Beatriz Garcia-Diaz
email: beatriz.garcia@icm-institute.org

Anne Baron-Van Evercooren

Beatriz Garcia Diaz

Schwann cells: Rescuers of central demyelination

Keywords: Schwann cells, central nervous system, remyelination, astrocytes, myelin, blood vessels

The presence of peripheral myelinating cells in the central nervous system (CNS) has gained the neurobiologist attention over the years. Despite the confirmed presence of Schwann cells in the CNS in pathological conditions, and the long list of their beneficial effects on central remyelination, the cues that impede or allow Schwann cells to successfully conquer and remyelinate central axons remain partially undiscovered. A better knowledge of these factors stand out as crucial to foresee a rational therapeutic approach for the use of Schwann cells in CNS repair. Here, we review the diverse origins of Schwann cells into the CNS, both peripheral and central, as well as the CNS components that inhibit Schwann survival and migration into the central parenchyma. Namely, we analyze the astrocyte-and the myelin-derived components that restrict Schwann cells into the CNS. Finally, we highlight the unveiled mode of invasion of these peripheral cells through the central environment, using blood vessels as scaffolds to pave their ways towards demyelinated lesions. In short, this review presents the so far uncovered knowledge of this complex CNS-peripheral nervous system (PNS) relationship.

Schwann cell presence in the CNS.

The ectopic presence of Schwann cells within the CNS has been extensively described over the years. Schwann cell presence in the human CNS, was first highlighted by [START_REF] Adelman | Intramedullary nerve fiber and Schwann cell proliferation within the spinal cord (schwannosis)[END_REF], and later, in the non-human primate CNS [START_REF] Raine | On the occurrence of Schwann cells within the normal central nervous system[END_REF]. This PNS-CNS transgression capacity of the endogenous Schwann cells was experimentally challenged in different demyelinating models including experimental autoimmune encephalomyelitis [START_REF] Raine | Glial bridges and Schwann cell migration during chronic demyelination in the C[END_REF], viral encephalomyelitis [START_REF] Dal Canto | Schwann cell remyelination and recurrent demyelination in the central nervous system of mice infected with attenuated Theiler's virus[END_REF], focal myelinotoxic injections [START_REF] Blakemore | Ethidium bromide induced demyelination in the spinal cord of the cat[END_REF], and focal compressive/contusive lesions of the spinal cord [START_REF] Blight | Central axons in injured cat spinal cord recover electrophysiological function following remyelination by Schwann cells[END_REF][START_REF] Griffiths | Nerve fibres in spinal cord impact injuries. Part 1. Changes in the myelin sheath during the initial 5 weeks[END_REF], demonstrating the capacity of endogenous (as opposed to grafted, exogenous) Schwann cells to colonize the CNS under pathological conditions.

The presence of these endogenous Schwann cells in the CNS opened the question of how and why this transgression occurs, and introduced the idea of the ability of Schwann cells to rescue the lesioned CNS. Advocating this notion, a large number of Schwann cells were also found myelinating CNS axons in human pathological conditions, such as multiple sclerosis [START_REF] Itoyama | Spinal cord multiple sclerosis lesions in Japanese patients: Schwann cell remyelination occurs in areas that lack glial fibrillary acidic protein (GFAP)[END_REF][START_REF] Itoyama | Schwann cell remyelination of demyelinated axons in spinal cord multiple sclerosis lesions[END_REF][START_REF] Yamamoto | Extensive proliferation of peripheral type myelin in necrotic spinal cord lesions of multiple sclerosis[END_REF] or spinal cord injury [START_REF] Bunge | Expanding roles for the Schwann cell: ensheathment, myelination, trophism and regeneration[END_REF][START_REF] Guest | Demyelination and Schwann cell responses adjacent to injury epicenter cavities following chronic human spinal cord injury[END_REF][START_REF] Wang | The expression of nerve growth factor receptor on Schwann cells and the effect of these cells on the regeneration of axons in traumatically injured human spinal cord[END_REF] as well as in long-lived rodent and canine myelin mutant [START_REF] Duncan | Schwann cell invasion of the central nervous system of the myelin mutants[END_REF]. In these mutants, Schwann cells were mainly found in the spinal cord, they were also present in the forebrain, brain stem, and cerebellum.

Origin of the Schwann cell presence in CNS.

For decades, these CNS remyelinating Schwann cells were considered to arise from outside the CNS [START_REF] Franklin | Requirements for Schwann cell migration within CNS environments: a viewpoint[END_REF][START_REF] Gilmore | Autoradiographic studies of intramedullary Schwann cells in irradiated spinal cords of immature rats[END_REF][START_REF] Gilmore | Autoradiographic and ultrastructural studies of areas of spinal cord occupied by Schwann cells and Schwann cell myelin[END_REF][START_REF] Jasmin | Schwann cells are removed from the spinal cord after effecting recovery from paraplegia[END_REF]Sims, Durgun, & Gilmore, 1998), with neural crest-derived Schwann cells migrating from the PNS into the CNS to contribute to myelin repair. In this situation, Schwann cells would need to trespass the PNS-CNS transition zone. However, the recent developments of genetic tools allowed digging into the source of these cells and demonstrated that their origin is not solely peripheral [START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF][START_REF] Ma | A Subpopulation of Foxj1-Expressing, Nonmyelinating Schwann Cells of the Peripheral Nervous System Contribute to Schwann Cell Remyelination in the Central Nervous System[END_REF][START_REF] Zawadzka | CNSresident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF].

As thought before, genetic fate mapping studies have proven that peripheral non-myelinating and myelinating Schwann cells are recruited from the periphery into the CNS where they provide axons with peripheral myelin, thus implying their ability to migrate and cross the CNS-PNS border to provide ensheathment to central axons [START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF][START_REF] Ma | A Subpopulation of Foxj1-Expressing, Nonmyelinating Schwann Cells of the Peripheral Nervous System Contribute to Schwann Cell Remyelination in the Central Nervous System[END_REF]. Despite this expected observation, genetic tools have also revealed more surprising findings. Non-neural crest derived resident cells of the CNS, the oligodendrocyte precursor cells (OPC), are able to differentiate into remyelinating Schwann cells in response to spinal cord demyelination or injury [START_REF] Zawadzka | CNSresident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF][START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF]. After spinal cord injury, Schwann cell myelin sheaths in the vicinity of the dorsal root entry zone, are typically derived from peripheral cells. However those myelinating Schwann cells at the epicentre of the lesion are derived from central OPC [START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF]. Interestingly, the number OPC-derived Schwann cells increases overtime indicating an ongoing production of Schwann cells by non-neural crest progenitors. In contrast, the number of neural crestderived Schwann cell does not change after the first days of remyelination, suggesting that the "outside-in" Schwann cell migration occurs only in the first steps of the lesion healing [START_REF] Zawadzka | CNSresident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF][START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF]. These unexpected observations support the view that most of the myelinating Schwann cells present within CNS are derived from the OPC, which upon activation by micro-environmental cues via BMP/Wnt signaling, differentiate into Schwann cells [START_REF] Ulanska-Poutanen | Injury-induced perivascular niche supports alternative differentiation of adult rodent CNS progenitor cells[END_REF] and remyelinate central axons both in demyelinating lesions [START_REF] Zawadzka | CNSresident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF] and spinal cord injury [START_REF] Assinck | Myelinogenic Plasticity of Oligodendrocyte Precursor Cells following Spinal Cord Contusion Injury[END_REF].

Although increasing studies have addressed the ability of OPC to differentiate into myelinating Schwann cells, based on their expression of pre-myelinating (SCIP and OCT6) or myelinating Schwann cell markers (P0 myelin protein or periaxin) [START_REF] Zawadzka | CNSresident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF], their capacity to give rise to nonmyelinating Remak glia remains unexplored. Due to Schwann cell plasticity and their capacity of transdifferentiation between myelinating and non-myelinating Schwann cells under [START_REF] Jessen | The Success and Failure of the Schwann Cell Response to Nerve Injury[END_REF], it will be of interest to further elucidate whether CNS-resident Schwann cell conserve this capacity in the central environment. Nevertheless, new genetic tools to specifically label their lineage independently of their myelination ability will be required to investigate this question.

Exogenous Schwann cells as potential candidates to enhance CNS remyelination

A large number of pre-clinical studies using cell transplantation corroborated overtime Schwann cell great capacity to contribute to CNS repair. Engraftment of nerve fragments [START_REF] Richardson | Regeneration and retrograde degeneration of axons in the rat optic nerve[END_REF] first, and of purified Schwann cells later, highlighted the role of myelinating Schwann cells in promoting CNS axonal survival [START_REF] Blakemore | Schwann cell remyelination of CNS axons following injection of cultures of CNS cells into areas of persistent demyelination[END_REF][START_REF] Pearse | Transplantation of Schwann cells and/or olfactory ensheathing glia into the contused spinal cord: Survival, migration, axon association, and functional recovery[END_REF], long-term maintenance of normal distribution of sodium and potassium channels [START_REF] Black | Remyelination of dorsal column axons by endogenous Schwann cells restores the normal pattern of Nav1.6 and Kv1.2 at nodes of Ranvier[END_REF] and restoration of axonal conduction [START_REF] Felts | Conduction properties of central nerve fibers remyelinated by Schwann cells[END_REF]. As a result, Schwann cell remyelination of experimental CNS lesions ultimately lead to functional rescue of neurological deficits [START_REF] Blight | Central axons in injured cat spinal cord recover electrophysiological function following remyelination by Schwann cells[END_REF][START_REF] Deng | Schwann cell transplantation and descending propriospinal regeneration after spinal cord injury[END_REF][START_REF] Girard | Grafts of brain-derived neurotrophic factor and neurotrophin 3-transduced primate Schwann cells lead to functional recovery of the demyelinated mouse spinal cord[END_REF][START_REF] Jasmin | Schwann cells are removed from the spinal cord after effecting recovery from paraplegia[END_REF]. Furthermore, the list of Schwann cell beneficial effects in CNS repair is not restricted to their myelinating capacity, and includes axon growth promoting activities by the secretion of trophic factors including NGF and BDNF [START_REF] Assouline | Rat astrocytes and Schwann cells in culture synthesize nerve growth factor-like neurite-promoting factors[END_REF][START_REF] Bampton | Effects of Schwann cell secreted factors on PC12 cell neuritogenesis and survival[END_REF], expression on their membrane of permissive extracellular matrix (ECM) proteins such as laminin and fibronectin [START_REF] Baron-Van Evercooren | Fibronectin promotes rat Schwann cell growth and motility[END_REF][START_REF] Chiu | Laminin and slaminin are produced and released by astrocytes, Schwann cells, and schwannomas in culture[END_REF], and a variety of adhesion molecules (NCAM, L1 etc) [START_REF] Reichardt | Integrins and cell adhesion molecules: neuronal receptors that regulate axon growth on extracellular matrices and cell surfaces[END_REF]. Recently, Wei and collaborators [START_REF] Wei | Proteomics analysis of Schwann cell-derived exosomes: a novel therapeutic strategy for central nervous system injury[END_REF] unveiled the promising role of the exosomes produced by Schwann cells in repairing the CNS. These Schwann cell-secreted exosomes harbor proteins related to important CNS repair mechanisms, such as axon regeneration and inflammation inhibition. To date, the therapeutic use of Schwann cells, by exogenous transplantation, has been broadly explored in a variety of animal models of CNS diseases such as toxin-induced demyelination [START_REF] Girard | Grafts of brain-derived neurotrophic factor and neurotrophin 3-transduced primate Schwann cells lead to functional recovery of the demyelinated mouse spinal cord[END_REF][START_REF] Kocsis | Schwann cells and their precursors for repair of central nervous system myelin[END_REF][START_REF] Woodhoo | Schwann cell precursors: a favourable cell for myelin repair in the Central Nervous System[END_REF], multiple sclerosis and spinal cord injury [START_REF] Bastidas | Human Schwann cells exhibit long-term cell survival, are not tumorigenic and promote repair when transplanted into the contused spinal cord[END_REF][START_REF] Kanno | Schwann cell transplantation for spinal cord injury repair: its significant therapeutic potential and prospectus[END_REF][START_REF] Pearse | Transplantation of Schwann cells and olfactory ensheathing glia after spinal cord injury: does pretreatment with methylprednisolone and interleukin-10 enhance recovery[END_REF][START_REF] Sparling | Schwann cells generated from neonatal skin-derived precursors or neonatal peripheral nerve improve functional recovery after acute transplantation into the partially injured cervical spinal cord of the rat[END_REF].

The idea of using Schwann cells to therapeutically enhance CNS myelin repair gained even more relevance due to the possibility of obtaining and expanding human and non-human primate Schwann cells [START_REF] Avellana-Adalid | In vitro and in vivo behaviour of NDF-expanded monkey Schwann cells[END_REF][START_REF] Casella | Improved method for harvesting human Schwann cells from mature peripheral nerve and expansion in vitro[END_REF][START_REF] Levi | The influence of heregulins on human Schwann cell proliferation[END_REF][START_REF] Rutkowski | Purification and expansion of human Schwann cells in vitro[END_REF]. Thus, these cells started being considered as promising candidates for autologous transplantation in CNS diseases [START_REF] Anderson | Safety of Autologous Human Schwann Cell Transplantation in Subacute Thoracic Spinal Cord Injury[END_REF][START_REF] Kocsis | Cell transplantation of peripheralmyelin-forming cells to repair the injured spinal cord[END_REF], avoiding concerns about immunological rejection of the grafted cells. Relieving any safety issues, pre-clinical studies showed that autologous Schwann cell transplantation could be a clinically safe approach to repair the CNS in rodents [START_REF] Bastidas | Human Schwann cells exhibit long-term cell survival, are not tumorigenic and promote repair when transplanted into the contused spinal cord[END_REF][START_REF] Guest | Clinical translation of autologous Schwann cell transplantation for the treatment of spinal cord injury[END_REF][START_REF] Pearse | Transplantation of Schwann cells and olfactory ensheathing glia after spinal cord injury: does pretreatment with methylprednisolone and interleukin-10 enhance recovery[END_REF][START_REF] Sparling | Schwann cells generated from neonatal skin-derived precursors or neonatal peripheral nerve improve functional recovery after acute transplantation into the partially injured cervical spinal cord of the rat[END_REF] and non-human primates [START_REF] Bachelin | Efficient myelin repair in the macaque spinal cord by autologous grafts of Schwann cells[END_REF]. To date, the therapeutic use of Schwann cells has been tested in clinical trials for spinal trauma [START_REF] Anderson | Safety of Autologous Human Schwann Cell Transplantation in Subacute Thoracic Spinal Cord Injury[END_REF]) (Clinical trial.gov: NCT01739023).

Despite these promising clinical effects, exogenous Schwann cell transplantation still opposes obvious limitations, hindering the possibility of complete success for these types of treatments. Although Schwann cells were found highly motile cells in vitro [START_REF] Baron-Van Evercooren | Fibronectin promotes rat Schwann cell growth and motility[END_REF][START_REF] Milner | Division of labor of Schwann cell integrins during migration on peripheral nerve extracellular matrix ligands[END_REF] and in vivo within the PNS (Cattin et al., 2015), they exhibit poor migration through the parenchyma, from their injection site once grafted in the CNS ( [START_REF] Baron-Van Evercooren | The fate of Schwann cells transplanted in the brain during development[END_REF][START_REF] Woodhoo | Schwann cell precursors: a favourable cell for myelin repair in the Central Nervous System[END_REF]. Their survival within the CNS parenchyma is also compromised (Iwashita & Blakemore, 2000;[START_REF] Iwashita | Schwann cells transplanted into normal and X-irradiated adult white matter do not migrate extensively and show poor long-term survival[END_REF]. This poor migration and survival in the CNS is stage-dependent since more immature stages of the lineage, such as boundary cap cells [START_REF] Zujovic | Boundary cap cells are peripheral nervous system stem cells that can be redirected into central nervous system lineages[END_REF] and Schwann cell precursors [START_REF] Woodhoo | Schwann cell precursors: a favourable cell for myelin repair in the Central Nervous System[END_REF] grafted in similar conditions survive and migrate more efficiently in the adult CNS parenchyma. These findings indicate that the CNS/PNS segregation is not exclusively due to a physical confinement of both compartments by the glia limitans and specialized glial cells, which together form the transitional zone [START_REF] Fontenas | Motor Exit Point (MEP) Glia: Novel Myelinating Glia That Bridge CNS and PNS Myelin[END_REF][START_REF] Fraher | The CNS-PNS transitional zone of the rat. Morphometric studies at cranial and spinal levels[END_REF] but rather to a more complex molecular and cellular inhibition from different CNS components.

What prevents Schwann cells to successfully remyelinate the injured CNS?

Hence, deciphering what prevents Schwann cells from extensively populate and myelinate CNS axons in physiological conditions, and what grants their incursion and survival under others, is of high relevance to myelin repair. Based on the original hypothesis of the exclusive peripheral origin of the CNS remyelinating Schwann cells, the main barrier preventing their invasion of the CNS, would be physical, and formed by astrocytes. However, despite this physical impediment, the migration failure of Schwann cells grafted into the CNS or centrally originated from OPCs to invade the system, indicates that other mechanisms ensure Schwann cell restriction from the CNS.

Here, we will review the known aspects of Schwann cell exclusion from the CNS and their ability to overpass this inhibition under certain conditions. In particular, we will review Schwann cell interactions with the major CNS components: astrocytes, oligodendrocyte and/or myelin.

Astrocyte

In the mature spinal cord, astrocyte processes branch profusely and come to form the principal central nervous tissue component of the transition zone, and therefore, constitute the main component of the physical barrier between CNS and PNS, the glia limitans [START_REF] Fraher | The CNS-PNS transitional zone of the rat. Morphometric studies at cranial and spinal levels[END_REF]. This astrocytic barrier is also found around blood vessels. As examples of their importance in delimiting both territories, ectopic entries of peripheral cells into the spinal cord are largely correlated with the disruption of astrocyte integrity in the mature nervous system [START_REF] Blakemore | Observations on the interactions of Schwann cells and astrocytes following X-irradiation of neonatal rat spinal cord[END_REF][START_REF] Duncan | Schwann cell myelination of the myelin deficient rat spinal cord following X-irradiation[END_REF][START_REF] Duncan | Schwann cell invasion of the central nervous system of the myelin mutants[END_REF][START_REF] Franklin | Requirements for Schwann cell migration within CNS environments: a viewpoint[END_REF].

In support of astrocyte inhibition, exogenous Schwann cells show poor survival and migration out of the site of injection, which is generally confined by reactive astrocytes [START_REF] Andrews | Evaluation of olfactory ensheathing and schwann cells after implantation into a dorsal injury of adult rat spinal cord[END_REF][START_REF] Baron-Van Evercooren | The fate of Schwann cells transplanted in the brain during development[END_REF][START_REF] Duncan | Schwann cell myelination of the myelin deficient rat spinal cord following X-irradiation[END_REF][START_REF] Franklin | Requirements for Schwann cell migration within CNS environments: a viewpoint[END_REF]Iwashita et al., 2000;[START_REF] Wilby | N-Cadherin inhibits Schwann cell migration on astrocytes[END_REF]. In contrast, endogenous [START_REF] Woodruff | Demyelination and remyelination of the caudal cerebellar peduncle of adult rats following stereotaxic injections of lysolecithin, ethidium bromide, and complement/anti-galactocerebroside: a comparative study[END_REF] and exogenous Schwann cell remyelination [START_REF] Shields | Schwann cell remyelination is restricted to astrocyte-deficient areas after transplantation into demyelinated adult rat brain[END_REF] is extensive in astrocyte-free areas. The astrocyte-Schwann cell exclusion also occurs during spontaneous remyelination in irradiated rats where astrocytes are ablated and Schwann cells conquer the territory [START_REF] Blakemore | Observations on the interactions of Schwann cells and astrocytes following X-irradiation of neonatal rat spinal cord[END_REF][START_REF] Gilmore | Autoradiographic and ultrastructural studies of areas of spinal cord occupied by Schwann cells and Schwann cell myelin[END_REF][START_REF] Heard | Intramedullary Schwann cell development following x-irradiation of mid-thoracic and lumbosacral spinal cord levels in immature rats[END_REF] . This constraint is far from being exclusively physical. In vitro co-culture studies showed sharp boundaries between Schwann cells and astrocytes [START_REF] Ghirnikar | Chondroitin sulfate proteoglycan staining in astrocyte-Schwann cell co-cultures[END_REF][START_REF] Lakatos | Olfactory ensheathing cells and Schwann cells differ in their in vitro interactions with astrocytes[END_REF][START_REF] Wilby | N-Cadherin inhibits Schwann cell migration on astrocytes[END_REF]. This observation led to investigate about the molecular cues responsible for this repulsion. In this line, in vitro studies demonstrated that Schwann cell Ncadherin-mediated adhesion to astrocytes, trigger astrocyte hypertrophy, reducing Schwann cell migration within astrocyte-rich environments [START_REF] Fairless | N-cadherin differentially determines Schwann cell and olfactory ensheathing cell adhesion and migration responses upon contact with astrocytes[END_REF][START_REF] Wilby | N-Cadherin inhibits Schwann cell migration on astrocytes[END_REF]. Moreover, Schwann cell-astrocyte contacts induce astrocytic-stress response consisting in cytoplasmic hypertrophy and elevated expression of GFAP, chondroitin sulfate proteoglycan (CSPG) and aggrecan [START_REF] Fishman | Astrogliosis limits the integration of peripheral nerve grafts into the spinal cord[END_REF][START_REF] Ghirnikar | Astrocyte-Schwann cell interactions in culture[END_REF], 1995;[START_REF] Lakatos | Olfactory ensheathing cells induce less host astrocyte response and chondroitin sulphate proteoglycan expression than Schwann cells following transplantation into adult CNS white matter[END_REF][START_REF] Plant | Inhibitory proteoglycan immunoreactivity is higher at the caudal than the rostral Schwann cell graft-transected spinal cord interface[END_REF][START_REF] Santos-Silva | FGF/heparin differentially regulates Schwann cell and olfactory ensheathing cell interactions with astrocytes: a role in astrocytosis[END_REF]. In turn, both CSPG and aggrecans block Schwann cell migration and induce the formation of a Schwann cell-astrocyte border line [START_REF] Afshari | Astrocyte-produced ephrins inhibit schwann cell migration via VAV2 signaling[END_REF][START_REF] Grimpe | The role of proteoglycans in Schwann cell/astrocyte interactions and in regeneration failure at PNS/CNS interfaces[END_REF][START_REF] Santos-Silva | FGF/heparin differentially regulates Schwann cell and olfactory ensheathing cell interactions with astrocytes: a role in astrocytosis[END_REF]. Recently, Barnett and collaborators reported the presence of heparan sulfate proteoglycans (HSPG) in astrocyte ECM preventing Schwann cells to mingle with astrocytes, and sequestering the soluble neuregulin required for their migration [START_REF] O'neill | Sulfatase-mediated manipulation of the astrocyte-Schwann cell interface[END_REF]. Finally, expression of NCAM by astrocytes and Schwann cells contributes to this borderline. Forced expression of the sialylated form of NCAM in Schwann cells hinders their self-self aggregation and promotes their migration and mixing with astrocytes in vitro [START_REF] Bachelin | Ectopic expression of polysialylated neural cell adhesion molecule in adult macaque Schwann cells promotes their migration and remyelination potential in the central nervous system[END_REF][START_REF] Lavdas | Schwann cells genetically engineered to express PSA show enhanced migratory potential without impairment of their myelinating ability in vitro[END_REF]. Furthermore, sialylation of NCAM on Schwann cells facilitates their migration in vivo, enhancing their recruitment and remyelination at the lesion site [START_REF] Bachelin | Ectopic expression of polysialylated neural cell adhesion molecule in adult macaque Schwann cells promotes their migration and remyelination potential in the central nervous system[END_REF] and promoting functional recovery in spinal cord injury [START_REF] Papastefanaki | Grafts of Schwann cells engineered to express PSA-NCAM promote functional recovery after spinal cord injury[END_REF].

Other molecules responsible for Schwann cell-astrocyte segregation are the Eph/ephrin family [START_REF] Afshari | Astrocyte-produced ephrins inhibit schwann cell migration via VAV2 signaling[END_REF]. Astrocytes producing ephrinA1, ephrinA3, and ephrinA5 inhibit Schwann cell migration on a laminin substrate. This response is mediated by the expression of the ephrin receptors EphA2, EphA4, and EphA7 in Schwann cell. In particular, blocking these inhibitory molecules by the soluble receptor EphA4-Fc enhances Schwann cell ability to migrate on and intermingle with astrocytes.

Astrocytes also hold a more indirect role in Schwann cell exclusion from the CNS. Beyond the role of astrocyte-derived inhibitory cues, activated astrocytes via STAT3, play a major role in determining the balance of OPC-derived oligodendrocytes vs. Schwann cells in favor of oligodendrocytes (Monteiro de Castro, Deja, [START_REF] Monteiro De Castro | Astrocyte Activation via Stat3 Signaling Determines the Balance of Oligodendrocyte versus Schwann Cell Remyelination[END_REF][START_REF] Talbott | Endogenous Nkx2.2+/Olig2+ oligodendrocyte precursor cells fail to remyelinate the demyelinated adult rat spinal cord in the absence of astrocytes[END_REF], and thus counting as another mechanism to maintain the specific CNS cellular composition.

Myelin

Other CNS components that have been suggested as potential candidates to restrain Schwann cell migration across the CNS/PNS border are the mature oligodendrocytes and CNS-myelin. Yet, in myelin mutants, where myelin is defective but oligodendrocytes are still present (such as myelin deficient (md), taiep rats, and canine shaking (sh) pups), spontaneous Schwann cell invasion occurs into the dysmyelinated CNS [START_REF] Duncan | Schwann cell invasion of the central nervous system of the myelin mutants[END_REF]. This pointed out that CNS-myelin, rather than oligodendrocytes, are the major players in Schwann cell exclusion from CNS white matter.

Several facts support this hypothesis. Langford and Owens [START_REF] Langford | Resolution of the pathway taken by implanted Schwann cells to a spinal cord lesion by prior infection with a retrovirus encoding beta-galactosidase[END_REF]) made the first observation that Schwann cells transplanted into the demyelinated spinal cord avoid the white matter parenchyma when migrating towards the lesion. Grafting Schwann cells in wild-type and myelin mutant mice revealed that Schwann cells do not interact directly with myelin sheaths nor with mature oligodendrocytes in the wild-type white matter, but do so in the hypomyelinated white matter of MBP deficient-mice (Baron- [START_REF] Baron-Van Evercooren | Cell-cell interactions during the migration of myelinforming cells transplanted in the demyelinated spinal cord[END_REF][START_REF] Baron-Van Evercooren | Pathways of migration of transplanted Schwann cells in the demyelinated mouse spinal cord[END_REF]). Yet these observations could have reflected the lack of compaction or altered composition of the mutant myelin.

While the poor migration and survival of exogenous Schwann cells within wild-type CNS white matter has been well documented over the years [START_REF] Bachelin | Ectopic expression of polysialylated neural cell adhesion molecule in adult macaque Schwann cells promotes their migration and remyelination potential in the central nervous system[END_REF]Iwashita & Blakemore, 2000;Iwashita et al., 2000), the molecular mechanisms involved in Schwann cells-myelin repellence was not addressed. We started to investigate on the potential mechanisms ruling this Schwann cellsmyelin inhibition, and discovered that two different myelin-associated inhibitors of axonal growth also negatively regulate Schwann cell migration [START_REF] Chaudhry | Myelin-Associated Glycoprotein Inhibits Schwann Cell Migration and Induces Their Death[END_REF][START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF].

The first player in this negative interaction is the myelin-associated glycol protein (MAG) [START_REF] Chaudhry | Myelin-Associated Glycoprotein Inhibits Schwann Cell Migration and Induces Their Death[END_REF]. In collaboration with Marie Filbin's group, we found that MAG, as well as CNS myelin, is able to inhibit Schwann cell migration and induces cell death through the p75 neurotrophin receptor (p75NTR) in vitro. MAG interaction with p75NTR undergoes γ-secretase-dependent cleavage, which in turn inhibits Schwann cell migration and induces their death. This mechanism of action was validated in vivo, by transplanting Schwann cell remotely from a lesion. We also found that blocking p75 cleavage improved their migration, and consequently, their participation in CNS remyelination [START_REF] Chaudhry | Myelin-Associated Glycoprotein Inhibits Schwann Cell Migration and Induces Their Death[END_REF].

Additionally, using different in vitro, ex vivo and in vivo paradigms, we recently demonstrated that EphrinB3, another myelin inhibitor of axonal growth [START_REF] Duffy | Myelin-derived ephrinB3 restricts axonal regeneration and recovery after adult CNS injury[END_REF], plays an essential role in Schwann cell exclusion from the CNS [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. We showed that EphrinB3, through EphA4 and EphB6 receptors, impairs their adhesion and process extension onto myelin, and modulates their cellular adhesion to ECM such as fibronectin. Of relevance, expression of these receptors is reduced in more immature-like mutant Schwann cells expressing low levels of Krox20 [START_REF] Le | Analysis of congenital hypomyelinating Egr2Lo/Lo nerves identifies Sox2 as an inhibitor of Schwann cell differentiation and myelination[END_REF]. This parallels with previous studies that correlated immature Schwann cell-lineage cells with a greater capacity of mingling and migration across white matter [START_REF] Woodhoo | Schwann cell precursors: a favourable cell for myelin repair in the Central Nervous System[END_REF][START_REF] Zujovic | Boundary cap cells are highly competitive for CNS remyelination: fast migration and efficient differentiation in PNS and CNS myelin-forming cells[END_REF]. Nevertheless, whether expression of the Eph receptors by Schwann cells plays a role in the PNS/CNS segregation during development, and/or whether their down-regulation occurs after injury remains unknown.

What facilitates Schwann cells to conquer the injured CNS?

Despite the above-mentioned mechanisms of successful maintenance of the PNS-CNS compartmentalization, the presence of Schwann cells into the CNS in normal and pathological conditions is unquestionable [START_REF] Adelman | Intramedullary nerve fiber and Schwann cell proliferation within the spinal cord (schwannosis)[END_REF][START_REF] Feigin | Schwann cells and peripheral myelin within human central nervous tissues: the mesenchymal character of Schwann cells[END_REF][START_REF] Guest | Demyelination and Schwann cell responses adjacent to injury epicenter cavities following chronic human spinal cord injury[END_REF][START_REF] Itoyama | Spinal cord multiple sclerosis lesions in Japanese patients: Schwann cell remyelination occurs in areas that lack glial fibrillary acidic protein (GFAP)[END_REF][START_REF] Itoyama | Schwann cell remyelination of demyelinated axons in spinal cord multiple sclerosis lesions[END_REF][START_REF] Raine | On the occurrence of Schwann cells within the normal central nervous system[END_REF][START_REF] Yamamoto | Extensive proliferation of peripheral type myelin in necrotic spinal cord lesions of multiple sclerosis[END_REF]. Therefore, there must be some routes that enable Schwann cells to bypass the astrocyte and white matter inhibitory cues to invade the CNS under certain conditions. In this review, we will discuss a newly identified route of migration used by the Schwann cells to invade the CNS: the vascular network.

The presence of CNS axons remyelinated by Schwann cells, has been frequently described in close association with blood vessels in dysmyelinating (reviewed in [START_REF] Duncan | Schwann cell invasion of the central nervous system of the myelin mutants[END_REF]) or demyelinating conditions (Sims et al., 1998). PNS myelin was also found in the perivascular spaces, close to vessel at the spinal cord surface in response to spinal cord irradiation [START_REF] Gilmore | Patterns of Schwann cell myelination of axons within the spinal cord[END_REF], 1997). Moreover, various cell tracing paradigms highlighted the presence of exogenously introduced Schwann cells restricted to the meninges [START_REF] Langford | Resolution of the pathway taken by implanted Schwann cells to a spinal cord lesion by prior infection with a retrovirus encoding beta-galactosidase[END_REF], and more precisely, the subarachnoid Virchow-Robin perivascular spaces [START_REF] Baron-Van Evercooren | Cell-cell interactions during the migration of myelinforming cells transplanted in the demyelinated spinal cord[END_REF] or close to blood vessels within the brain parenchyma (Brook, Lawrence, & Raisman, 1993;Raisman, Lawrence, & Brook, 1993).

Although these studies evidenced Schwann cell-blood vessel interaction, they did not investigate the role of the blood vessel network in Schwann cells migration. To address this issue, we grafted Green fluorescent protein (GFP) expressing Schwann cells remotely form a focal lesion of the spinal cord of wild-type mice. Tissue clarification allowed visualization of the grafted cells en route to the lesion, that are in close contact with the blood vessel network (Fig. 1). The same grafting paradigm and exvivo live imaging showed Schwann cells sliding along each other on vessels and jumping from one vessel to another to reach the lesion. Furthermore electron microscopy indicated that perivascular Schwann cells in the CNS were localized between the perivascular end-feet and endothelial cells, and embedded in the perivascular ECM without making direct contacts with the endothelial cells [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. Interestingly, Schwann cells also migrate along blood vessels in the injured nerve. However in the latter case, they migrate in direct contact with the endothelial cells rather than within the perivascular ECM (Cattin et al., 2015). Thus, despite the fact that Schwann cells share similar mechanisms to conquer both PNS and CNS injured nervous system, the different molecular and cellular environment existing between PNS and CNS, including different degrees of confinement are likely to result in the different migration modalities.

Upon arrival at the lesion site, Schwann cell affinity for axons released their association with blood vessels, as a first step towards myelin repair [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. While the above data were obtained with exogenous Schwann cells grafted remotely from a lesion, lineage specific tools combined with cell specific markers provided evidence that such a mechanism is shared with endogenous Schwann cells [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. However, whether these Schwann cells have a peripheral or central origin, or both, needs to be addressed further.

Despite the newly elucidated role of blood vessels as Schwann cell cargos, whether they passively support Schwann cell migration, or whether they play a more active role remains to be solved. Launching the answer to this question, we provided the evidence first, for the absence of direct contact between Schwann cells and blood vessels thus ruling out a potential mechanical intervention of blood vessels in Schwann cell migration, and second, for the existence of vascular remodeling in the demyelinated area with a concomitant increase in ECM in response to demyelination [START_REF] Ulanska-Poutanen | Injury-induced perivascular niche supports alternative differentiation of adult rodent CNS progenitor cells[END_REF], as shown by a significant increase of collagen 4 and blood vessel network (Glut1 positive) after 5 days of lysolecithin-induced demyelinating lesions (Fig. 2). These changes may trigger Schwann cells to use the vascular scaffold to migrate within the adult nervous system. Nevertheless, more functional studies should be performed to address this question.

Conclusion /perspectives

Important to mention, numerous studies have shown extensive intercellular communication and coordinated interaction between the vascular and the nervous systems [START_REF] Glebova | Growth and survival signals controlling sympathetic nervous system development[END_REF][START_REF] Park | Coordinated interaction of the vascular and nervous systems: from molecule-to cell-based approaches[END_REF]. Elucidating in part the mechanism that opens Schwann cell access to the damage CNS, we demonstrated that this Schwann cell-blood vessel interaction is of relevance to their contribution to CNS repair [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF].

Over the last years, the role of angiogenesis and vascular remodeling in demyelinating disease has been explored focusing on their correlation with inflammation, neurogenesis, and oligodendroglia maturation [START_REF] Girolamo | Angiogenesis in multiple sclerosis and experimental autoimmune encephalomyelitis[END_REF][START_REF] Kirk | Angiogenesis in multiple sclerosis: is it good, bad or an epiphenomenon?[END_REF][START_REF] Lengfeld | The role of angiogenesis in the pathology of multiple sclerosis[END_REF][START_REF] Roscoe | VEGF and angiogenesis in acute and chronic MOG((35-55)) peptide induced EAE[END_REF]. Other studies brought to light the importance of the perivascular niche in the balance of Schwann cell/oligodendrocyte in the remyelination of the CNS lesion [START_REF] Ulanska-Poutanen | Injury-induced perivascular niche supports alternative differentiation of adult rodent CNS progenitor cells[END_REF]. Our study reveals another important aspect of this response to injury, the role of the vasculature dynamics in the repair of the lesioned CNS by Schwann cells [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. In spite of these observations, whether angiogenesis or remodeling of blood vessels open the astrocytic barrier to free Schwann cells from the astrocytic confinement remains to be investigated.

Moreover, the formation of new vessels brings to play other components such as pericytes, which are of relevance for CNS remyelination [START_REF] De La Fuente | Pericytes Stimulate Oligodendrocyte Progenitor Cell Differentiation during CNS Remyelination[END_REF]. To add, angiogenesis also increases the blood vessel permeability [START_REF] Dvorak | Vascular permeability factor/vascular endothelial growth factor, microvascular hyperpermeability, and angiogenesis[END_REF] to new molecules such as chemokines and trophic factors that will change the lesion microenvironment and further enhance Schwann cell recruitment by the injured site. These new specific microenvironments will provide different signals for cell recruitment/trans-differentiation in the lesion, or supply blood/serum components (cytokines, growth factors, oxygen, nutrients, etc...). Although the spectrum of these signals that induce myelinating cell recruitment or differentiation are still poorly understood, some leads start to emerge. For example, TGF-β produced by microglial cells and/or by macrophages and profusely present in lesions, is a powerful mitogen for Schwann cells and plays a role in the production of extracellular matrix (reviewed in [START_REF] Li | The Regulatory Effects of Transforming Growth Factor-beta on Nerve Regeneration[END_REF]. To add, a recent study showed that macrophage activation boosts Schwann cell infiltration and remyelination within the lysolecithin lesion [START_REF] Church | E6020, a synthetic TLR4 agonist, accelerates myelin debris clearance, Schwann cell infiltration, and remyelination in the rat spinal cord[END_REF]. However, whether this effect on Schwann cells is direct or indirect remains unsolved as macrophage activation promoted also axon survival and oligodendrocyte remyelination.

Our study also shows that EphrinB3 in myelin favors the adhesion and migration of these cells onto ECM via Integrinβ1, while Schwann cell adhesion in the absence of ECM is impaired [START_REF] Garcia-Diaz | Blood vessels guide Schwann cell migration in the adult demyelinated CNS through Eph/ephrin signaling[END_REF]. This aspect elucidates another component of the balance between oligodendrocyte and Schwann cell remyelination of the lesioned CNS. While EphrinB3 impairs the differentiation of oligodendrocyte precursor cells into mature competent myelinating cells [START_REF] Syed | Antibody-mediated neutralization of myelin-associated EphrinB3 accelerates CNS remyelination[END_REF], it favors Schwann cell mobilization towards the lesion.

In conclusion, studies over the recent years have elucidated major aspects of Schwann cell transgression of the PNS-CNS border to repair the CNS (Fig. 3). In spite of gaining a clearer view of this scenario, several features remain to be uncovered. Are blood vessels the only route of migration across the CNS? or, can this pathway be extended to the lymphatic system? Are these routes the same regardless Schwann cell peripheral or central origin, and are they scaffold for the formation of schwannomas around cranial and spinal nerves [START_REF] Suresh | Unusual case of multiple cellular and malignant schwannomas of the cranial and spinal nerves[END_REF]? So far non-myelinating and myelinating Schwann cells participate to CNS repair. Stem cells are also present in the adult PNS and namely in the adult DRG (reviewed in [START_REF] Mehrotra | Adult tissue-derived neural crest-like stem cells: Sources, regulatory networks, and translational potential: Concise review[END_REF]). Yet their activation and involvement in response to CNS injury remains to be addressed. Is the stage of Schwann cell differentiation, which modulates their incursion during injury, of developmental relevance? How can this be therapeutically modeled to favor the CNS repair? Moreover, the close relation with blood vessels opens up an easy access for those cells to sense different local and systemic signals, which might influence their remyelinating success or failure. These are some of the questions that may provide important clues for the future. Novel lineage specific tools will be required to decipher these questions and to design successful therapies.

Figure 1 .

 1 Figure 1. A. Scheme of LPC lesion and SC graft targeted into the dorsal funiculus of the spinal cord. B. 3D Z stack reconstruction illustrating grafted SC (red) around blood vessels (green); C. Clarified spinal cord showing grafted Schwann cells (SC, C 1 ) expressing the Tomato Cherry protein (red) that migrate along blood vessels (green, C 2 ).

Figure 2 .

 2 Figure 2. Vascular remodelling in response to lysolecithin-induced demyelination of the spinal cord.Demyelination was induced by lysolecithin injection into the dorsal funiculus of the mouse spinal cord. A Immunolabeling of the vasculature using the endothelial marker Glut1 (red) 5 days post injection lysolecithin (5dpi), shows that the vascular network increases within the lesion site (dotted line) concomitantly with an increase in the basal lamina marker collagen 4 (red) in the demyelinated lesion. B. Quantification of the vasculature dynamics at different time-points after LPC injection (1, 3, 5 and 7 dpi) based on the ratio of Glut1+ area after LPC over PBS at 1dpi.) Data are expressed as mean value ± SD of control (PBS) (n=15), 1dpi (n=4), 3dpi (n=4), 5dpi (n=4), 7dpi (n=5). Kruskal-Wallis test (p=0.001) followed by comparison between each group with PBS group performed by two-tailed Mann Whitney test 3dpi (p=0.019); 5dpi (p=0.0005); and 7dpi (p=0.01).

Figure 3 .

 3 Figure 3. Graphical abstract on Schwann cell origins and interactions with CNS cell components. (1) CNS-located Schwann cells (yellow-brown cells) originate from the peripheral myelinating and nonmyelinating Schwann cells; (2) and the central transdifferentiated OPC (blue-grey cell) under BMP/Wnt and STAT3 signaling. (3) Schwann cell invasion of the CNS is impaired by astrocyte (green cells) at the level of the PNS-CNS transition zone (glia limitans) and the CNS lesion border (reactive astrocytes). Schwann cell-astrocyte repulsion is due to different components such as N-cad, NCAM, and EphAs in Schwann cells, and by GFAP, CSPG, aggrecan, HSPG, NCAM and EphrinAs in astrocytes. (4) Schwann cell migration within the CNS, is inhibited by myelin (blue), through MAG-p75NTR and EphrinB3-EphA4/B6 signaling. (5) Myelin-associated EphrinB3 modulates the adhesion of Schwann cells via upregulaion of Integringβ1, and thereby, increasing their affinity for ECM (red) migration on blood vessels (Garcia-Diaz et al., 2019).

We thank the National Multiple Sclerosis Society (NMSS), to A.B. INSERM, CNRS, ARSEP, and the program "Investissements d'Avenir" (ANR-10-IAIHU-06) to AB; and Junta de Andalucía and the European Commission under the Seventh Framework Program of the European Union (agreement Num. 291730, contract TAHUB-II-107) to B.G-D for having support our work on Schwann cells. We also thank past and present members of the laboratory and collaborators for their valuable contributions.


X J Shen

D Connétable

E Andrieu

D Tanguy
email: dome.tanguy@univ-lyon1.fr

Segregation of hydrogen and vacancies at the Σ5(210)[001] symmetric tilt grain boundary in Ni and influence on cohesion

The segregation of hydrogen and vacancies at the Σ5(210)[001] symmetric tilt grain boundary (GB) was studied by atomic scale simulations in Ni. First, the hydrogen segregation energies and hydrogen-hydrogen pair interaction energies were calculated on every interstitial site of the GB. The vacancy-hydrogen clusters' formation energies were also determined on the most favorable site. All these calculations were done using the Density Functional Theory (DFT). Second, based on these elementary energies, a free energy functional was built to determine the concentration of segregated hydrogen and of vacancy-hydrogen clusters, as a function of the bulk hydrogen concentration and the temperature. It was found that two configurations exits in typical conditions where embrittlement is observed experimentally: H segregation only, with up to 3 hydrogen atom per structural unit or 50% occupancy by V H 5 clusters (1 cluster every two structural unit). The cohesive stress and ideal work of fracture were evaluated by fracturing the GB with different degrees of hydrogen and vacancy segregation. H segregation alone (no vacancy) decreased the work of fracture by 25%. A significantly larger decrease of cohesion was obtained when considering vacancy-hydrogen clusters. A maximum drop of the cohesive stress, of a magnitude of 40%, was obtained when every structural unit was hosting a V H 4 cluster. Finally, these data were transformed into cohesive stress models. They were used to evaluate the degree of localization of the shear displacement at the crack tip. The conclusion is that, even if cohesion is very significantly decreased, shear localization is still effective, meaning that dislocation emission should occur at the expense of crack propagation. Therefore, extra ingredients should be considered to explain the embrittlement observed experimentally.

Introduction

Hydrogen embrittlement of metals is an important issue because it causes crack initiation and propagation at low load levels and at high speeds and is therefore potentially dangerous. A large research effort has been dedicated to characterizing the phenomenon in all sorts of metallic alloys and environments [START_REF]Gaseous hydrogen embrittlement of materials in energy technologies[END_REF][START_REF] Vehoff | [END_REF][3][4][5][6]. A number of models have been proposed [7; 8] based on fractography [7], in situ acoustic emission [9; 10] or in situ TEM [11]. The origin of the embrittlement remains unclear. Four microscopic mechanisms were proposed : decohesion (transgranular cleavage or separation along the core of grain boundaries), enhanced crack tip plasticity due to hydrogen adsorption, enhanced and localized plasticity ahead of the tip [11][12][13][14] and, more recently, aggregation of hydrogen stabilized vacancies [15; 16]. Some aspects of these mechanisms have been more precisely quantified by modern experimental techniques, with high spatial resolutions. For example, the trapping of hydrogen at interfaces has been demonstrated, at the atomic scale, by atom probe tomography [17] and a dislocation substructure with a typical length scale of 250 nm was imaged in the plastic wake, below the fracture surface [18; 19]. Small scale mechanical testing also produced new in situ observations, such as, the confinement of the plastic zone (50 nm) during transgranular cracking in bending micro beams [20] in FeAl, or the locking of dislocations by vacancy-hydrogen clusters using a cyclic compression of a nano pillar in a TEM [3]. Note the recent observations of the cracking of bcc Fe at low temperature [21; 22] which reveal a mixture of cleavage and localized plasticity and the critical review of the limitations of current atomistic simulations of dislocation emission at crack tips in bcc Fe [23]. They constitute a reference for the hydrogen embrittlement of steels at room temperature.

The efforts made by the modeling community in trying to validate or invalidate such micro-mechanisms have been intense and now covers all the different aspects. Adsorbed, or sub-surface, hydrogen does not seem to enhance dislocation emission at crack tips, at least in Al [24][25][26]. Intergranular diffusion, where both speed up and slow down have been measured experimentally, seems to be well understood [27][28][29][30], especially the H concentration effect. Preliminary results on pipe diffusion were also recently reported [31]. The effect of co-segregation has been intensively studied [32], in particular at the interface between carbides and the bcc-Fe matrix [33]. Concerning vacancies [START_REF] Fukai | The Metal-Hydrogen System: Basic Bulk Properties[END_REF], the origin of the enhancement of their concentration is the strong binding between hydrogen atoms and vacancies and the possibility of multiple occupation [34][35][36][37]. They also impact diffusion [38; 39], but in conditions which might not be those of embrittlement, at least if vacancies are considered in equilibrium with H. The impact of hydrogen on the mobility of screw dislocations in Fe, a key issue for the embrittlement of steels, has been modeled recently [14].

The most important aspect is fracture itself. In hydride forming systems, the crack tip, with its stress concentration and layer of adsorbed H, might act as a seed for stabilizing a local hydride, which will prevent the tip to relax by emitting dislocations and therefore promote brittle fracture [40]. In non-hydride forming systems, the Rice and Wang model [41], with parameters from Density Functional Theory (DFT) calculations, shows that beyond a critical chemical H potential, a phase transition occurs where, at a critical applied stress, the opening interface becomes abruptly fully populated by H. When this occurs, the cohesive stress is drastically reduced [42]. A kinetic version of this model was recently proposed for the embrittlement of grain boundaries in Ni [43]. In contrast, when the local H concentration is kept fixed during fracture, hydrogen's impact is weak: configurations which were initially ductile, i.e. with a glide plane properly oriented with respect to the crack tip for an easy activation of plasticity, remain ductile in the presence of segregated hydrogen, even if the concentration is representative of experiments [44]. In contrast, the cohesion never drops to zero because of hydrogen charging in experiments, at least in Ni, and crack propagation occurs, even along grain boundaries, with intense plastic deformation [18]. Therefore, some extra mechanisms should be considered in between the two extremes of the absence of diffusion during fracture and an instantaneous diffusion of H to the surface.

One way, in the intergranular case, is to complexify the grain boundary configurations by considering vacancies in addition to hydrogen. The driving force for stabilizing them is the same as in the bulk but, with a lower formation energy at grain boundaries, large concentrations of vacancies can be expected. A first study in this direction was done on the Σ3{112} 110 symmetrical tilt grain boundary (GB) of bcc Fe. Intergranular vacancies were found to significantly decrease the work of fracture, with respect to hydrogen alone [45]. Nevertheless, a limitation of this work is the lack of a clear connection of the local H and vacancy concentrations to experimental conditions.

In this context, the goal of the paper is to model realistic GB configurations in the presence of segregated hydrogen and vacancies. The method is first to obtain H segregation energies and vacancy-hydrogen cluster (VH n , n H for one vacancy) formation energies in the GB from reliable electronic structure calculations. These energies are then introduced in a free energy functional which gives the average concentration of H on the various interstitial sites of the GB and the VH n concentrations as a function of the thermodynamic parameters c bulk (the H concentration of regular bulk interstitial sites) and the temperature T. Finally, atomic configurations representative of the experimental conditions for H embrittlement are chosen and fractured. The influence of H and VH n on cohesion is quantified. The system chosen is Ni because there are numerous observations of intergranular embrittlement [18] and because vacancy effects were observed [46].

The paper is organized as follows. The construction of the GB and the methods are first described. Then, the structure of the GB and the formation energies of the vacancies are detailed. The segregation energies of isolated hydrogen atoms and the formation energy of the various clusters on the most favorable site of the GB are given. The hydrogen-hydrogen pair interaction energies are determined. Then, these data are used to parametrize a free energy functional which minimization gives the hydrogen concentration on regular interstitial sites. As the bulk concentration is increased the grain boundary becomes occupied by vacancy-hydrogen clusters. Finally, representative GB structures with hydrogen segregation alone, or with segregated vacancy-hydrogen clusters are selected and fractured along the interface plane. The absence of impact of the vacancies on the ideal work of fracture, compared to the effect of H alone, is discussed.

Models and Methods

Grain boundary model

The Coincidence Site Lattice (CSL) was used for the construction of the Σ5(210)[001] symmetrical tilt grain boundary. After the elimination of overlapping atoms in the GB plane and relaxation of stresses and forces, the minimal energy structure was obtained. Each CSL unit contains two equivalent GB structural units, as shown in the figure 1a. Characteristic atomic sites are labeled GB 1 , GB 2 and GB 3 . The x axis is oriented along [210], y along [120] and z along [001]. Two system sizes were used: one with only one CSL unit on each side of the GB and two periods along the tilt axis (z) (80 atoms) and a second one, elongated in the x direction (112 atoms) (Fig. 1). Periodic boundary conditions were imposed in the y and z directions. In the x direction, free surfaces were created by introducing a vacuum layer of thickness 7.0 Å. The surface layers are held rigid, at the perfect lattice parameter to mimic bulk behavior. In the small system, the rigid part starts beyond the seventh (210) layer, while in the enlarged region of the big system, it starts after the sixteenth layer. The box size was optimized in the x direction, while keeping the bulk lattice parameter in the other directions.

In the perfect face centered cubic (fcc) structure, which is the most stable for Ni, there are two tetrahedral and one octahedral sites for each fcc lattice site. Such interstitial sites were geometrically constructed, by displacement from the lattice site, for every atom of the left grain, including the sites of the GB plane. Then they were transformed by a planar symmetry with respect to the interface plane and used for the atoms of the right grain, including again the atoms of the GB plane. This procedure creates a high density of geometric interstitial sites in the core of the GB. Searching for the metastable sites for H segregation, 15 of such geometric sites were used as starting points. Many of them relaxed to the same configuration.

Density Functional Theory Calculations

In order to obtain reliable equilibrium atomic structures of GBs and accurate hydrogen segregation energies first-principles calculations were conducted to optimize structures and calculate system energies. Our calculations were performed within the density functional theory (DFT) and carried out with the generalized gradient approximations (GGA) to the exchange-correlation functional (Perdew-Burke-Ernzerhof -PBE-functional) [47], as implemented in the Vienna Ab initio Simulation Package (VASP) [48]. We used projector-augmented wave (PAW) [49] method for valence electrons and a 1×3×3 k-points grid for the Brillouin zone sampling. Spin-polarization effects for all the considered system were taken into account. Plane-waves were used for expanding the wave functions with a cutoff energy equal to 400 eV. These criteria are necessary when optimizing atomic forces (< 0.01 eV/ Å) and obtain accurate energies (<2-4 meV).

The zero-point vibrational energy (ZPE) of H atoms was computed for all Ni-H systems we selected. In calculating the zero-point vibrational energy of hydrogen atom in the Ni-H system, the dynamical matrix only for H atoms using the frozen phonon approach (the relative displacements was taken equal to 0.01 Å) was used to calculate the vibrational frequency. Using the real frequencies of hydrogen (ω n ), we calculated the ZPE of H atoms, where the ZPE is approximated by ZP E = Σ n ω n /2 at 0 K.

Mean Field Equations

The average hydrogen and vacancy concentrations in the GB are calculated using a free energy functional. Its simplest form, with hydrogen only, is detailed here. It will be complexified later to introduce also vacancies. In the case of hydrogen alone, the variables of the functional are the concentrations on every interstitial site (c i ) and the parameters are the temperature (T) and the hydrogen chemical potential (µ H ). Its optimization gives the equilibrium concentrations on the interstitial sites of the GB. A first, approximate, mean internal energy can be obtained from the segregation energies on each site i of the GB (∆E i seg ), defined in the absence of interactions between the occupied sites (dilute limit). As will appear clearly below, the specificity of the GB core requires that the H-H interactions are included in the model. This is done by calculating effective pair-interactions by taking the energy difference between two configurations containing two H atoms: the final one in which the two H atoms are close and the reference one in which each solute occupies its GB interstitial site, but far enough so that the interaction between them can be neglected. In DFT calculations, because of the size limitation, a reference energy (E ′ ref ) is calculated with one H atom on its GB interstitial site (for example site j ) and the second one on a bulk site. By using the value of the segregation energy on site i, the effective pair interaction ǫ ij between interstitial sites i and j is then defined by [37]:

ǫ ij = E ij -(E ′ ref + ∆E i seg ) (1)
where E ij is the energy of the configuration where the sites i and j are occupied. With these parameters, the free energy, as a function of the average occupancy of the GB sites c i and the bulk sites c bulk , is:

F N H ,V,T (c i ) = E 0 + i {c i ∆E i seg + j c i c j ǫ ij + k B T (c i ln c i + (1 -c i ) ln(1 -c i ))} (2)
The constraint of a fixed number of H atoms, N H , is taken into account by introducing a Lagrange multiplier µ H . Writing the optimization condition for each kind of site gives the equilibrium concentrations:

c i 1 -c i = e -(∆E i seg + j c j ǫ ij -µ H )/k B T c bulk 1 -c bulk = e µ H /k B T (3)
where c bulk is the H concentration on a bulk site (far from the GB). The equations, and approximations, specific to the GB structure are given in section 3.4.

Results

Atomic structure of the grain boundary and vacancy formation energies

The vacancy formation energy is evaluated on every site of the GB. In the case of a system containing n vacancies, the excess energy E f n , per vacancy (the average formation energy) is:

E f nv = (E def ect + n E bulk -E perf ect )/n (4)
where E perf ect is the energy of the reference structure (the one with the minimum energy) shown on Fig. 1a, E bulk is the energy of a Ni atom in a perfect crystal. It is calculated using a cell containing 4 Ni atoms and a 9×9×9 k point mesh. The atomic energy is -5.571 eV/atom. E def ect corresponds to the energy of the system containing n vacancies. In bulk Ni, with the same DFT parameters, the vacancy formation energy is about 1.40 eV [50], in good agreement with other theoretical values [35] (1.44 eV). It has been recently shown that the long standing discrepancy between the experimental values of the free formation energy obtained at high temperature and the low temperature values from DFT can be explained by an-harmonic effects [51]. Therefore, we take 1.40 eV as a reference value for the formation energy in the bulk.

After relaxation, the perfect Ni-Σ5(210)[001] symmetrical tilt GB remains symmetric. The single vacancy formation energy E f 1v was calculated on every GB site and gave the following values, for the small system: 1.843, -0.100 and 1.143 eV for sites GB 1 , GB 2 and GB 3 respectively and on the most remote site, GB 4 , 0.968 eV. The value on GB 4 is significantly different from the bulk one and therefore, this site is too close to the GB to be used as a reference for the vacancy segregation energies. Furthermore, with this system size, the perfect GB is unstable with respect to the formation of vacancies (the formation energy on site GB 2 is negative). The "large" system (Fig. 1) is asymmetric in order to contain sites further away from the GB with still an affordable computational effort. E f 1v on one of such sites, GB 5 , is 1.313 eV, closer to the bulk calculation (1.400 eV). It is therefore used as a reference site for segregation energies. With this system size, the vacancy formation energies on sites GB 2 and GB 4 are respectively: 0.210 eV and 0.972 eV. The other sites are not considered any longer because the formation energy, there is too high to lead to vacancy-H clusters in the thermodynamic conditions considered here. The symmetric GB is now stable with respect to vacancy formation (all formation energies are now significantly higher than 0). Note the large relaxation induced by the vacancy (Fig. 1c), especially the displacement of the occupied GB 2 site (left side of the GB) towards the interface plane.

In addition to single vacancies, we also studied divacancies aligned along the tilt axis. Because of the short dimension of the system in this direction, which corresponds to only two equivalent sites, and the periodic boundary conditions, the divacancy is in fact an infinite line of vacancies. The average formation energy per vacancy E f 2v for sites GB 1 , GB 2 GB 3 and GB 4 are respectively: 1.432 eV, 0.075 eV, 1.207 eV and 1.032 eV. Again, the reference GB structure is stable, even if removing a line of GB 2 sites creates a GB with an energy very similar to the reference. All vacancy formation energies are listed in Table 1 with the corresponding site positions.

Intergranular hydrogen segregation energies, effect of vacancies

For calculating the hydrogen segregation energies, a reference was created by placing the H atom as far from the GB as possible, in octahedral position. Then a series of DFT calculations were conducted on configurations where the solute was placed at the different geometrical interstitial sites in the GB core and relaxed, as discussed in subsection 2.1. The segregation energy (∆E i seg ) is the difference between such configurations, labeled i, and the reference:

∆E i seg = E jdg (H i ) -E jdg (H octa ) ( 5
)
where E jdg (H i ) and E jdg (H octa ) are the energy of an H atom occupying the i site of the GB and the energy of an H atom in a bulk octahedral site. A negative ∆E i seg (resp. positive) value means an enrichment (resp. a depletion) with respect to the bulk. Only 5 different metastable positions were found after minimization, with DFT. They were presented on Fig. 1a. The corresponding segregation energies are given in Table 2, as well as the positions. The zero-point energy corrections are also listed in Table 2. In bulk Ni, the octahedral and tetrahedral sites have a large energy difference, of the order of 0.22 eV [50], with the first one being the most stable. In the GB, the most stable position for hydrogen is also an octahedral site (site 6). The corresponding segregation energy is -0.244 eV (resp. -0.278) without (resp. with) the ZPE correction. The second deepest trap site is site 5 (-0.266 eV), which is tetrahedral and the third one is site 4 (-0.182 eV). These results are in good agreement with other DFT calculations [29; 52]. Site 1 is already a bulk site, which indicates that the influence of the GB is short range.

Next, a vacancy is created on the GB site with the lowest vacancy formation energy: site GB 2 . It has two effects on the segregation sites for H: it modifies the existing sites and it creates new ones (see Fig. 1 c andd). Because the system contains two cells along the tilt axis, removing one atom creates a concentration of vacancies of 50% on the GB 2 sites along the tilt axis. As a consequence, the interstitial sites are not always equivalent along the tilt axis direction anymore. The structural units are also no longer equivalent along the y axis. Nevertheless, we did not evaluate the impact of the vacancy on the H segregation energies on these structural units which are relatively remote from the vacancy. We expect the modifications to be minor. First, the two core interstitial sites minor segregation sites.

Hydrogen-hydrogen interactions

Large segregation energies, in absolute value, were obtained. It can therefore be anticipated that some sites will be almost fully occupied if the bulk hydrogen concentration is increased at low enough temperature. Mean field equations for isolated site occupancy (ǫ ij set to zero in Eq. 3), show that sites 6, 5 and 4 of the perfect GB are almost saturated, for embrittlement conditions typically used in experiments: c bulk below 1000 ppm and T=300K (Fig. 4). Solute-solute interactions can therefore play a significant role in the H enrichment of the GB, depending on the distance in between these sites. The energetics for this is given by solute-pair interactions [53] ǫ ij . A negative (resp. positive) pair interaction means attraction (resp. repulsion). The calculation of the pairs does not need to be exhaustive. To find which interactions are needed, we step by step increase the bulk concentration are follow the occupancies given by the mean field equations. The deepest traps are sites are 6, 5 and 4 for the perfect GB (resp.

Table 3. Interaction energy between hydrogen atoms (in eV) obtained for the large (small) perfect and defective GB structures. The site numbers (i) refer to Fig. 1. ǫ 6-i (in eV) is the pair interaction energy between site number 6 and its neighbors. ǫ 6-5-i (in eV) is the three-body interaction energy between the pair (6,5) and its neighbors.

Large(small) perfect GB structure site i ǫ 6-i ǫ 6-5-i

i ǫ O5-i ǫ O5-O4-i ǫ O5-O4-O3-i ǫ O5-O4-O3-5-i ǫ O5-O4-O3-O2-5-i 2
0.007 -0.010 -- -- -- O 4 -0.030 -- -- -- -- O 5 , O 1 , O 6
and O 4 in the presence of the vacancy). The first concentration to go up is the one on site 6 (resp. O 5 ), therefore the pair interaction between a site 6 (resp. O 5 ) and all the others is calculated first (table 3). The interaction with the next deepest trap site (site 5) is weak, so both sites can be enriched independently. In the vacancy, segregation on O 4 is enhanced by the filling of sites O 5 , while it is decreased on sites O 1 and O 6 (table 3). Site O 4 is therefore enriched together with site O 5 . The next step is to consider that both sites 6 and 5 (resp. O 5 and O 4 ) are saturated and evaluate the pair interactions with the other sites. Segregation on site 4 of the perfect GB is only slightly diminished (ǫ ∼ 0.015 eV). The other sites will be occupied at concentrations higher than 1000 ppm and therefore are of minor importance for embrittlement. In the vacancy case, sites O 3 , 5 and O 2 are consecutively occupied. The corresponding pair interactions are in table 3.

Grain boundary occupation by hydrogen and vacancies

The preceding sections have shown that the vacancy formation energy on site GB 2 is small. Furthermore, the hydrogen segregation energy to the GB 2 vacancies is strong.

It is therefore likely that vacancy-hydrogen clusters (VH n ) form, as previously found in the bulk [35; 37]. The goal is now to calculate the H and VH n concentrations in the grain boundary. The mean field model presented in section 2.3 can be modified to take into account the VH n on the GB 2 sites (the one where the vacancy formation energy is the lowest). The new free energy is:

F N H ,V,T ({c i }, {c V Hn }) = E 0 + N (1 - 6 n=0 c V Hn ) i (c i ∆E i seg + j c i c j ǫ ij ) + kT i (c i ln c i + (1 -c i ) ln(1 -c i )) + n=6 n=0 N(c V Hn E V Hn f + kT c V Hn ln c V Hn ) + N kT (1 - n=6 n=0 c V Hn ) ln(1 - n=6 n=0 c V Hn ) ( 6
)
where N is the number the equivalent GB 2 sites in the system (the number of structural units), n is the number of hydrogen atoms in the VH n cluster. Note that the label i for interstitial sites designates those interstitial sites which are not inner vacancy sites. Indeed, when a vacancy is created on a GB 2 site, the two sites 4 in first neighbor are replaced by sites O 1 and O 6 of the vacancy, sites 3 and 3' are replaced by sites O 4 and O 2 respectively and site 6 is replaced by site O 5 . Sites 5 and 2, which are core interstitial sites of the GB, still exist but are much less attractive than regular vacancy sites. The factor (1 -n=6 n=0 c V Hn ), ahead of terms which are function of c i , is used to mark which of the structural units do not host vacancies and therefore can host hydrogen on regular interstitial sites. There are also two different configurational entropy terms: one for the H atoms on the lattice of the interstitial sites of the structural units free of vacancies and one for the seven VH n species on the GB 2 plane (one GB 2 per structural unit). The fixed total number of hydrogen atoms N H = N(1 -n=6 n=0 c V Hn ) i c i + N n=6 n=0 nc V Hn is constrained. Introducing the Lagrange multiplier µ to take into account this constraint and taking the derivative with respect to c i and c V Hn gives the same equilibrium c i as Eq. 3, plus the additional relations:

c V Hn = A n 1 + 6 j=0 A j (7)
where

A n = e -(E V Hn f +n µ H -A µ H -B)/kT (8)
with

A = 0 if n = 0 (9) A = c 2 + 2c 3 + 2c 4 + c 5 + c 6 if n = 0 B = c 2 ∆E 2 seg + kT (c 2 log c 2 + (1 -c 2 ) log(1 -c 2 )) + 2(c 3 ∆E 3 seg + kT (c 3 log c 3 + (1 -c 3 ) log(1 -c 3 ))) + 2(c 4 ∆E 4 seg + kT (c 4 log c 4 + (1 -c 4 ) log(1 -c 4 ))) + c 5 ∆E 5 seg + kT (c 5 log c 5 + (1 -c 5 ) log(1 -c 5 )) + c 6 ∆E 6 seg + kT (c 6 log c 6 + (1 -c 6 ) log(1 -c 6 )) (10)
Ef V Hn is the formation energy of the clusters. As an approximation [37], only one cluster per class (i.e. per value of n) is taken, with the smallest energy. A list of such formation energies is given in the appendix (table A1).

Figure 2 shows the result for a vacancy formation energy E l f of 0.21 eV and a temperature of 300 K. The total number of vacancies is shown with crosses. The detail per cluster is also shown. With these parameters, sites GB 2 are saturated by V H 4 and V H 5 clusters beyond 100 ppm (resp. 1000 ppm at T=400K, Fig. 3, the temperature at which the isolated vacancies start to be mobile in the bulk [38]). Trying to extrapolate to other grain boundaries, the comparison of the V H n formation energies on site GB 2 of the grain boundary and in the bulk (appendix Appendix A and Table A1) show that the average segregation energy per atom is similar, at least for clusters with 5 and 6 hydrogen. A reasonable model for obtaining the saturation c bulk for a grain boundary, in general, could be to approximate the formation by E V Hn f ≈ E i f + n × ∆E seg with ∆E seg the average segregation energy of the bulk vacancy (-0.26 eV) and E i f , the formation energy of the vacancy on site i of the GB. Figure 3 shows that saturation can be obtained, within the c bulk range typical of embrittlement, i.e., below 2000 ppm, only at low temperature (below 400 K) and if E i f is low (below 0.5 eV). The model can be refined further by taking into account the large repulsive interaction between a vacancy and the neighbor sites 6': the segregation energy increases from -0.278 eV up to -0.100 eV (Table 2). The effective, repulsive, pair interaction is therefore ǫ 6-V = 0.178 eV. Its variation with the H occupancy of the vacancy is not considered. This effect is included in the mean field model by adding the term 2c 6 6 n=0 c V Hn ǫ 6-V in the free energy (Eq. 6). Then the model predicts a phase transition from a low c V Hn / high c 6 (i.e. high occupancy of regular interstitial sites) phase to a high c V Hn phase at high bulk hydrogen concentration. Figure 4 shows the c bulk value where these phases separate, close to 40 ppm. Saturation is obtained essentially because of VH 4 and VH 5 clusters (Fig. 4b). In the mean time, the concentration on sites 6 of the structural units which are not occupied by a vacancy, i.e. sites 6' in table 2, drops to almost zero. In addition, we can expect a repulsive interaction between the VH 5 along the tilt axis because of H-H repulsion between sites 5 and the O sites of the second vacancy. One way to avoid this repulsion is to order the vacancies on a checkerboard structure on the GB 2 plane. The maximum occupancy is therefore 50% and the repulsion between the VH 5 and sites 6' and 5' constrains these sites to a low occupancy. Therefore, there are 3 main relevant configurations for the fracture calculations: (i) one corresponds to a segregation in the absence of vacancies (in case vacancy production and diffusion are too slow to reach equilibrium). In this case sites 6 and 5 are fully occupied at c bulk = 100 ppm (T=300K) (see the insert of Fig. 5), i.e. the system contains 8 H, (ii) at c bulk = 1000 ppm (T=300K), sites 4 are occupied at 50%, but there are 2 sites "4" per structural units and therefore the configuration contains 12 H, (iii) a configuration corresponding to the high vacancy concentration where the GB 2 sites are occupied at 50% by VH 5 clusters (configuration 2 VH 5 on Fig. 6).

C vacancy C bulk C v total C VH 0 C VH 1 C VH 2 C VH 3 C VH 4 C VH 5 C VH 6

Influence on cohesion

In view of these results, the focus is now on the influence of the presence of hydrogen on the cohesion of the grain boundary, with limited diffusion. The situation where the GB is perfect is compared to representative cases where defects are created, with configurations which correspond to experimental conditions, as discussed above. In the simulations, there are four CSL. The cases considered are therefore: one vacancy in or far away from the GB, one V H 5 cluster (25% occupancy of the GB 2 sites), two V H 5 clusters in the checkerboard configuration (50% occupancy of the GB 2 sites), and finally, four V H 4 (100% occupancy of the GB 2 sites). Two additional cases were considered. They correspond to the low vacancy phase, where only regular interstitial sites are occupied. The GB was filled with 8 (sites 5 and 6 fully filled) and 12 (sites 4, 5 and 6 filled) H atoms (configuration labeled 8H and 12H below). To carry out the simulations, the Ni atoms were fixed to the edges of the box and the distance between the atoms of the grain boundary was increased. Only the atoms in the vicinity of the fracture (the first Ni planes on either side of the GB and the GB plane itself) were left free to relax, while all H atoms were fully relaxed. The cases with an empty vacancy (in and out the GB) are used as control configurations, to see how hydrogen atoms specifically modify the cohesion of the GB. The other cases are the configurations which represent the filled sites for desired experimental concentrations. Figure 6 shows the evolution of the excess energy as a function of the distance between the two slabs. We first note that the presence of an empty vacancy near the GB does not change the cleavage fracture. The difference in the excess energy between the three configurations (perfect and both cases with a vacancy) is low, smaller than the numerical accuracy. Significant effects appear when H atoms are included in the system. When all favorable interstitial sites are filled with H atoms, i.e. when the system contains 8 or 12 H atoms, the work of fracture decreases by about 25% (Fig. 6a). This value is coherent with the classical difference between surface segregation energy and intergranular segregation energy. The effect is not as clear when vacancy-hydrogen clusters are considered (Fig. 6b), however the maximum slope of the curve markedly decreases as a function of the number of vacancy-hydrogen clusters in the system. This slope, evaluated by the numerical gradient of the data in Fig. 6, is taken as an estimate of the cohesive stress σ max and reported in table 4. It decreases from 23 GPa in the "pure Ni" case, i.e. the case where the GB carries no hydrogen and no defects, to 20 GPa (13% drop) in the case of hydrogen segregation only (i.e. configurations 8H and 12H in Fig. 6a) and to 14 GPa when the interface is saturated with V H 4 clusters (40% drop). In this last case, the work of fracture is higher than any other case, and even higher than the perfect GB. This is because the breaking procedure is quasi-static with a very low temperature which does not anneal the surface. It generates a high energy surface state. It was checked that the conclusions regarding embrittlement are not changed when the work of fracture is diminished to represent an annealed surface (see table 4).

The calculations show that the presence of hydrogen qualitatively decreases cohesion, either by decreasing the work of fracture or the cohesive stress, but we would Different cases were considered: the perfect GB, the GB with one V H 5 , two V H 5 or four V H 4 clusters. In V H 5 -V H a 5 (resp. V H 5 -V H b 5 ), the vacancies are on the same (resp. opposite) side of the GB. like to go further by quantifying the embrittlement of the immediate vicinity of the crack tip. This is done by considering the competition between crack propagation and dislocation emission from the tip (intrinsic ductility). In a previous work dealing with the impact of nanocavities on fracture [54], it was shown, by comparison with classical atomistic simulations of cracks, that a cohesive zone model, with parameters taken from atomistics, can be used to quantify this competition. This model is used again here with parameters obtained from the work of fracture W and the cohesive stress σ max and presented in table 4. It was shown (article [54] and its supplemental material) that the crack opening profile, at least when some damage develops in the Table 4. The table gives the cohesive stress σ max (GPa) obtained from the gradient of the energy in Fig. 6, the critical opening δ c (nm), the work of fracture W (Fig. 6) and the maximum displacement shift ∆ũ z (nm) [54]. In parenthesis, in the last column, are the parameters taken to evaluate the impact of a lower work of fracture that could be obtained if the fracture surface was annealed. The impact on ∆ũ x is small: it decreases from 0.044 to 0.040 nm. The threshold for embrittlement is 0.035 nm. fracture process zone, can be accurately modeled by a simple triangular cohesive law:

system Pure Ni 8H-12H 1 V H 5 V H 5 -V H 5 a V H 5 -V H 5 b 4 V H 4 σ max (
σ(δ) = σ max (1 -δ/δ c )
, where δ is the opening (twice the displacement in the direction perpendicular to the crack plane, i.e. the x direction in Fig. 1) and δ c is the critical opening beyond which the cohesive stress σ(δ) is zero. δ does not include the elastic part of the displacement and is zero beyond the end of the fracture process zone where the elastic behavior is recovered. In the early stage of fracture, or if the structure does not reorganize during fracture like during cleavage cracking, the UBER model [23; 55] is more appropriate. With this triangular law, the critical opening is obtained by the relation W = 1/2 × σ max × δ c . It is of the order of 0.3 nm (table 4). Away from the fracture process zone, the system is elastic with the Voigt average elastic constants (isotropic) µ = 94.7 GPa and ν = 0.276 for Ni ([56] p. 835). The problem to be solved here is an internal crack, in an infinite elastic medium, submitted to a remote applied stress, with a nonlinear cohesive zone ahead of each crack tip. It was solved within the infinitesimal dislocation density formalism [54]. For every applied stress, the fracture process zone length L pz and the crack opening profile δ(y) were calculated. Upon increasing the applied load, the stiff fracture process zone forces the crack to bow out, inducing a localized shear in the vicinity of the crack tip. It is characterized by the displacement shift ∆ũ x which is the projection, in the direction of easy glide, of the difference in displacement of two atoms in first neighbor position on the surface. ∆ũ x is maximum in the vicinity of the tip. As the mechanical load increases, this maximum first increases up to a maximum value and then decreases (Fig. 7). Appendix B shows representative crack opening profiles and ∆ũ x profiles from which the data in Fig. 7 were obtained. For every configuration of the interface (pure Ni, segregated hydrogen, or various concentrations of vacancy-hydrogen clusters) the maximum value of the curve represents the maximum shear localization the crack tip undergoes during mechanical loading. This value is reported in table 4. It decreases from 0.061 nm down to 0.053 nm when segregated hydrogen is introduced in the system and then further down to 0.044 nm when the concentration of vacancy hydrogen clusters is set to its maximum (corresponding to 4 V H 4 clusters i.e. 100% occupancy of the GB 2 sites in the interface). This represents a drop by 28%. In the case of nanocavities in Al, it was shown in [54] that dislocation emission corresponds to a fairly low value of ∆ũ x , of the order 0.04 nm in the case of Al (approximately one half of the glide necessary to reach the unstable stacking configuration). Rescaling this value to take into the difference of lattice parameter between Al and Ni brings this threshold to 0.035 nm. This value corresponds to a massive drop of 43% with respect to the perfect GB, while the maximum drop of ∆ũ x is only of 28% in the best case of the V H 4 clusters. As a consequence, even if the presence of hydrogen, and even more in the presence of vacancy-hydrogen clusters, decreases the maximum value ∆ũ x , it is always much higher than the threshold. Therefore the tip will emit dislocations upon mechanical loading.

The conclusion is that even if the presence of hydrogen and vacancies very significantly weakens the interface in such a way that the fracture process zone is less stiff (the crack opening profile is less steep), dislocations will still be emitted from the tip upon mechanical loading. This will induce blunting and shielding which prevents the full development of the fracture process zone and ultimately the initiation of crack propagation. In appendix Appendix B, more details about the way ∆ũ x is calculated are given. In particular, two crack orientations and three slip systems were tested. They all remain ductile according to the model. Figure 7. Evolution of the maximum displacement shift ∆ũ x as a function of the applied stress intensity factor K app for different GB cases referred to in Fig. 6 and in table 4. The "pure Ni" case is the GB without hydrogen and without defects. These values are obtained for the most brittle crack / slip system orientation studied: a crack front parallel to [001] (with a crack propagation direction along [120] and the slip system (111)[121].

Conclusion

Realistic configurations for the Σ5(210)[001] symmetrical grain boundary, in Ni containing hydrogen and vacancies, were simulated. The basic energetic parameters, such as the intergranular segregation energy, the H-H pair interaction energy and the vacancy-hydrogen cluster formation energies were calculated by DFT. Then a mean field model was constructed to find which configurations are the most probable, at equilibrium, as a function of bulk hydrogen concentration and temperature. Two typical structures emerged from this analysis: one with only intergranular hydrogen, at a concentration of 2 hydrogen atoms per structural unit without vacancies and another one with 50% of V H 5 clusters (configuration V H 5 -V H a,b 5 ), which corresponds to 2.5 hydrogen atoms per structural unit (at 1000 ppm H in the bulk and 300 K). The limitation of the enrichment of the interface with H comes from, on the one hand, a repulsion between the V H 5 clusters by overlap of H positions, which limits their concentration to 50%, and on the other hand, a repulsion between the vacancy and the sites 5 and 6 of the nearest structural unit free of vacancies (sites 5 and 6'). This involves that a vacancy hydrogen cluster is not surrounded by segregated hydrogen.

Both structures were fractured in DFT. They show a similar reduction of the ideal work of fracture, but a lower cohesive stress is found in the presence of vacancies (configuration V H 5 -V H b 5 ). This tendency is confirmed by the fracture behavior of a configuration saturated with V H 4 clusters (1 cluster per structural unit). The embrittlement effect was quantified by calculating the intensity of the shear localization at the crack tip. It was concluded that the decrease of the cohesion of the GB is too limited to prevent dislocation emission at the crack tip. Therefore the "damage" considered in this paper is not sufficient to embrittle the Σ5(210)[001] GB in Ni, in conditions of H concentration typical of experiments where intergranular cracks are observed. Further work will be dedicated to other forms of damage, in particular time dependent, in line with the study of nanocavities in [54].

Table A1. Vacancy-hydrogen cluster formation energy E V Hn f and average segregation energy per hydrogen atom, as a function of n, the number of hydrogen in the vacancy. For comparison, the value for the bulk vacancy is also given [37]. ). The loads correspond to the maximum of shear localization at the tip, i.e. respectively 0.75 MPam 1/2 , 0.68 MPam 1/2 , 0.63 MPam 1/2 and 0.68 MPam 1/2 . u x (y + ∆y)], where ∆y is the distance between two atomic rows on the crack surface and u x (y) = δ(y)/2 is the displacement perpendicular to the crack plane at position y. α is the angle between the normal to the crack plane and the glide direction (the Burgers vector). ∆y is related to the distance between glide planes d 0 by ∆y = d 0 cos φ/ cos α, where φ is the angle between the trace of the slip plane in the crack plane and the crack front. Two crack orientations were tested. The first one has a crack front along [120] and a propagation direction along [001] (the tilt axis of the GB). The slip system studied, in interaction with this crack, is (111) [112], with parameters cos φ/ cos α = 1.65 and cos α = 0.55. The second crack orientation has a crack front along [001] and a propagation direction direction along [120]. It is orthogonal to the previous one. Two slip systems were considered: (111)[211] ( cos φ/ cos α = 0.87 and cos α = 0.92) and (111)[121] ( cos φ/ cos α = 1.09 and cos α = 0.73). The three crystallographic configurations have very similar ∆ũ x profiles, the last one being the most brittle. Examples of ∆ũ x profiles, for this crack/slip system orientation, are given on figure B1. The peak values are reported in Fig. 7, as a function of the applied mechanical load.

Figure 1 .

 1 Figure 1. (a) and (b) show the GB structural units and interstitial positions in the (x,y) plane and (x,z) planes respectively. (c) and (d) give the same information for a GB containing a single vacancy on a GB 2 site on the (x¿0) side of the interface, i.e. the plane is occupied by 25% of vacancies (the box contains 4 structural units). Note the relaxation towards the interface of the GB 2 site, from the left grain, symmetric of the vacancy.

  , 2 and 5 (tetrahedral) are largely affected. Trapping is reinforced on the first one (∆E 2 ZP E seg = -0.210 eV vs. -0.134 eV without vacancy) and decreased on the second one (∆E 5 ZP E seg = -0.193 eV vs. -0.266 eV without vacancy). Second, there are 6 octahedral sites in first neighboring position of the vacancy (the O 1 sites of the bulk vacancy [50]). Four of them are at the same z position as site GB 2 : O 2 ,O 4 ,O 5 and O 3 . They replace respectively the sites 3' (the symmetric of site 3), 3 and 6. Site O 3 is a new strong trap site. All the sites of the vacancy lead to a re-enforcement of trapping (Tab. 2), especially site O 5 with ∆E 0 5 ZP E seg = -0.363 eV vs. -0.278 eV for the site 6 of the perfect GB. In addition, there are two sites O 1 above and below GB 2 with ∆E 0 1 ZP E seg = -0.322 eV. Sites 4' (symmetric of 4, in the structure distorted by the vacancy) and 6' (the perfect GB contains two sites 6, which give 6' and O 5 , when the vacancy in introduced) are

Figure 2 .

 2 Figure 2. Vacancy-hydrogen clusters concentration on sites GB 2 at T=300K as a function of H bulk concentration. The formation energies of the various clusters are given in the appendix Appendix A.

Figure 3 .

 3 Figure 3. Influence of the vacancy formation energy on the vacancy-hydrogen clusters' concentration at T=300 K (open symbols) and at T=400 K (filled symbols) as a function of bulk concentration.

Figure 4 .

 4 Figure 4. Variation of the hydrogen concentration on site 6 (black points) and of the total vacancy concentration C vac on site GB 2 (open square symbols) given by the mean field model and taking into account the repulsion between vacancies and hydrogen atoms occupying sites 6. (a) (resp. b) shows the low (resp. high) vacancy concentration phase.

3 Figure 5 .

 35 Figure 5. Variation of the total hydrogen content, per structural unit, as a function of the bulk concentration at T=300 K according to Eq. 3 and 7. The insert shows the detail of the occupancy of the sites c i when the low vacancy phase is enriched in H c 2 (+),c 3 (⋄),c 4 ( * ),c 5 ( ),c 6 (•).

Figure 6 .

 6 Figure 6. Excess energy versus separation curve: (a) comparison between the GB without defects, with a single vacancy and the GB with segregated hydrogen (eight or twelve hydrogen atoms, without vacancies), (b) influence of vacancy hydrogen clusters. Different cases were considered: the perfect GB, the GB with oneV H 5 , two V H 5 or four V H 4 clusters. In V H 5 -V H a 5 (resp. V H 5 -V H b5), the vacancies are on the same (resp. opposite) side of the GB.

5 O 4 O 3 5O 2 O 1 -Figure A1 .

 54321A1 Figure A1. Crack opening profiles δ (nm) corresponding to four structures: GB without defects ("Pure Ni"), GB with segregated hydrogen ("8-12 H"), GB with vacancy-hydrogen clusters ("VH 5 -VH b 5 " and "4 VH 4 "). The loads correspond to the maximum of shear localization at the tip, i.e. respectively 0.75 MPam 1/2 , 0.68 MPam 1/2 , 0.63 MPam 1/2 and 0.68 MPam 1/2 .

Figure B1 .

 B1 Figure B1. Displacement shift profiles ∆ũ x for different mechanical loads applied to the GB (a) without any defect ("pure Ni" configuration) and (b) saturated with V H 4 clusters. The crack front is [001], the propagation direction is [120] and the slip system is (111)[121] (∆ y = 0.22 nm).

Table 1 .

 1 Positions (in a 0 ) and vacancy formation energies E f nv (in eV) obtained by DFT for the large (small) GB structures.

	site	x	y	z	E f 1v	E f 2v
	GB 1 0.023 1.120 -0.500 (1.843)	1.432
	GB 2 0.334 1.547 0.000	0.210 (-0.100) 0.075
	GB 3 0.475 1.994 -0.500 (1.143)	1.207
	GB 4 1.155 1.110 0.000	0.972 (0.968)	1.032
	GB 5 2.472 1.565 0.000	1.313

Table 2 .

 2 Positions (in a 0 ) and segregation energies ∆E i seg (in eV) obtained by energy minimization with the DFT method for the large (small) GB structures, without vacancy (top table) and with a vacancy on site GB 2 (bottom table). ∆E iZP E

	seg	(in

Acknowledgments

This work is supported by l'Agence Nationale de la Recherche (ANR) under grant EcHyDNA (Blanc 1019424). This work was granted access to the HPC resources from CALMIP (Toulouse, France, Grant 2018-p0749) and PSMN at the ENS de Lyon. CNRS (INP) is also gratefully acknowledged for additional funding.

Appendix A.

The formation energy of the various V H n configurations, on sites GB 2 , are given in table A1. They are obtained from the data in tables 2 and 3, following the expression

Figure A1 shows the crack opening profiles δ(y) which correspond to the mechanical equilibrium of an internal crack with nonlinear fracture process zones described by the triangular traction/opening relation presented in subsection 3.5. The profiles are converted into localized shear by computing the finite difference ∆ũ x = cos α[u x (y) -