Julius N Domfang Ngnekou

Yves Nadot

Gilbert Henaff

Julien Nicolai

Wen H Kan

Julie M Cairney

Lionel Ridosz

Fatigue properties of AlSi10Mg manufactured by Additive Layer Manufacturing

Keywords: ALM, AlSi10Mg, Fatigue, Kitagawa, T6

This work shows the impact of microstructure and defect on the fatigue life of an AlSi10MgSi manufactured by Additive Layer Manufacturing (ALM). Samples were manufactured via a laser powder-bed process: two configurations (0° and 90°) are considered in order to evaluate the impact of the building direction on fatigue properties. 3D X-Ray tomography was used to characterize the defect population. The microstructure was characterized by considering four parameters: melt-pools, crystallographic grains, dendritic structure and precipitates. The fatigue properties were determined by establishing S-N curves for machined samples, with and without T6 heat-treatment, at R= -1 under tensile loading. The size of the defect responsible for the fatigue failure was determined in each sample so as to establish a relationship between the fatigue limit and the defect size using Kitagawa-type diagrams. In order to study a broader range of defect size, artificial defects were introduced using electrodischarge machining. The following observations are made: (i) after heat-treatment, the boundaries of melt-pools and the dendritic structure are not visible. Si is organized into pure precipitates homogeneously distributed over space and intermetallic Fe based compounds are observed in the form of needles; (ii) The impact of building direction on fatigue life is seen only after T6 heat treatment; (iii) An improvement of the fatigue resistance is observed after T6, in spite of the presence of intermetallic needles; (iv) The fatigue limit is controlled by the

defect size both before and after T6 heat treatment, and it seems that the influence of T6 decreases as the defect size increases.

Introduction

Additive manufacturing is considered to be a disruptive technology, offering the possibility of producing topographically optimized parts with a complex shape [START_REF] Harun | A review of powder additive manufacturing processes for metallic biomaterials[END_REF][START_REF] Watson | A decision-support model for selecting additive manufacturing versus subtractive manufacturing based on energy consumption[END_REF][START_REF] Bose | Additive manufacturing of biomaterials[END_REF][START_REF] Bose | Surface modification of biomaterials and biomedical devices using additive manufacturing[END_REF][START_REF] Eyers | Industrial Additive Manufacturing: A manufacturing systems perspective[END_REF][START_REF] Olakanmi | A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties[END_REF]. It is changing the nature of manufacturing in fields such as biomaterial, automotive and aeronautical engineering. In the aeronautical context, the introduction of such an innovative process would require material qualification in which the control of the fatigue resistance is crucial [START_REF] Romano | Qualification of AM parts: Extreme value statistics applied to tomographic measurements[END_REF][START_REF] Portolés | A qualification procedure to manufacture and repair aerospace parts with electron beam melting[END_REF][START_REF] Mardaras | Airbus approach for F&DT stress justification of Additive Manufacturing parts[END_REF]. It is, therefore necessary to understand the relationship between the microstructure inherited from the manufacturing process and the fatigue behavior. The impact of the heat treatment is also important. This information will enable the building strategy to be optimized to maximize the local fatigue resistance. In this work, the relationship between microstructure, the defect and the fatigue behavior is addressed for the case of an AlSi10Mg alloy produced by the Additive Layer Manufacturing (ALM) process.

Many studies on AlSi10Mg alloy have focused on the characterization of specimens machined from built parts [START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF][START_REF] Kempen | Process optimization and microstructural analysis for Selective Laser Melting of AlSi10Mg[END_REF][START_REF] Ming | Inclusion, porosity, and Fatigue of AlSi10Mg Parts Produced by Selective Laser Melting[END_REF][START_REF] Domfang Ngnekou | Influence of defect size on the fatigue resistance of AlSi10Mg alloy elaborated by selective laser melting (SLM)[END_REF][START_REF] Takata | Change in microstructure of selectively laser melted AlSi10Mg alloy with heat treatments[END_REF], and this has led to a quantitative description of the microstructure along five characteristic parameters: (i) the melt-pools (ii) the dendritic structure, (iii) the grains, (iv) the precipitation structure and (v) the defect population. It has been observed that melt-pools, dendritic structure and grains are strongly anisotropic depending on the building direction [START_REF] Takata | Change in microstructure of selectively laser melted AlSi10Mg alloy with heat treatments[END_REF].

According to Domfang et al. [START_REF] Domfang Ngnekou | Influence of defect size on the fatigue resistance of AlSi10Mg alloy elaborated by selective laser melting (SLM)[END_REF], after a T6 heat treatment, the melt-pool boundaries are no longer visible via optical microscopy (without etching) due to the reorganization of the Si phase which provides the surface contrast. Takata et al. [START_REF] Takata | Change in microstructure of selectively laser melted AlSi10Mg alloy with heat treatments[END_REF] observed no influence of T6 heat treatment on the crystallographic anisotropy. Brandl et al. [START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF] demonstrated the impact of microstructure anisotropy, T6 and platform temperature on fatigue behavior. According to these authors, the impact of the anisotropy from the sample build orientation on the fatigue strength is observed when the building platform is maintained at 30 °C. By coupling a platform temperature of 300 °C and a post-fabrication T6 heat treatment, they found no difference between different growth directions. Maskery et al. [START_REF] Maskery | Fatigue performance enhancement of selective laser melted aluminium alloy by heat treatment[END_REF] evaluated the impact of a T6 heat-treatment on the fatigue performance of samples with an as-built manufactured surface and showed that the T6 treatment improved the fatigue limit. Aboulkhair et al. [START_REF] Aboulkhair | Improving the fatigue behaviour of a selectively laser melted aluminium alloy: Influence of heat treatment and surface quality[END_REF] also showed that the T6 heat treatment improves the fatigue resistance but only to a small degree. As the additive manufacturing process involves numerous parameters that potentially affect the microstructure and the residual stresses, it is important to bring up the material to a standardized microstructure so that one material can be compared to another. In that purpose, for aluminum alloys, the microstructure following a T6 heat treatment can be considered as a reference for this type of process. However, only a few studies so far have quantified the specific impact of defect size on the fatigue limit. Beretta and Romano [START_REF] Beretta | A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes[END_REF] recently published a literature survey on this topic, analyzing the impact of defect size on fatigue limit by means of Kitagawa-type diagrams. The fatigue limit obtained on machined samples fatigued at R=-1 was compared to the one determined for a cast Al-Si alloy with different Secondary Distance Arms Spacing values (SDAS). It appears that the ALM material is a little more tolerant to defects than the cast alloy. At R=0.1, according to Romano et al. [START_REF] Romano | Fatigue properties of AlSi10Mg obtained by additive manufacturing: Defect-based modelling and prediction of fatigue strength[END_REF], and based on results on machined surfaces [START_REF] Siddique | Very high cycle fatigue and fatigue crack propagation behavior of selective laser melted AlSi12 alloy[END_REF][START_REF] Buchbinder | Generative Fertigung von Aluminiumbauteilen für die Serienproduktion[END_REF], the selectively melted AlSi10Mg is as defect-tolerant as the equivalent cast heattreated alloy. According to Maskery et al. [START_REF] Maskery | Fatigue performance enhancement of selective laser melted aluminium alloy by heat treatment[END_REF], when ALM samples are tested with an asbuilt surface, the relative drop in fatigue resistance could reach 40%.

In this work, the impact of defect size on the fatigue limit is studied for as-machined samples with and without T6 heat treatment, by decoupling the effect of the microstructure anisotropy.

The approach consists of the evaluation of the fatigue resistance of XY and Z machined samples with or without T6. Firstly, the S-N curves at R=-1 are established, and thereafter the fatigue limit is quantified by a step-by-step method as a function of defect size. After the identification and characterization of the critical defect on the fracture surface, the Kitagawa diagram is plotted and discussed for the materials being studied. For the P1 production, the fabrication was operated under deliberately sub-optimal parameters. The layering in such a case is performed by means of a scraper. All P1 specimens have been machined from XY bars built on an aluminum platform maintained at 150°C. In order to release the stresses induced by the process, one hour post-processing heat treatment was performed at 210°C.

Nomenclature

For P2 production, the bars were fabricated by operating the machine under standard optimized parameters. The layering stage of the process is also performed by means of a scraper. P2 bars were built in two directions, namely XY and Z as defined in Figure 1-a. The platform was maintained at 200 °C and the recommended two hours stress relaxation treatment was performed at 300 °C.

The bars built in both P1 and P2 productions suffer from surface integrity effects such as the roughness and an expected population of under-layer defects due to edge lasing [START_REF] Yang | Porosity formation mechanisms and fatigue response in Al-Si-Mg alloys made by selective laser melting[END_REF][START_REF] Damon | Process dependent porosity and the influence of shot peening on porosity morphology regarding selective laser melted AlSi10Mg parts[END_REF].

Thus, for both P1 and P2 productions, the fatigue test specimens were machined (MA) from these bars in order to avoid the aforementioned process-induced surface effects. The fatigue test specimen geometry is shown in Figure 1-b. The samples were tested in the as-machined condition, with no surface polishing. After machining, some specimens were subjected to a T6 heat treatment under the conditions listed in Table 2. Table 3 indicates the different conditions in which the samples where produced and heat-treated.

In order to characterize the material, cubic samples were removed from the bars using electric discharge machining (EDM) and polished along three orthogonal directions using SiC paper (1000, 2000, and 4000 grades) and then with diamond suspensions (3 µm and 1 µm size).

Microstructural characterization of these cubic samples was carried before and after heat treatment (HT). The surfaces were then observed using an optical microscope without etching. The chemical composition and the microstructure of the samples were studied using a JEOL-7001F-TTLS (with operating voltage of 5 to 30 kV) high resolution scanning electron microscope (SEM), equipped with secondary and backscattered electron detectors and energy dispersive X-ray spectrometer (EDS). So, the composition of the specimen at the surface was quantified using EDS. As reported in Table 1, the composition determined is in accordance with the DIN EN 1706:2010 standard. Using EDS technique, the non-detection of some elements, especially that of Fe and Mn, confirms that the materials are within the recommended specifications as they would have been detected if they were in amounts exceeding their allowable limits. The local structure of the material was studied by transmission electron microscopy (TEM) using a JEOL 2200FS equipped with an omega filter. TEM samples were prepared using focused ion beam (HELIOS-Dual Beam equipped with an electron backscatter diffraction (EBSD) detector.

P2-XY-MA 0.7 Yes P2-XY-MA-T6 1.2 Z No P1-Z-MA 1.0 Yes P2-Z-MA-T6 1.0
In order to characterize the crystallographic orientation of grains, each sample was first coldmounted in epoxy resin and ground by using SiC abrasive papers. Those samples was then fine polished using 3 µm and 1 µm diamond suspensions followed by OP-S colloidal silica suspension. The morphology and orientation of Al grains were characterized by EBSD technique. Each EBSD scan was conducted on a Zeiss Ultra field emission gun scanning electron microscope equipped with an EBSD detector was used for the EBSD scans using the following condition: an accelerating voltage of 20 kV, a step-size of 0.8 µm, an aperture of 120 µm, and a scan area of 600 µm x 600 µm. The indexing rates for all scans were above 90 %. The data analysis was carried out using Oxford Instruments HKL Tango and Mambo software. Each dataset was cleaned by applying wild spikes and 3-nearest neighbours once. A 10 o misorientation angle and a grain boundary completion angle down to 0 o were both used to define grain boundaries. If a section(s) of a grain was found to lie outside the borders of the 600 µm x 600 µm EBSD scan area (i.e. the grain is incomplete), its grain size was then approximated by multiplying the calculated grain size by a factor of 2 (if it intersects one border), or a factor of 4 (if it intersects two borders).

Finally, in order to characterize the defect population, two cylindrical specimens of 3 mm diameter and 10 mm length were machined from the gauge section of the fatigue test samples.

These samples were analyzed by X-ray UltraTom® tomography with the following configuration: a 150 kV source with a resolution of 5 µm per voxel. The analysis of the defect distribution in the bulk of the samples was carried out with the commercial software Avizo.

Mechanical testing

Tensile tests were carried out in accordance with the standard NF EN 10002-1, using an Instron 4505 load-frame with a displacement rate of 0.22 mm/min at room temperature. The elongation was measured by an extensometer, with a gauge length of 12.5 mm. Two samples were tested for each condition. Vickers micro hardness was also measured in the core of each P2 samples as an average of 16 indentations under a 50 mN load.

Fatigue tests were conducted at room temperature on a resonance machine at a frequency of 80 Hz and a load ratio of R=-1. A 5 Hz drop in frequency was considered as a criterion for failure detection. This drop corresponds to a crack depth of half the diameter of the specimen.

The fatigue limit is defined as the amplitude of load, that is to say, the maximum load minus the average load. In this study, a step-by-step method described by Iben Houria et al. [START_REF] Houria | Experimental investigation and modeling the fatigue life of a cast aluminium alloy A356-T6 under multiaxial loading[END_REF] was used to determine the fatigue limit at 10 6 cycles. This is the only way to evaluate the fatigue limit in presence of a natural defects. It is assumed that no significant loading history effect is introduced by the loading steps applied prior to the step leading to failure, as shown by Roy et al. [START_REF] Roy | Multiaxial fatigue behaviour of A356-T6[END_REF] for the case of a A356 cast Al-alloy. In order to plot a Kitagawa-type diagram, the fatigue limit is determined for each specimen using the following rules:

 when the specimen fails during the first step, a Basquin equation is used to evaluate the fatigue limit. The parameters of Basquin equation are determined via experimental points on the S-N curves averaged by the least-squares method.

Eq.1  when the specimen fails after one or several loading steps, the fatigue limit is determined by a linear interpolation according to the following equation: Eq.2

Residual stresses were quantified using the X-ray diffraction according to the AFNOR NF EN 15305 standard. The measurement of residual stresses were performed at the surface of samples after fatigue loading. These measurement were carried out at the surface, in the axial and circumferential direction. The point of analysis is furthermore placed as far as possible from the fracture surface of the specimen. Four specimens were considered: two in the XY direction, and two in the Z direction. For both pairs of samples, one was not subjected to a T6 heat treatment.

Results

Microstructure

The microstructure of the P2 material was characterized along the four main characteristic features, namely: the melt-pools (1), dendritic structure (2), crystallographic grain (3), and silicon precipitates and intermetallic needles (4).

(1) The melt-pools, which can be geometrically described by their length, width and height.

These melt-pools reflect the imprint generated by the laser beam during the melting of the deposited powder. As shown in Figure 2-a, these melt-pools are strongly anisotropic in shape.

The mean dimensions of the melt-pool are (length: 600µm, width: 150µm and height in the Z direction: 80 µm). A previous study of the melt-pool boundaries by Thijs et al. [START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF] reported that the melt-pools consist of an heterogeneous distribution of eutectic silicon in the alphaphase of aluminum. In Figure 2-b it can be seen that, after T6 heat treatment, the melt-pool boundaries are no longer visible, presumably due to the demixing and coalescence of silicon in the aluminum matrix at sub-eutectic temperatures. According to Li et al. [START_REF] Li | Effect of heat treatment on AlSi10Mg alloy fabricated by selective laser melting: Microstructure evolution, mechanical properties and fracture mechanism[END_REF], a high solution-annealing temperature in the range of 450°C to 550°C leads to coarse distribution of silicon particles, typically around 2 to 4 µm. Additional growth of these particles was seen during artificial aging. Arm Spacing (DAS) was observed to be between 0.5 and 2 µm, which is significantly smaller than the characteristic SDAS parameter in cast Al-Si alloys (30 to 100 µm depending on the cooling rate). Previous studies have shown that this parameter has a large influence on the fatigue behavior [START_REF] Roy | Multiaxial fatigue behaviour of A356-T6[END_REF][START_REF] Houria | Influence of casting defect and SDAS on the multiaxial fatigue behaviour of A356-T6 alloy including mean stress effect[END_REF][START_REF] Rotella | Influence of natural defects on the fatigue limit of a cast Al-Si alloy[END_REF][START_REF] Linder | The influence of porosity on the fatigue life for sand and permanent mould cast aluminium[END_REF][START_REF] Yi | Effect of Fe-content on fatigue crack initiation and propagation in a cast aluminum-silicon alloy (A356-T6)[END_REF][START_REF] Wang | Fatigue behavior of A356-T6 aluminum cast alloys. Part I. Effect of casting defects[END_REF]. According to Wang et al. [START_REF] Wang | Fatigue behavior of A356-T6 aluminum cast alloys. Part I. Effect of casting defects[END_REF], in the absence of defects a refined SDAS leads to the high fatigue life. (3) Figure 4 shows that the morphology of the crystallographic grains is strongly anisotropic, and those grains were seem to grow epitaxially towards the centers of the melt-pools, as previously observed by L. Thijs et al. [START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF]. The grain growth was observed to encompass one to three melt pools. In Figure 4, the impact of T6 heat treatment can be observed. The T6 heat treatment does not strongly affect the grain structure; this observation is in agreement with the previous observations made by Takata et al. for AlSi10MgSi alloy prepared by ALM [START_REF] Takata | Change in microstructure of selectively laser melted AlSi10Mg alloy with heat treatments[END_REF] and by Wang et al. for cast A356 [START_REF] Wang | Fatigue behavior of A356-T6 aluminum cast alloys. Part I. Effect of casting defects[END_REF].

Defect population

The defect population was characterized using the computed X-ray tomography. The sources images was segmented by gray level. The defects was then extracted and analyzed. The top images in Figure 7 show that both P1 and P2 production leads to numerous and randomly distributed defects. P1 production contains 6666 defects while P2 contents 648 for the same volume sampled. It also suggested in Figure 7 that the defect shape can be different, so that for each defect, the shape was quantified using a sphericity index defined as follows:

Eq.3

A sphericity index of 1 represents the case of a pure spherical defect [START_REF] Damon | Process dependent porosity and the influence of shot peening on porosity morphology regarding selective laser melted AlSi10Mg parts[END_REF]. The defect size is given by the diameter of the equivalent sphere. Thereby, sphericity index was plotted as a function of the defect size for P1 and P2 productions as shown in Figure 6. The P1 production leads to defects two times larger than the P2 production. Figure 6 further indicates that the process parameters used for processing both P1 and P2 samples leads to the formation of mostly spherical defects, except for some large defects where the shape is not represented by a sphere.

Tensile properties and hardness

Figure 7 presents engineering stress-strain curves for the P1 and P2 productions. From these curves, the mechanical properties such as UTS, A% and YS were derived and are reported in Table 5. For the non-heat-treated materials, it is observed that the UTS value is higher for Z samples compared to XY. After T6 heat treatment, the UTS shows a scatter in the range of 300 MPa to 345 MPa, and, a strong reduction of the ductility of P1 production is noticed. For non-heat treated samples, the building direction strongly impacts the tensile elongation A% whereas the yield stress (YS) is not strongly affected. For P2 production, after the T6 heat treatment, there is no major difference in the ductility (A%) for both XY and Z samples. In addition, an increase in hardness of the material followed by an increase in yield stress is observed. This increase of micro-hardness after the T6 heat treatment, diminishes the work hardening capability of the material for P2 production, regardless of the building direction.

Likewise, the T6 heat treatment leads to a large scatter in hardening. Figure 8 shows that the indent size varies between 7 and 10 µm without heat treatment and is reduced to 5 µm after heat treatment.

S-N curves

Figure 9 presents the S-N curves for P1 production with only XY samples that was subjected to the T6 heat treatment, and P2 production with XY and Z samples, with and without T6.

Symbols with arrows indicates the fatigue limit determined at one million cycles by the stepby-step method while each other symbols correspond to sample failure. There is no significant difference on the fatigue resistance between the P2-XY-MA and P2-Z-MA samples. A 20% increase in the fatigue limit is observed for P2-XY-MA in comparison to P2-XY-MA-T6, while more than 45% is observed for P2-Z-MA-T6 in comparison to P2-Z-MA. Compared to P1-XY-MA, the fatigue limit of the P2-XY-MA samples is improved by about 40%.

Examination of the fracture surfaces, as shown in Figure 9, suggests that the significant increase in fatigue limit between P1 and P2 is due to a reduction in the critical defect size. An increase in the fatigue resistance is observed after T6 despite the presence of iron needles, which is known to degrade the fatigue properties in cast Al-Si alloys [START_REF] Gao | The effect of porosity on the fatigue life of cast aluminium-silicon alloys*[END_REF]. As P2 specimens contain the same type of critical defects and negligible residual stresses, this improvement in fatigue strength after heat treatment can be attributed to the strengthening of the matrix via the applied T6 treatment. However, it is also observed that such a peak hardening treatment leads to a highly pronounced difference in fatigue strength between XY and Z orientations.

Influence of defect size on the fatigue limit

The examination of the fracture surfaces as shown in Figure 10, indicates that the fatigue cracks always initiate from a defect. In order to plot the corresponding Kitagawa-type diagram, the defect size was assessed using Murakami's parameter ) [START_REF] Murakami | Effects of defects, inclusions and inhomogeneities on fatigue strength[END_REF]. Based on Iben Houria works [START_REF] Houria | Experimental investigation and modeling the fatigue life of a cast aluminium alloy A356-T6 under multiaxial loading[END_REF], Figure 11 explains in detail the criteria used to estimate the defect size as a function of its location with respect to the free surface and/or the presence of other defects in the vicinity of the considered defect. Based on this approach, examination of the fracture surfaces indicates that the P2 production introduces pore-type defects ranging from 40 µm to 100 µm. These defects are all located at the specimen surface or in sub-surface. The critical defect size measures by the Murakami parameter is higher than the maximum defect size provided by the tomography analysis. This could be partially explained by the fact that the criterion involve to quantify defect size on the fracture surfaces includes the contribution of the ligaments especially in the case of sub-surface defect.

In Figure 12, the fatigue limit is plotted as a function of the critical defect size derived from the observation on fracture surfaces. In order to enlarge the scope of this study, artificial spherical defects were introduced by EDM in specimens. For both non-treated and T6 treated materials, this Kitagawa-type diagram confirms that the fatigue limit is mainly sensitive to defect size. These data also confirm the contribution of the anisotropy effect noticed on S-N curves in Figure 9. The impact of the T6 heat treatment is however less pronounced for larger defects. The Figure 12 also shows that for a given size of a natural or an artificial defect, there is no influence of defect type on the fatigue limit, so that the results obtained for artificial defects can be extrapolated to natural.

Discussion

In this work, the AlSi10Mg alloy elaborated by additive manufacturing were described using five characteristic parameters as presented in the section 3.1. and 3.2. This paper exhibits the impact of the T6 heat treatment on the microstructure and it influence on the mechanical properties such as tension, hardness and fatigue.

Concerning the microstructure, it is observed a disappearance of the melt-pools boundaries and the appearance of pure silicon precipitates and iron contained intermetallic. In fact, these are the consequences of the diffusion and coalescence of particles during the heating at high temperature (540°C) followed by a rapid quenching.

Looking to the tensile properties, as the value of A% is higher for P2 than P1, it is suggested that the loss in the elongation is due to the fact that the P1 production contains much more number of defects than the P2 production. This analysis is consistent with the findings of Kempen et al. [START_REF] Kempen | Mechanical Properties of AlSi10Mg Produced by Selective Laser Melting[END_REF] who established that the ductility is related to the numbers of defects determined from the analysis of fracture surfaces. Furthermore, according to the theoretical models such as the one proposed by Rice and Tracey [START_REF] Rice | On the ductile enlargement of voids in triaxial stress fields *[END_REF], the higher the number of defects leads to the higher probability of coalescence of these defect i.e. in A% values. As it is well known that the T6 heat treatment impacts the mechanical properties of aluminum [START_REF] Nadot | Influence of casting defects on the fatigue limit of nodular cast iron[END_REF][START_REF] Roy | Multiaxial Kitagawa analysis of A356-T6[END_REF], this papers brings the fore the fact that after T6 heat treatment, there is a global increase of A% and all the results of P2 production are equivalent regardless the building direction. This last might be due to the the microstructural homogenization due to the T6 heat treatment, as it can be seen in Figure 2. This explanation suggests that that the obtained microstructure annihilates the potential crystallographic grain impact, as the Figure 4 shows a strong anisotropy of the grains.

Concerning the micro hardness, a significant increase is noticed on average, which is due to the structural hardening cause by the T6. Table 5 shows that the data present a large scatter after T6 heat treatment. Figure 5 shows coarse Si particles surrounded by Al. As the silicon is harder than aluminum [START_REF] Lin | Effects of solution treatment on microstructures and micro-hardness of a Sr-modified Al-Si-Mg alloy[END_REF], the presence of those silicon particles surrounded by aluminum explains the fact that the value of micro-hardness differs in the material. The resulting scatter is more important for T6 material than non T6 one, because for T6 material, Si particles are coarser and also the surrounded Al, which would increase the probability to indent in pure Al or in Si.

In terms of fatigue, it was observed that the T6 heat treatment leads to an increase in the fatigue resistance, which is a function of the building directions. According to Brandl et al. [START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF], the fatigue improvement due to T6 HT is the consequence of the spheroidization of eutectic silicon particles that would limit crack initiation and propagation. However, according to Aboulkhair et al. [START_REF] Aboulkhair | Improving the fatigue behaviour of a selectively laser melted aluminium alloy: Influence of heat treatment and surface quality[END_REF], the T6 HT would reduce the hardness, which would in turn account for the improvement in ductility and fatigue behavior. However, in the present study, it was observed that a T6 HT leads to a 20% increase in hardness for P2-XY samples, which can be correlated to a 20% increase in the fatigue limit. TEM analysis illustrated on Figure 13 shows that dislocations are locked by the Si precipitates and even intermetallic particles that appear after the T6 heat treatment. It is therefore suggested that these precipitates and intermetallic needles are not sheared by the fatigue crack. Even though the T6 heat treatment increases the fatigue strength, it further reveals an influence of the building direction which is not yet fully explained in the literature. As shown in this study, the T6 heat treatment makes all the sources of anisotropy in microstructure disappear except the grains. Figure 14 presents a sketch to explain the differences in fatigue resiatance observed between XY and Z after T6. In fact, during fatigue in Z T6 specimen, the initiation phase could be enhanced by the fine grain size, contrary to XY T6. This phenomenon is still valid without T6 but Z as the eutectic silicon particles make easier the fatigue crack propagation [START_REF] Yi | Effect of Fe-content on fatigue crack initiation and propagation in a cast aluminum-silicon alloy (A356-T6)[END_REF], the presence of a silicon that decorates the melt-pools boundaries should be taken into account when the T6 is not performed. As a consequence, all things equal otherwise, the impact of melt-pools on the fatigue life could be studied as the SDAS in cast AlSi alloys. The reduction in fatigue strength would therefore be controlled by the size of the melt pools. Thus, prior to T6 heat treatment, in Z specimens, the beneficial effect of the grain morphology could be counterbalanced by the presence of the large meltpools. Despite the significant role of the microstructure on the fatigue behavior, it has been shown that the defect size is the first order parameter that controls the fatigue limit. Given that engineering parts elaborated by ALM process will have to admit a certain size of defect, it is then necessary to get further insights into the relationship between the fatigue limit and the defect size. With this aim, the Kitagawa diagram is plotted in log-log scales. Furthermore, in order to compare to classical damage tolerance approach, the LEFM prediction is calculated by assuming that defect is equivalent to a pre-existing crack. The fatigue limit is related to the stress intensity factor threshold K th by the following equation:

Eq.4

Were Y is the shape factor of the crack, a is the defect size defined by the parameter.

The assumption of a semicircular crack front shape is considered here, so that Y is supposed to be constant and equal to 0.64. The fatigue limit is then calculated by considering a threshold value =2 MPa × m 1/2 obtained from da-dN/ΔK experimental curves test on a P2-Z-MA sample. Figure 15 exhibits the fatigue limit as a function of the defect size and compared to conventional cast alloy [START_REF] Beretta | A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes[END_REF][START_REF] Houria | Experimental investigation and modeling the fatigue life of a cast aluminium alloy A356-T6 under multiaxial loading[END_REF][START_REF] Roy | Multiaxial fatigue behaviour of A356-T6[END_REF][START_REF] Houria | Influence of casting defect and SDAS on the multiaxial fatigue behaviour of A356-T6 alloy including mean stress effect[END_REF][START_REF] Rotella | Influence of natural defects on the fatigue limit of a cast Al-Si alloy[END_REF][START_REF] Nadot | Influence of casting defects on the fatigue limit of nodular cast iron[END_REF][START_REF] Roy | Multiaxial Kitagawa analysis of A356-T6[END_REF]. Figure 15 suggests that the deviation from LEFM predictions is larger at smaller defect sizes, meaning that small natural defects such as those encountered in this study cannot be considered as a crack propagating in mode I with a long crack threshold of of 2 MPa × m 1/2 . A short crack correction should be applied.

Compared to conventional cast alloys, Figure 15 shows that for defect sizes below 100 µm, the ALM material is more resistant to fatigue.

Figure 15: Fatigue limit as a function of defect size, comparison between additive manufacturing and conventional cast alloys [START_REF] Beretta | A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes[END_REF][START_REF] Houria | Experimental investigation and modeling the fatigue life of a cast aluminium alloy A356-T6 under multiaxial loading[END_REF][START_REF] Roy | Multiaxial fatigue behaviour of A356-T6[END_REF][START_REF] Houria | Influence of casting defect and SDAS on the multiaxial fatigue behaviour of A356-T6 alloy including mean stress effect[END_REF][START_REF] Rotella | Influence of natural defects on the fatigue limit of a cast Al-Si alloy[END_REF][START_REF] Nadot | Influence of casting defects on the fatigue limit of nodular cast iron[END_REF][START_REF] Roy | Multiaxial Kitagawa analysis of A356-T6[END_REF].

Conclusions

This work describes the role of microstructure and defect on the fatigue life of an AlSi10MgSi alloy prepared by Additive Layer Manufacturing. The alloy was characterized and described using the following microstructural parameters: the melt-pools, the dendritic structure, the grains then, the precipitation and intermetallic particles, and the process inherited defects.

Due to T6 heat treatment, the diffusion of silicon in the matrix leads to the disappearance of the dendritic structure and melt-pools boundaries. At the same time pure silicon precipitates and Fe-contained, needle-shaped intermetallic particles are formed.

For non-heat treated machined samples, the tensile properties such as the ultimate tensile strength and ductility are strongly affected by the building direction while the T6 heat treatment tends to annihilate this effect and considerably increase the yield strength and ductility. Concerning the fatigue, two building directions was studied, with and without T6 heat treatment. In that way, the following conclusions can be drawn:

(1) Regardless if material where or not subjected to the T6 heat treatment, the defect size is the first order parameter that controls the fatigue limit.

(2) For non-heat-treated material, there is no impact of the building direction on fatigue resistance.

(3) After a T6 heat treatment, a significant effect of building direction on fatigue life is noticed to the benefit of Z specimen.

(4) Whatever the building direction, the T6 heat-treatment improves the fatigue resistance, especially at small defect sizes.

 It is shown that the microstructure is strongly anisotropic and that both microstructure and defect are process parameters depended.  It is shown that, due to the T6 heat treatment, Si phase is reorganized leading to the disappearance of the melt-pools boundaries that reflect the impact of laser spot and others process parameters. This makes suggest the T6 heat-treated material as a reference for this type of process.  A methodology for defining the defect size responsible to the fatigue failure is proposed and it influence on the fatigue limit is shown using Kitagawa-type diagrams.  In order to apply this study in an industrial context, a defect size sensibility of the fatigue limit is carried out for different microstructures process or T6 inherited, and compared to the LEFM prediction and to that of conventional cast alloys.

Figure 1 :

 1 Figure 1: (a) Position and orientation on the building platform of bars from which fatigue specimens are machined, (b) Fatigue test specimen geometry, one bar corresponds to one specimen.Specimens were fabricated by the ALM method using a pre-alloyed powder with an average

Figure 2 :( 2 )

 22 Figure 2: optical dark field microscopy 3D reconstructions of the microstructure after surface polishing, without etching, (a) without heat treatment (b) after T6 (2) The dendritic structure, shown in Figure 3 (taken along the scanning plane), is characterized by the size of the α-Al matrix surrounded by eutectic silicon. The rapid

Figure 3 :

 3 Figure 3: (a) SEI image without mapping. EDS chemical maps of elements present in the alloy without T6. Distribution of (b) silicon (green), (c) aluminium (red), (d) Magnesium (orange).

Figure 4 :( 4 )

 44 Figure 4: EBSD observations of the grain orientation, (a)3D observation before T6 heat treatment, (b) XZ image after T6 heat treatment.(4) Silicon precipitates and iron-rich needles are observed in the structure after T6 heat

Figure 5 :

 5 Figure 5: (a) SEI image without mapping. EDS mapping of chemical elements present in the alloy after T6. Distribution of (b) silicon (purple), (c) Iron (yellow), (d) aluminium (green), (e) Magnesium (orange).

Figure 6 :

 6 Figure 6: defect characterization of P1 and P2 production. The top images give the special repartition of defects in observed zone while bottom show the number of defect and sphericity distribution related to the equivalent diameter (a) P1 production, (b) P2 production.

Figure 7 :Figure 8 :

 78 Figure 7: influence of the building direction and T6 heat treatment on the tensile properties of ALM AlSi10Mg alloy

Figure 9 :

 9 Figure 9: influence of the building direction, process parameters and T6 heat-treatment on the fatigue properties.

Figure 10 :

 10 Figure 10: SEI images of fracture surfaces and initiation sites. (a) P1-XY-MA-T6, (b) P2-XY-MA, (c) P2-Z-MA, (d) P2-XY-MA-T6 and (e) P2-Z-MA-T6

Figure 11 :

 11 Figure 11: definition of the defect size depending on its location relative to the free surface, D1 and D2 are the diameters of a circles that encapsulates the corresponding defect.

Figure 12 :

 12 Figure 12: Kitagawa type diagram showing the impact of defect size on the fatigue limit after or not heat treatment for two building direction XY and Z

Figure 13 :

 13 Figure 13: TEM bright-field image of a thin foil removed from bulk T6 and fatigue tested specimen. (a) A matrix with a high dislocation density (b) a twinned crystal of silicon containing no dislocations (c) an intermetallic that is also dislocation-lean.

Figure 14 :

 14 Figure 14: sketch explaining the difference observed on fatigue properties between XY and Z, (a) fatigue crack related to the melt-pools size (b) fatigue crack related to the grain size.

Table 1 :

 1 a comparison of the DIN EN specifications of AlSi10Mg and the composition of the studied alloy measured by EDS.

		Al	Si	Fe	Mg		Mn	Zn	T
	DIN EN 1706:2010	Bal	9-11	<0.55	0.2-0.45	<0.45	<0.1	<0.15
	W% EDS measure	Bal	9.55		0.4
	Table 2: T6 conditions
	Steps			Temperature (°C)	Duration (h)	Environment
	Solid solutioning			540		8		Air
	Quenching			20				Water
	Tempering 1			20		24		Air
	Artificial ageing			160		10		Air

Table 3 :

 3

	Production	Platform temperature (°C)	Post process heating (°C) Orientation	T6	Designation	Ra
	P1	150	210	XY	No	P1-XY-MA	/
					No
	P2	200	300	XY

designation of each individual fatigue specimen is used in this paper, depending on the production number, the orientation and whether or not a T6 treatment was applied.

Table 4 :

 4 residual stresses measurement

		Axial stress (MPa)	Circumferencial stress (MPa)
	P2-XY-MA	4	8
	P2-Z-MA	-13	-11
	P2-XY-MA-T6	-39	-55
	P2-Z-MA-T6	-17	-26

Table 5

 5

	: tensile properties and micro hardness
		YS (MPa)	Rp (MPa)	0.02	UTS (MPa) A%	µHV
	P1-XY-MA-T6	/	/		320	1.05	/
		/	/		320	1.1	/
	P2-XY-MA	210	172		325	11	136 +/-28
		208	175		330	11
	P2-Z-MA	195	145		350	8	136 +/-24
		195	145		350	8
	P2-XY-MA-T6	275	/		330	14.3	178 +/-53
		285	/		345	15.7
	P2-Z-MA-T6	280	200		300	14.7	180 +/-50
		255	225		330	15.2
	Cast A356-T6[36-40]	210-300 /		220-330	0.3-4.3	/

Acknowledgement

The authors gratefully acknowledges funding provided by Zodiac Aerospace and French National Research and Technology Association (ANRT). This work partially pertains to the French Government program "Investissements d'Avenir" (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01). This work has been partially supported by « Nouvelle Aquitaine » Region and by European Structural and Investment Funds (ERDF reference: P-2016-BAFE-94/95). The authors acknowledge the facilities, and the scientific and technical assistance, of the Australian Centre for Microscopy and Microanalysis Research Facility at The University of Sydney. Finally the authors would like to thanks M. Monchatre and M. Brochu (Polytechnique Montreal) for performing the da-dN/ΔK experimental curves and Thierry Rouge-Carassat (Zodiac Engineering) for his comment on a present manuscript.


Yang Liu

Tao Wu

Qiang Wu

Weidong Chen

Chenwen Ye

Mengyu Wang

Xingdao He

A novel mid-infrared hollow waveguide gas sensor for measuring water vapor isotope ratios in the atmosphere

Keywords: Hollow waveguide, Gas sensor, Wavelength modulation spectroscopy, Water vapor-isotope ratio Investigation, Writing -original draft Conceptualization, Funding acquisition, Writing -Review

A novel mid-infrared hollow waveguide gas sensor was developed to target H2 18 O, H2 16 O, H2 17 O, and HDO absorption lines at 3662.9196, 3663.04522, 3663.32128, and 3663.84202 cm -1 , respectively, based on wavelength modulation spectroscopy using a 2.73m distributed feedback diode laser. A hollow waveguide fiber with a 5-m length and 1-mm inner diameter was used for gas absorption. A dew point generator with liquid water with known water-isotope ratios was used to calibrate the sensor. Detection limits of 35.18 ppbv, 4.69 ppmv, 60.53 ppbv, and 3.88 ppbv were obtained for H2 18 O, H2 16 O, H2 17 O, and HDO, respectively, in a 96-s integration time, which resulted in isotopic ratio measurement precision of 0.85‰, 0.57‰, and 10.48‰ for δ 18 O, δ 17 O, and δD, respectively. Field measurements of H2 18 O, H2 16 O, and H2 17 O concentration were conducted on the Nanchang Hangkong University campus to evaluate sensor performance.

Introduction

Water isotopes (H2 16 O, H2 18 O, H2 17 O, HDO) exist in various mass and combination forms. Phase transformation results in further fractionation of water isotopes. Light water isotopes are preferentially evaporated, whereas heavy isotopes are preferentially condensed. These phenomena considerably affect atmospheric physical characteristics, such as water migration and water vapor exchange and transmission, in water phase transformation, which is widely used as a climate information index in paleoclimate reconstruction and current water cycle research. In particular, the isotopic ratio in polar ice cores is used to reconstruct past temperature [START_REF] Dansgaard | The abundance of O18 in atmospheric water and water vapour[END_REF][START_REF] Jouzel | Water stable isotopes: Atmospheric composition and applications in polar ice core studies[END_REF]. The isotopic ratio of high-altitude ice cores and stalagmites in middle and low latitudes has been used to reconstruct the paleoclimate and precipitation rate [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF][START_REF] Hoffmann | Coherent isotope history of Andean ice cores over the last century[END_REF][START_REF] Steffensen | High-resolution Greenland ice core data show abrupt climate change happens in few years[END_REF].

Water vapor isotopologues in the upper troposphere and lower stratosphere can act as ideal tracers to test the various mechanisms of stratospheric aridity. Stable isotopes of water exhibit unique advantages in the atmospheric water cycle and atmospheric circulation simulation [START_REF] Sturm | An introduction to stable water isotopes in climate models: benefits of forward proxy modelling for paleoclimatology[END_REF][START_REF] Noone | Comprehensive dynamical models of global and regional water isotope distributions[END_REF].

Isotope ratio mass spectrometry (IRMS) and isotope ratio laser spectrometry (IRLS) are typically used for isotopic ratio measurement. IRMS is a conventional method used for isotope ratio analysis [START_REF] Hofstetter | CO 2 isotope sensor using a broadband infrared source, a spectrally narrow 4.4 μm quantum cascade detector, and a fourier spectrometer[END_REF]. Although the method can satisfy research requirements, it exhibits inherent disadvantages. IRMS instruments are bulky, expensive, and require well-trained technicians for operation, especially for the measurement of water isotopic ratio. Because of the condensation of water samples, the mass spectrometer cannot be directly used for analysis. Water samples should be first chemically transformed into gases, such as H2 and CO2, which can be easily analyzed, to determine the isotopic ratio of 2 H and 18 O [START_REF] Han | Reliable determination of oxygen and hydrogen isotope ratios in atmospheric water vapour adsorbed on 3A molecular sieve[END_REF]. However, H2 is usually produced by reduction of water over hot (~800 °C) uranium [START_REF] Karhu | Catalytic reduction of water to hydrogen for isotopic analysis using zinc containing traces of sodium[END_REF] or zinc [START_REF] Bigeleisen | Conversion of hydrogenic materials to hydrogen for isotopic analysis[END_REF] to determine δ 2 H. These chemical pretreatments are dangerous and time consuming, which limits its application and renders changing the measurement site at any time for real-time online measurement difficult. Because the molecular mass of 17 O 12 C 16 O and 16 O 13 C 16 O are the same, the isotopic ratio of 17 O cannot be measured.

IRLS technology is an alternative isotope measurement technology that exhibits a measurement accuracy that is comparable to the IRMS method. Furthermore, time consuming and chemical pretreatment are not required. Small volume and fast response time are critical for the miniaturization of instruments and online real-time detection. The IRLS method for measuring hydrogen and oxygen isotopes of water vapor has been widely applied to studies climate change, ecological cycle, and biomedicine. Kerstel et al. measured the abundance ratio of hydrogen and oxygen isotopes in low-pressure gas-phase water by means of tunable diode laser spectroscopy (TDLAS) at 1.39 μm [START_REF] Kerstel | Determination of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water by means of tunable diode laser spectroscopy at 1.39 μm[END_REF] and 2.7 μm [START_REF] Kerstel | Simultaneous determination of the 2H/1H, 17O/16O, and 18O/16O isotope abundance ratios in water by means of laser spectrometry[END_REF]. reported a compact, high-finesse optical-feedback CEAS spectrometer (OF-CEAS) for measuring water vapor isotope with a low concentration at 1.39 μm. Castrillo et al. [START_REF] Castrillo | Amount-ratio determinations of water isotopologues by dual-laser absorption spectrometry[END_REF] measured the isotope ratio 17 O/ 16 O in water by offset-frequency locked extended-cavity diode lasers at 1.39 μm with a precision of 0.6 ‰. Gianfrani et al. [START_REF] Gianfrani | Isotope analysis of water by means of nearinfrared dual-wavelength diode laser spectroscopy[END_REF] measured the 2 H/ 1 H, 17 O/ 16 O, and 18 O/ 16 O isotope ratios in water by TDLAS using a pair of 1.4-μm diode lasers. Dyroff et al. [START_REF] Dyroff | Compact diode-laser spectrometer ISOWAT for highly sensitive airborne measurements of water-isotope ratios[END_REF] developed a TDLAS instrument for airborne measurements of 18 O/ 16 O and D/H isotope ratios of water at 2.66 μm. Wu et al. [START_REF] Wu | Kalman filtering real-time measurements of H2O isotopologue ratios by laser absorption spectroscopy at 2.73 μm[END_REF][START_REF] Wu | Measurement of the D/H, 18O/16O, and 17O/16O isotope ratios in water by laser absorption spectroscopy at 2.73 μm[END_REF] measured the isotope ratios D/H, 18 O/ 16 O, and 17 O/ 16 O in water through TDLAS with a 20 m multi-pass cell (MPC) at 2.73 μm. Cui et al. [START_REF] Cui | Analysis of the Stable Isotope Ratios ( 18 O/ 16 O, 17 O/ 16 O, and D/H) in Glacier Water by Laser Spectrometry[END_REF] analyzed the 18 O/ 16 O, 17 O/ 16 O, and D/H isotope ratios in glacier water by TDLAS at 2.73 μm with a 100 m MPC . McManus et al. [START_REF] Mcmanus | Design and performance of a dual-laser instrument for multiple isotopologues of carbon dioxide and water[END_REF] designed a dual-laser instrument for measuring isotopologues of carbon dioxide at 4.3 μm and water at 2.77 μm. Lee et al. [START_REF] Lee | In Situ Measurement of the Water Vapor 18O/16O Isotope Ratio for Atmospheric and Ecological Applications[END_REF][START_REF] Wen | Continuous measurement of water vapor D/H and 18O/16O isotope ratios in the atmosphere[END_REF] measured D/H and 18 O/ 16 O in atmospheric water vapor based on TDLAS at 6.66 μm.

Sayres et al. [START_REF] Sayres | A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere[END_REF] used off-axis cavity-enhanced absorption spectroscopy (OA-ICOS) to measure the abundances of two isotopic molecules, HDO and H2 18 O, in water vapor in the stratosphere. Wang et al. [START_REF] Wang | A quantum cascade laser-based water vapor isotope analyzer for environmental monitoring[END_REF] designed a mid-infrared quantum cascade laser spectrometer to measure H2 16 O and H2 18 O at 7.12 μm. Table 1 summarized water isotope ratio measurements by various laser spectrometry methods reported in the literature and the corresponding key experimental parameters. Picarro Inc. [27] and

LGR Inc. [28] develop water vapor isotope analyzers by using cavity ring-down and cavity enhanced spectroscopy technology, which enables simultaneous measurement of δ 2 H, δ 18 O, and δ 17 O of water vapor with high precision (0.05‰ for δ 18 O, 0.05‰ for δ 17 O, and 0.2‰ for δ 2 H). In conventional IRLS methods, Herriott cells and optical cavities are used as gas cells, which have a large volume (>100 mL), a large physical size, and a high cost.

The hollow waveguide (HWG) fiber proposed by Garmire et al. [START_REF] Garmire | Propagation of infrared light in flexible hollow waveguides[END_REF] not only guides light but also samples gas. The fiber can be extended to tens of meters for high sensitivity [START_REF] Jaworski | Sub parts-per-billion detection of ethane in a 30-meters long mid-IR Antiresonant Hollow-Core Fiber[END_REF] and coiled to small spaces for miniaturization. Furthermore, the anti-electromagnetic interference ability of the HWG fiber is strong, which can be used for gas detection in a harsh environment. These advantages render the HWG-fiber-based gas sensing sensors suitable for environmental monitoring, biomedical diagnosis, and industrial production.

In this study, we present the design of a mid-infrared HWG gas sensor based on a fiber absorption cell formed by a 5 m long and 1 mm inner diameter HWG fiber, combined with wavelength modulation spectroscopy (WMS) technique. H2 18 O, H2 16 O, H2 17 O, and HDO absorption features at 2.73m were simultaneously targeted within the current tuning range of the laser. The Allan variance was used to evaluate the detection limit and stability of the sensor. Finally, the concentration of water vapor isotope molecules in the atmosphere was measured.

Experimental principle

According to the wavelength modulation spectroscopy principles [START_REF] Westberg | Fast and non-approximate methodology for calculation of wavelength-modulated Voigt lineshape functions suitable for real-time curve fitting[END_REF], the amplitude of 2f signal for optically thin samples (a(v)<0.05) can be linearly expressed as follows:

2, 2 , 0 ( )= - ( ) even in aa fL fL S v I SnL v   , (1)
where a v (va/vL) is the width-normalized modulation amplitude, va is the modulation amplitude, vL is the half-width at half-maximum of the Lorentzian profile,  is the gain of the lock-in amplifier, η is the constant associated with the system, I0 is the initial light intensity, S is the absorption line strength, n is the density of absorbers, and L is the effective absorption path length. Furthermore, 2, ()

even a fL v
 is the standardized Lorentzian lineshape function at the center of the absorption line, which is constant for the fixed modulation amplitude of the laser and constant pressure in the gas cell. Therefore, the 2f amplitude is linearly proportional to the gas density n.

The isotope ratio R is expressed as the ratio of the rare to the abundant isotopologues species as follows:

x x a n R n  , (2)
where x refers to the rare isotopic species (H2 18 O, H2 17 O, and HDO), and a represents the abundant isotopic species (H2 16 O).

The deviation of the abundance ratio of the sample with respect to the international standard reference (Vienna Standard Mean Ocean Water) is expressed in terms of the δ-value as follows [START_REF] Meijer | The use of electrolysis for accurate δ 17 O and δ 18 O isotope measurements in water[END_REF]:

( ) ( 1) 000 ‰ 1 x sam x VSMOW R x R     (3)

Experimental section

The selection of an appropriate gas molecular absorption spectral line for isotope ratio measurement is vital and directly affects the accuracy and sensitivity of the measurements. Interference of other molecular absorption lines and measurement of two or more absorption lines within the laser wavelength tuning range are the main consideration issue. The molecular absorption lines and the ground state energy of the selected isotopes to be measured should be similar. A commercially available and compact 2.73-μm DFB laser covering the absorption lines of H2 Schematic of the mid-infrared HWG gas sensor is displayed in Figure 2. The figure is divided into the optical, electrical, and gas delivery parts. A DFB laser centered with the wavelength of 2.73 m and integrated with a thermistor and a thermoelectric cooler packaged in a TO5 mount (physical size is 5×5×5 cm 3 ) from the Nanoplus, Gerbrunn, Germany was used as the light source for the simultaneous measurement of water vapor isotopologues (H2 18 O, H2 16 O, H2 17 O, and HDO). An aspheric lens was placed before the laser to collimate the emitting beam. The laser beam was injected into a 5-m-long and 1 mm-inner diameter HWG fiber (HWEA 10001600, Polymicro Technologies, USA) transparent for light from 2.6 to 10.6 μm with a max bending loss of 1.5 dB/m by a lens with a 75-mm focal length. The HWG fiber was coiled on the outer surface of a plastic hollow cylinder manufactured through 3D printing. The HWG fiber was inserted into the slot of the gas connector and sealed with silicon glue. The gas connector at the opposite end of the HWG fiber was sealed with a CaF2 window by using an O-ring. After reflection back and forth through the inner wall of the fiber, the light was emitted from the HWG fiber and received by a photovoltaic detector (PVI-4TE-10.6, VIGO System S.A, USA). To reduce the interference from ambient water vapor, the laser and detector were placed as close to the HWG fiber as possible.

The electrical part is used to provide laser driver signal, control the output signal of the detector, and control the temperature of the HWG fiber. The current and temperature of the laser were controlled by a commercial controller (LDC-3724, ILX Lightwave, USA) with a temperature control accuracy of 0.1°C and current output accuracy of 0.05%. A triangular signal (10 Hz and 0.3 Vpp) produced from a function generator and a sinusoidal wave (10 kHz and 0.09 V RMS) generated by a lock-in amplifier (SR830, Stanford Research System, USA) were superposed to the laser current to scan and modulate the laser wavelength. The laser modulation amplitude and modulation frequency, as well as gas pressure were all optimized. For signal processing, the output of the detector was sent to the lock-in amplifier for 2f demodulation at optimal sensitivity and time constants. A synchronous signal was provided by the function generator for the lock-in amplifier to ensure phase synchronization. The 2f harmonic signals were obtained with a 14-bit data acquisition card at a sampling rate of 40 kHz. For the selected lines of H2 18 O, H2 16 O, H2 17 O, and HDO in our study, the precision of the isotopic abundance measurement to 1‰ requires a temperature stability of more than 0.1 K. The HWG fiber was covered with silver foil, heater band, and insulation foam. To reduce the sticking effect of water vapor on the inner wall of the HWG fiber, the temperature of the HWG fiber was maintained at 313.15 K with an accuracy < 0.1 K using a heating belt associated with a platinum resistor and a PID controller. .

For the gas delivery system, the ambient air outside of the laboratory was sampled through a 4-meter-long PFA tube, filtered by a PTFE filter, and subsequently pumped into the HWG fiber by using a low-noise diaphragm pump (1.2 L, DIVAC, Germany). The pressure in the HWG fiber was controlled by a pressure controller (640B, MKS Instruments, USA) placed at the upstream of the HWG fiber and set to 160 mbar. The flow rate for the sampling gas was controlled by a mass flow controller (MFC, GV50A, MKS Instruments, USA) at the HWG outlet and set to 17 mL/s. The pressure difference for filling the sampling gas into the fiber was 90 mbar. A dew point generator (DPG, Li-610, Li-Cor, USA) filled with a liquid water working standard with known isotopic signatures (δ 18 O= -3.83 ‰, δ 17 O= -2.07 ‰ and δ 2 H= -28.2 ‰) were used in the calibrations. The DPG inlet was connected to high-purity nitrogen gas. A tee-split (N2 out in Fig. 2) was placed between the nitrogen gas and the inlet of DPG to avoid over-pressurization of the DPG. The flow rate of the DPG was set to 33 mL/s, which was faster than the sample gas flow rate. Excess water vapor flow was released into the atmosphere through another tee-split (H2O out in Fig. 2).

Figure 2 Schematic of the mid-infrared hollow waveguide gas sensor for simultaneous measurement of four water vapor isotopologues

Result and discussion

In order to obtain the calibration coefficients of 2f peak values and water vapor isotopologues concentrations, water vapor with various concentrations were provided by adjusting the operating temperature of the DPG. Pure nitrogen was supplied as the carrier gas for the DPG. The output gas flow contained a known water concentration determined by the set dew point temperature with an accuracy of ±0.02°C, which corresponding to water vapor concentration error of around ±20 ppm at 14°C with a relative uncertainty of 0.12 %. The dew point temperature was set from 6 to 24°C, which produced nine water vapor concentrations (0.93%, 1.06%, 1.39%, 1.58%, 1.80%, 2.05%, 2.32%, 2.62%, and 2.96%). After the set dew point temperature reached stable states, the DPG air pump was turned on. The mixture was delivered through PFA tubing by using the pressure controller into the HWG fiber. A plot of the 2f signals versus various water vapor concentrations is displayed in Figure 3. The etalon undulation was observed in nonabsorbance region. The free spectral range (FSR) of the etalon was 1.5 GHz, which could be resulted from light interference through two parallel surfaces of optical elements. If the reflecting surfaces were air spaced, the two parallel surfaces were separated by 10 cm. As the mid-infrared HWG gas sensor is exposed to room air and not temperature stabilized, the etalons are unstable and changed with temperature. Because of the sticking of water vapor, the potential intersample memory effects on the inner wall of the HWG fiber was considered. Continuous measurement of nine widely spaced H2 16 O concentration levels (1.06%, 1.21%, 1.39%, 1.58%, 1.80%, 2.05%, 2.32%, 2.62%, and 2.96%) were performed and repeated as displayed in Figure 5(a). Figure 5(a) reveals that all the measurements reached the same plateau level. Figure 5(b) displays plots of the averaged 2f peak values versus various H2 16 O concentration levels for two repeated measurements. The two fit curves agree well even at very high H2 16 O concentration (typical ambient water mixing ratio is 1.2%).

The difference in 2f peak values for each concentration level between two repeated measurements is displayed in Figure 5(c). The relative errors for two repeated measurements were less than 0.9%. These indicated negligible surface effects occurring on the cell and tube walls. Under this condition the precision improved with averaging time. Two peaks were observed in the concentration distributions of H2 18 O and HDO but not for Gaussian distribution. This phenomenon was attributed to the lower H2 18 O and HDO signals sensitive to the underlying time-dependent etalon signals superimposed onto the 2f signals displayed in Figure 3. Then the precision improved less than expected for averaging. Allan deviation [START_REF] Allan | Statistics of atomic frequency standards[END_REF] plots of H2 18 O, H2 16 O, H2 17 O, and HDO concentrations are displayed in Fig. 6. The detection limits was 35.18 ppbv for H2 18 O, 4.69 ppmv for H2 16 O, 60.53 ppbv for H2 17 O, and 3.88 ppbv for HDO for a 96-s integration times. Etalon effects limited the sensitivity of the sensor. In order to further evaluate the measurement performance of δ 18 O, δ 17 O, and δD with the present mid-infrared HWG gas sensor, δ 18 O, δ 17 O, and δD were calculated by equation ( 3)-( 5) based on H2 18 O, H2 16 O, H2 17 O, and HDO concentrations data displayed in Figure 6. The Allan variance analysis was used to determine the precision of δ 18 O, δ 17 O, and δD. Figure 7 shows the time series measurements of δ 18 O, δ 17 O, and δD, as well as the corresponding Allan variances. The precisions of δ 18 O, δ 17 O, and δD are estimated as 0.85 ‰, 0.57 ‰, and 10.48 ‰, respectively, at the same optimal integration time of 96 s. The distributions and precisions of δ 18 O and δD were affected by the etalon signals on the lower H2 18 O and HDO signals, which could be reduced by balanced detection [START_REF] Fetzer | Tunable diode laser absorption spectroscopy in coiled hollow optical waveguides[END_REF] or by combination of precise temperature stabilization of the entire optical sensor and background subtraction using zero-gas spectrum [START_REF] Wang | A quantum cascade laser-based water vapor isotope analyzer for environmental monitoring[END_REF]. The performance of the mid-infrared HWG gas sensor was evaluated based on atmospheric H2 18 O, H2 16 O, and H2 17 O concentration measurements on the Nanchang Hangkong University campus. Three measurements were performed using the on the daytime of July 22, 24, and 28, 2021, with continuous 6 h each day and measurement results recorded every 96 s, as displayed in Fig. 8. The H2 18 O, H2 16 O, and H2 17 O concentrations were calibrated before atmospheric measurement every day. In atmospheric detection, the mid-infrared HWG gas sensor is inevitably affected by environmental noise. To improve the measurement precision of the mid-infrared HWG gas sensor, Kalman adaptive filtering was applied and analyzed. Kalman adaptive filtering as described in Refs [START_REF] Riris | Kalman filtering of tunable diode laser spectrometer absorbance measurements[END_REF][START_REF] Leleux | Applications of Kalman filtering to real-time trace gas concentration measurements[END_REF], the standard deviation of the first 20 measurements was used as σv, and the ρ value was 100. The red lines in Fig. 8 display the Kalman filtering results and the actual concentration changes. The H2 18 O, H2 16 O, and H2 17 O concentrations with Kalman filtering for three daytime measurements varied from 21.85 to 30.40, 11357 to 15471, and 3.76-5.01 ppmv, with average values of 27.06, 13557.05, and 3.96 ppmv, respectively. The relatively stable concentrations of water vapor isotopologues around 50min (labeled with gray area) were selected for estimating the ambient measurement performance of water vapor isotopologues.

Figure 9 shows time series of H2 18 O, H2 16 O and H2 17 O for around 50min labeled with gray area in Figure 8, and time series of the determined δ 17 O and δ 18 O at the same time interval. The 96 seconds measured concentrations yielded a 1 σ precision of 291.78 ppbv, 61.28 ppmv, and 15.3 ppbv for H2 18 O, H2 16 O and H2 17 O, respectively.

The measurement precisions of δ 17 O and δ 18 O were 1.78 and 11.06 ‰, respectively.

The ambient measurement performance here shows slightly poorer than that determined by the Allan variance analysis, potentially due to the instability of the system like system drift, optical fringe effect et al..

Conclusion

In this study, a sensor system based on the HWG fiber was proposed to measure the isotopic abundance of water vapor by measuring concentrations of H2 18 O, H2 16 O, H2 17 O, and HDO as well as δ values of 18 O, 17 O, and D. Unlike conventional methods, the HWG fiber has small volume and excellent flexibility as the gas pool, which is suitable for the development of compact sensors. Standard water vapor with known concentration was produced by a dew point generator for calibration. The measured peak values of 2f signals and the water vapor isotopologue concentrations exhibited excellent linear relationships. To evaluate the measurement precision of the system, the water vapor with a concentration of 1.8% was measured for 30 min. Allan variance analysis revealed that the detection limits of H2 18 O, H2 16 O, H2

Figure 3 Figure 4

 34 Figure 3 2f signals for various water vapor concentrationsAccording to the natural abundance of H218 O, H216 O, H217 O, and HDO, the gas concentrations of the four-water vapor isotopologues were estimated. A plot of the measured 2f peak values versus various four water vapor isotopologues concentrations is displayed in Figure4. Each 2f peak value in Figure4was obtained by averaging 500 measured values for each concentration level. Figure4reveals that 2f peak values of H218 O, H216 O, H217 O, and HDO were related to their concentrations with linear correlations of 0.99915, 0.99949, 0.99985, and 0.98873, respectively. The fitted curves were used as the calibration function to determine H2O isotopologue concentrations.

Figure 5

 5 Figure 5 (a) Continuous two-time measurements of nine widely spaced H2 16 O concentration levels; (b) 2f peak values versus various H2 16 O concentrations for two repeated measurements; (c) difference in 2f peak values between two repeated measurements in (b) The detection limits of water vapor isotopologues by the present mid-infrared HWG gas sensor were assessed by the Allan variance. Continuous measurements of water vapor samples were performed using a DPG-generated gas flow. The DPG was operated at the set dew point of T = 16°C to produce a water vapor concentration of 1.8%. The 2f signals of the four water-vapor isotopologues were measured over 10500 consecutive 0.16 s spectral scans. The 2f peak values measured from the 2f signals were converted to concentrations using the calibration curve displayed in Figure 4.

Figure 6

 6 Figure 6 displays the time series of the four water-vapor isotopologues' concentrations and histogram plots of the concentration distribution for the four water-vapor isotopologues. The concentration distributions of H2 16 O and H2 17 O were characterized by Gaussian distribution, which implied random noise dominating the 2f signals.

Figure 6

 6 Figure 6 Time series of the measured concentrations of the four water vapor isotopologues, and the corresponding Allan deviation plots

Figure 7

 7 Figure 7 Time series and Allan deviation of calculated δ 18 O, δ 17 O, and δD

Figure 8 Figure 9

 89 Figure 8 Time series of H218 O, H216 O, and H217 O measured using the mid-infrared HWG gas sensor. A Kalman filter method was used to improve the detection precision (red lines).

Table 1

 1 Summary of water isotope ratio measurements by various laser spectrometry methods reported in the literature and the corresponding key experimental parameters.

	Ref.	 (m)	Method	Cell	Leff (m)	Volume (mL)	C (ppm)	Precision (‰) δ 2 H δ 17 O δ 18 O

  For the selected pair of lines, a variation of 1 K leads to a precision of -3.1‰ for δ18 O, -6.0‰ for δ17 O, and -8.0‰ for δ 2 H. Figure1displays the spectral absorption simulation of 1.8% H2O and 400 ppmv CO2 at a pressure of 160 mbar in the range of 3662.77-3663.93 cm -1 according to the HITRAN 2016 database. Figure1reveals that the HDO absorption line overlaps with the CO2 absorption line; therefore, the measurement of HDO concentration and corresponding δ 2 H at this spectral region is available only for liquid water not for ambient water vapor.

		0.07		H 2 16 O 3663.04522	H 2 17 O	H 2 H 2	16 O 18 O	H 2 HDO 17 O
		0.06			3663.32128	12 C 16 O 2	13 C 16 O 2
	Absorbance (a.u.)	0.02 0.03 0.04 0.05	H 2 3662.9196 18 O	16 O 12 C 18 O 12 C 16 O 2 3663.8504 P=160 mbar T=296 K L=5 m
						HDO
		0.01				3663.84202
		0.00
		3662.8	3663.0	3663.2 Wavenumber (cm -1 ) 3663.4	3663.6	3663.8
							18 O (3662.9196cm -1 ),
	H2 16 O (3663.04522 cm -1 ), H2 17 O (3663.32128 cm -1 ), and HDO (3663.84202 cm -1 )

with the corresponding absorption line strengths of 2.1  10 -23 , 8.5  10 -23 , 7.2  10 -23 , and 1.2  10 -23 cm/molecule, respectively, satisfies these requirements. Figure 1 Simulated absorption lines of 1.8% H2O, 400 ppmv CO2, and its isotopes in the range of 3662.77-3663.93 cm -1

  17 O, and HDO were 35.18 ppbv, 4.69 ppmv, 60.53 ppbv, and 3.88 ppbv, respectively, at the integration time of 96 s. The corresponding precision of δ18 O, δ17 O, and δD were 0.85‰, 0.57‰, and 10.48‰, respectively. The sensor measured the water vapor isotope in the atmosphere from 13:30 to 19:30 in three days. After Kalman filtering, the variation ranges of H218 O, H216 O, and H217 O concentrations in the atmosphere were 21.85-30.40 ppmv, 11357-15471 ppmv, and 3.76-5.01 ppmv, respectively, and the corresponding average concentrations were 27.06 ppmv, 13557.05 ppmv, and 3.96 ppmv. The 1 σ precision was 291.78 ppbv, 61.28 ppmv, and 15.3 ppbv for H218 O, H216 O and H2 17 O, respectively. The measurement precisions of δ17 O and δ 18 O were 1.78 and 11.06 ‰, respectively.

Acknowledgements

The authors acknowledge the support of the National Natural Science Foundation of China (Grant No. 42175130, 61965013, 61865013), the Key Research and Development Program of Jiangxi Province, China (20203BBG73039), the National Key Research and Development Program of China (No.2018YFE0115700) and Postgraduate Innovation Foundation of Nanchang Hangkong University (YC2020078).