Hydrogen embrittlement of a carbon segregated Σ5(310)[001] symmetrical tilt grain boundary in α-Fe

Author's Accepted Manuscript

Hydrogen embrittlement of a carbon segregated Σ5ð310Þ½001 symmetrical tilt grain boundary in α-Fe A.M. Tahir, R. Janisch, A. Hartmaier

www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(14)00788-6 http://dx.doi.org/10.1016/j.msea.2014.06.071 MSA31271

To appear in:

Materials Science & Engineering A

Received date: 11 April 2014 Revised date: 17 June 2014 Accepted date: 18 June 2014 Cite this article as: A.M. Tahir, R. Janisch, A. Hartmaier, Hydrogen embrittlement of a carbon segregated Σ5ð310Þ½001 symmetrical tilt grain boundary in α-Fe, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2014.06.071 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Hydrogen embrittlement of a carbon segregated Σ5(310)[001] symmetrical tilt grain boundary in α-Fe A M Tahir, R Janisch and A Hartmaier Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universit¨at Bochum, 44780 Bochum, Germany E-mail: [email protected] Abstract. The physical and mechanical properties of a Σ5(310)[001] symmetrical tilt grain boundary (STGB) in body centred cubic (bcc) Fe are investigated by means of ab-initio calculations with respect to the effect of a varying number of C and H atoms at the grain boundary. The obtained results show that with increasing number of C atoms the grain boundary energy is lowered, and the segregation energy remains negative up to a full coverage of the grain boundary with C. Thus, in a bcc Fe-C system with a sufficient amount of interstitial C, the C segregated state should be considered as the ground state of this interface. Ab-initio uni-axial tensile tests of the grain boundary reveal that the work of separation as well as the theoretical strength of the Σ5(310)[001] STGB increase significantly with increasing C content. The improved cohesion due to C is mainly a chemical effect, but the mechanical contribution is also cohesion enhancing. The presence of hydrogen changes the cohesion enhancing mechanical contribution of C to an embrittling contribution, and also reduces the beneficial chemical contribution to the cohesion. When hydrogen is present together with C at the grain boundary, the reduction in strength amounts to almost 20% for the co-segregated case and to more than 25% if C is completely replaced by H. Compared to the strength of the STGB in pure iron, however, the influence of H is negligible. Hence, H embrittlement can only be understood in the three component Fe-C-H system.

PACS numbers: 61.72Mm,62.20mm,68.35Gy

Hydrogen embrittlement of a C segregated grain boundary in Fe

2

1. Introduction The phenomenon of hydrogen embrittlement of metals and alloys is well known and has been investigated for almost 150 years [1], but the underlying mechanisms and their interdependencies are still not well understood. This is partly due to the fact that there is a strong dependency not only on the composition and microstructure of the material, but also on the in-service conditions. Furthermore, H is rather volatile and difficult to detect post-mortem. The main mechanisms that have been identified so far, and which have a different share in different fracture modes in different materials, are hydride formation and fracture, H-vacancy interactions, hydrogen enhanced decohesion (HEDE), hydrogen enhanced localised plasticity (HELP), and adsorption induced dislocation emission (AIDE). For recent reviews of these mechanisms and their experimental evidence see e.g. [2, 3, 4]. Ab-initio total energy and electronic structure calculations, as well as molecular dynamics (MD) simulations employing classical potentials provide a unique way to investigate fundamental mechanisms of H interaction with different elements of typical steel microstructures. In contrast to experimental studies, such simulations allow to isolate specific effects and mechanisms. For instance Song and Curtin [5] recently identified a ductile-to-brittle transition during crack propagation in Fe, which is caused by the suppression of dislocation emission at the crack tip due to aggregation of H. However, such MD simulations are still rare, due to the limited transferrability of the available potentials. Ab-initio calculations serve to quantify the interaction of H with vacancies [6, 7, 8, 9, 10, 11] and other point defects (alloying elements) [6, 7, 12]. The results reveal that, while the H-H interaction itself is weak [7] a vacancy in body-centered cubic [7, 9] as well as face centred cubic iron [10] can bind up to six H atoms depending on the reference chemical potential. Also several metal alloying elements have a negative binding energy to H [6, 12]. The trapping potential of these defects is an important input for hydrogen diffusion models for realistic microstructures [13]. The influence of H on the elastic constants of bcc iron obtained from ab-initio calculations [14] show a linear decrease with increasing H content, which supports the picture that the HELP mechanism is based on a shielding of stress fields of obstacles for dislocations. Itakura et al. [15] investigated the effect of H atoms on the kink pair nucleation energy of screw dislocations by combining the ab-initio interaction energy of H with a straight screw dislocation with a line tension model. Their results show that an increase of dislocation mobility by an enhanced kink-formation can be expected at low temperatures and high H concentrations, but in a limited range of applied shear stresses. The HEDE mechanism is expected to be most relevant at grain boundaries and interfaces, where H is trapped, but distributed along a crystallographic plane. Across these planes, H is expected to weaken the ineratomic bonds due to charge transfer from the host metal to the H impurity atom. H has a negative formation energy at the Σ 5

Hydrogen embrittlement of a C segregated grain boundary in Fe

3

grain boundary in TiFe [16], as well as at different grain boundaries in bcc and fcc Fe [17]. The reduction of the work of separation of single crystal cleavage planes [18] as well as several grain boundaries [17, 19, 20] in Fe in the presence of H has been shown in several studies, and this effect can be increased by co-segregation of alloying elements (Mo, V, Pd) [19]. However, as pointed out in Momida et al. [21] and Tahir et al. [22], it is the tensile strength rather than the work of separation which determines the probability of a crack to propagate along a grain boundary. Interestingly, Momida et al. observe that H alone has a negligible effect on the tensile strength of different Σ3 grain boundaries, but enhances vacancy embrittlement by forming vacancy-H2 complexes, leading to a reduction in strength by 35%. We investigate the HEDE mechanism at a Σ5 (310)[001] 36.9◦ symmetrical tilt grain boundary (STGB) in bcc Fe, taking into account the co-segregation of the most important alloying element C. As we have learned from a previous study of C solubility in Fe [23], C is only soluble in ferrite under strain, and we expect a pronounced segregation behaviour of C to defects. Indeed it has been observed both theoretically [24] and experimentally [25] that excess C segregates towards the grain boundaries present in the microstructure of steels. This phenomenon is beneficial for steels because C is known to be a cohesion enhancing element in bcc metals when present at the grain boundaries [26, 27, 28, 29]. In the work at hand, we investigate the consequences of cosegregation of H on work of separation and strength. Cohesion enhancing/embrittling effects are analyzed by splitting them into a chemical contribution and a mechanical contribution following the approach of Geng et al. [30, 31] (see section 2.), as well as by investigating the electronic structure at the interface. The paper is organized as follows: In section 2 the computational procedure, the grain boundary structure and the way of calculating the defining properties are summarized. In section 3, our results for the effect of C and H on the energy of the grain boundary, the segregation energy, the work of separation and the theoretical strength are presented. In the same section, the difference of charge distribution and density of states due to the presence of impurity atoms are shown and explained in detail. In section 3.3, the results for the grain boundary with same number but different type of impurity atoms are compared, and the effect of hydrogen embrittlement is explained. Finally the observations and findings are concluded and summarized in section 4. 2. Technical details The software used for ab-initio density functional theory (DFT) calculations was the Vienna ab-initio simulation package (VASP) [32, 33, 34]. The exchange-correlation effects were approximated within the generalized gradient approximation (GGA) and the projector augmented-wave (PAW) method [35] was used to describe the core-valence interaction. We used the functionals presented by Perdew, Burke and Ernzerhof in 1996 [36]. The ferro-magnetism of bcc Fe was treated in a scaler-relativistic fashion by carrying out spin-polarized calculations. A Σ5(310)[001] STGB was constructed using

Hydrogen embrittlement of a C segregated grain boundary in Fe

4

an orthorhombic primitive 80-atoms super-cell as shown in figure 1 (big blue atoms). The details of constructing such a grain boundary supercell and the nomenclature used can be found in our previous work [22]. In this supercell, the periodic images of the grain boundaries are separated by 10 layers of Fe atoms. The convergence of results w.r.t. the cell size was investigated by comparing the interplanar spacing in a grain boundary supercell and a bulk supercell. The comparison showed that as one moves away from the grain boundary and reaches at the fifth layer, the interplanar spacing in the grain boundary supercell and the bulk supercell match, i.e. in the center of the grain, bulk like conditions are obtained. The cut-off energy used during the calculations was 400 eV and a k-point mesh of Monkhorst-Pack type [37] used for the orthorhombic primitive 80-atoms grain boundary super-cell was 8×4×2. In such a supercell, it is

Figure 1. (a) Structure of Σ5(310)[001] STGB. Big (blue) atoms represent the Fe atoms, small (green) atoms are C atoms and smaller (red) atoms are H atom present at the two grain boundaries in this super-cell structure. Due to periodicity we see the GB#2 twice in this super-cell structure. (b) The grain boundary plane having full monolayer of C atoms as well as with 2 H atoms + 1 C atom is also shown (c) (colour online).

possible to place a maximum number of 4 impurity atoms per grain boundary in the structural unit that is the most favourable one [31], as shown in figure 1 by the small green atoms (the extra atom in figure 1b is due to the periodic boundary conditions). The grain boundary plane in the co-doping case is shown in figure 1c as well, with 2 H atoms and 1 C atom at the grain boundary. After obtaining the stable grain boundary configurations by performing rigid grain shifts in all the three directions of the grain boundary supercell and subsequent relaxation of atomic positions, the energy of the grain boundary γGB was calculated using the relation: Fe+nX Fe − EBulk − nμX EGB . (1) γGB = 2A Fe+nX Where EGB is the total energy of the grain boundary supercell containing a certain Fe number n of impurity atoms X, EBulk is the energy of the same number of Fe atoms in bulk environment, nμX is the reference energy of the same number of impurity atoms as at the grain boundary, and 2A represents the total area of the grain boundary in the supercell. The reference energy of C in the diamond phase is -9.12eV /atom and that of

Hydrogen embrittlement of a C segregated grain boundary in Fe

5

hydrogen in a H2 molecule is -6.77eV /atom. The segregation energy of impurity atoms towards the grain boundary can be obtained by considering the difference of solution GB Bulk and in the bulk Esol energy of impurity atoms in the grain boundary supercells Esol using the relation: Fe+(n−2)X

GB/Bulk Esol

Fe+nX EGB/Bulk − EGB/Bulk

− 2μX

, 2A here n can be 2, 4, 6 or 8. The segregation energy γseg will then be given by: =

GB Bulk − Esol γseg = Esol

.

(2)

(3)

A negative value of γseg means that the impurity atoms will segregate to the grain boundary. Ab-initio uni-axial tensile and compression tests were performed on the different grain boundary supercells by dividing them into two grains and separating them parallel to the [310] direction. Note that to avoid a free standing grain boundary layer for large displacements, the separation is performed by localising the strain in an asymmetric fashion between the grain boundary layer and one adjacent grain. More details can be found in our previous work [22]. The energy-displacement data was obtained and the work required to separate the two surfaces, i.e. the work of separation (WoS), was determined according to, FS+(n/2)X

WoS =

2 · Etot

Fe+nX − EGB

2A

.

(4)

FS+(n/2)X

Where Etot is the energy of free surface slab with equilibrium partitioning of impurity atoms on the two surfaces on the respective grain boundary. This distribution of impurity atoms was found to be favourable in our previous work [22]. According to Geng et al. [30, 31], the WoS which is also considered as the binding energy can be split into two parts i.e. a chemical contribution EBc which explains the interaction of the impurity atom with the host metal atoms and a mechanical contribution EBm that characterises the relaxation of metal lattice to accommodate the impurity atoms. The EBc is the difference between the WoS of a relaxed grain boundary structure with impurity atom(s) and the same grain boundary in which the impurity atom(s) is (are) removed without any subsequent relaxation of the atomic positions:  EBc = WoSX Relaxed − WoSRigid

.

(5)

Here  represents the vacant interstitial site(s) at the grain boundary which was (were) previously occupied by impurity atom(s) represent by X. For the calculation of WoS Rigid , m one can assume  instead of X in equation (4). EB can then be obtained by difference of WoS Rigid and the WoS of a pure relaxed grain boundary i.e. pure GB EBm = WoS Rigid − WoSRelaxed

.

(6)

As described in detail in [22], the energy-displacement data can be fitted using the universal binding energy relationship [38]. From the energy-displacement data, the

Hydrogen embrittlement of a C segregated grain boundary in Fe

6

theoretical strength σth of the interface can be calculated as the slope at the inflection point,  dE  σth = (7) dΔ E  (Δ)=0 where Δ is the displacement from the equilibrium inter-planar distance [39]. 3. Results 3.1. Grain boundary energy and segregation energy for Fe-C and Fe-H The energy of the fully relaxed grain boundary structures was calculated using equation (1) as function of the number of impurity atoms. As can be seen in figure 2a (filled squares) and table 1, the energy of the grain boundary decreases by more than 60% when a full monolayer of C is formed at the grain boundary. This indicates that the grain boundary is attractive for segregation of C atoms. The presence of H at the grain boundary also lowers its energy (filled circles in figure 2a and table 2) but the decrease is not as significant as it is the case for C. In addition to the grain boundary energy, the gradual segregation energy of impurity atoms at the grain boundary with reference to the bulk was calculated from the difference of solution energy of impurity atoms in the grain boundary and bulk using equations (2) and (3). The segregation energies are also plotted in figure 2a (open squares for C and open circles for H) and tabulated in table 1 for C and table 2 for H. The results show that the segregation energy remains negative throughout the concentration range investigated during the present work. Especially for C, which is always present in steel, this means that the ground state of the grain boundary should be considered to be the one where, proportional to the available amount of interstitial C, most of the possible segregation sites are occupied with C. 3.2. Work of separation and theoretical strength for Fe-C and Fe-H Based on the fully relaxed structures, we performed ab-inito tensile tests as described in section 2. The results are summarised in figure 2b and tables 1 and 2. For the case of C segregation, the work of separation increases up to ∼15% compared to the pure Fe STGB. Furthemore a significant increase of more than 50% in the theoretical strength value is observed. The difference of charge distribution in the vicinity of the grain boundary structural unit is plotted in figure 3 (left). In the plot, atom#1 and atom#5 belong to one grain, and atom#3 and atom#4 belong to the opposite grain. Fe atom#2 is the metal atom right at the grain boundary. We can observe that the C atom is sitting almost in the center of Fe atoms forming a grain boundary structural unit. Secondly the obtained plot shows a blue ring of charge accumulation between the C atom and all the neighboring Fe atoms. In addition to the charge distribution plot, the site-projected density of states (DoS) of the closest metal atom present in the adjacent layer to the grain boundary, atom#5 at a distance of 2.09˚ A is shown in figure 3 (right), where the spin up d-states of an atom in the bulk

Hydrogen embrittlement of a C segregated grain boundary in Fe

1.2

-0.2

seg [J/m2]

0.0

GB [J/m2]

1.6

GB (C) 0.8

7

-0.4

GB (H) seg (C) seg (H)

0.4

0

1

2

3

4

-0.6

No. of impurity atoms/GB

Figure 2. (a) Grain boundary and segregation energy with reference to the bulk as a function of number of C and H atoms at the grain boundary.(b) Effect of C and H on the work of separation and the theoretical strength.

region is compared with that of the atom in the pure grain boundary and C containing grain boundary atom’s d-states along with the p-states of the C atoms. Compared to the bulk (black), we can observe a very slight shift of the lower edge of the d valence band towards higher energies for an atom next to the grain boundary (red). When the same atom near the grain boundary has a C atom in its vicinity (blue line), split-off states are observed which overlap with the C p-states (green line) at the bottom of d-band. This common band between the C atom and the Fe atom results in the increased cohesion and strength (see inset in figure 3 (right) for magnified view). For the case of H segregation the work of separation at full coverage is reduced only by ∼6% compared to pure Fe, and in the theoretical strength (open circles in figure 2b) even a small increase of ≤10% is observed. Hence, in contrast to our initial assumption that H weakens the Fe-Fe bond, but in agreement with the calculations of Momida et al. [21], it can be concluded that H alone at grain boundaries in Fe shows a negligible effect on cohesion. However, when comparing the strength of the H-covered grain boundary with that of a grain boundary with a monolayer of C, a reduction of the WoS by 18% and in strength by 25% is observed. The difference of charge distribution in the presence of H as an impurity atom can

Hydrogen embrittlement of a C segregated grain boundary in Fe

8

Table 1. Energy of grain boundary (γGB ), segregation energy (γseg ), the work of separation (WoS), and theoretical strength (σth ) of the Σ5 STGB in Fe with different numbers of C atoms at the grain boundary.

Pure Fe STGB Fe STGB with 1C Fe STGB with 2C Fe STGB with 3C Fe STGB with 4C

atom atoms atoms atoms

γGB [J/m2 ]

γseg [J/m2 ]

WoS [J/m2 ]

σth [GPa]

1.55 1.25 0.90 0.73 0.58

-0.47 -0.55 -0.35 -0.44

3.50 3.67 3.88 3.94 4.00

23.2 25.9 30.0 32.8 36.2

Table 2. Energy of grain boundary (γGB ), segregation energy (γseg ), the work of separation (WoS), and theoretical strength (σth ) of the Σ5 STGB in Fe with different numbers of H atoms at the grain boundary.

Pure Fe STGB Fe STGB with 1H Fe STGB with 2H Fe STGB with 3H Fe STGB with 4H

atom atoms atoms atoms

γGB [J/m2 ]

γseg [J/m2 ]

WoS [J/m2 ]

σth [GPa]

1.55 1.49 1.42 1.34 1.27

-0.14 -0.13 -0.13 -0.13

3.50 3.44 3.39 3.35 3.30

23.2 23.6 24.1 24.3 25.3

be seen in figure 4 (left). The H atom is not in the centre of the structural unit, but shifted more towards atom#2 which is the grain boundary atom. A similar behaviour was found for H in vacancies [40], where H also prefers an off-centred site. It can be explained by the charge density distribution in vacancies, which according to effective medium theory are below the optimum for H in the centre [41]. In figure 4 we see that charge has accumulated in between the H and the closest Fe atom in the grain boundary plane, but not between H and a neighbour out of the plane. The site-projected DoS of atom#1 which has the shortest distance of 1.97˚ A to the H is shown in figure 4 (right). No considerable difference in the Fe d-state with and without H at the grain boundary is evident from the plot. Due to the H s-states, a small peak at around -7eV can be observed but these H s-states are separated by a gap from the Fe d-states. A slight charge transfer from Fe to H can be expected, with only little effect on the Fe-Fe bond strength. 3.3. Co-segregation effects In order to investigate the effect of co-doping of both C and H on the mechanical properties of the Σ5 STGB, a grain boundary supercell with 2 H and 1 C atom per grain boundary (forming 3/4th of a monolayer) was constructed. Again, the structure was fully optimised and subsequently an ab-initio tensile test was carried out. The

Hydrogen embrittlement of a C segregated grain boundary in Fe

9

Figure 3. (Left) The difference of charge density distribution due to the presence of C atom at the structural unit defining the grain boundary. (Right) Partial spin-up d-states of Fe atom#5 in bulk (black line), near pure STGB (red line), near carburized STGB (blue line) and p-states of C atom (green line) at the grain boundary.

Figure 4. (Left) The difference of charge density distribution due to the presence of H atom at the structural unit defining the grain boundary. (Right) Partial spin-up d-states of Fe atom#1 in bulk (black line), near pure STGB (red line), near STGB with H (blue line) and s-states of H atom (green line) at the grain boundary.

obtained results for grain boundary energy, work of separation, and tensile strength can be seen in table 3 and figure 5 along with a repetition of the respective properties for the cases of 3 C or 3 H atoms alone at the grain boundary. The energy of the co-doped grain boundary is higher than that of the C doped grain boundary, but still lower than that of the H doped grain boundary and the pure grain boundary (table 1). The segregation energy of 2 H atoms to the grain boundary having a C atom already present is lower than that of both the purely C and purely H doped grain boundaries, showing that such a segregation would be even more favorable. The presence of 2 H atoms along with 1 C atom decreases the work of separation by ∼10% and the theoretical strength by ∼18% when comparing it with the grain boundary having 3 C atoms (table 3), showing the embrittling nature of hydrogen. However, a single C atom along with 2 H atoms still tends to maintain its cohesion enhancing effect when comparing this case with the one of only 3 H atoms as shown in figure 5. Based on our electronic structure results, it can be speculated that the embrittling nature of hydrogen is due to elastic distortions in the structure rather than due to a weakening effect on the chemical bonds. In order to investigate this in detail, the approach of Geng et al. [30] (see section 2) was followed to distinguish between the

10

Hydrogen embrittlement of a C segregated grain boundary in Fe

Table 3. Comparison of energy of grain boundary (γGB ), segregation energy (γseg ), the work of separation (WoS), and theoretical strength (σth ) of Σ5 STGB in Fe having 3 C atoms, 3 H atoms and a co-doped grain boundary having 2 H and 1 C atom as impurities per grain boundary.

Fe STGB with 3C atoms Fe STGB with 3H atoms Fe STGB with 2H1C atoms

γGB [J/m2 ]

γseg [J/m2 ]

WoS [J/m2 ]

σth [GPa]

0.73 1.34 1.08

-0.35 -0.13 -0.45

3.94 3.35 3.59

32.8 24.3 26.8

Figure 5. Comparison of γGB , γseg , WoS and σth of Σ5 STGB in Fe having 3 C atoms, 3 H atoms and a co-doped grain boundary having 2 H and 1 C atom as impurities per grain boundary. Table 4. Splitting of the difference of WoS of a pure and impurity containing grain m c ) and chemical contribution (EB ) following boundary into mechanical contribution (EB the approach of Geng at al. [30].

Fe STGB with 3C atoms Fe STGB with 2H1C atoms

ΔWoS [J/m2 ]

m EB [J/m2 ]

c EB [J/m2 ]

0.44 0.09

0.04 -0.03

0.40 0.12

chemical contribution and the mechanical contribution of an impurity atom on the change in the WoS of a certain grain boundary. The obtained results can be seen in table 4. When C is present at the grain boundary as an impurity atom, the major part of the favourable contribution to the work of separation is the chemical one, and the mechanical one is also beneficial, but smaller in comparison. When both H and C atoms are present as impurities at the grain boundary, the WoS is still increased slightly with respect to pure iron, but reduced significantly with respect to the fully C covered grain boundary. This reduction is mainly caused by the now detrimental mechanical contribution, which we attribute to the 2 H atoms. The single C atom still maintains a positive value of the chemical contribution. Nevertheless, in total hydrogen weakens the cohesion of the grain boundary.

Hydrogen embrittlement of a C segregated grain boundary in Fe

11

Our results reveal a new aspect of the HEDE mechanism at grain boundaries in steels. In contrast to the initial definition given in the introduction, we do not find a reduced Fe-Fe bond strength, but - at least at the Σ5 grain boundary - the embrittling effect is due to the substitution of a cohesion enhancing element by H. Note however, that crack propagation along such a co-segregated grain boundary will not only be influenced by the reduced strength of the interface, but also by the change in mobility of grain boundary dislocations, as well as in the stress which is needed to emit a dislocation from the crack tip. Thus there will always be an interplay between the HEDE and the HELP mechanism. 4. Summary and Conclusions Ab-initio density functional theory calculations have been performed to investigate the physical and mechanical properties of a special grain boundary in α-Fe with a systematic increase in the number of C and H atoms as impurities at the interface, up to a full monolayer coverage. It has been observed that good mechanical strength of steels can partly be understood from the grain boundary strengthening due to C. We conclude from the immense reduction of the grain boundary energy and the negative segregation energy that in any Fe-C alloy with a sufficient amount of interstitial C, the C segregated state should be considered as the ground state of the interface. From this point of view, the HEDE mechanism at this grain boundary can be understood. The work of separation shows an increase of ∼15% and the theoretical strength an increase of ∼50% at a full monolayer coverage with C atoms at the grain boundary. From the overall beneficial contribution of C, 90% is due to the chemical contribution while 10% is an elastic contribution. The charge density difference shows an accumulation of charge between C and the neighboring Fe atoms, which illustrates the reason for the improved strength properties that can be seen in the DoS, a hybridization of Fe d-states and C p-states. In case of H, the work of separation shows a decrease of ∼6% compared to the pure Fe STGB, while the theoretical strength remains almost constant. In the presence of H in the grain boundary structural unit, the distribution of charge density difference shows a localization of charge between H atom and the metal atom present at the grain boundary. The DoS indicates a slight charge transfer between s-states without any overlapping of bands and hence no significant effect on the strength of the grain boundary. The co-doping study of C and H as impurities shows the HEDE mechanism at this grain boundary is the replacement of a cohesion enhancing element by H. We observed a 18% decrease in the work of separation and a 15% decrease in the strength value compared to the C-segregated grain boundary. This embrittling effect of H atoms is due to their detrimental mechanical contribution and a decrease of the beneficial chemical contribution of C atoms. This effect can probably be much more pronounced if more than one H atom is dissolved per segregation site at the grain boundary, which is a topic

Hydrogen embrittlement of a C segregated grain boundary in Fe

12

for future studies. Acknowledgments A. T. acknowledges financial support through the German Research Foundation (DFG grant number JA-1079/4). This work has been carried out at ICAMS. ICAMS is supported through Thyssen Krupp AG, Bayer Material Science AG, Salzgitter Mannesmann Forschung GmbH, Robert Bosch GmbH, Benteler Stahl/Rohr GmbH, Bayer Technology Services GmbH and the state of North-Rhine Westphalia as well as the European Commission in the framework of the European Regional Development Fund (ERDF). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

W. Johnson. Proc. Royal Society of London, 23:168, 1874. Q. Liu and A. Atrens. Corros. Rev., 31:85, 2013. S. Lynch. Corros. Rev., 30:105, 2012. Y. S. Nechaev. Physics - Uspekhi, 51:681, 2008. J. Song and W. A. Curtin. Nature Materials, 12:145, 2012. W. A. Counts, C. Wolverton, and R. Gibala. Acta Mater., 58:4730, 2010. W. Counts, C. Wolverton, and R. Gibala. Acta Mater., 59:5812, 2011. E. Hayward, B. Beeler, and C. Deo. Philos. Mag. Lett., 92:217, 2012. E. Hayward and C.-C. Fu. Phys. Rev. B, 87:174103, 2013. R. Nazarov, T. Hickel, and J. Neugebauer. Phys. Rev. B, 82:224104, 2010. Y. Tateyama and T. Ohno. Phys. Rev. B, 67:174105, 2003. D. Psiachos, T. Hammerschmidt, and R. Drautz. Comp. Mat. Sci., 65:235, 2012. A. Taha and P. Sofronis. Eng. Fracture Mechanics, 68:803, 2001. D. Psiachos, T. Hammerschmidt, and R. Drautz. Acta Mater., 59:4255, 2011. M. Itakura, H. Kaburaki, M. Yamaguchi, and T. Okita. Acta Mater., 61:6857, 2013. S. E. Kulkova, S. S. Kulkov, A. V. Bakulin, S. Hocker, and S. Schmauder. Int. J. Hydrogen Energy, 37:6666, 2012. Y. A. Du, L. Ismer, J. Rogal, T. Hickel, J. Neugebauer, and R. Drautz. Phys. Rev. B, 84:144121, 2011. D. E. Jiang and E. A. Carter. Acta Mater., 52:4801, 2004. Z. X. Tian, J. X. Yan, W. Hao, and W. Xiao. J. Phys.: Condens. Matter, 23:015501, 2011. M. Yamaguchi, J. Kameda, K.-I. Ebihara, M. Itakura, and H. Kaburaki. Philos. Mag., 92:1349, 2012. H. Momida, Y. Asari, Y. Nakamura, Y. Tateyama, and T. Ohno. Phys. Rev. B, 88:144107, 2013. A. M. Tahir, R. Janisch, and A. Hartmaier. Modelling Simul. Mater. Sci. Eng., 21:075005, 2013. E. Hristova, R. Janisch, R. Drautz, and A. Hartmaier. Comp. Mat. Sci, 50:1088, 2011. D. Raabe and D. A. Molodov. Wiley, 2013. J. M. Papazain and D. N. Beshers. Metallurgical Transactions, 2:497, 1971. J. M. Jardin, A. Kokylanski, and C. Goux. C. R. Acad. Sc. Paris, C(280):717, 1975. A. Kumar and B. L. Eyre. Royal Society Publishing, 370(1743):431, 1980. H. Kurishita, A. Oishi, H. Kubo, and H. Yoshinaga. Trans. of Japan institute of metals, 26(5):341, 1985. Y. Hiraoka. Material Trans. JIM, 31(10):861, 1990. W. T. Geng, A. J. Freeman, R. Wu, C. B. Geller, and J. E. Raynolds. Phys. Rev. B, 60:7149, 1999.

Hydrogen embrittlement of a C segregated grain boundary in Fe [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]

R. Janisch and C. Els¨asser. Phys. Rev. B, 67:224101, 2003. G. Kresse and J. Hafner. Phys. Rev. B, 48:13115, 1993. G. Kresse and J. Furthm¨ uller. Comp. Mater. Sci., 6:15, 1996. G. Kresse and J. Furthm¨ uller. Phys. Rev. B, 54:11169, 1996. P. E. Bl¨ochl. Phys. Rev. B, 50:17953, 1994. J. P. Perdew, K. Burke, and M. Ernzerhof. Phys. Rev. Lett., 77:3865, 1996. H. J. Monkhorst and J. D. Pack. Phys. Rev. B, 13:5188, 1976. J. H. Rose, J. R. Smith, and J. Ferrante. Physical Review B, 28:1835, 1983. R. Janisch, N. Ahmed, and A. Hartmaier. Physical Review, B(81):184108, 2010. E. Hayward and C. Deo. J. Phys. : Condens. Matter, 23:425402, 2011. J. K. Norskov and F. Besenbacher. J. Less-Common Metals, 130:474, 1987.

13