Some Advances on Antagonist Effects of Grain Boundaries between the Trapping Process and the Fast Diffusion Path Investigated on Nickel Bicrystals

Hydrogen-grain-boundaries interactions and their role in intergranular fracture are well accepted as one of the key features in understanding hydrogen embrittlement in a large variety of common engineer situations. These interactions implicate some fundamental processes classified as segregation, trapping and diffusion of the solute which can be studied as a function of grain boundary configuration. In the present study, we carried out an extensive analysis of four grain-boundaries based on the complementary of atomistic calculations and experimental data. We demonstrate that elastic deformation has an important contribution on the segregation energy which cannot be simply reduced to a volume change and need to consider the deviatoric part of strain. Additionally, some significant configurations of the segregation energy depend on the long-range elastic distortion and allows to rationalize the elastic contribution in three terms. By investigating the different energy barriers involved to reach all the segregation sites, the antagonist impact of grain boundaries on hydrogen diffusion and trapping process was elucidated. The segregation energy and migration energy are two fundamental parameters in order to classify the grain-boundaries as a trapping location or short circuit for diffusion. selection of grain boundaries. J. Li, A. Oudriss and X. Feaugas characterized the grain boundaries using TEM and SEM/EBSD and the hydrogen states based on TDS measurements. J. Li and M. Hallil conducted the atomistic calculation. X. Feaugas, A. Metsue,A. Oudriss and J. Bouhattate carried out the elastic calculation of stress field and elastic energy and manage this work. All the authors contribute to data interpretation and to manuscript preparation. We clearly established the impact of the geometry and the deformation of hydrogen insertion site on the diffusion path and segregation process along grain-boundaries. The analyses offer the opportunity to clearly precise the trapping process on grain-boundary. A well-defined effect of deviatoric and hydrostatic elastic energies on segregation energy was identified at a short-range scale and additionally significant impact of a long-range elastic distortion observed for some GBs configurations.


Introduction
Hydrogen has a strong tendency to segregate or interact with structural defects as point defects, solid solution species, precipitates, dislocations and internal interfaces (inter-phases, grainboundaries, …). This situation affects the apparent solubility and the mobility of hydrogen and consequently modifies the embrittlement process of metals and their alloys 1 . Many studies 2-6 support the role of hydrogen state in the control of the properties of hydrogenated materials in a large diversity of cases (hydrogen diffusion, hydrogen induced cracking, electrical properties in semiconductors, catalyze …) and more precisely their mechanical behavior (embrittlement itself).
In this context, hydrogen seems to have a larger implication on intergranular fracture [7][8][9][10][11][12][13] . While segregation and diffusion of hydrogen at grain boundaries (GBs) have been of great interest for understanding hydrogen embrittlement (HE), the difficulty of hydrogen analysis at grain boundary scale is the limited number of studies carried out in this subject for nickel alloys (see for a review on the subject references 14,15 ). The interactions of hydrogen with grains and grain boundaries are often treated numerically and experimentally so as to separate with a little confrontation [16][17][18] . Also, at the atomistic scale, there are many works that are rapidly interested in inter-granular decohesion [19][20][21][22][23] in relation to segregation without a precise focus on the elementary process which occurs at the grain boundary. In contrast, the short circuit of diffusion within the grain boundaries remains a remarkable complex subject that would require more in-depth analysis.
There is little available experimental data of the hydrogen segregation for properly defined GBs.
Indeed, adequately characterizing a GB persists to be an engineering challenge, especially the crystallographic orientation and the misorientation angle need to be suitably controlled. For two decades, a large debate was supported by many studies on the possible conflict between the fact that grain-boundaries can be a either a trapping site and/or a short circuit of diffusion [24][25][26][27][28] in fcc materials. More recently, based on a larger experimental investigation Oudriss et al. [27][28][29] have reported that the GBs with low misorientation (Σ1) and a category of "special" grain boundaries (Σ3-Σ29) are usually preferential areas for hydrogen trapping in polycrystalline nickel. In fact, considering their ordered structure, this kind of boundary is accommodated by defects (dislocations, vacancies and more complex organization) that represent potential traps of hydrogen. In opposite, the high angle "random" grain boundaries are considered as the "disordered phase" where the hydrogen diffusion is accelerated in relation to an eased path associated with lower energy barrier. The predominance of one phenomenon over the other depends on the grain boundary energy and the excess of free volume 28 . These results gathered from a correlation between large data of diffusion coefficient and grain boundary character seems to highlight some exceptions 29 which suggest a considerable diversity of local processes. These mechanisms were improved and discussed an extensive variety of experimental technics with a high spatial resolution which has been reviewed recently 14,15 . In fcc metals and alloys, the existence of short-circuit diffusion paths of hydrogen was illustrated using the hydrogen microprint technics and Secondary Ion Mass Spectrometry (SIMS) mapping 14,15,[29][30][31][32] . The preferential ingress of hydrogen along grain boundaries was observed by Tanaka et al. 32 using Ga-FIB-TOF-SIMS to directly visualize deuterium distribution in fcc steel. Microprint technic shows that not all grain boundaries are generally decorated with Ag crystals, which suggest that hydrogen transport capacity of a boundary depends on its microstructural specificity (character, orientation, …) 30,31 . More recently, Tof-SIMS and EBSD were combined to investigate statistically hydrogen distribution around grain boundaries in polycrystalline nickel 29 . Our results suggest that grain boundaries can be categorized into two families according to how hydrogen is distributed across the grain boundary. The first family designates random grain boundaries which reveal a sharp gap for hydrogen concentration profile across the grain boundaries. The second one is special Σ3 n grain boundaries which presents a smooth gradient of hydrogen concentration cross the grain boundary. Despite these new relevant results, it is clear to conclude that actually it stays difficult to demonstrate that hydrogen distribution results in a heterogeneous behavior of diffusion and segregation processes or both. Recent in situ SKPFM analyses using for detecting the local hydrogen distribution around GBs, demonstrate that a random GB with a misorientation of 43° does not significantly facilitate hydrogen diffusion, while a coherent Σ3 twin GB provides a fast path for hydrogen transport 33 . This last result seems in opposite with Oudriss works [28][29] and questions the simple view based on random and Coincidence Site Lattice character (CSL -S).
Additionally, SIMS mapping 29,34-36 and recent Atom Probe Tomography observations 37 highlight a gradient of hydrogen content with a path length higher than the GBs thickness which suggests that hydrogen diffusivity and segregation processes cannot be only discussed in relation to the local structure of grain boundaries.
Based on atomistic simulations, several computational efforts have focused on the hydrogen segregation and diffusion properties and embrittlement consequences for some selected grain boundary in nickel  . Classically, the grain boundaries are characterized by their energy, excess volume and geometric parameters such as Coincidence Site Lattice; easily accessible data using density functional theory (DFT) or molecular dynamics (MD) simulations 59,60 . These characteristics are determining factors on the interaction properties of solutes with the GB; however such global values sometimes appear to be far from representative of local behaviour.
According to extensive atomistic simulations, the segregation energy is essential to the understanding of dynamic processes of solute evolution in materials. The minimum segregation energy, commonly used to characterize GB capacity to interact with hydrogen, vary significantly from -0.04 to -0.37 eV depending on the GB character 40,46,47,[49][50][51][52][53]55 . The effects of last one can be evaluated on the base of literature data for S3(111) (-0.04 eV) 46,47 , S3(110) (-0.21 eV) 47 , S3(221) (-0.21 eV) 47 , S3(112) (-0.24 eV) 47 , S5(012) (-0.23 to -0.37 eV) 40,46,[49][50][51][52] , S5(001) (-0.16 eV) 53 , S5(310) (-0.32 eV) 55 , S9(221) (-0.2 eV) 47 , S99(557) (-0.15 eV) 47 and S17(140) (-0.34 eV) 55 . These values can be significantly modified as a function of the conditions applied to atomistic calculations (size of the box, DFT or EAM potential …) but globally the minimum segregation energy increases with the increases of the CSL index. Hallil et al. suggest that for S3 GBs, that the GB character (energy, and excess volume) can be treated by the notion of the inclination angle f between the two symmetrical tilt grain boundaries (STGB): coherent twin boundary (CTB) and symmetrical incoherent twin boundary (SITB) configurations 47,61 . Energy and excess volume expands with f and at the same time the minimum segregation energy of hydrogen grows 47 . Based on MD/MC simulations, larger systems can be investigated. On the other hand, Moody et al. 48 have pointed out that the hydrogen concentration is enhanced in tilt Σ9(221) high energy grain boundary in nickel. More recently, Brien and Foilles 44 have studied the hydrogen segregation in inclined Σ3<110> nickel GBs using the hybrid MC/MD and an analytic segregation model. The maximum concentration of hydrogen occurs at the boundary at the inclination with the highest enthalpy. This result also gives a correlation between the hydrogen segregation and the GBs energy since the GB energy amplifies with the inclination angle for the nickel GB Σ3<110>. The hydrogen segregation phenomenon is more pronounced for high energy GBs which may be explained by the high excess volume for these GBs. All these outcomes suggest a correlation with the geometric and energetic configuration of grain boundaries and segregation properties, but the physical bases of this relationship stay ambiguous. More recently, the local state was considered in some nickel grain-boundaries 47,57 . Some correlation seems to be possible between the local deformation of hydrogen segregation volume defined by polyhedrons using the Voronoi tessellation method. These studies suggest that elastic dilatation and distortion deformation of the site is partially responsible for the segregation energy. Based on these considerations, some authors have used a continuum approach to evaluate the impact of the elastic field associated with GBs on segregation processes 62 . The respective contribution of short and long-range stress continues to be an open question.
The roles of grain boundaries (GBs) in hydrogen diffusion processes were determined from density functional theory calculations by some authors in fcc metals 52,63,64 . The energy barriers along the diffusion path towards and within GBs has been related for Σ3<110>{111} and Σ11<110>{113) in fcc Fe-g 63 , and for Σ3<110>{111} 52,64 , Σ5<100>{210} 52,64 , Σ5<100>{310} 64 , Σ11<110>{113} 64 , Σ25<100>{430} 64 and Σ41<100>{540} 64 in fcc Nickel. In fcc Fe-g, the Σ3 GB repels hydrogen and the Σ11 offers an easy diffusion path parallel to the GB plane 63 . In fcc nickel, the Σ3 and Σ11 present a quite similar diffusion behavior tho the bulk 64 and Σ5 GBs exhibit lowbarrier paths to facilitate hydrogen diffusion along the GBs 52,64 while Σ25 and Σ41 exhibit highbarrier regions which suggest a slower diffusion of hydrogen than the bulk 64 . The authors suggest that a trapping model in relation with the dislocation density is sufficient to relate these data 64 .
Despite these appreciable results, a minor confrontation was proposed in the literature between hydrogen diffusivity and segregation capability of GBs which doesn't offer the opportunity to clarify the trapping process inside the GBs.
Despite numerous experimental and numerical studies, short-circuits of diffusion and trapping processes within grain boundaries in fcc metals and alloys remain a complex subject that is still poorly understood. Furthermore, the confrontation of experience and numerical works has not been currently used in this subject which reduces the quality of the interpretations.
In the present work, a substantial effort was made to gain further understanding of the key issues of hydrogen segregation and diffusion processes near GBs. The hydrogen/grain-boundaries interactions have been examined for four different configurations of nickel bi-crystal systems to question a considerable variety of grain boundaries energy and excess volume. The hydrogen mobility and trapping process have been investigated based on the electrochemical hydrogen charging technique and on atomistic simulations using an Embedded Atom Method (EAM) potential. The confrontation of both technics allows to elucidate some relevant queries on the contribution of grain-boundary geometry to the mobility and trapping of hydrogen. The segregation process is discussed in relation to the systematic determination of short and longrange elastic distortions and the short-circuit of diffusion process is clarified with a confrontation of the different diffusion paths and the segregation energy of each grain boundaries considered.
Both aspects offer new insight to disclose the impact of grain boundaries on some physical properties. on the coincidence lower than S29 seems unreasonable considering the energy of grain boundaries (see figure 2a as an example). Additionally, the hydrogen concentration CH increases with the fraction of random fR which suggests that random GB is also a specific location of trapping. This effect was clearly identified as a consequence of a vacancy cluster formation (SAV) process. A linear relationship with vacancy concentration and hydrogen was identified (Cvac=0.15×CH 28 which illustrates that the fact that the increase of hydrogen concentration is directly a consequence of vacancy formations without clearly establishing that the formation is directly promoted by random grain boundaries. The antagonist properties of trapping sites and short diffusion paths of random GBs illustrate some ambiguities of the interpretation of experimental data. More recently, we had the opportunity to use both TOF-SIMS and EBSD and combinate their analyses to retrieve the statistical information on the location of hydrogen near the GBs as a function of its character 29 .

Some remarkable results from experimental works -
Initially, these data were only analyzed in term CSL S3 n and random GBs, but in the present work, we show the opportunity to distinguish the coincident twin boundary CTB to other CSL boundaries (ATGB, asymmetric tilt grain boundary and SITB symmetric incoherent twin boundary). Figure 1b illustrates the different profiles of hydrogen content observed around GBs after pre-charging and releasing steps which corresponds to a study state. A gap of hydrogen concentration between both adjacent grains is mostly related to random GBs. Consequently, it seems that when hydrogen diffusion occurs along GBs, hydrogen does not cross the GB easily but moves along the GB. In opposite, a constant profile where no significant modification of hydrogen content is mainly related to both grains around GB is observed for coincident twin boundary CTB where no defect and elastic distortion are necessary to accommodate the misorientation between adjacent grains.
For the other CSL Σ3 n boundaries OTB, a hydrogen gradient around GBs is observed where a large density of defects is necessary to accommodate the misorientation between two adjacent grains. Additionally, it was reported at a micrometer length scale of the gradient of hydrogen concentration significantly higher than GBs thickness (nanometer) 29 which suggests the occurrence of the long-range internal stresses near OTB GBs. Considering these statistical results, we note that even though we associate a type of grain boundary type (random or special) with a hydrogen concentration profile, this result is by no means exclusive. This conclusion allows us to develop a work specifically on selected grain boundaries in a large domain of representative GBs.
We have followed the hydrogen content as a function of charging time for a specific electrochemical charging condition which corresponds to a thermodynamic system defined by PH2=800 atm and T=300K on two systems single and bicrystal with the same ingress surface. The evolution of hydrogen concentration CH as a function of charging time is presented in figure 1c for the {110} and {100} single crystals and bicrystal S11{332} with a hydrogen ingress orientation of {110}. In each case, hydrogen concentration increases with time and reaches a saturation plateau corresponding to an apparent solubility. No significant difference is observed between both single crystals. In opposite the hydrogen content is largely lower in the considered bicrystal (5 wppm instead of 9 wppm for single crystals). We provide the same comparison for three other configurations in figure 1d for the stationary state. A very low difference is observed between S3 CTB and S11 {311} in comparison with single crystal orientations. In opposite for S5 {310} and S11{332} the hydrogen content obtained are lower than the one determined for equivalent single crystals. To resume, the hydrogen content is lower for bicrystals with an intensity defined by DCH which depends on the grain boundary character and suggests that GBs act as a short-circuit of diffusion. The difference DCH between bi-crystals and single crystal are

CSL GBs
the segregation energy Eseg is a quite linear function of the hydrogen atomic volume, VH (domain I). However, this linear relationship is not available for high energy GBs with an atomic volume above 6.6 Å 3 (domain II) in accordance with our previous work related to S3 n special GBs 47 .
In domain II, a quasi-plateau is reached in terms of energy (-0.22 eV) with a large scatter.
Consequently, the hydrogen atomic volume seems to be insufficient to question the elastic energy contribution to the segregation energy which allows in the following to consider the morphology of the different sites. The segregation sites in the GB region have complicated local geometry structures, thus, we will describe the geometry of all the potential segregation sites in GBs core in detail. An illustration of this approach is shown in figure 3c where the segregation positions and their volume geometry are presented for the S11-{332} GB. The position numbers are ranked from the most to less stable segregation energy. According to the Voronoi tessellation, the   hydrogen volume at the octahedral site in nickel bulk is a cubic form with 14 neighbouring atoms.
The closer the hydrogen atoms get to the GB core region, the greater the geometry deformation occurs. Consequently, the segregation energy and the hydrogen volume size are extremely dependent on the local environment. However, a direct relationship cannot be found among these factors. The morphology of the different sites highlights the fact that the deformation of the site is not isotropic for most cases. We will discuss this crucial aspect in the next section. After the consideration of the local volume deformation, the hydrogen atom insertion at different sites can be discussed in terms of local energy of hydrogen EH (the energy of atom i in the EAM method with i=H). This energy is the sum of the kinetic and the potential energy, which differs from the segregation energy Eseg only if we have a long-range effect associated with the insertion of hydrogen. Figure

Diffusion paths
The short circuit of diffusion along GBs can be discussed as a function with a reference state defined as a diffusion path of the perfect crystal. The nudged elastic band method (NEB) method has been used to calculate the Minimum Energy Paths (MEP) and their associated energy barriers (Table 1). Several stable segregation sites in GBs were looked upon for three principal path The GB Σ11-{332} is a high energy/excess volume GB ( figure 6). It has several hydrogen segregations sites in the GB core (14 sites). For the segregation site A, the energy barrier along the X direction is higher than the reference energy in nickel bulk (  Consequently, the segregation energy can be formulated as a function of the different The Once hydrogen atom is localized in a GB, it is now appropriated to ask now how the atom will move or remain trapped using the evaluation of the migration energies.  52 : Two situations can be considered when the backward energy is higher than the one in bulk. The first one corresponds to the segregation of hydrogen to an easy migration path along the grain boundary (directions X and/or Z) where the E R ST,X [h Y is lower than in the bulk and consequently

Conclusion
We developed a methodology based on the confrontation between experimental hydrogen charging and atomistic modeling to elucidate the competition between hydrogen trapping and short circuit of diffusion along grain boundaries.
Using thermal desorption spectroscopy and electrochemical permeation testing, we measured the diffusivity of hydrogen and trapping energy in single and poly crystals of nickel on a large variety of configurations. Our experimental results are challenged by our atomistic simulations to provide a straightforward understanding of the apparently ambiguous and antagonist effects of grain boundaries between the trapping process and the fast diffusion path. The origin of the acceleration of the diffusivity along grain boundaries is observed when the excess volume increases, which is clarified in terms of migration energies and the distribution of segregation energies. The fast diffusion of hydrogen observed in some grain boundary configurations corresponds to high segregation energy sites and different paths along inter-connected sites of low migration energy.
In opposite, the trapping process occurs in grain boundaries of high segregation energy sites and high migration energies. We underline the importance of the elastic energy to global hydrogen incorporation energy in one specific site of grain boundaries. Due to the complex structure of the grain boundary, the distribution of the segregation energy depends not only on the hydrostatic strain energy but also on the deviatoric elastic energy and the long-range elastic distortion which can predominate far from GB. The present work can be extended to a large variety of grain boundaries to allow a more generic relationship between elastic, segregation and migration energies. The bicrystals were grown from a seed in an argon atmosphere using the horizontal boat method  (eq. A0)

Material design and structural characterization -
where Fa is the embedding energy function, is the partial electron density contribution, denotes the distance between atom i and j, is the pair potential, and are the element types of atom i and j. For a grain boundary in a bi-crystal system, the construction of grain boundary is built by finding the most optimal configuration. An example of a simulation cell for the grain boundary Σ5-36°87<100>{310} is illustrated in figure A1.
θ is the misorientation angle between two identical nickel crystals around the symmetric tilt axis along the grain boundary plane. The direction along the GB plane is designated by the tilt z-axis [001] in the simulation cell and common for both grains. Each GB simulation cell contains two-grain lattices which are characterized by two distinct crystallographic orientations in x and y directions. The GB simulation cells are considered in 3D periodic boundary conditions, this representation provides existence of two GBs in each simulation cell: one in the middle of the simulation cell and on another counting for a mirror image in the bound parts of the simulation cell. The separation distance between each GB is chosen to be large enough so that there will be no energetic interaction between two GB interfaces. A rigid body translation parallel to the GB plane has been applied following x and z-axis, all translational vectors are in a primitive cell of the displacement shift complete (DSC) lattice 60 and the lattice spacing in the planar directions of each grain is kept constant. The translation of one grain relative to the other yields to a re-arrangement of atoms at the GB plane. After testing hundreds of configurations, the one with the minimum energy at the grain boundary is obtained and the excess volume could be calculated using Voronoi tessellation method implemented in LAMMPS code.
Since the GB structure is well defined, we can insert an atom of hydrogen into the GB. The initial position of the hydrogen atom is at the vicinity of a nickel atom. Then the energy minimization occurs and the hydrogen atom will find its stable position using atomic simulation analysis GB plane x and z OVITO software. After determining several stable segregation sites in the core region, we focused on the diffusion paths among these different segregation sites using the nudged elastic band method (NEB) [100]. This method is used to detect saddle points and minimum energy paths (MEP) between the known initial and final states. Transition states of diffusion paths (referred to as images) identify the lowest possible energy while maintaining equal spacing to neighboring images. Once the images have converged sufficiently to the MEP, the image at the highest energy point is allowed to climb uphill along the MEP until it reaches the transition state enabling thus the transition geometry and energy to be accurately defined from the NEB method [101]. We have investigated the MEP and the energy barrier between the most stable segregation positions and the highest Voronoi volume positions (the volume occupied by the hydrogen atom) using LAMMPS code with NEB package. The GB energy is computed as the difference between the total energy of the relaxed GB atoms and the bulk energy in the whole system in GB plane. For a number of atoms Nat in the calculation, the grain boundary energy is given as: !" = 5 6 j !" m( ( 9' ) − "n1o m( ( 9' )l/ L (eq. A 1) Where !" m( ( 9' ) is the total energy of the relaxed GB, "n1o m( ( 9' ) is the total bulk energy, A0 is the area of the GB plane. ∆ !" the excess volume of a GB can be accessed with (volume variation per unit of GB area): ∆ !" = 5 6 j !" M%' ( 9' ) − "n1o M%' ( 9' )l/ L (eq. A 2) where !" M%' ( 9' ) is the volume of GB, "n1o M%' ( 9' ) is the volume of bulk.
When the stable configuration of GBs has been established, we started to insert the hydrogen atom in different locations in the GBs. The insertion energy (in some publications called also the adsorption energy) of a hydrogen atom in the nickel lattice -p)* is given in (eq. A3):  Huang et al. 55 . Thus, the segregation energy relative to the octahedral site is written in (eq. A4): -*#, = g !"@-M%' − !" M%' h − g m(@-%&' − m( %&' h (eq. A4) !"@-M%' is the total energy of GB with a hydrogen atom, !" M%' is the total energy of the GB and m(@-q&' is the total energy of the nickel lattice with a hydrogen atom at the octahedral site.