism from Vacancy Trapped H/HeAtoms to Initiation of Bubble in W under Low EnergyIons Irradiation
Yu-Wei You a , Xiang-Shan Kong a , Q. F. Fang a , Jun-Ling Chen b , G.-N.Luo b , C. S. Liu a, ∗ , B. C. Pan c, † , and Y. Dai d, ‡ a Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academyof Sciences, P. O. Box 1129, Hefei 230031, P. R. China b Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, P. R. China c Hefei National Laboratory for Physical Sciences at Microscale and Department ofPhysics, University of Science and Technology of China, Hefei 230026, P. R. China d Spallation Neutron Source Division, Paul Scherrer Institut, 5252 Villigen PSI,Switzerland
Abstract
With the first-principles calculations of H and He induced energetics changewe demonstrate that in W the accumulation of H (up to 9) and He (up to 4)in a single vacancy (V) surprisingly reduce the formation energy of first andsecond nearest vacancy (as low as ∼ n (He n ) to V -H n (He n )and with the potential to lead to the growth of H/He-vacancy complexes: aninitial step to H and He bubble. This finding well explains the long-standingproblem of why H and He bubbles being produced on W surface exposedto low-energy (far lower than displacement threshold energy) D or He ionsirradiation. The further identified repulsive (attractive) interaction between ∗ [email protected], † [email protected], ‡ [email protected] Preprint submitted to Journal of Nuclear Materials June 9, 2018 -H (V-He ) and additional H(He) illustrates the experimentally observedbig difference of deposition depth of H ( µm ) and He ( ∼
1. Introduction
Tungsten (W), a high-Z material, has been chosen to be the plasma fac-ing material (PFM) in the next step fusion device ITER [1] due to its ex-cellent properties of high melting point and low sputtering yield. However,as a PFM, W must be exposed to extremely high fluxes of deuterium (D),tritium and helium (He) ions and neutrons, which directly leads to the dis-placement damage, bubble formation, and ultimate failure of the material[2–5]. Therefore it is crucial to understand hydrogen (H)/He-metal-atomsand H/He-defects interactions in the material.Generally, defects in materials such as dislocations, grain boundaries andvacancies can act as traps for H and He, and origins of H and He bubbles.Among these defects, vacancy receives much more attention. A series ofworks by Fukai et al . indicated that H can stabilize and increase the con-centration of vacancy because the vacancy formation energies in metals arereduced substantially due to the insertion of H atoms [6–9]. The role of va-cancy on trapping H to form the V-H n complex and the maximum numberof n in the complex were emphasized in the cases of many metals such as2d [9–11], Al [12–14], Fe [10, 15, 16] and W [17–20]. Nucleation free ener-gies evaluated with density function theory indicated that H trapping assiststhe divacancy formation in bcc W crystal [21]. No doubt, these contributeenormously to our understanding of H bubble formation and blistering, butthe microscopic atom-level relationship between H bubble formation and Htrapping in vacancies is far from understood, i.e., it is still unclear that howthe V-H n complexes grow to form H bubbles.Particularly, the minimum energy of D ions for producing displacementdamage in W is calculated to be 940 eV on the basis of the displacementthreshold energy of 40 eV [22], whereas the experimental results have shownthat D plasmas with energy of tens of eV definitely produce blisters [23–27].In sharp contrast with the case of W, the experimental result [28] reportedno bubbles formation in Pd implanted by 10 keV D to a very high supersat-uration of about 1.7 D/Pd mole ratio. Shu thought that the lowered vacancyformation energy by trapping H might be responsible for the bubble forma-tion in W when the incident H ion energy is greatly lower than the thresholdvalue for the displacement [27]. Ogorodnikova et al. proposed that several Datoms in a single vacancy could cause the displacement of neighboring latticeatoms due to stress-induced atomic diffusion, creating a divacancy and thusinitiate bubble growth [29]. It is also found experimentally that the extent ofblistering in W depends on the crystal orientation [23–27]. Similar to H, He3rradiation also often leads to blister formation and subsequent degradationof the mechanical properties of metals [30]. Experimental results showedthat bubbles are formed in W so far as the incident He ion energy is above5 eV, which is the surface barrier potential energy for He penetrating intothe W and is much lower than the threshold energy (500 eV) [31]. Empiricalpotential studies in α -Fe and Ni suggested that a spontaneous emission ofa self-interstitial atom nearby He n , V-He n and V -He n complexes is possi-ble if n is large enough [32, 33]. Using first-principles methods, Fu et al .investigated the energetics of V m -He n complex in α -Fe and predicted thatthe emission of a self-interstitial atom close to He n complex is energeticallyfavorable for n > et al. suggested a mech-anism for the growth of small He bubbles in low-energy He implanted Wby performing molecular dynamics simulations: displacements of W atomnearby He n complex towards the surface via the formation of (111) crowdioninterstitials [36, 37].Therefore, two crucial questions arise. The first question is how the ener-getics of nearest neighboring metal atoms of the V-H n and V-He n complexeschange with the increase of n , in other words, what will happen to the neigh-boring metal atoms of the vacancy as the number of trapped H or He atomsincreases? Does the creation of new vacancy become more easily at theneighboring sites closest to the trapped H/He vacancy with the number of H4r He atoms? The second question is what are the similarity and differencein the local structures and energetics between V-H n and V-He n complexes.Here, the similarity should be related to the common feature that both Hand He bubbles can be formed under low energy ions irradiation; the differ-ence should be related to the different behaviors of H and He bubbles. Theanswers to the first question should play a dominant role in atomic-level un-derstanding the H and He bubble formation mechanism; the answers to thesecond question will help us understand the difference (for example, in depo-sition depth) between H and He bubbles. In this paper, we have performedsystematic first-principles calculations mainly to examine the energetics ofrelevant V-H/He n complexes in bcc W in hope of shedding light on the for-mation mechanism of H and He bubbles. In addition, some calculations inPd (its stable H-site is octahedral interstitial site) have been carried out tomake a comparison and explore the obvious difference mentioned above in Hbehaviors between W and Pd.
2. Computation method
The present calculations are performed within density functional theoryas implemented in the VASP code with the projector augmented wave poten-tial method [38]. The generalized gradient approximation and the Perdew-Wang functional are used to describe the electronic exchange and correlation5ffect [39]. The supercell composed of 128 lattice points (4 × ×
4) is used.The relaxations of atomic position and optimizations of the shape and sizeof the supecell are performed. The plane wave cutoff and k-point density,obtained using the Monkhorst-Pack method [40], are both checked for con-vergence for each system to be within 0.001 eV per atom. Following a seriesof test calculations a plane wave cutoff of 500 eV is used and a k-point griddensity of 3 × × E f = E nW,mFtot − nE W − mE F , (1)where F indicates foreign H or He, E nW,mFtot is the total energy of the systemwith n W atoms and m foreign atoms like H or He, E W is the energy peratom of pure crystal W and E F is one half of the energy of H molecule (-3.40eV) or the energy of an isolated He atom (0.00 eV). The binding energies ofinterstitial H or He atoms are determined for different configurations, whichis expressed by: E F ,F , ··· ,F nb = n X E F ntot − E F F ··· + F ntot − ( n − E puretot , (2)where E F ntot is the energy of the W system with foreign atom
F n , E F F ··· + F ntot is the energy of the system with foreign atoms from F F n , and E puretot
6s the total energy of pure crystal W. In such a scheme a positive bindingenergy indicates attractive interaction while a negative value means a re-pulsion. The trapping energy E V − F n tr , when the number of H(He) atoms isincreased from n − n in a vacancy, is defined as: E V − F n tr = E V − F n tot − E V − F n − tot − ( E F tet tot − E puretot ) , (3)where n is the number of F atoms and E V − F n tot is the total energy of the systemwith n F atoms in a vacancy, E F tet tot is the total energy of the W system witha H(He) tetrahedral interstitial defect. A negative value of E V − F n tr indicatestaking an interstitial H(He) atom and adding it to a vacancy that alreadycontains n − | E V − F n tr | being theenergy gained in that process. Here, we specially calculate the new vacancyformation energy of the W atom close to the V m − -F n complex using thefollowing equation: E V new f = E V m − F n tot + E W − E V m − − F n tot , (4)where E V m − F n tot is the total energy of the system with m vacancies holding n F atoms. Zero point energy corrections are not taken into account, as it hasvery little influence (10 − eV) on our results such as binding energy, trappingenergy and vacancy formation energy.7 . Results and discussion Our calculated defect formation energy results of H and He in the perfectW system are in good agreement with that previously reported [41, 42]:both H and He prefer to occupy tetrahedral interstitial site (TIS) ratherthan octahedral interstitial site (OIS), and the energy difference of H(He) atOIS and TIS is 0.39 eV(0.21 eV). So in the present work the interactionsof two H(He) atoms located at different TIS separated by a certain distanceare considered. The calculated binding energies as a function of the finaldistances of the two H(He) atoms in the W system are shown in Fig. 1. Theresults show that the binding energy increases with the increasing distancebetween the two H atoms, and fluctuates around zero when the distance islarger than 0.2 nm which agrees well with the results reported by Liu et al [43]. The negative value of binding energy indicates the existence of repulsiveinteractions between near interstitial H atoms. The minimum binding energyis -0.46 eV in the W system, corresponding to the nearest distance of the twoH atoms (0.16 nm). Due to the repulsive interactions of H atoms in the Wsystem, H atoms can not form cluster easily but diffuse deeper into the bulkfrom the H-implanted W surfaces. In contrast, the binding energy is positiveand decreases as the increase of the distance between the two He atoms,8nd fluctuates around zero when the distance is larger than 0.30 nm. Themaximum binding energy is 1.08 eV when the two He atoms are separatedapart by 0.15 nm, which is in good agreement with the results reported byBecquart et al [30]. Moreover, it is noticeable that when the distance betweenthe two He atoms ranges from 0.16 to 0.30 nm, they will aggregate togetherspontaneously to the distance of ∼ According to the relationship of defect concentration with temperatureand defect formation energy [14], at 300 K the equilibrium concentrationof vacancy is relatively low ( ∼ − ) due to the large vacancy formationenergy of 3.20 eV in the perfect W system. As pointed out above, underlow-energy D or He ion irradiation (below threshold energy) no W atom isdisplaced to form a vacancy, however bubbles are observed at the W surface[23–27, 31]. It is natural to firstly ask whether interstitial H and He atomscould result in substantial change in the vacancy formation energy. So, theeffects of tetrahedral interstitial H and He on the vacancy formation havebeen studied. As shown in Table 1, the vacancy formation energies of the Watoms surrounded by 1, 2, 3 and 4 nearest H atoms at TIS are 1.99 eV, 0.83eV, -0.35 eV and -1.39 eV, respectively. Meanwhile, the calculated binding9nergies suggest that the occupancy of two H atoms (the distance betweenthe two H atoms is optimized to more than 0.2 nm) around the same Watom is possible, however the occupancy of 3 and 4 H atoms around thesame W atom is difficult because of their repulsive interactions. In contrast,even one interstitial He atom can reduce the vacancy formation energy to-1.36 eV, suggesting the nearest W atom of interstitial He becomes unstable.The large positive binding energy indicates that there exist strong attractiveinteraction among the He atoms around the same W atom. Thus, both Hand He atoms at TIS do reduce the energy required for the nearby vacancyformation considerably, especially He. Once the new vacancy is formed, itwill change to the V-H n or V-He n complex. H and He diffuse with the barriers of as small as 0.2 eV [44] and 0.06eV [30, 44] in perfect W, respectively, indicating that H and He can migratequickly until they are tightly trapped by the defects to form H(He)-defectcomplex. In this part, our main objective is to explore the energetics relatedto the V-H n (V-He n ) complex. We firstly calculate the trapping energy perH and He atom displayed in Fig. 2 as a function of the number of H and Hetrapped sequentially in a single vacancy. For the case of H in single vacancy,with increasing number of H atoms the trapping energy shows a generally10ncreasing trend, and its occasional fluctuations originate from the presenceof H configurations with high symmetry. The atomic configurations of one totwelve H in the vacancy are in good agreement with the results reported byOhsawa [19]. The side length of the unit cell of having trapped 12 H atomsinside the vacancy expands by ∼
5% compared to the perfect unit cell. Andthe formation of a H molecule inside a vacancy is not observed. The Bader’scharge analysis [45] proves that H gains charge from surrounding W, and theaveraged charge around H changes from ∼ -0.54 | e | to ∼ -0.62 | e | , which re-sults in the repulsive interactions among the H atoms inside the vacancy, andthat is why H molecule is not observed. It is energetically favorable for a Wmonovacancy to trap as many as 12 H atoms. The further calculation hasbeen carried out of the binding energy between an additional H atom andthe V-H complex, which is shown in the inset of Fig. 2. The calculatedbinding energy clearly indicates that the presence of monotonically increas-ingly repulsive interaction with decrease of the distance between additionalH atom and the V-H complex. And when their distance is increased to atleast 0.44 nm the binding energy approaches zero, suggesting that H atomscan not aggregate around the V-H complex to grow and form H bubblesonly based on the trapping H role of vacancy.In contrast, the trapping energy of He in single vacancy is more nega-tive than that of H in vacancy, indicating that He atoms are more strongly11rapped in W vacancy than H atoms, which is consistent with the previouslyreported results that the binding of He and the vacancy is much strongerthan that of H and the vacancy [44]. As displayed in Fig. 2, the trappingenergy of He firstly increases rapidly from about -5 eV to about -3 eV andthen fluctuates around -2.7 eV, being always far below zero energy even if Heatoms is added up to 16. That is, He is extremely more favorable to aggregatein the vacancy rather than sit at the TIS far away from vacancy. Why canthe vacancy trap so many He atoms? The optimized structure configurationsfrom one to sixteen He atoms trapped in the vacancy are shown on the samescale in Fig. 3. Obviously, with increasing He atoms the systems expandand distort more and more strongly but the nearest distance of He-He keepsabout 0.16 nm. And 15th and 16th He atoms indeed move out of the originalunit cell with the vacancy, indicating that the vacancy can trap up to 14 Heatoms and additional He atoms prefer to cluster round the V-He complex,which is in agreement with the tendency to form He clusters confirmed inRef. [30]. Here it should be stressed that the binding energy of V-He com-plex with additional He atom is more than one eV larger than the strongestbinding energy between two interstitial He atoms. Therefore He atoms mayaggregate persistently inside/around vacancy to grow and form He bubbles.The unit cell of having trapped 14 He atoms expands by ∼
26% in lengthcompared to the perfect unit cell, indicating that the swelling from He atoms12s very heavy. There exist high symmetry configurations for the cases of 1,2, 3, 4, 6 and 8 He atoms, which are partially responsible for the fluctuationin the trapping energy with the number of He atoms.Based on the above obtained results: the existence of respective repulsion-and attraction-interactions of interstitial H pairs and interstitial He pairs inbulk W, single interstitial He atom yielding the negative vacancy formationenergy while single interstitial H atom leading to the reduced but still pos-itive vacancy formation energy, and the appearance of repulsive interactionbetween additional H and V-H complex and strongly attractive interactionof additional He with V-He complex, we may draw the following conclu-sions. During He atom diffuses into the bulk it can be easily attracted tothe V-He n complex or the other He atoms. Whereas during H atoms diffuseinto the bulk, because of the absence of the attractive force from the V-H complex or the other H atoms, H atoms can diffuse deeper into the bulkthan He atoms. Thus it could be understandable that even at temperatureswhere the migration rate of He is far larger than that of H at 500 K, He willform bubbles right at ∼ .4. Mutation from V-H/He n complex into V -H/He n to lead to the growthof H/He-vacancy complex Although the above obtained results clearly reveal that a single vacancyin W can trap as many as 12 H or 14 He atoms, it remains unclear how theV-H n and V-He n complexes grow to form H and He bubbles specially due tothe saturation of H trapped inside vacancy. Using Eq. (4), we systematicallycalculate the new (second) neighboring vacancy formation energy of the Watom closest to the vacancy trapped n H or He atoms (i.e., V-H n or V-He n complex). Note that the first nearest neighbor (1 nn ), second nearest neighbor(2 nn ) and third nearest neighbor (3 nn ) (see the inset of Fig. 4) vacancyformation energies around the already existed vacancy are 3.16 eV, 3.52 eVand 3.22 eV, respectively. Thus, it is much difficult that the vacancy grows toform large vacancy clusters spontaneously under low energy ions irradiation.However, to our surprise, after the already existed vacancy having trapped Hor He atoms the situation will be very different. As shown in Fig. 4, the 1 nn and 2 nn vacancy formation energies are displayed as a function of the numberof trapped H or He atoms inside the vacancy. The 1 nn and 2 nn vacancyformation energies of the V-H n complex reduce in a steplike way, slowly atthe first (i.e., when the number of H is between 1-5) and then decrease veryrapidly to ∼ nn and 2 nn vacancy formation14nergies presently observed is quite different from the previously reportedvacancy formation energies in metals due to the insertion of H [9, 53], wherethe energy of a vacancy is lowered mainly by the sum of binding energies of Hatoms with vacancy. In general, the 1 nn vacancy formation energy is smallerthan the 2 nn vacancy formation energy. Compared to the remarkably changein the 1 nn and 2 nn vacancy formation energies, the 3 nn vacancy formationenergy decreases very weakly, here which is not presented in Fig. 4 for clarity.In sharp contrast, as shown in Fig. 5 we have not observed much strongdecrease in the 1 nn and 2 nn new vacancy formation energies of H-vacancycomplex in Pd. It is found that the maximum of 6 H atoms can be held in avacancy in Pd and the configurations of the H atoms are in good agreementwith previous results [11]. The resulting neighboring vacancy formation en-ergy due to the trapped 6 H atoms is still larger than 1.2 eV, therefore, it isreasonable that as pointed out previously no bubbles form in Pd implantedby 10 keV D ions [28].For the case of V-He n complex as shown in Fig. 4, the 1 nn and 2 nn vacancy formation energies decrease sharply and almost linearly before Heinside vacancy adds up to 10 and then do not change obviously. It shouldbe pointed out that both 1 nn and 2 nn vacancy formation energies are lowerthan 0 eV when the number of trapped He is beyond 4. The 3 nn vacancyformation energy closest to the V-He n complex behaves like that of the V-15 n complex, being unsensitive to the trapped He atom number. The greatdifference in energetics between H and He trapped in a single vacancy is inthat the 1 nn and 2 nn vacancy formation energies decease to ∼ n and V-He n complexes can be understoodby the weakened W-W metal bond which originates from two parts: theincreased W-W bond length and the decrease of electron density between W-W atoms around the corresponding complex. The averaged nearest-neighbordistances of both the 1 nn and 2 nn W atoms increase by ∼ n complex and ∼ n complex when n changes from 1to 12. The increase of the W-W bond length weakens the W-W interactions,causing the reduction of vacancy formation energies nearby V-H n and V-He n complexes. The electron density around 1 nn and 2 nn W atoms is obviouslyreduced. The electron densities of (110) plane across 1 nn , 2 nn and 3 nn atoms (named by 1, 2 and 3 in Fig. 4) of the vacancy are calculated anddisplayed in Fig. 6. Specially, we take two different cases of the V-H and V-He complexes for example, and they are compared with the ‘empty’vacancy (Fig. 6(a)). As shown in Fig. 6(b), the accommodation of 10 Hatoms in the single vacancy directly results in the extension of the light blueregion, and the shrinking of the dark green region around the 1 nn and 2 nn
16 atoms, while the various color regions around the 3 nn W atoms do notshow evident changes. These indicate that the electron density around 1 nn and 2 nn W atoms reduces obviously, whereas the electron density aroundthe 3 nn W atoms shows little change. Similar phenomena are found for theV-He complex that the electron density round the 1 nn and 2 nn W atomsdecreases obviously (shown in Fig. 6(c)), and some dark green regions evendisappear, but the electron density around the 3 nn W atoms of the V-He complex changes little. The reduction of the electron density could furtherweaken the interactions of W-W, leading to the decrease of the 1 nn and 2 nn vacancy formation energies nearby both V-H and V-He complexes.From above results and discussion, we can conclude that the new va-cancy is much easily produced in the region closest to the V-H n and V-He n complexes when the number of H or He inside the vacancy is beyond a cer-tain number. This means that the V-H n and V-He n complexes can easily(even spontaneously) mutate into the V -H n and V -He n complexes when n is large enough, respectively. The further calculations have been performedabout the energetics of closest W atoms (nearby V -H (V -He ) complex)which are removed in a stepwise fashion to create V -H (V -He ) and V -H (V -He ) complexes, we find that the successive vacancy formation en-ergies to form these complexes are 1.87 eV(-2.26 eV) and 2.42 eV(-0.43 eV),respectively. If the trapped H or He atoms are larger than 10, these new17acancy formation energies will be further reduced. This finding suggests acascade mechanism, as recently reported in the large variation of vacancyformation energies in the surface of crystalline ice [54], whereby once a va-cancy is created and when this vacancy traps certain numbers of H or Heatoms, neighboring W atoms become very weakly bound and thus easily tobe removed to form a new vacancy, and with the potential to lead to thegrowth of H/He-vacancy complexes.A V-He-complex mutation growth mechanism for He bubble has beenmentioned by Caspers et al. in 1978 [55], which works as follows. Assumingthe He atoms are trapped in a single vacancy and form V-He n complex dueto the strong He-vacancy bonding energy. Some fraction of the V-He n com-plexes, which reach a critical size, mutate into a complex with two vacancies(V -He n ) by ejecting an interstitial into the metal matrix. By absorbing Heatoms and further ejecting interstitial metal atoms, the complexes becomelarger and larger and finally lead to He bubble formation. Our results in-dicate that the mechanism is also suitable for H. The presently observedsubstantial reduction of the 1 nn and 2 nn vacancy formation energies closeto the V-H n and V-He n complexes, to our best knowledge, not only gives thedirect evidence for this mechanism, but also gives the reasonable explanationof the experimental results: Why H and He bubbles with diameters of a fewto hundreds of microns could form on W surface even if the ion energy is so18ow that no displacement damage is created [23, 26, 47–50].
4. Conclusions
In summary, based on the first-principles method we have investigatedthe energetics of H/He-vacancy complex in W by calculating the trappingenergy of H/He and the new nearby vacancy formation energy. We findthat a monovacancy can accommodate up to 12 H and 14 He to form V-H and V-He complexes, respectively. And the V-H exhibits strong repulsiverole with the approach of additional H atoms, but the V-He shows greatattraction to the nearby He atoms. The aggregation of H and He in Wvacancy remarkably favors the creation of new vacancy around the H/He-vacancy complexes: the first-nearest-neighbor and second-nearest-neighborformation energies of vacancy close to the H/He-vacancy complex decreaseto about 0 eV when the trapped atom number is up to 9 for H and largerthan 4 for He. These results, not only provide the direct evidence of the He-vacancy complex mutation mechanism proposed by Caspers for the He bubbleformation, but also suggest a cascade mechanism, as recently reported in thelarge variation of vacancy formation energies in the surface of crystalline iceby Watkins et al, whereby once a vacancy is created and when this vacancytraps certain numbers of H or He atoms, neighboring W atoms become veryweakly bound and thus easily to be removed to form a new vacancy, and with19he potential to lead to the growth of H/He-vacancy complexes. Besides, theresults well explain the experimental phenomena — the huge discrepancy ofdeposition depth of H and He in W, and the formation of H/He bubble withdiameters of a few to hundreds of microns on W surface even if the ion energyis so low that no displacement damage is created. However, there is no quitelarge decrease in the new neighboring vacancy formation energy nearby avacancy having trapped H atoms in Pd, leading to the neighboring vacancyformation energy still being larger than 1.2 eV, thus no bubbles formation inPd even implanted by 10 keV D ions. Acknowledgement
This work was supported by the National Magnetic Confinement FusionProgram (Grant Nos.: 2011GB108004 and 2009GB106005), the NationalNatural Science Foundation of China (Nos.: 91026002, 91126002) and theStrategic Priority Research Program of Chinese Academy of Sciences (GrantNos.: KJCX2-YW-N35 and XDA03010303), and by the Center for Compu-tation Science, Hefei Institutes of Physical Sciences.
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Fig. 1. The binding energy as a function of the final distance of interstitialH-H(He-He) pair in the perfect W system. The diatomic He will aggregatetogether to a distance of ∼ complex as a function of thedistance between additional H atom and the center of the V-H complex.Fig. 3. The lowest-energy configurations of 1 to 16 He atoms inside (oraround) a single W vacancy, note that here all configurations are shown usingthe same scale. Big and small balls indicate W and He atoms, respectively.Fig. 4. The 1 nn and 2 nn vacancy formation energy of the V-H n andV-He n complexes as a function of the number of trapped H or He atoms.Lines are guides to the eyes.Fig. 5. The 1 nn and 2 nn vacancy formation energy of the V-H n complexas a function of the number of trapped H atoms in Pd. Lines are guides tothe eyes. Inset: trapping energy per H in a single Pd vacancy as a functionof the number of H atoms, here the zero point is the energy of H at the OIS27ar away from the vacancy. From the inset, a maximum of 6 H atoms couldbe held in a vacancy in Pd.Fig. 6. The electron density maps (electron/˚A ) of three different cases:the empty vacancy (a), the V-H (b) and V-He (c) complexes. In all cases,the slices are cut through the same (110) plane of the supercell considered.1, 2 and 3 denote the first, second and third nearest neighbor W atoms ofthe vacancy. ‘x’ and ‘y’ represent the directions of h ¯101 i and h i .28able 1 The vacancy formation energy E Vf (eV) of W atom that has mul-tiple (1-4) neighboring interstitial H(He) atoms are calculated. Meanwhile,the binding energy E b (eV) of these H(He) atoms are also calculated usingEq. 2. 1H 2H 3H 4H 1He 2He 3He 4He E b (eV) – 0.00 -0.06 -0.22 – 1.08 2.18 3.61 E Vf (eV) 1.99 0.83 -0.35 -1.39 -1.36 -3.38 -5.31 -6.6429 .5 2.0 2.5 3.0 3.5 4.0 4.5 5.0-0.50.00.51.0 E b ( e V ) E b ( e V ) Distance (Å)
H-HHe-He
Distance(Å) E t r V - F n ( e V ) n HHe H E b ( e V ) Distance(Å) nn V-H n nn V - H n nn V - He n nn V - He n E f V n e w ( e V ) n E f V n e w ( e V ) nn V-H n nn V - H n n E t r V - H n ( e V ) n
33 22 (a) x y (c)(b)(c)(b)