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Hydrogen-induced accelerated grain growth in vanadium
Acta Materialia 155 (2018) 262e267
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Hydrogen-induced accelerated grain growth in vanadium May L. Martin a, *, Astrid Pundt a, Reiner Kirchheim a, b a
€ttingen, Germany Institute für Materialphysik, University of Go I CNER (WPI), Kyushu University, Fukuoka, Japan
b 2
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2018 Received in revised form 4 June 2018 Accepted 4 June 2018 Available online 14 June 2018
Grain growth in nanocrystalline vanadium films was studied at 600 and 700 C in vacuum and in hydrogen atmosphere with partial pressures ranging from 1 to 1000 Pa. It is shown that grain growth is significantly increased in the presence of hydrogen. Thus the expected effect of retarding grain growth either by reducing grain boundary energy due to hydrogen segregation or by hydrogen drag on the moving boundary did not occur. Two explanations are given for the accelerated grain growth. First, hydrogen reduces the formation energy of ledges, assuming these ledges are required for initiating and advancing boundary motion. Second, grain growth requires the annihilation of excess volume which may be enhanced by reducing the formation energy of vacancies in the presence of hydrogen. © 2018 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Keywords: Grain growth Hydrogen Vanadium
1. Introduction Grain size control is an important aspect of materials engineering, and the use of solute additives for size control is a common technique. Grain growth is usually thought of in terms of lowering the system energy: since grain boundaries contribute energy to the system, grain growth, which reduces the total area of grain boundaries, lowers the total energy of the system. The presence of impurity atoms on the grain boundary lowers the grain boundary formation energy and, thereby reduces the driving force for grain growth, resulting in a smaller final grain size [1e5]. Some researchers propose that this energy consideration is insufficient to account for the reduced grain coarsening, and that it is the decrease of grain boundary mobility due to solute drag which accounts for the smaller final grain size [6,7]. In nanograined materials, this situation is complicated by the fact that the total number of atoms in the grain boundaries begins to approach the number of atoms in the bulk [8]. At this point, it is likely that other defects, such as grain boundary triple junctions and vacancies, play an important role in grain boundary motion, resulting in an interplay between energy considerations and mobility effects [6,9,10]. However, in the framework of a generalized Gibbs adsorption concept [11e13], the formation energy of these defects is reduced by solute segregating to the defects as well. Thus, the density of triple junctions and
vacancies is increased by the segregation of solute atoms. Hydrogen, though an interstitial solute, tends to behave differently from other impurities in metals regarding its interaction with defects. This arises from its high mobility at low temperatures, where hydrogen atoms are able to reach defects in reasonable times and the defects have not been annihilated due to recovery and/or recrystallization. This is particularly evident in its influence on dislocation behavior [14] and its creation of superabundant vacancies [15]. With respect to the influence of hydrogen on grain boundaries, research has been limited to investigations into the lowering of the grain boundary cohesion [14,16], while studies into the influence of hydrogen on grain growth in metals are missing. The present study was designed to address the issue. The vanadium-hydrogen system is used as a model system in this study. The body-centered cubic structure of vanadium leads to a high hydrogen diffusivity, similar to iron-based ferritic alloys, though the hydrogen solubility of those alloys is much lower. With the high solubility of hydrogen in vanadium, a large range of hydrogen concentrations can be explored. Nanocrystalline films allow easy sampling of a range of temperature, time and hydrogen conditions to investigate the effect of hydrogen on grain growth with the driving force for grain growth being largely due to the small grain size.
2. Experimental procedure * Corresponding author. Applied Chemicals and Materials Division, National Institute of Standards and Technology (NIST), USA. E-mail address: [email protected] (M.L. Martin). https://doi.org/10.1016/j.actamat.2018.06.011 1359-6454/© 2018 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Nanocrystalline films of vanadium were produced by argon ionbeam sputter deposition. The background pressure of the system
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was pback ¼ 2x108 Pa, while the Ar sputter pressure was 5x102 Pa. For a substrate, 3 mm gold grids with an amorphous carbon film were used to allow observation of the film microstructure in the transmission electron microscope (TEM) without further sample preparation. The vanadium deposition rate was ~0.6 nm/min. Films with thicknesses between 90 and 120 nm were prepared, such that they are electron transparent in the TEM. The average as-grown grain size was 8 nm for the first batch of samples, and 25 nm for a second batch. This difference is likely due to small changes in the deposition parameters, due to the system being cleaned and readjusted between the batches. The complete and even rings of the diffraction pattern suggest no obvious texture to the grain orientation. Samples were heated in a tube vacuum furnace at 600 or 700 C for 1e2 h, with a few tests sampling longer heat times. Base pressures of 106 Pa were achieved. Hydrogen gas was added to the system during heating at pressures ranging from 1 to 1000 Pa. Before and after heating, the microstructure was investigated in a Phillips CM12 TEM operated at 120 kV. Grain size determination was carried out on bright-field TEM images by the circle-intercept method. This technique consistently gave errors on the order of ±8%.
3. Results Grain growth in films with an initial grain size of 8 nm (Fig. 1a) starts in vacuum between 600 and 700 C. After 1 h at 600 C in vacuum, no grain growth is noticed, with a final grain size of 9 nm (Fig. 1b). The addition of hydrogen produces a marked change in behavior: heating at 600 C for 1 h in 1 Pa hydrogen already produces a final grain size of 30 nm, as shown in Fig. 1c. The addition of 1 Pa H2 corresponds to a solute concentration in vanadium of 0.013 at%, if the system is at equilibrium at 600 C [17]. Therefore, it is evident that the presence of this small amount of hydrogen has already caused substantial grain growth. Note that the given concentration was determined for coarse grained vanadium, where any segregation of hydrogen at grain boundaries has a negligible effect on the overall hydrogen concentration. Thus the value calculated from the pressure-composition isotherms in Ref. [17] corresponds to the hydrogen concentration within the vanadium grains. At 700 C, grain growth visibly occurs in vacuum (Fig. 2a), with the average final grain size of that sample increasing to 16 nm, and the effect of hydrogen is even more evident. With exposure to 1 Pa of hydrogen, we again see significant grain growth (Fig. 2b). However, as visible in the same figure, the growth mode is clearly bimodal, with the large grains averaging 37 nm in diameter and the smaller grains averaging 6 nm, which is below the average starting grain size of the film, suggesting that it is the smallest grains that do not grow or are partially consumed as in a ripening process. Increasing the hydrogen pressure to 10 Pa results in faster grain growth, but it is still bimodal in nature, with average diameters of
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50 and 13 nm (Fig. 2c). It is notable that the smaller grains appear to begin growing now with the addition of more hydrogen. According to Sieverts' Law and in agreement with measurements [17], the hydrogen concentration in the vanadium grains increases by a factor of square root 10, being about 0.04 at% at 10 Pa. Higher hydrogen pressures result in increased grain growth, but reaching steady state grain sizes at 700 C between 10 and 100 Pa hydrogen pressure. Samples heated at 700 C for 2 h with 100 Pa and 1000 Pa hydrogen gas (which according to Sieverts' Law corresponds to 0.13 and 0.4 at% in the vanadium grains, respectively [17]) showed a similar final grain size, increasing from an initial grain size of 21 nm (Fig. 3a) to 55 and 54 nm (Fig. 3ced, respectively). This suggests that there is a saturation point after which increasing the hydrogen pressure no longer results in an increase in the grain growth rate. Interestingly, there is also no longer a bimodal distribution. Whether this is due to the increased growth of all grains with the addition of this much hydrogen, or whether growth of selected grains occurred aggressively at the expense of smaller grains, now completely consumed, is not clear. As heating continues for longer periods of time, the difference in behavior due to hydrogen becomes more noticeable. As shown in Fig. 4, at 700 C, a larger final grain size of 110 nm is achieved after 6 h heating in only 1 Pa H2 when compared with reaching a final size of 35 nm in vacuum despite a longer heating time of 18 h. This corresponds to an order of magnitude higher growth rate (Fig. 5). It is also important to note that, as expected [5], grain growth in vacuum slows down with time, with the same amount of grain growth occurring between 2 and 4 h as occurs between 4 and 18 h. In the presence of hydrogen, after 6 h, grain growth likewise appears to slow down. However, in this case, as the grain size is approaching the film thickness (~120 nm), a geometric constraint may be artificially inhibiting grain growth [18]. This is supported by the apparent sharpness in the change in the slope of the hydrogen curve compared to the vacuum curve in Fig. 5a, where, between 1 and 4 h, the vacuum data gently curves towards a steady state value (likely unaffected by geometry), while the hydrogen data displays a higher slope initially before flattening more abruptly. Also, as highlighted in Fig. 5b, where parabolic grain growth behavior is plotted as straight lines, grain growth in hydrogen appears to be initially following a parabolic behavior before abruptly flattening out, while grain growth in air does not appear follow a parabolic curve at all.
4. Discussion The experimental results of the present study clearly demonstrate that the exposure of nanocrystalline vanadium to gaseous hydrogen produces a significant increase in grain growth rates. Even relatively low amounts of hydrogen cause a doubling in the final grain size compared to that achieved in vacuum. Higher pressures or chemical potentials of hydrogen result in further
Fig. 1. TEM micrographs of grain growth in vanadium film at 600 C for 1 h a) Starting microstructure with average grain size of 8 nm b) Microstructure after heating in vacuum with a final grain size of 9 nm c) Microstructure after heating in 1 Pa H2 gas with a final grain size of 30 nm.
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Fig. 2. TEM micrographs of grain growth in vanadium film at 700 C for 1 h. Starting microstructure equivalent to Fig. 1a). a) Microstructure after heating in vacuum with final grain size of 16 nm b) Microstructure after heating in 1 Pa H2 gas. Bimodal grain size distributions with averages of 37 nm and 6 nm c) Microstructure after heating in 10 Pa H2 gas. Bimodal grain size distributions with averages of 50 nm and 13 nm.
Fig. 3. TEM micrographs of grain growth in vanadium films heated in higher pressures of hydrogen at 700 C for 2 h a) Starting microstructure of films with average grain size of 21 nm b) Microstructure after heating in vacuum with final grain size of 27 nm c) Microstructure after heating in 100 Pa H2 gas with a final grain size of 55 nm d) Microstructure after heating in 1000 Pa H2 gas with a final grain size of 54 nm.
Fig. 4. TEM micrographs of grain growth in vanadium films heated for long times in vacuum and in hydrogen gas at 700 C. Initial grain size 21 nm, similar to Fig. 3a). a) Microstructure after heating for 18 h in vacuum with a final grain size of 35 nm b) Microstructure after heating in 1 Pa H2 gas with a final grain size of 110 nm.
increases in the grain growth rate. However, at high pressures, the grain diameter stabilizes for a given annealing time; in other words, the pressure dependence disappears at high pressures. In coarse grained materials, the hydrogen concentration is obtained via Sieverts' Law [17] because the total excess hydrogen at grain boundaries is negligible. This will be no longer the case in nanocrystalline materials, as the total excess hydrogen will contribute significantly to the total hydrogen concentration. With a differential excess of GH ¼ 3 105 mol H=m2 (about one monolayer) and a grain size of d ¼ 10nm the contribution to the H-concentration stemming from grain boundaries is GH =3d ¼ 103 mol H=m3 [3] which
corresponds to about 1 at% H in vanadium, which is much larger than the concentrations within the grains as calculated from Sieverts' Law (0.01e0.4 at% as discussed in the previous section). This analysis remains speculative, as it is not currently known how much hydrogen segregates to the grain boundaries in vanadium at temperatures of 600 and 700 C. However, in order to comprehend why effects on grain growth become so pronounced at the very low hydrogen pressures and the corresponding very low Sieverts' concentrations at the grain interior, it is reasonable to expect a pronounced segregation to the boundaries. The rate of grain growth is determined by the grain boundary velocity which is proportional to the product of grain boundary mobility and thermodynamic driving force [5]. Mobility can be related to grain boundary type, with certain misorientation angles being favored for selective growth [19]. The thermodynamic driving force is assumed to stem from the energy release during grain growth due to the reduction of grain boundary area. This driving force is decreased by hydrogen segregating to grain boundaries, because the corresponding excess hydrogen leads to a reduction of the grain boundary energy [3]. Therefore, our experimental findings of accelerated grain growth could only be explained by a hydrogen-induced increase of grain boundary mobility which overcompensates for the reduction in driving force. The presence of solute atoms, such as carbon or nitrogen, usually results in a reduction in grain growth. This is attributed to solutes reducing the energy of the grain boundaries [3,13]. However, similarly to how kink-pair nucleation can be the rate-limiting step in dislocation motion [20], step or ledge formation may be a rate-limiting step for grain boundary motion. The formation of this step requires the formation of new grain boundary area, and the presence of solutes may lower this formation energy based on the thermodynamic defactant concept [13]. Note that for the segregation of hydrogen to ledges, a smaller amount of hydrogen is required than for covering the whole grain boundary. Thus reducing the formation energy of ledges may occur at lower hydrogen concentrations leading to a higher rate of ledge nucleation with a concomitant increase in grain boundary mobility. In other words, although the presence of hydrogen reduces the driving force for grain boundary motion, the increases in mobility due to a higher frequency of ledge formation will be dominant. Typically, solute presence is associated with a drag effect on boundary mobility [5]. Besides step or ledge formation, the motion of steps along the boundary leading to a positional move of the whole boundary may be affected by these drag or frictional forces due to the presence of hydrogen. The interplay between step formation and step motion is analogous to that in the formation and motion of kink-pairs in dislocations, which leads to enhanced dislocation mobility at low H-concentration and reduced mobility at high concentrations [20]. Thus, the plateau in grain growth behavior at high hydrogen concentrations observed in this study may be due to similar compensation of the hydrogen effects on
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Fig. 5. Grain growth as a function of time. Samples heated at 700 C in vacuum (open square) or in 1 Pa H2 (filled circle). Grain growth calculated as the difference between the square of the final average diameter and the square of the initial grain size (d2f d2i ). b) shows same data plotted on log-log scale, with two straight lines representing parabolic grain growth.
boundary step formation and motion, where the increased formation rate of steps is no longer dominant at high H-concentrations due to an increased solute drag on moving steps. In the previous argument, all solute atoms, whether carbon, nitrogen or hydrogen, have been treated equally, so it would be expected that all would show similar behavior, which has generally been reduction in grain boundary motion. But, hydrogen appears to have the opposite effect. This difference in behavior may be due to the difference in diffusion coefficients. Even at the high temperatures needed for grain growth, the diffusivity of hydrogen is still several orders of magnitude higher than that of larger interstitial solutes [21]. While the larger solutes may be mobile at these temperatures, they are likely to be slow enough to cause a solute drag effect on grain boundaries and/or their steps. However, hydrogen itself with its high mobility may not be creating solute drag on either the whole boundary or the ledges, though by itself, this higher mobility is more likely to result in comparable rates of growth in hydrogen and in its absence, not result in an acceleration. Another potential difference between hydrogen and other solutes could be the chemical interactions that are possible with the material. Shvindlerman and Gottstein suggested an acceleration effect occurring by the removal of impurities from the grain boundary by the formation of precipitates [22]. In the present case, the removal of oxygen from grain boundaries by reaction with hydrogen could have a similar effect. Whether hydrogen could be reducing vanadium oxide that may be present at the grain boundaries is elucidated in the following by considering the reaction:
V þ H2 O 4VO þ H2 :
(1)
If the system is at equilibrium, the sum of the chemical potentials would be zero, leading to the relationship:
PH2 ¼ m0V m0VO þ m0H2 O m0H2 RT ln PH2 O
(2)
Using values from Lange [23], the ratio of PH2 P was calcuH2 O 10 lated to be on the order of 10 , suggesting that the oxide is stable in the presence of hydrogen. Therefore, it is unlikely that hydrogen is removing any other components (either precipitates or solutes) that may be obstructing grain boundary motion. It is important to note that the native oxide on the surface of the samples will be dissolved at temperatures above 400 C, according to the V-O phase
diagram [17]. The disappearance of the native oxide layer is required for hydrogen to be dissociated and absorbed by the samples. Another difference from other solutes is that hydrogen has been found to increase the number of vacancies found at equilibrium in metals [15,24e27]. This has been attributed to hydrogen decreasing the formation energy of vacancies, explained on thermodynamic grounds within the defactant concept [13]. A rate-limiting step in grain growth may be the accommodation of the free volume created by the elimination of grain boundaries, which is often thought to occur through the generation and migration of vacancies [6,10,28,29]. A consequence of this accommodation is that it could lead to a nonequilibrium supersaturation of vacancies, as suggested by the presence of defects such as stacking fault tetrahedra after grain growth [30], which could result in a thermodynamic force on the boundary, slowing grain boundary motion [6,28]. Estrin et al. posited that, in nanocrystalline materials, this force could be as effective as solute drag in inhibiting grain boundary motion [10]. Hydrogen, by reducing the formation energy of vacancies and stabilizing them, allows more free volume to be accommodated more easily, reducing the force against grain boundary motion. Additionally, many early studies, summarized in Ref. [5], found that grain boundary mobility increased with increasing vacancy concentration, with the rationale that it was easier for grain boundaries to restructure as needed for migration when more vacancies were available. Thus, the increased availability of vacancies due to the presence of hydrogen, both ahead of and behind the grain boundaries, may help increase mobility. It is likely that it is a combination of the factors mentioned above that contributes to hydrogen enhancing grain growth. The increase in grain boundary mobility and the ability to accommodate the free volume from the grain boundaries seems to predominate over the reduction in the driving force for grain growth due to the presence of hydrogen. The importance of one factor over another, such as grain boundary mobility compared to free volume accommodation, may be suggested by the presence of abnormal grain growth at shorter time periods. The occurrence of abnormal grain growth resulting in a bimodal grain size distribution in these experiments is perhaps not surprising, given the nanocrystalline structure of the material [18,30,31]. Though, it is interesting that the phenomenon is more prominent in the presence of hydrogen and is not noticeable in its absence, under the conditions examined. Previous studies have
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shown a dependence of abnormal grain growth on the film texture [32], though that should not have been a factor here, as the compared films were prepared under identical conditions. However, the idea that texture has a role may be related to an associated feature: the grain boundary types produced. Different grain boundaries types will have different structures, and have been shown to have different properties, for example, differences in passivity [33]. Accordingly, these different boundary types will likely trap hydrogen to different extents; likely resulting in different grain boundaries having different mobilities, especially in the presence of hydrogen [3,34,35]. This suggests that on short time scales, or with smaller grains, grain boundary mobility and its changes by hydrogen is a more dominant factor. More information is needed in this area, and the grain boundary character of the different grains is a subject for further study. Further evidence of the importance of grain boundary mobility may be seen in the higher pressure experimental results. While the exact hydrogen concentration at the grain boundaries is unknown, it is reasonable to assume that at a certain bulk concentration, the grain boundaries will saturate, and increasing bulk hydrogen content will have limited effect on the grain boundary mobility. At the same time, increasing the hydrogen concentration should increase the concentration of vacancies that can be accommodated at equilibrium, which is proposed to increase the overall mobility. While further study is needed to carefully define these regimes, as the grain growth rate appears to become independent of hydrogen pressure at higher pressures (Fig. 3), it suggests that the increase in vacancy accommodation is insufficient to produce further grain growth acceleration. Experimental results after long annealing times reveal a stagnation of grain growth. This may be due to grain sizes reaching the size of the thickness of the thin TEM samples. Alternatively, another factor which will come into play at larger grain sizes is that, independent of the rate-controlling processes, either ledge or vacancy formation, the moving grain boundary will collect impurities which are immobile at the annealing temperature. With increasing impurity segregation, the boundary mobility decreases due to solute drag and/or the driving force decreases due to reduced boundary energy. Within the concept of vacancy generation during grain growth, a stagnation of growth could be attributed to an oversaturation of vacancies counteracting any further vacancy generation. Further grain growth then requires the annihilation of vacancies at the surface and/or by sinks within the grains, like dislocations or stacking faults. If the efficiency of these sinks is reduced, oversaturation of vacancies within the grains will counteract grain boundary annihilation, or grain growth, respectively. With surfaces being very effective sinks for vacancies however, this scenario for stagnation of grain growth at high hydrogen pressures and long annealing times appears to be less likely. While further experiments are needed to fully explore the factors influencing the processes, the results presented here suggest that hydrogen increases the rate of grain growth in nanocrystalline vanadium thin films by 1. Increasing the grain boundary mobility, proposed to be due to a decrease in the formation energy of grain boundary steps, and 2. Easing accommodation of free volume created by the decrease in grain boundary volume due to lowering the formation energy of vacancies in the presence of hydrogen. Comparison of short time/small grain results with long time/ high hydrogen/large grain results, suggests that the increase in grain boundary mobility may be more important during the former conditions.
5. Conclusion The addition of hydrogen during the heating of nanocrystalline vanadium thin films resulted in substantial grain growth compared to in vacuum. This acceleration in grain growth increased with increasing hydrogen content, then stabilized at high hydrogen content. While the presence of hydrogen likely reduced the driving force for grain boundary motion by reducing grain boundary energy or increasing solute drag, it is proposed that it increased grain boundary mobility, i.e. by decreasing the formation energy of steps. Additionally, hydrogen could be reducing the barrier for grain boundary motion by lowering the formation energy of vacancies, allowing free volume to be accommodated more easily. More experiments and/or simulations are required to distinguish between the two scenarios. The results will not only shed light on the observed effect of hydrogen on grain boundary mobility but may allow a deeper insight into atomistic processes leading to grain boundary motion. Acknowledgements The Alexander von Humboldt foundation and the Heisenberg program of the Deutsche Forschungsgemeinschaft (project PU131/ 9-2) are gratefully acknowledged for funding of this project. References [1] J. Weissmüller, Alloy effects in nanostructures, Nanostruct. Mater. 3 (1) (1993) 261e272. [2] C.C. Koch, The synthesis and structure of nanocrystalline materials produced by mechanical attrition: a review, Nanostruct. Mater. 2 (2) (1993) 109e129. [3] R. Kirchheim, Grain coarsening inhibited by solute segregation, Acta Mater. 50 (2) (2002) 413e419. [4] F. Liu, R. Kirchheim, Comparison between kinetic and thermodynamic effects on grain growth, Thin Solid Films 466 (1e2) (2004) 108e113. [5] C.J. Simpson, W.C. Winegard, K.T. Aust, Grain boundary mobility and boundary solute interactions, in: G.A. Chadwick, D.A. Smith (Eds.), Grain Boundary Structure and Properties, Academic Press, 1976, pp. 201e234. [6] L.S. Shvindlerman, G. Gottstein, Cornerstones of grain structure evolution and stability: vacancies, boundaries, triple junctions, J. Mater. Sci. 40 (4) (2005) 819e839. [7] D.A. Molodov, U. Czubayko, G. Gottstein, L.S. Shvindlerman, On the effect of purity and orientation on grain boundary motion, Acta Mater. 46 (2) (1998) 553e564. [8] E. Rabkin, On the grain size dependent solute and particle drag, Scripta Mater. 42 (12) (2000) 1199e1206. [9] V.Y. Novikov, Grain growth in nanocrystalline materials, Mater. Lett. 159 (2015) 510e513. [10] Y. Estrin, G. Gottstein, E. Rabkin, L.S. Shvindlerman, On the kinetics of grain growth inhibited by vacancy generation, Scripta Mater. 43 (2) (2000) 141e147. [11] R. Kirchheim, Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation. I. Theoretical background, Acta Mater. 55 (15) (2007) 5129e5138. [12] R. Kirchheim, Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation: II. Experimental evidence and consequences, Acta Mater. 55 (15) (2007) 5139e5148. [13] R. Kirchheim, On the solute-defect interaction in the framework of a defactant concept, Int. J. Mater. Res. 100 (4) (2009) 483e487. [14] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. DeLeo, S.K. Estreicher, E.E. Haller, P. Jena, N.M. Johnson, R. Kirchheim, S.J. Pearton, M.J. Stavola, Hydrogen interactions with defects in crystalline solids, Rev. Mod. Phys. 64 (2) (1992) 559e617. [15] Y. Fukai, Superabundant vacancies formed in metalehydrogen alloys, Phys. Scripta 2003 (T103) (2003) 11. [16] C.J. McMahon Jr., Hydrogen-induced intergranular fracture of steels, Eng. Fract. Mech. 68 (6) (2001) 773e788. [17] E. Fromm, E. Gebhardt, Gase und Kohlenstoff in Metallen, Springer-Verlag Berlin Heidelberg, 1976. [18] C.V. Thompson, Grain growth in thin films, Annu. Rev. Mater. Sci. 20 (1) (1990) 245e268. [19] K. Verbeken, M.D. Nave, L. Kestens, M.R. Barnett, Selective growth in a scratched Fe-2.8%Si single crystal, THERMEC'2003, in: International Conference on Processing and Manufacturing of Advanced Materials, 7-11 July 2003, Trans Tech Publications, Switzerland, 2003, pp. 3757e3762. [20] R. Kirchheim, Solid solution softening and hardening by mobile solute atoms
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Full length article
Hydrogen-induced accelerated grain growth in vanadium May L. Martin a, *, Astrid Pundt a, Reiner Kirchheim a, b a
€ttingen, Germany Institute für Materialphysik, University of Go I CNER (WPI), Kyushu University, Fukuoka, Japan
b 2
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2018 Received in revised form 4 June 2018 Accepted 4 June 2018 Available online 14 June 2018
Grain growth in nanocrystalline vanadium films was studied at 600 and 700 C in vacuum and in hydrogen atmosphere with partial pressures ranging from 1 to 1000 Pa. It is shown that grain growth is significantly increased in the presence of hydrogen. Thus the expected effect of retarding grain growth either by reducing grain boundary energy due to hydrogen segregation or by hydrogen drag on the moving boundary did not occur. Two explanations are given for the accelerated grain growth. First, hydrogen reduces the formation energy of ledges, assuming these ledges are required for initiating and advancing boundary motion. Second, grain growth requires the annihilation of excess volume which may be enhanced by reducing the formation energy of vacancies in the presence of hydrogen. © 2018 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Keywords: Grain growth Hydrogen Vanadium
1. Introduction Grain size control is an important aspect of materials engineering, and the use of solute additives for size control is a common technique. Grain growth is usually thought of in terms of lowering the system energy: since grain boundaries contribute energy to the system, grain growth, which reduces the total area of grain boundaries, lowers the total energy of the system. The presence of impurity atoms on the grain boundary lowers the grain boundary formation energy and, thereby reduces the driving force for grain growth, resulting in a smaller final grain size [1e5]. Some researchers propose that this energy consideration is insufficient to account for the reduced grain coarsening, and that it is the decrease of grain boundary mobility due to solute drag which accounts for the smaller final grain size [6,7]. In nanograined materials, this situation is complicated by the fact that the total number of atoms in the grain boundaries begins to approach the number of atoms in the bulk [8]. At this point, it is likely that other defects, such as grain boundary triple junctions and vacancies, play an important role in grain boundary motion, resulting in an interplay between energy considerations and mobility effects [6,9,10]. However, in the framework of a generalized Gibbs adsorption concept [11e13], the formation energy of these defects is reduced by solute segregating to the defects as well. Thus, the density of triple junctions and
vacancies is increased by the segregation of solute atoms. Hydrogen, though an interstitial solute, tends to behave differently from other impurities in metals regarding its interaction with defects. This arises from its high mobility at low temperatures, where hydrogen atoms are able to reach defects in reasonable times and the defects have not been annihilated due to recovery and/or recrystallization. This is particularly evident in its influence on dislocation behavior [14] and its creation of superabundant vacancies [15]. With respect to the influence of hydrogen on grain boundaries, research has been limited to investigations into the lowering of the grain boundary cohesion [14,16], while studies into the influence of hydrogen on grain growth in metals are missing. The present study was designed to address the issue. The vanadium-hydrogen system is used as a model system in this study. The body-centered cubic structure of vanadium leads to a high hydrogen diffusivity, similar to iron-based ferritic alloys, though the hydrogen solubility of those alloys is much lower. With the high solubility of hydrogen in vanadium, a large range of hydrogen concentrations can be explored. Nanocrystalline films allow easy sampling of a range of temperature, time and hydrogen conditions to investigate the effect of hydrogen on grain growth with the driving force for grain growth being largely due to the small grain size.
2. Experimental procedure * Corresponding author. Applied Chemicals and Materials Division, National Institute of Standards and Technology (NIST), USA. E-mail address: [email protected] (M.L. Martin). https://doi.org/10.1016/j.actamat.2018.06.011 1359-6454/© 2018 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Nanocrystalline films of vanadium were produced by argon ionbeam sputter deposition. The background pressure of the system
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was pback ¼ 2x108 Pa, while the Ar sputter pressure was 5x102 Pa. For a substrate, 3 mm gold grids with an amorphous carbon film were used to allow observation of the film microstructure in the transmission electron microscope (TEM) without further sample preparation. The vanadium deposition rate was ~0.6 nm/min. Films with thicknesses between 90 and 120 nm were prepared, such that they are electron transparent in the TEM. The average as-grown grain size was 8 nm for the first batch of samples, and 25 nm for a second batch. This difference is likely due to small changes in the deposition parameters, due to the system being cleaned and readjusted between the batches. The complete and even rings of the diffraction pattern suggest no obvious texture to the grain orientation. Samples were heated in a tube vacuum furnace at 600 or 700 C for 1e2 h, with a few tests sampling longer heat times. Base pressures of 106 Pa were achieved. Hydrogen gas was added to the system during heating at pressures ranging from 1 to 1000 Pa. Before and after heating, the microstructure was investigated in a Phillips CM12 TEM operated at 120 kV. Grain size determination was carried out on bright-field TEM images by the circle-intercept method. This technique consistently gave errors on the order of ±8%.
3. Results Grain growth in films with an initial grain size of 8 nm (Fig. 1a) starts in vacuum between 600 and 700 C. After 1 h at 600 C in vacuum, no grain growth is noticed, with a final grain size of 9 nm (Fig. 1b). The addition of hydrogen produces a marked change in behavior: heating at 600 C for 1 h in 1 Pa hydrogen already produces a final grain size of 30 nm, as shown in Fig. 1c. The addition of 1 Pa H2 corresponds to a solute concentration in vanadium of 0.013 at%, if the system is at equilibrium at 600 C [17]. Therefore, it is evident that the presence of this small amount of hydrogen has already caused substantial grain growth. Note that the given concentration was determined for coarse grained vanadium, where any segregation of hydrogen at grain boundaries has a negligible effect on the overall hydrogen concentration. Thus the value calculated from the pressure-composition isotherms in Ref. [17] corresponds to the hydrogen concentration within the vanadium grains. At 700 C, grain growth visibly occurs in vacuum (Fig. 2a), with the average final grain size of that sample increasing to 16 nm, and the effect of hydrogen is even more evident. With exposure to 1 Pa of hydrogen, we again see significant grain growth (Fig. 2b). However, as visible in the same figure, the growth mode is clearly bimodal, with the large grains averaging 37 nm in diameter and the smaller grains averaging 6 nm, which is below the average starting grain size of the film, suggesting that it is the smallest grains that do not grow or are partially consumed as in a ripening process. Increasing the hydrogen pressure to 10 Pa results in faster grain growth, but it is still bimodal in nature, with average diameters of
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50 and 13 nm (Fig. 2c). It is notable that the smaller grains appear to begin growing now with the addition of more hydrogen. According to Sieverts' Law and in agreement with measurements [17], the hydrogen concentration in the vanadium grains increases by a factor of square root 10, being about 0.04 at% at 10 Pa. Higher hydrogen pressures result in increased grain growth, but reaching steady state grain sizes at 700 C between 10 and 100 Pa hydrogen pressure. Samples heated at 700 C for 2 h with 100 Pa and 1000 Pa hydrogen gas (which according to Sieverts' Law corresponds to 0.13 and 0.4 at% in the vanadium grains, respectively [17]) showed a similar final grain size, increasing from an initial grain size of 21 nm (Fig. 3a) to 55 and 54 nm (Fig. 3ced, respectively). This suggests that there is a saturation point after which increasing the hydrogen pressure no longer results in an increase in the grain growth rate. Interestingly, there is also no longer a bimodal distribution. Whether this is due to the increased growth of all grains with the addition of this much hydrogen, or whether growth of selected grains occurred aggressively at the expense of smaller grains, now completely consumed, is not clear. As heating continues for longer periods of time, the difference in behavior due to hydrogen becomes more noticeable. As shown in Fig. 4, at 700 C, a larger final grain size of 110 nm is achieved after 6 h heating in only 1 Pa H2 when compared with reaching a final size of 35 nm in vacuum despite a longer heating time of 18 h. This corresponds to an order of magnitude higher growth rate (Fig. 5). It is also important to note that, as expected [5], grain growth in vacuum slows down with time, with the same amount of grain growth occurring between 2 and 4 h as occurs between 4 and 18 h. In the presence of hydrogen, after 6 h, grain growth likewise appears to slow down. However, in this case, as the grain size is approaching the film thickness (~120 nm), a geometric constraint may be artificially inhibiting grain growth [18]. This is supported by the apparent sharpness in the change in the slope of the hydrogen curve compared to the vacuum curve in Fig. 5a, where, between 1 and 4 h, the vacuum data gently curves towards a steady state value (likely unaffected by geometry), while the hydrogen data displays a higher slope initially before flattening more abruptly. Also, as highlighted in Fig. 5b, where parabolic grain growth behavior is plotted as straight lines, grain growth in hydrogen appears to be initially following a parabolic behavior before abruptly flattening out, while grain growth in air does not appear follow a parabolic curve at all.
4. Discussion The experimental results of the present study clearly demonstrate that the exposure of nanocrystalline vanadium to gaseous hydrogen produces a significant increase in grain growth rates. Even relatively low amounts of hydrogen cause a doubling in the final grain size compared to that achieved in vacuum. Higher pressures or chemical potentials of hydrogen result in further
Fig. 1. TEM micrographs of grain growth in vanadium film at 600 C for 1 h a) Starting microstructure with average grain size of 8 nm b) Microstructure after heating in vacuum with a final grain size of 9 nm c) Microstructure after heating in 1 Pa H2 gas with a final grain size of 30 nm.
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Fig. 2. TEM micrographs of grain growth in vanadium film at 700 C for 1 h. Starting microstructure equivalent to Fig. 1a). a) Microstructure after heating in vacuum with final grain size of 16 nm b) Microstructure after heating in 1 Pa H2 gas. Bimodal grain size distributions with averages of 37 nm and 6 nm c) Microstructure after heating in 10 Pa H2 gas. Bimodal grain size distributions with averages of 50 nm and 13 nm.
Fig. 3. TEM micrographs of grain growth in vanadium films heated in higher pressures of hydrogen at 700 C for 2 h a) Starting microstructure of films with average grain size of 21 nm b) Microstructure after heating in vacuum with final grain size of 27 nm c) Microstructure after heating in 100 Pa H2 gas with a final grain size of 55 nm d) Microstructure after heating in 1000 Pa H2 gas with a final grain size of 54 nm.
Fig. 4. TEM micrographs of grain growth in vanadium films heated for long times in vacuum and in hydrogen gas at 700 C. Initial grain size 21 nm, similar to Fig. 3a). a) Microstructure after heating for 18 h in vacuum with a final grain size of 35 nm b) Microstructure after heating in 1 Pa H2 gas with a final grain size of 110 nm.
increases in the grain growth rate. However, at high pressures, the grain diameter stabilizes for a given annealing time; in other words, the pressure dependence disappears at high pressures. In coarse grained materials, the hydrogen concentration is obtained via Sieverts' Law [17] because the total excess hydrogen at grain boundaries is negligible. This will be no longer the case in nanocrystalline materials, as the total excess hydrogen will contribute significantly to the total hydrogen concentration. With a differential excess of GH ¼ 3 105 mol H=m2 (about one monolayer) and a grain size of d ¼ 10nm the contribution to the H-concentration stemming from grain boundaries is GH =3d ¼ 103 mol H=m3 [3] which
corresponds to about 1 at% H in vanadium, which is much larger than the concentrations within the grains as calculated from Sieverts' Law (0.01e0.4 at% as discussed in the previous section). This analysis remains speculative, as it is not currently known how much hydrogen segregates to the grain boundaries in vanadium at temperatures of 600 and 700 C. However, in order to comprehend why effects on grain growth become so pronounced at the very low hydrogen pressures and the corresponding very low Sieverts' concentrations at the grain interior, it is reasonable to expect a pronounced segregation to the boundaries. The rate of grain growth is determined by the grain boundary velocity which is proportional to the product of grain boundary mobility and thermodynamic driving force [5]. Mobility can be related to grain boundary type, with certain misorientation angles being favored for selective growth [19]. The thermodynamic driving force is assumed to stem from the energy release during grain growth due to the reduction of grain boundary area. This driving force is decreased by hydrogen segregating to grain boundaries, because the corresponding excess hydrogen leads to a reduction of the grain boundary energy [3]. Therefore, our experimental findings of accelerated grain growth could only be explained by a hydrogen-induced increase of grain boundary mobility which overcompensates for the reduction in driving force. The presence of solute atoms, such as carbon or nitrogen, usually results in a reduction in grain growth. This is attributed to solutes reducing the energy of the grain boundaries [3,13]. However, similarly to how kink-pair nucleation can be the rate-limiting step in dislocation motion [20], step or ledge formation may be a rate-limiting step for grain boundary motion. The formation of this step requires the formation of new grain boundary area, and the presence of solutes may lower this formation energy based on the thermodynamic defactant concept [13]. Note that for the segregation of hydrogen to ledges, a smaller amount of hydrogen is required than for covering the whole grain boundary. Thus reducing the formation energy of ledges may occur at lower hydrogen concentrations leading to a higher rate of ledge nucleation with a concomitant increase in grain boundary mobility. In other words, although the presence of hydrogen reduces the driving force for grain boundary motion, the increases in mobility due to a higher frequency of ledge formation will be dominant. Typically, solute presence is associated with a drag effect on boundary mobility [5]. Besides step or ledge formation, the motion of steps along the boundary leading to a positional move of the whole boundary may be affected by these drag or frictional forces due to the presence of hydrogen. The interplay between step formation and step motion is analogous to that in the formation and motion of kink-pairs in dislocations, which leads to enhanced dislocation mobility at low H-concentration and reduced mobility at high concentrations [20]. Thus, the plateau in grain growth behavior at high hydrogen concentrations observed in this study may be due to similar compensation of the hydrogen effects on
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Fig. 5. Grain growth as a function of time. Samples heated at 700 C in vacuum (open square) or in 1 Pa H2 (filled circle). Grain growth calculated as the difference between the square of the final average diameter and the square of the initial grain size (d2f d2i ). b) shows same data plotted on log-log scale, with two straight lines representing parabolic grain growth.
boundary step formation and motion, where the increased formation rate of steps is no longer dominant at high H-concentrations due to an increased solute drag on moving steps. In the previous argument, all solute atoms, whether carbon, nitrogen or hydrogen, have been treated equally, so it would be expected that all would show similar behavior, which has generally been reduction in grain boundary motion. But, hydrogen appears to have the opposite effect. This difference in behavior may be due to the difference in diffusion coefficients. Even at the high temperatures needed for grain growth, the diffusivity of hydrogen is still several orders of magnitude higher than that of larger interstitial solutes [21]. While the larger solutes may be mobile at these temperatures, they are likely to be slow enough to cause a solute drag effect on grain boundaries and/or their steps. However, hydrogen itself with its high mobility may not be creating solute drag on either the whole boundary or the ledges, though by itself, this higher mobility is more likely to result in comparable rates of growth in hydrogen and in its absence, not result in an acceleration. Another potential difference between hydrogen and other solutes could be the chemical interactions that are possible with the material. Shvindlerman and Gottstein suggested an acceleration effect occurring by the removal of impurities from the grain boundary by the formation of precipitates [22]. In the present case, the removal of oxygen from grain boundaries by reaction with hydrogen could have a similar effect. Whether hydrogen could be reducing vanadium oxide that may be present at the grain boundaries is elucidated in the following by considering the reaction:
V þ H2 O 4VO þ H2 :
(1)
If the system is at equilibrium, the sum of the chemical potentials would be zero, leading to the relationship:
PH2 ¼ m0V m0VO þ m0H2 O m0H2 RT ln PH2 O
(2)
Using values from Lange [23], the ratio of PH2 P was calcuH2 O 10 lated to be on the order of 10 , suggesting that the oxide is stable in the presence of hydrogen. Therefore, it is unlikely that hydrogen is removing any other components (either precipitates or solutes) that may be obstructing grain boundary motion. It is important to note that the native oxide on the surface of the samples will be dissolved at temperatures above 400 C, according to the V-O phase
diagram [17]. The disappearance of the native oxide layer is required for hydrogen to be dissociated and absorbed by the samples. Another difference from other solutes is that hydrogen has been found to increase the number of vacancies found at equilibrium in metals [15,24e27]. This has been attributed to hydrogen decreasing the formation energy of vacancies, explained on thermodynamic grounds within the defactant concept [13]. A rate-limiting step in grain growth may be the accommodation of the free volume created by the elimination of grain boundaries, which is often thought to occur through the generation and migration of vacancies [6,10,28,29]. A consequence of this accommodation is that it could lead to a nonequilibrium supersaturation of vacancies, as suggested by the presence of defects such as stacking fault tetrahedra after grain growth [30], which could result in a thermodynamic force on the boundary, slowing grain boundary motion [6,28]. Estrin et al. posited that, in nanocrystalline materials, this force could be as effective as solute drag in inhibiting grain boundary motion [10]. Hydrogen, by reducing the formation energy of vacancies and stabilizing them, allows more free volume to be accommodated more easily, reducing the force against grain boundary motion. Additionally, many early studies, summarized in Ref. [5], found that grain boundary mobility increased with increasing vacancy concentration, with the rationale that it was easier for grain boundaries to restructure as needed for migration when more vacancies were available. Thus, the increased availability of vacancies due to the presence of hydrogen, both ahead of and behind the grain boundaries, may help increase mobility. It is likely that it is a combination of the factors mentioned above that contributes to hydrogen enhancing grain growth. The increase in grain boundary mobility and the ability to accommodate the free volume from the grain boundaries seems to predominate over the reduction in the driving force for grain growth due to the presence of hydrogen. The importance of one factor over another, such as grain boundary mobility compared to free volume accommodation, may be suggested by the presence of abnormal grain growth at shorter time periods. The occurrence of abnormal grain growth resulting in a bimodal grain size distribution in these experiments is perhaps not surprising, given the nanocrystalline structure of the material [18,30,31]. Though, it is interesting that the phenomenon is more prominent in the presence of hydrogen and is not noticeable in its absence, under the conditions examined. Previous studies have
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shown a dependence of abnormal grain growth on the film texture [32], though that should not have been a factor here, as the compared films were prepared under identical conditions. However, the idea that texture has a role may be related to an associated feature: the grain boundary types produced. Different grain boundaries types will have different structures, and have been shown to have different properties, for example, differences in passivity [33]. Accordingly, these different boundary types will likely trap hydrogen to different extents; likely resulting in different grain boundaries having different mobilities, especially in the presence of hydrogen [3,34,35]. This suggests that on short time scales, or with smaller grains, grain boundary mobility and its changes by hydrogen is a more dominant factor. More information is needed in this area, and the grain boundary character of the different grains is a subject for further study. Further evidence of the importance of grain boundary mobility may be seen in the higher pressure experimental results. While the exact hydrogen concentration at the grain boundaries is unknown, it is reasonable to assume that at a certain bulk concentration, the grain boundaries will saturate, and increasing bulk hydrogen content will have limited effect on the grain boundary mobility. At the same time, increasing the hydrogen concentration should increase the concentration of vacancies that can be accommodated at equilibrium, which is proposed to increase the overall mobility. While further study is needed to carefully define these regimes, as the grain growth rate appears to become independent of hydrogen pressure at higher pressures (Fig. 3), it suggests that the increase in vacancy accommodation is insufficient to produce further grain growth acceleration. Experimental results after long annealing times reveal a stagnation of grain growth. This may be due to grain sizes reaching the size of the thickness of the thin TEM samples. Alternatively, another factor which will come into play at larger grain sizes is that, independent of the rate-controlling processes, either ledge or vacancy formation, the moving grain boundary will collect impurities which are immobile at the annealing temperature. With increasing impurity segregation, the boundary mobility decreases due to solute drag and/or the driving force decreases due to reduced boundary energy. Within the concept of vacancy generation during grain growth, a stagnation of growth could be attributed to an oversaturation of vacancies counteracting any further vacancy generation. Further grain growth then requires the annihilation of vacancies at the surface and/or by sinks within the grains, like dislocations or stacking faults. If the efficiency of these sinks is reduced, oversaturation of vacancies within the grains will counteract grain boundary annihilation, or grain growth, respectively. With surfaces being very effective sinks for vacancies however, this scenario for stagnation of grain growth at high hydrogen pressures and long annealing times appears to be less likely. While further experiments are needed to fully explore the factors influencing the processes, the results presented here suggest that hydrogen increases the rate of grain growth in nanocrystalline vanadium thin films by 1. Increasing the grain boundary mobility, proposed to be due to a decrease in the formation energy of grain boundary steps, and 2. Easing accommodation of free volume created by the decrease in grain boundary volume due to lowering the formation energy of vacancies in the presence of hydrogen. Comparison of short time/small grain results with long time/ high hydrogen/large grain results, suggests that the increase in grain boundary mobility may be more important during the former conditions.
5. Conclusion The addition of hydrogen during the heating of nanocrystalline vanadium thin films resulted in substantial grain growth compared to in vacuum. This acceleration in grain growth increased with increasing hydrogen content, then stabilized at high hydrogen content. While the presence of hydrogen likely reduced the driving force for grain boundary motion by reducing grain boundary energy or increasing solute drag, it is proposed that it increased grain boundary mobility, i.e. by decreasing the formation energy of steps. Additionally, hydrogen could be reducing the barrier for grain boundary motion by lowering the formation energy of vacancies, allowing free volume to be accommodated more easily. More experiments and/or simulations are required to distinguish between the two scenarios. The results will not only shed light on the observed effect of hydrogen on grain boundary mobility but may allow a deeper insight into atomistic processes leading to grain boundary motion. Acknowledgements The Alexander von Humboldt foundation and the Heisenberg program of the Deutsche Forschungsgemeinschaft (project PU131/ 9-2) are gratefully acknowledged for funding of this project. References [1] J. Weissmüller, Alloy effects in nanostructures, Nanostruct. Mater. 3 (1) (1993) 261e272. [2] C.C. Koch, The synthesis and structure of nanocrystalline materials produced by mechanical attrition: a review, Nanostruct. Mater. 2 (2) (1993) 109e129. [3] R. Kirchheim, Grain coarsening inhibited by solute segregation, Acta Mater. 50 (2) (2002) 413e419. [4] F. Liu, R. Kirchheim, Comparison between kinetic and thermodynamic effects on grain growth, Thin Solid Films 466 (1e2) (2004) 108e113. [5] C.J. Simpson, W.C. Winegard, K.T. Aust, Grain boundary mobility and boundary solute interactions, in: G.A. Chadwick, D.A. Smith (Eds.), Grain Boundary Structure and Properties, Academic Press, 1976, pp. 201e234. [6] L.S. Shvindlerman, G. Gottstein, Cornerstones of grain structure evolution and stability: vacancies, boundaries, triple junctions, J. Mater. Sci. 40 (4) (2005) 819e839. [7] D.A. Molodov, U. Czubayko, G. Gottstein, L.S. Shvindlerman, On the effect of purity and orientation on grain boundary motion, Acta Mater. 46 (2) (1998) 553e564. [8] E. Rabkin, On the grain size dependent solute and particle drag, Scripta Mater. 42 (12) (2000) 1199e1206. [9] V.Y. Novikov, Grain growth in nanocrystalline materials, Mater. Lett. 159 (2015) 510e513. [10] Y. Estrin, G. Gottstein, E. Rabkin, L.S. Shvindlerman, On the kinetics of grain growth inhibited by vacancy generation, Scripta Mater. 43 (2) (2000) 141e147. [11] R. Kirchheim, Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation. I. Theoretical background, Acta Mater. 55 (15) (2007) 5129e5138. [12] R. Kirchheim, Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation: II. Experimental evidence and consequences, Acta Mater. 55 (15) (2007) 5139e5148. [13] R. Kirchheim, On the solute-defect interaction in the framework of a defactant concept, Int. J. Mater. Res. 100 (4) (2009) 483e487. [14] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. DeLeo, S.K. Estreicher, E.E. Haller, P. Jena, N.M. Johnson, R. Kirchheim, S.J. Pearton, M.J. Stavola, Hydrogen interactions with defects in crystalline solids, Rev. Mod. Phys. 64 (2) (1992) 559e617. [15] Y. Fukai, Superabundant vacancies formed in metalehydrogen alloys, Phys. Scripta 2003 (T103) (2003) 11. [16] C.J. McMahon Jr., Hydrogen-induced intergranular fracture of steels, Eng. Fract. Mech. 68 (6) (2001) 773e788. [17] E. Fromm, E. Gebhardt, Gase und Kohlenstoff in Metallen, Springer-Verlag Berlin Heidelberg, 1976. [18] C.V. Thompson, Grain growth in thin films, Annu. Rev. Mater. Sci. 20 (1) (1990) 245e268. [19] K. Verbeken, M.D. Nave, L. Kestens, M.R. Barnett, Selective growth in a scratched Fe-2.8%Si single crystal, THERMEC'2003, in: International Conference on Processing and Manufacturing of Advanced Materials, 7-11 July 2003, Trans Tech Publications, Switzerland, 2003, pp. 3757e3762. [20] R. Kirchheim, Solid solution softening and hardening by mobile solute atoms
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