T Czerwiec
email: thierry.czerwiec@univ-lorraine.fr

A Andrieux

G Marcos

Ph H Michel

Bauer

Is "expanded austenite" really a solid solution? Mossbauer observation of an annealed AISI 316L nitrided sample

Keywords: Nitride materials, Surfaces and Interfaces, Mossbauer spectroscopy, gas solid reactions, X-ray diffraction, diffusion

Expanded austenite, also known as S phase, m phase or  N phase forms during low temperature (< 420°C) nitriding of austenitic materials containing chromium. In this communication, annealing of a nitrided sample is used as a tool to understand the nature of expanded austenite. Starting from an AISI 316LN sample plasma nitrided for 4 h. at 410 °C, the decomposition of expanded austenite is studied by conversion electron Mossbauer spectroscopy (CEMS) and X ray diffraction (XRD) for different annealing times at 400°C. For the as nitrided sample, the CEMS spectra are analysed using two hyperfine field distributions (HFD). HFD A is attributed to a nitrogen enriched expanded austenite, HFD B is attributed to a bcc environment without or with very low nitrogen content. Both the local deformation of the bcc lattice and the presence of other elements as iron neighbouring atoms explain the broad range of hyperfine field in HFD B. The vanishing of HFD A, after 2 h. of annealing, is explained by the formation of short-range order (SRO) between chromium and nitrogen and by the redistribution of nitrogen in excess. For the 3 h. of annealing, a bcc phase is observed by XRD. We propose to describe this phase as martensite. An interplay between local internal stress and local nitrogen content is proposed to explain the unexpected formation of such a martensitic phase in a strongly gamma stabilizing environment. From the microscopic point of view expanded austenite can be considered to be constituted of at least two different environments: a gamma environment supersaturated in nitrogen and a martensitic environment without nitrogen.

Introduction

Austenitic stainless steels (ASSs) are steels with faced-centred cubic (fcc) crystal lattice containing a minimum of 16 wt% chromium and sufficient nickel and/or manganese to retain the austenitic structure at room temperature (with or without fast quenching depending on the composition). In the mid-1980s [1-2], two teams discovered that low temperature nitriding of austenitic stainless steels forms a new phase known as expanded austenite, S phase, m phase or  N phase. For the last thirty years, significant progresses have been made and now, it is more or less recognized that this phase is a metastable nitrogen supersaturated solid solution with a disordered fcc structure and a distorted lattice that will be called  N phase in this paper (figures 1a and 1b) [START_REF] Czerwiec | Fundamental and Innovations in Plasma Assisted Diffusion of Nitrogen and Carbon in Austenitic Stainless Steels and Related Alloys[END_REF][START_REF] Dong | S-phase surface engineering of Fe-Cr, Co-Cr and Ni-Cr alloys[END_REF]. However, some recent reports introduced a doubt on such a simple description of expanded austenite [START_REF] Oddershede | Scripta Mater, Extended X-ray absorption fine structure investigation of nitrogen stabilized expanded austenite[END_REF][START_REF] Martinavicius | Nitrogen interstitial diffusion induced decomposition in AISI 304L austenitic stainless steel[END_REF]. The extended X-ray absorption fine structure spectroscopy (EXAFS) results from Oddershede et al. [START_REF] Oddershede | Scripta Mater, Extended X-ray absorption fine structure investigation of nitrogen stabilized expanded austenite[END_REF] show that short range ordering (SRO) of Cr and N atoms occurs (figure 1c). In this study, AISI 316 foils were nitrided at 445 °C in a 9% N 2 -91 % NH 3 (infinitely high nitrogen activity) for 18.5 h. From the authors, the nitrogen content is 33.8 at% and no Cr-N clusters (figure 1e) or CrN platelets or Guinier-Preston zones (figures 1f) are detected in such conditions. Using Field Ion Microscopy (FIM) Martinavicius et al. [START_REF] Martinavicius | Nitrogen interstitial diffusion induced decomposition in AISI 304L austenitic stainless steel[END_REF] observed small nanometric precipitates in AISI 304 samples treated by plasma nitriding at 400°C for 30 h. in a 60% N 2 -40 % H 2 . These authors used the corresponding X-ray absorption near edge structure spectroscopy (XANES) and EXAFS data to describe expanded austenite as being constituted by nanometric precipitates, attributed to CrN, embedded in a Fe 4 N-like matrix. The precipitates have irregular, sphere-like shapes with larger size near the surface. X-ray spectroscopic investigation revealed three different intermetallic distances and different chemical environments for Fe, Cr and Ni, accompanied by a large disorder. However, these authors were not able to evidence CrN precipitates by atom probe tomography. Some transmission electron microscopy (TEM) measurements done on low temperature nitrided stainless steels do not support the simple description of expanded austenite as a solid solution [START_REF] Xu | Study of microstructure of low-temperature plasma-nitrided AISI 304 stainless steel[END_REF][8]. Xu et al. have analysed by TEM AISI 304 samples plasma nitrided in the range 400-420 °C in NH 3 for 4 h. [8]. They describe expanded austenite as being constituted by a supersaturated nitrogen solid solution based on a '-Fe 4 N structure, in which the nitrogen atoms are in the form of Cr-N clusters. From high resolution TEM measurements, Strotz et al. [9] concluded that only the S-phase is formed in AISI 316L stainless steel plasma nitrided for 4 h. at 440°C in 50% N 2 -50% H 2 gas mixture. However, they suggested a tendency to short-range ordering of 'Fe 4 N type in a supersaturated solid solution of nitrogen. It was suggested that SRO of nitrogen atoms takes place and gives rise to appearance of forbidden {100} reflections from '. Unlike the paramagnetic austenite phase of the matrix, expanded austenite containing nitrogen is known to be ferromagnetic at room temperature [START_REF] Stroz | TEM studies of plasma nitrided austenitic stainless steel[END_REF][START_REF] Ozturk | Phase and composition depth distribution analyses of low energy, high flux N implanted stainless steel[END_REF][12][START_REF] Olzon-Dionysio | Application of Mössbauer spectroscopy to the study of corrosion resistance in NaCl solution of plasma nitrided AISI 316L stainless steel[END_REF]. Nevertheless, relatively little is known about the magnetic properties of expanded austenite. Such magnetic properties make backscattered conversion electron Mossbauer spectroscopy (CEMS) an interesting technique for studying expanded austenite since it provides information on backscattered electrons with an average escape depth of about 60 nm (80% are from the range 0-0.1 m) [START_REF] Basso | Magnetic and structural properties of ion nitrided stainless steel[END_REF].

In order to better understand expanded austenite, it can be useful to destabilize this phase by annealing at a temperature used for the nitriding treatment. It is important to remember that the migration of metal constituents during a low temperature nitriding treatment (< 420°C) for relatively short treatment times (few hours) is practically zero, while migration of nitrogen atoms occurs. The term paraequilibrium is sometimes used to characterize such a state of metastability whereby equilibration of the chemical potentials of carbon or nitrogen in solution with the atmosphere occurs, but not those of metal constituents [15-16]. As nitrogen is continuously supplied into expanded austenite during a nitriding treatment, its metastable nature is hindered. The situation is different when the nitrogen supply is suppressed during annealing. The purpose of this paper is to study expanded austenite through CEMS by following the evolution of a nitrided layer during several annealing steps.

Experimental

The sample used in this communication is a tempered AISI 316LM stainless steel cylinder (14.7 wt% Ni, 17.4 wt% Cr, 62.7 wt% Fe, 2.7 wt% Mo, 1.8 Mn, 0.4 wt% Si, 0.2 Cu, wt% …) cut from a cylindrical rod (20 mm of diameter) and with a thickness of less than 5 mm. The sample was mechanically polished to a mirror-like finish and cleaned in ethanol for 15 min. using ultrasonic cleaning just before being placed into the nitriding chamber. A multi-dipolar electron cyclotron resonance system (MDECR) was used for the nitriding experiments [START_REF] Michal | Carbon paraequilibrium in austenitic stainless steel[END_REF]. An in-situ cleaning pre-treatment, intended to remove the native oxide layer, was performed in 50% Ar-50% H 2 at a pressure of 1 Pa for 20 min. For this step, the incident microwave power was 600W and the bias voltage is -200V. The plasma was maintained in between the pre-treatment and the nitriding treatment to reach the treatment temperature. Additional heating of the substrate is provided by external heating integrated to the substrate holder. The temperature of the sample was controlled with a thermocouple embedded in the substrate holder. The nitriding treatment was performed in 90% N 2 -10% H 2 at a pressure of 1 Pa for 4 h. with an incident microwave power of 600W and a bias voltage of -50 V. Annealing were sequentially done in the nitriding chamber without plasma and under secondary vacuum (< 10-3 Pa) for different times. After each set of annealing, the sample was allowed to cool in the reactor under vacuum at room temperature before both X-ray diffraction and CEMS measurements. X-ray diffraction analysis was done using a Ge monochromator (111) to discriminate copper K α1 line (λ = 0.154056 nm) in the Bragg-Brentano type configuration (Brukers Advance diffractometer). The sample is positioned in the center of the goniometer on a spinner by an automated smuggler. We used the EVA software to subtract the background noise and to extract the characteristic data of the diffraction peaks. Glow Discharge Optical Emission Spectrometry (GDOES) measurements were performed using a Jobin-Yvon Horiba GD 1000 apparatus. A dedicated and calibrated method for these types of samples (nitrided iron-base) has been developed. It takes into account all the alloying elements. For the determination of nitrogen concentration, a calibration curve was carried out using a series of certified samples containing a wide range in nitrogen concentration (10 -5 to 22.633 % Wt). For recalibration or pre-measurements, a sample of nitrided pure iron sample (pure '-Fe 4 N phase controlled by X-rays diffraction) is routinely used. All calibration curves and measurements were made under the same operating conditions of the Grimm lamp (650 Pa of pressure, 30 W of RF power). We have verified with tactile profilometry that with these parameters the craters have an adequate shape (anisotropic sidewalls and flat bottom) for a good resolution (50 nm) monitoring of the concentrations with the depth. Room temperature 57Fe Mossbauer spectroscopy using both backscattered conversion electron (CEMS) was performed using a conventional spectrometer operating in constant acceleration mode. The detection of the backscattered conversion electrons was made using gas flow proportional counter (He -5% CH 4 ). The Mossbauer spectra exhibit magnetic Zeeman patterns with six broadened lines superimposed to a central paramagnetic component. The magnetic contribution arises from the existence of distributions of hyperfine magnetic fields B. In order to analyze our Mossbauer spectra, we use the method developed by Le Caer and Dubois [START_REF] Lacoste | Multi-dipolar plasmas for uniform processing: physics, design and performance[END_REF] for amorphous alloys, which is an improvement of that proposed by Hesse and Riibartsch [START_REF] Hesse | Model independent evaluation of overlapped Mossbauer spectra[END_REF]. The hyperfine field distributions (HFD) method assumes a linear correlation between the hyperfine field and the isomer shift  in order to take into account the Fe-environment distribution. It gives probability curves p(B). This type of correlation is justified because the isomer shift is directly proportional to the total s-electron density at the nuclear site. A change in HFD is due to a change in the spin-up or spin-down s-electron density which also modifies the total s-electron density and hence the isomer-shift proportionally [START_REF] Eymery | A Mössbauer comparative study of the local environment in metastable 304 stainless steel films depending on the preparation mode[END_REF].

Experimental results

Figure 2 represents the CEMS spectrum of a non nitrided AISI 316L sample. A single line, associated to a paramagnetic (see table 1) is observed in this figure. CEMS spectra, performed on the same sample nitrided for 4 h. at 410° C and then annealed for different conditions are presented in figure 3. The CEMS spectrum of the nitrided sample without annealing exhibits 2 kinds of magnetic components superimposed to a paramagnetic contribution. This last paramagnetic contribution, fitted with a lorentzian line shape, is attributed to an austenitic environment. The two major broad components exhibited by the CEMS spectra are analysed using hyperfine field distributions (distributions A and B) with linearly correlated isomer shifts (formerly known as smoothed histogram method). However, the histograms of the two distributions defer markedly. HFD A is nearly Gaussian and is associated to expanded austenite with magnetic characteristics (called   (m)) as proposed by Williamson et al. [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF]). These authors characterized the CEMS spectra either by a hyperfine field distribution or by a fit of six broadened Lorentzian lines (average field 15-16 T). In our case, the average magnetic field is 20-21 T. The origin and possible interpretation for HFD A will be discussed later. An interpretation of HFD B will be presented in the discussion of this paper.

The CEMS spectrum recorded after 1 h. of annealing at 400°C (figure 3 b) shows a decrease of the contribution from HFD A. After 2 h. of annealing at the same temperature, HFD A is not necessary to describe the CEMS spectra (figure 3c). Only HFD B and the paramagnetic contribution must be used to fit the data. The magnetic field and hyperfine parameters of distribution B are practically unchanged. It must be noted that it is necessary to include additional Zeeman sextets with high magnetic fields to describe HFD B after 2 h. of annealing. For 3 and 8 hours of annealing (figure 3d ande), some iron oxides (Fe 2 O 3 ) are detected in the CEMS spectra. The CEMS spectra resulting from the final step of annealing, additional 5 h. at 470 °C (figure 3f) can be described by three simple components without the need of HFDs. An austenitic environment contributes to 47% of the total signal, and two magnetic contributions at 34.3 T and 33.3 T with a respective proportion of 15% and 28%.

The lowest magnetic contribution is characterized by a perpendicular anisotropy. GDOES profiles of nitrogen content, performed on the same sample nitrided for 4 h. at 410° C before annealing and after annealing, are presented in figure 4. It can be seen that the layer thickness of the nitrided sample lies between 7.5 to 8 m and that the surface content in nitrogen is around 25 at%. The nitrogen content profile has the classic form found in low temperature nitriding experiments of austenitic stainless steels [START_REF] Czerwiec | Fundamental and Innovations in Plasma Assisted Diffusion of Nitrogen and Carbon in Austenitic Stainless Steels and Related Alloys[END_REF][START_REF] Dong | S-phase surface engineering of Fe-Cr, Co-Cr and Ni-Cr alloys[END_REF]. Some models were proposed to explain such nitrogen profile (see reference [START_REF] Jespersen | Modelling the evolution of composition-and stress depth profiles in austenitic stainless steels during low-temperature nitriding[END_REF] for more details). It is necessary to include composition-dependent diffusion coefficient of nitrogen in expanded austenite, short range ordering (trapping) of nitrogen atoms by chromium atoms, and the effect of composition-induced stress (elastic and plastic) on surface concentration and diffusive flux [START_REF] Jespersen | Modelling the evolution of composition-and stress depth profiles in austenitic stainless steels during low-temperature nitriding[END_REF]. At the end of the annealing process, the superficial nitrogen content decreases to 17.5 at% and the thickness of the layer containing nitrogen reaches 11.5 to 12 m. After annealing, the shape of the nitrogen profile is even more complex to describe than before annealing. It will be interesting to model such a profile. Nevertheless, the integral over the nitrogen profiles (total nitrogen content into the sample) respectively gives 95 and 87 at%.m before and after annealing. Approximately 8 % of the nitrogen atoms initially incorporated in the nitrided sample are lost during the annealing process. The loose of nitrogen can be explained by nitrogen atoms recombination at the sample surface [START_REF] Czerwiec | Low-pressure, high-density plasma nitriding: mechanisms, technology and results[END_REF]. The insert in figure 4 represents the depth profile of the difference between the measured nitrogen and chromium contents.

The corresponding X-ray diffraction (XRD) patterns are shown in figure 5. From this figure the characteristic set of diffraction lines corresponding to the  N phase can be recognized for the nitrided sample. Each diffraction line from the  phase substrate is associated to a diffraction line from the  N phase appearing at lower angles. Additional lines with low intensity appear in the XRD pattern of the as nitrided sample. The line at 38.29° cannot be identified. It does not correspond to any nitrides or any sulphides. The line at 44.7° (depicted by a star in figure 5) is difficult to interpret but the presence of ferrite is not completely excluded (possible lattice parameter 0.286 nm). After 2 h. of annealing, a new line attributed to a bcc structure appears in the XRD pattern, while the (200) line of the  N phase disappears. It is not the case for the (111) line attributed to the  N phase. For 8 h. of annealing, a new diffraction line appears. It is attributed to an fcc phase, called decomposition austenite  d because its appearance is linked to the disappearance of the  N phase. Finally, we are able to identify the XRD line belonging to CrN only at the end of the annealing process. Figure 6 represents the evolution of the lattice parameters calculated using the previously presented assumptions. Concerning the diffraction lines of the  N phase, a linear decrease is observed for both the (111) and the (200) lattice parameters. The anisotropic behaviour is explained by the anisotropy of the elastic constant of stainless steel and by the very high compressive internal stress observed in such nitrided layers [START_REF] Czerwiec | Fundamental and Innovations in Plasma Assisted Diffusion of Nitrogen and Carbon in Austenitic Stainless Steels and Related Alloys[END_REF]. Despite the fact that the (200) line cannot be observed for annealing times higher than 2 h., we can extrapolate the linear behavior of two lines to determine a theoretical annealing time of 4 h. for which the anisotropic behavior disappears. From our GDOES measurements, it can be seen that the superficial nitrogen content decreases with the annealing time. The decrease of the lattice parameters of  N is explained by a combination of internal stress and superficial nitrogen content decrease.

Discussion 4.1 Before annealing: origin of HFD A

Mossbauer studies concerning the effect of nitrogen on iron in austenite at low nitrogen content (less than 10 at%) are well documented in pure iron or in stainless steels [START_REF] Genin | Mössbauer spectroscopy of disordered and ordered iron-nitrogen solid solutions[END_REF][START_REF] Gielen | Mossbauer effect in iron-carbon and iron-nitrogen alloys[END_REF][START_REF] Nadutov | Mössbauer analysis of the effect of substitutional atoms on the electronic charge distribution in nitrogen and carbon austenites[END_REF][START_REF] Schaaf | Laser nitriding of metals[END_REF][START_REF] Oda | Interaction and arrangement of nitrogen atoms in FCC γiron[END_REF][START_REF] Ph | CEMS study of the carbon distribution in austenite[END_REF].

With such low nitrogen content, two kinds of components are observed in the Mossbauer spectra of 57 Fe: a singlet which is assigned to iron atoms having no nearest interstitial atoms and a doublet assigned to those having interstitial atoms at the nearest neighboring sites. A quadrupole splitting of resonance lines due to a breaking of symmetry of the electronic charge distribution near Fe atoms by the nearest interstitial nitrogen neighbor occurs. It was described as a paramagnetic austenite  (p) with two subcomponents   and   . The isomer shift increases with nitrogen interstitial content as a result of a decrease of the s electron charge density. Williamson et al. [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF] were the first to interpret the Mossbauer results obtained on austenitic stainless steels containing high nitrogen content (up to 30 at%) as being due to a ferromagnetic state of austenite (called   (m)). Using secondary neutral mass spectrometry combined to magnetic force microscopy image, it was shown that   can be found in two different magnetic states depending on the position in the nitrided layer [START_REF] Olzon-Dionysio | Application of Mössbauer spectroscopy to the study of corrosion resistance in NaCl solution of plasma nitrided AISI 316L stainless steel[END_REF]. An outermost ferromagnetic layer is found for nitrogen content higher than 14 at% (associated to   (m) in [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF]) while a paramagnetic layer (associated to   (p) in [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF]) lying beneath   (m) is observed for nitrogen content lower than 14 at%. The   (p) environment was not observed in our experiment, contrary to ref. [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF], probably because the layer thickness of our sample is higher: 7 m as compared to 1.4 m in ref. [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF].

From figure 4, it can be seen that the transition region (between   (m) and   (p)) lies between 3.5 to 4 m in the present experiment, fare away from the first hundreds of nanometres probed by CEMS. This explain why it is not possible to see any contribution from   (p) in our experiments. As the isomer shift of the paramagnetic component from our CEMS spectra is -0.1 m.s -1 , it can be concluded that it is associated to an austenitic environment of iron without nitrogen interstitials. It should be noted that Williamson et al. [START_REF] Williamson | Metastable phase formation and enhanced diffusion in fcc alloys under high dose, high flux nitrogen implantation at high and low ion energies[END_REF] also observed such an austenitic environment in AISI 304 stainless steel implanted at 400°C for 30 min. resulting in 1 to 2 m nitrided layers. They attributed this component to the signal coming from the substrate, despite the fact that CEMS is mainly sensitive to the first hundreds of nanometers from the top surface. We believe that this gamma phase without nitrogen is the result of a decomposition mechanism that will be discussed in the second part of this discussion. HFD A must be associated to the ferromagnetic state of expanded austenite called   (m). Cusenza et al. [START_REF] Cusenza | Nitrided Amorphous Stainless Steel Coatings Deposited by Reactive Magnetron Sputtering from an Austenitic Stainless Steel Target[END_REF] have obtained AISI 316 films enriched in nitrogen by reactive magnetron sputtering in argon-nitrogen gas mixtures. They were using an HFD, very similar to the one we use, in order to interpret the CEMS obtained on low nitrogen containing films (< 30 at%).

The mean magnetic field of this contribution, which was between 23.4 and 18.2 T depending on the conditions, was attributed to an amorphous stainless steel nitrogen alloy. Brink et al [31] also used two HFD to describe the Mossbauer spectra measured on fully expanded austenite samples obtained by foils nitriding. The mean magnetic field was between 18 and 19 T for IS of 0.33, 0.37 mm. s -1 for nitrogen content 25 to 30 at%. Olzon-Dionysio et al. [12] also analyzed CEMS spectra obtained on AISI 316L samples nitrided at 400°C from 1 h. using two magnetic components with magnetic field of 19.9 T (IS = 0.16 mm. s -1 ) and 15.4 T (IS = 0.07 mm. s -1 ). It must be noted that these authors used other magnetic phases to fit the CEMS for longer nitriding times: γ′-Fe 4 N (three components, magnetic field of 33.6, 21.5 and 21.1 T for IS of 0.29, 0.22 and 0.25 mm. s -1 respectively) and ε-Fe 2+x N (26.4 T and 0.23 mm. s -1 respectively). Recently, these authors introduced an HFD in their analysis of AISI 316 L nitrided samples analysis together with γ′-Fe 4 N and ε-Fe 3+x N components [32]. It is tempting to interpret HFD A as resulting from a deformed Fe 4 N cubic structure. As a matter of fact, Fe 4 N can be described as an anti-perovskite structure with two different Fe sites: Fe I atoms occupy the corners of the cubic unit cell and are surrounded by 12 nearest neighbours and Fe II atoms occupy the face centres of the unit cube and have two nitrogen atoms as nearest neighbours (respectively M in position I and M in position II on figure 7). Nitrogen occupies the body centre and the structure can also be considered as a -Fe where nitrogen is at the body centred position [START_REF] Costa-Krämer | Structure and magnetism of single-phase epitaxial γ′-Fe 4 N[END_REF][START_REF] Diao | 57Fe Mössbauer study of perovskite-type Fe-Ni nitrides γ′-(Fe1-xNix) 4N (0⩽ x⩽ 0.8)[END_REF]. The ferromagnetic nature of ' has an influence on the Mössbauer spectra giving quadrupole splitting due to combined magnetic and electric hyperfine interactions. As a consequence of the orientation of the internal magnetic field along the easy magnetization direction, crystallographically equivalent sites are magnetically non-equivalent (MIIA and MIIB in figure 7). For '-Fe 4 N, the hyperfine parameters are, at room temperature, 34.1-34.4, 21.7-22 and 21.8-21.9 T for the hyperfine field and 0.22-0.23, 0.29-0.3 and 0.29-0.3 mm. s -1 for the IS, respectively for Fe I, Fe IIA and Fe IIB [START_REF] Costa-Krämer | Structure and magnetism of single-phase epitaxial γ′-Fe 4 N[END_REF][START_REF] Panda | Enhancement of Hyperfine Fields for Iron Atoms in γ′-Fe 4-x Ni x N (0.2 ≤ x ≤ 0.8) Compounds[END_REF]. Note that the results are different at low temperature [START_REF] Diao | 57Fe Mössbauer study of perovskite-type Fe-Ni nitrides γ′-(Fe1-xNix) 4N (0⩽ x⩽ 0.8)[END_REF]. A direct comparison shows that HFD A has a too much broad range of hyperfine fields to be identified to'-Fe 4 N. Nevertheless, it must be emphasized that the maximum hyperfine field of HFD A is not so far from the hyperfine field of site Fe IIA from '-Fe 4 N. Both calculations [START_REF] Mohn | The γ-Fe 4 N system revisited: an ab initio calculation study of the magnetic interactions[END_REF][START_REF] Paduani | Local magnetic properties and electronic structure of γ'-Fe 4 N[END_REF] and experimental studies [START_REF] Yang | Pressure effects on the electronic properties and the magnetic ground state of γ′-Fe 4 N[END_REF][START_REF] Li | Electronic and magnetic properties of the ferromagnetic γ′-Fe4N under high pressure[END_REF] on the effect of pressure on the hyperfine parameters of 'Fe 4 N, show that a compressive state of stress, that results in a contraction of the lattice, reduces the hyperfine field and the IS of both Fe I and Fe II. The reverse holds for a tensile state of stress that expands the lattice. From the experimental data obtained at room temperature of Li et al. [START_REF] Li | Electronic and magnetic properties of the ferromagnetic γ′-Fe4N under high pressure[END_REF], the hyperfine field vary from 34.3 to 29.8 T (Fe I) and 21.9 to 19.4 T (Fe II) whereas the IS is not changing for Fe I (0.3 to 0.22-0.23 mm. s -1 ) and vary from 0.3 to 0.26 mm. s -1 for Fe II as the pressure increases from 0 to 5.6 GPa. Such observations can only partly explain our results but not the very broad range of hyperfine field of HFD A around its maximum. As AISI 316 L also contains nickel, some '-Fe 1-x Ni x ) 4 N can be formed during nitriding. The hyperfine parameters were measured for different compositions of 'in which nickel is substituted to iron [START_REF] Diao | 57Fe Mössbauer study of perovskite-type Fe-Ni nitrides γ′-(Fe1-xNix) 4N (0⩽ x⩽ 0.8)[END_REF][START_REF] Panda | Enhancement of Hyperfine Fields for Iron Atoms in γ′-Fe 4-x Ni x N (0.2 ≤ x ≤ 0.8) Compounds[END_REF]40]. All the authors observe an increase of the hyperfine field for Fe I from x = 0 to x = 0.4; the other hyperfine parameters were not so much affected by a change in the nickel content. The presented results are different for x > 0.4: the contribution from Fe I disappears for Diao et al. [START_REF] Diao | 57Fe Mössbauer study of perovskite-type Fe-Ni nitrides γ′-(Fe1-xNix) 4N (0⩽ x⩽ 0.8)[END_REF], decreases for El Khiraoui et al. [40] or stabilizes for Panda et al. [START_REF] Panda | Enhancement of Hyperfine Fields for Iron Atoms in γ′-Fe 4-x Ni x N (0.2 ≤ x ≤ 0.8) Compounds[END_REF]. Note that these last authors used HFD to describe the internal fields because of the alteration of the local environment. Again, taking into account nickel substitution to iron in'cannot explain the very broad range of hyperfine field of HFD A. However, one interesting point to consider is the disappearance of the contribution from Fe I as ' is enriched in nickel. "Given the comparison of our results with those of the literature, the distribution A must be attributed mainly to expanded austenite".

4.2

Before annealing: origin of HFD B In order to interpret HFD B, we had to discuss the role of nitrogen on the isomer-shift of iron in different structures. From the results presented before for the and ' structures, it results that the presence of nitrogen near iron is characterized by high values of isomer-shift (typically 0.2 to 0.3 mm. s -1 ). So HFD B cannot be interpreted as such type of environment that contains nitrogen. It corresponds neither to a   (p) or   (m) nor to a ' structure. Schaeffler or Delong diagrams show that AISI 316 is a metastable austenitic steel, mostly stabilized by fast quenching from the liquid state during elaboration [41]. Shabashov et al. [START_REF] Shabashov | Structure of the Surface Layers of Metastable Austenitic Stainless Steel Nitrided in Electron Beam Plasma[END_REF] performed electron beam plasma nitriding of austenitic stainless steels with lower Ni content (7-9 at%) as content as compared to AISI 316L. The formation of ' martensite was reported in surface after short time nitriding at 350°C [START_REF] Shabashov | Structure of the Surface Layers of Metastable Austenitic Stainless Steel Nitrided in Electron Beam Plasma[END_REF]. An HFD, similar to the one reported here but with lower hyperfine fields (maximum for 27 T), was used to describe the ' martensite obtained by nitriding. Shabashov et al [START_REF] Shabashov | Structure of the Surface Layers of Metastable Austenitic Stainless Steel Nitrided in Electron Beam Plasma[END_REF] justified this interpretation by comparing the HFD attributed to martensite obtained by nitriding and by high pressure torsion. In this study, it is clearly shown by successive removal of the nitrided layer, that the  martensite HFD observed in surface is different from the HFD resulting from γ′-Fe 4 N and ε-Fe 2+x N, observed deeper. It is well known that layers formed by PVD deposition of austenitic stainless steels are, most of the time, constituted by a bcc phase [START_REF] Li | 57Fe Mossbauer study of metastable 304 stainless steel film with BCC structure[END_REF][START_REF] Eymery | A Mössbauer comparative study of the local environment in metastable 304 stainless steel films depending on the preparation mode[END_REF][START_REF] Nomura | CEMS study of stainless steel films deposited by pulsed laser ablation of AISI 316[END_REF][START_REF] Cusenza | The Gibbs-Thomson effect in magnetron-sputtered austenitic stainless steel films[END_REF]. In all these works, the authors use HFDs to describe the structure observed by Mössbauer spectroscopy. For AISI 316L films elaborated at 450°C, the used HFD is very similar to HFD B reported here [START_REF] Cusenza | The Gibbs-Thomson effect in magnetron-sputtered austenitic stainless steel films[END_REF]. Some authors reported the formation of martensite in AISI 316 steels using different process: ion implantation (nitrogen and other elements), severe mechanical deformations, hydrogen absorption… [START_REF] Hayashi | Phase transformation in helium ion irradiated 316 stainless steel[END_REF][48][49][START_REF] Cook | Strain induced martensite formation in stainless steel[END_REF][51][START_REF] Varma | Effect of grain size on deformationinduced martensite formation in 304 and 316 stainless steels during room temperature tensile testing[END_REF][53][54][55][56][START_REF] Manjanna | Ferromagnetic fraction and exchange anisotropy in SUS 316LN austenitic stainless steel due to strain-induced deformation[END_REF]. Two types of martensite can form in stainless steels: martensite ' (a ferromagnetic body centered cubic structure) and martensite  (compact hexagonal structure which is not ferromagnetic). After 40 keV helium ions bombardment on AISI 316, Hayashi et al. [START_REF] Hayashi | Phase transformation in helium ion irradiated 316 stainless steel[END_REF] observed by CEMS a ferromagnetic phase they attributed to martensite. Three components were used to fit the spectra with respective isomer-shift of 0.05, -0.02 and 0.05 mm. s -1 corresponding to hyperfine field of 27.8, 30.3 and 33.4 T. Mottu et al. [48] observed ferrite by XRD during implantion of Xe and Mo ions at 49 keV at doses higher than 6 10 15 ions. cm -2 . Dudognon et al. [49] showed that the formation of ferrite does not depend on the nature of the implanted dose or elements, but rather on a threshold for the development of damage in the material. Referring works on the formation of martensite induced by deformation (deformation induced martensite: DIM) are relatively few with respect to AISI 316. Cook [START_REF] Cook | Strain induced martensite formation in stainless steel[END_REF] observed martensite formation on AISI 316 samples deformed by brushing using CEMS. In this paper, an HFD, very similar to HFD B reported here was used to describe the Mössbauer spectra [ [START_REF] Sort | Selective generation of local ferromagnetism in austenitic stainless steel using nanoindentation[END_REF][START_REF] Menéndez | Controlled generation of ferromagnetic martensite from paramagnetic austenite in AISI 316L austenitic stainless steel[END_REF] observed martensite by magneto-optical Kerr effect and magnetic force microscopy on indented AISI 316L samples. Etienne et al. [60] observed by XRD and Mossbauer spectroscopy the formation of ' martensite on very fine grained samples prepared by high pressure torsion from AISI 316. During cathodic charging of hydrogen (electrochemical solution method), observed by XRD  and ' martensite. It is interesting to note that a duplication of the diffraction peaks is attributed to the effect of internal stresses induced by the introduction of hydrogen into the steel [61-62]. We will now look at the role of nitrogen on the isomer-schift in martensite. Genin and Foct [START_REF] Genin | Mössbauer spectroscopy of disordered and ordered iron-nitrogen solid solutions[END_REF] distinguished four different environments for iron martensite as respect to nitrogen: class A* in which Fe atoms have no nitrogen within the first and second nearest neighbour shells (nn and nnn respectively), class A' in which Fe atoms have no nn nitrogen but one nitrogen nnn, class B includes iron atoms which have one isolated nitrogen nn, and finally class C* in which Fe atoms are close to several nitrogen atoms. A very weak isomer shift is found for classes A* and A' (about 0.04 mm. s -1 ) since Fe atoms ignore the presence of the interstitial except through the conduction band of iron. The values for class B is 0.40 ± 0.05 mm. s -1 . Such a positive value reveals a decrease of the s-electron density attributed to a more effective 3d screening effect. The isomer shift is found to be 0.23 mm/s for class C*. By comparing our results to those coming from the literature, it appears that HFD B must be attributed to a bcc environment with no or with very low nitrogen content. The broad range of hyperfine field in HFD B can be explained by both the local deformation of the bcc lattice and by the presence of Cr, Ni, Mo… elements as iron neighbouring atoms. It was shown that the hyperfine field experienced by a given Fe atom depends on the number and distance of Fe and non-Fe neighbouring atoms. Due to the reduction of the exchange interaction by each non-Fe nn and next-nearest neighbour (nnn) atom, the hyperfine field decrease is proportional to the numbers of nn and nnn foreign atoms [60]. So a martensitic environment with very low or no nitrogen content can be a good candidate to explain HFD B.

4.3

Annealing First of all we have to discuss the fact that HFD A does not longer exists for annealing times higher than 2 h. It is remarkable to note that this event occurs simultaneously with the appearance of the bcc phase and the vanishing of the  N (200) peak as observed by XRD (figure 6). As the nitrogen gas supply stops during the annealing process, nitrogen atoms will continue to diffuse from the superficial part of the nitrided layer into the steel. Thus, the nitrogen content in the superficial layer decreases and, in spite of the  stabilizing effect of nitrogen, the stainless steel-nitrogen system will tend to an equilibrium state producing CrN, a bcc phase (and a fcc phase if the temperature is high enough). The experimental data concerning the stability of expanded austenite are scare [START_REF] Li | The stability of the nitrogen S-phase in austenitic stainless steel[END_REF][START_REF] Ozturk | Thermal stability of the high-N solid-solution layer on stainless steel[END_REF][START_REF] Christiansen | Decomposition kinetics of expanded austenite with high nitrogen contents[END_REF][START_REF] Christiansen | Low-temperature gaseous surface hardening of stainless steel: the current status[END_REF][START_REF] Brink | Thermal expansion and phase transformations of nitrogen-expanded austenite studied with in situ synchrotron X-ray diffraction[END_REF]. In a first approach, Li et al. have obtained isothermal transformation (IT) diagrams from annealing and TEM in-situ heating observations [START_REF] Li | The stability of the nitrogen S-phase in austenitic stainless steel[END_REF]. The transformation time was found to be temperature dependent, ranging from several minutes at 600°C or over to a couple of years at 300°C or below. From the examination of these data, it appears that the decomposition time at a given temperature is strongly dependent on the initial state of expanded austenite (nitrogen content, thickness, treatment time…). In our experiment, it is surprising that the first stage of the decomposition process appears very early, after 2 h. of annealing at 400°C. As indicated by GDOES measurements, the maximum amount of nitrogen in the nitrided layer corresponds to the amount of chromium at the end of the annealing procedure. The insert in figure 4 shows the evolution of the difference between the nitrogen and the chromium content as a function of depth. This value is almost zero at the end of the annealing procedure, but it can be as high as 10 at% for the nitrided specimen. At the end of the annealing procedure, the combined observations of the 1:1 ratio of chromium and nitrogen, as well as the appearance of CrN diffraction lines, leads us to believe that the thermodynamic equilibrium tends to be established within the nitrided layer (figure 1e). Nevertheless, it very likely that the 1:1 interaction between Cr and N occurred earlier in the annealing procedure and also during the nitriding treatment itself. Indeed, SRO of Cr and N (figure 1c) is probably present at the early stage of nitriding in AISI 316L. Nitrogen atoms not strongly linked to chromium by SRO, can be considered as nitrogen atoms in excess. According to our Mossbauer measurements, these nitrogen atoms in excess are at the origin of HFD A and must be located near the chromium atoms, but are not strongly linked to chromium compared to the nitrogen atoms in SRO (figure 8). These excess nitrogen atoms are almost free to diffuse during annealing, but also during nitriding treatments. We are able to distinguish nitrogen atoms in excess from those involved in SRO only by performing annealing experiments. We believe that the vanishing of HFD A after 2 h. of annealing is related to the redistribution of these excess nitrogen atoms. Nitrogen atoms are associated to an enormous  stabilizing effect. However, they are located near chromium atoms and the consequence is the appearance in the nitrided samples of zones mostly containing iron atoms with no nitrogen atoms within the first and the second neighbour shells. Such an iron environment without nitrogen can be associated to HFD B (figure 8). A similar, but different approach was proposed by Jack et al. [START_REF] Jack | The structure of nitrided iron-titanium alloys[END_REF][START_REF] Rickerby | Structure and thermochemistry of nitrided iron-titanium alloys[END_REF][START_REF] Rickerby | Low-temperature aging of nitrided Fe Ti alloys[END_REF] within the frame of titanium nitrogen interaction in a ferritic environment. In this model, titaniumnitrogen atom clusters form one dimensional Guinier-Preston zones (figure 1g). The formation of SRO between chromium and nitrogen is associated to distortions producing expansion and contraction of the atomic spacing around the chromium atoms as suggested by Oda et al. [START_REF] Oda | Interaction and arrangement of nitrogen atoms in FCC γiron[END_REF]. Such distortions explain that distributions are required for the interpretation of the Mossbauer spectra. The occurrence of higher hyperfine magnetic field in HFD B for annealing times higher than 2 h. can be interpreted as a reordering of the bcc environment in favour of iron as neighbour of iron. The fact that the (200) line of  N disappears before the (111) line is interesting to discuss. Brink et al. [START_REF] Brink | Thermal expansion and phase transformations of nitrogen-expanded austenite studied with in situ synchrotron X-ray diffraction[END_REF] observed a low nitrogen content gamma phase (named  T ) by in-situ synchrotron XRD experiments during annealing experiments on low and high nitrogen content expanded austenite. Such an observation seems to be connected with our finding. In order to try to explain the persistence of the  N (111) line, we had to take into account the highly anisotropic character of both the elastic and plastic strains induced by internal stress in expanded austenite [START_REF] Czerwiec | Fundamental and Innovations in Plasma Assisted Diffusion of Nitrogen and Carbon in Austenitic Stainless Steels and Related Alloys[END_REF]71]. It was shown that the strain perpendicular to the sample surface is higher for (200) grains as compared to (111). It can be postulated that the deformation in (200) grains of expanded austenite is high enough to promote the formation of martensite by a Bain distortion scheme [72], while it is not in (111) oriented grains. Following this hypothesis, the bcc phase observed by XRD must be attributed to martensite, probably located in the (200) oriented grains at the early stage of the decomposition. Such a transformation mechanism is only able to occur if a certain amount of excess nitrogen, which stabilizes austenite, is locally removed from the superficial layer. A balance between the local internal stress, which decreases when the nitrogen content decreases, and the local nitrogen content, which stabilize austenite, must be reached in order to allow the formation of martensite. From our CEMS experiments, it can be deduced that a martensitic environment is initially found in the nitrided layer. The occurrence of a bcc phase, as detected by XRD after 2 h. of annealing, is connected to HFD B, a martensitic environment of iron with low nitrogen content or without nitrogen. A second interesting point to discuss is the evolution of the lattice parameter from the bcc phase observed by XRD (figure 6). The lattice parameter for  iron is between 0.2866 and 0.2868 nm [START_REF] Jack | The structure of nitrided iron-titanium alloys[END_REF][START_REF] Rickerby | Structure and thermochemistry of nitrided iron-titanium alloys[END_REF], and is around 0.287 nm for ' in Fe-10 to 20 wt% Ni [START_REF] Zwell | Lattice parameter of ferritic and martensitic Fe-Ni alloys[END_REF]. The lattice parameter from our bcc phase is higher than these values, but not high enough to be associated to martensite containing nitrogen. Indeed, c values starts from 0,298 nm for nitrogen content of 2.7 at% and linearly increase as the nitrogen content increases [74]. Our Mossbauer measurements suggest that the martensitic phase does not contain nitrogen and that internal stress is responsible for the evolution of the lattice parameter during annealing. Finally, we must note that significant oxidation occurs (figure 3c) after two hours of annealing, at the exact moment when the formation of the bcc phase is observed by XRD. We believe that the corrosion resistance of the nitrided stainless steel is strongly affected by this transformation that occurs for very short time of annealing (2 h.) at 400°C. Such an observation is important for industrial applications for which nitrided workpieces in austenitic stainless steel have to operate at moderate temperature (300-500°C) without losing their corrosion properties.

A recent modelling paper partially supports our conclusions [75]. Calculations, performed on the Fe-Cr-N system, show that expanded austenite can be described as an f.c.c. iron dispersively embedded with the short-range ordered clusters of type Fe 6-n Cr n N. In the more favourable configurations, one chromium atom has more than one nitrogen atom as first neighbour [75].

Conclusion

The decomposition of expanded austenite formed in AISI 316LN nitrided for 4 h. at 410 °C in a UDECR device was studied by CEMS and XRD for different annealing times at 400°C. For the as nitrided sample, the CEMS spectra show the paramagnetic contribution of austenite and two magnetic contributions. Two hyperfine field distributions (HFD A and HFD B) were used to describe the magnetic contribution. HFD A was attributed to a expanded austenite. It was shown that HFD A cannot be attributed solely to a ' M 4 N (M = Fe, Ni, Cr…) environment even if deformations induced by high internal stresses are taken into account. Our contribution is to attribute HFD B to a bcc environment. Such environment is associated to the first step for the formation of a bcc phase, ferrite or more presumably martensite without or with very low nitrogen content. The broad range of hyperfine field in HFD B can be explained by both the local deformation of the bcc lattice and by the presence of M elements as iron neighbouring atoms. After only 2 h. of annealing, HFD A and the (200) peak of expanded austenite disappear and a bcc phase is observed by XRD. The vanishing of HFD A was explained by the diffusion of nitrogen in excess from the superficial part of the nitrided layer to the bulk during annealing. Nitrogen in excess is nitrogen not linked to chromium by short-range ordering. The occurrence of the bcc phase after 2 h. of annealing was shown to be connected to HFD B, a martensitic environment of iron with low nitrogen content or without nitrogen The interplay between local internal stress and local nitrogen content was proposed to explain the formation of a martensitic phase from the martensitic environment as detected by CEMS in the as nitrided sample. Nitrogen atoms linked to chromium by SRO must be considered as inefficient for stabilizing a gamma phase. Our results clearly show that it does not seem relevant to consider expanded austenite as a solid solution. The nitrogen atoms are concentrated around chromium atoms in strongly or weakly linked forms, leaving in the structure areas where the iron atoms no longer undergo the influence of chromium and nitrogen. These zones are likely to give a bcc phase during annealing.

Legends

Table 1: Hyperfine parameters and relative abundance of identified sub-spectra for the CEMS spectra presented in figure 3.

Figure 1 :

 1 Figure 1 : Schematic illustration of the possible arrangements of nitrogen atoms in stainless steels: (a) 3 dimensional view of nitrogen in solid solution with a statistical distribution, (b) same in 2D, (c) short range order of nitrogen with chromium, (d) non ordered concentration of nitrogen (clusters), (e) ordered concentration zones leading to coherent precipitates of CrN or (f) Fe x N 1-x and (g) one dimensionalGuinier-Preston zones. For the 3 D view, the atomic compositions are 25% for N, 47 % for Fe, 14% for Cr and 14 % for other atoms. For 2D view, the atomic composition is not respected.

Figure 2 :

 2 Figure 2 : CEMS spectrum of a non nitrided AISI 316L sample.

Figure 3 :

 3 Figure 3 : CEMS spectra of an AISI 316L sample nitrided for 4 h. at 410° C and then annealed at 400 °C for different times : (a) as nitrided, (b) annealed for 1 h., (c) annealed for 2 h., (d) annealed for 3 h., (e) annealed for 8 h. and (f) annealed for 8 h. at 400°C and then for 5 h. at 470 °C. The given annealing times are cumulated times. The paramagnetic phase is indicated by the red curve.

Figure 4 :

 4 Figure4: GDOES profiles of nitrogen content for the AISI 316L sample nitrided for 4 h. at 410° C before and the end of the annealing process (annealed for 8 h. at 400°C and then for 5 h. at 470 °C). The insert represent the evolution of the difference between N and Cr content as a function of depth.

Figure 5 :

 5 Figure5: X-ray diffraction patterns of an AISI 316L sample nitrided for 4 h. at 410° C and then annealed at 400 °C for different times (same as figure3).

Figure 6 :

 6 Figure6: Evolution of the different lattice parameters calculated from the X-ray diffraction patterns of an AISI 316L sample nitrided for 4 h. at 410° C and then annealed at 400 °C for different times (same as figure3).

Figure 7 :Figure 8 :

 78 Figure 7: Schematic view of atomic arrangement in the ' structure

  Figure1

  Figure 3

  Figure 4

  49]. Varma et al. [51-52] observed martensite in AISI 316L during mechanical rolling tests, but not during tensile tests. Martensite was also observed in AISI 316 L by TEM on wires deformed by cold drawing [53]. Szymańska et al. [54] observed martensite by XRD and Mössbauer spectroscopy after powder grinding of AISI 316. When AISI 316 is previously subjected to neutron bombardment, the formation of martensite is observed during tensile tests [55]. Manjanna et al [55-56] showed that martensite is formed during compression tests on AISI 316LN. Menendez et al.

Table 1

 1

		Phases
	Experiment
				HFD A			HFD B			or'			Fe 3 O 4
		Isomer	Relative	Hyperfine	Isomer	Relative	Hyperfine	Isomer	Relative	Hyperfine	Isomer	Relative	Hyperfine	Isomer	Relative
		shift	abondance	field (T)	Shift	abondance	field (T)	Shift	abondance	field (T)	Shift	abondance	field (T)	Shift	abondance
		(mm.s -1 )			(mm.s -1 )			(mm.s -1 )			(mm.s -1 )			(mm.s -1 )
	Non nitrided	-0.1	100%
	Nitrided 4 h. at	-0.16	4 %	10 to 28 0.27 to	44.6 %	14.5 to	-0.009	51.4 %
	400°C				0.293		32.6	to 0.075
	Annealed 1 h.	-0.12	3 %	10 to 28 0.27 to	26.8 %	15 to	-0.009	70.2 %
	at 400°C				0.315		32.5	to 0.053
	Annealed 2 h.	-0.12	4 %				15 to	-0.117	80 %				48.8	0.363	8 %
	at 400°C						35.4
								to 0.039					46.2	0.783	8 %
	Annealed 3 h.	-0.11	3.4 %				15 to	0.005 to	71 %	34	-0.06	14.5 %	48	0.362	5.3 %
	at 400°C						34.6	0.041
													46.2	0.742	5.8 %
	Annealed 8 h.	-0.11	3.4 %				15 to	-0.012 to	64.4 %	34	0.002	21.2 %	48	0.362	5.3 %
	at 400°C						34.8	0.05
													46	0.742	5.7 %
	Annealed 8 h.	-0.08	47%							34.3	-0.06	15
	at 400°C + 5
	h. at 470 °C									33.3	-0.06	28

Acknowledgments

 [START_REF] Ozturk | Phase and composition depth distribution analyses of low energy, high flux N implanted stainless steel[END_REF]This work was supported by the French Government through the programs Institut Carnot ICÉEL, and "Investissements d'avenir" operated by the French National Research Agency (ANR) and referenced to as ANR-11-LABEX-0008-01 (LabEx DAMAS).


Gregory Vial
email: gregory.vial@hec.ca

Reflections on Quality Requirements for Digital Trace Data in IS Research

Keywords: Digital trace data, Data quality, GitHub

In recent years an increasing number of academic disciplines, including IS, have sourced digital trace data for their research. Notwithstanding the potential of such data in (re)investigations of various phenomena of interest that would otherwise be difficult or impossible to study using other sources of data, we view the quality of digital trace data as an underappreciated issue in IS research. To initiate a discussion of how to evaluate and report on the quality of digital trace data in IS research, we couch our arguments within the broader tradition of research on data quality. We explain how the uncontrolled nature of digital trace data creates unique challenges for IS researchers, who need to collect, store, retrieve, and transform those data for the purpose of numerical analysis. We then draw parallels with concepts and patterns commonly used in data analysis projects and argue that, although IS researchers probably apply such concepts and patterns, this is not reported in publications, undermining the reader's ability to assess the reliability, statistical power and replicability of the findings. Using the case of GitHub to illustrate such challenges, we develop a preliminary set of guidelines to help researchers consider and report on the quality of the digital trace data they use in their research. Our work contributes to the debate on data quality and provides relevant recommendations for scholars and IS journals at a time when a growing number of publications are relying on digital trace data.

Introduction

Data quality has been acknowledged as an enduring issue in research and in practice [START_REF] Khatri | Designing data governance[END_REF][START_REF] Strong | Data quality in context[END_REF][START_REF] Wand | Anchoring data quality dimensions in ontological foundations[END_REF]. Considering the rise of digital technologies, big data, analytics and artificial intelligence, all of which are large producers and consumers of data in various formats, discussions about the veracity of dataa notion related to data quality -have become common in teaching, practice as well as in research in computer science and software engineering [START_REF] Demchenko | Addressing big data issues in scientific data infrastructure[END_REF]. Notwithstanding, we concur with [START_REF] Marsden | Numerical data quality in IS research and the implications for replication[END_REF] arguments and view data quality in IS research as an issue that deserves much-needed attention for the advancement of scientific knowledge.

In this short paper, we build on Marsden and Pingry's taxonomy of numerical data types and apply it to digital trace data (DTD) [START_REF] Berente | Research Commentary-Data-driven computationally intensive theory development[END_REF][START_REF] Howison | Validity issues in the use of social network analysis with digital trace data[END_REF]) -which we define as digital records of activities and events that are produced, stored and retrieved using information technologies -as a variation of the "third party" data type discussed by the authors. We explain why data quality issues are particularly relevant in the context of DTD, and we provide a current illustration of those issues before offering guidelines for authors working with DTD. Although our work is by no means an authoritative list of data quality requirements for DTD research, it encourages IS researchers and journals to value discussions of data quality as the subject of DTD continues to grow in popularity.

Boundary Assumption

As an initial step, we wish to establish an important contextual boundary. We assume that high-quality data are "fit for use by data consumers" (Wang & Strong, 1996, p. 6). In the context of this paper, this means that high-quality data are fit for use in the numerical analyses1 supporting the study of a research question. As we develop our arguments, we refer to the four main categories of data quality and their underlying dimensions, which we have summarized in Table 1. Our core argument is that DTD quality is an important topic because DTD often exhibit low quality within each category, rendering their use in science challenging. Fitness for use based on the format and the presentation of data for the task at hand Interpretability, ease of understanding, concise representation, consistent representation

The Rise of Digital Trace Data in (IS) Research

DTD is broadly defined as "digital records of activity and events that involve information technologies." (Berente et al., 2018, p. 1) Although some authors argue that DTD are both "produced through and stored by an information system" (Howison et al., 2011, p. 770), for the purposes of this discussion we would add that DTD are also retrieved by researchers using information systems (the relevance of this point is discussed below). In recent years, researchers have begun to use DTD for a variety of phenomena and research questions that had been otherwise difficult, or sometimes even impossible, to study. This includes questions related to distributed coordination in complex knowledge work environments [START_REF] Dabbish | Social coding in GitHub: Transparency and collaboration in an open software repository[END_REF], participation in online communities [START_REF] Faraj | Network exchange patterns in online communities[END_REF], organizational routines [START_REF] Pentland | Using workflow data to explore the structure of an organizational routine[END_REF], and the diffusion of information across social media [START_REF] Vosoughi | The spread of true and false news online[END_REF], among others. The growing availability of DTD has mirrored the rise of digital technologies in our lives, driving new research opportunities and even, as some have argued, theory development [START_REF] Berente | Research Commentary-Data-driven computationally intensive theory development[END_REF].

Our reading of articles that have used DTD has led us to concur with [START_REF] Marsden | Numerical data quality in IS research and the implications for replication[END_REF] observation that IS articles often suffer from the fact that "the amount of space devoted to data collection, validation, and/or quality details pales in comparison to the space devoted to detailing and explaining why a relatively sophisticated model form and estimation technique(s) are employed." (p. A1) In our opinion, this does not imply that IS researchers do not consider DTD quality an important aspect of their work. Rather, the final result of their work (i.e. scientific publications) fails to incorporate information that could help us evaluate the quality of the data used in their analysis. This may be due to the fact that the IS community has not valued having such information in publications. Yet, as we discuss below, such information is in fact highly relevant.

Digital Trace Data as a Raw Material

Public and Private Digital Trace Data

At this point, it is important to distinguish between the two main types of DTD. Private DTD are essentially data that are provided to a researcher but that remain inaccessible to the general public (e.g., available for a fee). Private DTD can be sourced from application logs [START_REF] Pentland | Using workflow data to explore the structure of an organizational routine[END_REF], private source code repositories [START_REF] Zimmermann | Predicting defects using network analysis on dependency graphs[END_REF], databases or documentation, among others. The key issues here are that another researcher

would not be able to retrieve the same data to replicate the findings of a given study and that researchers may have few means to assess the quality of the data they have obtained [START_REF] Marsden | Numerical data quality in IS research and the implications for replication[END_REF].

Public DTD are accessible to the general public. The rise of digital platforms and

ecosystems and the open data movement have helped make public DTD increasingly available [START_REF] Dabbish | Social coding in GitHub: Transparency and collaboration in an open software repository[END_REF][START_REF] Tsay | Influence of social and technical factors for evaluating contribution in GitHub[END_REF]. Unlike private DTD, public DTD offer an unprecedented opportunity for researchers to build research that is replicable and transparent. Although our examples are based on public DTD, our arguments are equally relevant to private DTD.

Digital Trace Data as an Uncontrolled Source of Data

By emphasizing the use of increasingly complex methods and modeling techniques to make significant methodological contributions, we often forgo explanations of the quality of data in general, and that of DTD in particular. Yet, as the old adage says, "garbage in, garbage out."

Without high-quality data, a model will have poor explanatory and/or predictive power, regardless of whether sophisticated imputation techniques are used. By definition, the quality of most DTD is a priori questionable because researchers have little to no control over how the data are generated. Compared to other forms of numerical data, this creates a significant challenge. For instance, there is a long-standing tradition reflected in articles offering guidelines [START_REF] Churchill | A paradigm for developing better measures of marketing constructs[END_REF][START_REF] Gerbing | An updated paradigm for scale development incorporating unidimensionality and its assessment[END_REF] to help researchers design survey instruments to generate numerical data fit for their purpose. Instruments are designed with a purpose in mind, and the constructs are operationalized based on the requirements of numerical analysis. In contrast, DTD are taken as a given, and researchers must work with the data without any control over how they are generated. This raises issues about the intrinsic quality of such data as well as the alignment between the research question, methods, and data.

Extract, Transform, Load Pattern in Digital Trace Data Research

As researchers, we must often perform a number of steps to retrieve, transform and manipulate raw DTD, in order to generate numerical data (a curated data set) in a format that are fit for numerical analysis. For example, we may scrape reviews from an online source, extract sentiment features from the textual data contained in those reviews, and transform those features into numerical data points to investigate our research question. In many ways, the process followed in these steps mirrors the Extract, Transform, Load (ETL) pattern commonly used in data warehousing [START_REF] Kimball | The data warehouse toolkit: The complete guide to dimensional modeling[END_REF]) (see Table 2). The ETL pattern is for extracting data from sources that are not designed for analysis (e.g., data from operational systems, logs), transforming them into a structure and a format that are fit for analysis, and consolidating them into a single source of high-quality data that will be readily available to users. When we teach the ETL process to our analytics students, whose other courses focus primarily on applied statistics, they realize that the creation of curated data sets requires effort. ETL processes must not only be followed; they must also be documented, audited and tested to ensure that the quality of data loaded into a data warehouse/mart remains consistent over time. In theory, a properly designed ETL process is therefore both transparent and reproducible. Such efforts are paramount in order to draw meaningful deductions from numerical analysis. Referring to the data quality dimensions presented in Table 1, it is through these steps that data become accessible to the researcher, who can then interpret them and use them as relevant and accurate in the investigation of a research question.

Table 2. Applying the ETL Pattern to DTD Processing ETL Pattern DTD Processing

Extract the source data Retrieve DTD from information system(s) Transform the source data

Transform DTD into a format that is fit for analysis (e.g., convert variable types, assess quality/cleanse, and join across multiple sources) Load the transformed data Save the transformed data as a curated data set (e.g., in a CSV file) to be used as input in formal data analysis and modeling

Beyond a Vision of Data as "Given"

To understand the underlying issues in DTD quality, it is useful to consider the original meaning of the word "data". The etymology of the word data (the plural of datum2 ) means "given" in Latin. In IS, like in many other fields such as computer science and software engineering, the concept of data refers to something that is raw and largely devoid of meaning on its own before it has been used and processed. Simple examples of data are the height of Mount Everest, or the current temperature, as recorded by instruments. There is often an implicit assumption that data, as things that are given, are neutral and unbiased. This assumption is problematic because it creates a false sense of confidence in data as objective means for describing phenomena. Considering the above examples, faulty instruments may very well generate data, but such data will be inaccurate [START_REF] Alkhalil | IoT data provenance implementation challenges[END_REF].

Whether they are generated by machines and calibrated instruments or by human actors (e.g., from a customer relationship management system), DTD should be treated as highly susceptible to data quality issues.

From Data to Capta

Seeking to address this assumption, some researchers have advocated use of the term capta-"[things] taken" in Latin-as a more accurate depiction of the objects we use in numerical analysis [START_REF] Checkland | Systems thinking[END_REF][START_REF] Drucker | Humanities approaches to graphical display[END_REF]. More specifically, social constructivist approaches and scholars in the humanities acknowledge that the decisions we make to enable the collection, analysis and graphical representation of data are not neutral. Rather, "humanistic inquiry acknowledges the situated, partial, and constitutive character of knowledge production, the recognition that knowledge is constructed, taken, not simply given as a natural representation of pre-existing fact" [START_REF] Drucker | Humanities approaches to graphical display[END_REF]. While this position has some significant ontological and epistemological implications that may not be universally accepted, it calls upon us to question: (1) how things are given to us as researchers and (2) how we take (or retrieve) those things before using them in our research.

This is precisely the type of question that statisticians and data scientists are expected to ask before using raw data in their analyses [START_REF] Cox | Applied statistics: a review[END_REF]. In data analysis projects, as in data warehousing, data profiling is an important activity carried out iteratively to assess the fitness for use of data. However important data profiling may be, IS researchers spend little time describing the process used to assess the quality of their DTD and the transformations they performed to render those DTD amenable to their research question [START_REF] Clarke | Big data, big risks[END_REF]. This issue is becoming more relevant as an increasing amount of external data is gathered from sources that provide no guarantee as to their quality (e.g., there is no public data available on the number of robots or fake accounts on Twitter). Even in contexts where the widespread adoption of the "Internet of Things", sensors, and other machine-based data generation mechanisms has the potential to remove human intervention from the data generation process, this issue remains. For example, specific decisions made on the use and placement of sensors or RFID tags can influence the DTD generated by physical objects and the inferences and predictions we can make from these DTD.

A Concrete Illustration: The Case of GitHub Data

Collecting Digital Trace Data from GitHub

To illustrate DTD quality issues, consider the case of GitHub. GitHub is the largest host for public and private software code repositories and has become an important source of DTD in IS (e.g., [START_REF] Zhang | Generative diffusion of innovations and knowledge networks in open source projects[END_REF] and computer science (e.g., [START_REF] Dabbish | Social coding in GitHub: Transparency and collaboration in an open software repository[END_REF]. Each repository hosted on GitHub contains a source code repository (Git) as well as tools that are used to help manage and coordinate work among project contributors and with the general public (e.g., announcements, bug reports, feature requests etc.). To access GitHub data, researchers typically have four options:

• They can manually retrieve and code the data from project web pages.

• They can scrape HTML pages and extract pertinent data using software libraries (e.g., BeautifulSoup in Python).

• They can use the GitHub Application Programming Interface (API) to retrieve the DTD required for the research project. This is achieved by using a pre-written piece of software or by writing custom software to call the GitHub API over the Internet.

• The final and most widely used option (e.g., [START_REF] Zhang | Generative diffusion of innovations and knowledge networks in open source projects[END_REF] is to retrieve the data from a third party provider. For instance, GitHub data is freely available through the GitHub Archive project, hosted on Google BigQuery, a cloud database service.

GitHub Digital Trace Data Quality Issues

Each of these options present researchers with different data quality issues affecting all four data quality categories. The first option is time-consuming and likely to be error-prone due to the manual data entry process (intrinsic data quality). The second option can also yield intrinsic data quality issues if the HTML page structure is not uniform across repositories.

Due to API quotas and historical data restrictions, the third option may not allow for completeness and accessibility, thereby hindering contextual data quality as well as other dimensions of intrinsic data quality. Although the fourth option appears to be the most viable, it also has drawbacks. To explain these issues, we have summarized the DTD extraction and transformation process in Figure 1, where every arrow has a potential impact on data quality.

Figure 1. Using DTD from GitHub

In theory, every event generated by a user or a machine interacting with GitHub generates an API event that is intercepted by the GitHub Archive service. The data contained within the event are saved at a temporary destination. At frequent intervals, the data contained in the temporary destination are archived in a Google BigQuery database. In practice, data quality issues can arise in the processing and saving of data at every step of this process, whether in the production and storage of DTD by third parties or in the retrieval of DTD by the researcher, even before the DTD are transformed and manipulated for numerical analysis.

Turning to the GitHub Archive project's repository (which is hosted on GitHub), there are indeed a number of reports of DTD that are either not saved properly or not saved at all, often with no explanation provided as to why problems occurred. In other instances, changes to GitHub's API went unnoticed by the GitHub Archive's team, who later modified their code to accommodate these changes. Beyond these issues, the researcher is still responsible for ensuring that the data are retrieved, transformed and manipulated in an appropriate manner and that the processes used for this purpose (or the software packages used) are free of bugs.

In every one of these steps, we should have confidence that appropriate decisions were made (e.g., by discarding certain classes of events, or certain types of projects) based on the research objectives rather than on convenience, so that each dimension of the data quality categories can be addressed.

Addressing Quality Issues in Digital Trace Data

Considering that sets of DTD may be rather large, it could be argued that some level of data quality issues (e.g., accuracy) may not impact the final results of a numerical analysis.

Although this argument may hold true from a statistical standpoint, our main concern is not that some of the data may be inaccurate or incomplete. Rather, it is the fact that we have no clear idea as to how much of the data is of low quality, and which dimension(s) of data quality are affected. It is only when these aspects are assessed and explained within the context of the research question at hand that we can make an informed decision about the data's suitability for the analysis and the potential impacts of low data quality on the power of the numerical analyses.

Applying the Seven W's

This raises the issue of whether we are able to propose practical criteria for assessing the quality of the numerical data extracted or derived from DTD. Although desirable, the high degree of variability in DTD across different sources means that we may not be able to establish clear-cut, universal criteria. Rather, we argue that researchers should make a number of considerations explicit in their work, to show that they were mindful of data quality issues and took appropriate steps to address them. Marsden and Pingry (2018, p. A2) argue that a scientific article should strive to answer the Seven W's (what, when, where, how, who, which, and why) about data quality. In our view, these seven questions provide a solid foundation for making statements about the quality of DTD more explicit in IS research.

Table 3 summarizes these seven questions and their application to DTD.

Relevance to DTD (private or public)

"What provides an explanation of exactly what is captured in the data."

• Provide an explanation of the nature of DTD (private, public), the elements of the DTD, their intrinsic quality, as well as their relationship to real-life activities or events as they relate to the research question. • Justify mismatches or approximations that are loosely associated with core aspects of the research question based on empirical or conceptual fitness rather than convenience. "When refers to the time at which the data is collected."

• Provide a detailed account of data collection period(s) as well as the period when access to the data was granted, if applicable.

"Where refers to the location (virtual or real) of the data collection."

• Although we expect that DTD are always virtual, researchers can sometimes triangulate DTD with real-life observations to increase confidence that the DTD reflect real-life processes. Virtual sources should be clearly identified (e.g., data providers). "How describes the

• Provide comprehensive coverage of the techniques used to retrieve the data precise process(es) of data collection."

and manipulate it from their raw format for use as a curated data set for numerical analysis. This includes extraction, transformation and loading techniques, as well as data profiling and quality assurance processes that support the generation of high-quality data. • Explain in detail which criteria were used to exclude any data from the original data set and justify the impact(s) of this decision on the curated data set and the analysis (e.g., reduced sample size, higher intrinsic quality). • Whenever possible, explain how the DTD were originally generated.

"Who details the individual(s) involved in the data collection."

• Explain how many individuals were involved in the collection, storage, retrieval, manipulation and analysis of the raw data set in order to generate the curated data set. • Provide detailed information on the various roles of those individuals, whether they implemented computational data collection processes (e.g., writing a service, an API) or performed quality assurance for those processes. • In some instances, these processes can be automated and performed by machines (e.g., quality assurance through continuous integration). "Which details instruments or artifacts used in collecting the data."

• Provide a detailed account of the artifacts used to collect and manipulate the original DTD. This includes third party services, custom software, APIs and any other form of IT artifact used to create the curated data set. When relevant, provide version numbers as well. "Why provides the set of reasons or goals for collecting the data."

• Ensure that there is a clear and well justified link between the data collected and the research question. Strive for fitness rather than convenience.

Bridging Data Quality Categories and the Seven W's

Researchers working with DTD spend a significant amount of time studying their data to identify and address outstanding quality issues. Returning to the specific case of GitHub, [START_REF] Kalliamvakou | An in-depth study of the promises and perils of mining GitHub[END_REF]Kalliamvakou et al. ( , p. 2041) provide an excellent description of what they aptly refer to as the perils of GitHub data. Without proper knowledge of how the GitHub platform and Git, its underlying source control system, work (along with their known bugs at the time of data collection) and how they are configured for a given repository, it is easy to make assumptions that can impact representational data quality and adversely affect findings.

In our view, readers should be able to find answers to these seven questions and understand how they relate to the four data quality categories. A comprehensive description of the data set (e.g., what type of data are contained within event payloads for different types of events) helps increase intrinsic, contextual data quality (e.g., completeness, amount of data), as well as representational data quality (e.g., interpretability, consistent representation).

Dimensions of accessibility (accessibility, access security) as well as other dimensions of contextual data quality (e.g., timeliness, completeness) are addressed by identifying when and where the data collection took place. How, who, and which questions contribute to all four data quality categories because they help us understand what data were collected as well as how they were transformed and manipulated to generate a curated data set in response to a specific research question. Last but not least, the why question is of paramount importance in order to contextualize the data collection process.

Encouraging Transparency and Replication

In the natural sciences, replication and transparency are key elements of the scientific process and the accumulation of knowledge. In IS, the push for replication remains largely absent, save for a few notable exceptions such as the journal AIS Transactions on Replication

Research. However, we argue that DTD, and especially public DTD, are viable candidates for transparency and replication. Indeed, since a large portion of the data collection and transformation process is aided by IT, detailed explanations of the steps performed with these IT enable transparency over the process used to generate the curated data set. It should even be possible, in many instances, to share any piece of written software used to generate this curated data set. For example, if a program is written to retrieve and manipulate data from the GitHub Archive in order to generate a curated data set that is then used to perform some form of numerical analysis, the researcher could upload the source code to a repository on GitHub.

This repository could be made public using an open source software license, or kept private but shared with reviewers. One could then re-execute the source code, and/or actually validate the code, to ensure that the quality of the curated data set satisfies the requirements of the study.

In this manner we could build better, more accessible tools to help us engage with DTD more efficiently, e.g., by using design science research principles to create artifacts that help the IS research community. Replication is an important aspect of scientific progress. Public DTD lend themselves to replication, but their inherent lack of quality means that, even if they are publicly available, they need to be collected and transformed before they can be used.

Given that such collection and transformation processes are often extensive, raw DTD alone will not be sufficient to foster transparency and replication.

Concluding Remarks

DTD carry tremendous potential for the advancement of scientific knowledge in IS and other disciplines. In order for this potential to be realized and in the interests of producing replicable research, we need to engage in discussions on the quality of DTD. How DTD are collected, stored, retrieved and transformed into data that are fit for numerical analysis are important matters in the context of building methodological and theoretical contributions.

With this short paper, we hope to encourage researchers to reflect on DTD quality and its relevance to their work. At a higher level, we hope to motivate the IS community to value DTD quality in research. Current efforts by publishers3 in this area often go unnoticed or are perceived by researchers as not adding value. In our view this is far from the truth, since data quality, especially in the context of DTD, is an issue that we address on a constant basis in our research. It is high time that these efforts begin to percolate into our publications.

Table 1 . Data Quality Categories and Dimensions (adapted from Strong et al., 1997; Wang & Strong, 1996) Data Quality Category Description Data Quality Dimensions

 1

	Intrinsic data quality	Fitness for use based on the inherent	Accuracy, objectivity, believability,
		properties of the data	reputation
	Accessibility data	Fitness for use based on the ability to	Accessibility, access security
	quality	retrieve the data
	Contextual data quality Fitness for use based on the task at	Relevancy, value-added, timeliness,
		hand	completeness, amount of data
	Representational data
	quality

Table 3 . Asking the Seven W's for DTD Consideration (from Marsden & Pingry, 2018, p. A2)

 3

We use the term "numerical analysis" as a general term referring to any form of data analysis technique, whether qualitative or quantitative, exploratory, explanatory, or predictive.

While the term "data" is often conjugated as a singular noun, we treat it as a plural noun, in accordance with its etymology.

https://www.elsevier.com/authors/author-services/research-data

Acknowledgments

This work was supported by the Fonds de recherche du Québec -Société et culture (FRQSC). The author is grateful to the editor and the reviewers for their comments and suggestions.