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The effects of boron and hydrogen on the embrittlement of polycrystalline Ni3Al
Intermetallics 8 (2000) 589±593
The eects of boron and hydrogen on the embrittlement of polycrystalline Ni3Al Fu-He Wang a,b,c,*, Jia-Xiang Shang d, Jia-Ming Li a,b, Chong-Yu Wang d a
Center of Atomic and Molecular Sciences, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China b Institute of Physics, Chinese Academy of Sciences P.O. Box 603-22, Beijing 100080, People's Republic of China c Department of Physics, Capital Normal University, Beijing 100037, People's Republic of China d Central Iron and Steel Research Institute, Beijing 100081, People's Republic of China
Abstract The discrete-variational method within the framework of density functional theory is used to study the eects of both boron and hydrogen on the embrittlement of polycrystalline Ni3Al. The calculated results show that there are strong repulsive interaction between the boron and the hydrogen atoms, if they occupy the nearest interstitial sites, respectively, in the Ni3Al grain boundaries. It indicates that the boron atoms inhibit the diusion of hydrogen atoms along the grain boundary. It may be the main reason why boron can suppress the moisture induced hydrogen embrittlement. Our results also show that the attractive interactions between boron and some substrate atoms are weakened, but the attractive interactions between boron and other substrate atoms are enhanced, when hydrogen atoms are forced into the grain boundary and occupy the nearest interstitial sites to boron atoms. As a result, the bonding states are polarized in the local region of the grain boundary. It may suppress the movement of slips across the grain boundary. Furthermore, the weakening eects of hydrogen to the grain boundary are hardly aected by the boron atoms, even though they are very near to each other. It can be concluded that hydrogen embrittlement takes place when the boron-doped polycrystalline Ni3Al are charged with hydrogen. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Nickel aluminides, based on Ni3Al; B. Environmental embrittlement; D. Grain boundaries, structure; E. Ab-initio calculations
1. Introduction As high temperature structural material, Ni3Al has many attractive properties such as high temperature strength, low density, resistance to oxidation, etc. However, the brittle grain boundary fracture is the major problem of polycrystalline Ni3Al for the use of mechanics [1]. Many works concentrated on how to improve the ductility of polycrystalline Ni3Al [1±5]. It was found that the tensile ductility of the polycrystalline Ni3Al can be improved eectively, when it is doped with boron. Traditionally, the grain boundaries in Ni3Al were concluded to be intrinsically brittle [2]. The main doping eect of boron was taken to be enhancement of the cohesion of grain boundaries [2,6,7]. However, recent work from Liu et al. [8±12] has shown that the extrinsic fracture: environmental or hydrogen embrittlement, is the major cause of low ductility and brittle intergranular fracture in binary Ni3Al. Can boron prevent * Corresponding author. Tel.: +86-10-6890-2567; fax: +86-106890-2938. E-mail address: [email protected] (Fu-He Wang).
Ni3Al from hydrogen embrittlement? Many works studied the hydrogen embrittlement of boron-doped Ni3Al [4,13±18]. It was found that the sensitivity of ductility to test environment of boron-doped Ni3Al depends on the content of boron. When doped with 0.012 wt% of boron, the Ni3Al is susceptible to environmental embrittlement; but when doped with 0.05 wt% boron, the tensile ductility of Ni3Al is insensitive to test environment [4]. However, when pre-charged with hydrogen, the ductility and the ultimate tensile strength of borondoped Ni3Al is much decreased, and the fracture mode is changed from ductile transgranular to brittle intergranular, though the yield stress is not aected by hydrogen [15,16]. Furthermore, the hydrogen embrittlement is sensitive to the strain rate, and is less at the higher strain rate [16±18]. On the theoretical side, Sun et al. [19] studied the eects of boron and hydrogen on the atomic bonding when they co-exist in bulk Ni3Al by use of full-potential linear mun-tin orbital (FPLMTO) method. Their calculated results showed that both boron and hydrogen prefer to occupy octahedral interstitial sites that are entirely coordinated by six-nickel atoms. The changes in
0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(99)00143-0
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F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
the electronic structure and bonding induced by hydrogen are small relative to those induced by boron. Recently, Wang et al. studied the eects of boron [7] and hydrogen [20] on the electronic structure of grain boundaries when they exist alone in Ni3Al by use of discrete variational method (DVM). The calculated results show that both boron and hydrogen atoms prefer to segregate at the grain boundaries, and occupy the Ni-rich interstitial holes in the polycrystalline Ni3Al. Boron enhances the cohesive strength of grain boundary in Ni3Al. However, hydrogen decreases the cohesive strength of Ni3Al grain boundaries. What happens when both boron and hydrogen are present in Ni3Al grain boundaries? Can boron suppress hydrogen embrittlement? To answer these questions, we used DVM [21±26] to study the eects of boron and hydrogen on the electronic structure of grain boundaries in Ni3Al, and the interactions between boron and hydrogen atoms. 2. Computation method and cluster model The DVM, which is a ®rst principles numerical method for solving the local density functional equations [21±26], has been used successfully to study the electronic structure of metals and alloys [25,26]. Recently, it was used successfully to study doping eects on the electronic structure of grain boundaries in Ni3Al [7,20], and to predict the self-diusion mechanisms on metallic FCC{001} surfaces [27]. In this work, the DVM is used to study the interactions between boron and hydrogen atoms when they co-exist in the Ni3Al grain boundary. In order to approach the real grain boundary systems by cluster models, the embedded cluster model [25,26] is used. In constructing the self-consistent potential, the charge density of several hundreds of atoms surrounding the cluster is included. In the calculation, the exchange-correlation potential of Von Barth and Hedin formula [28] is adopted. In order to study the interaction between atoms, the interatomic energy between atoms l and m is derived [29] XX Nn an l an m H m l 1 Elm n
P Fig. 1. The atomic con®gurations around 13[001](320) tilt grain boundaries in Ni3Al. The Ni and Al atoms are represented by the circles and squares, the dierent sizes represent dierent layers, and the atoms shown as large symbols are in the YZ plane. The atoms shown as solid symbols and labeled by numbers are in the cluster, which is embedded by several hundreds of surrounding atoms (labeled by hollow symbols). These crosses labeled with X1 (or X10 ) and X2, X3 represent the possible occupation sites of boron and hydrogen, respectively.
boundary in Ni3Al. Based on our previous works [20], we only choose the cluster, in which the more stable occupation sites for hydrogen and boron are included, as the computational model. In order to discuss the interaction between atoms clearly, the atoms in the cluster are labeled with numbers. The possible occupation sites for boron is labeled by X1 (or X10 ), and that for hydrogen are labeled by X2 and X3. The atomic relaxation at the grain boundary is carried out as in our previous work [7,20]. To discuss the changes of energy for the system induced by the doping of impurities, the impurity formation energies Eimp can be de®ned as Eimp Eb GB impurity ÿ Eb GB
2
where Eb is the binding energy for a system.
where Nn is the occupation number for molecular orbital n , an l is the expanded coecient of n on atomic orbital ' l , and H m l is the Hamiltonian matrix element connecting the atomic orbital of atom m and the atomic orbital of atom l. The grain boundary 13[001](320), which is constructed by use of the coincidence site lattice (CSL) model and atomistic simulations [30], is investigated. Fig. 1 shows the atomic con®guration for 13 grain
3. Results and discussion 3.1. The impurity formation energy In order to get the most stable occupation sites for boron, hydrogen or both of them, we change symmetrically the coordinates of boron and hydrogen and calculate the corresponding formation energies. The formation energies only for several most possible occupation sites labeled by X1 (or X10 ) for boron and X2,
F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
X3 for hydrogen atoms are listed in Table 1. These sites locate in the YZ plane (x 0). X1 locates at the hole of the capped trigonal-prism, which is composed of nos. 2, 3, 21, 4, 5 and 22 with the cap 1, 19 and 20 atoms. The size of this hole is the largest one in the Ni3Al 13 grain boundaries, and boron atom prefers to occupy this interstitial site for its large size. X2 locates near to the middle points between Ni2 and Ni4, Ni3 and Ni5, respectively. X3 locates in the hole of distorted octahedrons, which is composed of nos. 10, 23, 35, 13, 15, 17, and nos. 10, 24, 36, 14, 16, 18 atoms, respectively. X2 and X3 sites are not in the center of these interstitial holes, instead, the hydrogen atom tends to interact strongly with a certain Ni atom [20]. From the calculated impurity formation energy results of boron, the X1 site is not in the center of the interstitial hole too. This behavior of boron was not considered in our previous work [7]. When both of boron and hydrogen atom are present in the Ni3Al 13 grain boundary, and they occupy the separated X1 and X3 sites, respectively [denoted by GB+B(X1)+H(X3)], their position is hardly changed comparing to cases when boron and hydrogen exist alone in the grain boundary [denoted by GB+B(X1) and GB+H(X3), respectively]. At the same time, the impurity formation energy for the system GB+ B(X1)+H(X3) is almost same as the sum of that for the system GB+B(X1) and GB+H(X3). In this case, boron does not interact with hydrogen atoms for their large distance. When boron atom occupies the X10 site and two hydrogen atoms occupy the nearest interstitial X2 site [denoted by GB+B(X10 )+H(X2)], there is a strong repulsive interaction between boron and hydrogen atoms. As a result, the stable position of boron is changed from X1 as in the case of GB+B(X1) to X1' as in the case of GB+B(X10 )+H(X2), at the same time, the position of hydrogen is hardly changed. The displacement of boron is 0.88 AÊ. The nearest neighbor is changed from Ni1 to Ni19 and Ni20. The impurity formation energy is raised 2.9 eV comparing to the systems GB+B(X1) and GB+H(X2) (the sum of the impurity formation energies for boron and hydrogen occupy the X1 and X2 sites alone in the grain boundary). From the energy point of view, boron and hydrogen prefer to
591
occupy the separated interstitial X1 and X3 sites rather than the X10 and X2 sites. Only when there is an external factor such as cathodic charging of hydrogen, it is possible for hydrogen atoms to take the X2 site in the boron-doped Ni3Al grain boundary. The experimental results show that the hydrogen embrittlement of boron-doped Ni3Al is very sensitive to strain rate and it is severer at the lower strain rate [16± 18]. This indicates that the easier for hydrogen transportation to the crack tip, the serverer of hydrogen embrittlement. Grain boundaries are the main passageway for atom diusion. Boron atom is more dicult to diuse than hydrogen atom, because the bonding between boron and its neighbor metal atoms is stronger and its size is larger than that of hydrogen. Our calculated results show that there is a strong repulsive interaction between boron and hydrogen atoms when they approach each other. As a result, the diusion of hydrogen along the grain boundary is blocked by the presence of boron atoms, especially when the concentration of boron is higher. This may be the reason why the sensitivity of ductility to test environment of boron-doped Ni3Al depends on the content of boron. 3.2. Interatomic energy In order to investigate the interaction between adjacent atoms, the interatomic energies de®ned by Eq. (1) are calculated and some main results are listed in Table 2. As references, the results for the case with only one boron atom and only two hydrogen atoms alone in the grain boundary are also listed. Let us pay attention to the cases of both boron and hydrogen atoms present in the grain boundary. First, let us see the case of GB+B(X1)+H(X3). Comparing the interatomic energies of the system GB+B(X1)+H(X3) with that of the system GB+B(X1) and GB+H(X3), it can be found that the bonding states of boron and hydrogen with their neighboring host atoms, and the changes of bonding strength between host metal atoms when both of boron and hydrogen atoms are present in the grain boundary are almost same as that in the case when only boron and only hydrogen alone are present. In the GB+B(X1)+H(X3) system, the action of boron atom
Table 1 The impurity formation energy Eimp (in eV), the nearest neighboring (NN) atoms, and the distance dNN (in AÊ) between boron or hydrogen and its NN atoms, when boron and hydrogen occupies dierent sites in the Ni3Al grain boundary System
GB+B(X1)
GB+H(X2)
GB+B(X10 )+H(X2)
GB+H(X3)
GB+B(X1)+H(X3)
NN(B) dNN (B)
Ni1 1.79
± ±
Ni19,20 2.02
± ±
Ni1 1.79
NN(H) dNN H
± ±
Ni1,11 1.62
Ni11 1.57
Ni23 1.46
Ni23 1.51
Eimp
ÿ9.89
ÿ11.58
ÿ18.57
ÿ11.25
ÿ21.85
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F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
Table 2 The interatomic energy Elm (in eV) for the typical pairs of atoms l and m, when boron and hydrogen occupies the dierent sites in the Ni3Al grain boundarya Pair of atoms lÿm
GB Elm
GB+B(X1) Elm Elm
GB+H(X3) Elm Elm
GB+B(X10 )+H(X2) Elm Elm
GB+H(X3) Elm Elm
GB+B(X1)+H(X3) Elm Elm
Ni1±Ni2 Ni1±Ni11 Ni2±Ni11 Ni15±Ni23 Ni15±Ni35 Ni23±Ni35 H1±Ni1 H1±Ni2 H1±Ni10 H1±Ni11 H1±Ni13 H1±Ni19 H1±Ni23 B±Ni1 B±Ni2 B±Ni19 B±H1
ÿ1.39 ÿ1.66 ÿ1.78 ÿ2.02 ÿ2.35 ÿ1.84
ÿ1.00 ÿ1.66 ÿ1.76 ÿ2.01 ÿ2.33 ÿ1.80
ÿ0.95 ÿ0.78 ÿ1.17 ÿ2.04 ÿ2.34 ÿ1.82 ÿ1.75 ÿ1.27 0.00 ÿ1.83 0.00 ÿ0.87 0.00
ÿ0.95 ÿ0.78 ÿ1.11 ÿ1.99 ÿ2.36 ÿ1.84 ÿ1.67 ÿ1.13 0.00 ÿ2.33 0.00 ÿ0.49 0.00 ÿ0.25 ÿ1.36 ÿ4.10 ÿ0.57
ÿ1.38 ÿ1.64 ÿ1.80 ÿ1.44 ÿ2.16 ÿ1.08 0.00 0.00 ÿ0.34 0.00 ÿ0.67 0.00 ÿ2.60
ÿ0.99 ÿ1.68 ÿ1.70 ÿ1.46 ÿ2.06 ÿ1.02 0.00 0.00 ÿ0.22 0.00 ÿ0.76 0.00 ÿ2.26 ÿ4.30 ÿ2.29 ÿ2.21 0.00
a
ÿ4.48 ÿ2.30 ÿ2.21
0.39 0.00 0.02 0.001 0.02 0.04
0.44 0.88 0.68 ÿ0.02 0.01 0.02
0.44 0.88 0.72 0.03 ÿ0.01 0.00
0.01 0.02 ÿ0.02 0.58 0.19 0.76
0.40 ÿ0.02 0.08 0.56 0.29 0.82
Elm Elm GB impurity ÿ Elm GB (in eV) is the change of interatomic energy induced by the presence of boron and hydrogen.
are almost same as that of boron in the GB+B(X1) system, i.e. the interaction between boron and its neighboring Ni atoms are very strong (boron acts as a ``bridge''), and the bonding between the adjacent host metal atoms are hardly changed; the action of hydrogen atom are almost same as that of hydrogen in the GB+H(X3) system, i.e. hydrogen only interacts strongly with a certain host metal atom, but less with other atoms, and at the same time, the bonding strength between host atoms, which are near to H atoms, are reduced evidently by the presence of hydrogen. As a result, boron enhances but hydrogen weakens the cohesive strength of grain boundary in Ni3Al. (The detailed discussion can be seen in Refs. [7] and [20]). Second, let us see the case of GB+B(X10 )+H(X2). The boron atom is removed from X1 to X10 by the presence of hydrogen atoms in X2 site. The interatomic energy for the pairs of atoms such as B±Ni1, B±Ni2,3,4,5 is raised a lot, so that the bonding strength for boron with these atoms is weakened very much. At the same time, the weakening of the bonds for the pairs of the host metal atoms such as Ni1±Ni2, Ni1±Ni11, and Ni2± Ni11 etc., is even more serious than that of the system with only two hydrogen atoms on the X2 site. As a result, the cohesive strength of grain boundary in boron doped Ni3Al is weakened by the occupation of hydrogen in the nearest interstitial site. That may be the reason why the ultimate tensile strength drops drastically and the fracture mode changes from transgranular to intergranular when boron-doped Ni3Al is cathodic charged with hydrogen [15]. The theoretical results con®rm the suggestion that hydrogen counteract the strengthening eect of boron on grain boundaries and reduces the cohesive strength of the grain boundaries,
which is proposed from TEM experimental results [14]. On the other side, the bonds for B±Ni19,20 is made very strong. So that the bonding states around boron atom are polarized seriously, and the slips may be made dicult to move in the region of grain boundary. This may be another cause of hydrogen embrittlement of borondoped Ni3Al. 4. Conclusion We have studied the eects of both boron and hydrogen on the embrittlement of polycrystalline Ni3Al using ®rst-principles numerical calculations. It is found that there are strong repulsive interaction between the boron and the hydrogen atoms, if they occupy the nearest interstitial sites respectively in the Ni3Al grain boundaries. It indicates that the boron atoms inhibit the diusion of hydrogen atoms along the grain boundary. It may be the main reason why boron can suppress the moisture induced hydrogen embrittlement. Our results also show that boron and hydrogen atoms prefer to occupy the interstitial sites, which are not near to each other. In this case, the boron enhances locally the cohesive strength of the grain boundary, but the hydrogen weakens it locally and counteracts the strengthening eect of boron on the grain boundary. When hydrogen atoms are forced into the grain boundary and occupy the nearest interstitial sites to boron atoms, the boron atoms will be displaced a short distance away from the hydrogen atoms. As a result, the ``bridge'' eects of boron are removed, and the bonding states are polarized in the local region of the grain boundary. It may suppress the movement of slips across the grain boundary.
F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
Furthermore, the weakening eects of hydrogen to the grain boundary are hardly aected by the boron atoms, even though they are very near to each other. It can be concluded that hydrogen embrittlement takes place when the boron-doped polycrystalline Ni3Al are charged with hydrogen. Acknowledgements This work was supported by the National Natural Science Foundation of China and Ministry of Science and Technology of China. References [1] Aoki K, Izumi O. J Japan Inst Metals 1979;43:1190. [2] Liu CT, White CL, Horton JA. Acta Metall 1985;33:213. [3] Schulson EM, Weihs TP, Baker I, Frost HJ, Horton JA. Acta Metall 1986;34:1395. [4] Wan XJ, Zhu JH, Jing KL. Scr Metall 1992;26:473; Scr Metall 1992;26:479. [5] Takasugi T, Izumi O, Masahashi N. Acta Metall 1985;33:1259. [6] White CL, Padgett PA, Liu CT, Yalisov SM. Scrip Metall 1985;18:1417. [7] Wang F-H, Wang C-Y, Yang J-L. J Phys: Condens Matt 1996;8:5527.
[8] [9] [10] [11] [12]
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]
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Liu CT. Scr Metall 1992;27:25. George EP, Liu CT, Pope DP. Scr Metall 1992;27:365. George EP, Liu CT, Pope DP. Scr Metall 1993;28:857. George EP, Liu CT, Pope DP. Scr Metall 1994;30:37. George EP, Liu CT, Pope DP. In: Darolia R, Lewandowski JJ, Liu CT, Martin PL, Miracle DB, Nathal BV, editors. Structural Intermetallics, The Minerals, Metals and Materials Society, 1993. p. 431. Wan XJ, Zhu JH, Jing KL, Liu CT. Scr Metall 1994;31:677. Bond GM, Bobertson IM, Birnbaum HK. Acta Metall 1989;37:1407. Kuruvilla AK, Stolo NS. Scr Metall 1985;19:83. Li HX, Chaki TK. Acta Metall 1993;41:1979. Li HX, Chaki TK. Mat Sci Eng 1995;A192/193:387. Chen M-W, Lin D-L, Liu CT. Scr Metall 1998;38:293. Sun SN, Kioussis N, Lin SP, Gonis A, Gourdin WH. Phys Rev 1995;B52:14421. Wang F-H, Wang C-Y. Phys Rev 1998;B57:289. Ellis DE, Painter GS. Phys Rev 1970;B2:2887. Baerends EJ, Ellis DE, Ros P. Chem Phys 1973;2:41. Averill FW, Ellis DE. J Chem Phys 1973;59:6412. Delley B, Ellis DE, Freeman AJ, Baerends EJ, Post D. Phys Rev 1983;B27:2132. Ellis DE, Benesh GA, Byrom E. Phys Rev 1977;B16:3308. Guenzburger D, Ellis DE. Phys Rev 1992;B45:285. Li J-M, Zhang P-H, Yang J-L, Liu L. Chin Phys Lett 1997;14:768. Von Barth U, Hedin L. J Phys 1972;C5:1629. Wang C-Y, An F, Gu B-L, Liu F-S, Chen Y. Phys Rev 1988;B38:3905. Chen SP, Voter AF, Srolovitz DJ. Scr Metall 1986;20:389.
The eects of boron and hydrogen on the embrittlement of polycrystalline Ni3Al Fu-He Wang a,b,c,*, Jia-Xiang Shang d, Jia-Ming Li a,b, Chong-Yu Wang d a
Center of Atomic and Molecular Sciences, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China b Institute of Physics, Chinese Academy of Sciences P.O. Box 603-22, Beijing 100080, People's Republic of China c Department of Physics, Capital Normal University, Beijing 100037, People's Republic of China d Central Iron and Steel Research Institute, Beijing 100081, People's Republic of China
Abstract The discrete-variational method within the framework of density functional theory is used to study the eects of both boron and hydrogen on the embrittlement of polycrystalline Ni3Al. The calculated results show that there are strong repulsive interaction between the boron and the hydrogen atoms, if they occupy the nearest interstitial sites, respectively, in the Ni3Al grain boundaries. It indicates that the boron atoms inhibit the diusion of hydrogen atoms along the grain boundary. It may be the main reason why boron can suppress the moisture induced hydrogen embrittlement. Our results also show that the attractive interactions between boron and some substrate atoms are weakened, but the attractive interactions between boron and other substrate atoms are enhanced, when hydrogen atoms are forced into the grain boundary and occupy the nearest interstitial sites to boron atoms. As a result, the bonding states are polarized in the local region of the grain boundary. It may suppress the movement of slips across the grain boundary. Furthermore, the weakening eects of hydrogen to the grain boundary are hardly aected by the boron atoms, even though they are very near to each other. It can be concluded that hydrogen embrittlement takes place when the boron-doped polycrystalline Ni3Al are charged with hydrogen. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Nickel aluminides, based on Ni3Al; B. Environmental embrittlement; D. Grain boundaries, structure; E. Ab-initio calculations
1. Introduction As high temperature structural material, Ni3Al has many attractive properties such as high temperature strength, low density, resistance to oxidation, etc. However, the brittle grain boundary fracture is the major problem of polycrystalline Ni3Al for the use of mechanics [1]. Many works concentrated on how to improve the ductility of polycrystalline Ni3Al [1±5]. It was found that the tensile ductility of the polycrystalline Ni3Al can be improved eectively, when it is doped with boron. Traditionally, the grain boundaries in Ni3Al were concluded to be intrinsically brittle [2]. The main doping eect of boron was taken to be enhancement of the cohesion of grain boundaries [2,6,7]. However, recent work from Liu et al. [8±12] has shown that the extrinsic fracture: environmental or hydrogen embrittlement, is the major cause of low ductility and brittle intergranular fracture in binary Ni3Al. Can boron prevent * Corresponding author. Tel.: +86-10-6890-2567; fax: +86-106890-2938. E-mail address: [email protected] (Fu-He Wang).
Ni3Al from hydrogen embrittlement? Many works studied the hydrogen embrittlement of boron-doped Ni3Al [4,13±18]. It was found that the sensitivity of ductility to test environment of boron-doped Ni3Al depends on the content of boron. When doped with 0.012 wt% of boron, the Ni3Al is susceptible to environmental embrittlement; but when doped with 0.05 wt% boron, the tensile ductility of Ni3Al is insensitive to test environment [4]. However, when pre-charged with hydrogen, the ductility and the ultimate tensile strength of borondoped Ni3Al is much decreased, and the fracture mode is changed from ductile transgranular to brittle intergranular, though the yield stress is not aected by hydrogen [15,16]. Furthermore, the hydrogen embrittlement is sensitive to the strain rate, and is less at the higher strain rate [16±18]. On the theoretical side, Sun et al. [19] studied the eects of boron and hydrogen on the atomic bonding when they co-exist in bulk Ni3Al by use of full-potential linear mun-tin orbital (FPLMTO) method. Their calculated results showed that both boron and hydrogen prefer to occupy octahedral interstitial sites that are entirely coordinated by six-nickel atoms. The changes in
0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(99)00143-0
590
F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
the electronic structure and bonding induced by hydrogen are small relative to those induced by boron. Recently, Wang et al. studied the eects of boron [7] and hydrogen [20] on the electronic structure of grain boundaries when they exist alone in Ni3Al by use of discrete variational method (DVM). The calculated results show that both boron and hydrogen atoms prefer to segregate at the grain boundaries, and occupy the Ni-rich interstitial holes in the polycrystalline Ni3Al. Boron enhances the cohesive strength of grain boundary in Ni3Al. However, hydrogen decreases the cohesive strength of Ni3Al grain boundaries. What happens when both boron and hydrogen are present in Ni3Al grain boundaries? Can boron suppress hydrogen embrittlement? To answer these questions, we used DVM [21±26] to study the eects of boron and hydrogen on the electronic structure of grain boundaries in Ni3Al, and the interactions between boron and hydrogen atoms. 2. Computation method and cluster model The DVM, which is a ®rst principles numerical method for solving the local density functional equations [21±26], has been used successfully to study the electronic structure of metals and alloys [25,26]. Recently, it was used successfully to study doping eects on the electronic structure of grain boundaries in Ni3Al [7,20], and to predict the self-diusion mechanisms on metallic FCC{001} surfaces [27]. In this work, the DVM is used to study the interactions between boron and hydrogen atoms when they co-exist in the Ni3Al grain boundary. In order to approach the real grain boundary systems by cluster models, the embedded cluster model [25,26] is used. In constructing the self-consistent potential, the charge density of several hundreds of atoms surrounding the cluster is included. In the calculation, the exchange-correlation potential of Von Barth and Hedin formula [28] is adopted. In order to study the interaction between atoms, the interatomic energy between atoms l and m is derived [29] XX Nn an l an m H m l 1 Elm n
P Fig. 1. The atomic con®gurations around 13[001](320) tilt grain boundaries in Ni3Al. The Ni and Al atoms are represented by the circles and squares, the dierent sizes represent dierent layers, and the atoms shown as large symbols are in the YZ plane. The atoms shown as solid symbols and labeled by numbers are in the cluster, which is embedded by several hundreds of surrounding atoms (labeled by hollow symbols). These crosses labeled with X1 (or X10 ) and X2, X3 represent the possible occupation sites of boron and hydrogen, respectively.
boundary in Ni3Al. Based on our previous works [20], we only choose the cluster, in which the more stable occupation sites for hydrogen and boron are included, as the computational model. In order to discuss the interaction between atoms clearly, the atoms in the cluster are labeled with numbers. The possible occupation sites for boron is labeled by X1 (or X10 ), and that for hydrogen are labeled by X2 and X3. The atomic relaxation at the grain boundary is carried out as in our previous work [7,20]. To discuss the changes of energy for the system induced by the doping of impurities, the impurity formation energies Eimp can be de®ned as Eimp Eb GB impurity ÿ Eb GB
2
where Eb is the binding energy for a system.
where Nn is the occupation number for molecular orbital n , an l is the expanded coecient of n on atomic orbital ' l , and H m l is the Hamiltonian matrix element connecting the atomic orbital of atom m and the atomic orbital of atom l. The grain boundary 13[001](320), which is constructed by use of the coincidence site lattice (CSL) model and atomistic simulations [30], is investigated. Fig. 1 shows the atomic con®guration for 13 grain
3. Results and discussion 3.1. The impurity formation energy In order to get the most stable occupation sites for boron, hydrogen or both of them, we change symmetrically the coordinates of boron and hydrogen and calculate the corresponding formation energies. The formation energies only for several most possible occupation sites labeled by X1 (or X10 ) for boron and X2,
F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
X3 for hydrogen atoms are listed in Table 1. These sites locate in the YZ plane (x 0). X1 locates at the hole of the capped trigonal-prism, which is composed of nos. 2, 3, 21, 4, 5 and 22 with the cap 1, 19 and 20 atoms. The size of this hole is the largest one in the Ni3Al 13 grain boundaries, and boron atom prefers to occupy this interstitial site for its large size. X2 locates near to the middle points between Ni2 and Ni4, Ni3 and Ni5, respectively. X3 locates in the hole of distorted octahedrons, which is composed of nos. 10, 23, 35, 13, 15, 17, and nos. 10, 24, 36, 14, 16, 18 atoms, respectively. X2 and X3 sites are not in the center of these interstitial holes, instead, the hydrogen atom tends to interact strongly with a certain Ni atom [20]. From the calculated impurity formation energy results of boron, the X1 site is not in the center of the interstitial hole too. This behavior of boron was not considered in our previous work [7]. When both of boron and hydrogen atom are present in the Ni3Al 13 grain boundary, and they occupy the separated X1 and X3 sites, respectively [denoted by GB+B(X1)+H(X3)], their position is hardly changed comparing to cases when boron and hydrogen exist alone in the grain boundary [denoted by GB+B(X1) and GB+H(X3), respectively]. At the same time, the impurity formation energy for the system GB+ B(X1)+H(X3) is almost same as the sum of that for the system GB+B(X1) and GB+H(X3). In this case, boron does not interact with hydrogen atoms for their large distance. When boron atom occupies the X10 site and two hydrogen atoms occupy the nearest interstitial X2 site [denoted by GB+B(X10 )+H(X2)], there is a strong repulsive interaction between boron and hydrogen atoms. As a result, the stable position of boron is changed from X1 as in the case of GB+B(X1) to X1' as in the case of GB+B(X10 )+H(X2), at the same time, the position of hydrogen is hardly changed. The displacement of boron is 0.88 AÊ. The nearest neighbor is changed from Ni1 to Ni19 and Ni20. The impurity formation energy is raised 2.9 eV comparing to the systems GB+B(X1) and GB+H(X2) (the sum of the impurity formation energies for boron and hydrogen occupy the X1 and X2 sites alone in the grain boundary). From the energy point of view, boron and hydrogen prefer to
591
occupy the separated interstitial X1 and X3 sites rather than the X10 and X2 sites. Only when there is an external factor such as cathodic charging of hydrogen, it is possible for hydrogen atoms to take the X2 site in the boron-doped Ni3Al grain boundary. The experimental results show that the hydrogen embrittlement of boron-doped Ni3Al is very sensitive to strain rate and it is severer at the lower strain rate [16± 18]. This indicates that the easier for hydrogen transportation to the crack tip, the serverer of hydrogen embrittlement. Grain boundaries are the main passageway for atom diusion. Boron atom is more dicult to diuse than hydrogen atom, because the bonding between boron and its neighbor metal atoms is stronger and its size is larger than that of hydrogen. Our calculated results show that there is a strong repulsive interaction between boron and hydrogen atoms when they approach each other. As a result, the diusion of hydrogen along the grain boundary is blocked by the presence of boron atoms, especially when the concentration of boron is higher. This may be the reason why the sensitivity of ductility to test environment of boron-doped Ni3Al depends on the content of boron. 3.2. Interatomic energy In order to investigate the interaction between adjacent atoms, the interatomic energies de®ned by Eq. (1) are calculated and some main results are listed in Table 2. As references, the results for the case with only one boron atom and only two hydrogen atoms alone in the grain boundary are also listed. Let us pay attention to the cases of both boron and hydrogen atoms present in the grain boundary. First, let us see the case of GB+B(X1)+H(X3). Comparing the interatomic energies of the system GB+B(X1)+H(X3) with that of the system GB+B(X1) and GB+H(X3), it can be found that the bonding states of boron and hydrogen with their neighboring host atoms, and the changes of bonding strength between host metal atoms when both of boron and hydrogen atoms are present in the grain boundary are almost same as that in the case when only boron and only hydrogen alone are present. In the GB+B(X1)+H(X3) system, the action of boron atom
Table 1 The impurity formation energy Eimp (in eV), the nearest neighboring (NN) atoms, and the distance dNN (in AÊ) between boron or hydrogen and its NN atoms, when boron and hydrogen occupies dierent sites in the Ni3Al grain boundary System
GB+B(X1)
GB+H(X2)
GB+B(X10 )+H(X2)
GB+H(X3)
GB+B(X1)+H(X3)
NN(B) dNN (B)
Ni1 1.79
± ±
Ni19,20 2.02
± ±
Ni1 1.79
NN(H) dNN H
± ±
Ni1,11 1.62
Ni11 1.57
Ni23 1.46
Ni23 1.51
Eimp
ÿ9.89
ÿ11.58
ÿ18.57
ÿ11.25
ÿ21.85
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F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
Table 2 The interatomic energy Elm (in eV) for the typical pairs of atoms l and m, when boron and hydrogen occupies the dierent sites in the Ni3Al grain boundarya Pair of atoms lÿm
GB Elm
GB+B(X1) Elm Elm
GB+H(X3) Elm Elm
GB+B(X10 )+H(X2) Elm Elm
GB+H(X3) Elm Elm
GB+B(X1)+H(X3) Elm Elm
Ni1±Ni2 Ni1±Ni11 Ni2±Ni11 Ni15±Ni23 Ni15±Ni35 Ni23±Ni35 H1±Ni1 H1±Ni2 H1±Ni10 H1±Ni11 H1±Ni13 H1±Ni19 H1±Ni23 B±Ni1 B±Ni2 B±Ni19 B±H1
ÿ1.39 ÿ1.66 ÿ1.78 ÿ2.02 ÿ2.35 ÿ1.84
ÿ1.00 ÿ1.66 ÿ1.76 ÿ2.01 ÿ2.33 ÿ1.80
ÿ0.95 ÿ0.78 ÿ1.17 ÿ2.04 ÿ2.34 ÿ1.82 ÿ1.75 ÿ1.27 0.00 ÿ1.83 0.00 ÿ0.87 0.00
ÿ0.95 ÿ0.78 ÿ1.11 ÿ1.99 ÿ2.36 ÿ1.84 ÿ1.67 ÿ1.13 0.00 ÿ2.33 0.00 ÿ0.49 0.00 ÿ0.25 ÿ1.36 ÿ4.10 ÿ0.57
ÿ1.38 ÿ1.64 ÿ1.80 ÿ1.44 ÿ2.16 ÿ1.08 0.00 0.00 ÿ0.34 0.00 ÿ0.67 0.00 ÿ2.60
ÿ0.99 ÿ1.68 ÿ1.70 ÿ1.46 ÿ2.06 ÿ1.02 0.00 0.00 ÿ0.22 0.00 ÿ0.76 0.00 ÿ2.26 ÿ4.30 ÿ2.29 ÿ2.21 0.00
a
ÿ4.48 ÿ2.30 ÿ2.21
0.39 0.00 0.02 0.001 0.02 0.04
0.44 0.88 0.68 ÿ0.02 0.01 0.02
0.44 0.88 0.72 0.03 ÿ0.01 0.00
0.01 0.02 ÿ0.02 0.58 0.19 0.76
0.40 ÿ0.02 0.08 0.56 0.29 0.82
Elm Elm GB impurity ÿ Elm GB (in eV) is the change of interatomic energy induced by the presence of boron and hydrogen.
are almost same as that of boron in the GB+B(X1) system, i.e. the interaction between boron and its neighboring Ni atoms are very strong (boron acts as a ``bridge''), and the bonding between the adjacent host metal atoms are hardly changed; the action of hydrogen atom are almost same as that of hydrogen in the GB+H(X3) system, i.e. hydrogen only interacts strongly with a certain host metal atom, but less with other atoms, and at the same time, the bonding strength between host atoms, which are near to H atoms, are reduced evidently by the presence of hydrogen. As a result, boron enhances but hydrogen weakens the cohesive strength of grain boundary in Ni3Al. (The detailed discussion can be seen in Refs. [7] and [20]). Second, let us see the case of GB+B(X10 )+H(X2). The boron atom is removed from X1 to X10 by the presence of hydrogen atoms in X2 site. The interatomic energy for the pairs of atoms such as B±Ni1, B±Ni2,3,4,5 is raised a lot, so that the bonding strength for boron with these atoms is weakened very much. At the same time, the weakening of the bonds for the pairs of the host metal atoms such as Ni1±Ni2, Ni1±Ni11, and Ni2± Ni11 etc., is even more serious than that of the system with only two hydrogen atoms on the X2 site. As a result, the cohesive strength of grain boundary in boron doped Ni3Al is weakened by the occupation of hydrogen in the nearest interstitial site. That may be the reason why the ultimate tensile strength drops drastically and the fracture mode changes from transgranular to intergranular when boron-doped Ni3Al is cathodic charged with hydrogen [15]. The theoretical results con®rm the suggestion that hydrogen counteract the strengthening eect of boron on grain boundaries and reduces the cohesive strength of the grain boundaries,
which is proposed from TEM experimental results [14]. On the other side, the bonds for B±Ni19,20 is made very strong. So that the bonding states around boron atom are polarized seriously, and the slips may be made dicult to move in the region of grain boundary. This may be another cause of hydrogen embrittlement of borondoped Ni3Al. 4. Conclusion We have studied the eects of both boron and hydrogen on the embrittlement of polycrystalline Ni3Al using ®rst-principles numerical calculations. It is found that there are strong repulsive interaction between the boron and the hydrogen atoms, if they occupy the nearest interstitial sites respectively in the Ni3Al grain boundaries. It indicates that the boron atoms inhibit the diusion of hydrogen atoms along the grain boundary. It may be the main reason why boron can suppress the moisture induced hydrogen embrittlement. Our results also show that boron and hydrogen atoms prefer to occupy the interstitial sites, which are not near to each other. In this case, the boron enhances locally the cohesive strength of the grain boundary, but the hydrogen weakens it locally and counteracts the strengthening eect of boron on the grain boundary. When hydrogen atoms are forced into the grain boundary and occupy the nearest interstitial sites to boron atoms, the boron atoms will be displaced a short distance away from the hydrogen atoms. As a result, the ``bridge'' eects of boron are removed, and the bonding states are polarized in the local region of the grain boundary. It may suppress the movement of slips across the grain boundary.
F.-H. Wang et al. / Intermetallics 8 (2000) 589±593
Furthermore, the weakening eects of hydrogen to the grain boundary are hardly aected by the boron atoms, even though they are very near to each other. It can be concluded that hydrogen embrittlement takes place when the boron-doped polycrystalline Ni3Al are charged with hydrogen. Acknowledgements This work was supported by the National Natural Science Foundation of China and Ministry of Science and Technology of China. References [1] Aoki K, Izumi O. J Japan Inst Metals 1979;43:1190. [2] Liu CT, White CL, Horton JA. Acta Metall 1985;33:213. [3] Schulson EM, Weihs TP, Baker I, Frost HJ, Horton JA. Acta Metall 1986;34:1395. [4] Wan XJ, Zhu JH, Jing KL. Scr Metall 1992;26:473; Scr Metall 1992;26:479. [5] Takasugi T, Izumi O, Masahashi N. Acta Metall 1985;33:1259. [6] White CL, Padgett PA, Liu CT, Yalisov SM. Scrip Metall 1985;18:1417. [7] Wang F-H, Wang C-Y, Yang J-L. J Phys: Condens Matt 1996;8:5527.
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