Yu Ma

Ahmed Addad

G Ji

Ming-Xing Zhang

Williams Lefebvre

Zhe Chen
email: zhe.chen@sjtu.edu.cn

Vincent Ji

Ji Gang
email: gang.ji@univ-lille.fr

Atomic-scale investigation of the interface precipitation in a

Keywords: Metal matrix composites, Aluminum alloys, Precipitation, Interface structure, STEM HAADF

come

Introduction

Age-hardenable Al alloys (e.g., 2xxx, 6xxx and 7xxx series) have been widely applied as structural materials in aerospace and automobile industries, due mainly to their high specific strength and excellent processability [START_REF] Williams | Progress in structural materials for aerospace systems1[END_REF][START_REF] Liddicoat | Nanostructural hierarchy increases the strength of aluminium alloys[END_REF][START_REF] Sun | Precipitation strengthening of aluminum alloys by room-temperature cyclic plasticity[END_REF]. Commonly, one of the most effective strengthening mechanisms involves precipitation hardening, i.e., a homogenous distribution of nanosized precipitates originating from solid-state precipitation reactions during aging treatments [START_REF] Ardell | Precipitation hardening[END_REF][START_REF] Zhao | Simultaneously increasing the ductility and strength of nanostructured alloys[END_REF][START_REF] Cao | Experimental and DFT characterization of η′ nano-phase and its interfaces in Al-Zn-Mg-Cu alloys[END_REF]. In addition, micron-(or submicron-) sized reinforcement particles (MRPs), such as SiC and B4C, have successfully been introduced to Al alloys, providing an alternative approach to further enhance their mechanical performance, particularly in case high Young's modulus is necessary [START_REF] Mcdanels | Analysis of stress-strain, fracture, and ductility behavior of aluminum matrix composites containing discontinuous silicon carbide reinforcement[END_REF][START_REF] Chawla | Three-dimensional (3D) microstructure visualization and finite element modeling of the mechanical behavior of SiC particle reinforced aluminum composites[END_REF][START_REF] Kai | Mechanical behavior of B4C particulate-reinforced 7091 aluminum composite[END_REF]. It has been largely recognized that MRP/Al interface structure critically influences the precipitation reactions to promote the formations of coarse precipitate zone (CPZ) and precipitate free zone (PFZ) in the surrounding matrix [START_REF] Vogelsang | Anin situ HVEM study of dislocation generation at Al/SiC interfaces in metal matrix composites[END_REF][START_REF] Christman | Microstructural development in an aluminum alloy-SiC whisker composite[END_REF][START_REF] Dutta | Influence of dislocation density and distribution on the aging behavior of 6061 AlSiCw composites[END_REF][START_REF] Starink | Microstrucure and strengthening of Al-Li-Cu-Mg alloys and mmcs: I. Analysis and modelling of microstructural changes[END_REF][START_REF] Nieh | Aging characteristics of B4C-reinforced 6061-aluminum[END_REF][START_REF] Papazian | Effects of SiC whiskers and particles on precipitation in aluminum matrix composites[END_REF][START_REF] Wu | Precipitation phenomena in Al-Zn-Mg alloy matrix composites reinforced with B4C particles[END_REF][START_REF] Hong | Microstructure and microchemistry of an Al-Zn-Mg-Cu alloy matrix-20 vol.% SiC composite[END_REF][START_REF] Starink | S′ and δ′ phase precipitation in SiCp reinforced Al-1.2wt.%Cu-1wt.% Mg-xLi alloys[END_REF][START_REF] Hu | Microstructural investigation on B4C/Al-7093 composite[END_REF][START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF], This, in turn, has a significant impact on overall mechanical properties of the Al-based metal matrix composites (MMCs) [START_REF] Starink | Microstrucure and strengthening of Al-Li-Cu-Mg alloys and MMCs: II. Modelling of yield strength[END_REF][START_REF] Papazian | Tensile properties of short fiber-reinforced SiC/Ai composites: Part I. effects of matrix precipitates[END_REF][START_REF] Nutt | Non-equilibrium phase distribution in an Al-SiC composite[END_REF].

It has been well established that the CPZ is caused by thermoelastic stress induced dislocations (TSIDs) near the MRP/Al interface [START_REF] Vogelsang | Anin situ HVEM study of dislocation generation at Al/SiC interfaces in metal matrix composites[END_REF][START_REF] Christman | Microstructural development in an aluminum alloy-SiC whisker composite[END_REF][START_REF] Dutta | Influence of dislocation density and distribution on the aging behavior of 6061 AlSiCw composites[END_REF][START_REF] Starink | Microstrucure and strengthening of Al-Li-Cu-Mg alloys and mmcs: I. Analysis and modelling of microstructural changes[END_REF]. The interaction between solute atoms and TSIDs leads to a solute flux towards dislocations resulting in faster and coarser precipitation on them [START_REF] Christman | Microstructural development in an aluminum alloy-SiC whisker composite[END_REF][START_REF] Dutta | Influence of dislocation density and distribution on the aging behavior of 6061 AlSiCw composites[END_REF][START_REF] Starink | Microstrucure and strengthening of Al-Li-Cu-Mg alloys and mmcs: I. Analysis and modelling of microstructural changes[END_REF].

When it comes to the PFZ formation, particularly in Al-Zn-Mg(-Cu) matrix composites, the underlying mechanism remains controversial. Some researchers have claimed that the PFZ formation is related to vacancy depletion [START_REF] Nieh | Aging characteristics of B4C-reinforced 6061-aluminum[END_REF][START_REF] Papazian | Effects of SiC whiskers and particles on precipitation in aluminum matrix composites[END_REF][START_REF] Wu | Precipitation phenomena in Al-Zn-Mg alloy matrix composites reinforced with B4C particles[END_REF]. As proposed, precipitation reactions at the MRP/Al interface are analogous to those at high-angle grain boundaries (GBs) in (unreinforced) Al alloys. The weakly-bonded and incoherent MRP/Al interface as well as TSIDs can act as ideal sinks to absorb and cause the annihilation of vacancies during the solution treatment [START_REF] Nieh | Aging characteristics of B4C-reinforced 6061-aluminum[END_REF][START_REF] Papazian | Effects of SiC whiskers and particles on precipitation in aluminum matrix composites[END_REF][START_REF] Wu | Precipitation phenomena in Al-Zn-Mg alloy matrix composites reinforced with B4C particles[END_REF].

Considering the nucleation of Guinier-Preston (GP) zones in Al alloys requiring a critical vacancy concentration [START_REF] Embury | The nucleation of precipitates: the system Al-Zn-Mg[END_REF][START_REF] Unwin | The origin of the grain boundary precipitate free zone[END_REF], the precipitation process in the vicinity of MRPs is thereby hindered leading to the PFZ formation. On the contrary, some studies revealed that the number of quenchedin vacancies has no influence on the GP zone formation in Al-Zn-Mg(-Cu) alloys [START_REF] Ryum | The influence of a precipitate-free zone on the mechanical properties of an Al-Mg-Zn alloy[END_REF][START_REF] Murakami | The formation and reversion of guinier-preston zones in an aluminium-6.7 at.% zinc alloy and the effects of small concentrations of magnesium and silver[END_REF]. It was thus indicated that the PFZ formation is likely attributed to the solute atoms rather than vacancy depletion [START_REF] Hong | Microstructure and microchemistry of an Al-Zn-Mg-Cu alloy matrix-20 vol.% SiC composite[END_REF][START_REF] Starink | S′ and δ′ phase precipitation in SiCp reinforced Al-1.2wt.%Cu-1wt.% Mg-xLi alloys[END_REF][START_REF] Hu | Microstructural investigation on B4C/Al-7093 composite[END_REF]. For example, Hong et al. [START_REF] Hong | Microstructure and microchemistry of an Al-Zn-Mg-Cu alloy matrix-20 vol.% SiC composite[END_REF] observed the formation of numerous MgO particles with the size of tens of nanometers at the SiC/Al interface in the A1-Zn-Mg-Cu matrix composite reinforced with 20 vol.% SiC particles. They proposed that this results in the depletion of Mg atoms in the surrounding matrix and then the suppression of precipitation in the vicinity of SiC particles during the aging process [START_REF] Hong | Microstructure and microchemistry of an Al-Zn-Mg-Cu alloy matrix-20 vol.% SiC composite[END_REF].

In addition to the two well-documented CPZ and PFZ mentioned above, Strangwood et al. [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF] reported that the MRP/Al interface can play the role as an ideal nucleation substrate to promote interracial segregation and precipitation on it in the SiC particles reinforced 2xxx and 7xxx matrix composites. They also found that the heterogeneous interfacial precipitations have a close correlation with the aging conditions [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF]. In the case of 7xxx matrix composite, it was found that, in the underaged composite, the SiC/Al interface was covered by a continuous precipitate layer which extended the thickness of around 10-20 nm into the Al matrix. Within the precipitate layer, discrete η particles (MgZn2) with 24-40 nm in diameter and spaced at approximately 70-80 nm intervals were discerned. However, in the overaged composite, the diffuse interfacial η'/η layer dissolved, giving rise to a series of fairly regularly (45-70 nm) spaced T phase (Mg32(Al, Zn) [START_REF] Ju | Microstructure of multi-pass friction-stir-processed Al-Zn-Mg-Cu alloys reinforced by nano-sized TiB2 particles and the effect of T6 heat treatment[END_REF] with the size ranging from 20 to 30 nm in dimeter surrounding the interface.

In parallel with the developments in nanotechnology, the dimensions of reinforcement particles (RPs) have decreased from micron/submicron scale to nanoscale (≤ 100 nm) over the last decades [START_REF] Tjong | Microstructural and mechanical characteristics of in situ metal matrix composites[END_REF][START_REF] Chen | Processing and properties of magnesium containing a dense uniform dispersion of nanoparticles[END_REF]. Accordingly, volume fraction of the particle/matrix interfaces increases proportionally as: In spite of this, some hypotheses based on the pioneer works can be proposed. Firstly, Kim et al. [START_REF] Kim | Plastic relaxation of thermoelastic stress in aluminum/ceramic composites[END_REF] proposed that the intensity of TSIDs shows a strong particle size dependence. It increases significantly only when the size of RPs reaches the micron level. At the finer scales the thermoelastic stress can be lower than the effective yield stress such that no TSIDs and no CPZ (caused by TSIDs) in the surrounding matrix should be generated [START_REF] Ashby | On the generation of dislocations at misfitting particles in a ductile matrix[END_REF][START_REF] Johnson | A dislocation model for the plastic relaxation of the transformation strain energy of a misfitting spherical particle[END_REF]. Secondly, in contrast to the incoherent MRP/Al interface [START_REF] Luo | Crystallography of SiC/MgAl2O4/Al interfaces in a pre-oxidized SiC reinforced SiC/Al composite[END_REF][START_REF] Jiang | Influence of length-scales on spatial distribution and interfacial characteristics of B4C in a nanostructured Al matrix[END_REF], semi-coherent NRP/Al interface is more analogous to low-angle GBs, becoming inefficient vacancy sinks [START_REF] Kostka | TEM study of the interface in ceramic-reinforced aluminum-based composites[END_REF][START_REF] Mitra | Interfaces in as-extruded XD Al/TiC and Al/TiB2 metal matrix composites[END_REF][START_REF] Ardell | On the coarsening of grain boundary precipitates[END_REF][START_REF] Unwin | The nucleation and initial stages of growth of grain boundary precipitates in Al-Zn-Mg and Al-Mg alloys[END_REF]. The NRP/Al interface is thus incapable to lead to vacancy depletion in the surrounding matrix. It was also reported that no oxide particles or amorphous layers have been found at the NRP/Al interface, suggesting no solute depletion caused by interfacial oxide formation [START_REF] Tang | Quantitative study of particle size distribution in an in-situ grown Al-TiB2 composite by synchrotron X-ray diffraction and electron microscopy[END_REF][START_REF] Li | Selective laser melting of nano-TiB2 decorated AlSi10Mg alloy with high fracture strength and ductility[END_REF][START_REF] Ma | Experimental study of the mechanisms of nanoparticle influencing the fatigue crack growth in an in-situ TiB2/Al-Zn-Mg-Cu composite[END_REF]. Consequently, no PFZ shall generate in NRPs reinforced Al-based MMCs whatever its formation mechanisms due to vacancy or solute depletion. Thirdly, unlike the MRP/Al interface, it has been well established that NRPs generally have preferential crystallographic orientation relationships (ORs) with the Al alloy matrix [START_REF] Tjong | Microstructural and mechanical characteristics of in situ metal matrix composites[END_REF][START_REF] Jiang | Influence of length-scales on spatial distribution and interfacial characteristics of B4C in a nanostructured Al matrix[END_REF].

𝑉𝑉 2 = (𝑟𝑟 1 𝑟𝑟 2 ⁄ ) 3 𝑉𝑉
As such, it is of theoretical possibility to have ORs in between the NRPs, interfacial precipitates and Al alloy matrix in order to minimize the nucleation energy barrier [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF][START_REF] Christian | The theory of transformations in metals and alloys[END_REF]. Finally, considering the NRP/Al interfacial precipitation reactions being analogous to those at low-angle GBs, the transformation of precipitates from η to T phases observed at the SiC/Al interface (being analogous to high-angle GBs) during the ageing treatments [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF], can most probably occur in a different way in NRPs reinforced 7xxx matrix composites [START_REF] Unwin | The origin of the grain boundary precipitate free zone[END_REF][START_REF] Unwin | The nucleation and initial stages of growth of grain boundary precipitates in Al-Zn-Mg and Al-Mg alloys[END_REF].

In view of the discussions above, the present work aims to provide a fundamental insight into the influences of NRPs on the precipitation reactions in Al-based MMCs. With high melting point (3173 K), high modulus (565 GPa), high hardness (2500 HV) and good thermal stability [START_REF] Munro | Material properties of titanium diboride[END_REF], TiB2

nanoparticles have widely been used as one of the most ideal NRPs in Al-based MMCs [START_REF] Ma | High cycle fatigue behavior of the insitu TiB2/7050 composite[END_REF][START_REF] Chen | Multi-scale study of microstructure evolution in hot extruded nano-sized TiB 2 particle reinforced aluminum composites[END_REF][START_REF] Liu | Simultaneously increasing strength and ductility of nanoparticles reinforced Al composites via accumulative orthogonal extrusion process[END_REF].

In this work, an Al-Zn-Mg-Cu matrix composite reinforced with homogenously distributed TiB2 nanoparticles was successfully fabricated and heat treated at different conditions, including solidsolution, peak-ageing and over-ageing treatments, followed by comprehensive characterization.

Probe-corrected (high-resolution) scanning transmission electron microscopy ((HR)STEM), in particular, high-angle annular dark-field (HAADF) imaging associated with energy dispersive spectrometer (EDS) mapping was used, which provides access to the nature of the precipitation reactions with spatial resolution at the nano-and atomic scales. We found significant microstructural evolutions at the TiB2/Al interface during the aging treatments. The interface was initially clean after solid-solution treatment. Heterogeneous interfacial precipitates (hereafter referred to as interphase, abbr. IP), determined to be (Zn1.5Cu0.5)Mg phase, were only formed at the preferential TiB2/Al interfaces during ageing. The crystallographic ORs between the TiB2 nanoparticle, interphase and Al matrix were determined. The atomic structure of the Al/interphase/TiB2 multi-interfaces was systematically characterized and analyzed. Based on these experimental evidences, the kinetics of the TiB2 nanoparticles exerted to the interface precipitation, including nucleation, growth rate, preferential precipitation TiB2/Al interfaces, effects of aging conditions are discussed in detail.

Experimental procedure

An in-situ mixed salt method was used to produce the TiB2 nanoparticles (6 wt.%) reinforced

Al-Zn-Mg-Cu composite ingot using high-purity reactive salts of K2TiF6 and KBF4 [START_REF] Chen | Multi-scale study of microstructure evolution in hot extruded nano-sized TiB 2 particle reinforced aluminum composites[END_REF].

Composite melts were synthesized at 900 °C in an electrical resistance furnace, and then cast into a graphite mould. 200 × 100 × 16 mm plates were then cut from the equal-axis grain zones of the ingot and homogenized at 465 °C for 24 h. Subsequently, a 4-pass friction stir processing (FSP) process was carried out with a tool rotation rate of 600 rpm, a tool tilt angle of 2.5°, a traverse speed of 80 mm/min and a processing depth of 8 mm [START_REF] Ju | Microstructure of multi-pass friction-stir-processed Al-Zn-Mg-Cu alloys reinforced by nano-sized TiB2 particles and the effect of T6 heat treatment[END_REF]. Afterwards, hot extrusion with an extrusion ratio of 20:1 was carried out on the samples cut from the nugget zone. Finally, the asextruded samples were subjected to T6 (470 °C/70 min + water quenching + 120°C/20h) and T76

(470 °C/70 min + water quenching + 120°C/5h + 160°C/18h) heat treatments. The as-quenched and both aged samples were characterized in more details using STEM. The hardness curves as a function of ageing time at the T6 and T76 states were plotted in Figs. S1(a) and (b), respectively.

The hardness increased by increasing the ageing time in the range 0-10h at 120 °C. A plateau of the highest hardness of around 205 HV was reached after ageing for more than 10h. The peak hardness of around 208 HV was obtained after ageing at 160 °C for 6h, and then the hardness gradually reduced by extending the ageing time.

STEM specimens with 3 mm in diameter were prepared through mechanical polishing and final ion milling in a GATAN precision ion polishing system, operated at -150 °C. A state-of-theart FEI Titan Themis 300 microscope equipped with a probe aberration corrector, operated at 200 kV, was used to acquire (HR)STEM images. The probe size was set to 0.1 nm with a convergence semi-angle of 22.5 mrad. Collection angle of the HAADF detector was in the range 80-150 mrad.

Contrasts in an HAADF image is proportional to Z ~1.7-2 , meaning that the bright contrast indicates relatively heavy atomic composition [START_REF] Jesson | Incoherent imaging of crystals using thermally scattered electrons[END_REF]. In this case, the bright and dark contrasts can be considered as Zn (Cu)-rich and Mg-rich areas in the Al matrix, respectively. The equipped highly efficient (4 quadrant) EDS system was used for chemical analyses of possible precipitates formed at the TiB2/Al interface. Interface characterization was done by tilting the Al matrix to the [101] orientation in terms of the well-documented preferential ORs of the TiB2/Al interfaces [START_REF] Schaffer | Crystallography of engulfed and pushed TiB2 particles in aluminium[END_REF]. JEMS software was used for generating theoretical electron diffraction patterns by considering the kinematic approximation [START_REF] Stadelmann | JEMS JAVA electron microscopy software[END_REF]. Dr. Probe software was used for simulating atomic-scale HRSTEM-HAADF images [START_REF] Barthel | Probe: A software for high-resolution STEM image simulation[END_REF]. VESTA, a 3-D visualization program for structural models, was used to construct interfacial atomic structure configurations [START_REF] Momma | VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data[END_REF]. Note that quantitative estimations of compositions by STEM/EDS are inevitably affected by the channeling of electrons along atomic columns in zone axis conditions. The composition results were hence presented as semi-quantitative.

Results

The TiB 2 /Al interface structure in the solid-solution treated composite

Our previous studies of the TiB2/Al-Mg-Si [START_REF] Ma | Microstructure and mechanical properties of friction stir processed Al-Mg-Si alloys dispersion-strengthened by nanosized TiB2 particles[END_REF] and TiB2/Al-Zn-Mg-Cu composites [START_REF] Ju | Microstructure of multi-pass friction-stir-processed Al-Zn-Mg-Cu alloys reinforced by nano-sized TiB2 particles and the effect of T6 heat treatment[END_REF] demonstrated that the fabrication process combining casting (in-situ reaction), FSP and extrusion is efficient to acquire a desired microstructure in the nugget zone. It is featured with a fine equiaxed grain structure (a few micrometers in the average size) and uniformly distributed TiB2 nanoparticles. Fig. 1a shows the uniform distribution of the majority TiB2 nanoparticles within an Al grain. Fig. 1b shows the typical TiB2 nanoparticle that has a facetted shape with identified basal {0001}, prismatic {011 � 0} and pyramidal {011 � 1} facets, which is illustrated in Fig. 1c. This is consistent with the previous results [START_REF] Wulff | On the question of speed of growth and dissolution of crystal surfaces[END_REF][START_REF] Abdel-Hamid | Crystal morphology of the compound TiB2[END_REF]. The TiB2/Al interface is tightly bonded and free of oxide particles, where solute-enriched zones having a size of several nanometers are present. In addition to such interphase precipitates, finer precipitates with a high density can also be seen being homogeneously distributed in the Al matrix away from TiB2 nanoparticles, as shown in Fig. 3b. These finer precipitates are the plate-like GP zones with the diameter of ~8 nm (Fig. 3c) and rectangle η' phase on the {111}Al planes, which is roughly 2 nm in thickness and 8 nm in length (Fig. 3d). Both GP zones and η' phase are fully coherent with the Al matrix.

Similar to the peak-aged sample, neither obvious CPZ nor PFZ were observed in the over-aged sample, but interphase precipitates formed at the TiB2/Al interface with the contact angles (θ) of around 60° and 100° measured as the projected angles, as shown in Fig. 3e. In addition, dense rectangle η (type MgZn2 [START_REF] Thackery | The nature and morphology of precipitate in aluminum-zink-magnesium alloys[END_REF]) precipitates on {111}Al planes are found being uniformly distributed in the matrix (Fig. 3f). They are about 7 nm thick and 26 nm long (Fig. 3g). This η phase is semicoherent with the Al matrix due to the misfit dislocations at the Al/η interface (Fig. 3h).

Results in Figs. 2 and3 indicate that the TiB2/Al interfaces were preferred sites for promoting the precipitation reactions. While, within the Al matrix away from the interface, the observed precipitation sequence was supersaturated solid solution → GP zones → metastable η' → stable η. This agrees with the results well-documented in the Al-Zn-Mg-Cu alloy [START_REF] Sha | Influence of equal-channel angular pressing on precipitation in an Al-Zn-Mg-Cu alloy[END_REF].

Structure determination of the formed interphase precipitate

Using STEM/EDS elemental mapping, it was identified that the interphase precipitates in both the peak-aged and over-aged samples were enriched with Zn, Mg, Cu and Al as exemplified in Fig. S1) [START_REF] Ellner | Neutron-diffraction analysis of ternary laves phases of the MgCu2 type[END_REF]. From a HAADF image as shown in Fig. 5 the interplanar spacing of the (0004) and (1 � 1 � 20) planes were measured to be 0.421 nm and 0.256 nm, respectively, which accords with that of the (Zn1.5Cu0.5)Mg phase.

The corresponding FFT pattern of the (Zn1.5Cu0.5)Mg phase matches the structure of this phase well [START_REF] Ellner | Neutron-diffraction analysis of ternary laves phases of the MgCu2 type[END_REF]. Furthermore, the simulated HAADF image of (Zn1.5Cu0.5)Mg phase (overlapped in Fig. 5a) fits with the intensity of the experimental result of the interphase. Thus, the interphase is identified to be the (Zn1.5Cu0.5)Mg phase. Note that this method was also used to identify the interphase precipitates formed in the overaged sample, confirming the same crystal structure of the phase.

OR-dependent precipitations at the TiB2/Al interfaces

As shown in Fig. 6, the prismatic {01 1 � 0} and pyramidal {01 1 � 1} facets of the TiB2 nanoparticles are the preferential heterogeneous precipitation sites at the OR1 condition (Figs. 6a-6c), while the two basal {0001} facets are the sites at the OR2 (Figs. 6d-6f). Figs. 7 and8 show the ORs between the interphase precipitates, the TiB2 nanoparticle and the Al matrix. At the peakaged/OR1 condition (Fig. 7), the reproducible ORs, namely the OR3 between interphase and Al matrix and the OR4 between interphase and TiB2 were determined. They are:

The OR3: [ 2), respectively. As detailed in Fig. 10, the interphase/TiB2 interface (11 2 � 8)IP//(011 � 0)TiB 2 contains two periodically spaced misfit dislocations (Fig. 10b)

having the low mismatch of 2.94 % (Table 2). However, the interface (0008)IP//(011 � 1)TiB 2 displays four misfit dislocations (Fig. 10c), suggesting that the observed interphase was not directly nucleated at this interface considering the precipitation kinetics and the very high mismatch of 60.74 % (Table 2).

At the overaged/OR2 condition (Fig. 11), the interphase grew based on the (0004)IP planes along the growth direction <0001>IP, being the same as in the peak-aged/OR1 case. Only the misfit dislocations, spaced at approximately 2.7 and 1.25 nm intervals (Table 2), are observed at the arclike (Figs. 11a and11b) and shape interphase/Al interfaces (Figs. 11c andd), respectively. Finally, Fig. 12 shows that the interphase/TiB2 interface displays only one misfit dislocation, being in agreement with the theoretical mismatch of 2.34 % (Table 2).

Discussion

In the TiB2/Al-Zn-Mg-Cu composite, our atomic scale investigation clearly demonstrates that the homogenous distribution of TiB2 nanoparticles has exerted disparate influences on the precipitation reactions in the Al matrix near the TiB2/Al interface (i.e. the NRP/Al type). Such an interface had following features: (1) No CPZs were formed (Figs. 3a and3e) due to the absence of TSIDs (Fig. 1a). ( 2) The semi-coherent and clean TiB2/Al interface (Figs. 2a and2d) is incapable to lead to vacancy or solute depletion, and thus no PFZs formed [START_REF] Kostka | TEM study of the interface in ceramic-reinforced aluminum-based composites[END_REF][START_REF] Mitra | Interfaces in as-extruded XD Al/TiC and Al/TiB2 metal matrix composites[END_REF][START_REF] Ardell | On the coarsening of grain boundary precipitates[END_REF][START_REF] Unwin | The nucleation and initial stages of growth of grain boundary precipitates in Al-Zn-Mg and Al-Mg alloys[END_REF]. It has been well

documented that the formation of CPZs or PFZs is detrimental to mechanical properties of MMCs [START_REF] Starink | Microstrucure and strengthening of Al-Li-Cu-Mg alloys and MMCs: II. Modelling of yield strength[END_REF][START_REF] Papazian | Tensile properties of short fiber-reinforced SiC/Ai composites: Part I. effects of matrix precipitates[END_REF][START_REF] Nutt | Non-equilibrium phase distribution in an Al-SiC composite[END_REF]. Thus, it is expected that their absence would be beneficial to the present MMCs.

(3) The OR-dependent heterogeneous precipitations were promoted at the TiB2/Al interface considering the much larger sizes of the interphase in comparison with those of the nano-precipitates formed in the matrix away from the interface (Fig. 3). The interphase precipitates in both the peak-aged and overaged samples were identified to be the (Zn1.5Cu0.5)Mg phase and show specific ORs with the TiB2 nanoparticle and the Al matrix (Figs. 678). The corresponding underlying mechanisms of the heterogeneous precipitation reactions at the TiB2/Al interfaces are discussed in detail below.

Reduced nucleation energy barrier for the interphase precipitation

For the homogenous precipitation in the Al alloy matrix, the minimum activation energy barrier ∆𝐺𝐺 ℎ𝑜𝑜𝑜𝑜 * can be expressed using the following equation [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF]:

∆𝐺𝐺 ℎ𝑜𝑜𝑜𝑜 * = - 16𝜋𝜋𝛾𝛾 𝛼𝛼𝛼𝛼 3 3(∆𝐺𝐺 𝑉𝑉 -∆𝐺𝐺 𝑆𝑆 ) 2 (1)
where 𝛾𝛾 𝛼𝛼𝛼𝛼 and ∆𝐺𝐺 𝑉𝑉 are the interfacial energy and difference in free energy (per unit volume) between the Al matrix (α) and the precipitate (β), respectively; ∆𝐺𝐺 𝑆𝑆 is the misfit strain energy (per unit volume) of the precipitate. Analogously, for the heterogeneous precipitation at the TiB2/Al interface, the equation for the minimum activation energy barrier ∆𝐺𝐺 ℎ𝑒𝑒𝑒𝑒 * is expressed by [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF][START_REF] Christian | The theory of transformations in metals and alloys[END_REF]:

∆𝐺𝐺 ℎ𝑒𝑒𝑒𝑒 * = - 4 3 𝜋𝜋 𝛾𝛾 𝛼𝛼𝛼𝛼 3 (∆𝐺𝐺 𝑉𝑉 -∆𝐺𝐺 𝑠𝑠 ) 2 (2 -3𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 3 ) (2)
where 𝛾𝛾 𝛼𝛼𝛼𝛼 , ∆𝐺𝐺 𝑉𝑉 and ∆𝐺𝐺 𝑆𝑆 are the same as in Eq. ( 1), 𝐶𝐶 is the contact angle between the nucleus of the interphase and the TiB2 substrate.

Consequently, the relationship between ∆𝐺𝐺 ℎ𝑜𝑜𝑜𝑜 * and ∆𝐺𝐺 ℎ𝑒𝑒𝑒𝑒 * is acquired and expressed by the following equation:

∆𝐺𝐺 ℎ𝑒𝑒𝑒𝑒 * ∆𝐺𝐺 ℎ𝑜𝑜𝑜𝑜 * = 1 4 (2 -3𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 3 ) = 𝑓𝑓(𝐶𝐶) (3)
Thus, as long as the contact angle between the interphase and TiB2 substrate is lower than 180 o , being obvious in Fig. 3, the calculated f(θ) is always smaller than 1. This means that the energy barrier for the heterogeneous precipitations at the TiB2/Al interface is reduced compared with the homogeneous nucleation in the Al matrix away from the interface.

In addition, from Fig. 2, highly-dense misfit dislocations are observed at the TiB2/Al interfaces in the sample after solid-solution treatment. The stress field generated by these misfit dislocations could be the driving force for the migration of solute atoms (Zn, Mg, Cu etc.) on the substitutional sites towards the dislocations [START_REF] Blavette | Three-dimensional atomic-scale imaging of impurity segregation to line defects[END_REF][START_REF] Thompson | Imaging of arsenic Cottrell atmospheres around silicon defects by three-dimensional atom probe tomography[END_REF]. The segregation of solute atoms along the misfit dislocation lines at the TiB2/Al interfaces therefore led to the formation of Cottrell atmospheres. This is in good agreement with the observed solute-enriched regions at the TiB2/Al interfaces in Fig. 1b.

Moreover, it has been well-documented that vacancies, being essential for the nucleation of precipitates, are readily affected by the stress field caused by dislocations [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF][START_REF] Seitz | On the generation of vacancies by moving dislocations[END_REF]. Vacancies could migrate towards the misfit dislocations at the TiB2/Al interfaces during the subsequent aging treatments [START_REF] Seitz | On the generation of vacancies by moving dislocations[END_REF]. Solute-vacancy clusters thus form and transform to the nucleus once vacancies approach solute atoms in the solute-enriched regions located at the TiB2/Al interfaces [START_REF] Sha | Early-stage precipitation in Al-Zn-Mg-Cu alloy (7050)[END_REF][START_REF] Sha | Kinetic Monte Carlo simulation of clustering in an Al-Zn-Mg-Cu alloy (7050)[END_REF].

The interactions between the solute atoms, vacancies and misfit dislocations at the TiB2/Al interfaces can be beneficial to the nucleation of the interphase precipitates [START_REF] Blavette | Three-dimensional atomic-scale imaging of impurity segregation to line defects[END_REF][START_REF] Larché | Overview no. 41 the interactions of composition and stress in crystalline solids[END_REF].

Accelerated growth rate for the interphase precipitation

As proposed by the previous studies, the lattice distortion near dislocation cores effectively lower the activation energy for solute atoms diffusion [START_REF] Allen | The oriented growth of precipitates on dislocations in Al-Zn-Mg-part I. Experimental observations[END_REF][START_REF] Huang | Is pipe diffusion in metals vacancy controlled? A molecular dynamics study of an edge dislocation in copper[END_REF][START_REF] Rabier | Atomistic calculations of point-defect interaction and migration energies in the core of an edge dislocation in NaCl[END_REF]. The dislocation cores can act as fast diffusion paths for solute atoms enabling the rapid growth of precipitates on dislocations [START_REF] Unwin | The origin of the grain boundary precipitate free zone[END_REF][START_REF] Deschamps | Influence of predeformation and ageing of an Al-Zn-Mg alloy-II. Modeling of precipitation kinetics and yield stress[END_REF] and promoting the precipitation of nanoscale precipitates [START_REF] Eckert | Thermal stability and grain growth behavior of mechanically alloyed nanocrystalline Fe-Cu alloys[END_REF][START_REF] Hu | Precipitation phenomena in an ultrafine-grained Al alloy[END_REF]. In this case, the accelerated growth of the interphase (Fig. 3) is also attributed to the misfit dislocations presenting at the semicoherent TiB2/Al interface (Fig. 2).

As a diffusion-controlled phase transformation, the precipitation in Al-Zn-Mg(-Cu) alloys depends on the diffusion of solute atoms, i.e., Mg, Zn (Cu) in the Al matrix [START_REF] Christian | The theory of transformations in metals and alloys[END_REF]. For the ideal crystal structure with no defects, the solute atoms diffuse randomly by substitution, advancing a radial distance according to the following equation [START_REF] Shewmon | Diffusion in solids[END_REF]:

� 𝑥𝑥 = √6𝐷𝐷𝐷𝐷 𝐷𝐷 = 𝐷𝐷 0 𝑒𝑒𝑥𝑥𝑒𝑒 -𝑄𝑄 𝑅𝑅𝑅𝑅 ( 4
)
where D is the bulk diffusivity with units (m 2 /s); D0 is a material constant; Q is the activation energy for substitutional diffusion; R is the universal gas constant (=8.3145 J/mol K); and T is the absolute temperature in Kelvin. According to the reports of Ma et al. [START_REF] Ma | Coupling of dislocations and precipitates: impact on the mechanical behavior of ultrafine grained Al-Zn-Mg alloys[END_REF], the bulk diffusivity rates of Mg and Zn (Cu) are 1.7 × 10 -21 m 2 /s and 7.4 × 10 -22 m 2 /s at the aging temperature of 120 °C, respectively. Zn (Cu) thus is the diffusion-rate limiting elements in Al-Zn-Mg(-Cu) alloys.

For the homogenous precipitations in Al-Zn-Mg(-Cu) alloys, the radius of the initially nucleated embryo can be illustrated by the Zener-Hillert model [START_REF] Christian | The theory of transformations in metals and alloys[END_REF]:

𝑑𝑑𝑟𝑟 𝑑𝑑𝐷𝐷 = 𝐷𝐷(𝑐𝑐 -𝑐𝑐 𝑒𝑒 ) 𝑟𝑟 𝑝𝑝 �𝑐𝑐 𝑝𝑝 -𝑐𝑐 𝑒𝑒 � �1 - 𝑟𝑟 𝑐𝑐 𝑟𝑟 𝑝𝑝 � + 1 𝑁𝑁 𝑑𝑑𝑁𝑁 𝑑𝑑𝐷𝐷 (𝛼𝛼𝑟𝑟 * -𝑟𝑟) ( 5
)
where r is the radius of the η' phase; c is the current solute concentration of the matrix; ce is the equilibrium solute concentration of the matrix and cp is the solute concentration at the equilibrium precipitate/matrix interface; rp is the radius of platelet tip and rc is the critical platelet tip radius at which growth would stop for capillarity effects reducing the driving force for solute diffusion to zero; N is the precipitate density; 𝛼𝛼 is the numerical factor accounts for the fact that nucleated precipitates can grow only when their radius is slightly larger than the radius r*, (r > r* and dN/dt > 0), otherwise, they dissolve into the matrix.

When dislocations are involved, the growth rate of the precipitate is accelerated by an enhancement factor expressed as [START_REF] Wang | Growth of δ′ on dislocations in a dilute Al-Li alloy[END_REF][START_REF] Deschamps | In situ evaluation of dynamic precipitation during plastic straining of an Al-Zn-Mg-Cu alloy[END_REF]:

𝑓𝑓 = 1 + 𝑏𝑏√2 𝜋𝜋𝑟𝑟 �𝑓𝑓(𝐷𝐷 ′ ) � 𝐷𝐷 𝑝𝑝 √𝐷𝐷 ( 6
)
where 𝑓𝑓 is the enhancement factor that pipe diffusion enhancing the precipitate growth rate, 𝐷𝐷 is the bulk diffusivity of the rate-controlling solute species; 𝐷𝐷 𝑝𝑝 is the diffusivity of the rate-limiting species along the dislocation core; 𝑏𝑏 is the Burgers vector; the core width of the dislocation is assumed to be equal to 2𝑏𝑏; 𝑓𝑓(𝐷𝐷 ′ ) can be expressed by the following equation:

𝑓𝑓(𝐷𝐷 ′ ) = � exp(-𝐷𝐷 ′ 𝑥𝑥 2 ) 𝑥𝑥[𝐽𝐽 0 2 (𝑥𝑥) + 𝑌𝑌 0 2 (𝑥𝑥)] 𝑑𝑑𝑥𝑥 ∞ 0 ( 7
)
where 𝐽𝐽 0 (𝑥𝑥) and 𝑌𝑌 0 (𝑥𝑥) are the zeroth-order Bessel functions of the first and second kind.

The integral in Eq. ( 7) is time dependent but for typical values of time from 100-1000 s has a value from 0.85 to 0.62 [START_REF] Deschamps | In situ evaluation of dynamic precipitation during plastic straining of an Al-Zn-Mg-Cu alloy[END_REF]. Deschamps et al. [START_REF] Deschamps | Influence of predeformation and ageing of an Al-Zn-Mg alloy-II. Modeling of precipitation kinetics and yield stress[END_REF][START_REF] Deschamps | In situ evaluation of dynamic precipitation during plastic straining of an Al-Zn-Mg-Cu alloy[END_REF] have estimated that in Al-Zn-Mg(-Cu) alloys 𝐷𝐷 𝑝𝑝 is on the order of 10 -17 m 2 /s at the aging temperature of 120 °C. D for the rate-limiting solute species Zn(Cu) is 7.4 × 10 -22 m 2 /s [START_REF] Ma | Coupling of dislocations and precipitates: impact on the mechanical behavior of ultrafine grained Al-Zn-Mg alloys[END_REF]. 𝑏𝑏 is 0.286 nm for Al [START_REF] Ma | Mechanical behavior and strengthening mechanisms in ultrafine grain precipitationstrengthened aluminum alloy[END_REF]. 𝑟𝑟 is approximate to 4 nm as shown in Fig. 3b. Substituting these parameters to Eq. ( 6), the enhancement factor is approximated to be ~3.95. According to Fig. 3a, the radius of the interphase heterogeneously precipitated at the TiB2/Al interfaces is around 17 nm. Consequently, the enhanced precipitate growth factor observed experimentally at the peak-aged state is calculated to be 4.25, which is approximate to the enhancement factor of 3.95 acquired by Eq. ( 6).

Preferential TiB 2 /Al interfaces for suppressing the interphase precipitation

As shown in Fig. 6, the precipitation depended on the ORs between the TiB2 nanoparticles and the Al matrix. For the OR1, the interphase preferentially formed on the prismatic {011 � 0} and pyramidal {011 � 1} facets of the TiB2 nanoparticle. But, the OR2 resulted in the precipitation on the basal {0001} facets. The common feature is that the TiB2/Al interface was parallel to the closepacked {111} planes of the Al matrix and remained 'clean' after the ageing treatments, i.e. the suppression of the interphase precipitation.

It has been well established that the precipitation in the Al-Zn-Mg(-Cu) alloys is caused by diffusional nucleation followed by effective growth [START_REF] Cao | Experimental and DFT characterization of η′ nano-phase and its interfaces in Al-Zn-Mg-Cu alloys[END_REF][START_REF] Berg | GP-zones in Al-Zn-Mg alloys and their role in artificial aging[END_REF]. As discussed above (Section 4.1), the TiB2/Al interfaces are the favorable sites for nucleation of the interphase. Indeed, a closer look confirm that, for example for the OR1 (Figs. 13a and13b), the interphase has nucleated at the TiB2/Al interface being parallel to the basal {0001} facets of the TiB2 particle, while its growth has been suppressed. It is well-known that the growth of precipitates is essentially the process where a nucleus/matrix interface migrates into the surrounding parent phase by transferring atoms across the moving interface [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF]. In this case, the suppression of the precipitation can be understood by the fact that a coherent close-packed interface between the embryo of the hcp interphase and the fcc Al matrix was formed during the nucleation stage (Fig. 13a). As schematically illustrated in Figs. 13c and13d and was reported in Refs. [START_REF] Li | HREM study and structure modeling of the η′ phase, the hardening precipitates in commercial Al-Zn-Mg alloys[END_REF][START_REF] Li | High-resolution characterization of the precipitation behavior of an Al-Zn-Mg-Cu alloy[END_REF][START_REF] Martin | Stability of microstructure in metallic systems[END_REF] that the atom on a C site in the fcc Al matrix must change into a B position to make the interphase growth happen.

This should result in a very high energy and unstable configuration with two atoms directly above each other on B sites [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF]. In addition, a loop of Shockley partial dislocation should be necessarily created around the atom [START_REF] Martin | Stability of microstructure in metallic systems[END_REF]. An atom attempting such a jump will, therefore, be unstable and be forced back to its original position [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF][START_REF] Martin | Stability of microstructure in metallic systems[END_REF]. Thus, the suppressed growth at the coherent closepacked interphase/Al interface can be explained by very low accommodation factors and low mobility.

Crystallographic ORs between TiB 2 nanoparticles, interphase and Al alloy matrix

In order to further understand the experimentally determined ORs, the edge-to-edge matching It is a = 0.40494 nm [START_REF]JCPDS-International Centre for Diffraction Data[END_REF]. As a simple FCC structure, there are three possible close packed or nearly close packed directions. They are <110>Al, <100>Al and <112>Al. The close packed plane for FCC is {111}Al and this contains the <110>Al directions and the <112>Al directions. {200}Al is the second close packed plane and this contains the <110>Al directions and the <100>Al directions. This OR-H actually is consistent with the OR4. Similarly, the OR6 can also be deduced from the OR-C and the OR-G.

The above crystallographic analysis indicates that the interfaces in between the TiB2 nanoparticles and the Al matrix in the composite produced using the in-situ mixed salt method were either coherent or semi-coherent. Such interfaces acted as preferred sites for precipitation of the (Zn1.5 Cu0.5)Mg interphase during ageing treatment, this in turn impact on the mechanical properties of the composites.

Effect of the aging conditions on the interphase evaluation

It was reported that the precipitation of T phase requires a high vacancy boundary diffusivity, i.e., at high-angle GBs or MRP/Al interface [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF][START_REF] Embury | The nucleation of precipitates: the system Al-Zn-Mg[END_REF][START_REF] Unwin | The origin of the grain boundary precipitate free zone[END_REF]. Different from as observed in the SiC/Al MMC [START_REF] Strangwood | Segregation to SiC/Al interfaces in Al based metal matrix composites[END_REF], no transformation of the interphase from η to T phases is found when the aging condition is shifted from the peak-aged to overaged states (Figs. 4 and5). This is due to the low boundary diffusivity of the semi-coherent TiB2/Al interface being unfavorable for promoting this transformation. Further, it is well known that the precipitation in Al-Zn-Mg(-Cu) alloys involves the formation of precipitates with a different composition compared to the matrix, and therefore long-range diffusion is required [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF]. This is a continuous and time-consuming phase transformation process featured by thermally activated atomic movements [START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF][START_REF] Christian | The theory of transformations in metals and alloys[END_REF]. As such, a metastable transitional zone should always exist at the growth front as long as the phase transformation process has not completely accomplished, although it cannot be confirmed in this work. It would be interesting in the future to carry out in-situ TEM heating tests, starting from the as-quenched state, to track the whole interface precipitation process.

Conclusions

In (2) Preferential heterogeneous interface precipitates are closely related to the OR1 or OR2 conditions between the TiB2 and Al matrix, while being independent on the ageing conditions.

The interphase is identified to be the (Zn1.5Cu0.5)Mg phase both at the peak-aged and overaged states. At the OR1, The ORs between the TiB2 nanoparticles, interphase and the Al matrix are: 201606230212). The TEM facility in Lille, France, is supported by the Conseil Regional du Nord-Pas de Calais and the European Regional Development Fund (ERDF). Prof. A. Deschamps (Grenoble INP, France) is also thanked for fruitful discussions. See the text for more details.

FIGURE CAPTIONS

Fig. 2

 2 Fig. 2 presents two typical HRSTEM images and the associated fast Fourier transform (FFT)

3. 2 . 3 .

 23 Atomic structure of the Al/(Zn1.5Cu0.5)Mg interphase/TiB2 interfaces At the interphase/Al interfaces (i.e. the OR3, Fig. 9), the interphase precipitate grew based on (0008)IP planes along the growth direction <0001>IP. Misfit dislocations exist in the zone near the growth front of the interphase, where the measured interplanar spacing values are slightly different compared with those of the typical structure of (Zn1.5Cu0.5)Mg phase in the fully-grown zone. A most likely explanation is that this zone is out of focus regions of the interphase, due to being below the sample surface. As a result, broadening of the atomic-scale electron beam through the specimen locally resulted in a blurry image. Apart from the interphase/Al interface located at the growth front zone, it was found that the two formed interphase/Al interfaces (1 � 1 � 20)IP 3 o from (2 � 02)Al and (112 � 4)IP//(111 � )Al contain one misfit dislocation and agree with the theoretical mismatch values of 3.31 and 0.08 % (Table

(

  E2EM) model is used to predict/calculate the possible ORs between the phases based on the basic crystallographic data, including lattice parameters and actual atomic positions, of the phases [83-85]. The E2EM calculation process includes: (a) identifying the closed-packed (CP) atomic row pairs and the CP plane pairs in phases; (b) calculating the values of interatomic spacing misfit (fr)and interplanar spacing mismatch (fd); and (c) predicting and refining the ORs between any two phases based on the rules that the matching directions must be on the matching planes and the parallel Δgs conditions[START_REF] Zhang | O-lattice analyses of interfacial misfit. I. General considerations[END_REF][START_REF] Zhang | A comparative study of the theory of the O-lattice and the phenomenological theory of martensite crystallography to phase transformations[END_REF]. The lattice parameter of pure Al metal is used in the present work.

  The OR-G:[11 � 00]IP//[101]Al, (112 � 4 � )IP 1.3 o from (202 � )Al Although the OR-D and the OR-E were not experimentally observed in the present work, one can see that the OR-F consists with the OR3 and the OR-G agrees well with the OR5. From the OR-A and the OR-F, following OR can be deduced. The OR-H: [21 � 1 � 0]TiB 2 //[11 � 00]IP, (011 � 1)TiB 2 < 4.3 o from (0008)IP

( 1 )

 1 this work, the TiB2/Al-Zn-Mg-Cu nanocomposite component produced by casting (in-situ reaction), FSP and hot extrusion was used as the model material for (HR)STEM characterization at the atomic scale. The specific structures of the TiB2/Al interface and the matrix away from the interface at the as-quenched, peak-aged and overaged states were revealed. The results indicate the significant effects of the TiB2 nanoparticle on the precipitation reactions in the Al matrix surrounding the TiB2/Al interfaces, the formation of the interphase in particular depends on the ORs between the TiB2 and Al matrix. The following conclusions can be drawn. The majority of TiB2 nanoparticles are uniformly dispersed inside Al grains, featured with the basal {0001}, prismatic {011 � 0} and pyramidal {011 � 1} facets. At the as-quenched state, the well-documented crystallographic OR1 ([21 � 1 � 0]TiB 2 //[101]Al, (0001)TiB 2 //(1 � 11)Al) as well as the new OR2 ([21 � 1 � 0]TiB 2 //[101]Al, (011 � 0)TiB 2 //(111 � )Al) at the TiB2/Al interface are determined. Periodically spaced misfit dislocations and solute-enriched regions and no obvious TSIDs are observed in the surrounding Al matrix next to this interface.

[2 1 ( 3 )( 4 )( 5 )

 1345 � 1 � 0]TiB 2 //[1 1 � 00]IP//[101]Al, (01 1 � 1)TiB 2 //(0004)IP 3 o from (020)Al, (01 1 � 0)TiB 2 //(11 2 � 8)IP, (112 � 4)IP//(111 � )Al, (1 � 1 � 20)IP 3 o from (2 � 02)Al. At the OR2, the ORs are: [21 � 1 � 0]TiB 2 //[11 � 00]IP //[101]Al, (011 � 0)TiB 2 //(112 � 0)IP//(111 � )Al, (0001)TiB 2 //(0004)IP, (1 � 1 � 24)IP 3 o from (2 � 02)Al, (112 � 8)IP 3 o from (020)Al. These determined ORs agree with the predictions using the E2EM calculation. At the peak-aged and overaged states, the mismatch of the Al/(Zn1.5Cu0.5)Mg interphase/TiB2 multi-interfaces formed at the OR1 condition are generally very low (below 5 %) except the (0008)IP//(011 � 1)TiB 2 interphase/TiB2 interface planes. Comparatively, when formed at the OR2, the Al/interphase and interphase/TiB2 interfaces show very low (below 5 %) and intermediate mismatch values (in the range 5-25 %), respectively. The energy barrier for the heterogeneous precipitations at the TiB2/Al interface is considerably reduced compared to the homogeneous nucleation in the Al matrix away from such an interface. Highly-dense misfit dislocations at the TiB2/Al interfaces are beneficial for the nucleation and effective growth of the interphase since they provide short-circuit diffusion paths for solute atoms and vacancies. The growth of the precipitates at the TiB2/Al interfaces parallel to the close-packed {111} planes of the Al matrix is severely suppressed due to the ultra-low accommodation factor. No transformation of the interphase from η to T phases is found when the aging condition is shifted from the peak-aged to overaged states due to the low boundary diffusivity of the semicoherent TiB2/Al interface. Acknowledgement Y. Ma is grateful for his Ph.D. project supported by the China Scholarship Council (Grant No.

Figure 1 :

 1 Figure 1: (a) Bright-field TEM image showing homogenous distribution of TiB 2 nanoparticles in the Al-Zn-Mg-Cu matrix grain at the as-quenched state, (b) STEM-HAADF image showing a typical TiB 2 /Al interface and (c) schematic drawing illustrating the facetted shape of the TiB 2 nanoparticle. Insets in (b) at the left bottom and top right sides highlight corresponding FFT pattern of the TiB 2 nanoparticle and soluteenriched regions, respectively.

Figure 2 :

 2 Figure 2: (a) and (d) HRSTEM-HAADF images showing TiB 2 /Al interface structures at the OR1 and OR2 conditions, respectively, (b) and (e) corresponding FFT patterns of (a) and (d), and (c) and (f) corresponding simulated diffraction patterns for indexation, respectively. The projection direction is [21 � 1 � 0] TiB 2 //[101] Al .

Figure 3 :

 3 Figure 3: (a) and (b) STEM-HAADF images showing heterogeneous precipitates at the TiB 2 /Al interfaces and finer precipitates in the matrix away from the interface at the peak-aged state, respectively. HRSTEM-HAADF images highlighting (c) plate-like GP zone and (d) elongated η' phase in (b); (e) and (f) STEM-HAADF image showing the heterogeneous precipitates at the TiB 2 /Al interfaces and finer precipitates in the matrix away from the interface at the overaged state, respectively. (g) HRSTEM-HAADF image highlighting lath-like η phase in (f) and (h) corresponding inverse FFT pattern of (g) showing misfit dislocations at the Al/η interfaces. Inset in (h) shows the corresponding FFT pattern of (g). The projection direction is [101] Al .

Figure 4 :

 4 Figure 4: STEM-HAADF image of the Al/interphase/TiB 2 interfaces and corresponding Al, Zn, Mg, Cu and Ti elemental EDS maps.

Figure 5 :

 5 Figure 5: (a) HRSTEM-HAADF image showing atomic structure of the interphase, (b) and (c) corresponding FFT and simulated diffraction patterns, respectively. Insets in (a) are the simulated HRSTEM-HAADF image of [11 � 00] (Zn 1.5 Cu 0.5 )Mg phase overlapped and intensity profiles used for measuring interplanar spacing.

Figure 6 :

 6 Figure 6: (a) STEM-HAADF image showing interphase formed at the TiB 2 /Al interface exhibiting the OR1 between TiB 2 nanoparticle and Al matrix revealed by corresponding FFT pattern (b) and schematic drawing (c). (d) STEM-HAADF image showing another interphase formed at the TiB 2 /Al interfaces exhibiting the OR2 between TiB 2 nanoparticle and Al matrix by corresponding FFT pattern (e) and schematic drawing (f). The projection direction is [21 � 1 � 0] TiB 2 //[101] Al . See the text for more details.

Figure 7 :

 7 Figure 7: (a) HRSTEM-HAADF image showing the Al/IP/TiB 2 multi-interfaces at the OR1; (b), (c) and (e) corresponding FFT patterns of box areas namely b, c and e given in (a) exhibiting the mutual ORs between the TiB 2 nanoparticle, interphase and Al matrix; (d) and (f) simulated diffraction patterns corresponding to (c) and (e), respectively. The projection direction is [21 � 1 � 0] TiB 2 //[11 � 00] IP //[101] Al . See the text for more details.

Figure 8 :

 8 Figure 8: (a) HRSTEM-HAADF image showing the Al/IP/TiB 2 multi-interfaces at the OR2. (b), (c) and (e) corresponding FFT patterns of box areas namely b, c and e given in (a) exhibiting the mutual ORs between the TiB 2 nanoparticle, interphase and Al matrix; (d) and (f) simulated diffraction patterns corresponding to (c) and (e), respectively. The projection direction is [21 � 1 � 0] TiB 2 //[11 � 00] IP //[101] Al . See the text for more details.

Figure 9 :

 9 Figure 9: (a) HRSTEM-HAADF image showing atomic structure of the Al/IP interfaces at the OR1. (b) and (c) inverse FFT patterns of (a) using different reflection pairs selected in corresponding FFT patterns in insets and (d) simulated atomic structure model showing the Al/IP interface (111 � ) Al //(112 � 4) IP . The projection direction is [11 � 00] IP //[101] Al . See the text for more details.

Figure 10 :

 10 Figure 10: (a) HRSTEM-HAADF image showing atomic structure of the IP/TiB 2 interfaces at the OR1. (b) and (c) inverse FFT patterns of (a) using different reflection pairs selected in corresponding FFT patterns in insets and (d) simulated atomic structure model showing the IP/TiB 2 interface (112 � 8) IP //(011 � 0) TiB 2 . The projection direction is [21 � 1 � 0] TiB 2 //[11 � 00] IP . See the text for more details.

Figure 11 :

 11 Figure 11: HRSTEM-HAADF images showing atomic structure of the Al/IP interfaces at the OR2: (a) the arc-shaped interface at the growth front of the interphase and (c) interface (1 � 11) Al //(112 � 0) IP . (b) and (d) inverse FFT patterns of (a) and (c) using different reflection pairs selected in corresponding FFT patterns in insets, respectively and (e) Simulated atomic structure models showing the Al/IP interface (1 � 11) Al //(112 � 0) IP . The projection direction is [11 � 00] IP //[101] Al . See the text for more details.

Figure 12 :

 12 Figure 12: (a) HRSTEM-HAADF image showing atomic structure of the IP/TiB 2 interface at the OR2. (b) inverse FFT pattern of (a) using reflection pairs selected in corresponding FFT pattern in inset and (c) simulated atomic structure model showing the IP/TiB 2 interface (0001) TiB 2 //(0008) IP . The projection direction is [21 � 1 � 0] TiB 2 //[11 � 00] IP . See the text for more details.

Figure 13 :

 13 Figure 13: (a) HRSTEM-HAADF image showing coherent Al/IP/TiB 2 interfaces parallel to the closepacked (11 � 1 � ) Al planes, (b) EDX line profiles across the interface showing the embryo of the interphase rich in Zn, Mg and Cu elements; (c) and (d) Simulated atomic structure models illustrating the precipitation suppression mechanism associated with the growth of coherent close-packed interface between the hcp embryo of the interphase and fcc Al matrix.

  [START_REF] Williams | Progress in structural materials for aerospace systems1[END_REF] , where 𝑟𝑟 1 and 𝑟𝑟 2 are the radius of spherical reinforcements, 𝑉𝑉 1 and 𝑉𝑉 2 are corresponding interface volumes of the spherical reinforcements[START_REF] Jiang | The microstructural design of trimodal aluminum composites[END_REF]. Thus, it is expected that structure evolution of nanosized reinforcement particle (NRP)/Al interfaces during the aging treatments can play a more important and critical role in influencing mechanical properties of the Al-based MMCs. Furthermore, considering interfacial structure of the NRP/Al interface being very different compared with that of the MRP/Al one, one realized that the presence of NRPs should have a disparate influence on the precipitation reactions in the Al alloy matrix. But, up to now no

experimental evidences, at the nano-and atomic scales, have been properly disclosed, which constitutes one of the most important fundamental problems still unclear in the NRPs reinforced Al-based MMCs.

  4. However, it was hard to figure out if Al is the constituent element considering possible overlapping with the Al matrix. To solve this problem, semi-quantitative EDS data were randomly acquired from different areas containing the interphase, and the results are listed in Table1.Despite the variations of Al content, the elemental content ratio of Zn, Mg and Cu remains constant

and presents a specific value approximately 3:2:1. This indicates the absence of Al and suggests that the interphase precipitate is possibly the (Zn1.5Cu0.5)Mg phase (Hexagonal, a=5.124 Å, c=16.820 Å, P63/mmc, No. 194, atomic coordinates given in Table

Table 1

 1

	Interphase Atomic composition (at. %)
	number	Al	Zn	Mg	Cu
	1	46.16	25.30	18.29	10.26
	2	59.72	19.63	12.80	7.85
	3	63.32	18.71	11.64	6.33
	4	69.51	15.28	9.91	5.31

Elemental content ratio of Al, Zn, Mg and Cu recorded from the four interphases acquired by STEM/EDS mapping.

  11 � 00]IP//[101]Al, (112 � 4)IP//(111 � )Al, (1 � 1 � 20)IP 3 o from (2 � 02)Al, (0008)IP 3 o from (020)Al The OR4: [21 � 1 � 0]TiB 2 //[11 � 00]IP, (011 � 1)TiB 2 //(0008)IP, (011 � 0)TiB 2 //(112 � 8)IP

	At the overaged/OR2 condition (Fig. 8), two ORs, the OR5 between interphase and Al matrix, and
	the OR6 between TiB2 and interphase, were observed. They are:
	The OR5: [11 � 00]IP//[101]Al, (112 � 0)IP//(111 � )Al, (1 � 1 � 24)IP 3 o from (2 � 02)Al, (112 � 8)IP 3 o from (020)Al
	The OR6: [21 � 1 � 0]TiB 2 //[11 � 00]IP, (0001)TiB 2 //(0004)IP, (011 � 0)TiB 2 //(112 � 0)IP

It should be noted, in terms of extensive STEM examinations, that the ORs related to the interphase are only associated with the initial OR1 and OR2 between the TiB2 nanoparticle and Al matrix at the solid-solution state. There is no correlation with the ageing treatments (peak-or over ageing).

Table 2

 2 Coherency of the Al/interphase/TiB 2 multi-interfaces at the OR1 and OR2 conditions. Note that high, intermediate and low interface coherency are defined as the interface mismatch below 5%, in the range 5-25% and above 25%, respectively.

	ORs between	Interface	Interface planes	Interface	Misfit dislocation	Interface
	TiB 2 and Al	type		mismatch (%) interval (nm)	Coherency
	OR1 (Fig.7)	Al/IP	(111 � ) Al //(112 � 4) IP	0.08	322.99	High
		(Fig. 9)	(2 � 02) Al 3 o from (1 � 1 � 20) IP	3.31	6.35	High
		IP/TiB 2	(112 � 8) IP //(011 � 0) TiB 2	2.94	11.35	High
		(Fig. 10)	(0008) IP //(011 � 1) TiB 2	60.74	0.68	Low
	OR2 (Fig. 8)	Al/IP	Arc-shaped	9.40	2.70	Intermediate
		(Fig. 11)	(111 � ) Al //(112 � 0) IP	20.10	1.25	Intermediate
		IP/TiB 2 (Fig. 12)	(112 � 0) IP //(011 � 0) TiB 2	2.34	11.18	Low δ

The third close packed plane is {220}Al, and this contains all three of the above directions. TiB2 has hexagonal lattice structure with a = 0.3038 nm and c = 0.3262 nm [START_REF]JCPDS-International Centre for Diffraction Data[END_REF] and belongs to P6/mmm space group. There are four possible close or nearly close packed directions and planes of TiB2.

They are <112 � 0>TiB2, <101 � 0>TiB2, <112 � 3>TiB2, <0001>TiB2 and {101 � 1}TiB2, {101 � 0}TiB2, {0001}TiB2, {112 � 0}TiB2. The interphase (Zn1.5Cu0.5)Mg (IP) also has an hexagonal lattice structure with lattice parameters a = 0.5124 nm and c = 1.682 nm and space group of P63/mmc [START_REF] Ellner | Neutron-diffraction analysis of ternary laves phases of the MgCu2 type[END_REF]. Each unit cell


T A G G E D

P Rapha € El Pietton

Mercedes David

Alisa Hisaund

Tristan Langlais

Wafa Skalli

Rapha € El Vialle

Claudio Vergari Z T A G G E D E N D

Raphael Pietton
email: raphael.pietton@aphp.fr

BIOMECHANICAL EVALUATION OF INTERCOSTAL MUSCLES IN HEALTHY CHILDREN AND ADOLESCENT IDIOPATHIC SCOLIOSIS: A PRELIMINARY STUDY

Keywords: Respiratory muscles, Elasticity imaging techniques, Elastography, Young modulus, Intercostal muscles, Adolescent idiopathic scoliosis, Rib cage, Feasibility study

Spine deformity during adolescent idiopathic scoliosis can induce a rib-cage deformity. This bone deformity can have direct consequences on the chest-wall muscles, including intercostal muscles, leading to respiratory impairments in individuals with severe cases. The aim of this study was to determine whether shear-wave elastography can be used to measure intercostal-muscle shear-wave speed (SWS) in healthy children and those with adolescent idiopathic scoliosis (AIS). Nineteen healthy participants and 16 with AIS took part. SWS measurements were taken by three operators, twice each. Average SWS was 2.3 § 0.4 m/s, and inter-operator reproducibility was 0.2 m/s. SWS was significantly higher during apnea than in normal breathing (p < 0.01) in both groups. No significant difference was observed between groups in apnea or in normal breathing. Characterization of the intercostal muscles by ultrasound elastography is therefore feasible and reliable for children and adolescents with and without scoliosis.

INTRODUCTION

Adolescent idiopathic scoliosis (AIS) is a trunk deformity with no obvious cause, which begins at the time of the pubertal peak after the age of 10 y. The 3-D deformation of the spine can cause rib-cage deformity [START_REF] Dreimann | Scoliosis and chest cage deformity measures predicting impairments in pulmonary function: A cross-sectional study of 492 patients with scoliosis to improve the early identification of patients at risk[END_REF]). In severe cases, spinal penetration into the rib cage on the concave side [START_REF] Dubousset | Spinal penetration index: New three-dimensional quantified reference for lordoscoliosis and other spinal deformities[END_REF]) and rib changes [START_REF] Erkula | Rib deformity in scoliosis[END_REF]) can lead to respiratory impairment. Respiratory involvement is most often manifested by the appearance of a restrictive syndrome [START_REF] Pehrsson | Pulmonary function in adolescent idiopathic scoliosis: A 25 year follow up after surgery or start of brace treatment[END_REF]). An obstructive effect can also be caused by inflammation of the respiratory routes (Tsiligiannis and Grivas 2012). Pulmonary function tests currently represent the standard of reference for evaluating the restrictive syndrome, but obtaining reliable spirometry depends on the individual's compliance. [START_REF] Bouloussa | Biplanar stereoradiography predicts pulmonary function tests in adolescent idiopathic scoliosis: A cross-sectional study[END_REF] were able to highlight the relationship between 3-D rib-cage volume using biplanar radiographs and total lung capacity assessed by pulmonary function tests. However, this estimate remains imperfect. Characterization of the muscular and tendinous repercussions of rib-cage deformity could therefore improve estimation of the functional consequences of scoliosis on the trunk.

The intercostal muscles (ICMs) actively participate in respiratory mechanics. Several studies have shown that pulmonary ventilation asymmetry can be observed in AIS, albeit not correlated with scoliosis severity as estimated by the Cobb angle [START_REF] Redding | Lung function asymmetry in children with congenital and infantile scoliosis[END_REF][START_REF] Inez-Llorens | Muscle dysfunction and exercise limitation in adolescent idiopathic scoliosis[END_REF]. Another study has investigated the electromyographic activity of the ICMs and found that ICM activity appears to be affected by scoliosis deformity [START_REF] Mohammadi | Comparison of respiratory muscles activity and exercise capacity in patients with idiopathic scoliosis and healthy individuals[END_REF]. It is therefore of interest to characterize in vivo the biomechanical characteristics of the ICMs in healthy individuals and those with scoliosis. Alterations of these properties might be related to the changes in respiratory function of individuals with AIS.

Ultrasound techniques have shown potential in evaluating muscle disorders [START_REF] Chang | Limb muscle quality and quantity in elderly adults with dynapenia but not sarcopenia: An ultrasound imaging study[END_REF][START_REF] Chang | Association between metabolic syndrome and limb muscle quantity and quality in older adults: A pilot ultrasound study[END_REF]. Shear-wave elastography (SWE) is a good candidate for such measurement, as it is a non-invasive, ultrasoundbased imaging technique that enables quantitative mapping of tissue mechanical properties [START_REF] Gennisson | Ultrasound elastography: Principles and techniques[END_REF]. SWE can be used to measure the shear-wave speed (SWS) within tissue, and this speed is directly related to the tissue's mechanical properties. In particular, SWS % (E/3r) 0.5 , where E is the tissue's Young modulus and r its mass density. This technique has been used in clinical practice to evaluate breast, liver, prostate and muscle lesions [START_REF] Tanter | Quantitative assessment of breast lesion viscoelasticity: Initial clinical results using supersonic shear imaging[END_REF][START_REF] Rouvi Ere | Stiffness of benign and malignant prostate tissue measured by shear-wave elastography: A preliminary study[END_REF][START_REF] Yoon | Liver stiffness measured by shear-wave elastography for evaluating intrahepatic portal hypertension in children[END_REF]. More recently, an in vivo study has demonstrated the potential of SWE of the lumbar intervertebral disc in the study of disc changes in AIS [START_REF] Langlais | Shear wave elastography can evaluate annulus fibrosus alteration in adolescent scoliosis[END_REF]. Such a non-invasive and accessible means of evaluating the ICMs could provide a better understanding of the pathophysiology of respiratory involvement and the modification of the chest wall in AIS. Nevertheless, measurement can be operator dependent, and its reliability depends on operator experience as well as the anatomic structure being measured and the protocol adopted [START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF]. The rib cage presents the added difficulty of the individual's respiration; contraction or elongation of the muscle changes the tissue's elasticity, so this has to be accounted for in the measurement.

The main objective of the present work was to establish a protocol to measure SWS of the ICMs, establish its reliability and perform a preliminary comparison between children and adolescents with and without AIS.

MATERIALS AND METHODS

Participants

Data were collected prospectively from a pediatric spine center between December 2018 and April 2019; 420 elastographic acquisitions were performed with 35 participants (age, 12.8 § 2.1 y; range, 9À16; 29 girls and six boys), which were divided in two age-matched groups. Nineteen asymptomatic participants (age, 12.6 § 1.7 y; range, 10À15; 14 girls and five boys) were included in the first group if they had no history of spinal pathology. Clinical examination was performed in all asymptomatic children to ensure that there was no spinal deformity. Sixteen children and adolescents with AIS were included in the second group (age, 13 § 2.5 y; range, 9À16; 15 girls and one boy; average Cobb angle, 31.5˚ § 16.3˚). This group was composed of patients followed for AIS at stages of varying severity, either in the pre-treatment stage (n = 11; Cobb angle, 29˚ § 16˚) or during brace treatment (n = 5; Cobb angle, 36˚ § 18˚). Each AIS patient underwent low-dose radiographs in a standing position. Spinal deformity was assessed by two independent observers, and the Cobb angle was measured to quantify the curve severity. The Cobb angle was measured by drawing two lines parallel to the endplates of the vertebral bodies at the beginning and the end of the curve in the anteroposterior radiograph. A third and fourth line were drawn perpendicular to the first two lines to measure the Cobb angle. Trustees of parental authority gave informed consent, as approved by the institutional review board (C.P.P. Île de France IV, Records 14 409).

Intercostal acquisition and protocol

All SWS measurements were made with an Aixplorer (Supersonic Imagine, Aix-en-provence, France) and a linear SL10-2 probe. The depth, size of the elastographic image and position of the focus were adapted for each measurement. Participants were in a supine position, with the arms along the body, and measurements were made at the T5ÀT6 right intercostal space both during normal breathing and in apnea. Apnea was performed at tidal volume. The probe was placed orthogonally to the skin and to the courses of the ribs at the level of the mid-axillary line. The fascia between the anterior serratus and latissimus dorsi was used as a sonographic anteroposterior reference, as previously described in a serratus plane block protocol [START_REF] Blanco | Serratus plane block: A novel ultrasound-guided thoracic wall nerve block[END_REF]. Ribs appeared as ovoid structures connected by a muscle band whose leaflets could be distinguished, and which corresponded to the ICMs (Fig. 1).

Two 10-s clips were recorded, one during normal breathing and one in apnea, and measurements were performed twice by each of three operators. The probe was repositioned after each measurement. This represented a total of 420 clips for the entire study (2 conditions £ 2 repetitions £ 3 operators £ 35 participants).

The data were then post-processed by dedicated software [START_REF] Vergari | Lumbar annulus fibrosus biomechanical characterization in healthy children by ultrasound shear wave elastography[END_REF] written in MATLAB version 2016b (The MathWorks Inc., Natick, MA, USA).

A region of interest (ROI) was defined in the ICM width, without including the ribs. The average SWS was calculated for the entire surface of the ROI, then ROIs of all frames (10 frames/clip) were averaged to obtain one SWS per clip. Frames with too much noise or saturation were discarded. The acquisition lasted about 10 min per operator (four clips).

Statistical analysis

Reproducibility and repeatability were evaluated according to the ISO 5725 standard in terms of standard deviation and coefficient of variation (CV). Intra-class correlation coefficients (ICC A-1 ) and their 95% confidence intervals were also calculated to assess inter-operator reproducibility; an ICC greater than 0.75 was considered to signify good agreement. BlandÀAltman plots were used to represent the limits of agreement [START_REF] Bland | Statistical methods for assessing agreement between two methods of clinical measurement[END_REF]. Data were not normally distributed, according to the Lilliefors normality test, so non-parametric tests were used: differences between conditions were analyzed with a paired Wilcoxon rank test, and differences between groups with non-paired tests. Correlations were tested with the Spearman correlation test. The statistical analysis was performed using IBM SPSS. Significance was set at 0.05.

RESULTS

Average weight in the healthy group was 48.7 § 7 kg, and body mass index (BMI) was 19.3 § 2 kg/m 2 , whereas for the AIS group, average weight was 44.2 § 9.3 kg and BMI was 17.9 § 1.6 kg/m 2 . The BMI of the AIS was significantly lower than in the healthy group (p = 0.03). The mean of SWS and ICC values for both groups are given in Table 1.

Asymptomatic group

The average SWS of the ICMs in apnea (2.2 § 0.5 m/s) was slightly but significantly higher than in normal breathing (2.1 § 0.4 m/s, p < 0.01, paired statistical test). There was a significant correlation of BMI with both apnea (p = 0.02, Spearman r = À0.53; Fig. 2) and normal respiration measurements (p = 0.04, Spearman r = À0.48). A weak correlation was also observed between weight and apnea measurements (p = 0.045, Spearman r = 0.46). Inter-operator reproducibility (Table 1) was 0.3 m/s in apnea (CV = 12.7%) and 0.2 m/s in normal breathing (CV: 10.6%). The average inter-operator ICC was 0.77 in apnea and 0.83 in normal breathing.

Scoliosis group

The average SWS in apnea was 2.5 § 0.6 m/s, and it was significantly lower in normal breathing (2.2 § 0.3 m/s, p < 0.01). There was no significant correlation with height, weight or BMI. A tendency was observed for SWE in apnea to increase with Cobb angle, although this relationship was not significant (p = 0.3; Fig. 3). No tendency was observed with measurement during normal respiration (p = 0.9).

Inter-operator reproducibility was 0.3 m/s in apnea (CV = 10.8%) and 0.2 m/s in normal breathing (CV = 9%). The average inter-operator ICC was 0.81 in apnea and 0.85 in normal breathing.

Group comparison

As shown in Figure 4, there was no significant difference between groups in either apnea or normal breathing (p > 0.05). However, no participant with AIS presented an SWS lower than 1.9 m/s, either in apnea or in normal respiration, whereas eight participants in the healthy group (42%) were below this threshold during normal respiration (six during apnea).

BlandÀAltman plots for both groups in breathing and apnea are represented in Figure 5. They show good agreement between operators, and no outliers. Better reliability can be noticed for measurement in normal breathing than in apnea.

DISCUSSION

The present study shows that biomechanical assessment of the ICMs by shear-wave elastography is feasible and reliable, in both healthy individuals and those with scoliosis. The images obtained provide two types of information: an echographic image allowing access to static structural characteristics and dynamic behavior of the ribs and inter-costal membranes and an elastographic clip reflecting the intrinsic stiffness of the muscle. In recent years, the contribution of this new imaging method has been highlighted for biomechanical evaluation of the musculoskeletal system [START_REF] Hardy | Normal range of patellar tendon elasticity using the sharewave elastography technique: An in vivo study in normal volunteers[END_REF][START_REF] Vola | Use of ultrasound shear wave to measure muscle stiffness in children with cerebral palsy[END_REF]. Recent studies have been able to clarify the biomechanical behavior of the intervertebral disc in adolescent idiopathic scoliosis [START_REF] Vergari | Lumbar annulus fibrosus biomechanical characterization in healthy children by ultrasound shear wave elastography[END_REF][START_REF] Langlais | Shear wave elastography can evaluate annulus fibrosus alteration in adolescent scoliosis[END_REF].

This imaging technique could allow a refinement of the current knowledge of respiratory involvement secondary to scoliosis [START_REF] Ito | Scoliosis associated with airflow obstruction due to endothoracic vertebral hump[END_REF]. It is conventionally accepted that in severe cases of thoracic scoliosis, a Fig. 3. Relationship between Cobb angle and shear-wave speed in participants with scoliosis during apnea and normal respiration. The relationships were not significant (p = 0.3 and 0.9, respectively). The horizontal shaded areas represent the 5th and 95th quartiles of the healthy population; in other words, 90% of the healthy population was within the shaded area.

Fig. 4. Shear-wave speed differences between participants with and without adolescent idiopathic scoliosis during apnea and normal respiration.

restrictive syndrome can develop as a result of spinal penetration into the rib cage on the concave side. Asymmetry of pulmonary perfusion on the concave side has also been reported [START_REF] Redding | Lung function asymmetry in children with congenital and infantile scoliosis[END_REF]). However, respiratory involvement in this pathology is more complex, with an increase in the inspiratory pressure of the chest wall and obstructive phenomena that can occur [START_REF] Mcphail | Obstructive lung disease in children with idiopathic scoliosis[END_REF].

It has recently been shown that inspiratory muscle dysfunction can be observed in mild scoliosis before the diagnosis of restrictive syndrome. [START_REF] Mohammadi | Comparison of respiratory muscles activity and exercise capacity in patients with idiopathic scoliosis and healthy individuals[END_REF] have observed a decrease in strength for fatigue exercise in individuals with scoliosis, and shown a decrease of surface electromyographic activity of the ICMs on the concave side. The ICMs therefore seem to be involved in the respiratory dysfunction in these individuals.

The relatively long duration of the examination required for this first validation step (about 10 min) can easily be shortened to a few min by an operator in current practice. The inter-operator reproducibility of the measurements in this study was 0.2 m/s (10.6% coefficient of variation). This is similar to the uncertainty obtained in vivo with other musculoskeletal tissues, such as muscles of the lower and upper limbs (between 4% and 20% CV; [START_REF] Lacourpaille | Supersonic shear imaging provides a reliable measurement of resting muscle shear elastic modulus[END_REF][START_REF] Dubois | Reliable protocol for shear wave elastography of lower limb muscles at rest and during passive stretching[END_REF], the multifidus (1.3À4.3 m/s, 11%À19% CV;) and the intervertebral disc (0.25 m/s, 9% CV; [START_REF] Vergari | Lumbar annulus fibrosus biomechanical characterization in healthy children by ultrasound shear wave elastography[END_REF]). More recently, several studies have shown the value of elastography in diaphragm assessment [START_REF] Chino | Diaphragmatic shear modulus at various submaximal inspiratory mouth pressure levels[END_REF]. Some biomechanical studies have focused on sternocostal movement [START_REF] Beyer | Relationship between costovertebral joint kinematics and lung volume in supine humans[END_REF] or on the effect of ICM contraction on rib motion [START_REF] Zhang | Effect of intercostal muscle contraction on rib motion in humans studied by finite element analysis[END_REF]). To our knowledge, this is the first work on ICM elastography.

No significant difference was observed between participants with and without scoliosis. This could be explained by the small size of our cohort and the diversity in the severity of scoliosis. Nevertheless, participants in the AIS group showed a tendency toward higher SWS than in the healthy group, both in apnea and during normal respiration. Moreover, no participant with AIS had an SWS lower than 1.9 m/s, whereas 42% of those without did.

For this feasibility study, measurements were performed on participants' right side. It is possible that more severe alterations could have been measured on the left side-that is, the concave side, with AIS being mainly thoracic right. However, in this preliminary study the aim was to compare individuals with and without AIS, not to assess the potential ICM asymmetry in these individuals; that will be the object of further studies. Some limitations to this work may be noted. This examination uses ultrasound, which is operator dependent-hence the need to establish inter-operator reproducibility-and it requires a learning curve. The three operators had 2 y, 6 mo and 2 mo experience of ultrasound measurements, respectively. A training period was necessary to obtain reliable measurements, as shown by preliminary tests not included in this study. The most important points are learning to apply the lowest pressure possible with the probe, avoiding any trembling of the probe by finding a suitable and comfortable position and finding the correct anatomic landmarks in the image to maintain a repeatable probe position and orientation. The second main limitation is that the cohorts could be too small to prove a significant difference. A post hoc analysis based on the current preliminary data shows that 43 participants in each group would be needed to show a statistical difference in measurement during apnea (a = 0.05, 1 À b = 0.8). Although measurement during normal breathing was more reliable than during apnea, the latter seems to accentuate the difference between groups.

However, it was difficult to standardize rib-cage volume in apnea for the different operators, which could explain the better reproducibility in normal breathing. Participants could fill their lungs to a different degree for each measurement, stretching or contracting the intercostal membrane and therefore altering its mechanical properties. Moreover, measurement during normal breathing was more comfortable for the participants; further work should concentrate on measurement during breathing, as it is easier to perform and produces more reliable results. Differences in reproducibility between breathing conditions were expected because muscle activation and stretch have already been shown to significantly affect shear-wave elastography. However, in the case of the intercostal muscles it was difficult to hypothesize a priori whether breathing or apnea would be more reproducible. Hence, both conditions were tested. Furthermore, several parameters may alter ICM activity and stiffness that are not under the individual's voluntary control. However, these confounding factors were taken into account when repeating measurements in the reproducibility study.

On the other hand, if the current results on measurements during normal breathing were to be confirmed on a larger cohort, the actual difference between individuals with and without AIS might be too small to be clinically useful. The difference between groups (0.3 m/s in apnea and 0.1 m/s during respiration) was similar to the measurement reproducibility (0.1À0.2 m/s), and therefore such a small deviation from the normal value might be difficult to detect. Other parameters should be further investigated, such as the asymmetry between the convex and concave sides or the variation of SWS throughout the respiratory cycle. Still, a small but significant alteration of the ICMs of individuals with AIS could open the way to new research questions on respiratory impairment due to scoliosis.

In this work it was possible, after the implementation of a controlled measurement protocol, to demonstrate that intercostal ultrasound elastography is reliable, especially during normal breathing. This paves the way for further studies of the functional consequences on respiratorymuscle adaptation of chest-wall deformity or any pathologic phenomenon affecting inspiratory pressure.

CONCLUSION

This study describes a reliable and reproducible imaging technique to evaluate the biomechanical behavior of the intercostal muscles in individuals with and without AIS. This opens the way to further studies that may lead to a better understanding of respiratory failure in AIS.

Fig. 1 .

 1 Fig. 1. Example of elastography image (top) and ultrasound (bottom) of intercostal muscles in an 11-y-old girl. The white arrow shows the limit between the serratus anterior and latissimus dorsi. The intercostal muscles are visible between the ribs. The dashed rectangle is the region of interest in the intercostal muscles.

Fig. 2 .

 2 Fig. 2. Relationship between shear-wave speed measurement and body mass index. Correlations were significant in healthy individuals during apnea (p = 0.02, Spearman r = À0.53) and normal respiration (p = 0.04, Spearman r = À0.48). No correlation was observed in participants with scoliosis.

Fig. 5 .

 5 Fig. 5. BlandÀAltman plots representing the limits of agreement of shear-wave speed measurements. Horizontal lines represent 95% confidence intervals.

Table 1 .

 1 Repeatability and reproducibility of intercostal-muscle shear-wave speed

	Measurement (m/s)	Mean § SD	Reproducibility (CV%)	Repeatability (CV%)	ICC (95% CI)
	Healthy, apnea	2.2 § 0.5	0.3 (12.7)	0.2 (8)	0.8 (0.6, 0.9)
	Healthy, respiration	2.1 § 0.4	0.2 (10.6)	0.1 (6.5)	0.8 (0.7, 0.9)
	Scoliosis, apnea	2.5 § 0.6	0.3 (10.8)	0.2 (6.4)	0.9 (0.7, 0.9)
	Scoliosis, respiration	2.2 § 0.3	0.2 (9.0)	0.1 (6.0)	0.8 (0.6, 0.9)
	All participants	2.3 § 0.4	0.3 (12.6)	0.2 (10.4)	0.8 (0.7, 0.9)
	CI = confidence interval; CV = coefficient of variation; ICC = intra-class correlation coefficient.

Conflict of interest disclosure-No funds were received in support of this work. No benefits in any forms have been or will be received form a commercial party related directly or indirectly to the subject of this manuscript.