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First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces
Journal Pre-proof First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces
Xu Zhang, Xuebang Wu, ChunJu Hou, Xiangyan Li, C.S. Liu PII:
S0169-4332(19)32811-9
DOI:
https://doi.org/10.1016/j.apsusc.2019.143995
Reference:
APSUSC 143995
To appear in:
Applied Surface Science
Received date:
2 July 2019
Revised date:
3 September 2019
Accepted date:
12 September 2019
Please cite this article as: X. Zhang, X. Wu, C. Hou, et al., First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces, Applied Surface Science(2018), https://doi.org/10.1016/j.apsusc.2019.143995
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© 2018 Published by Elsevier.
Journal Pre-proof
First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces Xu Zhang a, b, c, Xuebang Wu a, *, ChunJu Hou d, Xiangyan Li a, and C. S. Liu a, ** a
Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of
Sciences, P. O. Box 1129, Hefei 230031, PR China b
University of Science and Technology of China, Hefei, 230036, PR China
c
School of Material Science and Engineering, JiangXi University of Science and Technology,
Ganzhou, 34100, PR China
of
of Science, Jiangxi University of Science and Technology, GanZhou, 34100, PR China
ro
dSchool
Abstract:
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In this work, the stability and adhesion of twelve tungsten-zirconium carbide (W-ZrC) interfaces as well as the migration of hydrogen (H) and helium (He) near the interface were
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investigated by first-principles calculations. The results of interface energy show that the coherent ZrC(200)C/W(100) interface is the most stable configuration with the smallest value in all the
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investigated stoichiometric structures. The stability of non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) is also analyzed. The electronic structure analysis reveals that the interfacial
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C-W bonds have a mixed property of covalent and ionic feature. Furthermore, the interface acts as strong traps for H and He with segregation energies of -0.97eV and -2.03eV, respectively. The
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diffusion of H and He across the ZrC(200)C/W(100) interface demonstrates that H and He atoms can reach the favorable segregation sites at the interface from the W matrix by overcoming energy barriers of about 0.3 eV and 0.58 eV, respectively, but it is quite difficult for the trapped H and He to escape out of the interface due to the higher diffusion energy barriers. Our results agree well with the experimental findings about the microstructure and H isotope retention in W-ZrC alloys.
Keywords: W-ZrC interface; interface energy; stability; hydrogen; diffusion; first-principles calculations
*
E-mail addresses: [email protected] (X.B. Wu), [email protected] (C.S. Liu). 1
Journal Pre-proof 1. Introduction Tungsten (W) is considered as the most promising candidate for the plasma-facing material (PFM) of fusion reactors due to its excellent properties such as high melting point, high thermal conductivity, low tritium retention and high resistance to sputtering[1-3]. However, one of the critical problems of W that hinders its application is the poor thermo-mechanical properties, such as high ductile-to-brittle transition temperature and embrittlement after recrystallization and irradiation by neutrons or ions [4-7]. Therefore, substantial research is being under taken internationally towards manufacturing advanced W-based materials [8], with improved mechanical properties based on micro-alloying and compositing. Among these fine-grained and
of
toughened W-based materials, nanostructured W doping with carbide nanoparticles such as TiC and ZrC are quite promising due to their improved ductility at low temperature and improved
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thermal shock resistance [9-13]. The formation of interface between W matrix and the carbides is believed to be the main reason for the improved excellent ductility and strength of carbide
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dispersed strengthened W materials, especially the formation of coherent or semi-coherent interfaces [14, 15]. Therefore, so far, much effort is made to obtain detailed information about the
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interfaces from experimental [16-18] and theoretical views [19-22].
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Recently, W-ZrC and W-TiC alloys were fabricated with advanced mechanical properties such as high strength, good thermal shock resistance and lower ductile-to-brittle transition temperature about 100 ºC. The observed coherent Kurdjumov-Sachs (K-S) orientation interface
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structure between ZrC/TiC and W plays an important role in the improvement of mechanical properties, thermal shock behaviors, and irradiation resistance to plasma and ions [17, 23].
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However, based on the experimental observations, it is difficult to clarify the mechanism about how the interface microstructure affects the properties. The first-principles calculations based on the density functional theory (DFT) can accurately provide the detailed atomic and electronic structures of interfaces and predict the stability, adhesion strength and fracture toughness[10, 24]. Recently, researchers have tried to understand the cohesion of W-TiC and W-ZrC interface. Dang et al. found that the W(110)-TiC(100) interface is energetically favorable with lower interface energies and has higher strength than the W(100)-TiC(100) interface [21]. The W(110)-ZrC(111) interface is reported to be more favorable than others with strong W-C bond [25]. However, due to the complexity of interface structures, the properties about the W/ZrC interface such as cohesion, stability, and especially the irradiation resistance to H/He plasma are still missing. In this work, first-principles calculations are performed to study the interface properties of bcc W and NaCl structured ZrC. First, the bulk and surface properties of W and ZrC are studied and compared with others. Then, twelve possible interface structures between W and ZrC are constructed to evaluate the stability and cohesion properties by analyses of energetics and
2
Journal Pre-proof electronic structures. Finally, the trapping and diffusion of H and He atoms around the most stable interface are investigated. Our calculations will provide a deep insight into the properties of W-ZrC alloy.
2. Computational method The first-principles calculations are performed within the DFT framework as implemented in the Vienna Ab Initio Simulation Package (VASP) [26] code with projector-augmented wave (PAW) potential method. The electrons 4d105s1 for W, 4d105s25p2 for Zr and 2s22p2 for C are treated explicitly as valence electrons, and their wave-functions are described by plane-wave basis. The
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ionic potential of the nuclei and inner electrons is described by pseudopotentials that follows the projector augmented wave (PAW) approach [27]. Exchange and correlation functions are taken in
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a form proposed by Perdew and Wang (PW91) [28] within the generalized gradient approximation (GGA)[28]to describe the electronic exchange and correlation effect [29].The cutoff energy is
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taken to a value of 500 eV. The K-point mesh is sampled within 0.003 Å-1 by using the Monkhorst-Pack scheme [30].The atomic positions are relaxed using the conjugated gradient
3. Results and discussion 3.1 Bulk and surface properties
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method until the force on each atom was less than 0.01 eV/Å.
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The calculated equilibrium lattice constant is 3.176 Å for bcc W, in good agreement with the previous value of 3.175 Å [31], while it is 4.726 Å for rock-salt structured ZrC, which matches
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well with the previous calculation value of 4.72 Å [32, 33] and experimental one of 4.698 Å [34]. Before constructing the interface models, the properties of W and ZrC surfaces in typical Miller planes, i.e. W(100), W(110), ZrC(200), ZrC(110) and ZrC(111) surfaces are investigated. A series of test calculations with different thickness of layers and vacuum are carried out to determine the minimum layers necessary to represent a bulk-like slab. The surface energies, Esurf, of different surfaces are calculated using the following formula [35-37] Esurf =
bulk Etot slab -NZr μZrC +(NZr -NC )μC
2A
,
(1)
bulk where Etot slab is the total energy of the W or ZrC slab, μZrC is the energy of per unit in bulk ZrC
material, NZr and NC are the numbers of Zr atoms and C atoms in the slab, μC is the chemical potential of C, and A is area of W or ZrC surface. The chemical potential of Zr or C in the slab must be less than that of its bulk. Therefore, the range of μC -μbulk is C ∆H0f ≤μC -μbulk ≤0, C
(2)
∆H0f =μbulk -μbulk -μbulk , ZrC C Zr
(3)
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Journal Pre-proof Here, ∆H0f (-2.95 eV) is the formation heat of bulk ZrC. μbulk and μbulk are the chemical C Zr potential of bulk C and Zr, respectively. However, NZr and NC are equal when the ZrC slab is stoichiometric. Accordingly, the Eq. (1) can be simplified to [38] Esurf =
bulk Etot slab -NZr μZrC
2A
,
(4)
The surface energy of Esurf converges to a constant value when the number of layers reaches 15 for W(100) and W(110) surfaces, and 9 for ZrC(200) and ZrC(110) surfaces. As shown in Table 1, our calculated Esurf agrees well with previous theoretical and experimental results, for example, the calculated Esurf of W(110) surface is 3.19 J/m2, which agrees with the previous theoretical value of
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3.21 J/m2 [31] and the experimental value of 3.27 J/m2 [39], and that of ZrC(110) of 3.23 J/m2 is consistent with the previous theoretical value of 3.199 J/m2 [40].
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The polar ZrC(111) surface consists only one species of Zr or C atom. It is impossible for a stoichiometric slab to terminate both surfaces with the same species. So a symmetric slab is used
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and a non-stoichiometric slab with identical surfaces is used to obtain the surface energy of a
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particular termination. Using the similar method by Liu et al. [35, 41], the convergence tests of ZrC (111) surface are performed by comparing the relaxations of the first few interlayer spacings
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as a function of slab thickness. The calculations show that a 9-layer slab is thick enough to mimic the bulk behavior. According to Eq. (1), the surface energies of ZrC(111) slabs as a function of carbon chemical potential are shown in Fig. 1. It is found that the Esurf value of the C-terminated
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ZrC(111) surface decreases with increasing the chemical potential μC -μbulk but that of the C Zr-terminated.
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Zr-terminated increases. The values of Esurf for C-terminated surfaces are larger than those of
3.2 Interface model and stability
To systematically investigate the interface, we constructed twelve possible candidate models for
W/ZrC
interfaces,
ZrC(110)Zr/W(110),
i.e.,
ZrC(200)C/W(100),
ZrC(110)C/W(100),
ZrC(200)Zr/W(100),
ZrC(110)Zr/W(100),
ZrC(110)C/W(110), ZrC(200)C/W(110),
ZrC(200)Zr/W(110), as well as non-stoichiometric C(or Zr)-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, in which the subscript C (Zr) denotes the C (Zr) atom on the top of the W atom near the interface. Based on the above surface calculations, these interface models are formed with a fifteen-layer W(100) or W(110) slab connected to a nine-layer ZrC(200), ZrC(110) or ZrC(111) slab along with 12 Å of vacuum. Fig. 2 shows the atomic configurations of six typical ZrC/W interfaces, where only three layers close to the interface are presented to clearly show the stacking sequences of atoms in the interfaces. To establish the interface models, A 2×2 surface unite cell is selected for both ZrC(200) and W(100) for constructing the ZrC(200)/W(100)
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Journal Pre-proof interface, 1×1 of ZrC(110) and W(110) for the ZrC(110)/W(110) interface, 1×4 of ZrC(200) and 1×3 of W(110) for the ZrC(200)/W(110) interface, 1×2 of ZrC(110) and 1×3 of W(100) for the ZrC(110)/W(100) interface, 1×4 of ZrC(111) and 1×7 of W(100) for the ZrC(111)/W(100) interface, and 1×3 of ZrC(111) and 1×4 of W(110) for the ZrC(111)/W(110) interface. The interface energy (Eint) can be used to evaluate the stability and the adhesive strength of an interface. The interface with smaller Eint has better stability. The value of Eint can be obtained by the following equation [35, 42] Eint =
bulk bulk Eint tot -EW -NZr μZrC +(NZr -NC )μC
S
f surf -Esur W -EZrC ,
(5)
bulk where S is the area of the ZrC/W interface, Eint is tot is the total energy of the interface, and EW
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f surf the energy of bulk W. Esur W and EZrC are surface energies of W and ZrC slabs, respectively. The
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Eint values of eight stoichiometric interfaces are shown in Fig. 3. It can be seen that the interfaces with C atoms on the top of W atoms have lower Eint than those with Zr on the top of W atoms,
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indicating a higher stability of the configurations with C atoms on the top of W atoms. In addition, it is noted that the coherent ZrC(200)C/W(100) interface has the lowest Eint and exhibits the best
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stability.
For the non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the interface
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energies as a function of carbon chemical potential μC -μbulk are plotted in Fig. 4. Also included C in the figure is the interface energy of stoichiometric ZrC(200)C/W(100) interface. At the low
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carbon potential, the non-stoichiometric interface energies of C-terminated ZrC(111)/W interface are higher than those of the Zr-terminated interfaces and that of ZrC(200)C/W(100) interface,
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indicating that the latter is more stable. Second, at the high carbon chemical potential, the non-stoichiometric interface energies of the Zr-terminated ZrC(111)/W interfaces are higher than that of the ZrC(200)C/W(100) interface, which means that the ZrC(200)C/W(100) interface is more stable. In addition, the C-terminated interfaces are more stable than the Zr-terminated interfaces and the ZrC(200)C/W(100) interface with increasing the carbon chemical potential because of the lower interface energies. The ideal work of adhesion (Ead ) is an important parameter to describe the adhesive properties of interfaces [36], which is defined as the minimum reversible energy needed to separate the interface into two free surfaces. And Ead can be expressed by the difference in total energy between the interface and the relevant isolated slabs using the following formula [22, 43-45], Ead =
Ew +EZrC -Etot A
,
(6)
where EW and EZrC represents the total energies of the 15-layer W slab and the 9-layer ZrC slab , respectively. A is area of the ZrC/W interface. The interface with a larger Ead shows the stronger interfacial
bonding
strength.
The Ead of eight stoichiometric interfaces and four 5
Journal Pre-proof non-stoichiometric interfaces are calculated and also presented in Fig. 3. The Ead of C-terminated ZrC(111)/W(110) interface is the largest, and followed by the ZrC(111)/W(100) and ZrC(200)C/W(100) interfaces, indicating that the C-terminated ZrC(111)/W(110) interface has the strongest interaction between the interfacial atoms, which agrees well with other reported theoretical result [25]. In addition, the local atomic structures of ZrC(200)C/W(100), C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces are examined. The shortest C-W bond length near the ZrC(200)C/W(100) interface is 2.09 Å, which is smaller than the experimental value of 2.197 Å [46] in WC bulk and previous theoretical result of 2.196 Å [47] in C/W interface. For the
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C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the shortest W-C bonding length are 1.866 Å, and 2.02 Å, respectively. This indicates a strong interface interaction of these two
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interfaces, which agrees well with the result of adhesive energy. Therefore, based on the analyses of interface energy, adhesive energy and interface distance, the interfaces of coherent
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ZrC(200)C/W(100) and semi-coherent C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) exhibit better stability than others. It should be noted that for both the C-terminated
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ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the layer of ZrC slab closest to the W slab is
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all occupied by C atoms, and this may be responsible for the strong interface interaction of these two interfaces due to the strong W-C bonding. However, this situation of layered Zr and C may be not realistic in experiments, and a fracture plane that gives the minimum adhesive energy may be
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not the plane between two different slabs. Furthermore, the experimental result of the microstructure of W-ZrC materials shows a coherent interface between W matrix and ZrC
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dispersoids [17]. Therefore, the stable coherent ZrC(200)C/W(100) interface seems to be the dominating type of W-ZrC interfaces. The stability and strength of an interface are closely related to its bonding features. Therefore, the electronic structure of the interface is calculated. The charge densities and charge density differences of the stable ZrC(200)C/W(100) interface are shown in Fig. 5. It can be seen that for the interfacial W and C atoms, the charge polarizes along the direction perpendicular to the interface (dash line in Fig. 5(a)). The charge densities of W atoms redistribute within the second W layer and even exist slightly in the third. However, the charge densities of C atoms are localized at the first layer in the ZrC slab, and those of interfacial Zr atoms does not show obvious change. The charge accumulating between the interfacial C atoms and W atoms implies the formation of chemical bonds at the interface. In Fig. 5(b), one can see that the interfacial C atoms get electrons and the W atoms lose electrons, meaning a charge transfer from W to C atoms along the direction perpendicular to the interface. This may be caused by the higher electronegativity of C than W. In addition, the charges are shared by the interfacial C atoms and W atoms, which indicates a
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Journal Pre-proof typically characteristic of a polar covalent bond between the interfacial C atoms and W atoms. Therefore, the C-W bonds close to the interface have a mixed property of covalent and ionic feature. To gain further insight into electronic states, the partial density of state (PDOS) of ZrC(200)C/W(100) interface is presented in Fig. 6. The PDOS of W, Zr, C atoms in bulk W and ZrC are also shown for comparison. Sharp peaks near the Fermi level for are observed in the PDOS of interfacial Zr and W atoms, indicating that the interface has certain metallic character mainly coming from C-2p, W-5d and Zr-4d orbitals. Furthermore, the state of C-2s states between -11 eV and -9 eV overlap with those of W-5d in the energy range of -10.5 eV ~ -9.5 eV. From -6
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eV to -2 eV, the overlap of C-2p states and W-5d states demonstrates a strong hybridization between them, which implies the formation of the strong covalent W-C bonding in interface. This
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is responsible for the stability and adhesion of the interface. Compared to the bulk states, a localized peak for the W 5d and Zr 4d states is observed near the Fermi level, indicating the strong
-p
bonding near the interface. In addition, the PDOS of Zr and C at the interface shifts to low energies a little, which may be because of the distinct local environments between the interface
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and the bulk ZrC.
3.3 Segregation and migration of hydrogen and helium As plasma facing materials, W materials will be subject to high fluxes of H isotope as well as
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He ions. Therefore, it is necessary to investigate the segregation and diffusion behaviors of H and He in the W-ZrC interface. At first, the migration of H and He in bulk W and ZrC were studied by
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using the nudged elastic band (NEB) method [48]. A 3×3×3 supercell with 216 atoms for bulk ZrC and 4×4×4 with 128 atoms for W are adopted in the NEB calculations. Several interstitial sites are considered for finding the most stable position. For both H and He, the most stable sites are tetrahedral sites (T-sites) in W and also T-sites surrounding by one C atom and three Zr atoms in ZrC, as shown in Fig. 7(a) and 7(d). The migration paths between two nearest-neighbor T-sites have been considered using 5 sequential images from the initial site (number 1) to the final (number 7) as presented in Fig. 7(b) and 7(e). For the diffusion of H and He in W in Fig. 7(c), One can see that the migration energy barrier of H is 0.21 eV, which agrees well with the previous theoretical result, 0.22 eV [49, 50], while that of He is 0.08 eV, which is consistent with the previous value of 0.07 eV [51, 52]. For the diffusion of H and He in ZrC in Fig. 7(f), the diffusion of H needs to overcome an energy barrier of 0.27 eV, and the migration of He needs to overcome a barrier of 0.71 eV, which agrees well with the previous theoretical value of 0.77 eV [53]. The segregation energies of H and He in the coherent ZrC(200)C/W(100) interface are calculated by
7
Journal Pre-proof Eseg Etot ( X ) Etot (0) [ Ebulk_W ( X ) E bulk_W (0)] ,
(7)
where Etot(X) and Etot(0) are the total energies of the interface with and without a H or He atom, respectively, while Ebulk_W(X) and Ebulk_W(0) are the total energies of a bulk W supercell with and without H or He, respectively. Negative values of Eseg means that the interface site is energetically more favorable for H or He than the T-sites in bulk W. In the present work, the zero-point energy (ZPE) of H (or He) atom is calculated by summing up the vibration energies of the normal modes by the expression: 𝑍𝑃𝐸 = 1/2 ∑𝑖 ћ𝜈𝑖 ,
(8)
where ћ and νi are Plank’s constant and the normal vibration frequencies, respectively. The
of
vibration frequencies of H (or He) atom are calculated allowing harmonic vibrations only for H
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(or He) atom. The ZPE corrections on diffusion barriers of H (or He) are calculated by the difference in vibration energies of saddle point and the ground state.
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In order to find the most favorable sites of H and He near the interface, the formation energies of both interstitial and substitutional cases are calculated near the ZrC(200)C/W(100) interface.
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When H or He occupies an interstitial site, the formation energy is expressed by ,
(9)
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E f Etot ( X ) Etot (0) EF
where EF is the energy of an isolated H or He atom. When the impurity replaces a X (X=W, C, Zr) atom, the formation energy can be obtained by
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E f Etot ( X ) Etot (0) E X EF
,
(10)
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where EX is the energy of an X atom in the bulk. Here we consider the substitution of a H or He atom for the W/Zr/C atom at the first and second layer close to the interface. As shown in Fig. 8, the H or He atom has been set up in different interstitial (I1-I5) and substitutional (S1-S6) sites in the interface, and the formation energies of H and He with and without ZPE corrections are shown in Table 2. As for H, the interstitial site I2 has the lowest formation energy of -0.03 eV. While for He, the interstitial site I2 exhibit a comparable formation energy with the substitutional S2, which is in good agreement with the result of He in pure W grain boundary [54]. When ZPE corrections are taken into account, the formation energies of H and He generally increases but the site preferences of H and He do not change. As for the most favorable interstitial site I2 of H and He, their segregation energies are calculated according to Eq. (7). The Eseg values of H and He are -0.97 eV, and -2.03 eV, respectively. This indicates that the interface could act as strong traps for H and He. When ZPE corrections are considered, the segregation energies of H and He are -1.00 eV, and -2.01 eV, respectively. Therefore, ZPE corrections do not affect the segregation behavior of H and He to the interface. 8
Journal Pre-proof To investigate the diffusion of interstitial H and He near the coherent ZrC(200)C/W(100) interface, we use the NEB method to calculate the minimum energy paths in two distinct cases: (i) a jump between two stable sites along the interface plane, and (ii) a jump across the interface plane. A 3×3×3 supercell of the ZrC(200)C/W(100) interface containing 298 atoms and 12 Å of vacuum is adopted. For the case along the interface, we choose three adjacent stable interstitial sites in the interface, i.e. 1, 7, and 13, as illustrated in Fig. 9(a). The diffusion energy profiles of H and He are shown in Fig. 9(b). The diffusion energy barriers of H or He along and across the interface are calculated and displayed in Table 3. As H diffuses along the path 1713, the energy barriers are 0.37 and 0.27 eV, while they are 0.15 eV and 0.33 eV for the migration of He
of
along the path. Therefore, the diffusion energy barriers of H and He along the interface are 0.37 eV and 0.33 eV, respectively. Note that the diffusion barrier of H is higher than that in bulk W and
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ZrC, while that of He is higher than that in bulk W but smaller than that in bulk ZrC. Note that the diffusion barriers of H and He are much lower than their corresponding segregation energies at the
-p
interface, which suggests that the trapped H and He should easily aggregate at the interface [55]. As for the H and He jumping across the interface, the migration pathways are much more
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complex. We identified a minimum energy path joining the stable site 7 via a bulk-like site 1 in the
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ZrC slab and a bulk-like site 19 in the W slab, as illustrated in Fig. 9(c) and 9(d). As for the migration of H and He from the ZrC slab to the interface (17), the diffusion energy barriers of H and He from the site 1 to site 7 through the site 3 or 4 across the interface are 0.69 eV and 1.45 eV,
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respectively, as shown in Fig. 9(d). In reverse from the interface back to the ZrC slab, if the H and He atoms are trapped by the interface, they need to overcome bigger energy barriers of 1.53 eV
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and 1.55 eV, respectively. As for the migration of H and He from the interface to W slab (719), the energy barriers are 0.72 eV and 1.72 eV, respectively. But in reverse from the W slab to the interface, the H and He atoms only overcome smaller diffusion barriers of about 0.30 eV and 0.58 eV, respectively. The ZPE corrections for the H and He energy barriers of the two diffusion paths are also calculated, as shown in Table 3.When the ZPE is considered, the energy barriers of H and He along the interface plane change slightly by 0-0.01 eV, while the barriers across the interface generally increases by 0-0.13 eV. This indicates that the ZPE has a greater influence on the diffusion barriers of H and He across the interface. The above results indicate that under a certain condition such as high temperature or plasma irradiation, the H and He atoms can easily reach the favorable segregation sites at the interface from the W matrix by overcoming relatively low energy barriers. But the escape rates are much lower due to significantly higher migration barriers for the reverse jumps [56]. As a result, the interface can behave as a barrier of H and He diffusion across the interface. However, by comparing these two migration pathways along and across the interface, it is found that the
9
Journal Pre-proof diffusion energy barriers of H and He along the interface are much lower than those across the interface. This indicates that H and He atoms are easy to diffuse along the interface. And so it is expected that H or He could jump out of the interface by thermal desorption, which explains why the W-ZrC material with a multi-scale interfacial microstructure exhibits much lower hydrogen retention than pure W under the low-energy high flux deuterium plasma irradiation [57].
4. Conclusions In this work, the stability and adhesion of twelve possible W-ZrC interfaces are systematically investigated by first-principles calculations. The segregation and migration behaviors of H and He
of
atom along and towards the stable coherent interface are also discussed. The key results of our study can be summarized into the following points.
For all considered interfaces, the coherent ZrC(200)C/W(100) interface shows the highest
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(i)
interfacial stability with the lowest interface energy, which agrees well with the experimental
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observed coherent interface between W matrix and ZrC dispersoids. (ii) For the coherent ZrC(200)C/W(100) interface, the electronic structure analysis shows a strong
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bonding between interfacial C and W atoms with a mixed feature of covalent bond and ionic
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bond. This is responsible for the stability and adhesion of the interface. (iii) The segregation energies of H and He to the ZrC(200)C/W(100) interface are -0.97eV and -2.03eV, respectively, implying that the interface acts as strong traps for both H and He.
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(iv) Two migration pathways of H and He along and across the ZrC(200)C/W(100) interface are examined. It is found that the diffusion energy barriers of H and He along the interface are
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much lower than those across the interface. This indicates that H and He atoms can easily diffuse in the direction to parallel the interface. The zero-point energy has a stronger influence on the diffusion barriers of H and He across the interface than along the interface. The present results not only provide a deep insight into the interface properties in W-ZrC materials, but also help us to improve the understanding about the influence of interface on the H/He behaviors in W materials under irradiation.
Acknowledgments This work is supported by the National Key Research and Development Program of China (Grant No.: 2017YFE0302400 and 2017YFA0402800), National Natural Science Foundation of China (Nos.: 11735015, 51871207, 11575229, U1832206), Anhui Provincial Natural Science Foundation (No. 1908085J17), and Special Fund for Theoretical Physics of the National Natural Science Foundation of China (No. 11547026).
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Journal Pre-proof Data availability Data not available / Data will be made available on request.
Reference [1] R. Causey, K.Wilson, T. Venhaus, W. R. Wampler, Tritium retention in tungsten exposed to intense fluxes of 100 eV tritons, J. Nucl. Mater. 266-269 (1999) 467–471. [2] M. Rieth, S.L. Dudarev, S.M. Gonzalez de Vicente, et. al. Recent progress in research on tungsten materials for nuclear fusion applications in Europe, J. Nucl. Mater. 432 (2013) 482-500. [3] V. Philipps, Tungsten as material for plasma-facing components in fusion devices, J. Nucl. Mater. 415 (2011) S2-S9.
of
[4] M.S. Wechsler, C. Lin, W.F. Sommer, L..L. Daemen, P.D. Ferguson, Radiation effects in materials for accelerator-driven neutron technologies, J. Nucl. Mater. 244 (1997) 177-184.
ro
[5] Y. Nemoto, A. Hasegawa, M. Satou, K. Abe, Microstructural development of neutron irradiated W-Re alloys, J. Nucl. Mater. 283-287 (2000) 1144-1147.
-p
[6] H. Kurishita, H. Arakawa, S. Matsuo, T. Sakamoto, S. Kobayashi, K. Nakai, G. Pintsuk, J. Linke, S. Tsurekawa, V. Yardley, K. Tokunaga, T. Takida, M. Katoh, A. Ikegaya, Y. Ueda, M. Kawai, N. Yoshida, Development of
re
Nanostructured Tungsten Based Materials Resistant to Recrystallization and/or Radiation Induced Embrittlement, Mater. Trans. 54 (2013) 456-465.
[7] Z.M. Xie, R. Liu, S. Miao, X.D. Yang, T. Zhang, Q.F. Fang, X.P. Wang, C.S. Liu, Y.Y. Lian, X. Liu, G.N. Luo,
lP
High thermal shock resistance of the hot rolled and swaged bulk W–ZrC alloys, J. Nucl. Mater. 469 (2016) 209-216.
[8] H. Kurishita, S. Matsuo, H. Arakawa, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, M. Kato, M. Kawai, N.
na
Yoshida, Development of re-crystallized W–1.1%TiC with enhanced room-temperature ductility and radiation performance, J. Nucl. Mater. 398 (2010) 87-92.
Jo ur
[9] N. Jin, Y.Q. Yang, X. Luo, S. Liu, Z.Y. Xiao, P.F. Guo, B. Huang, First-principles calculation of W/WC interface: Atomic structure, stability and electronic properties, Appl. Surf. Sci. 324 (2015) 205-211. [10] M.W. Finnis, The theory of metal–ceramic interfaces, J. Phys.: Condens. Matter 8 (1996) 5811–5836. [11] A. Luo, D.L. Jacobson, K.S. Shin, Solution Softening Mechanism of Iridium and Rhenium in Tungsten at Room Temperature, Refract. Met. Hard Mater. 10 (1991) 107-114. [12] Y. Mutoh, K. Ichikawa, K. Nagata, M. Takeuchi, Effect of rhenium addition on fracture toughness of tungsten at elevated temperatures, J. Mater. Sci. 30 (1995) 770-775. [13] S. Wurster, B. Gludovatz, R. Pippan, High temperature fracture experiments on tungsten–rhenium alloys, Int. J. Refract. Met. Hard Mater. 28 (2010) 692-697. [14] Y. Ishijima, S. Kannari, H. Kurishita, M. Hasegawa, Y. Hiraoka, T. Takida, K. Takebe, Processing of fine-grained W materials without detrimental phases and their mechanical properties at 200–432K, Mater. Sci. Eng. , A 473 (2008) 7-15. [15] K. Lu, L. Lu, S. Suresh, Strengthening Materials by Engineering Coherent Internal Boundaries at the Nanoscale, Sci. 324 (2009) 349–352. [16] G.M. Song, Y.J. Wang, Y. Zhou, Thermomechanical properties of TiC particle-reinforced tungsten composites for high temperature applications, Int. J. Refract. Met. Hard Mater. 21 (2003) 1-12. [17] Z.M. Xie, R. Liu, S. Miao, X.D. Yang, T. Zhang, X.P. Wang, Q.F. Fang, C.S. Liu, G.N. Luo, Y.Y. Lian, X. Liu, Extraordinary high ductility/strength of the interface designed bulk W-ZrC alloy plate at relatively low
11
Journal Pre-proof temperature, Sci. Rep. 5 (2015) 16014. [18] S.M. Zhang, S. Wang, W. Li, Y.L. Zhu, Z.H. Chen, Microstructure and properties of W–ZrC composites prepared by the displacive compensation of porosity (DCP) method, J. Alloys Compd. 509 (2011) 8327-8332. [19] J.X. Yang, L. Chen, J.L. Fan, H.R. Gong, Doping of helium at Fe/W interfaces from first principles calculation, J. Alloys Compd. 686 (2016) 160-167. [20] J.W. Wang, J.L. Fan, H.R. Gong, Effects of Zr alloying on cohesion properties of Cu/W interfaces, J. Alloys Compd. 661 (2016) 553-556. [21] D.Y. Dang, L.Y. Shi, J.L. Fan, H.R. Gong, First-principles study of W–TiC interface cohesion, Surf. Coat. Technol. 276 (2015) 602-605. [22] H.Y. Wang, S. Zhang, D.J. Li, S.Y. Liu, The simulation of adhesion, stability, electronic structure of W/ZrB 2 interface using first-principles, Surf. Coat. Technol. 228 (2013) S583-S587. [23] H. Kurishita, Y. Amano, S. Kobayashi, K. Nakai, H. Arakawa, Y. Hiraoka, T. Takida, K. Takebe, H. Matsui,
of
Development of ultra-fine grained W–TiC and their mechanical properties for fusion applications, J. Nucl. Mater. 367 (2007) 1453-1457.
ro
[24] M.W. Finnis, C. Kruse, U. Schönberger, Ab initio calculations of metalceramic interfaces what have we learned what can we learn, Nanostruct. Mater. 6 (1995) 145-155.
calculation, J. Alloys Compd. 768 (2018) 387-391.
-p
[25] J. Qian, C.Y. Wu, H.R. Gong, S.F. Zhou, Cohesion properties of W-ZrC interfaces from first principles
re
[26] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 1169-1186.
[27] G. Kresse, J. Hafner, Ab initiomolecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558-561.
lP
[28] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B 46 (1992) 6671-6687.
(1996) 3865-3868.
na
[29] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77
Jo ur
[30] D.J. Chadi, Special points for Brillouin-zone integrations, Phys. Rev. B 16 (1977) 1746-1747. [31] C. Wei, Q.Q. Ren, J.L. Fan, H.R. Gong, Cohesion properties of W/La2O3 interfaces from first principles calculation, J. Nucl. Mater. 466 (2015) 234-238. [32] X.Y. Yang, Y. Lu, P. Zhang, First-principles study of native point defects and diffusion behaviors of helium in zirconium carbide, J. Nucl. Mater. 465 (2015) 161-166. [33] S. Méçabih, N. Amrane, Z. Nabi, B. Abbar, H. Aourag, Description of structural and electronic properties of TiC and ZrC by generalized gradient approximation, Phys. A 285(2000) 392-396. [34] F. Birch, Finite Elastic Strain of Cubic Crystals, Phys. Rev. 71 (1947) 809-824. [35] L.M. Liu, S.Q. Wang, H.Q. Ye, First-principles study of polar Al/TiN(111) interfaces, Acta Mater. 52 (2004) 3681-3688. [36] H.L. Wang, J.J. Tang, Y.J. Zhao, J. Du, First-principles study of Mg/Al2MgC2 heterogeneous nucleation interfaces, Appl. Surf. Sci.355 (2015) 1091-1097. [37] Z.M. Zhuo, H.K. Mao, H. Xu, Y.Z. Fu, Density functional theory study of Al/NbB2 heterogeneous nucleation interface, Appl. Surf. Sci. 456 (2018) 37-42. [38] S.J. Lee, Y.K. Lee, A. Soon, The austenite/ɛ martensite interface: A first-principles investigation of the fcc Fe(111)/hcp Fe(0001) system, Appl. Sur. Sci. 258 (2012) 9977-9981. [39] Q. Jiang, H.M. Lu, M. Zhao, Modelling of surface energies of elemental crystals, J. Phys.: Condens. Matter 16 (2004) 521-530.
12
Journal Pre-proof [40] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the ZrC(100)/Fe(110) interface from first principles, Surf. Sci. 560 (2004) 103-120. [41] L.M. Liu, S.Q. Wang, H.Q. Ye, First-principles study of metal/nitride polar interfaces: Ti/TiN, Surf. Interface Anal. 35 (2003) 835-841.
[42] I. G. Batyrev, A. Alavi, M. W. Finnis, Equilibrium and adhesion of Nb/sapphire: The effect of oxygen partial pressure, Phys. Rev. B 62 (2000) 4698-4706. [43] N. Jin, Y.Y. Yang, X. Luo, J. Li, B. Huang, S. Liu, Z.Y. Xiao, Theoretical calculations on the adhesion, stability, electronic structure and bonding of SiC/W interface, Appl. Sur. Sci. 314 (2014) 896-905. [44] K. Nagao, J.B. Neaton, N.W. Ashcroft, First-principles study of adhesion at Cu/SiO2interfaces, Phys. Rev. B 68 (2003) 125403. [45] D.J. Siegel, L.G. Hector, Jr., J.B. Adams, Adhesion, atomic structure, and bonding at the Al(111)/α−Al2O3(0001)interface: A first principles study, Phys. Rev. B 65 (2002) 084515.
of
[46] A.D. Krawitz, D.G. Reichel, R. Hitterman, Thermal expansion of tungsten carbide at low temperature, J. Am. Ceram. Soc. 72 (1989) 515-517.
ro
[47] Q.Q. Ren, D.Y. Dang, H.R. Gong, J.L. Fan, Y.M. Zhao, Cohesion properties of carbon–tungsten interfaces, Carbon 83 (2015) 100-105.
-p
[48] G. Mills, H. Jónsson, G.K. Schenter, Reversible work transition state theory application todissociative adsorption of hydrogen, Surf. Sci. 324 (1995) 305-337.
re
[49] X.S. Kong, S. Wang, X.B. Wu, Y.W. You, C.S. Liu, Q.F. Fang, J.L. Chen, G.N. Luo, First-principles calculations of hydrogen solution and diffusion in tungsten: Temperature and defect-trapping effects, Acta Mater. 84 (2015) 426-435.
Phys. 107 (2010) 113531.
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[50] K. Heinloa, T. Ahlgren, Diffusion of hydrogen in bcc tungsten studied with first principle calculations, J. Appl.
[51] X.B. Wu, X.S. Kong, Y.W. You, C.S. Liu, Q.F. Fang, J.L. Chen, G.N. Luo, Z.G. Wang, Effects of alloying and
Fusion 53 (2013) 073049.
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transmutation impurities on stability and mobility of helium in tungsten under a fusion environment, Nucl.
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[52] L. Yang, H.K. Liu, X.T. Zu, First-principles study of the migration of helium in tungsten, Int. J. Mod. Phys. B 23 (2009) 2077-2082.
[53] X.Y. Yang, Y. Lu, P. Zhang, The temperature-dependent diffusion coefficient of helium in zirconium carbide studied with first-principles calculations, J. Appl. Phys. 117 (2015) 164903. [54] H.B. Zhou, Y.L. Liu, Y. Zhang, S. Jin, G.H. Lu, First-principles investigation of energetics and site preference of He in a W grain boundary, Nucl. instrum. Methods Phys. Res. B 267 (2009) 3189-3192. [55] H.B. Zhou, Y.L. Liu, S. Jin, Y. Zhang, G.N. Luo, G.H. Lu, Investigating behaviours of hydrogen in a tungsten grain boundary by first principles: from dissolution and diffusion to a trapping mechanism, Nucl. Fusion 50 (2010) 025016.
[56] D.D. Stefano, M. Mrovec, C. Elsässer, First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel, Acta Mater. 98 (2015) 306-312. [57] R. Liu, Z.M. Xie, J.F. Yang, T. Zhang, T. Hao, X.P. Wang, Q.F. Fang, C.S. Liu, Recent progress on the R&D of W-ZrC alloys for plasma facing components in fusion devices, Nucl. Mate. Energy 16 (2018) 191-206.
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Journal Pre-proof Table 1. Surface energies (in J/m2) of W(100), W(110), ZrC(200) and ZrC(110) surfaces. The available DFT and experimental results are presented for comparison. W(100)
W(110)
ZrC(200)
ZrC(110)
Present work
3.93
3.19
1.65
3.23
Previous work
3.904a
3.21b, 3.27c
1.592d
3.199d
d
Ref. [40].
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Ref. [39].
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c
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Ref. [31].
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b
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Ref. [21].
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a
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Esurf (J/m2)
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Journal Pre-proof Table 2. Formation energies (in eV) of the H and He atom at the interstitial sites (I1-I5) and substitutional sites (S1-S6) in the ZrC(200)C/W(100) interface with and without ZPE corrections. Site
I1
I2
I3
I4
I5
S1
S2
S3
S4
S5
S6
0.81
-0.03
0.39
0.54
/
7.50
0.99
1.72
6.32
2.46
3.03
1.11*
0.20*
0.62*
0.80*
/
7.73*
1.13*
1.88*
6.46*
2.63*
3.11*
4.13
4.02
/
5.53
5.16
9.22
4.01
5.18
7.40
4.48
5.56
4.26*
4.12*
/
5.63*
5.24*
9.31*
4.04*
5.24*
7.49*
4.56*
5.63*
H
He
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ZPE corrected.
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*
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Journal Pre-proof Table 3. Diffusion energy barriers (in eV) of H and He along and across the interface plane. ZPE corrections are considered for each barrier. Along the interface
Path
Across the interface
17
713
17
71
719
197
0.37
0.27
0.69
1.53
0.72
0.30
0.36*
0.26*
0.75*
1.66*
0.75*
0.33*
0.15
0.33
1.45
1.55
1.72
0.58
0.15*
0.32*
1.48*
1.61*
1.72*
0.60*
H
He
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ZPE corrected.
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*
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Journal Pre-proof Figure captions Fig. 1. Surface energies of C-terminated and Zr-terminated ZrC(111) vs μC -μbulk , where the C C-term and Zr-term denote the C-terminated and Zr-terminated ZrC(111) surfaces, respectively.
Fig. 2. Schematic plot of typical six kinds of ZrCC/W interfaces (C atoms on the top of W atoms), i.e., (a) ZrC(200)C/W(100), (b) ZrC(110)C/W(110), (c) ZrC(110)C/W(100), (d) ZrC(200)C/W(110), (e) non-stoichiometric ZrC(111)/W(110), and (f) non-stoichiometric ZrC(111)/W(100). The green, gray and brown spheres represent Zr, W, and C, respectively. The upper and lower figures are the
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side and top view, respectively. The location of interface is indicated by a gray parallelogram.
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Fig. 3. Interface energies (Eint) and ideal work of adhesion (Ead) of eight stoichiometric and four non-stoichiometric ZrC/W interfacial configurations. Eint-C(Zr) and Ead-C(Zr) represent the
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interface energies and ideal works of adhesion of the interfaces with the C or Zr atoms on the top
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of the W atoms close to the interface, respectively.
Fig. 4. Interface energies of non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) interfaces.
Zr-terminated
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The Ein value of ZrC(200)C/W(100) interface is also shown for a comparison. (a)-(d) present the ZrC(111)/W(100),
Zr-terminated
ZrC(111)/W(110),
ZrC(200)/W(100),
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C-terminated ZrC(111)/W(100) and C-terminated ZrC(111)/W(110) interfaces, respectively.
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Fig. 5. (a) Charge density of the coherent ZrC(200)C/W(100) interface, where the value of charge density increases as color changing from blue to red, and the horizontal dashed line represents the location of the interface. (b) Charge density difference of ZrC(200)C/W(100) interface. Blue contour denotes regions of charge accumulation and red contour denotes regions of charge depletion.
Fig. 6. Partial density of state (PDOS) of the W, Zr, and C atoms located at the ZrC(200)C/W(100) interface and those in the bulk W and ZrC. The line represents the Fermi energy level.
Fig. 7. Migration of H and He in bulk W and ZrC, where (a)-(c) represent the most stable interstitial site, diffusion paths and diffusion energy profiles of H and He in W, and (d)-(f) are those of He and He in ZrC. The number 1 and 7 denote the two nearest-neighboring stable tetrahedral sites, and the number 4 represents the saddle point. The red, green, brown, gray spheres are H/He, Zr, C, and W atoms, respectively.
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Journal Pre-proof Fig. 8. The possible positions of H and He segregated at the interface after relaxation. The green, gray and brown spheres denote Zr, W, and C, respectively. The small blue spheres (numbers of I1-I5) represent the five different interstitial sites, and numbers of S1-S6 represent the six different substitutional sites.
Fig. 9. H and He migration in the vicinity of the ZrC(200)C/W(100) interface through two pathways, i.e., along the interface and across the interface, where (a) and (b) represent the stable interstitial site of H and He at the interface, the diffusion paths (113), and diffusion energy profiles, respectively, and (c) and (d) denote those of H and He migration from ZrC slab to W slab
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across the interface (119). The green, gray, brown, red, blue spheres denote Zr, W, C, H, and He,
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respectively. The gray parallelogram represents the location of interface.
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Fig. 1
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Fig. 2
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Fig. 6
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Journal Pre-proof 1)
The coherent ZrC(200)C/W(100) interface shows the highest interfacial stability with the lowest interface energy.
2)
There is a strong bonding with some property of strong covalent bond and ionic bond between the interfacial C and W atoms.
3)
The interface acts as strong traps for both H and He.
4)
The diffusion energy barriers of H and He along the interface are much lower than those across the interface.
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The zero-point energy has a stronger influence on the diffusion barriers of H and He across
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the interface than along the interface.
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5)
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Xu Zhang, Xuebang Wu, ChunJu Hou, Xiangyan Li, C.S. Liu PII:
S0169-4332(19)32811-9
DOI:
https://doi.org/10.1016/j.apsusc.2019.143995
Reference:
APSUSC 143995
To appear in:
Applied Surface Science
Received date:
2 July 2019
Revised date:
3 September 2019
Accepted date:
12 September 2019
Please cite this article as: X. Zhang, X. Wu, C. Hou, et al., First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces, Applied Surface Science(2018), https://doi.org/10.1016/j.apsusc.2019.143995
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© 2018 Published by Elsevier.
Journal Pre-proof
First-principles calculations on interface stability and migration of H and He in W-ZrC interfaces Xu Zhang a, b, c, Xuebang Wu a, *, ChunJu Hou d, Xiangyan Li a, and C. S. Liu a, ** a
Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of
Sciences, P. O. Box 1129, Hefei 230031, PR China b
University of Science and Technology of China, Hefei, 230036, PR China
c
School of Material Science and Engineering, JiangXi University of Science and Technology,
Ganzhou, 34100, PR China
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of Science, Jiangxi University of Science and Technology, GanZhou, 34100, PR China
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dSchool
Abstract:
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In this work, the stability and adhesion of twelve tungsten-zirconium carbide (W-ZrC) interfaces as well as the migration of hydrogen (H) and helium (He) near the interface were
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investigated by first-principles calculations. The results of interface energy show that the coherent ZrC(200)C/W(100) interface is the most stable configuration with the smallest value in all the
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investigated stoichiometric structures. The stability of non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) is also analyzed. The electronic structure analysis reveals that the interfacial
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C-W bonds have a mixed property of covalent and ionic feature. Furthermore, the interface acts as strong traps for H and He with segregation energies of -0.97eV and -2.03eV, respectively. The
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diffusion of H and He across the ZrC(200)C/W(100) interface demonstrates that H and He atoms can reach the favorable segregation sites at the interface from the W matrix by overcoming energy barriers of about 0.3 eV and 0.58 eV, respectively, but it is quite difficult for the trapped H and He to escape out of the interface due to the higher diffusion energy barriers. Our results agree well with the experimental findings about the microstructure and H isotope retention in W-ZrC alloys.
Keywords: W-ZrC interface; interface energy; stability; hydrogen; diffusion; first-principles calculations
*
E-mail addresses: [email protected] (X.B. Wu), [email protected] (C.S. Liu). 1
Journal Pre-proof 1. Introduction Tungsten (W) is considered as the most promising candidate for the plasma-facing material (PFM) of fusion reactors due to its excellent properties such as high melting point, high thermal conductivity, low tritium retention and high resistance to sputtering[1-3]. However, one of the critical problems of W that hinders its application is the poor thermo-mechanical properties, such as high ductile-to-brittle transition temperature and embrittlement after recrystallization and irradiation by neutrons or ions [4-7]. Therefore, substantial research is being under taken internationally towards manufacturing advanced W-based materials [8], with improved mechanical properties based on micro-alloying and compositing. Among these fine-grained and
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toughened W-based materials, nanostructured W doping with carbide nanoparticles such as TiC and ZrC are quite promising due to their improved ductility at low temperature and improved
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thermal shock resistance [9-13]. The formation of interface between W matrix and the carbides is believed to be the main reason for the improved excellent ductility and strength of carbide
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dispersed strengthened W materials, especially the formation of coherent or semi-coherent interfaces [14, 15]. Therefore, so far, much effort is made to obtain detailed information about the
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interfaces from experimental [16-18] and theoretical views [19-22].
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Recently, W-ZrC and W-TiC alloys were fabricated with advanced mechanical properties such as high strength, good thermal shock resistance and lower ductile-to-brittle transition temperature about 100 ºC. The observed coherent Kurdjumov-Sachs (K-S) orientation interface
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structure between ZrC/TiC and W plays an important role in the improvement of mechanical properties, thermal shock behaviors, and irradiation resistance to plasma and ions [17, 23].
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However, based on the experimental observations, it is difficult to clarify the mechanism about how the interface microstructure affects the properties. The first-principles calculations based on the density functional theory (DFT) can accurately provide the detailed atomic and electronic structures of interfaces and predict the stability, adhesion strength and fracture toughness[10, 24]. Recently, researchers have tried to understand the cohesion of W-TiC and W-ZrC interface. Dang et al. found that the W(110)-TiC(100) interface is energetically favorable with lower interface energies and has higher strength than the W(100)-TiC(100) interface [21]. The W(110)-ZrC(111) interface is reported to be more favorable than others with strong W-C bond [25]. However, due to the complexity of interface structures, the properties about the W/ZrC interface such as cohesion, stability, and especially the irradiation resistance to H/He plasma are still missing. In this work, first-principles calculations are performed to study the interface properties of bcc W and NaCl structured ZrC. First, the bulk and surface properties of W and ZrC are studied and compared with others. Then, twelve possible interface structures between W and ZrC are constructed to evaluate the stability and cohesion properties by analyses of energetics and
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Journal Pre-proof electronic structures. Finally, the trapping and diffusion of H and He atoms around the most stable interface are investigated. Our calculations will provide a deep insight into the properties of W-ZrC alloy.
2. Computational method The first-principles calculations are performed within the DFT framework as implemented in the Vienna Ab Initio Simulation Package (VASP) [26] code with projector-augmented wave (PAW) potential method. The electrons 4d105s1 for W, 4d105s25p2 for Zr and 2s22p2 for C are treated explicitly as valence electrons, and their wave-functions are described by plane-wave basis. The
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ionic potential of the nuclei and inner electrons is described by pseudopotentials that follows the projector augmented wave (PAW) approach [27]. Exchange and correlation functions are taken in
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a form proposed by Perdew and Wang (PW91) [28] within the generalized gradient approximation (GGA)[28]to describe the electronic exchange and correlation effect [29].The cutoff energy is
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taken to a value of 500 eV. The K-point mesh is sampled within 0.003 Å-1 by using the Monkhorst-Pack scheme [30].The atomic positions are relaxed using the conjugated gradient
3. Results and discussion 3.1 Bulk and surface properties
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method until the force on each atom was less than 0.01 eV/Å.
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The calculated equilibrium lattice constant is 3.176 Å for bcc W, in good agreement with the previous value of 3.175 Å [31], while it is 4.726 Å for rock-salt structured ZrC, which matches
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well with the previous calculation value of 4.72 Å [32, 33] and experimental one of 4.698 Å [34]. Before constructing the interface models, the properties of W and ZrC surfaces in typical Miller planes, i.e. W(100), W(110), ZrC(200), ZrC(110) and ZrC(111) surfaces are investigated. A series of test calculations with different thickness of layers and vacuum are carried out to determine the minimum layers necessary to represent a bulk-like slab. The surface energies, Esurf, of different surfaces are calculated using the following formula [35-37] Esurf =
bulk Etot slab -NZr μZrC +(NZr -NC )μC
2A
,
(1)
bulk where Etot slab is the total energy of the W or ZrC slab, μZrC is the energy of per unit in bulk ZrC
material, NZr and NC are the numbers of Zr atoms and C atoms in the slab, μC is the chemical potential of C, and A is area of W or ZrC surface. The chemical potential of Zr or C in the slab must be less than that of its bulk. Therefore, the range of μC -μbulk is C ∆H0f ≤μC -μbulk ≤0, C
(2)
∆H0f =μbulk -μbulk -μbulk , ZrC C Zr
(3)
3
Journal Pre-proof Here, ∆H0f (-2.95 eV) is the formation heat of bulk ZrC. μbulk and μbulk are the chemical C Zr potential of bulk C and Zr, respectively. However, NZr and NC are equal when the ZrC slab is stoichiometric. Accordingly, the Eq. (1) can be simplified to [38] Esurf =
bulk Etot slab -NZr μZrC
2A
,
(4)
The surface energy of Esurf converges to a constant value when the number of layers reaches 15 for W(100) and W(110) surfaces, and 9 for ZrC(200) and ZrC(110) surfaces. As shown in Table 1, our calculated Esurf agrees well with previous theoretical and experimental results, for example, the calculated Esurf of W(110) surface is 3.19 J/m2, which agrees with the previous theoretical value of
of
3.21 J/m2 [31] and the experimental value of 3.27 J/m2 [39], and that of ZrC(110) of 3.23 J/m2 is consistent with the previous theoretical value of 3.199 J/m2 [40].
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The polar ZrC(111) surface consists only one species of Zr or C atom. It is impossible for a stoichiometric slab to terminate both surfaces with the same species. So a symmetric slab is used
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and a non-stoichiometric slab with identical surfaces is used to obtain the surface energy of a
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particular termination. Using the similar method by Liu et al. [35, 41], the convergence tests of ZrC (111) surface are performed by comparing the relaxations of the first few interlayer spacings
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as a function of slab thickness. The calculations show that a 9-layer slab is thick enough to mimic the bulk behavior. According to Eq. (1), the surface energies of ZrC(111) slabs as a function of carbon chemical potential are shown in Fig. 1. It is found that the Esurf value of the C-terminated
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ZrC(111) surface decreases with increasing the chemical potential μC -μbulk but that of the C Zr-terminated.
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Zr-terminated increases. The values of Esurf for C-terminated surfaces are larger than those of
3.2 Interface model and stability
To systematically investigate the interface, we constructed twelve possible candidate models for
W/ZrC
interfaces,
ZrC(110)Zr/W(110),
i.e.,
ZrC(200)C/W(100),
ZrC(110)C/W(100),
ZrC(200)Zr/W(100),
ZrC(110)Zr/W(100),
ZrC(110)C/W(110), ZrC(200)C/W(110),
ZrC(200)Zr/W(110), as well as non-stoichiometric C(or Zr)-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, in which the subscript C (Zr) denotes the C (Zr) atom on the top of the W atom near the interface. Based on the above surface calculations, these interface models are formed with a fifteen-layer W(100) or W(110) slab connected to a nine-layer ZrC(200), ZrC(110) or ZrC(111) slab along with 12 Å of vacuum. Fig. 2 shows the atomic configurations of six typical ZrC/W interfaces, where only three layers close to the interface are presented to clearly show the stacking sequences of atoms in the interfaces. To establish the interface models, A 2×2 surface unite cell is selected for both ZrC(200) and W(100) for constructing the ZrC(200)/W(100)
4
Journal Pre-proof interface, 1×1 of ZrC(110) and W(110) for the ZrC(110)/W(110) interface, 1×4 of ZrC(200) and 1×3 of W(110) for the ZrC(200)/W(110) interface, 1×2 of ZrC(110) and 1×3 of W(100) for the ZrC(110)/W(100) interface, 1×4 of ZrC(111) and 1×7 of W(100) for the ZrC(111)/W(100) interface, and 1×3 of ZrC(111) and 1×4 of W(110) for the ZrC(111)/W(110) interface. The interface energy (Eint) can be used to evaluate the stability and the adhesive strength of an interface. The interface with smaller Eint has better stability. The value of Eint can be obtained by the following equation [35, 42] Eint =
bulk bulk Eint tot -EW -NZr μZrC +(NZr -NC )μC
S
f surf -Esur W -EZrC ,
(5)
bulk where S is the area of the ZrC/W interface, Eint is tot is the total energy of the interface, and EW
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f surf the energy of bulk W. Esur W and EZrC are surface energies of W and ZrC slabs, respectively. The
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Eint values of eight stoichiometric interfaces are shown in Fig. 3. It can be seen that the interfaces with C atoms on the top of W atoms have lower Eint than those with Zr on the top of W atoms,
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indicating a higher stability of the configurations with C atoms on the top of W atoms. In addition, it is noted that the coherent ZrC(200)C/W(100) interface has the lowest Eint and exhibits the best
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stability.
For the non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the interface
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energies as a function of carbon chemical potential μC -μbulk are plotted in Fig. 4. Also included C in the figure is the interface energy of stoichiometric ZrC(200)C/W(100) interface. At the low
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carbon potential, the non-stoichiometric interface energies of C-terminated ZrC(111)/W interface are higher than those of the Zr-terminated interfaces and that of ZrC(200)C/W(100) interface,
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indicating that the latter is more stable. Second, at the high carbon chemical potential, the non-stoichiometric interface energies of the Zr-terminated ZrC(111)/W interfaces are higher than that of the ZrC(200)C/W(100) interface, which means that the ZrC(200)C/W(100) interface is more stable. In addition, the C-terminated interfaces are more stable than the Zr-terminated interfaces and the ZrC(200)C/W(100) interface with increasing the carbon chemical potential because of the lower interface energies. The ideal work of adhesion (Ead ) is an important parameter to describe the adhesive properties of interfaces [36], which is defined as the minimum reversible energy needed to separate the interface into two free surfaces. And Ead can be expressed by the difference in total energy between the interface and the relevant isolated slabs using the following formula [22, 43-45], Ead =
Ew +EZrC -Etot A
,
(6)
where EW and EZrC represents the total energies of the 15-layer W slab and the 9-layer ZrC slab , respectively. A is area of the ZrC/W interface. The interface with a larger Ead shows the stronger interfacial
bonding
strength.
The Ead of eight stoichiometric interfaces and four 5
Journal Pre-proof non-stoichiometric interfaces are calculated and also presented in Fig. 3. The Ead of C-terminated ZrC(111)/W(110) interface is the largest, and followed by the ZrC(111)/W(100) and ZrC(200)C/W(100) interfaces, indicating that the C-terminated ZrC(111)/W(110) interface has the strongest interaction between the interfacial atoms, which agrees well with other reported theoretical result [25]. In addition, the local atomic structures of ZrC(200)C/W(100), C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces are examined. The shortest C-W bond length near the ZrC(200)C/W(100) interface is 2.09 Å, which is smaller than the experimental value of 2.197 Å [46] in WC bulk and previous theoretical result of 2.196 Å [47] in C/W interface. For the
of
C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the shortest W-C bonding length are 1.866 Å, and 2.02 Å, respectively. This indicates a strong interface interaction of these two
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interfaces, which agrees well with the result of adhesive energy. Therefore, based on the analyses of interface energy, adhesive energy and interface distance, the interfaces of coherent
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ZrC(200)C/W(100) and semi-coherent C-terminated ZrC(111)/W(100) and ZrC(111)/W(110) exhibit better stability than others. It should be noted that for both the C-terminated
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ZrC(111)/W(100) and ZrC(111)/W(110) interfaces, the layer of ZrC slab closest to the W slab is
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all occupied by C atoms, and this may be responsible for the strong interface interaction of these two interfaces due to the strong W-C bonding. However, this situation of layered Zr and C may be not realistic in experiments, and a fracture plane that gives the minimum adhesive energy may be
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not the plane between two different slabs. Furthermore, the experimental result of the microstructure of W-ZrC materials shows a coherent interface between W matrix and ZrC
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dispersoids [17]. Therefore, the stable coherent ZrC(200)C/W(100) interface seems to be the dominating type of W-ZrC interfaces. The stability and strength of an interface are closely related to its bonding features. Therefore, the electronic structure of the interface is calculated. The charge densities and charge density differences of the stable ZrC(200)C/W(100) interface are shown in Fig. 5. It can be seen that for the interfacial W and C atoms, the charge polarizes along the direction perpendicular to the interface (dash line in Fig. 5(a)). The charge densities of W atoms redistribute within the second W layer and even exist slightly in the third. However, the charge densities of C atoms are localized at the first layer in the ZrC slab, and those of interfacial Zr atoms does not show obvious change. The charge accumulating between the interfacial C atoms and W atoms implies the formation of chemical bonds at the interface. In Fig. 5(b), one can see that the interfacial C atoms get electrons and the W atoms lose electrons, meaning a charge transfer from W to C atoms along the direction perpendicular to the interface. This may be caused by the higher electronegativity of C than W. In addition, the charges are shared by the interfacial C atoms and W atoms, which indicates a
6
Journal Pre-proof typically characteristic of a polar covalent bond between the interfacial C atoms and W atoms. Therefore, the C-W bonds close to the interface have a mixed property of covalent and ionic feature. To gain further insight into electronic states, the partial density of state (PDOS) of ZrC(200)C/W(100) interface is presented in Fig. 6. The PDOS of W, Zr, C atoms in bulk W and ZrC are also shown for comparison. Sharp peaks near the Fermi level for are observed in the PDOS of interfacial Zr and W atoms, indicating that the interface has certain metallic character mainly coming from C-2p, W-5d and Zr-4d orbitals. Furthermore, the state of C-2s states between -11 eV and -9 eV overlap with those of W-5d in the energy range of -10.5 eV ~ -9.5 eV. From -6
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eV to -2 eV, the overlap of C-2p states and W-5d states demonstrates a strong hybridization between them, which implies the formation of the strong covalent W-C bonding in interface. This
ro
is responsible for the stability and adhesion of the interface. Compared to the bulk states, a localized peak for the W 5d and Zr 4d states is observed near the Fermi level, indicating the strong
-p
bonding near the interface. In addition, the PDOS of Zr and C at the interface shifts to low energies a little, which may be because of the distinct local environments between the interface
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and the bulk ZrC.
3.3 Segregation and migration of hydrogen and helium As plasma facing materials, W materials will be subject to high fluxes of H isotope as well as
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He ions. Therefore, it is necessary to investigate the segregation and diffusion behaviors of H and He in the W-ZrC interface. At first, the migration of H and He in bulk W and ZrC were studied by
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using the nudged elastic band (NEB) method [48]. A 3×3×3 supercell with 216 atoms for bulk ZrC and 4×4×4 with 128 atoms for W are adopted in the NEB calculations. Several interstitial sites are considered for finding the most stable position. For both H and He, the most stable sites are tetrahedral sites (T-sites) in W and also T-sites surrounding by one C atom and three Zr atoms in ZrC, as shown in Fig. 7(a) and 7(d). The migration paths between two nearest-neighbor T-sites have been considered using 5 sequential images from the initial site (number 1) to the final (number 7) as presented in Fig. 7(b) and 7(e). For the diffusion of H and He in W in Fig. 7(c), One can see that the migration energy barrier of H is 0.21 eV, which agrees well with the previous theoretical result, 0.22 eV [49, 50], while that of He is 0.08 eV, which is consistent with the previous value of 0.07 eV [51, 52]. For the diffusion of H and He in ZrC in Fig. 7(f), the diffusion of H needs to overcome an energy barrier of 0.27 eV, and the migration of He needs to overcome a barrier of 0.71 eV, which agrees well with the previous theoretical value of 0.77 eV [53]. The segregation energies of H and He in the coherent ZrC(200)C/W(100) interface are calculated by
7
Journal Pre-proof Eseg Etot ( X ) Etot (0) [ Ebulk_W ( X ) E bulk_W (0)] ,
(7)
where Etot(X) and Etot(0) are the total energies of the interface with and without a H or He atom, respectively, while Ebulk_W(X) and Ebulk_W(0) are the total energies of a bulk W supercell with and without H or He, respectively. Negative values of Eseg means that the interface site is energetically more favorable for H or He than the T-sites in bulk W. In the present work, the zero-point energy (ZPE) of H (or He) atom is calculated by summing up the vibration energies of the normal modes by the expression: 𝑍𝑃𝐸 = 1/2 ∑𝑖 ћ𝜈𝑖 ,
(8)
where ћ and νi are Plank’s constant and the normal vibration frequencies, respectively. The
of
vibration frequencies of H (or He) atom are calculated allowing harmonic vibrations only for H
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(or He) atom. The ZPE corrections on diffusion barriers of H (or He) are calculated by the difference in vibration energies of saddle point and the ground state.
-p
In order to find the most favorable sites of H and He near the interface, the formation energies of both interstitial and substitutional cases are calculated near the ZrC(200)C/W(100) interface.
re
When H or He occupies an interstitial site, the formation energy is expressed by ,
(9)
lP
E f Etot ( X ) Etot (0) EF
where EF is the energy of an isolated H or He atom. When the impurity replaces a X (X=W, C, Zr) atom, the formation energy can be obtained by
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E f Etot ( X ) Etot (0) E X EF
,
(10)
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where EX is the energy of an X atom in the bulk. Here we consider the substitution of a H or He atom for the W/Zr/C atom at the first and second layer close to the interface. As shown in Fig. 8, the H or He atom has been set up in different interstitial (I1-I5) and substitutional (S1-S6) sites in the interface, and the formation energies of H and He with and without ZPE corrections are shown in Table 2. As for H, the interstitial site I2 has the lowest formation energy of -0.03 eV. While for He, the interstitial site I2 exhibit a comparable formation energy with the substitutional S2, which is in good agreement with the result of He in pure W grain boundary [54]. When ZPE corrections are taken into account, the formation energies of H and He generally increases but the site preferences of H and He do not change. As for the most favorable interstitial site I2 of H and He, their segregation energies are calculated according to Eq. (7). The Eseg values of H and He are -0.97 eV, and -2.03 eV, respectively. This indicates that the interface could act as strong traps for H and He. When ZPE corrections are considered, the segregation energies of H and He are -1.00 eV, and -2.01 eV, respectively. Therefore, ZPE corrections do not affect the segregation behavior of H and He to the interface. 8
Journal Pre-proof To investigate the diffusion of interstitial H and He near the coherent ZrC(200)C/W(100) interface, we use the NEB method to calculate the minimum energy paths in two distinct cases: (i) a jump between two stable sites along the interface plane, and (ii) a jump across the interface plane. A 3×3×3 supercell of the ZrC(200)C/W(100) interface containing 298 atoms and 12 Å of vacuum is adopted. For the case along the interface, we choose three adjacent stable interstitial sites in the interface, i.e. 1, 7, and 13, as illustrated in Fig. 9(a). The diffusion energy profiles of H and He are shown in Fig. 9(b). The diffusion energy barriers of H or He along and across the interface are calculated and displayed in Table 3. As H diffuses along the path 1713, the energy barriers are 0.37 and 0.27 eV, while they are 0.15 eV and 0.33 eV for the migration of He
of
along the path. Therefore, the diffusion energy barriers of H and He along the interface are 0.37 eV and 0.33 eV, respectively. Note that the diffusion barrier of H is higher than that in bulk W and
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ZrC, while that of He is higher than that in bulk W but smaller than that in bulk ZrC. Note that the diffusion barriers of H and He are much lower than their corresponding segregation energies at the
-p
interface, which suggests that the trapped H and He should easily aggregate at the interface [55]. As for the H and He jumping across the interface, the migration pathways are much more
re
complex. We identified a minimum energy path joining the stable site 7 via a bulk-like site 1 in the
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ZrC slab and a bulk-like site 19 in the W slab, as illustrated in Fig. 9(c) and 9(d). As for the migration of H and He from the ZrC slab to the interface (17), the diffusion energy barriers of H and He from the site 1 to site 7 through the site 3 or 4 across the interface are 0.69 eV and 1.45 eV,
na
respectively, as shown in Fig. 9(d). In reverse from the interface back to the ZrC slab, if the H and He atoms are trapped by the interface, they need to overcome bigger energy barriers of 1.53 eV
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and 1.55 eV, respectively. As for the migration of H and He from the interface to W slab (719), the energy barriers are 0.72 eV and 1.72 eV, respectively. But in reverse from the W slab to the interface, the H and He atoms only overcome smaller diffusion barriers of about 0.30 eV and 0.58 eV, respectively. The ZPE corrections for the H and He energy barriers of the two diffusion paths are also calculated, as shown in Table 3.When the ZPE is considered, the energy barriers of H and He along the interface plane change slightly by 0-0.01 eV, while the barriers across the interface generally increases by 0-0.13 eV. This indicates that the ZPE has a greater influence on the diffusion barriers of H and He across the interface. The above results indicate that under a certain condition such as high temperature or plasma irradiation, the H and He atoms can easily reach the favorable segregation sites at the interface from the W matrix by overcoming relatively low energy barriers. But the escape rates are much lower due to significantly higher migration barriers for the reverse jumps [56]. As a result, the interface can behave as a barrier of H and He diffusion across the interface. However, by comparing these two migration pathways along and across the interface, it is found that the
9
Journal Pre-proof diffusion energy barriers of H and He along the interface are much lower than those across the interface. This indicates that H and He atoms are easy to diffuse along the interface. And so it is expected that H or He could jump out of the interface by thermal desorption, which explains why the W-ZrC material with a multi-scale interfacial microstructure exhibits much lower hydrogen retention than pure W under the low-energy high flux deuterium plasma irradiation [57].
4. Conclusions In this work, the stability and adhesion of twelve possible W-ZrC interfaces are systematically investigated by first-principles calculations. The segregation and migration behaviors of H and He
of
atom along and towards the stable coherent interface are also discussed. The key results of our study can be summarized into the following points.
For all considered interfaces, the coherent ZrC(200)C/W(100) interface shows the highest
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(i)
interfacial stability with the lowest interface energy, which agrees well with the experimental
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observed coherent interface between W matrix and ZrC dispersoids. (ii) For the coherent ZrC(200)C/W(100) interface, the electronic structure analysis shows a strong
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bonding between interfacial C and W atoms with a mixed feature of covalent bond and ionic
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bond. This is responsible for the stability and adhesion of the interface. (iii) The segregation energies of H and He to the ZrC(200)C/W(100) interface are -0.97eV and -2.03eV, respectively, implying that the interface acts as strong traps for both H and He.
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(iv) Two migration pathways of H and He along and across the ZrC(200)C/W(100) interface are examined. It is found that the diffusion energy barriers of H and He along the interface are
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much lower than those across the interface. This indicates that H and He atoms can easily diffuse in the direction to parallel the interface. The zero-point energy has a stronger influence on the diffusion barriers of H and He across the interface than along the interface. The present results not only provide a deep insight into the interface properties in W-ZrC materials, but also help us to improve the understanding about the influence of interface on the H/He behaviors in W materials under irradiation.
Acknowledgments This work is supported by the National Key Research and Development Program of China (Grant No.: 2017YFE0302400 and 2017YFA0402800), National Natural Science Foundation of China (Nos.: 11735015, 51871207, 11575229, U1832206), Anhui Provincial Natural Science Foundation (No. 1908085J17), and Special Fund for Theoretical Physics of the National Natural Science Foundation of China (No. 11547026).
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Journal Pre-proof Data availability Data not available / Data will be made available on request.
Reference [1] R. Causey, K.Wilson, T. Venhaus, W. R. Wampler, Tritium retention in tungsten exposed to intense fluxes of 100 eV tritons, J. Nucl. Mater. 266-269 (1999) 467–471. [2] M. Rieth, S.L. Dudarev, S.M. Gonzalez de Vicente, et. al. Recent progress in research on tungsten materials for nuclear fusion applications in Europe, J. Nucl. Mater. 432 (2013) 482-500. [3] V. Philipps, Tungsten as material for plasma-facing components in fusion devices, J. Nucl. Mater. 415 (2011) S2-S9.
of
[4] M.S. Wechsler, C. Lin, W.F. Sommer, L..L. Daemen, P.D. Ferguson, Radiation effects in materials for accelerator-driven neutron technologies, J. Nucl. Mater. 244 (1997) 177-184.
ro
[5] Y. Nemoto, A. Hasegawa, M. Satou, K. Abe, Microstructural development of neutron irradiated W-Re alloys, J. Nucl. Mater. 283-287 (2000) 1144-1147.
-p
[6] H. Kurishita, H. Arakawa, S. Matsuo, T. Sakamoto, S. Kobayashi, K. Nakai, G. Pintsuk, J. Linke, S. Tsurekawa, V. Yardley, K. Tokunaga, T. Takida, M. Katoh, A. Ikegaya, Y. Ueda, M. Kawai, N. Yoshida, Development of
re
Nanostructured Tungsten Based Materials Resistant to Recrystallization and/or Radiation Induced Embrittlement, Mater. Trans. 54 (2013) 456-465.
[7] Z.M. Xie, R. Liu, S. Miao, X.D. Yang, T. Zhang, Q.F. Fang, X.P. Wang, C.S. Liu, Y.Y. Lian, X. Liu, G.N. Luo,
lP
High thermal shock resistance of the hot rolled and swaged bulk W–ZrC alloys, J. Nucl. Mater. 469 (2016) 209-216.
[8] H. Kurishita, S. Matsuo, H. Arakawa, T. Sakamoto, S. Kobayashi, K. Nakai, T. Takida, M. Kato, M. Kawai, N.
na
Yoshida, Development of re-crystallized W–1.1%TiC with enhanced room-temperature ductility and radiation performance, J. Nucl. Mater. 398 (2010) 87-92.
Jo ur
[9] N. Jin, Y.Q. Yang, X. Luo, S. Liu, Z.Y. Xiao, P.F. Guo, B. Huang, First-principles calculation of W/WC interface: Atomic structure, stability and electronic properties, Appl. Surf. Sci. 324 (2015) 205-211. [10] M.W. Finnis, The theory of metal–ceramic interfaces, J. Phys.: Condens. Matter 8 (1996) 5811–5836. [11] A. Luo, D.L. Jacobson, K.S. Shin, Solution Softening Mechanism of Iridium and Rhenium in Tungsten at Room Temperature, Refract. Met. Hard Mater. 10 (1991) 107-114. [12] Y. Mutoh, K. Ichikawa, K. Nagata, M. Takeuchi, Effect of rhenium addition on fracture toughness of tungsten at elevated temperatures, J. Mater. Sci. 30 (1995) 770-775. [13] S. Wurster, B. Gludovatz, R. Pippan, High temperature fracture experiments on tungsten–rhenium alloys, Int. J. Refract. Met. Hard Mater. 28 (2010) 692-697. [14] Y. Ishijima, S. Kannari, H. Kurishita, M. Hasegawa, Y. Hiraoka, T. Takida, K. Takebe, Processing of fine-grained W materials without detrimental phases and their mechanical properties at 200–432K, Mater. Sci. Eng. , A 473 (2008) 7-15. [15] K. Lu, L. Lu, S. Suresh, Strengthening Materials by Engineering Coherent Internal Boundaries at the Nanoscale, Sci. 324 (2009) 349–352. [16] G.M. Song, Y.J. Wang, Y. Zhou, Thermomechanical properties of TiC particle-reinforced tungsten composites for high temperature applications, Int. J. Refract. Met. Hard Mater. 21 (2003) 1-12. [17] Z.M. Xie, R. Liu, S. Miao, X.D. Yang, T. Zhang, X.P. Wang, Q.F. Fang, C.S. Liu, G.N. Luo, Y.Y. Lian, X. Liu, Extraordinary high ductility/strength of the interface designed bulk W-ZrC alloy plate at relatively low
11
Journal Pre-proof temperature, Sci. Rep. 5 (2015) 16014. [18] S.M. Zhang, S. Wang, W. Li, Y.L. Zhu, Z.H. Chen, Microstructure and properties of W–ZrC composites prepared by the displacive compensation of porosity (DCP) method, J. Alloys Compd. 509 (2011) 8327-8332. [19] J.X. Yang, L. Chen, J.L. Fan, H.R. Gong, Doping of helium at Fe/W interfaces from first principles calculation, J. Alloys Compd. 686 (2016) 160-167. [20] J.W. Wang, J.L. Fan, H.R. Gong, Effects of Zr alloying on cohesion properties of Cu/W interfaces, J. Alloys Compd. 661 (2016) 553-556. [21] D.Y. Dang, L.Y. Shi, J.L. Fan, H.R. Gong, First-principles study of W–TiC interface cohesion, Surf. Coat. Technol. 276 (2015) 602-605. [22] H.Y. Wang, S. Zhang, D.J. Li, S.Y. Liu, The simulation of adhesion, stability, electronic structure of W/ZrB 2 interface using first-principles, Surf. Coat. Technol. 228 (2013) S583-S587. [23] H. Kurishita, Y. Amano, S. Kobayashi, K. Nakai, H. Arakawa, Y. Hiraoka, T. Takida, K. Takebe, H. Matsui,
of
Development of ultra-fine grained W–TiC and their mechanical properties for fusion applications, J. Nucl. Mater. 367 (2007) 1453-1457.
ro
[24] M.W. Finnis, C. Kruse, U. Schönberger, Ab initio calculations of metalceramic interfaces what have we learned what can we learn, Nanostruct. Mater. 6 (1995) 145-155.
calculation, J. Alloys Compd. 768 (2018) 387-391.
-p
[25] J. Qian, C.Y. Wu, H.R. Gong, S.F. Zhou, Cohesion properties of W-ZrC interfaces from first principles
re
[26] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 1169-1186.
[27] G. Kresse, J. Hafner, Ab initiomolecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558-561.
lP
[28] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B 46 (1992) 6671-6687.
(1996) 3865-3868.
na
[29] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77
Jo ur
[30] D.J. Chadi, Special points for Brillouin-zone integrations, Phys. Rev. B 16 (1977) 1746-1747. [31] C. Wei, Q.Q. Ren, J.L. Fan, H.R. Gong, Cohesion properties of W/La2O3 interfaces from first principles calculation, J. Nucl. Mater. 466 (2015) 234-238. [32] X.Y. Yang, Y. Lu, P. Zhang, First-principles study of native point defects and diffusion behaviors of helium in zirconium carbide, J. Nucl. Mater. 465 (2015) 161-166. [33] S. Méçabih, N. Amrane, Z. Nabi, B. Abbar, H. Aourag, Description of structural and electronic properties of TiC and ZrC by generalized gradient approximation, Phys. A 285(2000) 392-396. [34] F. Birch, Finite Elastic Strain of Cubic Crystals, Phys. Rev. 71 (1947) 809-824. [35] L.M. Liu, S.Q. Wang, H.Q. Ye, First-principles study of polar Al/TiN(111) interfaces, Acta Mater. 52 (2004) 3681-3688. [36] H.L. Wang, J.J. Tang, Y.J. Zhao, J. Du, First-principles study of Mg/Al2MgC2 heterogeneous nucleation interfaces, Appl. Surf. Sci.355 (2015) 1091-1097. [37] Z.M. Zhuo, H.K. Mao, H. Xu, Y.Z. Fu, Density functional theory study of Al/NbB2 heterogeneous nucleation interface, Appl. Surf. Sci. 456 (2018) 37-42. [38] S.J. Lee, Y.K. Lee, A. Soon, The austenite/ɛ martensite interface: A first-principles investigation of the fcc Fe(111)/hcp Fe(0001) system, Appl. Sur. Sci. 258 (2012) 9977-9981. [39] Q. Jiang, H.M. Lu, M. Zhao, Modelling of surface energies of elemental crystals, J. Phys.: Condens. Matter 16 (2004) 521-530.
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Journal Pre-proof [40] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the ZrC(100)/Fe(110) interface from first principles, Surf. Sci. 560 (2004) 103-120. [41] L.M. Liu, S.Q. Wang, H.Q. Ye, First-principles study of metal/nitride polar interfaces: Ti/TiN, Surf. Interface Anal. 35 (2003) 835-841.
[42] I. G. Batyrev, A. Alavi, M. W. Finnis, Equilibrium and adhesion of Nb/sapphire: The effect of oxygen partial pressure, Phys. Rev. B 62 (2000) 4698-4706. [43] N. Jin, Y.Y. Yang, X. Luo, J. Li, B. Huang, S. Liu, Z.Y. Xiao, Theoretical calculations on the adhesion, stability, electronic structure and bonding of SiC/W interface, Appl. Sur. Sci. 314 (2014) 896-905. [44] K. Nagao, J.B. Neaton, N.W. Ashcroft, First-principles study of adhesion at Cu/SiO2interfaces, Phys. Rev. B 68 (2003) 125403. [45] D.J. Siegel, L.G. Hector, Jr., J.B. Adams, Adhesion, atomic structure, and bonding at the Al(111)/α−Al2O3(0001)interface: A first principles study, Phys. Rev. B 65 (2002) 084515.
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[46] A.D. Krawitz, D.G. Reichel, R. Hitterman, Thermal expansion of tungsten carbide at low temperature, J. Am. Ceram. Soc. 72 (1989) 515-517.
ro
[47] Q.Q. Ren, D.Y. Dang, H.R. Gong, J.L. Fan, Y.M. Zhao, Cohesion properties of carbon–tungsten interfaces, Carbon 83 (2015) 100-105.
-p
[48] G. Mills, H. Jónsson, G.K. Schenter, Reversible work transition state theory application todissociative adsorption of hydrogen, Surf. Sci. 324 (1995) 305-337.
re
[49] X.S. Kong, S. Wang, X.B. Wu, Y.W. You, C.S. Liu, Q.F. Fang, J.L. Chen, G.N. Luo, First-principles calculations of hydrogen solution and diffusion in tungsten: Temperature and defect-trapping effects, Acta Mater. 84 (2015) 426-435.
Phys. 107 (2010) 113531.
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[50] K. Heinloa, T. Ahlgren, Diffusion of hydrogen in bcc tungsten studied with first principle calculations, J. Appl.
[51] X.B. Wu, X.S. Kong, Y.W. You, C.S. Liu, Q.F. Fang, J.L. Chen, G.N. Luo, Z.G. Wang, Effects of alloying and
Fusion 53 (2013) 073049.
na
transmutation impurities on stability and mobility of helium in tungsten under a fusion environment, Nucl.
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[52] L. Yang, H.K. Liu, X.T. Zu, First-principles study of the migration of helium in tungsten, Int. J. Mod. Phys. B 23 (2009) 2077-2082.
[53] X.Y. Yang, Y. Lu, P. Zhang, The temperature-dependent diffusion coefficient of helium in zirconium carbide studied with first-principles calculations, J. Appl. Phys. 117 (2015) 164903. [54] H.B. Zhou, Y.L. Liu, Y. Zhang, S. Jin, G.H. Lu, First-principles investigation of energetics and site preference of He in a W grain boundary, Nucl. instrum. Methods Phys. Res. B 267 (2009) 3189-3192. [55] H.B. Zhou, Y.L. Liu, S. Jin, Y. Zhang, G.N. Luo, G.H. Lu, Investigating behaviours of hydrogen in a tungsten grain boundary by first principles: from dissolution and diffusion to a trapping mechanism, Nucl. Fusion 50 (2010) 025016.
[56] D.D. Stefano, M. Mrovec, C. Elsässer, First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel, Acta Mater. 98 (2015) 306-312. [57] R. Liu, Z.M. Xie, J.F. Yang, T. Zhang, T. Hao, X.P. Wang, Q.F. Fang, C.S. Liu, Recent progress on the R&D of W-ZrC alloys for plasma facing components in fusion devices, Nucl. Mate. Energy 16 (2018) 191-206.
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Journal Pre-proof Table 1. Surface energies (in J/m2) of W(100), W(110), ZrC(200) and ZrC(110) surfaces. The available DFT and experimental results are presented for comparison. W(100)
W(110)
ZrC(200)
ZrC(110)
Present work
3.93
3.19
1.65
3.23
Previous work
3.904a
3.21b, 3.27c
1.592d
3.199d
d
Ref. [40].
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Ref. [39].
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Ref. [31].
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b
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Ref. [21].
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Esurf (J/m2)
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Journal Pre-proof Table 2. Formation energies (in eV) of the H and He atom at the interstitial sites (I1-I5) and substitutional sites (S1-S6) in the ZrC(200)C/W(100) interface with and without ZPE corrections. Site
I1
I2
I3
I4
I5
S1
S2
S3
S4
S5
S6
0.81
-0.03
0.39
0.54
/
7.50
0.99
1.72
6.32
2.46
3.03
1.11*
0.20*
0.62*
0.80*
/
7.73*
1.13*
1.88*
6.46*
2.63*
3.11*
4.13
4.02
/
5.53
5.16
9.22
4.01
5.18
7.40
4.48
5.56
4.26*
4.12*
/
5.63*
5.24*
9.31*
4.04*
5.24*
7.49*
4.56*
5.63*
H
He
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ZPE corrected.
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Journal Pre-proof Table 3. Diffusion energy barriers (in eV) of H and He along and across the interface plane. ZPE corrections are considered for each barrier. Along the interface
Path
Across the interface
17
713
17
71
719
197
0.37
0.27
0.69
1.53
0.72
0.30
0.36*
0.26*
0.75*
1.66*
0.75*
0.33*
0.15
0.33
1.45
1.55
1.72
0.58
0.15*
0.32*
1.48*
1.61*
1.72*
0.60*
H
He
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ZPE corrected.
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Journal Pre-proof Figure captions Fig. 1. Surface energies of C-terminated and Zr-terminated ZrC(111) vs μC -μbulk , where the C C-term and Zr-term denote the C-terminated and Zr-terminated ZrC(111) surfaces, respectively.
Fig. 2. Schematic plot of typical six kinds of ZrCC/W interfaces (C atoms on the top of W atoms), i.e., (a) ZrC(200)C/W(100), (b) ZrC(110)C/W(110), (c) ZrC(110)C/W(100), (d) ZrC(200)C/W(110), (e) non-stoichiometric ZrC(111)/W(110), and (f) non-stoichiometric ZrC(111)/W(100). The green, gray and brown spheres represent Zr, W, and C, respectively. The upper and lower figures are the
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side and top view, respectively. The location of interface is indicated by a gray parallelogram.
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Fig. 3. Interface energies (Eint) and ideal work of adhesion (Ead) of eight stoichiometric and four non-stoichiometric ZrC/W interfacial configurations. Eint-C(Zr) and Ead-C(Zr) represent the
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interface energies and ideal works of adhesion of the interfaces with the C or Zr atoms on the top
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of the W atoms close to the interface, respectively.
Fig. 4. Interface energies of non-stoichiometric ZrC(111)/W(100) and ZrC(111)/W(110) interfaces.
Zr-terminated
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The Ein value of ZrC(200)C/W(100) interface is also shown for a comparison. (a)-(d) present the ZrC(111)/W(100),
Zr-terminated
ZrC(111)/W(110),
ZrC(200)/W(100),
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C-terminated ZrC(111)/W(100) and C-terminated ZrC(111)/W(110) interfaces, respectively.
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Fig. 5. (a) Charge density of the coherent ZrC(200)C/W(100) interface, where the value of charge density increases as color changing from blue to red, and the horizontal dashed line represents the location of the interface. (b) Charge density difference of ZrC(200)C/W(100) interface. Blue contour denotes regions of charge accumulation and red contour denotes regions of charge depletion.
Fig. 6. Partial density of state (PDOS) of the W, Zr, and C atoms located at the ZrC(200)C/W(100) interface and those in the bulk W and ZrC. The line represents the Fermi energy level.
Fig. 7. Migration of H and He in bulk W and ZrC, where (a)-(c) represent the most stable interstitial site, diffusion paths and diffusion energy profiles of H and He in W, and (d)-(f) are those of He and He in ZrC. The number 1 and 7 denote the two nearest-neighboring stable tetrahedral sites, and the number 4 represents the saddle point. The red, green, brown, gray spheres are H/He, Zr, C, and W atoms, respectively.
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Journal Pre-proof Fig. 8. The possible positions of H and He segregated at the interface after relaxation. The green, gray and brown spheres denote Zr, W, and C, respectively. The small blue spheres (numbers of I1-I5) represent the five different interstitial sites, and numbers of S1-S6 represent the six different substitutional sites.
Fig. 9. H and He migration in the vicinity of the ZrC(200)C/W(100) interface through two pathways, i.e., along the interface and across the interface, where (a) and (b) represent the stable interstitial site of H and He at the interface, the diffusion paths (113), and diffusion energy profiles, respectively, and (c) and (d) denote those of H and He migration from ZrC slab to W slab
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across the interface (119). The green, gray, brown, red, blue spheres denote Zr, W, C, H, and He,
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respectively. The gray parallelogram represents the location of interface.
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Fig. 2
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Fig. 5
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Fig. 6
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Fig. 7
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Journal Pre-proof 1)
The coherent ZrC(200)C/W(100) interface shows the highest interfacial stability with the lowest interface energy.
2)
There is a strong bonding with some property of strong covalent bond and ionic bond between the interfacial C and W atoms.
3)
The interface acts as strong traps for both H and He.
4)
The diffusion energy barriers of H and He along the interface are much lower than those across the interface.
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The zero-point energy has a stronger influence on the diffusion barriers of H and He across
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the interface than along the interface.
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