Viet Q Vu

O Prokof'eva

Laszlo S Toth
email: laszlo.toth@univ-lorraine.fr

V Usov

N Shkatulyak

Y Estrin

R Kulagin

V Varyukhin

Y Beygelzimer

Obtaining Hexagon-Shaped Billets of Copper with Gradient Structure by Twist Extrusion

Keywords: twist extrusion, gradient structure, different shear deformation modes

Processing by twist extrusion was used to produce copper billets with a hexagonal crosssection. A special feature of the billets is their gradient microstructure owing to a specific strain pattern: an undeformed core and a deformed outer sheath. The initial sample with a 40 mm diameter was processed at room temperature by four twist extrusion passes through a twist die having a hexagonal cross-section and a small twist-line slope angle β=40° with a back-pressure of 100 MPa. The results showed that the processed sample had an undeformed core 20 mm in diameter and a deformed outer sheath with a gradient microstructure in which the average grain size decreased gradually from 50 µm to 0.5 µm towards the periphery along a radius direction.

The microstructure gradient represented the various stages of the grain refinement process corresponding to increasing shear strain. The texture revealed two different shear deformation modes whose shear planes were perpendicular and parallel to the extrusion axis. The measured Vickers hardness showed good agreement with the microstructure. In the deformation zone, the classical Hall-Petch relation between the hardness and the grain size of the various characteristic areas formed by twist extrusion was found.

Introduction

In the context of this study, a gradient structure material is defined as a material exhibiting a gradual transition from an ultrafine-grain (UFG) microstructure at the periphery to a coarse-grain (CG) microstructure in the middle of a sample [START_REF] Hughes | Graded nanostructures produced by sliding and exhibiting universal behavior[END_REF][START_REF] Suresh | Graded materials for resistance to contact deformation and damage[END_REF]. Such materials have recently been shown to possess exceptional mechanical properties, especially a combination of high strength and good ductility [START_REF] Yang | Back stress strengthening and strain hardening in gradient structure[END_REF][START_REF] Wei | Evading the strength-ductility trade-off dilemma in steel through gradient hierarchical nanotwins[END_REF][START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF][START_REF] Bian | Gradient structure produces superior dynamic shear properties[END_REF][START_REF] Lu | Making strong nanomaterials ductile with gradients[END_REF][START_REF] Li | On strain hardening mechanism in gradient nanostructures[END_REF][START_REF] Fang | Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper[END_REF][START_REF] Wu | Synergetic strengthening by gradient structure[END_REF]. Therefore, characterization of gradient structures and especially development of new processes that allow producing this kind of structures have been of great interest to the materials research community.

Severe plastic deformation (SPD) techniques [START_REF] Estrin | Extreme grain refinement by severe plastic deformation: A wealth of challenging science[END_REF][START_REF] Valiev | Producing bulk ultrafine-grained materials by severe plastic deformation: ten years later[END_REF] which impart a strain gradient to a billet offer an efficient way of producing gradient structures. For instance, surface mechanical attrition treatment (SMAT) was used to produce plates with a CG core and near-surface layers with an UFG microstructure [START_REF] Lu | Nanostructured surface layer on metallic materials induced by surface mechanical attrition treatment[END_REF][START_REF] Yin | Strength and ductility of gradient structured copper obtained by surface mechanical attrition treatment[END_REF]. Repetitive three-roll planetary milling, also referred to as screw rolling, was employed to produce gradient structures in copper or magnesium rods [START_REF] Wang | Gradient structure produced by three roll planetary milling: Numerical simulation and microstructural observations[END_REF][START_REF] Diez | Improving the mechanical properties of pure magnesium by three-roll planetary milling[END_REF]. A sliding wear process was proposed to introduce a UFG gradient microstructure within a surface layer of copper slabs [START_REF] Figueroa | Ultrafine gradient microstructure induced by severe plastic deformation under sliding contact conditions in copper[END_REF]. Plastic flow machining (PFM) was used for inducing gradients in both microstructure and texture across the thickness of aluminum sheets [START_REF] Vu | Mechanical modelling of the plastic flow machining process[END_REF][START_REF] Vu | The new plastic flow machining process for producing thin sheets[END_REF][START_REF] Vu | The plastic flow machining: a new SPD process for producing metal sheets with gradient structures[END_REF].

Twist extrusion (TE) [START_REF] Beygelzimer | Twist Extrusion as a Potent Tool for Obtaining Advanced Engineering Materials[END_REF] can also be considered as an effective SPD method to create gradient structures and harness their benefits in terms of improved mechanical properties. In Ref. [START_REF] Prokof'eva | Producing of ultrafine grained composites with a large uniform elongation by twist extrusion: Mathematical simulation[END_REF], it was shown by means of mathematical simulation that metal bars with an UFG shell and a CG core can be obtained by TE with a small twist-line slope angle. The key advantage of this method is the ability to regulate the thickness of the outer UFG shell, from a very thin layer to the entire cross-section of the produced billet. This enables optimization of the mechanical properties of the billet in terms of a balance between strength and ductility, which can solve the long-standing problem of strength-ductility trade-off in materials science. Another benefit is seen in the case when after deformation the billet is machined to remove part of the surface layer, for instance, producing threads. This paper presents an experimental study demonstrating the ability of TE with a small twistline slope angle to produce a gradient structure. The technique was applied to a copper bar with a hexagonal cross-section as a representative case of producing a gradient structure, thus providing a proof of concept by way of example.

Experimental procedures

In this study, commercial purity copper (Cu 99.8%) samples with a hexagonal cross-section were used for the TE processing. The samples were produced by hot forward extrusion and had a diameter of a circumscribed circle of 40 mm and the length of 80 mm. Before the TE processing, they were annealed for an hour at 550°C to improve the homogeneity of the microstructure. TE was performed at room temperature using a twist die with a hexagonal cross-section and a twistline slope β=40° (see Fig. 1). The processing schedule included four TE passes with a backpressure of 100 MPa. After TE processing, the microstructure on the plane perpendicular to the extrusion axis was characterized by electron back-scattering diffraction (EBSD) operated in a JEOL JSM-6500F field-emission gun-scanning electron microscopy (FEGSEM) system. The EBSD scanning was conducted at various positions along a diagonal of a hexagon-shaped cross-section (Figs. 3a-b). The EBSD data was acquired using Aztec HKL software. Orientation mapping and data analysis were conducted using the Atex software [START_REF] Beausir | Analysis Tools for Electron and X-ray diffraction[END_REF].

Crystallographic texture gradients and the substructure parameters, including the size of coherent scattering regions (CSR) and the lattice micro-distortion hkl ε in a plane perpendicular to the extrusion axis was also determined by using synchrotron radiation (DESY, Hamburg, Germany). The measurements were carried out in the transmission mode employing hard synchrotron radiation (wavelength 0.14235 Å, beam size 0.5 mm × 0.5 mm, distance of a Perkin Elmer XRD 1622 detector from the sample: 950 mm). The samples for the study were rectangular parallelepipeds with sides of 2.5 mm × 2.5 mm, cut along the diagonal of the hexagon and along the direction perpendicular to it. Using experimental direct {111}, {200}, and {220} pole figures, the three-dimensional orientation distribution functions (ODF) was calculated according to Bunge's method [START_REF] Bunge | Mathematische Methoden der Texturanalyse[END_REF].

For mechanical property characterization, Vickers hardness was measured on the plane perpendicular to the extrusion axis, along the diagonal direction. To correlate the mechanical properties with the microstructure, the measurements were taken at the same positions where the microstructure was observed. The applied load was 100 gf and the loading time was 10 s.

Results

Microstructure gradient

Fig. 2 displays the EBSD results of the microstructure on the plane perpendicular to the extrusion axis. They show that within a core area up to 10 mm from the center of the sample the microstructure is that of the undeformed material. By contrast, outside of this non-deformed zone, the microstructure is modified by the deformation and exhibits a gradient along the centerto-edge direction. The microstructures of the initial sample (Fig. 2c) and of the areas located at 5 and 10 mm away from the center of the processed sample (maps 1-2, Figs. 2d-e) were about the same.

For example, they all contained coarse equiaxed grains with the same average grain size of about 6 50 µm (Fig. 2b) and displayed many annealing twins originating from the annealing treatment before the TE processing. They can also be detected in the next-neighbor grain disorientation distributions in Figs. 4a-c. In other words, within a zone up to 10 mm from the center of the processed sample, the material was not deformed and retained the initial microstructure. A change starts to be seen at a distance of 15 mm from the center (map 3, Fig. 2f), as reflected in numerous regions containing low angle grain boundaries (LAGBs). In this area, the average grain size was reduced to 14 µm. Moving further towards the edge of the sample, from map 4 to map 7, the transformation of microstructure is seen to be more significant. The average grain size was gradually decreased to 2.8 µm in the area 17 mm away from the center and to 0.5 µm at the sample edge. In addition, the grain morphology also changed from elongated shape (nearly perpendicular to the radial axis; maps 4-5, Figs. 2g-h) to more equiaxed shape (maps 6-7, Figs.

2i-j).

The next-neighbor grain disorientation distributions are shown in Fig. 3. Grains were identified by high-angle grain boundaries (HAGBs) with boundary disorientation greater than 15°. Then the average orientation of the grain was computed, finally, the disorientation between neighbor grains was calculated from these average orientations [START_REF] Tóth | Effect of grain refinement by severe plastic deformation on the next-neighbor misorientation distribution[END_REF][START_REF] Toth | Ultrafine-grain metals by severe plastic deformation[END_REF]. As can be seen, large HAGB fractions (95%) occurred in the microstructures of the initial sample (Figs. 3a,i) and also in the undeformed zone of the processed sample (93-95%; Figs. 3b-c, i). A large number of annealing twins with a disorientation about 60° across the twin boundary were also observed in these microstructures (Figs. 3a-c). The fraction of HAGBs started to decrease in the area located 15 mm away from the center of the processed sample (Figs. 3d,i) and kept declining to 73% at the position 17 mm away from the center (Figs. 3e,i). However, outside of this region, further away from the center, it increased gradually and reached the value of 90% at the sample rim.

We note that the gradient microstructure obtained in this work is a foot-print of the various stages of the grain refinement process with shear strain. Hence, a continual increase of the shear strain from the sample axis to its periphery permits an evaluation of the strain dependence of the grain size. The areas located at a distance 15-17 mm from the center (maps 3-4, Figs. 2f-g), in which the grain size dropped to 14 µm and 2.8 µm, respectively, represents the initial stage of the grain refinement process, which is well known from SPD studies. At this stage, geometrically necessary dislocations (GNDs) are formed to accommodate strain heterogeneity within and between the grains [START_REF] Pantleon | Dislocation boundaries -the distribution function of disorientation angles[END_REF]. In Ref. [START_REF] Tóth | A model of grain fragmentation based on lattice curvature[END_REF], a particular mechanism of GND generation was associated with the formation of lattice curvature within a grain induced by the impeded lattice rotation near the grain boundaries. GNDs were considered to emerge in order to accommodate the lattice curvature and to agglomerate into new boundaries -initially LAGBs, or subgrain boundaries. This GND-induced grain subdivision into subgrains is accompanied with concurrent occurrence of stochastically stored dislocations [START_REF] Pantleon | Dislocation boundaries -the distribution function of disorientation angles[END_REF]. In accord with the model considerations, various substructures with LAGBs were also observed in our experiments (Fig. 2f), which revealed grain fragmentation into elongated subgrains (Fig. 2h). This process can be linked to a concomitant decrease in the fraction of HAGBs, from about 95% in the undeformed zone to 82% and 73% in the regions located 15 and 17 mm away from the center, respectively (Figs. 3d-e, i). This is a consequence of the mentioned increase in the fraction of LAGBs in the initial stage of the grain refinement process.

The area outside of the 17 mm wide zone corresponds to a next stage of the grain refinement process with increased strain. Here, the accumulation of the disorientation between subgrains with growing distance from the sample axis converts LAGBs to HAGBs (cf. maps 5-7, Figs. 2h-j). Continuous dynamic recrystallization (DRX) in which grain boundaries migrate in the heavily deformed structure may also play a role in the grain refinement process [START_REF] Sakai | Dynamic and post-dynamic recrystallization under hot, cold and severe plastic deformation conditions[END_REF]. The experimental manifestation of grain refinement in areas 5-7 was an observed drop of the average grain size from 1.1 to 0.5 µm (Fig. 2b). It was accompanied with an increase of the fraction of HAGBs from 75% to 90% (Figs. 3f-i). A change in grain morphology should also be mentioned:

the grains became more equiaxed towards the sample edge (Figs. 2h-j), which is a clear manifestation of DRX by grain boundary migration.

It is interesting to note that twins were detected only in the undeformed zone (Figs. 3a-c).

Outside this zone, the twin orientation relation did not appear to hold any longer (Figs. 3e-h).

This is attributed to the varied lattice rotation within the grains, which is believed to brake the orientation relation between the twins and the parental grains of the initial microstructure.

Gradient of the texture and the parameters of substructure

EBSD study

The results showed that within the undeformed zone of the processed sample, the texture was almost the same as in the initial state. Outside of this zone, the texture was different and varied from position to position, eventually turning into a simple shear texture at the edge of the sample. 1.

Specifically, the initial texture was axisymmetric with two dominant fibers: a strong 〈100〉 and a weak 〈111〉 fiber parallel to the axis of the sample (Figs. 4a-b). This texture was inherited from the forward extrusion process which had been used to produce the initial sample.

As seen from the pole figures in Figs. 4b-d 1. In this case, the shear plane normal (SPN) and shear direction (SD) were defined to be parallel to X and Y axes, respectively. This means that the shear plane was parallel to the extrusion axis. This feature is not commonly seen in regular TE processing and will be addressed in the discussion section. Analysis revealed that the crystallographic texture of the TE processed samples gives rise to anisotropy of physical broadening of the diffraction lines. Therefore, the substructure parameters, e.g. the size of CSRs (D) and lattice micro-distortion (ε), were estimated using the modified Williamson-Hall method [START_REF] Rzychoñ | Microstructure characterization of deformed copper by XRD line broadening[END_REF]. This method can effectively account for the effect of dislocation contrast caused by non-uniform distribution of dislocations. The average values of the dislocation parameters for copper were calculated using the open access computer program ANIZC [START_REF] Borbely | ANIZC-computer program for the calculation of dislocation orientation factors in anisotropic cubic, hexagonal and trigonal crystals[END_REF]. Thus, the effect of both the edge dislocations of the {111} <110> type and the screw dislocations of the <110> type was considered with the same weight. The results are presented in Table 2.

As can be seen, with the increasing distance from the center of the sample, the magnitude of the lattice micro-distortion increases, and the size of CSR decreases. The maximum of the ε value and a minimum of the D value correspond to position 5 along the X axis. The modified Williamson-Hall method for analyzing the broadening of X-ray diffraction lines [START_REF] Rzychoñ | Microstructure characterization of deformed copper by XRD line broadening[END_REF] makes it possible to estimate the dislocation density (ρ) in the processed sample. For this purpose, the values of parameters for copper were adopted from [START_REF] Ungár | Grain size, size-distribution and dislocation structure from diffraction peak profile analysis[END_REF]. The results of the dislocation density evaluation in the processed samples are also presented in Table . 2. The dislocation density increases with the distance from the sample center and reaches its maximum at position 5 on the X axis. This corresponds to the maximum value of lattice distortions, and, consequently, to the highest value of internal micro stress.

Figure 6 shows the {111} pole figures of the initial and the processed sample for various scanning areas. The ODF sections for the edge region are presented in Fig. 7. It is clearly seen that the results of the study of the texture gradient by synchrotron radiation are in general agreement with those obtained by the EBSD analysis, which proves the adequacy of both sets of results. Fig. 7: ODF sections for the edge area of the processed sample, obtained from synchrotron measurements.

Gradient of hardness

The gradient nature of the mechanical properties of the TE-processed material was evaluated by measuring the Vickers hardness. As can be seen from Fig. 8, the Vickers hardness in the undeformed zone (within 10 mm from the sample center) was unchanged and amounted to 13 82 HV. Outside of this zone, the hardness rose precipitously from a position 15 mm away from the center to about 117 HV at the edge area. It should be noted that due to discreteness of hardness measurements, the exact size of the core region can only be estimated as lying somewhere between 10 mm and 15 mm. Indeed, also the 10 mm zone is labelled as 'undeformed zone' in Fig. 8, the increase of the Vickers hardness was rather insignificant between the points located 10 mm and 15 mm away from the extrusion axis, and it only became pronounced outside of the 15 mm zone. The value of 15 mm is also more consistent with that following from the EBSD measurements. It should be mentioned that the Vickers hardness of initial annealed copper is 48 HV, to be compared with 82 HV in the central zone of the processed billet. The reason for the enhanced hardness not being accompanied with any detectable change in the initial grain structure (Fig. 2 d, e) in this zone is an increased dislocation density, exceeding the initial one by an order of magnitude (see Table 2). This indicates that the central zone of the billet was plastically deformed, but this deformation did not give rise to grain refinement.

Discussion

According to the results reported above, a cross-section of a TE-processed sample can be subdivided into two fundamentally different zones. The first one is located within 10 -15 mm from the sample axis. This notionally 'non-deformed' zone preserved the initial texture and grain structure. The second one occupies the remaining area of the sample adjacent to its surface. This plastically deformed zone exhibits a strain gradient attaining the highest values at the sample periphery. The gradient of texture indicates a change in the deformation mode within the second zone. In proximity to the surface of the sample, the predominant deformation mode is simple shear, with a shear plane parallel to the extrusion axis. This is not typical for TE with a large helix slope, where numerous studies have shown that the principal deformation mode is simple shear in a plane perpendicular to the axis. In our view this is caused by the following two features of the TE deformation process.

The first one is that the process involves simple shear with alternating sense in a plane normal to the extrusion axis, whose magnitude decreases towards the axis [START_REF] Beygelzimer | Twist Extrusion as a Potent Tool for Obtaining Advanced Engineering Materials[END_REF]. It is known (see, for example, [START_REF] Orlov | Plastic flow and grain refinement under simple shear-based severe plastic deformation processing[END_REF][START_REF] Orlov | Role of strain reversal in grain refinement by severe plastic deformation[END_REF][START_REF] Petryk | A quantitative model of grain refinement and strain hardening during severe plastic deformation[END_REF][START_REF] Beygelzimer | Grain refinement versus voids accumulation during severe plastic deformations of polycrystals: mathematical simulation[END_REF]), that with a decrease of the alternating strain amplitude the degree of grain refinement decreases -down to a complete cessation below a certain critical value of the strain amplitude. At small angles of the twist-line slope, the value of the strain amplitude near the billet axis drops below this grain refinement threshold. This explains the retention of the initial grain structure in the mentioned non-deformed zone.

According to [START_REF] Beygelzimer | Twist Extrusion as a Potent Tool for Obtaining Advanced Engineering Materials[END_REF], the magnitude of the shear strain γ , at a distance r from the axis of the TE die, is determined by the relation:

tan r R γ β = , ( 1
)
where R is the distance from the axis to the most distant point in the billet cross-section, and β is the twist angle. Introducing * γ -the above-mentioned threshold value of the shear strain amplitude below which the grain refinement does not occur -and using Eq. ( 1), one can define a

critical radial distance * * tan R r γ β = . (2)
The significance of this quantity lies in the recognition that when * r r > , a UFG structure is formed after a sufficiently large number of TE passes. In the opposite case of * r r < a CG microstructure is retained regardless of the number of TE passes.

According to the literature analysis performed in [START_REF] Prokof'eva | Producing of ultrafine grained composites with a large uniform elongation by twist extrusion: Mathematical simulation[END_REF], the critical shear strain can be estimated as * ~0.4 ). This estimate of the radius of the core with an initial CG structure corresponds well to the experimental results (see Fig. 2b and Fig. 8).

The second deformation feature of TE is the cross-flow described in detail in [START_REF] Kulagin | Cross flow during twist extrusion: theory, experiment, and application[END_REF]. As a result of cross-flow, simple shear occurs in a plane parallel to the extrusion axis [START_REF] Kulagin | Cross flow during twist extrusion: theory, experiment, and application[END_REF][START_REF] Beygelzimer | Shears, vortices, and mixing during twist extrusion[END_REF]. Below, it will be called 'shear 2', while shear in a plane normal to the extrusion axis will be referred to as 'shear 1'. For large twist-line slope angles (55-60°), the magnitude of shear 2 is much smaller than the magnitude of shear (i) [START_REF] Beygelzimer | Twist Extrusion as a Potent Tool for Obtaining Advanced Engineering Materials[END_REF]. At a small angle of the twist-line slope, the cross-flow is localized near the billet surface causing a large strain in that region.

In Refs. [START_REF] Latypov | Finite element analysis of plastic deformation in twist extrusion[END_REF][START_REF] Latypov | Microstructure and Mechanical Properties of Copper Processed by Twist Extrusion with a Reduced Twist-Line Slope[END_REF][START_REF] Latypov | Simple shear model of twist extrusion and its deviations[END_REF][START_REF] Akbari Mousavi | Computational study of Ti-6Al-4V flow behaviors during the twist extrusion process[END_REF] the TE process was simulated numerically by means of the Finite Element Method. The numerical calculations provided a quantitative assessment of strain distribution over a billet cross-section and an estimate of the ratio of shear 1 and shear 2.

Specifically, it was shown in [START_REF] Latypov | Simple shear model of twist extrusion and its deviations[END_REF] that in a near-surface layer of a billet the strain exceeds the values predicted by Eq. ( 1). This is associated with the occurrence of shear 2. We can analyse this effect qualitatively. For this purpose, we applied a method described in detail in [START_REF] Beygelzimer | Kinematics of metal flow during twist extrusion investigated with a new experimental method[END_REF]. It is based on constructing a velocity field that accounts for the characteristic features of plastic flow through the twist die.

Fig. 9 shows the distortion of the shape of the markers in a cross-section of the billet after four passes of TE associated with this velocity field. When constructing it, we used the values of the die parameters corresponding to our experiment.

Figure 9b shows that, in the vicinity of the billet surface, a non-uniform shear occurs along its faces. In this case, the near axis zone stays practically undeformed, but rotates as a whole. In terms of the deformed state, the surface layer of the billet for TE with a small angle of the twist-line slope is similar to that of a tubular sample in the High Pressure Tube Twisting process [START_REF] Tóth | Severe plastic deformation of metals by high-pressure tube twisting[END_REF]. In the TE case, the axial zone of the billet serves as a mandrel. As can be clearly seen from these data, the classical Hall-Petch relation was obtained in which the local Vickers hardness is inversely proportional to the square-root of the grain size in the corresponding local region. Interestingly, the gradient in microstructure in the deformed zone produced a gradient in the hardness, which followed the classical Hall-Petch relation [START_REF] Armstrong | 60 Years of Hall-Petch: Past to Present Nano-Scale Connections[END_REF]. It is worth mentioning that an inverse Hall-Petch effect often found in nanostructured materials [START_REF] Pande | Nanomechanics of Hall-Petch relationship in nanocrystalline materials[END_REF] did not occur in this case since the grain size was far above the range where this inverse effect usually occurs (for less than about 25 nm [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF]) .

Conclusion

• Twist extrusion with a small angle of the twist-line slope was used to produce copper billets with a hexagonal cross-section. The diameter of the cylinder circumscribing the billets was 40 mm. It was shown that a strongly non-uniform microstructure ensued. It consisted of a core with a notionally undeformed coarse-grained microstructure with a radius of 10-15 mm and an exterior sheath with deformed gradient microstructure. The average grain size varied from 50 µm in the undeformed core to 0.5 µm near the billet surface.

• The microstructure gradient obtained reflects a gradient in the shear strain, and as such provides an insight into the various stages of the grain refinement process. The microstructure of the region contained within 15-17 mm from the axis of a billet with a decrease in the fraction of HAGBs corresponded to that of the initial state. Outside of this region, for locations 18 mm away from the axis or more, the observed rise of the fraction of HAGBs reflected the next stages of the grain refinement process.

• The texture in the deformed zone was shown to be a mixed texture of two different shear deformation modes. Hence, it was not an ideal simple shear texture, except at the billet edge. The first mode corresponded to shear in a plane perpendicular to the extrusion axis, while the second one had its shear plane parallel to the axis. At the billet edge, the magnitude of the second shear component was completely dominant. Accordingly, the texture of this region exhibited only features of the second shear mode, which was the ideal simple shear with the shear plane parallel to the extrusion axis. The result obtained was confirmed by two methods: EBSD analysis and texture measurements using synchrotron radiation.

• The investigation of substructure characteristics showed that the minimum size of the coherent scattering regions, and the maximum values of micro-distortions and the dislocation density correspond to the near-surface region of the billet, where the shear deformation was the largest. No grain refinement was found in the central zone of the billet. An increase in the dislocation density in the central zone is seen as the cause of increased hardness in this zone despite a coarse-grained structure found there.

• A solid correlation between the measured Vickers hardness and the microstructure was found. In the deformed sheath zone, the classical Hall-Petch relation between the hardness and the grain size in various locations was found to hold.

Declaration of conflict of interest

There is no conflict of interest associated with this publication.

Fig. 1 :

 1 Fig. 1: (a): Schematic of a twist die channel used to obtain a gradient material. (b): Reference directions on the deformed sample and micrographs of the deformed microstructure after four TE passes.

Fig. 2 :

 2 Fig. 2: EBSD microstructures obtained from an initial sample (c) and a processed sample (d-j) at different scanning positions (a) along the radial direction corresponding to various average grain sizes (b). The average grain sizes were determined from full EBSD maps; the maps (c-j) are fragments of the full EBSD maps shown for representation only. NA means: not applicable.

Fig. 3 :

 3 Fig. 3: Next-neighbor grain disorientation distributions of an initial sample (a) and a processed sample at various positions along its diagonal (b-h), and the corresponding fraction of HAGBs for all locations considered (i).

Fig. 4 :

 4 Fig. 4: Texture representation of initial and processed samples. (a) and (b): inverse pole figure and {111} pole figure of the initial sample, respectively. (c-i): {111} pole figures of the various areas from the center to the edge of the processed sample. (j): ODF sections shown for the edge area of the processed sample. The list of the ideal orientations is given in Table1.

  , the texture obtained within the undeformed zone of the processed sample was similar to that of the initial sample. Outside this zone, the texture changed and varied along the diagonal of the sample (Figs.4e-h). It is noteworthy that the texture eventually transformed into a simple shear texture near the sample edge (Figs.4i-j). The {111} pole figure and the ϕ2 = 0° and ϕ2 = 45° sections of the orientation distribution function (ODF) in Figs. 4i-j show that the texture components are situated in the same positions as for the ideal simple shear texture for face centered cubic (FCC) materials with the dominance of the C component. The identification of texture components is shown in the Table

Figure 5

 5 Figure 5 presents a map showing the scanning area of the sample along X and Y axes used to determine the diffraction peak width for synchrotron radiation. For texture investigation, only the indicated positions along the X axis were used.

Fig. 5 :

 5 Fig. 5: The positions of the scanning areas used in synchrotron radiation experiments.

Fig. 6 :

 6 Fig. 6: {111} pole figures for the initial sample shown alongside pole figures for areas located at different distances from the center of the processed sample, obtained from synchrotron measurements.

Fig. 8 :

 8 Fig. 8: Vickers hardness measured on a plane perpendicular to the extrusion axis of the processed sample along the diameter.

γ.

  Substituting this value into Eq. (2), one obtains * ~10 r mm for the experimental conditions in the tests described above (

Figs. 9 cFig. 9 :

 99 Figs. 9 c,d show the distribution of the equivalent von Mises strain over a billet crosssection after one TE pass. A pronounced strain gradient is clearly visible in a near-surface layer.Within this zone, the von Mises strain reaches values of 3 to 5.

Fig. 10 :

 10 Fig. 10: The dependence of the Vickers hardness, H (in HV), on the grain size, d (in µm), of the processed sample. The dashed line corresponds to the Hall-Petch relation shown within a frame.

Table 1 :

 1 Simple shear texture components for FCC materials.

	A	Ab	A1	A2	B	Bb	C
	{ } 1 1 1 110 { } 111 1 10 { } 1 11 112 { } 11 1 112 { } 112 110 { } 1 12 1 10	{ } 100 110
	3.2.2. Synchrotron study

Table 2 :

 2 Substructure parameters

	Scanning area	Position X, mm	D, nm ε, 10 -3 ρ×10 14 , m -2	Position Y, mm	D, nm ε, 10 -3 ρ×10 14 , m -2
	Initial	NA	69	0.16	0.20	NA	69	0.16	0.20
	1	1.00	85	1.15	3.06	0.00	107	1.10	1.73
	2	5.38	99	1.14	3.07	3.85	94	1.34	4.79
	3	10.25	62	1.16	5.39	8.55	99	1.37	5.24
	4	15.15	77	1.89	7.26	13.08	81	1.64	5.84
	5	19.50	57	2.71	9.72	17.10	62	1.73	6.64

Acknowledgements

This work was supported by the French State through the program "Investment in the future" operated by the National Research Agency (ANR) and referenced by ANR-11-LABX-0008-01 (LabEx DAMAS). Viet Q. Vu acknowledges the PhD scholarship awarded by the Vietnamese Government (Project 911).


N Seignour

J Masurier #

B Johansson #

G Dayma $

P Dagaut $

F Foucher

Ozone-assisted combustion of hydrogen: a comparison with isooctane

Keywords: HCCI combustion, Hydrogen, Isooctane, Ozone

Homogeneous Charge Compression Ignition (HCCI) engines have the potential to achieve low emissions of nitrogen oxides and particulate matter but the use of carbon-based fuels leads to significant emissions of carbon monoxide and unburned hydrocarbon which hinder the widespread development of HCCI. Nonetheless, HCCI engines have also the potential to use various types of fuel such as hydrogen, a carbon free fuel. The present study examined hydrogen combustion in an HCCI engine comparing hydrogen with isooctane. The sensitivities of CA05, CA50 and ringing intensity to intake pressure, intake temperature and ozone were investigated for both fuels. Results highlighted that hydrogen autoignites more easily than isooctane despite its higher-octane number. Ozone seeding was therefore used to shift the combustion region of isooctane in order to perform a viable comparison between the two fuels while starting with the same initial conditions. From this point, all of the three parameters were found to promote the HCCI combustion of both fuels but greater sensitivities were observed for hydrogen than for isooctane. Ozone was observed to have the strongest influence, making it a good strategy for a future control approach. The noise level of hydrogen was very high due its high reactivity. Finally, the use of hydrogen together with ozone should enable a very clean engine cycle to be achieved cycle with only water and nitrogen as engineout emissions.

Introduction

The main challenges for internal combustion engines are to drastically reduce fuel consumption and to meet ever more stringent emission standards. Low Temperature Combustion (LTC) engines, and particularly Homogeneous Charge Compression Ignition (HCCI) engines, have demonstrated their potential for achieving high efficiency while keeping low levels of NOx, soot and particulate matter emissions. However, several issues must be solved before a widespread implementation of such concepts. A reliable cycle-to-cycle combustion phasing control in particular is the main issue discussed in current HCCI research [START_REF] Dec | Advanced compression-ignition engines -understanding the in-cylinder processes[END_REF][START_REF] Saxena | Fundamental phenomena affecting low temperature combustion and HCCI engines, high load limits and strategies for extending these limits[END_REF].

Several studies have explored HCCI combustion control by varying intake thermodynamic parameters, especially intake temperature. All the studies showed that increasing the intake temperature reduced the ignition timing and promoted combustion. Machrafi et al. [START_REF] Machrafi | An experimental and numerical analysis of the influence of the inlet temperature, equivalence ratio and compression ratio on the HCCI autoignition process of Primary Reference Fuels in an engine[END_REF] and Dubreuil et al. [START_REF] Dubreuil | Effect of EGR Chemical Components and Intake Temperature on HCCI Combustion Development[END_REF] reported such a trend with Primary Reference Fuels (PRF). Mohammadi et al. [START_REF] Mohammadi | Study on combustion control in natural-gas PCCI engines with ozone addition into intake gas[END_REF] also studied the impact of intake temperature and obtained similar results with natural gas.

The implementation of Exhaust Gas Recirculation (EGR) has also been widely studied in HCCI engines in order to control the combustion phasing. Dubreuil et al. [START_REF] Dubreuil | Effect of EGR Chemical Components and Intake Temperature on HCCI Combustion Development[END_REF], Lü et al. [START_REF] Lü | A fundamental study on the control of the HCCI combustion and emissions by fuel design concept combined with controllable EGR. Part 1. The basic characteristics of HCCI combustion[END_REF][START_REF] Lü | A fundamental study on the control of the HCCI combustion and emissions by fuel design concept combined with controllable EGR. Part 2. Effect of operating conditions and EGR on HCCI combustion[END_REF] and Fathi et al. [START_REF] Fathi | The influence of Exhaust Gas Recirculation (EGR) on combustion and emissions of nheptane/natural gas fueled Homogeneous Charge Compression Ignition (HCCI) engine[END_REF] performed experiments with PRF mixtures and nheptane/natural gas mixtures. Results showed that EGR delays ignition timing due to the dilution of air and the modification of the heat capacity which limits the rise in temperature.

Another strategy to control combustion phasing is related to the ability of HCCI engines to run with various fuels. Fuel properties can therefore be a key parameter in combustion phasing. Lü et al. [START_REF] Lü | A fundamental study on the control of the HCCI combustion and emissions by fuel design concept combined with controllable EGR. Part 1. The basic characteristics of HCCI combustion[END_REF], Machrafi et al. [START_REF] Machrafi | An experimental and numerical analysis of the influence of the inlet temperature, equivalence ratio and compression ratio on the HCCI autoignition process of Primary Reference Fuels in an engine[END_REF], Masurier et al. [START_REF] Masurier | Homogeneous Charge Compression Ignition Combustion of Primary Reference Fuels Influenced by Ozone Addition[END_REF] conducted investigations with PRF mixtures and showed that the higher the Octane Number (ON), the later the ignition timing. Experiments were also performed with gaseous fuels by Aceves et al. [START_REF] Aceves | Compression ratio effect on methane HCCI combustion[END_REF], Ibrahim et al. [START_REF] Ibrahim | Investigation on the effects of the intake temperature and charge dilution in a hydrogen fueled HCCI engine[END_REF], and Masurier et al. [START_REF] Masurier | Effect of Additives on combustion characteristics of a natural gas fueled HCCI engine[END_REF], and alcohols, by He et al. [START_REF] He | Combustion and characteristics of a nbutanol HCCI engine[END_REF], Maurya et al. [START_REF] Maurya | Experimental investigations of performance, combustion and emissions characteristics of ethanol and methanol fueled HCCI engine[END_REF], and Masurier et al. [START_REF] Masurier | Ozone applied to the homogeneous charge compression ignition engine to control alcohol fuels combustion[END_REF]. As HCCI engines can operate with a wide range of alternative fuels [START_REF] Bhaduri | HCCI engine operated with unscrubbed biomass syngas[END_REF][START_REF] Contino | Screening method for fuels in homogeneous charge compression ignition engines: Application to valeric biofuels[END_REF], hydrogen looks to be the ideal fuel for HCCI engines to eliminate CO, HC and particulate matter emissions. Hydrogen combined with HCCI combustion has been one of the main topics in HCCI research over the last decade [START_REF] Rosati | Hydrogen SI and HCCI Combustion in a Direct-Injection optical engine[END_REF][START_REF] Caton | Homogeneous charge compression ignition of hydrogen in a single-cylinder diesel engine[END_REF][START_REF] Stenlaas | Hydrogen as homogeneous charge compression ignition engine fuel[END_REF][START_REF] Antunes | An investigation of hydrogen-fuel HCCI engine performance and operation[END_REF].

However, hydrogen combustion unfortunately leads to NOx emissions because of the high local temperatures in the combustion chamber. Hydrogen has also been studied under conventional CI combustion [START_REF] Naber | Hydrogen combustion under diesel engine conditions[END_REF][START_REF] Szwaja | Hydrogen combustion in a compression ignition diesel engine[END_REF] and as an additive for a dual fuel combustion strategy [START_REF] Shudo | HCCI combustion of hydrogen, carbon monoxide and dimethyl ether[END_REF][START_REF] Shudo | Hydrogen as an ignition-controlling agent for HCCI combustion engine by suppressing the low-temperature oxidation[END_REF][START_REF] Yap | Effect of hydrogen addition on natural gas HCCI combustion[END_REF]. Results showed that hydrogen HCCI combustion maintains the same level of performances as conventional fuels while eliminating HC and CO emissions. However, the main issue for hydrogen combustion remains noise, because of the fast combustion of hydrogen.

Lastly, the need to achieve a reliable control of combustion, which is mainly governed by chemical kinetics in HCCI engines, led research to focus on new approaches such as seeding the engine intake ports with oxidizing species. Masurier et al. [START_REF] Masurier | Investigation of iso-octane combustion in a homogeneous charge compression ignition engine seeded by ozone, nitric oxide and nitrogen dioxide[END_REF] investigated the potential of ozone, nitric oxide, and nitrogen dioxide to control the combustion phasing. Among all these species, ozone appeared to be the most promising species by increasing the air/fuel reactivity. A few ppm of ozone was found to be enough to significantly improve the autoignition of high-octane fuel.

Hydrogen is among the high-octane fuels which could lead to clean combustion while burning under HCCI conditions. The present study investigated experimentally the impact of ozone on hydrogen combustion and compared it with the effect of varying either the intake pressure or the intake temperature. Additionally, hydrogen combustion was compared to the combustion of isooctane, a reference fuel, while varying the same parameters.

Experimental Setup

Experiments were performed using a PSA DW10 four-stroke Diesel engine modified to operate as a single-cylinder Homogeneous Charge Compression Ignition (HCCI) engine. The engine is directly coupled to an electric motor to maintain a constant rotation speed. The main characteristics of the engine are listed in Table 1 and a schematic of the experimental setup is given in Figure 1. The inlet manifold was modified to work under HCCI conditions. A plenum was set upstream of the intake valves of the engine and all the gases were injected in this plenum to allow a long mixing time and therefore a homogeneous mixture. Homogeneity of the mixing was validated in a previous work [START_REF] Lü | A fundamental study on the control of the HCCI combustion and emissions by fuel design concept combined with controllable EGR. Part 1. The basic characteristics of HCCI combustion[END_REF]. Gases were supplied using Brooks mass flow controllers, with an accuracy of ± 0.7% of the full scale, and liquids were supplied using Bronkhorst mass flow controllers, with an accuracy of ± 1 % of the full scale. Intake pressure was measured by a Kistler 4075A piezo-resistive absolute pressure sensor, with an accuracy of ± 0.3% of the full scale, and was controlled by the mass flow controllers with respect to the equivalence ratio required and the fraction of each component. The fuels used in this work are hydrogen (H2) and isooctane (C8H18). Hydrogen was injected directly into the intake plenum after being heated. Isooctane was injected into the plenum after an initial dilution with air and a preheating allowing its evaporation.

Parameters

Intake temperature was measured with two Ktype thermocouples, one in each intake port, with an accuracy of ± 2K, and was controlled by a main heater warming up the main air flow and a band heater set around the plenum. In-cylinder pressure was measured by a Kistler 6043A piezo-electric sensor, with an accuracy of ± 2%. For all the experiments, intake and in-cylinder pressures were recorded with a resolution of 0.1 CAD using a Külber 8.5020.D842.3600 encoder set on the crankshaft and data were analyzed over 100 consecutive cycles.

The engine intake was seeded with ozone using an Anseros COM-AD-01 coronadischarge ozone generator operating with pure oxygen. A nitrogen flow was added to maintain an oxygen/nitrogen ratio similar to that of air. Lastly, ozone concentration was measured by an ozone analyzer (Anseros Ozomat MP6060) by collecting a sample from one of the intake ports.

Kinetics support

In addition to experimental results, kinetic analyses were conducted. Simulations were performed using the CHEMKIN PRO package [START_REF]CHEMKIN: a general-purpose, problemindependent, transportable[END_REF]. An isooctane detailed kinetic mechanism developed by Curran et al. [START_REF] Curran | A comprehensive modeling study of isooctane oxidation[END_REF] and an ozone sub-mechanism [START_REF] Halter | Experimental and Detailed Kinetic Modeling Study of the Effect of Ozone on the Combustion of Methane[END_REF][START_REF] Contino | CFD simulations using the TDAC method to model iso-octane combustion for a large range of ozone seeding and temperature conditions in a single cylinder HCCI engine[END_REF] were selected. This mechanism has already been used and validated by Masurier et al. [START_REF] Masurier | Investigation of iso-octane combustion in a homogeneous charge compression ignition engine seeded by ozone, nitric oxide and nitrogen dioxide[END_REF].

Results and discussion

In the present study, all the experiments with hydrogen and isooctane were performed at a rotation speed and an equivalence ratio of 1500 rpm and 0.3, respectively. First, a way to compare hydrogen and isooctane, under HCCI conditions was investigated. Second, three parameters -the intake pressure, the intake temperature and the ozone concentration seeded in the intake -affecting HCCI combustion were investigated with both fuels and finally, a discussion will oppose each parameter and the impact of each parameter on hydrogen and isooctane combustion was compared.

Towards a comparison of hydrogen with isooctane

Comparing the combustion of two fuels in an HCCI engine is complex because fuels do not autoignite under the same conditions. Hydrogen and isooctane are no exceptions. To conduct a suitable comparison, it is essential to find a unique experimental condition in which the intake pressure, intake temperature, rotation speed, equivalence ratio and therefore amount of energy injected will be the same. This first section therefore focuses on finding common intake conditions to enable a comparison between hydrogen and isooctane in terms of intake pressure, intake temperature and ozone concentration seeded in the intake.

The combustion of hydrogen and isooctane was investigated experimentally to find the couples of intake pressure and intake temperature leading to a suitable combustion behavior. In the present work, a suitable combustion behavior is reflected by the CA50, i.e. the crank angle degree at which 50 % of the total energy is released, when CA50 is in the range 1 to 6 crank angles (CAD). These limits correspond respectively to the maximum acceptable noise level and to misfires. Combustion regions for both hydrogen and isooctane with respect to intake pressure and intake temperature are shown in Figure 2. The lower limit of each region corresponds to a CA50 of 6 CAD and the upper limit corresponds to a CA50 of 1 CAD. Results show unexpectedly that hydrogen autoignites more easily than isooctane. Indeed, hydrogen has a research octane number (RON) greater than 120 and even greater than the RON of isooctane (100). In other words, hydrogen should require higher intake conditions than isooctane to autoignite but the experiments conducted show the opposite. These results suggest that RON is inappropriate for describing HCCI autoignition, especially for hydrogen fuel, and similar observations were reported by other groups with different fuels [START_REF] Rapp | Predicting Fuel Performance for Future HCCI Engines[END_REF]. In fact, RON was initially applied to SI combustion and characterizes the autoignition of the endgases leading to knock. This phenomenon depends on the turbulent flame propagation, the conditions in the unburnt gases (pressure, temperature and equivalence ratio) and how fast the energy of the unburnt gases is released whereas autoignition in HCCI only depends on the conditions in the unburnt gases. The difference in the autoignition processes should make RON an unsuitable rating for HCCI. Nonetheless, the motor octane number (MON), based on a higher engine speed (900 rpm vs. 600 rpm for RON determination), was rated at 60 for hydrogen [START_REF] Verhelst | A Critical Review of Experimental Research on Hydrogen Fueled SI Engines[END_REF][START_REF] Verhelst | Hydrogen-fueled internal combustion engines[END_REF] while isooctane, which is still the reference, is rated at 100. MON therefore indicates that under high engine speed hydrogen should autoignite more easily than isooctane. Finally, observing more carefully Figure 2, extrapolations of the respective linear trends for both hydrogen and isooctane towards high intake pressure will make the trends cross each other meaning that under very high intake pressure -low intake temperature conditions, hydrogen could autoignite more easily than isooctane, thus making RON a viable criterion. Further investigations are required to confirm this statement and an experimental setup allowing very high intake pressure should be used. Moreover, finding a similar initial point to perform our comparison cannot be achieved with the present experimental setup except by using ozone. Ozone showed in previous studies its ability to shift the combustion region of isooctane (as in Figure 2) towards a lower intake temperature without impacting too much the combustion sensitivity to both intake pressure and intake temperature [START_REF] Masurier | Towards HCCI Control by Ozone[END_REF].

To find a suitable similar point at 1 bar intake pressure to perform our comparison, ozone concentration required to get a combustion phasing (CA50) near 6 CAD, the misfire limit for HCCI combustion, with respect to the intake temperature was studied. Considering these conditions, hydrogen required an intake temperature of 150 °C meaning that the intake temperature for isooctane should be 60 °C lower to obtain a similar point. 15 ppm of ozone were found suitable to complete the requirements. New sweeps in intake pressure and temperature were therefore conducted to ensure that the sensitivities of isooctane combustion did not change. The new combustion region obtained is shown in Figure 2 where the shift can be clearly observed. The sensitivities to both intake parameters are further discussed below. With the similar point for our comparison between hydrogen and isooctane found at 1 bar and 150 °C, the sensitivity of isooctane to a change in both the intake pressure and the intake temperature was studied and compared to the sensitivity to the same parameters at 1 bar and 210 °C, i.e. a comparison of the cases with and without ozone seeding. The sensitivity is here expressed by observing the pressure traces, the heat release traces, as well as CA05 and CA50, representing respectively the onset of the combustion and the combustion phasing.

Figure 3 shows in-cylinder pressure and heat release rate traces for both isooctane at 210°C without ozone and isooctane at 150 °C with ozone. A small increase in intake pressure, about 130 mbar, increases the in-cylinder pressure peak by 13 bar for isooctane at 210 °C and by 17 bar for isooctane with ozone addition at 150 °C. Meanwhile, the crank angle associated to the maximum in-cylinder pressure peak moves forward by 3 CAD for pure isooctane and by 4 CAD for isooctane with ozone. A rise in intake pressure therefore enhances the combustion of isooctane in both cases. Heat release rate traces show that the combustion enhancement is even more noticeable as the peak of heat release rate is twice higher and moves towards the top dead center while the combustion duration decreases. In both conditions, results in Figure 3 highlight a similar combustion enhancement with a slight advantage at 150 °C as the amount of energy injected in the engine is slightly higher. A similar enhancement is better observed with CA05 and CA50 in Figure 4. Figure 4 shows that both CA05 and CA50 linearly decrease with respect to the increase in intake pressure. The small difference shows that the case at 150 °C is perhaps slightly more sensitive to the intake pressure. However, these results are based on 100 consecutive cycles which generate a standard deviation of 0.25 CAD. The sensitivity of these parameters to the intake pressure can be considered as similar.

Similarly to the intake pressure, sensitivity to an increase in intake temperature was investigated. Figure 5 shows the in-cylinder pressure and heat release rate traces at 1 bar with respect to intake temperature. Traces show a similar dependence on the temperature, i.e. a combustion enhancement. Again, cases with ozone lead to higher pressure and heat release peaks than cases without ozone because of the energy injected into the combustion chamber. CA05 and CA50 are also plotted with respect to the rise in temperature, i.e. the difference with the initial temperature for each case, 150 °C with ozone and 210 °C without ozone (Figure 6). All the results evolve linearly and while a slight gap can be observed at a low temperature difference, it can be concluded from the standard deviation on CA05 and CA50 that there is a similar dependence on intake temperature.

Figure 5: In-cylinder pressure (top) and heat release rate (bottom) as a function of the intake temperature for isooctane as a fuel with and without ozone.

To sum up, this preliminary study shows that the dependence of isooctane combustion on intake pressure and intake temperature is preserved for the two points investigated, i.e. at 1 bar and 210 °C and at 1 bar and 150 °C with ozone. As a result, a comparison between hydrogen and isooctane according to a change of intake pressure, intake temperature and ozone seeding in the intake can now be conducted.

Comparison between hydrogen and isooctane

The previous section examined the sensitivities of isooctane at two different experimental points in order to enable an accurate comparison between hydrogen and isooctane. The intake pressure and the intake temperature set respectively at 1 bar and 150 °C were found suitable to compare hydrogen combustion to isooctane combustion when the intake pressure, intake temperature and ozone seeded in the intake vary. Under this intake pressure and temperature, the FuelMEP for isooctane and hydrogen are 9.14 bar and 9.28 bar respectively. The following sections discuss separately the impact of intake pressure, intake temperature, and ozone on both hydrogen and isooctane and a final discussion compares these parameters.

Intake pressure effect

The increase in intake pressure on the combustion of pure hydrogen and isooctane with a small amount of ozone at 1 bar and 150 °C was investigated first. Figure 7 shows incylinder pressure and heat release rate traces under different intake pressures. As for isooctane, increasing the intake pressure enhances the combustion of hydrogen. In-cylinder pressure traces show that hydrogen always ignites later than isooctane regardless of the intake pressure.

Nevertheless, hydrogen burns faster and more strongly as per the rapid increase in the incylinder pressure and the high pressure peaks. Heat release rate traces showed even better that the reactivity of hydrogen is higher than that of isooctane due to the high heat release peak and the shorter combustion duration.To better observe intake pressure dependance, CA05 and CA50 were analyzed. Figure 8 shows that both the onset of the combustion and the combustion phasing depend linearly on the intake pressure for both fuels. Moreover, the sensitivities of both CA05 and CA50 are similar regardless of the fuel. However, the noticeable difference between hydrogen and isooctane in Figure 8 is the gap between CA05 and CA50 which is fixed over the intake pressure sweep but smaller in the case of hydrogen indicating its rapid combustion. The last parameter examined to compare the dependence of hydrogen and isooctane on the intake pressure was the ringing intensity. Ringing intensity (RI) is defined by Equation 1and used here as an indicator of the level of noise [START_REF] Eng | Characterization of pressure waves in HCCI combustion[END_REF].

≈ • . • . . (1)
In Equation 1, γ is the ratio of specific heats, Pmax is the maximum in-cylinder pressure, (dP/dt)max represents the maximum pressure rise rate, β is the tuning parameter which correlates the pressure and the maximum pressure rise rate, R denotes the ideal gas constant, and Tmax is the maximum in-cylinder temperature. Ringing intensities with respect to the intake pressure for both hydrogen and isooctane are plotted in Figure 9. Noise linearly increases with respect to the intake pressure but hydrogen rapidly reaches high ringing intensity values as soon as combustion occurs due to a higher reactivity than isooctane. Moreover, the maximum ringing intensity for the engine, fixed here at 20 MW/m 2 , is rapidly reached with a small increase of intake pressure (roughly 100 mbar) while isooctane shows a smoother linear increase.

Intake temperature effect

The effect of Intake temperature was also investigated starting from the same initial point, i.e. 1 bar and 150 °C for pure hydrogen and for isooctane with a small amount of ozone. Figure 10 shows in-cylinder pressure traces and the corresponding heat release rate traces for different intake temperatures. Intake temperature promotes both combustion of hydrogen and isooctane and yet, hydrogen burns more intensively than isooctane. At the initial temperature of 150 °C, hydrogen ignites later than isooctane progressively catches up with isooctane ignition when the intake temperature increases. Even if the last temperature tested shows an ignition around the same crank angle, hydrogen ignition will likely overtake isooctane by raising the intake temperature. CA05 and CA50 trends show that hydrogen might ignite earlier than isooctane (Figure 11). Both parameters evolve linearly and in parallel with respect to the two fuels used. However, hydrogen combustion exhibits a higher sensitivity mainly due to its higher reactivity and the fact that a change in temperature highly impacts the chemical reactivity of fuels.

Figure 12 presents the ringing intensity for the two fuels with respect to intake temperature. As intake temperature promotes combustion of hydrogen and isooctane, a linear increase in the ringing intensity was expected. Again, the ringing intensity of hydrogen fuel is much higher than that of isooctane and the threshold of 20 MW/m 2 is rapidly reached for hydrogen without a high increase in the intake temperature. Isooctane shows an even smoother trend with intake temperature compared to intake pressure for the same variation of ringing intensity with hydrogen.

Ozone Effect

Lastly, the impact of ozone seeding in the intake port was investigated for both hydrogen and isooctane. In-cylinder pressure traces and heat release rate traces are presented in Figure 13 with respect to ozone seeding. It is worth noting that for isooctane experiments were performed with 15 ppm more ozone than in hydrogen experiments to allow the same initial CA50 for both fuels at 1 bar and 150 °C. The impact of these additional 15 ppm will be discussed later in this section but as a result, the comparison of the results with ozone is discussed based on a difference in ozone concentration. In other words, the results in Figure 13 correspond to the same ozone addition with respect to the initial concentration. Initially, hydrogen ignites later than isooctane but the combustion of both fuels is rapidly promoted as soon as a small concentration of ozone seeds the intake.

However, hydrogen appears to be more promoted than isooctane regarding the shift in both in-cylinder pressure and heat release rate peaks and the shift in the onset of combustion.

A better observation can be made from CA05 and CA50 with respect to the ozone concentration in Figure 14. Unlike intake pressure and intake temperature which show a linear dependency on CA05 and CA50, the first few ppm of ozone have a strong impact but then, although ozone continuously improves combustion, the impact becomes weaker. An increase of 10 ppm ozone advances hydrogen combustion phasing by 6 CAD while 10 ppm of ozone, added to the 15 required to operate at 150 °C with isooctane, advances isooctane combustion phasing by 4.5 CAD. Ozone therefore shows more impact on hydrogen combustion than on isooctane combustion for the same increase in the ozone proportion. However, as previously stated, an initial ozone concentration is required to burn isooctane at the same pressure and temperature conditions as hydrogen. Previous studies conducted by Masurier et al. [START_REF] Masurier | Homogeneous Charge Compression Ignition Combustion of Primary Reference Fuels Influenced by Ozone Addition[END_REF][START_REF] Masurier | Effect of Additives on combustion characteristics of a natural gas fueled HCCI engine[END_REF][START_REF] Masurier | Ozone applied to the homogeneous charge compression ignition engine to control alcohol fuels combustion[END_REF][START_REF] Masurier | Investigation of iso-octane combustion in a homogeneous charge compression ignition engine seeded by ozone, nitric oxide and nitrogen dioxide[END_REF] showed that a small addition of ozone has a stronger impact on the combustion phasing than a high addition of ozone. As the ozone concentration with isooctane is 15 ppm more than with hydrogen, the higher impact on hydrogen observed in Figure 14 is questionable. In their study, Masurier et al. [START_REF] Masurier | Homogeneous Charge Compression Ignition Combustion of Primary Reference Fuels Influenced by Ozone Addition[END_REF]. highlighted that 9 ppm of ozone advanced the combustion phasing of isooctane by 9 CAD by running the engine with an intake temperature set at 200 °C. Comparing those results with the present hydrogen results, ozone should have more impact on isooctane combustion because the present isooctane results use higher ozone concentrations than in the study by Masurier et al. However, intake temperature is a key parameter in this comparison. Temperature has a strong influence on ozone reactivity [START_REF] Eliasson | Ozone synthesis from oxygen in dielectric barrier Discharges[END_REF][START_REF] Sung | Optimum conditions for ozone formation in a micro dielectric barrier discharge[END_REF] which in turn promotes combustion, meaning that the same concentration of ozone under two engine intake temperatures, such as 150 °C and 200 °C, will lead to a stronger impact with the higher of the two temperatures. Finally, it is likely that 15 ppm of ozone compensates for the lower intake temperature for isooctane ignition, and that additional ozone concentrations only enhance isooctane combustion. As a result, hydrogen combustion is much more promoted by ozone than isooctane.

Furthermore, to confirm that ozone promotes hydrogen combustion more than isooctane combustion, a set of simulations were performed at constant volume for several ozone concentratons to observe ignition delay. Initial conditions were chosen with respect to the experimental conditions, i.e. the equivalence ratio was set at 0.3 for both fuels and intial pressure and temperature were derived from the experimental traces (35 bar and 1000 K corresponding to the ignition). Computed Ignition delays are presented in Figure 15 as a function of initial ozone concentration with respect to the fuel. Figure 15 shows distinctly that hydrogen is more sensitive to ozone addition than isooctane. A few ppm of ozone (~ 10 ppm) significantly advance the ignition delay of hydrogen compared to that of isooctane. High concentrations of ozone show less impact on ignition delays but hydrogen is still more impacted than isooctane.

Finally, the impact of ozone on ringing intensity was also observed. Results are shown in Figure 16. Similarly to the intake pressure and the intake temperature, noise is more intense and more sensitive for hydrogen when using ozone. Moreover, it is worth noting that a small ozone concentration is enough to rapidly reach the threshold of 20 MW/m 2 . Nonetheless, it is highly due to hydrogen itself which ignites rapidly when seeded with ozone.

Discussion

Pressure and temperature impact the oxidation of the two fuels in a similar way. Increasing one of them promotes autoignition as per the Arrhenius equation. Ozone has the potential to change the chemical pathway via new reactions and strongly promotes combustion. As a result, in the new approach proposed here, ozone is a key parameter. Moreover, results with isooctane showed that ozone can shift the combustion region towards lower intake temperatures. Using this benefit with hydrogen could lead to lower incylinder temperatures, and a clean combustion cycle might be reached, i.e. reducing potential NOx emissions. In terms of control, temperature can easily be increased but with some hysteresis using heaters. However, if decreasing this parameter is required, no control could be easily made. Nonetheless, some concepts have been developed in order to rapidly handle this parameter [START_REF] Haraldsson | HCCI Closed-Loop Combustion Control Using Fast Thermal Management[END_REF]. Pressure can be handled via turbochargers/superchargers but with some lag. Perhaps the ringing intensiy limits will be reached even faster than with the other parameters. Finally, ozone can be injected directly in the intake port when needed and could give good combustion control [START_REF] Masurier | Application of an Ozone Generator to Control the Homogeneous Charge Compression Ignition Combustion Process[END_REF]. To conclude, it is easier to control the combustion of hydrogen than that of isooctane with ozone under HCCI conditions.

Conclusion

The present study assessed the combustion of hydrogen in an HCCI engine and compared it to the combustion of isooctane, a reference fuel. Three parameters --the intake pressure, the intake temperature and the concentration of ozone seeded into the intake port --were investigated and compared in order to control HCCI combustion of both fuels. Analyses were performed mainly based on CA05, CA50, and ringing intensity. Results showed that hydrogen autoignition required lower intake pressures and intake temperatures than isooctane despite its higher octane number. In order to perform a viable comparison between the two fuels while varying the three parameters, he combustion region of isooctane seeded with ozone was shifted, without altering the dependency on the intake thermodynamic conditions. Comparison while varying the three parameters was therefore conducted at 1 bar and 150 °C. All the parameters were identified as combustion improvers for both hydrogen and isooctane but with a noticeable effect of ozone seeding. Compared with isooctane combustion, hydrogen was found to be more sensitive to increases in intake temperatures and ozone concentrations while it was slightly less impacted than isooctane by changes in intake pressure. In terms of noise, hydrogen was always the most impacted due to its high reactivity. Finally, in the new approach proposed here, ozone is a key parameter to control combustion. Furthermore, with hydrogen fuel, a clean combustion cycle might be achieved.

Figure 1 :

 1 Figure 1: Schematic of the experimental setup.

Figure 2 :

 2 Figure 2: Fuel regions of optimal HCCI combustion as a function of the intake pressure and the intake temperature. Upper and lower limits of each region correspond to a CA50 of 1 CAD and 6 CAD, respectively.

Figure 3 :

 3 Figure 3: In-cylinder pressure (top) and heat release rate (bottom) as a function of the intake pressure for isooctane as a fuel with and without ozone.

Figure 4 :

 4 Figure 4: CA05 and CA50 as a function of the intake pressure for isooctane as fuel with and without ozone.

Figure 6 :

 6 Figure 6: CA05 and CA50 as a function of the temperature difference with reference to the initial temperature for a CA50 phased at 6 CAD.

Figure 7 :

 7 Figure 7 : In-cylinder pressure (top) and heat release rate (bottom) as a function of the intake pressure for isooctane and hydrogen.

Figure 8 :

 8 Figure 8 : Comparison of the CA05 and the CA50 for hydrogen and isooctane as a function of the intake pressure.

Figure 1 :

 1 Figure 1 : Comparison of the ringing intensity (top) and maximum pressure rise rate (bottom) of hydrogen and isooctane as a function of the intake pressure.

Figure 10 :

 10 Figure 10: In-cylinder pressure and heat release rate as a function of the CAD and intake temperature for isooctane and hydrogen.

Figure 11 :

 11 Figure 11: Comparison of the CA05 and the CA50 for hydrogen and isooctane as a function of the intake temperature

Figure 12 :

 12 Figure 12: Comparison of the ringing intensity (top) and maximum pressure rise rate (bottom) of hydrogen and isooctane as a function of the intake temperature.

Figure 13 :

 13 Figure 13: Comparison of In-cylinder pressure and heat release rate as a function of CAD and ozone concentration for isooctane and hydrogen.

Figure 14 :

 14 Figure 14 : Comparison of the CA05 and the CA50 of hydrogen and isooctane as a function of ozone concentration.

Figure 15 :

 15 Figure 15 : Computed ignition delay in reference to the initial ignition delay without ozone and as a function of ozone concentrations.

Figure 16 :

 16 Figure 16 : Comparison of the ringing intensity (on the top) and maximum pressure rise rate (on the bottom) of hydrogen and isooctane as a function of ozone concentration.

Table 1 :

 1 Engine characteristics

		Unit	Value
	Bore	mm	85
	Stroke	mm	88
	Connecting Rod	mm	145
	Displaced Volume	cc	499
	Geometric	-	16:1
	Compression Ratio
	Effective Compression	-	16.13:1
	Ratio
	Number of Valves	-	4
	Intake Valve Closure	CAD 351 ATDC
	Intake Valve Opening	CAD 157 BTDC
	Exhaust Valve Opening	CAD 140 ATDC
	Exhaust Valve Closure	CAD 366 ATDC
	Coolant Temperature	°C	90
	Oil Temperature	°C	90

Table 2

 2

	lists

Table 2 :

 2 Characteristics of the mass flow controllers.

Acknowledgments

The work performed at the University of Orléans was supported by the CICCO project from the French National Research Agency, ANR-15-CE22-0004. The research reported in this publication was also supported by funding from King Abdullah University of Science and Technology (KAUST).

Abbreviations


O V Naumenko

A V Lukashevskaya

S Kassi

S Béguier

A Campargue
email: alain.campargue@univ-grenoble-alpes.fr

The ν1+3ν3 absorption band of nitrogen dioxide ( 14 N 16 O2) by CRDS near 6000 cm -1

Keywords: Nitrogen dioxide, NO2, cavity ring down spectroscopy, CRDS, electron spinrotation interaction, effective Hamiltonian

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The NO2 molecule contributes to the pollution of the troposphere as well as to the ozone layer depletion. Its absorption spectrum is of interest not only for our atmosphere but also for astrophysical objects like exoplanets (see for example [START_REF] Tennyson | Laboratory spectra of hot molecules: Data needs for hot super -Earth exoplanets[END_REF] and references quoted therein).

Experimental rotation-vibration NO2 transitions from about 20 original sources in the 0-7920 cm -1 spectral range were recently involved in global fitting of the line positions [START_REF] Lukashevskaya | Global modelling of NO2 line positions[END_REF]. The results of some experimental studies were included in the last versions of the HITRAN [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF] and GEISA [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] databases. However, these databases do not contain line parameters of NO2 above 3074 cm - 1 . Since 2010, we have been systematically investigating the weak NO2 spectrum in the 5800-8000 cm -1 region by high-sensitivity cavity ring down spectroscopy (CRDS). A ten of new absorption bands were assigned and modeled in the frame of the effective Hamiltonian (EH) model [START_REF] Perrin | First high resolution analysis of the 4ν1+ν3 band of nitrogen dioxide near 1.5 µm[END_REF][START_REF] Mondelain | First high resolution analysis of the 5ν3 band of nitrogen dioxide near 1.3 µm[END_REF][START_REF] Lukashevskaya | High sensitivity cavity ring down spectroscopy of NO2 between 7760 and 7917 cm -1[END_REF][START_REF] Lukashevskaya | High sensitivity cavity ring down spectroscopy of the 3ν1+3ν2+ν3 band of NO2 near 7587 cm -1[END_REF][START_REF] Lukashevskaya | First detection and analysis of the 3ν1+ν2+ν3 band of NO2 by CRDS near 6156 cm -1[END_REF][START_REF] Lukashevskaya | High sensitivity Cavity Ring Down Spectroscopy of the 2ν1+3ν2+ν3 band of NO2 near 1.57 μm[END_REF][START_REF] Lukashevskaya | High sensitivity Cavity Ring Down Spectroscopy of the 4ν3 band of NO2 near 1.59 µm[END_REF][START_REF] Lukashevskaya | High sensitivity cavity ring down spectroscopy of the ν1+4ν3 band of NO2 near 1.34 µm[END_REF]. This work is devoted to the analysis of the CRDS NO2 spectrum in the 5855-6006 cm -1 region. The vibrational-rotation transitions of the ν1+3ν3 band at 5984.7 cm -1 dominate the spectrum. This band is the strongest vibrational band above 5800 cm -1 . Its first study was reported in 1970 by Blank et al. [START_REF] Blank | Upper State Molecular Constants for the (0,0,3) and(1, 0,3)Vibration-RotationBands ofNitrogenDioxide[END_REF]. More recently, it was analyzed from a spectrum of a NO2/NO/ICl mixture recorded by Fourier transform spectroscopy [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. 1147 transitions with N up to 47 and Ka up to 8 were identified and modeled. Only a very approximate value of the band intensity was reported in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] based on an estimated value of the NO2 partial pressure in the used gas mixture. In the present work, we report an extended analysis of 3154 identified 14 N 16 O2 transitions with accurately measured positions and intensities up to N and Ka rotational quantum numbers of 59 and 13, respectively.

Experimental details and line parameters retrieval

The reader is referred to Refs. [START_REF] Kassi | Cavity ring down spectroscopy with 5×10 -13 cm -1 sensitivity[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF] for a detailed description of the used fiberconnected cavity ring down spectrometer. Seven Distributed Feedback (DFB) laser diodes were used as light sources to cover the 5855-6006 cm -1 spectral region under study. The frequency calibration was performed using a commercial Fizeau type wavemeter. We estimate the accuracy on the line position to be 1×10 -3 cm -1 for well isolated lines. The considered NO2 band is not very weak which makes possible to use low pressure for the recordings. Most of the forthcoming data analysis relies on a spectrum recorded at a pressure of 0.05 Torr measured by a capacitance gauge (MKS, Baratron 626B 1.0 Torr, 0.15% accuracy of the reading), only, and a temperature of 297.3 K. Additional recordings at 1.0 Torr were used for the lower energy region below 5910 cm -1 . Fig. 1 shows an overview of the 0.05 Torr recordings. The successive zooms included in this figure illustrate the sensitivity of the recordings and the high dynamic on the intensity scale. The noise-equivalent absorption of the spectrum is on the order of αmin~ 1×10 -10 cm -1 . For these low pressure values, the dimerization is very limited and N2O4 concentration can be neglected.

Fig. 1.

Comparison of the CRDS spectrum of the ν1+3ν3 band of NO2 recorded at 0.05 Torr to a simulation using the effective operator approach.

The line parameter retrieval was performed using an homemade multiline fitting program. The spectral line shape used at 0.05 Torr is very close to a Doppler profile.

Nevertheless, the achieved signal to noise ratio of the spectrum requires using a Voigt profile for some strong lines. Note that in the case of unresolved spin-rotational doublets, we often fitted the absorption feature as a single line. The line list retrieved from the 0.05 Torr spectra includes 3420 lines in the 5911-6005 cm -1 region with intensities ranging between 10 -26 and 10 - 23 cm/molecule at 297 K. A separate list of about 3500 lines was constructed from the 1 Torr recordings in the 5854-5911 cm -1 region. Only a small fraction of this set of weak lines (intensities in the 10 -27 -10 -25 cm/molecule range) belongs to the ν1+3ν3 band.

Spectrum assignment and line position modeling

The overview of the experimental spectrum is displayed on the upper panel of Fig. 1.

The spectrum was assigned on the basis of EH calculations which account for explicitly the spin-rotational interactions as well as rotation-vibration resonance coupling. The resonance scheme proposed in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] is confirmed by the present analysis. It involves a strong interaction of the (103) bright state with two dark states -( 122) and (080) -already included in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] and a newly evidenced interaction with the (410) nearby dark state. The scheme of the effective Hamiltonian matrix is presented in Fig. 2

(V1,V2,V3) N=J-1/2 N=J+1/2 (V'1,V'2,V'3) N=J-1/2 H C N=J+1/2 H C Fig.2. Scheme of the H eff matrix.
The reader is referred to Ref. [START_REF] Watson | Aspects of quartic and sextic centrifugal effects on rotational energy levels[END_REF] for the explicit expression of the Watson-type Hamiltonian (HVR), and to Ref. [START_REF] Brown | A reduced form of the spin-rotation Hamiltonian for asymmetric-top molecules, with applications to HO2 and NH2[END_REF] for the electron spin-rotation interaction operator (HSR).

Note that the V-off diagonal block does not include an anharmonic interaction term. The Coriolis interaction operator was used in the following form:

= + , + , + , , + , + ++ , (1)
C0, CK, CKK, CKKK, CNK, CKKN, are the Coriolis coupling constants and the parameters describing their rotational dependence.

The values of the spectroscopic parameters derived in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] were used as initial parameters. As soon as new rotation-vibration transitions were assigned, the spectroscopic parameters were refined from the fitting to observed positions and intensities providing more accurate spectrum simulation for further identification. Resonance interactions are discussed in details below. For poorly resolved SR doublets or strongly blended lines, the calculated line positions might be more accurate than experimental values. The summary of the assignments obtained from the spectrum analysis is presented in Table 1.A final rms deviation of 0.0023 cm -1 was achieved by varying 41 parameters listed in Table 2.

Table 1 includes a comparison to the results reported in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. About 3 times more transitions were assigned (3154 vs 1147) with maximal N and Ka rotational quantum numbers equal to 59 and 13, respectively, while only transitions with N ≤ 47 and Ka ≤ 8 were identified in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. Overall, the average and rms deviation of the differences of the FTS and CRDS position values are 0.0016 and 0.0020 cm -1 , respectively for 1038 transitions (corresponding to 92 % of the transitions measured by FTS). We note a significant decrease of the rms deviation if only well resolved or fully degenerate lines are considered. On the opposite, comparison of our measured doublet positions with those calculated using the parameters of Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] resulted in an rms deviation of 0.0028 cm -1 for 692 lines while a value of 0.0010 cm -1 is obtained using our parameters, confirming that our peaklist provides better accuracy for close lying spectral lines.

Taking into account multiple assignments attached to the same observed line, 2754 NO2 absorption lines were identified in the large set of about 7500 measured lines. The assigned lines bring 94% of the total selective absorption in the considered spectral region. The large set of weak unidentified lines may belong to the (103)-(000) band of minor NO2 isotopologues, to "hot" bands of the main isotopologue originating from the (010) lower vibrational state or to impurities. -7 ) -0.25899(1300) Notes 1σ confidential intervals are given in unit of the last digit. In absence of parameter value, the parameter was constrained to the ground state value of Ref. [START_REF] Semmoud-Monnanteuil | New measurements in the millimeter wave spectrum of NO2[END_REF] given in the 2nd column a Ref. [START_REF] Semmoud-Monnanteuil | New measurements in the millimeter wave spectrum of NO2[END_REF] b Ref. [START_REF] Delon | Laser induced dispersed fluorescence spectra of jet cooled NO2: the complete set of vibrational levels up to 10,000 cm -1 and the onset of the à 2 B2-2 A1 vibronic interaction[END_REF] c Ref. [START_REF] Lukashevskaya | Global modelling of NO2 line positions[END_REF]

Spin-rotation splittings

The SR splittings due to the S= ½ electronic spin of the 2 A1 ground electronic state are a characteristic feature of the NO2 rovibrational spectrum. The SR splittings can provide an additional criterion for the assignments. Due to the low pressure of the recordings, line profiles are mostly Doppler limited (HWHM of 0.0054 cm -1 ) and SR doublets with splitting as low as 0.003 cm -1 could be resolved, though the accuracy of experimental positions in this case may be lower than that for isolated line. In general, SR splittings smoothly depend on N and Ka rotational quantum numbers increasing with Ka and decreasing with N for a given Ka value.

This is indeed what it is observed for the (103) state as illustrated on Fig. 3.

The resonance interaction between the (103) and (080) dark state destroys the smooth dependence of their SR splittings on the N rotational quantum number, as illustrated in Fig. 4.

Note that, within the resonance range (24 < N <40), the measured and calculated SR splittings of the Ka= 5 (103) and Ka= 4 (080) interacting energy levels deviate importantly from those of Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. We cannot rule out that this perturbed behavior combined with a limited set of observations resulted in distortion of some of the (080) varied SR parameters. The FTS calculated values [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] are compared to our measured and calculated values.

Resonance interactions and intensity transfer

The strong couplings of the ( 122) and ( 080 81 transitions belonging to the highly excited 8ν2 bending band were assigned for the first time (Fig. 7). The corresponding line positions could be reproduced by varying both some diagonal (080) state parameters and the (103)-(080) coupling constants (see Table 2). However, it turned out that some (080) parameters responsible for SR splittings seem to be distorted compared to those derived in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. In fact, all the fitted parameters of the (080) state should be considered as effective parameters allowing to reproduce satisfactorily the (080)-(000) Ka=4 line positions for J values between 23 and 43 (see also next Section). At the final stage of the spectrum assignment, the calculated positions of the Ka= 2 series of the ( 103)-(000) band were found to deviate importantly (up to 0.25 cm -1 ) from their measured values for N between 44 and 54. These line position perturbations were interpreted as due to an additional resonance interaction between (103) and the (410) vibrational dark state at 5930.66 cm -1 [START_REF] Delon | Laser induced dispersed fluorescence spectra of jet cooled NO2: the complete set of vibrational levels up to 10,000 cm -1 and the onset of the à 2 B2-2 A1 vibronic interaction[END_REF]. Although affecting a limited range of N values, the (103)-(410) resonance results in a strong (48%) resonance mixing for the (103) 50 2 49 SR energy levels and is confirmed by the observation of 3 transitions reaching the 50 3 47 SR upper levels of the (410) state.

Line intensity modeling

The absorption line intensity, Sb←a(T) of a b←a vibration-rotation transition (in cm/molecule), is given by:

← = !" # ← $%& (!") * +, ⁄ . , /1 -234 -ℎ6# ← 7 ⁄ 89 ← , (3)
where T is the temperature in K, C is the isotopic abundance (C= 0.991616 for the main 14 N 16 O2 isotopologue), νb← a is the wavenumber of the vibration-rotation-spin transition b←a, Ea is the energy of the lower state, c is the velocity of light, h is the Plank constant, k is the Boltzmann constant, Q(T) is the partition function and Wb← a is the transition dipole moment squared. The partition function Q(297 K)= 1.365162 ×10 4 was taken from Ref. [START_REF] Fischer | Total internal partition sums for molecular species in the 2000 edition of the HITRAN database[END_REF].The equation for the transition dipole moment squared of the : ; ; < ; < ; " = ; ← : < < " = transition derived in

Ref. [START_REF] Devi | Diode laser measurements of intensities, N2-broadening, and self-broadening coefficients of lines of the ν2 band of 14 N 16 O2[END_REF] in our case can be written in the following form: In case of a line corresponding to an overlapped SR doublet, as a rule, the intensity value provided by the line profile fitting is more accurate for the sum of the SR doublet than for each of the individual component. Indeed, the line intensity modeling showed a number of large (Meas.-Calc.) deviations for the SR components while the sum of measured and calculated intensities of the blended line agree very well. In these cases of close SR doublets (separation < 0.005 cm -1 ), the calculated intensities may be more accurate than the measured values.

In the FTS study of Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF], the band was analysed from a spectrum of a NO2/NO/ICl mixture where the sum of the NO2 and NO partial pressures was less than 20 %. The band intensity reported in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF], S= (9±4)×10 -21 cm/molecule, is about three times larger than measured in this work (S= 2.96×10 -21 cm/molecule). We do not have a firm explanation of this strong disagreement. We checked that the intensity values derived from our recordings at 0.05 and 1 Torr are consistent within 10 % and are inclined to believe that the NO2 partial pressure might have been strongly underestimated in the gas mixture used in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] (no details on the determination are given in Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] and the value is not provided). New recordings with a new tank of NO2 are suitable for a final checking and for ruling out the possible contamination (by air) or the possible degradation of NO2 in the gas tank used for the CRDS recordings.

The list of assigned transitions of the ( 103)-( 000), ( 122)-( 000), (080-(000) bands as well as 3 extra lines due to the (410)-(000) band is provided as Supplementary Material 1. The list includes measured line positions and their corresponding deviations from the calculated values, measured and calculated intensities followed by vibrational and rotational quantum numbers.

Note that three "dark" bands involved in the analysis are responsible for only 4% of the total measured intensity of the assigned lines. The sum of the measured line intensities for the (122)-( 000), ( 080)-(000), and (410)-(000) bands is 1.03×10 -22 , 1.30×10 -23 and 2.95×10 -25 cm/molecule, respectively, compared to total value of 2.96×10 -21 cm/molecule. The list of the selected experimental lines included into the intensity modeling is also provided in Supplementary Material 2.

Conclusion

The absorption spectrum of the NO2 molecule between 5860 and 6000 cm -1 has been revisited by high sensitivity CRDS. More than 3000 rotational-vibrational transitions were attributed to the (103)-(000), ( 122)-( 000), (080-(000) vibrational bands, while only 1147 transitions were previously assigned [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. About 80 transitions belonging to the highly excited 8ν2 bending band and borrowing their intensities from the resonance coupling with the strong ν1+3ν3 band were observed for the first time. The most significant differences compared to the FTS results of Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] concern the line (and band) intensities which are presently measured to be three times smaller than reported. SR splittings of the ( 103) and (080) interacting energy levels deviate by up to 0.06 cm -1 from those of Ref. [START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]. The observed line positions and intensities were modeled with an accuracy of 0.0023 cm -1 and 3.7%, respectively, close to the experimental uncertainty, and detailed synthetic spectrum is generated limited to the observed upper energy levels. An additional resonance coupling between the (103) and (410) vibrational states was found to perturb Ka= 2 series of the (103) energy levels with N quantum number between 44 and 54.

Fig. 3 .

 3 Fig. 3. Calculated spin-rotation splitting of the energy levels of the (103) vibrational state. The plot is limited to the observed levels.

Fig. 4 .

 4 Fig. 4. SR splittings of the Ka= 5 (103) and Ka= 4 (080) energy levels involved in resonance interaction.The FTS calculated values[START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF] are compared to our measured and calculated values.

Fig. 5 .

 5 Fig. 5.Mixing coefficients for the (103) wavefunctions due to resonance interaction with the (122), (080) and (410) vibrational states.

Fig. 6 .

 6 Fig. 6. Part of the CRDS NO2 spectrum around 5958 cm -1 . Lines of the (122)-(000) and (103)-(000) bands coming on the upper levels in close resonance are indicated. Upper panel: CRDS spectrum (P= 0.05 Torr) Lower panel: Simulated spectrum The strong (103)-(080) resonance induces a maximal mixing of about 48% for N= 35.

Fig. 7 .

 7 Fig. 7. Part of the CRDS NO2 spectrum near 5986 cm -1 . Weak lines assigned to the 8ν2 band are indicated.

F

  are the expansion coefficients determining the eigenfunction of the effective Hamiltonian for the upper and lower vibration-spin-rotation states respectively, I =, = ; , , ; are the functions describing the intensity redistribution between transitions with different spin components, M103 is the effective dipole moment parameter, L M F , , < is equal to the 10=<|= ; < Clebsh-Gordan coefficient. The explicit equation for I =, = ; , , ; is given in Ref.[START_REF] Devi | Diode laser measurements of intensities, N2-broadening, and self-broadening coefficients of lines of the ν2 band of 14 N 16 O2[END_REF].The main parameter in the transition moment series (M1=1.12592(80)×10 -3 Debye), was sufficient to reproduce the selected set of 713 experimental intensities with an rms deviation of 3.7%. The very small quoted error bar corresponds to the statistical error of the fit, the real error bar being considerably larger, probably on the order of 10 %). The agreement of the CRDS and simulated spectra is illustrated on Figs. 1, 6 and 7. It is worth underlining that the intensity of the weak lines of the dark bands resulting from an intensity transfer from the (103)-(000) band are very well reproduced (see Figs. 6 and 7) while all transition moment parameters of the (122) and (080) dark states were fixed to zero.

Scheme of HVR+HSR,V-diagonal block:

  .

		(103)		(122)	(410)	(080)
	(103) HVR+HSR	H C	H C	H C
	(122)	H C		HVR+HSR
	(410)	H C			HVR+HSR
	(080)	H C			HVR+HSR
					(V1,V2,V3)
				N=J-1/2 N=J+1/2
	(V1,V2,V3)	N=J-1/2 HVR+HSR N=J+1/2 HSR	HSR HVR+HSR

Scheme of H C , V-off diagonal block:

Table 1 .

 1 Summary of the assignments

	State	Vib. term, cm -1	Number of lines	Nmax	Kamax
	(103)	5984.704	2878(1087 b )	59(47 b ) 13(8 b )
	(122)	5898.94 a	192(60 b )	45(34 b )	5
	(080)	5965.61 a	81	47	4
	(410)	5930.66 a	3	50	3

Notes:

a Vibrational term value obtained by LIDFS

[START_REF] Delon | Laser induced dispersed fluorescence spectra of jet cooled NO2: the complete set of vibrational levels up to 10,000 cm -1 and the onset of the à 2 B2-2 A1 vibronic interaction[END_REF]

b Value from Ref.

[START_REF] Miljanic | New high resolution analysis of the ν1+3ν3 band of nitrogen dioxide[END_REF]

Table 2 .

 2 Spectroscopic

	NO2 in cm -1	parameters for the {(103),(122),(410),(080)} interacting vibrational states of
	Parameter				(000) a	(103)	(122)	(410)	(080)
	Ev				0		5984.7041266(1721) 5984.705 b	5898.94 b	5930.66 b	5965.61 b
	A	8.00235469	7.41131179(2600)	8.3329234(4700)	8.653730(7800)	12.5472741(1700)
	(B+C)/2	0.422074669 0.4112220702(7200) 0.412461271(3600) 0.41248350(2700) 0.40723230(3100)
	(B-C)/4(10 -2 )	0.58160645	0.60155475(4300)	0.620654(1600)	0.564 c	0.8308 c
	ΔK (10 -2 )	0.26878757	0.2392589(1100)	0.220699(1900)	1.18 c
	ΔNK (10 -4 )	-0.196822	-0.2986780(9900)	-0.484637(1600)	-0.219 c	-3.66307(1900)
	ΔN (10 -6 )	0.2992447	0.3160513(1000)	0.311 c	0.302 c
	δK (10 -5 )			0.40547	0.691033(4500)	42.89315(7000)
	δN (10 -7 )	0.3192774	0.3621363(9100)	0.332 c	0.153 c
	HK(10 -5 )	0.3031569	0.285941(1200)	3.030 c
	HKN(10 -7 )		-0.27044	-0.262 c	-0.261 c
	HNK(10 -10 )			0.2995	0.152 c	0.151 c
	HN(10 -12 )			0.2866	1.126 c
	hK(10 -7 )			0.29297
	hKN(10 -10 )			-0.3637
	hN(10 -12 )			0.1057	0.246 c	0.246 c
	LK(10 -8 )		-0.51104	-0.58591(1200)	1.43 c	-6.90 c
	LKKN(10 -10 )			0.35117	-1.79264(7300)	0.301 c	0.301 c
	LKN(10 -12 )			0.12158	0.138 c	0.138 c
	PK(10 -11 )				0.867	1.12975(2900)
	QK(10 -14 )			-0.8439
							Spin-rotational parameters
	εaa		0.180353	0.15764945(9200)	0.1988798(3000)	0.77205(8100)
	(εbb+εcc)/2(10 -2 )	-0.1460137	-0.1611325(4400)	-0.173315(1800)	-0.1619 c	0.15282(1700)
	(εbb-εcc)/4(10 -3 )		0.858985	0.943954(6200)	0.853 c	-11.1645(9400)
	δKS (10 -6 )			0.3769
	δNS (10 -7 )				0.244
	ΔKS (10 -3 )		-0.17606	-0.1594140(7700)	-0.241 c	-0.697 c
	ΔNS (10 -9 )			0.6322
	ΔNKS (10 -5 )			0.1678	0.280935(1200)
	ΔKNS (10 -5 )		-0.10775	0
	HKS(10 -6 )			0.29673	0.3096 c	0.309 c
	LKS(10 -9 )		-0.35689	-0.398 c	-0.398 c
	Coriolis resonances
		Parameter	(103)↔(122)	(103)↔(080)	(103)↔(410)
		C 2	0(10	-1 )	-0.4561674(3200)	0.0602384(2000)
		C 2	KK (10 -3 )	0.922150(5600)
		C 2	KKK (10 -3 )	-0.095351(9900)
		C 2	NK (10 -6 )	-0.187088(2100)	-0.436370(4700)
		C 2	KKN (10

Acknowledgements

This research is supported by CNRS (France) in the framework of the Laboratoire International Associé SAMIA (Spectroscopie d'Absorption des Molécules d'Intérêt Atmosphérique). This work was performed in the frame of the LabexOSUG@2020 (ANR10 LABX56). Part of the work related to the modeling of the spectrum was performed under the financial support of the Russian Science Foundation (No. 18-35-00575). We thank Prof. Perevalov V. I. (IAO SB RAS) for careful reading and discussing the manuscript.