Experimental observation of dislocation motion during H desorption
Typical results of our experiments are shown in Fig. 2. These tests on the fcc Fe-Mn–based alloy revealed motion of dislocations over large distances (>1.5 μm), triggered solely by removing diffusible H from the sample. An example of this phenomenon is shown in Fig. 2A. Here, in the series of ECCI micrographs, as H desorbs out of the sample surface, the increase of the spacing in a planar dislocation array is seen. For clarity, each dislocation is labeled with a letter, and a movie of the dislocation motion is provided online (see movie S1). The largest spacing change takes place after 2 hours (Fig. 2A, third and fourth images), as shown schematically in Fig. 2B. We also provide the full quantitative evolution of the dislocation spacing in this array in Fig. 2C. Several similar observations are made investigating this material further—see Fig. 2 (D to F) for three other zones where rearrangement or disappearance of dislocations in pileups or entanglements are observed (see movies S2 to S4). More examples from this Fe-Mn alloy can be seen in fig. S1 and movie S5. To explore the generality of the observation of dislocation motion, similar experiments were performed on a duplex stainless steel (details in Materials and Methods). Dislocation activities (rearrangements and slip-step formations) can be seen in the austenite phase as shown in fig. S2 and movie S6.
Two characteristics of these results need to be emphasized, in comparison to earlier studies on dislocation motion due to H-charging (15, 23, 27). First, the experiments presented here were specifically designed to minimize the influence of other effects that could cause dislocation motion. There were no externally applied heat or stresses. Similarly, there were no beam heating effects, since the experiments are carried out at room temperature using the SEM-based ECCI method (28, 29). To further ensure that the observed dislocation motions are not driven by surface stresses due to preparation or stresses from the electron beam, control experiments were conducted on samples without H-charging. The dislocations remain immobile (see fig. S3), indicating that the ECCI technique and the presented sample preparation method are not the causes of the observed dislocation activity. Furthermore, there were no TEM sample preparation artifacts (that arise, e.g., due to focused ion beam milling), since ECCI enables imaging of surface dislocations in bulk samples. The experiment did not trigger any phase transformations, since this alloy has a stable microstructure (30). Second, the observed glide distances are larger [from ~3 times (15, 22) to ~2 orders of magnitude (15, 23)] than those reported in previous studies in the literature where a similar H-induced phenomenon was observed.
Numerical simulations investigating the origin of the dislocation mobility
To study the origin of the driving force for the observed dislocation motion, we first investigated the possibility of surface high concentration of H inducing dislocation motion by creating sufficiently high shear stresses. To this end, we calculated the maximum level of stresses that can be generated, by assuming the extreme condition that only the surface expands due to large H content segregation. In this case, the compressive stress along the surface of the sample is equivalent in all directions and equal to
(31). The stress perpendicular to the surface is zero as it can freely expand in this direction. By considering E = 200 GPa for the Young’s modulus, w = 2 × 10−6 m3/mol for the molar expansion (32), c ~ 3 mol/m3 for H concentration calculated for our experiment at the sample surface, and ν = 0.3 for the Poisson ratio of the material, the maximum shear stress occurring at 45° with respect to the sample surface is obtained as ~1 MPa. This value is at least one order of magnitude below the required activation stress for dislocation glide, which indicates that the surface expansion due to the uniform increase in H concentration cannot be the main factor causing the observed dislocation motion in the experiments. The H distribution needs to be nonuniform to achieve higher stress magnitudes.
Next, we conducted hybrid molecular dynamics (MD)/grand canonical Monte Carlo (GCMC) simulations to investigate the fundamentals of the competition among different microstructural constituents [e.g., grain boundaries (GBs) and dislocations] to act as potential sites for H segregation. Using the GCMC algorithm enables bridging the time scale limitations of MD simulations, which is necessary to capture microstructural H diffusion tendencies. As in the case of the experiments, when designing these simulations, the factors that can influence these tendencies need to be strategically minimized. As the resolved stress required for dislocation motion can be influenced by stochastic interactions of the present dislocations with randomly distributed substitutional alloying elements (33), a pure metal was chosen for simulations, which exhibits fcc crystal structure (as in the experiments). Note, however, that pure Fe at room temperature exhibits body-centered cubic structure, and stabilization of fcc Fe requires alloying of nickel (Ni), manganese, carbon, or other austenite stabilizers. Also, for such multicomponent Fe-based fcc alloys containing H, currently reliable interatomic potentials do not exist. Therefore, to elucidate the fundamentals of the underlying mechanisms, we conducted simulations on pure Ni, for which the interatomic potential is available for atomistic-scale simulations (18, 34). Note that Ni is the nearest fcc metal to Fe in the periodic table; thus, it has minimal difference in the atomic size and in the stress due to the presence of H in the interstitial sites or at GB (free volume sites).
A three-dimensional (3D) polycrystalline sample with a grain size of 7.5 nm was modeled (see fig. S4). A total deformation strain of 10% was applied to produce a dislocation network. Then, two simulations were performed on this prestrained sample. In the first one, H atoms were inserted in the sample using hybrid MD/GCMC simulations for 6 ns. The H atomic ratio was increased to 0.45 atomic % (at %) in the sample excluding free surfaces. This percentage is identical to the H percentage in the experimental samples (see fig. S5). For the second simulation and as a reference, the prestrained simulation box was relaxed for 6 ns, and the dislocation network was traced for comparison to the H-charged sample. Application of the hybrid MD/GCMC technique results in a hydrogenated sample in chemical equilibrium for a given H2 chemical potential/partial pressure, in which, for example, the same H percentage migrates from GBs to the free surface and vice versa. Moreover, due to the application of the GCMC technique, no preassumption about the location of H is required, and the energetically favorable sites are chosen by the algorithm automatically. The simulation details are provided in Materials and Methods.
As seen in the 3D view in Fig. 3A, and more clearly in Fig. 3B, which is a 2D slice from the H-charged sample, H atoms exhibit a nonuniform distribution: They are mainly located on free surfaces and GBs. Observations of H segregation in GBs were reported in various investigations, for example, by using cryo-transfer atom probe tomography (35) or by silver-decoration experiments (36, 37), carried out with various metals including Fe and Ni. An important consequence of these results in Fig. 3 (and the mentioned supporting experimental evidence) is regarding direct effects of H on dislocations: As H atoms prefer to stay in GBs rather than dislocations, they impose little pinning effect on dislocation motion (5). Thus, present dislocations in our simulations move without constraint in the sample. The snapshots of a dislocation network in a grain of a H-charged and a H-free sample are shown in Fig. 3 (C and D, respectively) (see movies S7 and S8). A comparison of these two figures reveals that after 700 ps, the spacing between dislocations 1 to 3 increases as a newly generated dislocation 5 moves in the H-charged sample, similar to the experimental observations shown in Fig. 2. As dislocation 5 moves forward in the grain, the stress distribution changes and the dislocations in the pileup rearrange once more. The H-free sample, on the other hand, exhibits relatively less dislocation activity both in the shown region and elsewhere in the sample.
We next computationally investigate the underlying mechanisms for the rearrangement of dislocations seen experimentally in Fig. 2 and computationally in Fig. 3C. In these simulations, an undeformed polycrystalline Ni sample is charged with H to the same H percentage as in the experiment. The atomic-level von Mises stress distribution of the H-charged sample is shown in Fig. 4A. The contour is the temporal average of the stress for each atom over 6 ns. The calculation method of the von Mises stress is presented in Materials and Methods. Higher stress levels are observed on GBs, compared to the bulk of the grains. The atomic-level von Mises stress distributions of the atoms in the bulk (grain interiors) and in the GBs before and after H-charging are plotted in Fig. 4B. To verify the stability of the presented curves, the temporal average was calculated over different time periods. Figure 4C shows that the temporal average saturates by increasing the averaging time period. For example, it is seen that the curve of 6 ns has a shift of less than 5 MPa with respect to the curve of 5.5 ns averaging time. The saturation indicates that the stress fluctuation due to atomic vibrations is not significant, and the average value is the decisive parameter.
The von Mises stress in Fig. 4B spans from zero to tens of gigapascals in both the GBs and the bulk of the sample. These high values compared to the experimentally measured yield strength values (on the order of megapascals) may raise questions on physical validity of these atomic-level stresses. It should be noted, however, that at nanoscale, the crystal can tolerate stress magnitude up to the ideal shear strength (on the order of 1/10 of shear modulus G/10) (38, 39), which can be three orders of magnitude higher than the macroscopic stress values measured by testing highly defected polycrystals.
In Fig. 4B, the bottom inset shows that H segregation at GBs imposes a change of ~200 MPa in von Mises stress of atoms located in GBs. This level of change can influence dislocation emissions from GBs, the structure of the already absorbed dislocations in GBs (40), and, more importantly, the dislocation interactions near GBs. For example, Fig. 4B demonstrates that the induced long-range stress effect can reach ~200 MPa on bulk atoms, near the boundaries. We have also plotted the von Mises stress of individual atoms before and after H-charging in the sample. This plot also presents a change of 150 to 200 MPa in the stress due to the H-charging of the sample (see fig. S6). Stresses at this level should not only induce dislocation activity but also cause local variation of crystallographic orientation near boundaries. This was validated by our in situ electron backscattered diffraction analysis during H-charging of duplex stainless steel (see fig. S7). The observed increase in point-to-point misorientation angle along the phase boundary during H-charging may reflect the localized stress induced by H segregation at the boundary.
In Fig. 4 (B and C), the change in von Mises stress is presented; however, what actually relocates dislocations in the crystal is the resolved shear stress along the slip direction. Therefore, the change of shear stress due to H, directly on two arbitrary slip directions of the Ni crystal, was also investigated for three representative GBs (Σ9, Σ41c, and Σ99b) (see fig. S8). As seen in fig. S9, the shear stress varies depending on the slip direction and GB type (i.e., between 50 and 200 MPa). This clarifies why dislocation activity due to H-charging or desorption should not be expected to be at the same level near every GB. The resolved shear stress is highly dependent on the GB type and also the slip direction. This point once more underlines the importance of experimenting with and simulating polycrystalline samples, to be able to embrace the stochasticity of this problem. Under a given H2 partial pressure, only a certain percentage of dislocations will be relocating, which is highly dependent on several influential parameters such as the GB orientation, slip systems, dislocation type, dislocation density, and residual stress due to dislocation interactions with other dislocations and microstructural features.