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Molecular dynamics simulation of Surface-Adsorbed-Hydrogen-Induced Dislocation Motion in a thin film
Computational Materials Science 171 (2020) 109240
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics simulation of Surface-Adsorbed-Hydrogen-Induced Dislocation Motion in a thin film
T
Ryosuke Matsumotoa,c, , Shinya Taketomib ⁎
a
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Room a2S03, Building C3, Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8246, Japan b Department of Mechanical Engineering, Graduate School of Science and Engineering, Saga University, 1 Honjo-machi, Saga 840-8502, Japan c Nagamori Institute of Actuators, Kyoto University of Advanced Science, 18, Yamanouchi-Gotandacho, Ukyo-ku, Kyoto 615-8577, Japan
ARTICLE INFO
ABSTRACT
Keywords: Hydrogen embrittlement Molecular dynamics (MD) Transmission electron microscopy (TEM) Dislocation mobility Surface effect
Elucidating the effects of hydrogen on dislocation activities is important for revealing hydrogen embrittlement mechanisms. In situ transmission electron microscopy observations have shown that dislocation motion is enhanced or activated when hydrogen gas is introduced into the sample chamber, supporting the hydrogen-enhanced localized-plasticity mechanism. However, adsorbed hydrogen atoms affect dislocation activities in thin films. Here we analyzed the effects of hydrogen and sample thickness on the motion of screw dislocations through molecular dynamics simulations. The surface effect becomes significant with decreasing sample thickness, and the change in surface energy upon hydrogen adsorption induces motion of screw dislocations in ultrathin films.
1. Introduction The strength degradation of metals in hydrogen environments, known as hydrogen embrittlement (HE), has been well known for more than 100 years [1]. Because mechanical properties and dislocation mobility are closely related, various studies to clarify the effects of hydrogen on dislocation mobility have been conducted continuously. Beachem originally reported material softening by hydrogen and pointed out that the origin of HE is microscopic ductile fracture [2]. Matsui et al. reported the softening of highly purified iron during electrical hydrogen-charging at room temperature [3]. These two studies addressed macroscopic phenomena. To elucidate the microscopic effect of hydrogen, other researchers used in situ transmission electron microscopy (TEM) to observe small groups of dislocations [4–6]. These observations revealed that dislocation configurations are substantially altered by hydrogen injection into the sample chamber, and solute hydrogen has been speculated to enhance dislocation motion. This phenomenon has been reported for edge, screw, and mixed dislocations in various metals, including body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures. Furthermore, it was clarified that the origin of this phenomenon is not the pressure from hydrogen gas because it was observed only when hydrogen was introduced into the chamber. These results strongly support the hydrogen-enhanced localized-plasticity mechanism.
⁎
Sofronis et al. used finite-element-method simulations to show that solute-hydrogen atoms around dislocations reduce the dislocation interaction [7]. However, some researchers have argued that this effect does not appear under practical hydrogen concentrations in metals with typical hydrogen solubility [8,9]. The diffusion coefficient of hydrogen in most FCC and HCP metals is not as high as that in BCC metals; thus, hydrogen migration to a dislocation core requires considerable time. On the contrary, in the aforementioned in situ TEM observations, dislocation motion was observed for various metals immediately after hydrogen was introduced into the chamber. For example, the diffusion coefficient of hydrogen in SUS304 is quite low as 1.8 × 10−16 m2/s at x2 room temperature [10]. Thus, it takes td = 2D 28[s] for solute hydrogen to diffuse 100 nm. Furthermore, the time to overcome the surface potential (≈1 eV) is necessary for adsorbed hydrogen atom on the surface to penetrate into lattice. Of course, the solute hydrogen near surface may change the mobility of dislocation. But, in some metals such as Al, the hydrogen solubility is very low and hydrogen atoms are not trapped by dislocations even in equilibrium [11,12]. Numerous studies have reported hydrogen-induced hardening of metals, i.e., an increase of the yield stress and strain-hardening coefficient [13–15]. Furthermore, recent atomistic simulations of interactions between dislocations and solute-hydrogen atoms have shown that a decrease in dislocation mobility occurs [9] or that either a decrease or increase occurs depending on the deformation conditions [16,17]. For
Corresponding author. E-mail addresses: [email protected], [email protected] (R. Matsumoto), [email protected] (S. Taketomi).
https://doi.org/10.1016/j.commatsci.2019.109240 Received 20 May 2019; Received in revised form 26 August 2019; Accepted 28 August 2019 Available online 03 September 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 171 (2020) 109240
R. Matsumoto and S. Taketomi
Fe-H system, we reported that hydrogen reduces edge-dislocation mobility at wide conditions except very weak hydrogen environment and low applied stress [16,18]. The TEM experiment for pure iron may correspond to the enhancement condition of dislocation motion (low hydrogen concentration and low applied stress). On the other hand, for Al-H system, we concluded that the hydrogen concentration around dislocation is too low to affect the dislocation mobility [11,19], and thus another mechanism is sought to explain the TEM experiments where the dislocation migration by hydrogen is observed for various material systems such as steels and aluminum alloys. Because many hydrogen atoms are strongly adsorbed onto the free surfaces of various metals, unlike the atoms of an inactive gas [20], the hydrogen atoms might affect the mobility and stable configuration of dislocations in a thin film, where surface effects become strong. Here, we analyze the influence of adsorbed hydrogen atoms on the dislocation configuration by molecular dynamics (MD) simulations and clearly show that the surface energy change caused by the hydrogen adsorption induces dislocation motion in thin films.
migrated, especially for the thinnest specimens. Through these structure relaxations, hydrogen atoms initially artificially adsorbed onto surfaces distributed depending on their interaction energy with different surfaces. We confirmed that no hydrogen atoms existed in interstitial sites or dislocation cores; i.e., all hydrogen atoms existed on the surfaces. The surface coverage of hydrogen on the {1 1 1} surface (θ: the fraction of total hydrogen atoms on the {1 1 1} surface relative to the total number of iron atom in the outermost {1 1 1} surfaces) for two hydrogen-adsorbed models after relaxation were θ = 0.78 and θ = 1.11. It is well known that θ > 1 is realized for iron in a wide range of hydrogen gas environments [22,23]. Hydrogen fugacity is expected to be very high during in situ TEM experiments because of the effect of the electron beam. Thus, it is considered that these values are realized in various metals and alloys. Although the steady velocity of edge dislocation can be easily evaluated by applying PBC along the gliding direction, this is not applicable for the screw dislocation because the slip plane is not determined by cross-slip mechanisms. Herein, we estimate the varying velocity under increasing or decreasing stress without PBCs. We believe that the influence on the screw dislocation motion is considerably small for quantitative analysis of the surface effects that could be significant. Thus, deformation was induced by increasing or decreasing the shear stress (τzy) by 20 MPa every 100 ps at 300 K. To apply a shear stress on the screw dislocation under reduced artificial effect of fixed boundaries and preventing the translation and rotation of the specimen, we employed the following boundary conditions: During the loading simulation, the motion along the z-axis was constrained for all the boundary atoms; also, the total angular momentum around the z-axis of all the boundary atoms as well as the total momentum along the y-axis of all the boundary atoms in the lower region were kept at zero. Furthermore, an additional force along the y-axis, corresponding to the intended shear stress, was added to the boundary atoms in the top region. It was confirmed that all hydrogen atoms exist on the surfaces, not along dislocation core. We used the Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS) in our study [24,25].
2. Analytical We used the Fe–H system described by embedded atom method potential, as developed by Ramasubramanian et al. (parameter set B) [21]. The dislocation motion is strongly influenced by the interatomic potentials. Herein, we focused on the general effect of the surface step on the screw dislocation motion in a thin film and not for particular metal systems because dislocation migration by hydrogen has been observed for various metals and alloys by in situ TEM. We defined the x, y, and z axes along [1¯10], [1¯1¯1], and [112], respectively. The model size was w = 22.8 nm and h = 5.5 nm parallel to the x and z axes, respectively. Eight specimens with different lengths parallel to the y-axis (=l) from 1.2 nm to 10.1 nm were constructed (13,680–112,176 atoms). Periodic boundary conditions (PBCs) were not applied for any direction to analyze the motion of isolated one screw dislocation in thin films. We constructed two hydrogen-adsorbed models for a specimen with l = 3.7 nm and with different coverage by placing hydrogen atoms on free surfaces ((Fe, H) = (41,040, 1,824), (41,040, 3,504) atoms). A screw dislocation (b = 〈1 1 1〉/2) along the y-axis on the xy plane was introduced at the center of the specimens by displacing each atom a distance corresponding to the linear elastic solution for an isotropic material. Herein, we choose the (1 1 2) plane as the initial slip plane; it will be the maximum-resolved shear stress plane in the following loading simulations (instead of the {1 1 0} plane) to highlight the surface-step effects. The motion of all the Fe atoms within 0.2 nm from both surfaces (herein referred to as boundary atoms) along the z-axis was fully constrained during structural relaxation. First, structural relaxation was performed using the conjugate gradient method. After the screw dislocation was introduced, a step with width b was generated along the x-axis from the dislocation core on both free surfaces parallel to the zx plane (see Fig. 1). Then, structural relaxation was performed at 300 K for each specimen. This relaxation was conducted for a maximum of 140 ps and the duration was shortened when the dislocation
3. Results 3.1. Dislocation motion under no-load The total surface energy of the specimen decreased with decreasing length of the surface steps. Thus, the dislocation tended to migrate toward the positive x-axis direction to eliminate the surface steps even under no load. Fig. 2 shows the relationship between the dislocation velocity V along x-axis and the thickness parallel to the y-axis l for the case without hydrogen (θ = 0). The dislocation velocity was calculated from the position of the dislocation from t = 50 ps to 3.2 ns or time when the dislocation reaches 3 nm to right side surface. The results confirmed that the dislocation migrated on (1 1 2) plane toward the positive x-axis direction and that the velocity slowed with increasing thickness.
Fig. 1. Simulation model: the figure shows the central plane parallel to the zx plane. 2
Computational Materials Science 171 (2020) 109240
R. Matsumoto and S. Taketomi
Fig. 4. Influence of adsorbed hydrogen on the dislocation velocity.
Fig. 2. Relationship between specimen thickness and dislocation velocity.
the dislocation initially migrates in the positive x-axis direction by tracing the surface steps at a small load in the absence of hydrogen. As the applied load increases (a larger negative shear stress is applied), the dislocation motion suspends, then begins to move in the negative x-axis direction, and finally migrates to the bottom surface by causing crossslips. On the other hand, as shown in Fig. 3(b) (ii) and (iii), the dislocation does not move in the positive x-axis direction at small negative loads and the cross-slips occur earlier at higher hydrogen coverage. We believe that the asymmetry of the boundary conditions, that is, the
3.2. Dislocation motion under shear stress Fig. 3 shows the time evolution of the dislocation-core position at every 2 ps under positive and negative shear stress for l = 3.7 nm at different hydrogen coverages. Fig. 3 (a) shows the dislocation position until 100 MPa because the image force from the surfaces becomes considerable at higher stress. It is obvious that the migration distance decreases as the hydrogen coverage increases. As shown in Fig. 3(b) (i),
Fig. 3. Effect of adsorbed hydrogen on the time evolution of the dislocation-core position for l = 3.7 nm. 3
Computational Materials Science 171 (2020) 109240
R. Matsumoto and S. Taketomi
stepwise increase in external force applied on the boundary atoms in the top region, is the reason why the dislocation migrates to the bottom surface in the three cases. Fig. 4 shows the relationship between dislocation velocity along xaxis and applied shear stress τzy for l = 3.7 nm at different hydrogen coverages. The dislocation velocities at no load were obtained by the same evaluation procedure as that used in Fig. 2, and the velocities under stress were obtained from Fig. 3. Since the dislocation velocities fluctuate, we calculated the average velocity during a 100 MPa increase or decrease. In the figure, the points where the slip plane clearly changes are indicated by arrows. After the cross-slip, the applied stress and dislocation velocity are not estimated correctly because the velocity is calculated from the displacement parallel to the x-axis and the resolved shear stress decreases. The dislocation velocity differs substantially depending on the sign of the applied shear stress; i.e., the dislocation motion with relation to the applied stress is anisotropic. Furthermore, with increasing hydrogen coverage, the dislocation mobility increases when negative shear stress is loaded and the dislocation mobility decreases when positive shear stress is loaded; i.e., the anisotropy of the dislocation motion becomes weak.
(∼Δa per 100 ps). Hydrogen atoms adsorbed on the flat surfaces swiftly migrate toward newly generated trap sites on the surface steps when they are extended, or the hydrogen atoms on the surface steps are driven out toward the flat surfaces when surface steps are shortened. The hydrogen occupancy on the surface steps becomes higher at higher hydrogen coverage. Because of the energy reduction that accompanies this configuration change, the apparent surface-step energy is considered to become small with increasing hydrogen coverage; thus, the anisotropy of dislocation motion becomes weak, as described in Fig. 4. As shown in Figs. 3(b) and 4, the cross-slips occurred earlier at higher hydrogen coverages under negative shear stress. This is also qualitatively explained from the reduction in apparent surface-step energy. If the surface-step is generated due to the screw dislocation motion, an extra energy is necessary as already mentioned. The extra energy is expressed by the product of extended length and surface-step energy. Thus, despite the difficulties to glide, a shorter migration distance is preferred at higher surface-step energies; i.e. the dislocation glide on (1 1 2) plane which is parallel to xy plane is preferred at a lower hydrogen coverage. On the other hand, easy-gliding planes which need longer migration distance (because the planes are inclined from xy plane) are easily selected owing to the reduced surface-step energies by hydrogen at a higher hydrogen coverage. When the second and third terms are balanced, the dislocation motion suspends except for thermal diffusion. This condition is expressed as
4. Discussions 4.1. Energetics of straight screw-dislocation motion in thin film Dislocations migrate by crossing a potential barrier that exists periodically in the lattice. A dislocation in the bulk thermally migrates along opposite glide directions with the same frequency as in the stressfree case. However, if a difference exists in the potential barrier along opposite directions, the frequency with which dislocations pass across the lower potential barrier increases compared with the frequency with which dislocations pass the opposite direction; thus, the dislocation migrates one direction on average. Here, we roughly estimated the potential energy change caused by dislocation migration parallel to the x-axis in Fig. 1. The energy change ΔE caused by the quasi-static motion of screw dislocation Δa/2 (onehalf of the periodicity of the potential barrier) under shear stress τzy is expressed by the equation
E = l × EPeierls
zy l
a ×b 2
a × Estep
zy-eq
=
2Estep
(2)
bl −11
where Estep is evaluated to be 6.89 × 10 J/m for the present system. To evaluate Estep, relaxation at 300 K, followed by energy minimization at 0 K, was performed because a structure reconstruction occurs in the vicinity of the surface steps. When b = 0.247 nm and l = 3.7 nm are used, τzy-eq ≈ −151 MPa is obtained. From Fig. 4, the dislocation motion suspends at approximately −150 to −200 MPa for θ = 0; these values agree well with each other. 4.3. Adsorbed-hydrogen effect on dislocation motion in TEM experiment The dimensions of a specimen that can be directly treated by MD simulation are small even by comparison with the sample used for TEM observations. Furthermore, directly treating the dissociation of hydrogen molecules and the adsorption of hydrogen atoms onto the surface steps generated by dislocation migration is also difficult because the activation energy of the dissociation is too large for MD simulations. Hereafter, we discuss the motion of a screw dislocation in a thicker specimen in a hydrogen gas environment by using Eq. (2), the validity of which was established in the previous discussion. When the motion of a screw dislocation whose end terminates at a free surface is suspended under in situ TEM observation, which is carried out with an ultrathin specimen, internal stress is assumed to exist and the stress is assumed to balance the surface effect (the third term on the right-hand side of Eq. (1)). If we assume that l = 100 nm, which is the typical specimen thickness used for TEM observations, we obtain τzy-eq = −5.6 MPa as the equilibrium stress for the hydrogen-free condition. Here, the apparent step energy is approximately estimated to be half under the assumptions that hydrogen molecules dissociate and hydrogen atoms fully adsorb onto the newly formed steps [23]; we also obtain τzy-eq = −2.8 MPa for the scenario of a gaseous hydrogen environment. This result means that the introduction of hydrogen gas induces dislocation motion equivalent to the application of τzy = 2.8 MPa. The assumption that the dislocation keeps a straight shape is not maintained as the thickness of the specimen increases. Especially, kinks will preferably form at the surface, and dislocation segments near the surface drag the dislocation line inside the material. Although Eq. (1) will be invalid in this case, the effect of the adsorbed hydrogen is still present and the above calculation will be an
(1)
where EPeierls is the Peierls potential, l is the dislocation length (thickness of the specimen), and Estep is the energy of the surface step of unit length. We assumed that the dislocation maintains a straight shape during the migration. The first term on the right-hand side of Eq. (1) represents the contribution from the Peierls potential, and the second term represents the contribution from applied stress which is expressed by the combination of external force (τzylw) and boundary displacement (Δa/2w × b). The third term is the surface-effect term, which represents the energy change caused by the change in length of surface steps accompanied by the migration of the screw dislocation. This term is the origin of the anisotropy of the dislocation motion. 4.2. Comparison with MD results In the case of τzy = 0, ΔE decreases when the dislocation moves toward the positive direction (Δa > 0) because of the contribution of Estep. As thickness l decreases, the contribution of the first term becomes small; thus, the velocity of the dislocation increases. Actually, the dislocation is expected to migrate toward the positive x-axis direction without thermal activation when l < (Δa × Estep/EPeierls). These consequences qualitatively agree well with the simulation results described in Fig. 2. Furthermore, the difference in ΔE along opposite directions becomes small as Estep decreases. Hydrogen diffusion on the surfaces is much faster than the dislocation motion observed in the present work 4
Computational Materials Science 171 (2020) 109240
R. Matsumoto and S. Taketomi
underestimation because the dislocation can move without overcoming the Peierls potential of the whole dislocation line at the same time. The dislocation velocity estimated from TEM observations is very slow: on the order of micrometers per second [4]. Thus, the shear stress that arises from hydrogen adsorption can induce such dislocation motion in a real TEM specimen. We speculate that the edge dislocation also migrates, influenced by the configuration change of a screw component that ends at a free surface, because the assumption that all dislocations terminate at a free surface end with a pure edge component is unreasonable. According to A. Tehranchi [26], although the separation distance between dislocations is reduced upon introduction of hydrogen in the TEM observations, the pile-ups returned to their original structure upon removal of the hydrogen. If the enhancement of dislocation mobility (reduction of Peierls potential) is caused by solute hydrogen, the dislocations migrated along shear stress and stress is relaxed. After removal of hydrogen, the dislocations with original mobility cannot return to initial structure. The configuration change of dislocations caused by absorbed hydrogen which was proposed in this paper can clearly explain the dislocation motion and return to the original position upon H introduction (absorption) and removal (desorption). This Surface-Adsorbed-Hydrogen-Induced Dislocation Motion mechanism can operate even for materials with low hydrogen solubility and diffusivity.
Funding
5. Conclusions
[12] [13] [14] [15]
This work was supported by JSPS KAKENHI, Japan [Grant Numbers 23686022, 16K05976, 16H06062]. CRediT authorship contribution statement Ryosuke Matsumoto: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Visualization, Supervision, Project administration, Funding acquisition. Shinya Taketomi: Software, Validation, Resources, Data curation, Writing - review & editing, Visualization, Funding acquisition. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
In this study, we analyzed the effects of hydrogen and sample thickness on the motion of a screw dislocation using MD simulations. The results revealed that the influence of surface steps, which are extended or shortened by the screw dislocation, on the screw dislocation motion increases with decreasing specimen thickness. Furthermore, we clarified that the hydrogen weakens the influence of the surface steps by reducing their apparent energy. Finally, we showed that the shear stress that arises from hydrogen adsorption can potentially induce screw dislocation motion in a real TEM specimen. Although in situ TEM observations provide valuable information, consideration of the surface effects on dislocation motion is essential not only for hydrogen-related phenomena but also for the fracture and deformation of nanosized structures.
[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
5
W.H. Johnson, Proc. R. Soc. London 23 (1875) 168. C.D. Beachem, Metall. Trans. 3 (1972) 441. H. Matsui, H. Kimura, A. Kimura, Mater. Sci. Eng. 40 (1976) 207–216. T. Tabata, H.K. Birnbaum, Scr. Metall. 17 (1983) 947–950. P.J. Ferreira, I.M. Robertson, H.K. Birnbaum, Acta Mater. 46 (1998) 1749–1757. I.M. Robertson, Eng. Fract. Mech. 68 (2001) 671–692. P. Sofronis, H.K. Birnbaum, Mech. J. Mech. Phys. Solids 43 (1995) 49–90. S. Taketomi, R. Matsumoto, N. Miyazaki, J. Mater. Sci. 43 (2008) 1166–1169. J. Song, W.A. Curtin, Acta Mater. 68 (2014) 61–69. S. Sakamoto, H. Katayama, J. Jpn. Inst. Met. 46 (1982) 805–814. T. Enomoto, R. Matumoto, S. Taketomi, N. Miyazaki, J. Soc. Mater. Sci. Japan 59 (2010) 596–603. R. Matsumoto, M. Sera, N. Miyazaki, Comput. Mater. Sci. 91 (2017) 211–222. P. Bastien, P. Azou, Compt. Rend. 232 (1951) 69–71. S. Asano, R. Otsuka, Scr. Metall. 10 (1976) 1015–1020. H. Kamei, Y. Matsumoto, H. Suzuki, K. Takai, IOP Conf Ser. Mater. Sci. Eng. 461 (2019) 012034. S. Taketomi, R. Matsumoto, N. Miyazaki, J. Mater. Res. 26 (2011) 1269–1278. M. Itakura, H. Kabutaki, M. Yamaguchi, T. Okita, Acta Mater. 61 (2013) 6857–6867. S. Taketomi, R. Matsumoto, S. Hagihara, ISIJ Int. 57 (2017) 2058–2064. R. Matsumoto, T. Enomoto, S. Taketomi, N. Miyazaki, Effects of Hydrogen on Materials, ASME Press, 2014, pp. 757–763. F. Bozso, G. Ertl, M. Grunze, M. Weiss, Appl. Surf. Sci. 1 (1977) 103–119. A. Ramasubramaniam, M. Itakura, E.A. Carter, Phys. Rev. B 79 (2009) 174101. M. Yamaguchi, J. Kameda, K. Ebihara, M. Itakura, H. Kaburaki, Philos. Mag. 92 (2012) 1349–1368. R. Matsumoto, S. Seki, S. Taketomi, N. Miyazaki, Comp. Mater. Sci. 92 (2014) 362–371. http://lammps.sandia.gov. S. Plimpton, J. Comp. Phys. 117 (1995) 1–19. A. Tehranchi, W.A. Curtin, Eng. Frac. Mech. 216 (2019) 106502.
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics simulation of Surface-Adsorbed-Hydrogen-Induced Dislocation Motion in a thin film
T
Ryosuke Matsumotoa,c, , Shinya Taketomib ⁎
a
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Room a2S03, Building C3, Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8246, Japan b Department of Mechanical Engineering, Graduate School of Science and Engineering, Saga University, 1 Honjo-machi, Saga 840-8502, Japan c Nagamori Institute of Actuators, Kyoto University of Advanced Science, 18, Yamanouchi-Gotandacho, Ukyo-ku, Kyoto 615-8577, Japan
ARTICLE INFO
ABSTRACT
Keywords: Hydrogen embrittlement Molecular dynamics (MD) Transmission electron microscopy (TEM) Dislocation mobility Surface effect
Elucidating the effects of hydrogen on dislocation activities is important for revealing hydrogen embrittlement mechanisms. In situ transmission electron microscopy observations have shown that dislocation motion is enhanced or activated when hydrogen gas is introduced into the sample chamber, supporting the hydrogen-enhanced localized-plasticity mechanism. However, adsorbed hydrogen atoms affect dislocation activities in thin films. Here we analyzed the effects of hydrogen and sample thickness on the motion of screw dislocations through molecular dynamics simulations. The surface effect becomes significant with decreasing sample thickness, and the change in surface energy upon hydrogen adsorption induces motion of screw dislocations in ultrathin films.
1. Introduction The strength degradation of metals in hydrogen environments, known as hydrogen embrittlement (HE), has been well known for more than 100 years [1]. Because mechanical properties and dislocation mobility are closely related, various studies to clarify the effects of hydrogen on dislocation mobility have been conducted continuously. Beachem originally reported material softening by hydrogen and pointed out that the origin of HE is microscopic ductile fracture [2]. Matsui et al. reported the softening of highly purified iron during electrical hydrogen-charging at room temperature [3]. These two studies addressed macroscopic phenomena. To elucidate the microscopic effect of hydrogen, other researchers used in situ transmission electron microscopy (TEM) to observe small groups of dislocations [4–6]. These observations revealed that dislocation configurations are substantially altered by hydrogen injection into the sample chamber, and solute hydrogen has been speculated to enhance dislocation motion. This phenomenon has been reported for edge, screw, and mixed dislocations in various metals, including body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures. Furthermore, it was clarified that the origin of this phenomenon is not the pressure from hydrogen gas because it was observed only when hydrogen was introduced into the chamber. These results strongly support the hydrogen-enhanced localized-plasticity mechanism.
⁎
Sofronis et al. used finite-element-method simulations to show that solute-hydrogen atoms around dislocations reduce the dislocation interaction [7]. However, some researchers have argued that this effect does not appear under practical hydrogen concentrations in metals with typical hydrogen solubility [8,9]. The diffusion coefficient of hydrogen in most FCC and HCP metals is not as high as that in BCC metals; thus, hydrogen migration to a dislocation core requires considerable time. On the contrary, in the aforementioned in situ TEM observations, dislocation motion was observed for various metals immediately after hydrogen was introduced into the chamber. For example, the diffusion coefficient of hydrogen in SUS304 is quite low as 1.8 × 10−16 m2/s at x2 room temperature [10]. Thus, it takes td = 2D 28[s] for solute hydrogen to diffuse 100 nm. Furthermore, the time to overcome the surface potential (≈1 eV) is necessary for adsorbed hydrogen atom on the surface to penetrate into lattice. Of course, the solute hydrogen near surface may change the mobility of dislocation. But, in some metals such as Al, the hydrogen solubility is very low and hydrogen atoms are not trapped by dislocations even in equilibrium [11,12]. Numerous studies have reported hydrogen-induced hardening of metals, i.e., an increase of the yield stress and strain-hardening coefficient [13–15]. Furthermore, recent atomistic simulations of interactions between dislocations and solute-hydrogen atoms have shown that a decrease in dislocation mobility occurs [9] or that either a decrease or increase occurs depending on the deformation conditions [16,17]. For
Corresponding author. E-mail addresses: [email protected], [email protected] (R. Matsumoto), [email protected] (S. Taketomi).
https://doi.org/10.1016/j.commatsci.2019.109240 Received 20 May 2019; Received in revised form 26 August 2019; Accepted 28 August 2019 Available online 03 September 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 171 (2020) 109240
R. Matsumoto and S. Taketomi
Fe-H system, we reported that hydrogen reduces edge-dislocation mobility at wide conditions except very weak hydrogen environment and low applied stress [16,18]. The TEM experiment for pure iron may correspond to the enhancement condition of dislocation motion (low hydrogen concentration and low applied stress). On the other hand, for Al-H system, we concluded that the hydrogen concentration around dislocation is too low to affect the dislocation mobility [11,19], and thus another mechanism is sought to explain the TEM experiments where the dislocation migration by hydrogen is observed for various material systems such as steels and aluminum alloys. Because many hydrogen atoms are strongly adsorbed onto the free surfaces of various metals, unlike the atoms of an inactive gas [20], the hydrogen atoms might affect the mobility and stable configuration of dislocations in a thin film, where surface effects become strong. Here, we analyze the influence of adsorbed hydrogen atoms on the dislocation configuration by molecular dynamics (MD) simulations and clearly show that the surface energy change caused by the hydrogen adsorption induces dislocation motion in thin films.
migrated, especially for the thinnest specimens. Through these structure relaxations, hydrogen atoms initially artificially adsorbed onto surfaces distributed depending on their interaction energy with different surfaces. We confirmed that no hydrogen atoms existed in interstitial sites or dislocation cores; i.e., all hydrogen atoms existed on the surfaces. The surface coverage of hydrogen on the {1 1 1} surface (θ: the fraction of total hydrogen atoms on the {1 1 1} surface relative to the total number of iron atom in the outermost {1 1 1} surfaces) for two hydrogen-adsorbed models after relaxation were θ = 0.78 and θ = 1.11. It is well known that θ > 1 is realized for iron in a wide range of hydrogen gas environments [22,23]. Hydrogen fugacity is expected to be very high during in situ TEM experiments because of the effect of the electron beam. Thus, it is considered that these values are realized in various metals and alloys. Although the steady velocity of edge dislocation can be easily evaluated by applying PBC along the gliding direction, this is not applicable for the screw dislocation because the slip plane is not determined by cross-slip mechanisms. Herein, we estimate the varying velocity under increasing or decreasing stress without PBCs. We believe that the influence on the screw dislocation motion is considerably small for quantitative analysis of the surface effects that could be significant. Thus, deformation was induced by increasing or decreasing the shear stress (τzy) by 20 MPa every 100 ps at 300 K. To apply a shear stress on the screw dislocation under reduced artificial effect of fixed boundaries and preventing the translation and rotation of the specimen, we employed the following boundary conditions: During the loading simulation, the motion along the z-axis was constrained for all the boundary atoms; also, the total angular momentum around the z-axis of all the boundary atoms as well as the total momentum along the y-axis of all the boundary atoms in the lower region were kept at zero. Furthermore, an additional force along the y-axis, corresponding to the intended shear stress, was added to the boundary atoms in the top region. It was confirmed that all hydrogen atoms exist on the surfaces, not along dislocation core. We used the Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS) in our study [24,25].
2. Analytical We used the Fe–H system described by embedded atom method potential, as developed by Ramasubramanian et al. (parameter set B) [21]. The dislocation motion is strongly influenced by the interatomic potentials. Herein, we focused on the general effect of the surface step on the screw dislocation motion in a thin film and not for particular metal systems because dislocation migration by hydrogen has been observed for various metals and alloys by in situ TEM. We defined the x, y, and z axes along [1¯10], [1¯1¯1], and [112], respectively. The model size was w = 22.8 nm and h = 5.5 nm parallel to the x and z axes, respectively. Eight specimens with different lengths parallel to the y-axis (=l) from 1.2 nm to 10.1 nm were constructed (13,680–112,176 atoms). Periodic boundary conditions (PBCs) were not applied for any direction to analyze the motion of isolated one screw dislocation in thin films. We constructed two hydrogen-adsorbed models for a specimen with l = 3.7 nm and with different coverage by placing hydrogen atoms on free surfaces ((Fe, H) = (41,040, 1,824), (41,040, 3,504) atoms). A screw dislocation (b = 〈1 1 1〉/2) along the y-axis on the xy plane was introduced at the center of the specimens by displacing each atom a distance corresponding to the linear elastic solution for an isotropic material. Herein, we choose the (1 1 2) plane as the initial slip plane; it will be the maximum-resolved shear stress plane in the following loading simulations (instead of the {1 1 0} plane) to highlight the surface-step effects. The motion of all the Fe atoms within 0.2 nm from both surfaces (herein referred to as boundary atoms) along the z-axis was fully constrained during structural relaxation. First, structural relaxation was performed using the conjugate gradient method. After the screw dislocation was introduced, a step with width b was generated along the x-axis from the dislocation core on both free surfaces parallel to the zx plane (see Fig. 1). Then, structural relaxation was performed at 300 K for each specimen. This relaxation was conducted for a maximum of 140 ps and the duration was shortened when the dislocation
3. Results 3.1. Dislocation motion under no-load The total surface energy of the specimen decreased with decreasing length of the surface steps. Thus, the dislocation tended to migrate toward the positive x-axis direction to eliminate the surface steps even under no load. Fig. 2 shows the relationship between the dislocation velocity V along x-axis and the thickness parallel to the y-axis l for the case without hydrogen (θ = 0). The dislocation velocity was calculated from the position of the dislocation from t = 50 ps to 3.2 ns or time when the dislocation reaches 3 nm to right side surface. The results confirmed that the dislocation migrated on (1 1 2) plane toward the positive x-axis direction and that the velocity slowed with increasing thickness.
Fig. 1. Simulation model: the figure shows the central plane parallel to the zx plane. 2
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Fig. 4. Influence of adsorbed hydrogen on the dislocation velocity.
Fig. 2. Relationship between specimen thickness and dislocation velocity.
the dislocation initially migrates in the positive x-axis direction by tracing the surface steps at a small load in the absence of hydrogen. As the applied load increases (a larger negative shear stress is applied), the dislocation motion suspends, then begins to move in the negative x-axis direction, and finally migrates to the bottom surface by causing crossslips. On the other hand, as shown in Fig. 3(b) (ii) and (iii), the dislocation does not move in the positive x-axis direction at small negative loads and the cross-slips occur earlier at higher hydrogen coverage. We believe that the asymmetry of the boundary conditions, that is, the
3.2. Dislocation motion under shear stress Fig. 3 shows the time evolution of the dislocation-core position at every 2 ps under positive and negative shear stress for l = 3.7 nm at different hydrogen coverages. Fig. 3 (a) shows the dislocation position until 100 MPa because the image force from the surfaces becomes considerable at higher stress. It is obvious that the migration distance decreases as the hydrogen coverage increases. As shown in Fig. 3(b) (i),
Fig. 3. Effect of adsorbed hydrogen on the time evolution of the dislocation-core position for l = 3.7 nm. 3
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stepwise increase in external force applied on the boundary atoms in the top region, is the reason why the dislocation migrates to the bottom surface in the three cases. Fig. 4 shows the relationship between dislocation velocity along xaxis and applied shear stress τzy for l = 3.7 nm at different hydrogen coverages. The dislocation velocities at no load were obtained by the same evaluation procedure as that used in Fig. 2, and the velocities under stress were obtained from Fig. 3. Since the dislocation velocities fluctuate, we calculated the average velocity during a 100 MPa increase or decrease. In the figure, the points where the slip plane clearly changes are indicated by arrows. After the cross-slip, the applied stress and dislocation velocity are not estimated correctly because the velocity is calculated from the displacement parallel to the x-axis and the resolved shear stress decreases. The dislocation velocity differs substantially depending on the sign of the applied shear stress; i.e., the dislocation motion with relation to the applied stress is anisotropic. Furthermore, with increasing hydrogen coverage, the dislocation mobility increases when negative shear stress is loaded and the dislocation mobility decreases when positive shear stress is loaded; i.e., the anisotropy of the dislocation motion becomes weak.
(∼Δa per 100 ps). Hydrogen atoms adsorbed on the flat surfaces swiftly migrate toward newly generated trap sites on the surface steps when they are extended, or the hydrogen atoms on the surface steps are driven out toward the flat surfaces when surface steps are shortened. The hydrogen occupancy on the surface steps becomes higher at higher hydrogen coverage. Because of the energy reduction that accompanies this configuration change, the apparent surface-step energy is considered to become small with increasing hydrogen coverage; thus, the anisotropy of dislocation motion becomes weak, as described in Fig. 4. As shown in Figs. 3(b) and 4, the cross-slips occurred earlier at higher hydrogen coverages under negative shear stress. This is also qualitatively explained from the reduction in apparent surface-step energy. If the surface-step is generated due to the screw dislocation motion, an extra energy is necessary as already mentioned. The extra energy is expressed by the product of extended length and surface-step energy. Thus, despite the difficulties to glide, a shorter migration distance is preferred at higher surface-step energies; i.e. the dislocation glide on (1 1 2) plane which is parallel to xy plane is preferred at a lower hydrogen coverage. On the other hand, easy-gliding planes which need longer migration distance (because the planes are inclined from xy plane) are easily selected owing to the reduced surface-step energies by hydrogen at a higher hydrogen coverage. When the second and third terms are balanced, the dislocation motion suspends except for thermal diffusion. This condition is expressed as
4. Discussions 4.1. Energetics of straight screw-dislocation motion in thin film Dislocations migrate by crossing a potential barrier that exists periodically in the lattice. A dislocation in the bulk thermally migrates along opposite glide directions with the same frequency as in the stressfree case. However, if a difference exists in the potential barrier along opposite directions, the frequency with which dislocations pass across the lower potential barrier increases compared with the frequency with which dislocations pass the opposite direction; thus, the dislocation migrates one direction on average. Here, we roughly estimated the potential energy change caused by dislocation migration parallel to the x-axis in Fig. 1. The energy change ΔE caused by the quasi-static motion of screw dislocation Δa/2 (onehalf of the periodicity of the potential barrier) under shear stress τzy is expressed by the equation
E = l × EPeierls
zy l
a ×b 2
a × Estep
zy-eq
=
2Estep
(2)
bl −11
where Estep is evaluated to be 6.89 × 10 J/m for the present system. To evaluate Estep, relaxation at 300 K, followed by energy minimization at 0 K, was performed because a structure reconstruction occurs in the vicinity of the surface steps. When b = 0.247 nm and l = 3.7 nm are used, τzy-eq ≈ −151 MPa is obtained. From Fig. 4, the dislocation motion suspends at approximately −150 to −200 MPa for θ = 0; these values agree well with each other. 4.3. Adsorbed-hydrogen effect on dislocation motion in TEM experiment The dimensions of a specimen that can be directly treated by MD simulation are small even by comparison with the sample used for TEM observations. Furthermore, directly treating the dissociation of hydrogen molecules and the adsorption of hydrogen atoms onto the surface steps generated by dislocation migration is also difficult because the activation energy of the dissociation is too large for MD simulations. Hereafter, we discuss the motion of a screw dislocation in a thicker specimen in a hydrogen gas environment by using Eq. (2), the validity of which was established in the previous discussion. When the motion of a screw dislocation whose end terminates at a free surface is suspended under in situ TEM observation, which is carried out with an ultrathin specimen, internal stress is assumed to exist and the stress is assumed to balance the surface effect (the third term on the right-hand side of Eq. (1)). If we assume that l = 100 nm, which is the typical specimen thickness used for TEM observations, we obtain τzy-eq = −5.6 MPa as the equilibrium stress for the hydrogen-free condition. Here, the apparent step energy is approximately estimated to be half under the assumptions that hydrogen molecules dissociate and hydrogen atoms fully adsorb onto the newly formed steps [23]; we also obtain τzy-eq = −2.8 MPa for the scenario of a gaseous hydrogen environment. This result means that the introduction of hydrogen gas induces dislocation motion equivalent to the application of τzy = 2.8 MPa. The assumption that the dislocation keeps a straight shape is not maintained as the thickness of the specimen increases. Especially, kinks will preferably form at the surface, and dislocation segments near the surface drag the dislocation line inside the material. Although Eq. (1) will be invalid in this case, the effect of the adsorbed hydrogen is still present and the above calculation will be an
(1)
where EPeierls is the Peierls potential, l is the dislocation length (thickness of the specimen), and Estep is the energy of the surface step of unit length. We assumed that the dislocation maintains a straight shape during the migration. The first term on the right-hand side of Eq. (1) represents the contribution from the Peierls potential, and the second term represents the contribution from applied stress which is expressed by the combination of external force (τzylw) and boundary displacement (Δa/2w × b). The third term is the surface-effect term, which represents the energy change caused by the change in length of surface steps accompanied by the migration of the screw dislocation. This term is the origin of the anisotropy of the dislocation motion. 4.2. Comparison with MD results In the case of τzy = 0, ΔE decreases when the dislocation moves toward the positive direction (Δa > 0) because of the contribution of Estep. As thickness l decreases, the contribution of the first term becomes small; thus, the velocity of the dislocation increases. Actually, the dislocation is expected to migrate toward the positive x-axis direction without thermal activation when l < (Δa × Estep/EPeierls). These consequences qualitatively agree well with the simulation results described in Fig. 2. Furthermore, the difference in ΔE along opposite directions becomes small as Estep decreases. Hydrogen diffusion on the surfaces is much faster than the dislocation motion observed in the present work 4
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underestimation because the dislocation can move without overcoming the Peierls potential of the whole dislocation line at the same time. The dislocation velocity estimated from TEM observations is very slow: on the order of micrometers per second [4]. Thus, the shear stress that arises from hydrogen adsorption can induce such dislocation motion in a real TEM specimen. We speculate that the edge dislocation also migrates, influenced by the configuration change of a screw component that ends at a free surface, because the assumption that all dislocations terminate at a free surface end with a pure edge component is unreasonable. According to A. Tehranchi [26], although the separation distance between dislocations is reduced upon introduction of hydrogen in the TEM observations, the pile-ups returned to their original structure upon removal of the hydrogen. If the enhancement of dislocation mobility (reduction of Peierls potential) is caused by solute hydrogen, the dislocations migrated along shear stress and stress is relaxed. After removal of hydrogen, the dislocations with original mobility cannot return to initial structure. The configuration change of dislocations caused by absorbed hydrogen which was proposed in this paper can clearly explain the dislocation motion and return to the original position upon H introduction (absorption) and removal (desorption). This Surface-Adsorbed-Hydrogen-Induced Dislocation Motion mechanism can operate even for materials with low hydrogen solubility and diffusivity.
Funding
5. Conclusions
[12] [13] [14] [15]
This work was supported by JSPS KAKENHI, Japan [Grant Numbers 23686022, 16K05976, 16H06062]. CRediT authorship contribution statement Ryosuke Matsumoto: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Visualization, Supervision, Project administration, Funding acquisition. Shinya Taketomi: Software, Validation, Resources, Data curation, Writing - review & editing, Visualization, Funding acquisition. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
In this study, we analyzed the effects of hydrogen and sample thickness on the motion of a screw dislocation using MD simulations. The results revealed that the influence of surface steps, which are extended or shortened by the screw dislocation, on the screw dislocation motion increases with decreasing specimen thickness. Furthermore, we clarified that the hydrogen weakens the influence of the surface steps by reducing their apparent energy. Finally, we showed that the shear stress that arises from hydrogen adsorption can potentially induce screw dislocation motion in a real TEM specimen. Although in situ TEM observations provide valuable information, consideration of the surface effects on dislocation motion is essential not only for hydrogen-related phenomena but also for the fracture and deformation of nanosized structures.
[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
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