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Towards suppressing H blistering by investigating the physical origin of the H–He interaction in W
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2010 Nucl. Fusion 50 115010
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IOP P UBLISHING and I NTERNATIONAL A TOMIC E NERGY A GENCY N UCLEAR F USION Nucl.Fusion50(2010)115010(8pp)doi:10.1088/0029-5515/50/11/115010
Towards suppressing H blistering by investigating the physical origin of the
H–He interaction in W
Hong-Bo Zhou1,Yue-Lin Liu1,Shuo Jin1,Ying Zhang1,
G.-N.Luo2and Guang-Hong Lu1
1Department of Physics,Beihang University,Beijing100191,People’s Republic of China
2Institute of Plasma Physics,Chine Academy of Sciences,Hefei230031,
People’s Republic of China
E-mail:LGH@buaa.edu(G-H Lu)
Received5March2010,accepted for publication27September2010
Published25October2010
Online at stacks.iop/NF/50/115010
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Abstract
双卡
We investigate the physical origin of H–He interaction in W in terms of optimal charge density by calculating the energetics and diffusion properties using afirst-principles method.On the one hand,we show a strong attraction between H and He in W originated from the charge density redistribution due to the prence of He,driving H gregation towards He.This can block the permeation of H into deeper bulk and thus suppress H blistering.On the other hand,we demonstrate that He,rather than H,energetically prefers to occupy the vacancy centre due to its clod-shell structure,which can block H2formation at the vacancy centre.This is becau He caus a redistribution of charge density inside the vacancy to make it‘not optimal’for the formation of H2molecules,which can be treated as a preliminary nucleation of the H bubbles.We thus propo that H retention and blistering in W can be suppresd by doping the noble gas elements.
(Somefigures in this article are in colour only in the electronic version)
1.Introduction
Nuclear fusion energy,as an environmentally clean and infinite energy source,is a way to reduce our reliance on fossil fuel sources in the future.Nowadays,energy shortage has driven us to make consid
鸡蛋拌黄瓜erable effort to develop nuclear fusion and thereby it is going to be of practical u in the foreeable future.Fusion energy is being developed internationally via the International Thermonuclear Experimental Reactor(ITER) Project[1],which aims to demonstrate the extended burn of deuterium–tritium(D–T)plasma in a fusion reaction.The property of plasma-facing materials(PFMs)under D–T plasma irradiation is one of the crucial issues in the u of nuclear fusion energy[2].
W as a high-Z material is considered to be the most promising candidate for PFMs in fusion reactors becau of its high melting point,high thermal conductivity and low sputtering yield for light elements[3].However,as a PFM, W will be expod to extremely highfluxes of H isotope ions,and He as well as high energy neutrons in a fusion reaction,which lead to blister formation,surface sputtering erosion and displacement damage.Therefore,the mechanical properties and the structural strength of W under H isotope ions and He irradiation are some of the key concerns for W PFM and have been under intensive investigation.So far,solution,accumulation,blister formation and retention behaviours with H or He solely in W have been investigated both experimentally and computationally[4–13].Detailed descriptions of an individual He or H atom in W have become attainable bad on the recent advances infirst-principles theory and computing power.An individual H[9]or He [10]atom is calculated to energetically occupy the tetrahedral interstitial site(TIS)in bulk W.
Vacancy and grain boundary defects in W rve as trapping centres for H[11,12]or He [13].We reveal the microscopic vacancy trapping mechanism for H bubble formation in W with a vacancy defect,which provides an isosurface of optimal charge density that induces collective H binding on its internal surface,a prerequisite for the formation of H2molecules and nucleation of H bubbles inside the vacancy[11].
The synergistic effect of H and He is shown to be quite different from that with single H or He irradiation alone [14–18].The trapping state of H is largely changed by the He ion irradiation in W[14].After He pre-implantation on W materials,the subquent H has been obrved to accumulate in the He saturated layer[15,16].The prence of He increas
0029-5515/10/115010+08$30.001©2010IAEA,Vienna Printed in the UK&the USA
D trapping at the near surface,limiting D diffusion into the W bulk[16–18].D retention can be reduced by as large as∼50% [14]or∼70%[17]due to the prence of He depending on the irradiation conditions.However,the prence of D has little effect on He retention[16,17].Computationally,only very limited work focud on the synergistic effects of H and He in W[19,20].Removing a He atom from H–He–V complexes is found to be more energy consuming than removing a H atom(∼2–3eV hi
gher),indicating that He substitution in a He–V complex by a H atom is almost impossible[20]. This suggests that He binds more strongly with a vacancy in comparison with H.In a previous work,in Ta,using nuclear reaction analysis and the ion implantation technique,D is found to energetically prefer to occupy the vacancies and internal surfaces of the He bubbles in comparison with the interstitial site[21].This is becau He induces H trapping at the vacancies or the internal surface of He bubbles produced by atomic displacements during the energetic implantation of He.The binding of H is therefore similar to chemisorption of H at clean external surfaces,which one calls a‘chemisorption-like mechanism’.However,the physical intrinsic mechanism for the experimentally obrved H trapping by He in W is still unclear.
In this work,we try to explore the physical origin of the H–He interaction in W by investigating the synergistic dissolution and diffusion behaviour of H and He in W using afirst-principles method.The revelation of the mechanism is able to pave a theoretical way to suppress H bubble formation in W PFMs.
2.Computational method
Ourfirst-principles calculations were performed using the pudopotential plane-wave method imple
mented in the Vienna Ab-initio Simulation Package(V ASP)code[22,23] bad on density functional theory.We ud the generalized gradient approximation of Perdew and Wang[24]and projected augmented wave potentials[25],with a plane wave energy cutoff of350eV.A bcc W supercell of128atoms containing a monovacancy was ud,and their Brillouin zones were sampled with(3×3×3)k-points by the Monkhorst–Pack scheme[26].The calculated equilibrium lattice constant is3.17Åfor bcc W,in good agreement with the corresponding experimental value of3.16Å.Both supercell size and atomic positions are relaxed to equilibrium,and energy minimization is continued until the forces on all atoms are converged to less than10−3eVÅ−1.
3.Results and discussion
3.1.Interaction of H and He in intrinsic W
Compared with the octahedral interstitial site(OIS),the TIS has been demonstrated to be the most stable site for H and He in intrinsic W.Table1shows that the solution energy of H at the TIS is0.38eV lower than that at the OIS[9,19,27], in which the zero-point energy(ZPE)of H is not considered. However,the ZPE should be taken into account for the light elements H and He,becau it plays an important role in the dissolution behaviour of H and He in bulk W.We examine here
Table1.The calculated ZPE and solution energies(eV)of a H or He atom in W in comparison with the previous studies.All the solution energies are referred to one-half of the energy of a H2 molecule(−3.38eV).
Configuration H TIS H OIS He TIS He OIS
ZPE0.2630.2560.0780.034 with ZPE This work 1.00 1.38 6.14 6.37
without ZPE This work0.88 1.26 6.07 6.34
[9]0.88 1.26——
[10]—— 6.16 6.38
[19]0.86 1.26 6.23 6.48
the energy state of H in very different environments in bulk W.Our computation shows that the ZPE of H is0.263eV and 0.256eV at the TIS and OIS,respectively.Table1suggests that the ZPE of H has a significant effect on the solution energies of H in bulk W,but the relative stability of H at the TIS and the OIS remains unchanged.On the other hand,an individual He atom is also energetically favourabl老年疑心病
e sitting at the TIS in W[10,19]as shown in table1,similar to that of H.The ZPE of He is calculated to be0.078eV and0.034eV at the TIS and the OIS,respectively.Again,the ZPE will not change the order of the relative stability of He at the TIS and the OIS.
cad操作
In order to investigate the interaction between H and He in bulk W,one He atom is t at a TIS while the H atom occupies a different TIS.The H solution energy(E sol H)can be obtained by
E sol H=E N W,He(TIS),H(TIS)−E N W,He(TIS)−12E H2,(1) where E N W,He(TIS),H(TIS)is the total energy of bulk W with interstitial He and H atoms,and E N W,He(TIS)is the total energy of bulk W with a single interstitial He atom.The third term
1
2
E H
2
is one-half of the energy of a H2molecule(−3.38eV) according to the prent calculation.For the H2m
olecule,the ZPE of H is calculated to be∼0.135eV with a vibrational frequency of4315cm−1,which agrees reasonably well with the experimental value of4395cm−1[28].In addition,the ZPE of H in the prence of He is∼0.236–0.263eV depending on the H–He distance.The ZPE is taken into account for the computation of H solution energy surrounding He.
Figure1shows the H solution energy as a function of the H–He distance,which suggests that the existence of He substantially affects the dissolution behaviour of the interstitial H in bulk W.The H–He interaction is repulsive with certain H–He distance that is∼1.6Å.Beyond this distance,H gains additional energy due to the prence of He,leading to a lower H solution energy in comparison with that of H at the TIS without He.The solution energy increas with increasing H–He distance,and converges to that of H at the TIS without He at∼3.4Å.The lowest solution energy occurs at a H–He distance of1.95Å(TIS C,0.76eV).Therefore,the binding energy of H–He at the most stable configuration is0.23eV, which is consistent with that from Becquart and Domain[20], but0.09eV larger than that from Lee et al[19].In addition, the H–He equilibrium distance is intermediate between tho of H–H(∼2.2Å)and He–He(∼1.6Å)in W[9,20,27].
We further investigate the atomic configuration in order to explore the origin of the H solution energy gain due to the prence of He.Ourfirst-principles calculations indicate that the variation in the volum
e of the supercell induced by the 2
Figure1.H solution energy in W with He as a function of the H–He distance.
prence of He is so small that it can be neglected.However, the atomic distance between He and the nearest neighbour W extends to1.94Åas compared with1.77Åfor the ca without He.Further,the distances between the neighbouring W atoms increa by∼0.30Ådue to the prence of He at the TIS centre.The suggest the volume expansion of the local TIS with He,which leads to a further expansion of the neighbouring TISs becau they share W atom(s)with the TIS with He.For example,
as shown infigure1,the TIS volumes of A–G all extend,but that of J remains unchanged.As a result,the charge density in the TISs decreas due to the volume expansion.Physically,the occupation behaviour of H in a metal can be understood via the optimal charge density [11,12,29].The TIS in W is shown to have an electron density of∼0.27electronÅ−3[11],which is higher than H prefers to occupy in W.Thus,the lower charge density at the TIS surrounding He due to the volume expansion can reduce the solution energy of H.This is why the TISs of B–G exhibit lower H solution energies due to the prence of He in comparison with that without He(figure1).For the TIS of C with the lowest solution energy,the charge density is shown to reduce to as low as∼0.21electronÅ−3.This suggests that He can rve as a trapping centre of H in bulk W by providing a lower charge density for H dissolving,similar to the dissolution behaviour of H in a monovacancy[11].However,although the TIS of A has a lower charge density(∼0.22electronÅ−3),it exhibits a much higher solution energy.This is becau the interaction of H and He for the A ca is strongly repulsive due to the shorter H–He interatomic distance(∼1.6Å).This can be understood by the binding energy as a function of H–He distance in vacuum.
As shown infigure2,we display the calculated binding energy between free H and He as a function of the H–He interatomic distance in vacuum.It shows a strong repulsive interaction between H and He
when their interatomic distance is lower than∼2.5Å.Beyond this distance,the binding energy increas rapidly and converges to zero,but experiences a very small peak at a H–He equilibrium distance of∼3.25Åwith the lowest binding energy of0.012eV,95%lower than the H–He binding energy in W.This implies that a direct interaction between H and He in W can be neglected.Conquently,the strong attraction between H and He in W originates from
the
Figure2.The calculated binding energy(eV)of a H–He pair in vacuum as a function of the H–He spatial paration(Å).Positive values indicate attraction,while negative ones indicate repulsion.
charge density redistribution induced by the prence of He. The H–He interaction is quite different from tho between two He atoms and two H atoms in W.Previous studies[20,27] show an elastic interaction between two He atoms with a larger binding energy(∼1.0eV)and a shorter equilibrium distance (∼1.6Å).In contrast,the interaction between double H atoms is much weaker with a binding energy of∼0.01eV[9,20,27].
3.2.Single H at a He–vacancy complex in W
In the previous study,it has been demonstrated that a vacancy can rve as a trapping centre for H due to the strong binding between H and the vacancy[11].The solution energy of H in a monovacancy is−0.31eV,which is much lower than that of H at the TIS in bulk W.This is becau the vacancy provides an isosurface of low charge density(0.11electronÅ−3),and H energetically prefers to stay on such an isosurface[11].In addition to H,He is also shown to prefer to occupy the vacancy. The vacancy centre is the most stable site for He in a vacancy with a solution energy of1.57eV according to the prent calculation.Becau H and He coexist in a fusion reactor, we investigate the synergistic behaviour of H and He in W. The H solution energy in the vicinity of a He–vacancy(He–V) complex has been calculatedfirst.The energy minimization finds the most stable site for H to be at an off-He position (∼1.63Åfrom He)clo to a TIS.H prefers to stay on an isosurface of the same charge
density of0.16electronÅ−3 surrounding the He–V complex,as shown infigure3.The solution energy is the same on the isosurface with24minimum sites very clo to the TISs.Figure3(a)shows four minimum sites clo to the TISs on the front face.The H solution energy at the sites is demonstrated to be−0.07eV taking into account the ZPE of H at the sites(0.20eV).This value is1.07eV lower than that of H at the TIS in bulk W,while 0.21eV higher than that at a monovacancy.
According to the above analysis,the optimal charge density of H at the He–V complex is0.05electronÅ−3higher than that of H in the He-free vacancy.This is becau the prence of He changes the charge density distribution at the vacancy.In addition,the configuration effect also 3
Figure3.Isosurface of optimal charge density for H binding at a He–V complex:(a)without H,(b)with one H.The cross mark the four minimum-energy H binding sites on the front side of the isosurface.
plays a role becau vacancy volume increas by0.9Å3due to He occupancy at the vacancy centre.Conquently,the isosurface of optimal charge density for H expands from20.58 to35.45Å2,producing more possible‘optimal charge density sites’for H(24sites)in comparison with that for a He-free vacancy(6sites)[11].Further,the optimal charge density of H provided by the He–V complex is lower than that at the TIS in bulk W by0.11electronÅ−3,resulting in a stronger binding between the H and He–V complex in comparison with H at the TIS.This implies that the He–V complex can act as a trapping centre which drives gregation of H towards it.
In addition,it can be found infigure3that another smaller sphere with a radius of∼0.8Åexists,having the same value as the optimal charge density for H(0.16electronÅ−3),which is different from the ca for H at the He-free vacancy.Such a sphere appears due to the prence of He.It is not suitable for H to stay owing to a strong repulsive interaction between
H and He at this distance as shown infigure2.
3.3.H trapping surrounding a He–V complex Theoretically,24equivalent most stable sites for H atoms surrounding the He–V complex exist.However,all the sites cannot be occupied together by H becau of the H–H repulsive interaction in W[9].To investigate the trapping of multi-H atoms surrou
nding the He–V complex in W,we calculate the trapping energy of additional H atoms gregating to the He–V complex and determine the number of H atoms that a He–V complex can accommodate and the stability.We bring the H atoms one by one to the He–V complex and minimize the energy tofind the optimal dissolving site at each step.Each H atom occupies,one by one,the‘clo-to-TISs’surrounding the He–V complex on the isosurface of optimal charge density.It is important to note that as more H atoms are added,the surface of optimal density shrinks so that there will be less available optimal-density sites to accommodate additional H.
In this work,we try to calculate the number of H atoms that one He–vacancy complex can trap.This depends on the ways of calculating the H trapping energy at the He–vacancy complex.Generally,diffusion of H towards the vacancy in W should be associated with the H concentration.Qualitatively, at a high H concentration,multi-H atoms can diffu to the He–vacancy complex at the same time(the simultaneous way).At a low H concentration,H atoms can diffu to the He–vacancy complex quentially(the quential way).As a matter
of
Figure4.The trapping energy per H as a function of the number of H atoms trapped by the He–V complex in W.The zero point is the energy of H in the TIS far away from the He–V complex.
fact,both ways are ud to determine the number of trapping impurity atoms in defects,but there is no direct comparison between the two ways.For example,for H in Al,Lu and Kaxiras[30]demonstrated that a single vacancy can trap12 H atoms using‘the simultaneous way’,while Ismer et al[31] reported that a single vacancy can only trap8H atoms using ‘the quential way’.
For‘the simultaneous way’,the average trapping energy (E trap
sim
)per H atom is defined as
E trap
sim
=1
n
[E(N−1)W,HeV,H
n
−E(N−1)W,HeV]
−[E N W,H(TIS)−E N W],(2)
where E(N−1)W,HeV,H
n
and E(N−1)W,HeV are the total energies of the He–V complex system with and without H atoms, respectively.E N W,H(TIS)and E N W are the energies of the W supercell with and without H atoms,respectively.A negative
E trap
sim
means energy gain when the H atoms are trapped by the He–V complex relative to dispersion into n different TISs.On the other hand,for the‘the quential way’,the quential
trapping energy(E trap
q
)per H atom can be obtained by
E trap
q
厝火积薪的意思=E(N−1)W,HeV,H
n
−E(N−1)W,HeV,H
n−1
word清除格式−E N W,H(TIS)+E N W.(3) The trapping energy as a function of the number of H trapped by the He–V complex in W is illustrated infigure4.
For‘the simultaneous way’,according to equation(2), we calculate the average H trapping energy per H atom as a function of the number of H trapped by the He–V complex,as shown infigure4.Thefirst H atom attains a trapping energy of−1.07eV as it sits on the optimal charge density isosurface. As more H atoms are added,they experience an interaction of H with each other.The average trapping energy becomes a little lower(−0.97eV)when the cond H atom is embedded in comparison with th
at of thefirst one(−1.07eV).With an increasing number of H atoms,the trapping energy per H atom increas,as shown infigure4.When the number of H atoms is up to13,the average H trapping energy is still negative at−0.50eV.It is lower than that of H at the TIS far away from the He–V complex(t as the ZPE infigure4),which indicates that the number of H atoms trapped by the He–V 4
Figure5.The atomic configuration of the(HeV)H12complex in W. complex should be larger than13.After carefully checking the atomic configurations of each H addition,we found that a He–V complex can only accommodate12H atoms.The 13th embedded H atom will fall into one of the TISs out of the vacancy,although the average H trapping energy is still lower than that of H in the TIS.
On the other hand,‘the quential way’gives different results.As illustrated infigure4,with an increasing number of H atoms added from1to5,the trapping energy increas. It is important to note that the trapping energy becomes lower (−0.69eV)when the6th H atom is added in comparison with the5th one(−0.53eV),suggesting that(HeV)H6is stabler than(HeV)H5in W.This may be attributed to the fact that the symmetry of(HeV)H6is higher than that of(HeV)H5.When the7th H atom is added,the trapping energy is much larger than that of the6th H atom by0.31eV.After the7th H atom is added,the variation of trapping energies becomes weak until the13th H atom is added,and even slowly decreas from 9th to12th.Similar results were also given by a recentfirst-principles study[32].Finally,the13th H atom addition gives ri to a positive trapping energy of0.22eV in reference to that of H at the TIS in bulk W.This suggests that the13th H atom will prefer to occupy the TIS in bulk W rather than the He–V complex.Therefore,the maximal number of H atoms that can be trapped by the He–V complex is12via‘the quential way’.
We show the above two different ways to bring the H atoms into a He–V complex,showing different trapping energetics.However,one He–V complex can hold up to 12H atoms,independent of the trapping ways.Atomic configurations show that the shortest distance between H atoms is always much longer than that of the H2molecule(0.75Å). This implies no H2molecule forms with He at the v
acancy centre.Interestingly,H forms an icosahedron in the(HeV)H12 complex,as shown infigure5.The icosahedron consists of12 isosceles and8equilateral triangles.The distance between H and its1NN is∼1.74Å,and that between H and its2NN is ∼2.00Å.As a comparison,the equilibrium H–H distance in W is∼2.2Å[9,20,27].
3.4.H diffusion into a He–V complex
Clearly,the above results demonstrate the thermodynamic feasibility of H gregation towards the He–V complex trap so as to initiate a stable complex(HeV)H12.Next,we will investigate the kinetic process for such a trapping.We calculated the energy barriers for H atoms diffusing one by
one from a far-away bulk TIS to the He–V complex.We ud a drag method relaxing the atomic positions constrained in a hyperplane perpendicular to the vector from the initial to the final position[33].
In our previous investigation,it was found that the optimal diffusion path of H is TIS→TIS with a diffusion energy barrier of0.20eV in the intrinsic bulk W[9].Away from the He–V complex,H atoms also jump from one TIS to another with the same diffusion energy for H in the intrinsic bulk W. As they move clo towards the He–V complex,the diffusion barrier is reduced to0.18eV from the3NN(si
te1)to2NN (site2)TIS and0.15eV from the2NN to1NN(site3)TIS of the He–V complex,respectively,as shown infigure6(a).H jumps into the He–V complex from the1NN TIS into the He–V complex occupying site4(figure6(a)),one of the24minimum sites at the isosurface of optimal charge density(figure3), with a much reduced barrier of0.06eV.Obviously,the barrier as well as the site solution energy of H become lower with H approaching the He–V complex.Thefirst6H atoms will diffu into the He–V complex via the same diffusion barrier as thefirst H from the six different faces(up and down,back and front,left and right).It is important to note that the1NN TIS of the He–V complex is no longer a local stable site for H shown infigure6,different from the TIS in bulk W.
On the other hand,the7th–12th H atoms will diffu into the He–V complex via a similar way but differently from the first six atoms,since the6H atoms exist clo to six different faces.We take the12th H atom as an example.As shown infigure6(b),when it moves clo towards the(HeV)H11 complex,the diffusion barrier is also0.18eV from the3NN (site1 )to2NN(site2 )TIS of the He–V complex,similar to thefirst H atom.However,other diffusion barriers become 0.19eV and0.12eV,respectively.They are higher than that of thefirst H by0.04eV and0.06eV,respectively,but still lower than that in bulk W.This suggests that H diffusion into the He–V complex is kinetically feasible.
3.5.Competency of H and He occupation at a vacancy in W As mentioned in ction1,H and He coexist in nuclear fusion reactions.Now we investigate the capability of H and He to occupy a vacancy in W,which plays an important role in the understanding of the interaction between H and He. Energetically,a vacancy can provide stable sites for H in W[11].The most stable site for H in a vacancy is found to be at an off-vacancy-centre position(∼1.28Åfrom the vacancy centre)clo to an OIS with a solution energy of−0.31eV.As mentioned above,the vacancy centre is the most stable site for He in a vacancy with a solution energy of1.57eV according to the prent calculation.However,the binding energies for H and He with the vacancy are1.18eV and
4.59eV with respect to their solution energies at the TIS in W,respectively.This suggests that He can gregate towards the vacancy from the interstitial site much more easily than H.Therefore,He is more energetically favourable to occupy the vacancy in comparison with H.
The above results demonstrate the thermodynamic feasibility of He gregation towards a vacancy trap. Kinetically,one should explore the process in order to understand how He diffus into the vacancy.Although He 5
