Özge Özgüç

Jean-Léon Maître
email: jean-leon.maitre@curie.fr

Multiscale morphogenesis of the mouse blastocyst by actomyosin contractility

During preimplantation development, the mouse embryo forms the blastocyst, which consists of a squamous epithelium enveloping a fluid-filled lumen and a cluster of pluripotent cells. The shaping of the blastocyst into its specific architecture is a prerequisite to implantation and further development of the embryo. Recent studies identified the central role of the actomyosin cortex in generating the forces driving the successive steps of blastocyst morphogenesis. As seen in other developing animals, actomyosin functions across spatial scales from the subcellular to the tissue levels. In addition, the slow development of the mouse embryo reveals that actomyosin contractility operates at multiple timescales with periodic cortical waves of contraction every ~80 s and tissue remodeling over hours.

1-Mouse preimplantation development

Within 4 days after fertilization, the mouse embryo forms the blastocyst, a structure that mediates implantation in the uterus [START_REF] Maître | Mechanics of blastocyst morphogenesis[END_REF][START_REF] Chazaud | Lineage specification in the mouse preimplantation embryo[END_REF]. From the zygote stage, blastomeres undergo cleavage divisions, producing smaller cells after each successive round. Blastomeres remain spherical and of equivalent size until they reach the 8-cell stage on the 3 rd day. Then, the mouse embryo undergoes compaction, a morphogenetic process during which blastomeres draw themselves into closer contact (Fig 1A). Concomitantly, blastomeres gather their apical material into an apical domain [START_REF] Ducibella | Changes in cell surface and cortical cytoplasmic organization during early embryogenesis in the preimplantation mouse embryo[END_REF][START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF]. This domain affects the divisions from the 8-to 16-cell stage by tethering one pole of the mitotic spindle, which can result both in the asymmetric partitioning of the apical domain among sister cells and in divisions oriented perpendicularly to the embryo surface [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Dard | Orientation of mitotic spindles during the 8-to 16-cell stage transition in mouse embryos[END_REF][START_REF] Niwayama | A Tug-of-War between Cell Shape and Polarity Controls Division Orientation to Ensure Robust Patterning in the Mouse Blastocyst[END_REF][START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. During the 16-cell stage (Fig 1B ), cells adopt inner or outer positions causing them to initiate distinct differentiation processes: inner cell mass (ICM) and trophectoderm (TE) [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Hirate | Polarity-dependent distribution of angiomotin localizes Hippo signaling in preimplantation embryos[END_REF][START_REF] Stephenson | Disorganized epithelial polarity and excess trophectoderm cell fate in preimplantation embryos lacking E-cadherin[END_REF][START_REF] Cockburn | The Hippo pathway member Nf2 is required for inner cell mass specification[END_REF][START_REF] Hirate | Tead4 is constitutively nuclear, while nuclear vs. cytoplasmic Yap distribution is regulated in preimplantation mouse embryos[END_REF]. TE cells progressively epithelialize and, during the 32-cell stage (Fig 1C ), pump fluid into the intercellular space to create the first mammalian lumen called the blastocoel [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF][START_REF] Chan | Hydraulic control of mammalian embryo size and cell fate[END_REF][START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF]. The formation of this lumen is accompanied with further differentiation of the ICM, turning either into epiblast (Epi) or primitive endoderm (PrE). Eventually, Epi cells become sandwiched between the TE and PrE cells, which line the lumen [START_REF] Plusa | Distinct sequential cell behaviours direct primitive endoderm formation in the mouse blastocyst[END_REF]. When the blastocyst reaches its full expansion, it consists of nearly a hundred cells and is ready to implant.

Shaping the blastocyst relies on the deformation of cells and the rearrangement of their contacts (Fig 1). These result from the generation of forces and changes in the mechanical properties of cells and tissues. In animals, cell shape and mechanics are controlled in large part by the actomyosin cortex. As reported in several recent studies, the early mammalian embryo is no exception.

2-Contractility of the actomyosin cortex

The actomyosin cortex consists of a cross-linked meshwork of dynamic actin filaments that are tethered to the plasma membrane [START_REF] Clark | Stresses at the cell surface during animal cell morphogenesis[END_REF]. The contractility of the actomyosin cortex is controlled by the dynamics and cross-linking of actin filaments as well as the activity of the myosin motor non-muscle myosin II [START_REF] Bovellan | Cellular Controlof Cortical Actin Nucleation[END_REF][START_REF] Chugh | Actin cortex architecture regulates cell surface tension[END_REF][START_REF] Naganathan | Morphogenetic degeneracies in the actomyosin cortex[END_REF]. The spatio-temporal regulation of contractility patterns the stresses at the surface of animal cells and drives several key cellular processes. For example, stronger contractility at the cleavage furrow cleaves cells into two during cytokinesis [START_REF] Padmanabhan | Nonjunctional E-Cadherin Clusters Regulate the Actomyosin Cortex in the C. elegans Zygote[END_REF]; contractility at the back of migrating cells help them retract their cell body [START_REF] Tsai | Efficient Front-Rear Coupling in Neutrophil Chemotaxis by Dynamic Myosin II Localization[END_REF]; weaker contractility at cell-cell contacts relaxes them and promotes their spreading [START_REF] Maitre | Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells[END_REF][START_REF] Heuzé | Myosin II isoforms play distinct roles in adherens junction biogenesis[END_REF]. Importantly, surface stresses generated by contractility can be controlled across multiple scales: from the subcellular [START_REF] Sun | Basolateral protrusion and apical contraction cooperatively drive Drosophila germ-band extension[END_REF] to the tissue levels [START_REF] Bailles | Genetic induction and mechanochemical propagation of a morphogenetic wave[END_REF] and from seconds [START_REF] Armon | Ultrafast epithelial contractions provide insights into contraction speed limits and tissue integrity[END_REF] to hours [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. Mouse morphogenesis begins on the 3 rd day after fertilization with compaction and polarisation (A) driven by increased contractility (green) and accumulation of apical material in a restricted domain (red), respectively [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. (B) Some 16-cell stage blastomeres inherit the apical domain from symmetric or asymmetric divisions and remain at the embryo surface [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Niwayama | A Tug-of-War between Cell Shape and Polarity Controls Division Orientation to Ensure Robust Patterning in the Mouse Blastocyst[END_REF][START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. Cells without apical material further increase their contractility until they pull themselves inside the embryo. As this cell sorting takes place, cells initiate lineage specification into either TE (blue) or ICM (red) [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Hirate | Polarity-dependent distribution of angiomotin localizes Hippo signaling in preimplantation embryos[END_REF]. (C) When tight junctions of the TE seal, microlumens filled with intercellular fluid appear at cell-cell contacts [START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF]. Contractility repairs these fractures [START_REF] Casares | Hydraulic fracture during epithelial stretching[END_REF] and pushes the fluid into a single large lumen [START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF].

The first description of actomyosin during preimplantation development dates to 1983 [START_REF] Sobel | Localization of myosin in the preimplantation mouse embryo[END_REF]. Since then, actomyosin was found to be involved in all of the morphogenetic processes forming the blastocyst (Fig 1). Here, we elaborate on how actomyosin contractility acts at multiple spatial and temporal scales to shape the early mouse embryo.

3-Tempos of the beating blastocyst

Unlike other model organisms typically used to study animal morphogenesis, the mouse embryo develops slowly (Fig 1). However, actomyosin keeps beating with the same tempo in the mouse as it does in fastdeveloping organisms. In this section, we discuss how contractility acts at short and long timescales.

3.1-Seconds to minutes

Morphogenetic processes such as compaction, cell internalization, or lumen formation take ~10 hours each, while actomyosin contractility typically acts within seconds to minutes. On such short timescale, mouse blastomeres show rapid and reversible deformations. Initially spotted in 1980 [START_REF] Lehtonen | Changes in cell dimensions and intercellular contacts during cleavage-stage cell cycles in mouse embryonic cells[END_REF], these movements were later identified as Periodic Cortical Waves of Contraction -in short, "PeCoWaCo" [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. PeCoWaCo consists of a surface deformation that propagates around the cell with a speed of ~0.8 µm.s -1 (Fig 2). They require intact actin and myosin function and, as such, resemble waves of compression and dilations of the actomyosin cortex [START_REF] Kapustina | Compression and dilation of the membrane-cortex layer generates rapid changes in cell shape[END_REF][START_REF] Driscoll | Spatiotemporal relationships between the cell shape and the actomyosin cortex of periodically protruding cells[END_REF] rather than pure actin waves [START_REF] Xiao | Mitotic Cortical Waves Predict Future Division Sites by Encoding Positional and Size Information[END_REF], which were both described in cell lines. The ~80 s oscillation period of PeCoWaCo is similar to the ones of periodic contractions observed in other early embryos such as in the fly [START_REF] Martin | Pulsed contractions of an actinmyosin network drive apical constriction[END_REF][START_REF] Munjal | A self-organized biomechanical network drives shape changes during tissue morphogenesis[END_REF], frog or starfish [START_REF] Bement | Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium[END_REF]. In fly embryos, actomyosin turnover, the architecture of the meshwork and a mechanical feedback [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. In cells isolated from the embryo, PeCoWaCo can be observed circulating freely [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. When in contact, PeCoWaCo is locally weakened by adhesion molecules (purple) [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. The apical domain (red), also shows reduced actomyosin levels and PeCoWaCo becomes further confined [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. As polarized cells enlarge their apical domains [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF], the most contractile part of the cortex disappears when eventually the apical domain reaches tight junctions (yellow) [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF].

PeCoWaCo (black arrows) is most visible on the most contractile regions of the cortex (dark green)

on Rho GTPases are thought to regulate the duration of pulsed contractions [START_REF] Munjal | A self-organized biomechanical network drives shape changes during tissue morphogenesis[END_REF][START_REF] Vasquez | Dynamic myosin phosphorylation regulates contractile pulses and tissue integrity during epithelial morphogenesis[END_REF][START_REF] Coravos | Apical Sarcomere-like Actomyosin Contracts Nonmuscle Drosophila Epithelial Cells[END_REF]. However, what sets the travelling motion of contractions observed in mouse, frog and starfish embryos remain unknown [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF][START_REF] Bement | Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium[END_REF]. In C. elegans embryos, pulsed contractions move towards the anterior pole of the zygotes as a result of tension anisotropies triggered by local downregulation of contractility ensuing signals mediated by the sperm entry [START_REF] Munro | Cortical flows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Mayer | Anisotropies in cortical tension reveal the physical basis of polarizing cortical flows[END_REF]. This cortical flow advects polarity proteins as it couples to the cytoplasm and induces its streaming (Fig 3) [START_REF] Goehring | Polarization of PAR proteins by advective triggering of a pattern-forming system[END_REF][START_REF] Mittasch | Non-invasive perturbations of intracellular flow reveal physical principles of cell organization[END_REF]. However, such cytoplasmic streaming is not observed in mouse blastomeres. This could be explained by weak coupling of the cortex with the cytoplasm and/or by the absence of cortical flow altogether. Indeed, it remains to be established whether PeCoWaCo involves any movement of material or if they simply consist of a local deformation that would occur successively in adjacent parts of the cortex.

3.2-Hours to days

In mouse embryos, PeCoWaCo can be detected most often from the 8-cell stage onwards [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF], when actomyosin begins a slower, longer-term reorganisation. This reorganisation is mirrored by changes in surface tension and leads to the compaction of the embryo over a timescale of ~10 h [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. As in other species [START_REF] Maitre | Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells[END_REF][START_REF] Steinberg | Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation[END_REF][START_REF] Brodland | The Differential Interfacial Tension Hypothesis (DITH): a comprehensive theory for the self-rearrangement of cells and tissues[END_REF][START_REF] Manning | Coaction of intercellular adhesion and cortical tension specifies tissue surface tension[END_REF], compaction of the mouse embryo is set by the ratio of surface tensions between cell-cell contacts and the embryo surface [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF][START_REF] Goel | Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy[END_REF]. During mouse compaction, the tension ratio gradually changes primarily thanks to the elevation of contractility throughout the 8-cell stage (Fig 1A) [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. What controls contractility increase and, therefore, the timing of compaction? As noted in the 1980s, protein synthesis inhibitors applied from the late 2cell stage on do not block compaction. Moreover, this treatment could induce compaction as early as at the 2-or 4-cell stage, suggesting the presence of an inhibitor of compaction that would be continuously produced [START_REF] Kidder | Timing of transcription and protein synthesis underlying morphogenesis in preimplantation mouse embryos[END_REF][START_REF] Levy | The timing of compaction: control of a major developmental transition in mouse early embryogenesis[END_REF]. The timing of compaction could be controlled by PKC signalling since PKC activators trigger premature compaction at the 4-cell stage [START_REF] Winkel | Activation of protein kinase C triggers premature compaction in the fourcell stage mouse embryo[END_REF][START_REF] O'sullivan | Staurosporine advances interblastomeric flattening of the mouse embryo[END_REF]. Recently, PKC activation was proposed to activate actomyosin contractility via the Rho GTPase [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF], which was earlier found to be required for compaction [START_REF] Clayton | A role for Rho-like GTPases in the polarisation of mouse eight-cell blastomeres[END_REF]. What would occur downstream of Rho remains unclear since Rho kinase (Rock), the usual suspect for controlling actomyosin contractility, does not seem to be involved in compaction as neither Rock inhibitors [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF][START_REF] Laeno | Rho-Associated Kinase Activity Is Required for Proper Morphogenesis of the Inner Cell Mass in the Mouse Blastocyst1[END_REF][START_REF] Samarage | Cortical Tension Allocates the First Inner Cells of the Mammalian Embryo[END_REF], nor Rock knockout [START_REF] Kamijo | Impaired vascular remodeling in the yolk sac of embryos deficient in ROCK-I and ROCK-II[END_REF] show a compaction phenotype (or other signs of contractility inhibition). What controls the onset of contractility and kick-starts preimplantation morphogenesis remains unclear.

4-Spatial control of actomyosin contractility

While contractility rises during the 8-cell stage, it becomes spatially patterned at the cellular and tissue levels, definitively transforming a loosely-organised cluster of cells into an elaborate cyst.

4.1-Sub-cellular scale

During the 8-cell stage, blastomeres gather their apical material into the apical domain, a master regulator of preimplantation development. Indeed, the apical domain provides positional information that guides cell differentiation by sequestering regulators of the TE fate promoting Yap co-transcriptional regulator [START_REF] Hirate | Polarity-dependent distribution of angiomotin localizes Hippo signaling in preimplantation embryos[END_REF]. It also determines cell positioning by orienting the spindle during the 4 th and 5 th cleavages [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Niwayama | A Tug-of-War between Cell Shape and Polarity Controls Division Orientation to Ensure Robust Patterning in the Mouse Blastocyst[END_REF][START_REF] Dard | Inactivation of aPKClambda reveals a context dependent allocation of cell lineages in preimplantation mouse embryos[END_REF] and by controlling contractility [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. While enriched in microvilli [START_REF] Ducibella | Changes in cell surface and cortical cytoplasmic organization during early embryogenesis in the preimplantation mouse embryo[END_REF] and apical proteins [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Niwayama | A Tug-of-War between Cell Shape and Polarity Controls Division Orientation to Ensure Robust Patterning in the Mouse Blastocyst[END_REF][START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF][START_REF] Dard | Inactivation of aPKClambda reveals a context dependent allocation of cell lineages in preimplantation mouse embryos[END_REF], the apical domain is depleted in actomyosin (Fig 2) [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. The absence of actomyosin at the apical domain seems to depend on the apical kinase aPKC, as double mutants for the zeta and iota isoforms of aPKC show ectopic actomyosin enrichments at what remains of their apical domain [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. Since the apical domain can be asymmetrically distributed during the 8-to 16-cell stage division, sister cells inherit distinct contractility [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. This translates into distinct amplitudes of PeCoWaCo on the short timescale and into the sorting of cells on the long timescale with the most contractile cells being internalised [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Samarage | Cortical Tension Allocates the First Inner Cells of the Mammalian Embryo[END_REF]. After their spatial allocation, outer cells initiate their differentiation in TE, while inner cells opt for the ICM fate (Fig 1B). This differentiation relies in part on the Yap co-transcriptional activator, which responds to mechanical stimuli [START_REF] Elosegui-Artola | Force Triggers YAP Nuclear Entry by Regulating Transport across Nuclear Pores[END_REF][START_REF] Xia | Lateral Inhibition in Cell Specification Mediated by Mechanical Signals Modulating TAZ Activity[END_REF], including the ones generated by actomyosin contractility [START_REF] Dupont | Role of YAP/TAZ in mechanotransduction[END_REF]. During the internalization of the ICM, surface cells become stretched, and Yap becomes nuclear while it remains cytoplasmic in the rounder inner cells [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. Interestingly, myosin function is essential for both the positioning of cells and the correct localization of Yap [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. Whether this phenomenon is controlled by mechanosensing requires further experiments.

What controls the formation of the apical domain at the 8-cell stage? Interestingly, de novo polarization in C. elegans zygotes relies on actomyosin contractility (Fig 3) [START_REF] Munro | Cortical flows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Mayer | Anisotropies in cortical tension reveal the physical basis of polarizing cortical flows[END_REF][START_REF] Goehring | Polarization of PAR proteins by advective triggering of a pattern-forming system[END_REF][START_REF] Mittasch | Non-invasive perturbations of intracellular flow reveal physical principles of cell organization[END_REF]. Inhibiting actomyosin contractility in the mouse embryo leads to conflicting results when it comes to apical domain establishment. Blebbistatin, a direct inhibitor of nonmuscle myosin II [START_REF] Straight | Dissecting temporal and spatial control of cytokinesis with a myosin II Inhibitor[END_REF], efficiently blocks cell division, PeCoWaCo, and lowers surface tension [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF] but does not affect apical domain formation [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF].

Similarly, heterozygous knockout of the myosin Early C. elegans (top) and mouse (bottom) embryos undergo de novo polarisation at the zygote and 8-cell stage respectively. In C. elegans, anisotropic pulsed contractions (green) produce cortical flows that entrain the cytoplasm, which starts streaming (middle) [START_REF] Munro | Cortical flows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Mayer | Anisotropies in cortical tension reveal the physical basis of polarizing cortical flows[END_REF]. These help segregating polarity proteins into distinct domains (red and blue) [START_REF] Goehring | Polarization of PAR proteins by advective triggering of a pattern-forming system[END_REF].

In the 8-cell stage mouse embryo (bottom), contractility gradually rises and generates PeCoWaCo (left, green) [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. Concomitantly, cells undergo cell-autonomous de novo polarisation but, contrary to C. elegans, no cytoplasmic streaming is observed (middle) and contractility seems unnecessary to form the apical domain (right) [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF][START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. heavy chain isoform Myh9 or homozygous knockout of another isoform Myh10 does not seem to affect polarity since these mutants successfully go through processes requiring polarity (they form a blastocyst with TE, ICM and a blastocoel) [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF]. Nevertheless, Zhu and colleagues conclude that contractility is required for apical domain establishment [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF][START_REF] Zhu | Building an apical domain in the early mouse embryo: Lessons, challenges and perspectives[END_REF] based on the effect of ML7, an inhibitor of the myosin regulatory light chain kinase [START_REF] Saitoh | Selective inhibition of catalytic activity of smooth muscle myosin light chain kinase[END_REF], which prevents the formation of the apical domain.

From these conflicting observations, we suspect that ML7 affects mouse blastomeres beyond their contractility and we do not think that contractility is required for apical polarity establishment in the early mouse embryo.

4.2-Tissue scale

Additionally to the apical domain, cell-cell contacts also downregulate contractions (Fig 2). Originally discovered in the compacting mouse embryo [START_REF] Hyafil | A cell surface glycoprotein involved in the compaction of embryonal carcinoma cells and cleavage stage embryos[END_REF], the cell-cell adhesion molecule E-cadherin (or Cdh1) signals to reduce contractility locally at contacts between cells [START_REF] Maitre | Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells[END_REF][START_REF] Ratheesh | Centralspindlin and αcatenin regulate Rho signalling at the epithelial zonula adherens[END_REF][START_REF] Pinheiro | Transmission of cytokinesis forces via E-cadherin dilution and actomyosin flows[END_REF] as well as globally [START_REF] Padmanabhan | Nonjunctional E-Cadherin Clusters Regulate the Actomyosin Cortex in the C. elegans Zygote[END_REF]. The control of contractility by cadherins can be mediated via regulators of the small GTPase Rho, which are recruited by p120-catenin, a core component of adherens junctions [START_REF] Wildenberg | p120catenin and p190RhoGAP regulate cell-cell adhesion by coordinating antagonism between Rac and Rho[END_REF][START_REF] Yu | p120catenin controls contractility along the vertical axis of epithelial lateral membranes[END_REF]. During compaction, actomyosin levels decrease at cell-cell contacts as compared to the cell-medium interface in a Cdh1dependent manner [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. On the long timescale, the local downregulation of contractility could account for up to 1/4 of the entire compaction of the mouse embryo [START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF].

As actomyosin is reduced at cellcell contacts and at the apical domain, PeCoWaCo becomes confined to the nonapical part of the non-contact interface (Fig 2). This contractile interface disappears when embryos develop further at 16-cell stage, as cells which do not inherit the apical domain from their mother cell internalize [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF], and polarized cells enlarge their apical domain [START_REF] Korotkevich | The Apical Domain Is Required and Sufficient for the First Lineage Segregation in the Mouse Embryo[END_REF][START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF] until the most contractile part of the exposed surface disappears [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF]. This is concomitant with the sealing of the tight junctions when the apical domains of contacting cells zip together and seal the embryo (Fig 2) [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF]. Zenker and colleagues conclude that the expansion of the apical domain does not result from the difference in contractility between the apical and non-apical part of the cell. This is based on experiments with drugs that were thought to inhibit contractility. However, as stated by the authors [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF], these drugs did not affect cell shape, which is inconsistent with a number of other studies in which contractility is inhibited [START_REF] Zhu | Actomyosin polarisation through PLC-PKC triggers symmetry breaking of the mouse embryo[END_REF][START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Chan | Hydraulic control of mammalian embryo size and cell fate[END_REF][START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. At that point, it is worth highlighting a technical note on Blebbistatin, a potent contractility inhibitor, which is, as many other drugs, hydrophobic and not compatible with usual mouse embryo culture conditions under mineral oil [START_REF] Maître | Asymmetric division of contractile domains couples cell positioning and fate specification[END_REF][START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF].

Therefore, it remains conceivable that the expansion of the apical domain results from the different contractility between the apical and nonapical part of the exposed cell surface.

Once tight junctions are sealed [START_REF] Wang | Zonula occludens-1 (ZO-1) is involved in morula to blastocyst transformation in the mouse[END_REF], intercellular fluid becomes trapped within the intercellular space [START_REF] Zenker | Expanding Actin Rings Zipper the Mouse Embryo for Blastocyst Formation[END_REF] and accumulates to form the blastocoel. This occurs after the fracturing of cell-cell contacts by pressurized fluid leading to the formation of micron-size water pockets (Fig 1C) [START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF]. As observed in vitro [START_REF] Casares | Hydraulic fracture during epithelial stretching[END_REF], contractility mediates the healing of these fractures and can redistribute the extracellular fluid. The higher contractility of the ICM, as compared to the TE, squishes the fluid away from the ICM and progressively coarsens the many smaller water pockets into a larger one until there is only one lumen remaining [START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF]. Interestingly, on short time scales, water pockets seem to pulse at a rhythm close to the one of PeCoWaCo [START_REF] Dumortier | Hydraulic fracturing and active coarsening position the lumen of the mouse blastocyst[END_REF][START_REF] Maître | Pulsatile cellautonomous contractility drives compaction in the mouse embryo[END_REF]. After a few hours of expansion, the blastocoel undergoes cycles of collapse and re-growth reaching a long term steady state [START_REF] Ruiz-Herrero | Organ size control via hydraulically gated oscillations[END_REF]. Collapses seem to result from transient seal rupture due to cell division within the TE [START_REF] Chan | Hydraulic control of mammalian embryo size and cell fate[END_REF][START_REF] Leonavicius | Mechanics of mouse blastocyst hatching revealed by a hydrogel-based microdeformation assay[END_REF]. Once again, tight junction repair is aided by contractility [START_REF] Chan | Hydraulic control of mammalian embryo size and cell fate[END_REF], which could be recruited by Rho, as observed in the surface epithelium of Xenopus gastrula [START_REF] Stephenson | Rho Flares Repair Local Tight Junction Leaks[END_REF].

5-Concluding Remarks

After the many discoveries on actomyosin contractility during worm, fly or fish development, the mammalian embryo finally joined the club. With its comparably slow development, the mammalian embryo can now provide unique information on the different timescales at which actomyosin functions. This will become possible thanks to the advancements in imaging technologies, which will require preserving long-term viability while enabling high temporal resolution. In this regard, lightsheet microscopy will be key to put the multiple scales of contractility under the spotlight [START_REF] Strnad | Inverted light-sheet microscope for imaging mouse pre-implantation development[END_REF][START_REF] Mcdole | In Toto Imaging and Reconstruction of Post-Implantation Mouse Development at the Single-Cell Level[END_REF].

Figure 1 :

 1 Figure 1: Morphogenetic events during mouse preimplantation development.

Figure 2 :

 2 Figure 2: Spatio-temporal control of contractility during the 8-and 16-cell stages.

Figure 3 :

 3 Figure 3: Contractility and de novo polarity establishment in early embryos of C. elegans and mouse

Acknowledgements

We thank J. Firmin and D. Pelzer for critical reading of the manuscript. Ö.Ö. is funded from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 666003. Research in the lab of J.-L.M., who is supported by the Institut Curie and the CNRS, is funded by the FSER via the FRM, the INSERM transversal program HuDeCA, an ERC-2017-StG 757557, QLife grants and Labex DEEP (ANR-11-LBX-0044) which are part of the IDEX PSL (ANR-10-IDEX-0001-02 PSL).


Takahiro Masuda
email: masuda-takahiro-fk@ynu.ac.jp

Xavier Sauvage

Shoichi Hirosawa

Zenji Horita

Achieving highly strengthened Al-Cu-Mg alloy by grain refinement and grain boundary segregation

Keywords: aluminum alloys, severe plastic deformation, grain refinement, high strength, grain boundary segregation

come   L'archive ouverte pluridisciplinaire

Introduction

Since the discovery of age hardening in an Al-Cu-Mg alloy by Wilm in 1906 [START_REF] Wilm | Physikalisch-metallurgische Untersuchungen über magnesiumhaltige Aluminiumlegierungen[END_REF], age-hardenable aluminum alloys, such as 2xxx series (Al-Cu-Mg system), 6xxx series (Al-Mg-Si system) and 7xxx series (Al-Zn-Mg-Cu system), have been extensively studied for wide ranges of compositions. These alloys are used as high-specific-strength structural materials for aircraft and automotive industries [START_REF] Miller | Recent development in aluminium alloys for the automotive industry[END_REF][START_REF] Dursun | Recent developments in advanced aircraft aluminium alloys[END_REF]. These commercial aluminum alloys usually rely on two strengthening contributions, namely solute atoms and precipitates, but do not take advantage of grain boundary (GB) strengthening since they exhibit coarsegrained structures.

It is well known that the strength of metallic materials also increases with the reduction in grain size through the Hall-Petch relation [START_REF] Hall | The deformation and ageing of mild steel: III Discussion of results[END_REF][START_REF] Petch | The Cleavage Strength of Polycrystals[END_REF]. The grain size is easily reduced to the submicron level when processes of se vere plastic deformation (SPD) are utilized [START_REF] Valiev | Producing bulk ultrafine-grained materials by severe plastic deformation[END_REF]. Main SPD processes are ECAP (equalchannel angular pressing) [START_REF] Segal | Plastic Working of Metals by Simple Shear[END_REF], HPT (high-pressure torsion) [START_REF] Bridgman | Effects of High Shearing Stress Combined with High Hydrostatic Pressure[END_REF], ARB (accumulative roll bonding) [START_REF] Saito | Novel ultra-high straining process for bulk materials-development of the accumulative roll-bonding (ARB) process[END_REF], MDF (multi-directional forging) [START_REF] Valiakhmetov | Mechanical properties of the titanium alloy VT8 with submicrocrystalline structure[END_REF] and HPS (high-pressure sliding) [START_REF] Fujioka | Development of High-Pressure Sliding Process for Microstructural Refinement of Rectangular Metallic Sheets[END_REF]. It has been reported that the grain size of pure aluminum (99.99%) can be reduced to ~1 μm by ECAP, HPT, ARB and HPS [START_REF] Fujioka | Development of High-Pressure Sliding Process for Microstructural Refinement of Rectangular Metallic Sheets[END_REF][START_REF] Terhune | An investigation of microstructure and grain-boundary evolution during ECA pressing of pure aluminum[END_REF][START_REF] Ito | Microstructural evolution in pure aluminum processed by high-pressure torsion[END_REF][START_REF] Tsuji | Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing[END_REF]. It typically gives rise to a significant increase in the yield stress following the Hall-Petch law [START_REF] Hall | The deformation and ageing of mild steel: III Discussion of results[END_REF][START_REF] Petch | The Cleavage Strength of Polycrystals[END_REF]. This strategy can also be applied to commercial Al alloys [START_REF] Liddicoat | Nanostructural hierarchy increases the strength of aluminium alloys[END_REF][START_REF] Valiev | On the origin of the extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation[END_REF][START_REF] Mohamed | Age hardening and thermal stability of Al-Cu alloy processed by high-pressure torsion[END_REF][START_REF] Mohamed | Strengthening of A2024 alloy by high-pressure torsion and subsequent aging[END_REF][START_REF] Tang | Concurrent strengthening of ultrafine-grained age-hardenable Al-Mg alloy by means of high-pressure torsion and spinodal decomposition[END_REF][START_REF] Kim | Optimization of strength and ductility of 2024 Al by equal channel angular pressing (ECAP) and post-ECAP aging[END_REF][START_REF] Lee | Age-hardening of an Al-Li-Cu-Mg alloy (2091) processed by high-pressure torsion[END_REF][START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF][START_REF] Deschamps | Precipitation kinetics in a severely plastically deformed 7075 aluminium alloy[END_REF][START_REF] Zhao | Microstructures and mechanical properties of ultrafine grained 7075 Al alloy processed by ECAP and their evolutions during annealing[END_REF][START_REF] Ghosh | Characterisation of high pressure torsion processed 7150 Al-Zn-Mg-Cu alloy[END_REF]. Liddicoat et al. reported that the tensile strength increased to > 1 GPa in an ultrafine-grained (UFG) A7075 alloy processed by HPT [START_REF] Liddicoat | Nanostructural hierarchy increases the strength of aluminium alloys[END_REF]. It was considered that this high strengthening is due to non-equilibrium structures such as the formation of solute clusters and the segregation of solute atoms along GBs.

Significant strengthening was also reported for UFG A2024 alloys processed by SPD [START_REF] Mohamed | Strengthening of A2024 alloy by high-pressure torsion and subsequent aging[END_REF][START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF]. Interestingly, the precipitation sequence usually takes a diffe rent type, with the easy nucleation of stable phase without the classical sequence (through formation of Guinier-Preston-Bagarysatsky (GPB) zones [START_REF] Ringer | Precipitation processes during the early stages of ageing in A1-Cu-Mg alloys[END_REF]). Besides, strain-induced segregations of solute atoms along GBs have been reported in the Al-Cu system [START_REF] Nasedkina | Mechanisms of precipitation induced by large strains in the Al -Cu system[END_REF][START_REF] Xu | Deformation induced grain boundary segregation in nanolaminated Al-Cu alloy[END_REF] and other alloys [START_REF] Sauvage | Strain induced segregations in severely deformed materials[END_REF]. In addition, three dimensional atom probe tomography (APT) by Sha et al. [START_REF] Sha | Nanostructure of aluminium alloy 2024: Segregation, clustering and precipitation processes[END_REF] showed that such segregation of Cu and Mg also occurred during aging in an A2024 alloy. They could efficiently stabilize UFG structures but also contribute to strengthening [START_REF] Sauvage | Strain induced segregations in severely deformed materials[END_REF].

The aim of this research is threefold: first, to achieve ultra -high strengthening to a level as high as ~1 GPa in an age-hardenable A2024 alloy. HPT process is applied for adequate grain refinement, and subsequent aging is undertaken for precipitation and segregation of solute atoms. Second, to evaluate accurately microstructural features down to the nanoscale with a special emphasis on solute atom distribution using scanning transmission electron microscopy (STEM) and APT. Third, to clarify strengthening mechanisms thanks to a quantitative evaluation of strengthening contributions. We will then show that the ultrahigh strength achieved in an A2024 alloy is not only controlled by grain refinement but also by segregation of solute atoms along GBs including subgrain boundaries.

Experimental procedures

Disk samples with 10mm diameter were prepared from a 1mm thickness commercially available A2024 alloy sheet with the composition of Al -4.5Cu-1.4Mg-0.56Mn-0.07Fe-0.02Si-0.01Ti (in wt.%). The disks were subjected to solution treatment (ST) at 793 K for 1 h followed by water quenching. The average grain size for the ST sample was determined to be 62 μm.

Samples were processed by HPT at room temperature (R.T.) for 0.75, 1, 5 and 10 revolutions with a rotation speed of 1 rpm under a pressure of 6 GPa. The imposed strain introduced by HPT processing can be represented using equivalent strain (eq) through the following equation:

𝜀 𝑒𝑞 = 2π𝑟𝑁 √3𝑡 ⁄ . ( 1
)
where, r is the distance from the disk center, N is the number of revolutions and t is the thickness of the disk after HPT processing. Thus, the equivalent strain introduced in each sample by HPT processing was determined to be 6, 8, 26, 44

and 88 for 0.75, 1, 3, 5 and 10 revolutions, respectively, at the gauge area (corresponding to r = 2 mm) where the thickness was taken after HPT processing as 0.8~0.85 mm. Following HPT processing, some of the samples were subsequently aged at 423 K in an oil bath for 35 min and 3 h.

Samples processed by HPT and post-HPT aging were ground to the midplane of the thickness by abrasive papers and polished to a mirror-like surface with an alumina suspension. Hardness measurements were made along 8 different radial directions with an interval of 0.5 mm on the same line as shown in Fig. 1.

For the hardness measurements, a load of 0.3 kgf was appli ed for 15 s using a Mitutoyo HM-102 tester.

The dimensions of the tensile specimens are also depicted in Fig. 1 (gauge part: 1.5mm long, 0.6mm wide, 0.6mm thick) and the specimens were extracted at 2 mm away from the disk center. Tensile tests were performed at R.T. with an initial strain rate of 3.0×10 -3 s -1 . Tensile tests were repeated at least four time for each condition.

Microstructural observations after HPT processing and post -HPT aging were conducted on the plane perpendicular to the rotation axis using transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM)

and energy Dispersive X-ray Spectroscopy (EDS) analyses. For preparation of electron-transparent thin specimens for TEM, disks with 3mm diameter were extracted from HPT-processed samples as shown in Fig. 1 and they were ground on both sides with abrasive papers to a thickness of 0.15 mm. These disks were further thinned using a twin-jet electrochemical polisher in a solution of 20% HNO3-80% CH3OH (in vol.%) at a temperature of 253 K under 10 V. Further thinning was carried out by low-energy ion milling conducted with a GATAN® Precision Ion Polishing System (accelerating voltage: 3 kV, incidence angle of Ar ions: ±3 o , duration: 3 min). Observations were performed using a Hitachi -8100 and a JEOL-ARM200F microscopes operated at 200 kV. The average grain size was determined from more than 100 grains imaged in dark-field mode.

Second phase identification and dislocation density measurements were carried out by X-ray diffraction (XRD) analyses using CuKα radiation with a scanning speed of 0.2 o /min and a scanning step of 0.01 o .

APT analyses were carried out with a CAMECA LEAP 4000HR instrument.

Samples were prepared by a classical two step electro -polishing method starting from small rods (0.3×0.3 mm 2 in cross-section) cut at a distance of 3 ± 1 mm from the disk center. Sharpening of tips was done with a solution of 2% perchloric acid in ethylene glycol monobutyl ether at R.T. under an applied voltage of 20 V.

Samples were field-evaporated at 30 K with electric pulsing (pulse repetition rate 200kHz, pulse fraction 20%). Data processing was performed using "GPM 3D data software". It should be noted that the analyses for TEM, STEM, XRD and APT were conducted in the areas well away from the disk center aft er N=10

and/or subsequent aging, where the microstructure including the grain size is considered to be the same and uniform according to an earlier report [START_REF] Ito | Microstructural evolution in pure aluminum processed by high-pressure torsion[END_REF]. also includes, for comparison, the results after ST and standard T6 aging (at 463 K for 12 h) for the A2024 alloy. Fig. 2 shows that processing through N=0.75 led to an increase in the strength to 750 MPa which is already 50% higher than that of the T6 sample. The tensile strength was further increased with increasing N and it reached 910 MPa with the total elongation of 5% after N=10. It should be noted that the higher tensile strength was achieved as compared to an earlier study (890 MPa) [START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF]. This may be attributed to the larger imposed strain (eq =88 against 13 in [START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF]).

Experimental results

Tensile tests and hardness measurements

Fig. 3 shows (a) Vickers microhardness plotted against equivalent strain and (b) stress-strain curves after tensile testing at R.T., where the samples were processed by HPT through N=10 and subsequently aged at 423 K for 35 min. It should be noted that the aging period for 35 min corresponds to peak aging as reported before [START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF]. Fig. 3 also includes the strength level for the ST and T6 samples. Fig. 3(a) clearly shows that the hardness was further increased up to 285 HV during aging, appreciably above the hardness of 260 HV reached after HPT processing. The results after tensile testing in Fig. 3(b) confirm that the mechanical strength has increased during aging, with a tensile strength up to 1

GPa. Thus, the HPT-processed sample combined with subsequent aging exhibits the tensile strength twice as high as the sample after T6 treatment. ). Thus, a significant grain refinement was achieved from the initial grain size of 62 μm. A slight grain growth occurred during the aging but the UFG structure was kept with a mean grain size of 16 0 nm (Fig. 4(b)). The UFG structures observed in this study are consistent with the results reported by Mohamed et al. [START_REF] Mohamed | Strengthening of A2024 alloy by high-pressure torsion and subsequent aging[END_REF], Alhamidi et al. [START_REF] Alhamidi | Grain refinement and high strain rate superplasticity in alumunium 2024 alloy processed by high-pressure torsion[END_REF], Chen et al. [START_REF] Chen | Strengthening of an Al-Cu-Mg alloy processed by high-pressure torsion due to clusters, defects and defect-cluster complexes[END_REF][START_REF] Chen | Microstructural evolution, strengthening and thermal stability of an ultrafine -grained Al-Cu-Mg alloy[END_REF] and Dobatkin et al. [START_REF] Dobatkin | Grain refinement and superplastic flow in an aluminum alloy processed by high-pressure torsion[END_REF] with the grain sizes of 240 nm, 240 nm, 160 nm and 150 nm, respectively. Fig. 5 shows XRD profiles of the samples after N=10 and subsequent aging at 423 K for 35 min (peak-aged) and 3 h (over-aged). The XRD profile for the ST sample is also included for comparison. These profiles, except for the over-aged sample, do not show any peak that could be attributed to Al2Cu () or Al2CuMg (S) phases. A small volume fraction of intermetallic particles, identified as Al20Cu2Mn3 dispersoids (by STEM-EDS analysis, data not shown here), was

Grain size and dislocation density

detected. An extra peak corresponding to the stable S phase also appeared in the over-aged condition (e.g., in the vicinity of 35 o ). This is consistent with earlier works carried out on a similar material processed by SPD where the S phase was also observed in over-aged conditions [START_REF] Mohamed | Strengthening of A2024 alloy by high-pressure torsion and subsequent aging[END_REF][START_REF] Masuda | Extra Strengthening and Superplasticity of Ultra¬ne-Grained A2024 Alloy Produced by High-Pressure Sliding[END_REF].

Dislocation densities were estimated from peak broadening using the Williamson-Hall method [START_REF] Williamson | X-ray line broadening from filed aluminium and wolfram[END_REF][START_REF] Williamson | III. Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray debyescherrer spectrum[END_REF]. The calculation was carried out using five different full widths at half maximum (FWHMs) obtained from ( 111), ( 200), ( 220), ( 311) and ( 222) planes after normalization by calibrating the instrument [START_REF] Warren | The Structure of Silica Glass by X-Ray Diffraction Studies[END_REF]. The dislocation density measured in the as-HPT-processed sample was 5.5×10 15 m -2 and it decreased to 1.0×10 15 m -2 after peak-aging.

Microstructures

6(f)). The mean distance between such boundaries (λ) with enhanced local Cu and

Mg concentration was estimated from the HAADF images. It should be noted, however, that the measurement of λ was difficult for the as-HPT-processed sample because the fraction of the segregated boundaries was low ( ≦0.1) and thus contrast was poor (Fig. 6(b)). After aging, the solute enrichment is appreciable at almost all boundaries, so that λ could be estimated as 40±10 nm. Mg respectively. Interestingly, few precipitates could be observed within the interior of the grains surrounded by the segregated boundaries, despite the analyzed volume which was large enough to cover more than several grains. This was also confirmed with repeated APT analysis. The APT analysis was further repeated with two more samples in the same peak-aged state. Essentially, the same conclusion is reached as documented in Fig. 9. The intensive segregations of Cu and Mg are confirmed in Fig. 9 (a) and (b). In Fig. 9(c), the data was filtered with a 4at.% threshold for a better visualization of solute rich regions. This filtering analysis reveals that the typical length scale o f these segregations stands in a range of 20 to 50 nm which is considerably smaller than the grain size of ~160 nm determined for grains with HAGBs in Fig. 4(b) and in agreement with STEM-HAADF observations (Fig. 6(d)). This finding confirms that segregations occurred not only at HAGBs but also at LAGBs. To check any presence of precipitates within the grains, the data were filtered with a highe r composition threshold (15at.%Cu) (Fig. 9(d)). Only two Cu-rich nanoscaled precipitates could be detected as circled in Fig. 9(d). One appears elongated (about 5 nm in diameter and 20 nm long), the other is spherical (about 5 nm in diameter), and both contain about 22±7 at.%Cu. Thus, they correspond to the Al2Cu (θ') precipitates even if the Cu content is slightly lower than expected for this phase, as reported in other studies [START_REF] Nasedkina | Mechanisms of precipitation induced by large strains in the Al -Cu system[END_REF][START_REF] Biswas | Precipitates in Al-Cu alloys revisited: Atom-probe tomographic experiments and first-principles calculations of compositional evolution and interfacial segregation[END_REF].

Then, to determine if some nanoscaled precipitates have nucleated during aging at 423 K, frequency distribution histograms of Cu and Mg atoms located between segregated boundaries were calculated and compared to histograms where atom positions were randomized (Fig. 10(a,b)). These histograms clearly show that Cu and Mg atoms in the solid solution are randomly distributed both in the as-HPT-processed and in the subsequently peak-aged states. Thus, only atomic clusters [START_REF] Chen | Strengthening of an Al-Cu-Mg alloy processed by high-pressure torsion due to clusters, defects and defect-cluster complexes[END_REF][START_REF] Chen | Microstructural evolution, strengthening and thermal stability of an ultrafine -grained Al-Cu-Mg alloy[END_REF] should exist in these two states.

Concentration profiles (such as in Fig. 10(c)) were computed to quantify the segregated Cu and Mg levels. They are relatively similar to that measured in the as-HPT-processed state (Fig. 7(d)). The mean solute excesses at the segregated boundaries correspond to about one eighth of Cu monolayer and one eighth of Mg monolayer. The difference of composition between the whole volume and the concentration measured in regions along boundaries with segregations (Table 1) shows that about 0.5at.% of solutes has segregated to the boundaries. As GBs being shared between two grains, the fraction of atomic sites at boundaries (fs_GB) can be written as:

𝑓 𝑠_𝐺𝐵 = 𝑆 𝑉 𝑎𝑡 1 3 /2𝑉 , ( 2
)
where S is the grain surface area, V is the grain volume and Vat is the mean atomic volume (Vat ~ 0.016 nm 3 in fcc Al). For spherical grains with a diameter of 150 nm, a monolayer of solute is achieved with 0.5at.% of solute. This is much larger than the length scale measured by APT (Fig. 9) and seen in the HAADF images (Fig. 6). However, in the corresponding images, it should be noted that boundaries exhibit an elongated shape with average dimensions close to 100x100x20 nm 3 . Such dimensions give a decrease in solute to ~0.5at.% to cover boundaries with one quarter of Cu and Mg monolayer (from eq.( 2)).

Discussion

Microstructural features

Fig. 11 illustrates the summary of microstructural features based on the results by XRD, TEM, STEM and APT. In the as-HPT-processed state (N=10) (Fig. 11(a)), the UFG structure with the grain size of 130 nm containing a high density of LAGBs is well developed, and XRD shows much distortion due to a high density of dislocations. Intriguingly, the solute segregation was observed along a few boundaries but the fraction of this segregation is as small as ~10%.

The segregation occurred throughout all types of GBs inclu ding high-and low-angles of misorientations after subsequent peak-aging (Fig. 11(b)), leading to the extra reduction in the mean distance between segregated boundaries to 20 -50 nm as is evident from the APT analysis, while the amount of precipitates is ne gligibly small as observed by APT. It should be also noted that the ultrafine -grained structure is well retained after aging (d = 160 nm) owing to the strong solute segregation onto GBs, although a significant reduction in dislocation density occurred due to recovery.

Strengthening mechanism

In this study, the strength of the A2024 alloy reached 1 GPa and it is important to clarify the mechanism for this notable strengthening. The factors affecting this strengthening can be due to the interaction of dislocations with solute atoms and clusters, the mutual interaction of dislocations, the pinning of dislocations by dispersed particles and the blocking of dislocations by GBs, each of which corresponds to, so called, solid-solution hardening (ss), cluster hardening (cluster), work hardening (dis), dispersion hardening (pre) and grain boundary hardening (gb), in addition to overcoming the Piers potential (o). The total strength may then be described by the summation of all the strengthening factors [START_REF] Sabirov | Nanostructured aluminium alloys produced by severe plastic deformation: New horizons in development[END_REF].

𝜎 0.2 = 𝜎 0 + Δ𝜎 𝑠𝑠 + Δ𝜎 𝑑𝑖𝑠 + Δ𝜎 𝑝𝑟𝑒 + Δ𝜎 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 + Δ𝜎 𝑔𝑏 . (3)
Here,  is the yield strength and o is the friction stress equivalent to the Piers stress.

The values of the yield stress were measured as  =770 MPa and 955

MPa for the as-HPT-processed sample and the subsequently peak-aged sample, respectively, from the stress-strain curves in Fig. 3(b). The strength increased during aging despite grain growth and the decrease in dislocation density as illustrated in Fig. 11. Numerical estimation of each strengthening factor is derived as follows.

Evaluation of strengthening factors

Friction stress: The value of o is taken from the yield stress reported in pure Al (99.999 %) so that o = ~5 MPa [START_REF] Hansen | The effect of grain size and strain on the tensile flow stress of aluminium at room temperature[END_REF].

Solid-solution hardening:

The value of ss is estimated from the Fleischer [START_REF] Fleischer | Substitutional solution hardening[END_REF] and the Labusch [START_REF] Labusch | Statistical theories of solid solution hardening[END_REF] equations so that ss =~50 MPa. Here, this estimation is due to the average of the both values predicted from the Fleischer and the Labusch equations, which are 37 MPa and 59 MPa, respectively.

Work hardening: For the estimation of dis, the following Bailey-Hirsch equation [START_REF] Bailey | The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver[END_REF] is used:

∆𝜏 𝑑𝑖𝑠 = 𝛼𝐺𝑏√𝜌 . (4)
The dislocation density is input from the values measured from the XRD profile shown in Fig. 5, and thus it follows that dis =406+11 MPa for the as-HPTprocessed state, but dis decreases to 174+8 MPa after the subsequent peakaging. This calculation has used =0.24 for Al [START_REF] Hansen | Microstructure and flow stress of polycrystals and single crystals[END_REF] and the Taylor factor (M=3.06 [START_REF] Taylor | Plastic Strain in Metals[END_REF][START_REF] Chin | Computer Solutions of the Taylor Analysis for Axisymmetric Flow[END_REF][START_REF] Clausen | Characterisation of Polycrystal Deformation by Numerical Modelling and Neutron Diffraction Experiments[END_REF]).

Precipitation hardening:

The contribution of pre is considered to be zero as is evident from the APT analysis that the presence of the ' phase is negligible.

Cluster hardening: For the value of cluster, it was estimated from tensile testing of the sample after ST and subsequent aging at 423 K for 35 min which corresponds to the peak-aged condition for the HPT-processed sample. It was confirmed that the values of yield stress for each sample are 175 MPa and 280

MPa as y(ST) and y(aged), respectively, but these include the contributions of o, ss and gb. Thus, cluster=y-(o+ss+gb)= ~110 MPa (for y(ST)) and ~215 MPa (for y(aged)). (Note that gb was estimated as 10 MPa from the Hall-Petch equation.) Sha et al. [START_REF] Sha | Nanostructure of aluminium alloy 2024: Segregation, clustering and precipitation processes[END_REF] reported that the hardness of a solution-treated A2024 alloy increased by aging at 443 K for 30 min although no precipitation was detected. Instead, they concluded that the hardness in creased due to the formation of clusters. It should be noted that the cluster formation in the HPTprocessed sample may not be the same way as the ST sample. Nevertheless, the APT analysis clearly indicated that the clusters are present as shown in Fig. 9(d).

Grain boundary hardening:

The value of gb is estimated using the following Hall-Petch equation [START_REF] Hall | The deformation and ageing of mild steel: III Discussion of results[END_REF][START_REF] Petch | The Cleavage Strength of Polycrystals[END_REF]:

∆𝜎 𝑔𝑏 = 𝜎 -𝜎 0 = 𝑘 𝑦 √𝑑 , ( 5
)
where ky is a constant depending on the alloy type and composition. In this study, ky =0.08 MPa m 1/2 was used from the report by Shanmugasundaram in an Al -4%Cu alloy where the effect of dislocations and precipitations were minimized [START_REF] Shanmugasundaram | On the Hall-Petch relationship in a nanostructured Al-Cu alloy[END_REF]. As observed in Fig. 4(a) and (b), the grain sizes surrounded by high-angle boundaries were of 130 nm and 160 nm for the as-HPT-processed and the subsequently peak-aged samples, respectively. These grain sizes were then adopted for d in the above Hall-Petch equation, and thus it follows that gb(HAGB)

= 222+40 MPa and 200+50 MPa, respectively.

The comparison between the measured value and the estimated value ( y (with gb(HAGB))) in Table 2 shows that the estimated strength is almost comparable to the measured one for the as-HPT-processed sample, but the difference is significant for the sample subjected to aging after HPT processing (Table 2). In order to explain this difference, we consider the additional contribution to the strengthening: the segregation of solute elements onto GBs including not only high-angle misorientations but also low-angle misorientations as observed by APT (Fig. 8,9).

Segregation on low-angle grain boundaries

Based on the analytical results by APT that Cu and Mg were segregated on GBs by 5 at% on average, it can be estimated if the presence of such solute atom s is effective to stabilize the GBs in terms of the local strain developed by dislocations. Here, we considered that the GB is low-angle tilt boundary with an inclination of 10 degrees, which is typical of LAGBs. Provided that the angle for the lattice inclination is formed due to an alignment of edge dislocation, the distance between the dislocations, h, may be h=1.6 nm from the relation as h=b/, where b is the Burgers vector and  is the tilt angle. Because Mg atom is bigger and Cu atom is smaller than Al atom in diameter, they will relax the local strain around edge dislocations as illustrated in Fig. 12 where the dashed lines and solid lines are before and after the segregation of solute atoms, respectively. Note that the solute atoms are arbitrarily located in Fig. 12 so that the lattice becomes aligned with less strain and thus the dislocations becomes more stable. The dislocation movement through such a tilt boundary requires m ore energy as it creates lattice distortion, and it is reasonable to consider that the dislocation movement was impeded by the boundaries even they are low angles. The segregation of solute atoms on GBs prevents the dislocation movement, and it is then necessary to take into account the contribution to such strengthening even if they are segregated on LAGBs.

Several reports demonstrate the contribution of GB segregation to the strengthening. Molecular dynamic simulation by Vo et al. [START_REF] Vo | Reaching theoretical strengths in nanocrystalline Cu by grain boundary doping[END_REF] suggested that the segregation of Nb on GBs in nanograined Cu reduced the grain boundary energy and gave rise to higher strength equivalent to the one close to the ideal strength.

Zhao et al. [START_REF] Zhao | Segregation of Mg, Cu and their effects on the strength of Al Σ5 (210)[001] symmetrical tilt grain boundary[END_REF] also showed using the first-principles calculation that Cu segregation on Al grain boundaries increases the grain boundary strength, suggesting that dislocations are more effectively blocked by the GBs. Wang et al.

[52] conducted a finite element analysis compared with experimental results for a SUS316 stainless steel, and found that the segregation of solute atoms on subgrain boundaries (i.e., LAGBs) with a network structure well blocks the dislocation movement. This then deduces that the subgrain size with segregation should be applicable to the Hall-Petch relation rather than the grain size with high-angle misorientations.

Grain boundary fraction with solute segregation

In order to make a rigorous estimation for the contribution of GBs with high-angle and low-angle misorientations to the total strengthening, the grain size should be re-evaluated in terms of grain boundaries with solute segregation. The volume fraction of GBs ( f ) is related to the grain size (d) through the following equation:

𝑓 = 𝐴𝑑 - , (6)
where A and  are constants depending on the width of GB. Here, this form of the relation has been derived as described in Appendix. We define fall and fgb as volume fractions of all GBs and of the GBs that contribute to the strengthening:

𝑓 𝑎𝑙𝑙 = 𝑓 𝐻𝐴𝐺𝐵 + 𝑓 𝐿𝐴𝐺𝐵 , (7)
𝑓 𝑔𝑏 = 𝑓 𝐻𝐴𝐺𝐵 +  𝑠𝑒𝑔 × 𝑓 𝐿𝐴𝐺𝐵 , (8)
where fHAGB and fLAGB are the volume fractions of high-angle and low-angle GBs, and seg is the fraction of segregated GBs. This expression then involves a condition that the segregation occurs on all HAGBs and contributes to the strengthening together with the LAGBs with the fraction of seg. Thus, the effective grain size for strengthening (deff) may be approximated as

𝑑 𝑒𝑓𝑓 = 𝐴 1/ 𝑓 𝑔𝑏 -1/ . (9)
Putting eq.( 7) and eq.( 8) in eq.( 9), deff is expressed by

𝑑 𝑒𝑓𝑓 = ( 1-𝜅 𝑠𝑒𝑔 𝑑 𝐻𝐴𝐺𝐵  + 𝜅 𝑠𝑒𝑔 𝑑 𝑎𝑙𝑙  ) -1/ , (10)
under the condition that the constants A and  are independent of the grain boundary types (i.e., high-angle or low-angle misorientation). The value of deff is then determined through eq.( 10) from the measurements of seg, dHAGB and dall.

In this study, the value of seg was used as 0.1 and 1 (from STEM and APT results)

for the as-HPT-processed and subsequently peak-aged samples, respectively.

Likewise, the values of 130 nm and 160 nm for dHAGB, and 20 nm (from APT results) for dall were input, leading to the grain boundary strengthening of gb(eff)

= 274+40 MPa and 565 MPa for the as-HPT-processed and the subsequently peakaged states, respectively. The strengthening is achieved almost twice by aging after HPT processing. Zhao et al. showed that the average grain size obtained by a harmonic form well represents the Hall-Petch relation when grains are present in a bimodal distribution [START_REF] Zhao | Relationship between yield strength and grain size for a bimodal structural ultrafine -grained ferrite/cementite steel[END_REF]. Eq.( 10) is also a harmonic form except that it involves the constant .

Total strengthening

We now evaluate the total strength by adding the contributions of cluster formation and segregation onto GBs including LAGBs. The total strengths are of 845+51 MPa and 904~1009+8 MPa for the as-HPT-processed and the subsequently peak-aged samples as shown in reported ultra-high strengthening to ~950 MPa in an A7475 alloy and an Al -5.7wt.%Mg alloy [START_REF] Valiev | On the origin of the extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation[END_REF]. Otherwise, there is no report in other aluminum alloy systems by the use of SPD technique. The present study has demonstrated that the highest record is attained in the 2xxx series of aluminum alloys by HPT processing.

Conclusions

1. A solution-treated A2024 (Al-Cu-Mg) alloy reduced the grain size to 130 nm by HPT processing for 10 revolutions at room temperature. The tensile strength of ~910 MPa was achieved by HPT processing.

2. The subsequent aging after HPT processing further increased the tensile strength as high as ~1 GPa, despite the grain growth to 160 nm and the decrease in dislocation density.

Transmission electron microscopy (TEM) and atom probe tomography (APT)

revealed that precipitate particles were less present in the matrix. Instead, the analyses by TEM and APT showed that solute atoms such as Cu and Mg were segregated on grain boundaries including low-angle grain boundaries.

Figure and table captions Table 1

Compositions measured from APT data of Fig. 10. About 0.5at.% of solute (Cu plus Mg) has segregated along boundaries after processing by HPT (N=10) and aging for 35 min at 423 K.

Table 2 Contribution of strengthening factors estimated using theoretical approach, and comparison with theoretical values for as -HPT-processed and subsequently peak-aged states.

Fig. 2

 2 Fig. 2 shows (a) representative stress-strain curves and (b) the tensile strength and elongation to failure plotted as a function of the number of revolutions for the samples processed by HPT through N=0.75 to N=10. Fig. 2(a)

Fig. 4 shows

 4 Fig. 4 shows TEM bright-field images (left), dark-field images (right) and the corresponding SAED patterns (inset) recorded with an aperture size of 1.3 μm for (a) the as-HPT-processed (N=10) sample and (b) the subsequently peak-aged sample. Each dark-field image was taken using the diffracted beam indicated by the arrow in the corresponding SAED pattern. The TEM observations revealed that the grain size was refined to 130 nm. The SAED pattern exhibits Debye -

Fig. 6

 6 Fig.6shows STEM images obtained in (a, b) the as-HPT-processed sample

Fig. 7

 7 Fig. 7 shows the three-dimensional atom distribution maps of (a) Al, Cu and Mg, (b) Cu and (c) Mg obtained by APT for the as-HPT-processed sample. A GB is visible at the center, where the segregation of Cu and Mg is evident. The segregation is well demonstrated from the compositional profiles across the GB shown in Fig. 7(d). The concentrations of Cu and Mg are significantly increased at the boundary which is fully consistent with STEM-EDS data (Fig. 6(f)). The distributions of Cu and Mg at the nanoscale were also investigated by APT after subsequent peak-aging. Intensive segregations along two-dimensional defects are clearly visible in Fig. 8(a) and (b) with the distributions of Cu and

4 .

 4 The mechanism for the high strengthening achieved in this study was clarified in terms of the factors such as work hardening, solid -solution hardening, cluster hardening, precipitation hardening and grain boundary hardening. The analyses by TEM and APT including X-ray diffraction suggested that the segregation of Cu and Mg solute atoms not only onto high -angle grain boundaries but also onto low-angle grain boundaries plays an important role for the enhancement of the tensile strength.

Fig. 1

 1 Fig. 1 Sample dimensions of HPT disk with positions marked for Vickers microhardness measurement, position extracted for tensile specimen with dimensions, and location of TEM specimen.

Fig. 2

 2 Fig.2(a) Stress-strain curves and (b) variation of tensile strength and elongation to failure obtained after deformation at R.T. with initial strain rate of 3.0×10 -3 s -1 after N= 0.75, 1, 3, 5 and 10 including ST and T6 sample.

Fig. 3

 3 Fig.3(a) Hardness variations plotted against corresponding to equivalent strain and (b) stress-strain curves obtained after deformation at R.T. with initial strain rate of 3.0×10 -3 s -1 for the sample after N=10 and subsequent peak-aging including ST and T6 sample.

Fig. 4

 4 Fig. 4 TEM bright-field images (left), dark-field images (right) and selected area electron diffraction patterns (inset) for sample after (a) N=10 and (b) subsequent peak-aging.

Fig. 5

 5 Fig. 5 XRD profiles for samples after N=10 and subsequent peak-aging (35 min) and over-aging (3 h) including ST sample.

Fig. 6

 6 Fig. 6 STEM microstructures for sample after (a,b) N=10 and (c,d) subsequent peak-aging, and (e) intensity variation of HAADF signal and (f) EDS line profiles obtained along x in (c,d).

Fig. 7

 7 Fig. 7 Reconstructed three-dimensional atom maps of (a) Al, Cu and Mg, (b) Cu and (c) Mg obtained by APT analysis for as-HPT processed sample.

Fig. 8

 8 Fig. 8 Reconstructed three-dimensional atom maps of (a) Cu and (b) Mg obtained by APT analysis for subsequently peak-aged sample.

Fig. 9

 9 Fig. 9 Three-dimensional reconstruction of other volume analyzed by APT for subsequently peak-aged sample; (a) distribution of Al and Cu, (b) distribution of Al and Mg, same volume viewed in another direction and filtered to exhibit only atoms where local compositions exceed (c) 4at.%Cu and (d) 15at.%Cu and 4at.%Mg.

Fig. 10

 10 Fig.[START_REF] Valiakhmetov | Mechanical properties of the titanium alloy VT8 with submicrocrystalline structure[END_REF] Typical frequency distribution histograms of Cu and Mg computed far from segregated region in (a) as-HPT-processed (Fig.7) and (b) subsequently peak-aged samples (Fig.9). Frequency distribution histograms of measured data are compared to histograms of same data set where atom positions were randomized (sampling volume 2x2x2 nm 3 ). Concentration profiles computed across two GBs (sampling volume thickness: 0.1 nm) in Fig.9are also shown in (c).

Fig. 11

 11 Fig. 11 Schematic illustration of microstructures in terms of solute atoms for (a) as-HPT-processed and (b) subsequently peak-aged states.

Fig. 12

 12 Fig. 12 Schematic illustration of segregated subgrain boundary with 10 o of misorientation.

Fig. A

 A Fig. A Relationship between average grain size and volume fraction of grain boundary.

Fig. 1

 1 Fig. 1 Sample dimensions of HPT disk with positions marked for Vickers microhardness measurement, position extracted for tensile specimen with dimensions, and location of TEM specimen.

Fig. 2

 2 Fig. 2 (a) Stress-strain curves and (b) variation of tensile strength and elongation to failure obtained after deformation at R.T. with initial strain rate of 3.0×10 -3 s - 1 after N= 0.75, 1, 3, 5 and 10 including ST and T6 sample.

Fig. 3

 3 Fig. 3 (a) Hardness variations plotted against corresponding to equivalent strain and (b) stress-strain curves obtained after deformation at R.T. with initial strain rate of 3.0×10 -3 s -1 for the sample after N=10 and subsequent peak-aging including ST and T6 sample.

Fig. 4

 4 Fig. 4 TEM bright-field images (left), dark-field images (right) and selected area electron diffraction patterns (inset) for sample after (a) N=10 and (b) subsequent peak-aging.

Fig. 5

 5 Fig. 5 XRD profiles for samples after N=10 and subsequent peak-aging (35 min) and over-aging (3 h) including ST sample.

Fig. 6

 6 Fig. 6 STEM microstructures for sample after (a,b) N=10 and (c,d) subsequent peak-aging, and (e) intensity variation of HAADF signal and (f) EDS line profiles obtained along x in (c,d).

Fig. 7

 7 Fig. 7 Reconstructed three-dimensional atom maps of (a) Al, Cu and Mg, (b) Cu and (c) Mg obtained by APT analysis for as-HPT-processed sample. Concentration profiles of Cu and Mg across GB (sampling volume thickness: 0.1 nm) are also shown in (d).

Fig. 8

 8 Fig. 8 Reconstructed three-dimensional atom maps of (a) Cu and (b) Mg obtained by APT analysis for subsequently peak-aged sample.

Fig. 9

 9 Fig. 9 Three-dimensional reconstruction of other volume analyzed by APT for subsequently peak-aged sample; (a) distribution of Al and Cu, (b) distribution of Al and Mg, same volume viewed in another direction and filtered to exhibit only atoms where local compositions exceed (c) 4at.%Cu and (d) 15 at.%Cu and 4at.%Mg.

Fig. 10

 10 Fig. 10 Typical frequency distribution histograms of Cu and Mg computed far from segregated region in (a) as-HPT-processed (Fig. 7) and (b) subsequently peak-aged samples (Fig. 9). Frequency distribution histograms of measured data are compared to histograms of same data set where atom positions were randomized (sampling volume 2x2x2 nm 3 ). Concentration profiles computed across two GBs (sampling volume thickness: 0.1 nm) in Fig. 9 are also shown in (c).

Fig. 11

 11 Fig. 11 Schematic illustration of microstructures in terms of solute atoms for (a) as-HPT-processed and (b) subsequently peak-aged states.

Fig. 12

 12 Fig. 12 Schematic illustration of segregated subgrain boundary with 10 o of misorientation.

Table 2 (

 2 y (with gb(eff))). It should be noted that the estimation of the strength after aging does not include extra hardening due to nucleation of dislocations within small grains as discussed by Huang et al.[START_REF] Huang | Hardening by Annealing and Softening by Deformation in Nanostructured Metals[END_REF]. Nevertheless, these values are well in agreement with those measured by tensile tests as shown in Fig.3(b). In particular, the increase due to grain boundary strengthening through the Hall-Petch relation is prominent and this demonstrates that the segregation of Cu and Mg atoms on LAGBs plays a significant role in strengthening the alloy to as high as 1 GPa. Then, the conclusion can be reached that, thanks to segregations of solute atoms, the strength of LAGBs becomes almost equivalent to HAGBs, suggesti ng that new method to achieve high strength in UFG alloys is successfully developed. Ultra-high strengthening to 1 GPa in aluminum alloy was thus far attained by Liddicoat et al. in an A7075 alloy using HPT processing[START_REF] Liddicoat | Nanostructural hierarchy increases the strength of aluminium alloys[END_REF].Valiev et al.

Acknowledgements

One of the authors (TM) would like to acknowledge the Research Fellowship for Young Scientists from the Japan Society for Promotion of Science (JSPS) (No. JP16J07050 and No. JP19J01767). This work was supported in part by the Light Metals Educational Foundation of Japan, and in part by Grant-in-Aids for Scientific Research (S) and (A) from JSPS (No. JP26220909 and No. JP19H00830). HPT was carried out in the International Research Center on Giant Straining for Advanced Materials (IRC-GSAM) at Kyushu University. The authors would like to thank the Agence Nationale de la Recherche (ANR) for financial support (PRASA project -ANR-15-CE08-0029).

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Appendix

The volume fraction of grain boundaries is calculated through the following procedures. First, the grain shape is approximated to be the Kelvin's tetrakaidecahedron (inset of Fifth, the values of A and  are adjusted and the best fit is achieved with A=4.3 and =0.97. These constant values are then used in this study

Table 1

Compositions measured from APT data of Fig. 10. About 0.5at.% of solute (Cu plus Mg) has segregated along boundaries after processing by HPT (N=10) and aging for 35 min at 423 K.

Table 2

Contribution of strengthening factors estimated using theoretical approach, and comparison with theoretical values for as-HPT-processed and subsequently peak-aged states.