Moulay Marcus Fehse
email: marcus.fehse@esrf.fr

Tahar Sougrati

Ali Darwiche

Vincent Gabaudan

Camille La Fontaine

Laure Monconduit

Lorenzo Stievano
email: lorenzo.stievano@umontpellier.fr

Moulay T Sougrati

Elucidating the origin of superior electrochemical cycling performance: new insights on sodiation-desodiation mechanism of SnSb from operando spectroscopy

Keywords: X-ray absorption spectroscopy, Mössbauer spectroscopy, Chemometrics, MCR-ALS, Na-ion batteries, Alloy-type reaction, SnSb

Introduction

Although SnSb-based alloy-type materials were already proposed as candidates for lithiumion battery negative electrodes more than 20 years ago, 1 their application as an alternative high-capacity anode material for sodium-based batteries (NIB) has only shifted in the focus of research in the last five years. While severe volume changes upon sodiation poses a serious degradation threat, recent studies have shown encouraging results that these obstacles can be mitigated and reversible capacities in the range of 350-525 mAh g -1 for 100-200 cycles with decent coulombic efficiency are attainable. [START_REF] Ji | Controlling SEI formation on SnSb-porous carbon nanofibers for improved Na ion storage[END_REF][START_REF] He | Monodisperse SnSb nanocrystals for Li-ion and Na-ion battery anodes: synergy and dissonance between Sn and Sb[END_REF][START_REF] Ji | Reduced Graphene Oxide/Tin-Antimony Nanocomposites as Anode Materials for Advanced Sodium-Ion Batteries[END_REF][START_REF] Walter | Inexpensive colloidal SnSb nanoalloys as efficient anode materials for lithium-and sodium-ion batteries[END_REF][START_REF] Yi | One-pot chemical route for morphology-controllable fabrication of Sn-Sb micro/nano-structures: Advanced anode materials for lithium and sodium storage[END_REF] Moreover we have recently shown that a SnSb electrode without any sophisticated preparation can reach a capacity of 700 mAh g -1 at low rate (11 mA g -1 ) and a stable capacity of 500-550 mAh g -1 at high rate (111 mA g -1 ) over many cycles. [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF] In their very recent study Qin et al. demonstrate that via embedding SnSb nanocrystalls in a graphene scaffold the capacity can be stabilized over thousands of cycles. [START_REF] Qin | A Top-Down Strategy toward SnSb In-Plane Nanoconfined 3D N-Doped Porous Graphene Composite Microspheres for High Performance Na-Ion Battery Anode[END_REF] Such outstanding electrochemical performance make SnSb one of the most promising negative electrode materials for NIB. The remarkable cycle life of SnSb vs. Na, which exceeds by far the one observed vs. Li for the same electrode, comes as a surprise considering the huge volume expansion (226%) expected for the reaction of SnSb with ≈4.9 Na. The fact that Sn metal cycles poorly vs. Na but within SnSb alloy the sodiation of tin contributes strongly to the reversible capacity is another curiosity.

The exceptional electrochemical performance of SnSb vs. Na has spurred several studies investigating the electrochemical sodiation process. Xiao et al. were the first to suggest that the sodiation of SnSb occurs via a two-step reaction process. [START_REF] Xiao | High capacity, reversible alloying reactions in SnSb/C nanocomposites for Na-ion battery applications[END_REF] In a recent study we have shown that the electrochemical mechanism of SnSb vs. Na is not the simple combination of those of Sn and Sb metals vs. Na, and that it is clearly distinct from the SnSb lithiation mechanism. [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF] Baggetto et al. studied the reaction mechanism via an ex situ XRD and Mössbauer analysis. However, due to amorphization upon reaction and the extended use of only ex situ characterizations, the obtained information content is somewhat limited and remains partially ambiguous. [START_REF] Baggetto | The reaction mechanism of SnSb and Sb thin film anodes for Na-ion batteries studied by X-ray diffraction, 119Sn and 121Sb Mössbauer spectroscopies[END_REF] In particular, the authors claimed the simultaneous formation of sodiated Sn and Sb species, providing a rather questionable interpretation of their Mössbauer spectra and justification of the unexpected presence of unusual quadrupole splitting and isomer shift values by the occurrence of nanosizing and large disorder in the obtained phases. Allan et al. carried out NMR and PDF analysis to elucidate the intermediate species but focusing solely on the sodiation of Sb and not on SnSb. [START_REF] Allan | Tracking Sodium-Antimonide Phase Transformations in Sodium-Ion Anodes: Insights from Operando Pair Distribution Function Analysis and Solid-State NMR Spectroscopy[END_REF] Consequently, in spite of the above mentioned studies, the scientific community still lacks a thorough understanding of the processes occurring upon sodiation of SnSb.

In order to elucidate the excellent performance of SnSb in NIB, superior to those measured in LIB under similar conditions, [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF] we carried out an in-depth analysis of the reversible sodiation reaction of SnSb via operando X-ray diffraction (XRD), XAS, and Mössbauer spectroscopy. For data analysis and extraction of reliable information, a chemometric approach including Principal Component Analysis (PCA) and Multivariate Curve Resolution -Alternating Least Squares (MCR-ALS) was used. In previous studies, it was shown that the application of PCA and MCR-ALS on operando X-ray absorption spectroscopy (XAS) data sets is a smart and elegant way to analyze large data sets and extract key information which are rather difficult to access otherwise. [START_REF] Conti | Multivariate Curve Resolution Analysis for Interpretation of Dynamic Cu K-Edge X-ray Absorption Spectroscopy Spectra for a Cu Doped V 2 O 5 Lithium Battery[END_REF][START_REF] Cassinelli | Multivariate curve resolution analysis applied to time-resolved synchrotron X-ray Absorption Spectroscopy monitoring of the activation of copper alumina catalyst[END_REF][START_REF] Giorgetti | Structural and electronic studies of metal hexacyanoferrates based cathodes for Li rechargeable batteries[END_REF][START_REF] Iadecola | Li deinsertion mechanism and Jahn-Teller distortion in LiFe0.75Mn0.25PO4: an operando X-ray absorption spectroscopy investigation[END_REF][START_REF] Broux | Disproportionation Upon Sodium Extraction from Na3V2(PO4)2F3 Observed by Operando X-ray Absorption Spectroscopy and Solid-State NMR[END_REF][START_REF] Loaiza | Understanding the lithiation/delithiation mechanism of Si(1-x)Gex alloys[END_REF] Very recently we demonstrated that it can also be applied to operando Mössbauer data sets. [START_REF] Coquil | FeSi4P4: A novel negative electrode with atypical electrochemical mechanism for Li and Na-ion batteries[END_REF] This chemometric approach allows the identification of the main contributing components as well as the analysis of their local structure and their order of appearance and disappearance during the electrochemical reaction.

Experimental

Material synthesis and electrode formulation

Electrode materials were prepared via ball milling as previously reported. [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF] Self-supported electrodes were made from an aqueous slurry containing SnSb active material, carbon black ground carbon fibres VGCF-S and PTFE binder in the ratio 70:6:6:18 with a loading variable from ≈ 2 to 15 mg cm -2 . High-loading electrodes were necessary for the operando XAS analysis, in order to obtain a sufficiently high signal-to-noise ratio in the measured spectra.

The mixture was thoroughly mixed in a planetary ball-mill for 1 h, tape casted on a thin aluminum foil (thickness ≈ 7 µm), dried at room temperature and subsequently at 100 • C under vacuum.

Operando X-ray Absorption Spectroscopy

XAS measurements at the Sn and Sb K-edge were performed in the transmission mode at the SAMBA beamline of Synchrotron SOLEIL in Gif-sur-Yvette (France). A Si(220) double crystal monochromator with an energy resolution of 1 eV at 30 keV was used. The intensity of the monochromatic X-ray beam was measured by three consecutive ionization detectors. The operando electrochemical cell [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] was placed between the first and the second ionization chambers. The homogeneity of the sample was checked before running the electrochemical test. The latter was carried on continuously for the first cycle and a half (discharge/charge/discharge) with a cycling rate of C/3, whereas 1 C corresponds to the reaction of 1 mol of Na with 1 mol of SnSb.

In the XANES (X-ray absorption near-edge structure) region of Sn and Sb K-edges (29200 and 30491 eV , respectively), equidistant energy steps of E = 1 eV were used. For all measured spectra, the exact energy calibration was established with simultaneous absorption measurements on a SnSb reference pellet placed between the second and the third ionization chamber. The first inflection point of the XAS pattern of Sb (30491 eV ) was used for the energy calibration. The absolute energy reproducibility of the measured spectra was ±0.1 eV . EXAFS (Extended X-ray Absorption Fine Structure) spectra were collected up to k = 15 Å-1 . The spectra of the pure reference compounds (Sb, Na 3 Sb, Sn) were extracted and fitted using the IFEFFIT software package. [START_REF] Ravel | HEPHAESTUS: Data analysis for X-ray absorption spectroscopy using IFEFFIT[END_REF] Fourier transform of EXAFS oscillations with different k weights was carried out in k-range from 3.0 to 12.0 Å-1 . Fitting was performed in R-range from 1.6 to 4.6 Å using k 2 and k 3 weights. EXAFS amplitudes and phase-shifts were calculated by FEFF starting from the calculated lattice parameters of SnSb, Na 3 Sb, Na 15 Sn 4 , α-Sn and Sb metal (vide infra). Interatomic distances (R) and the Debye-Waller factors (σ 2 ) were calculated for all paths included in the fits.

119 Sn Mössbauer spectroscopy

Transmission 119 Sn Mössbauer spectroscopy measurements were carried out with a source of 119m Sn in a matrix of CaSnO 3 . During the measurement, the source was always kept at room temperature. The velocity scale was calibrated with the magnetically split sextet spectrum of a high-purity α-Fe foil as the reference absorber, using a 119 Co:Rh source. 119 Sn isomer shifts are given relative to the CaSnO 3 source. The Mössbauer spectrometer was operated with a triangular velocity wave. A LiF scintillation detector was used for the detection of the γ-rays. The measured spectra (or the derived MCR-ALS components, vide infra) were fitted to appropriate combinations of Lorentzian profiles by least-squares methods. In this way, spectral parameters such as quadrupole splitting (∆), isomer shift (δ), linewidth (Γ) and relative resonance areas of the different spectral components were determined. These data are reported in Tab. 3. Simultaneously to Mössbauer acquisition, X-ray diffraction patterns were collected in joint setup previously reported. [START_REF] Jumas | Analyse des caracteristiques d'un matériau d'électrode d'une cellule électrochimique[END_REF][START_REF] Mccalla | Understanding the Roles of Anionic Redox and Oxygen Release during Electrochemical Cycling of Lithium-Rich Layered Li<inf>4</inf>FeSbO<inf>6</inf>[END_REF] Operando measurements were performed at room temperature using the same in situ cell used for the operando XAS measurements. [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] Ex situ measurements at variable temperature were performed in a close-cycle helium flow cryostat (Janis SH-850). For the ex situ measurements of cycled electrodes, the cells were discharged at C/6 rate, and then transferred to the glove box before disassembly.

The electrodes were mounted in air-tight sealed sample holders to avoid any contamination from ambient atmosphere before and during the collection of Mössbauer spectra. Debye temperatures Θ D were calculated from the temperature dependence of the Mössbauer spectra measured between ambient temperature (300 K) and 12 K following the procedure which has been described in detail elsewhere. [START_REF] Conte | BPO4]1-x composites as negative electrodes for lithium ion cells: Comparison with amorphous SnB0.6P0.4O2.9 and effect of composition[END_REF]

Chemometric data analysis

The operando EXAFS and Mössbauer spectra were first globally analyzed using a statistical tool named Principal Component Analysis (PCA) using the computer program Matlab. [START_REF] Massart | Handbook of Chemometrics and Qualimetrics: Part A[END_REF] PCA is a chemometric factor analysis tool, and is generally used to discover the minimal particular structures in multivariate spectral data sets. More precisely, it is used here to determine the number of independent components contributing to the whole series of collected spectra during electrochemical cycling. The number of principal components determined in this way was used as the basis for Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis. [START_REF] Jaumot | A graphical user-friendly interface for MCR-ALS: A new tool for multivariate curve resolution in MATLAB[END_REF][START_REF] Jaumot | MCR-ALS GUI 2.0: New features and applications[END_REF] This algorithm allows the stepwise reconstruction of the spectral components which are necessary for interpreting the whole multiset of operando spectra.

The MCR-ALS analysis for EXAFS data was performed on normalized absorption spectra with the following constraints: (i) non-negativity of the concentration of the components, (ii) unimodality for one of the components, reflecting the irreversible transformation of the pristine material and (iii) closure (sum of the components concentrations always equal to 100%). The reconstructed spectral components were then fitted using the IFEFFIT software package in the same way as for the reference compounds.

For Mössbauer spectra only unimodality and non-negativity conditions were applied but no closure constraint was applied to allow for an additional degree of freedom. The reconstructed components were fitted to appropriate combinations of Lorentzian profiles by least-squares methods, as described in Sec. 2.3.

Results

Operando XAS

The electrochemical signature of the SnSb alloy during the first three processes (sodiation/desodiation/sodiation) is shown in Fig. 1 along with markers indicating the acquisition of XAS spectra. A characteristic feature of the electrochemical cycling curve is the presence of two plateaus suggesting a two-step process reaction. Similar to conversion-type materials, the first discharge is taking place at lower potentials than subsequent. [START_REF] Cabana | Beyond intercalation-based Li-ion batteries: the state of the art and challenges of electrode materials reacting through conversion reactions[END_REF] This can be linked to restructuring and nanosizing of the electrode material, in line with previous reports. The operando Sn and Sb K-edges EXAFS spectra collected during the first three processes are shown in Fig. 2 (left) and (right), respectively. Even though the absorption edges shift noticeably during the different electrochemical processes, their features are rather broad and badly defined, and their shape varies only very little. This result is somehow expected, since the very high energy of the absorption K-edges of Sb and Sn is connected to a very short lifetime of the core-hole, resulting in a low energy resolution of the absorption edge.

Consequently, the XANES part of the spectra carry very little information and could not be used to identify the different species formed during the process.

When comparing the evolution of EXAFS spectra shown in Fig. 2, it is striking that the main changes of Sn and Sb do not occur simultaneously. During first discharge Sb spectra change strongly up to spectra #15 and then remain almost unaltered during remainder of discharge. Sn spectra on the other hand reveal only a shift of the EXAFS oscillation to higher k values up to spectra #15 but then the amplitude of the EXAFS oscillation strongly decreases upon continuous sodiation. These differences suggest a complex multistep electrochemical process. The oscillations of the EXAFS part are rather intense and visible up to k = 12 Å-1 for both Sn and Sb K-edge spectra, and can thus be used successfully to describe the average coordination around the Sn and Sb centres, respectively. The two sets of operando EXAFS data were analysed separately using PCA in order to avoid an over-interpretation of the experimental data, and to extract the maximum amount of useful information independently for Sn and Sb. The variance plots obtained is shown in Fig. 3 and indicates that over 94% of the variance of the EXAFS spectra can be described by using three principal components for Sb, whereas four components were included in the case of Sn to achieve over 98% of variance. The residual part stems from the experimental noise.

Even though the so-obtained principal components are only orthogonal mathematical functions and not real EXAFS spectra, their determination reveals the number of independent spectral components that can be used to fit the whole set of experimental data. Several methodologies are then available to reconstruct the corresponding real EXAFS components as well as their evolution. In this case, the MCR-ALS analysis was used [START_REF] Jaumot | A graphical user-friendly interface for MCR-ALS: A new tool for multivariate curve resolution in MATLAB[END_REF][START_REF] Jaumot | MCR-ALS GUI 2.0: New features and applications[END_REF] producing pure component EXAFS spectra (see S.I) along with their evolution throughout electrochemical These components correspond perfectly to specific spectra measured along the operando measurements, in line with their observed evolution: component 1 produced from the analysis of the Sb spectra, for instance, is practically identical to the Sb K-edge EXAFS spectrum of pristine SnSb. On the other hand, component 2 is identical to spectrum obtained at the end of the first discharge, i.e., to full sodiation, whereas component 3 resembles perfectly the spectrum obtained at the end of the charge process, corresponding to the fully desodiated electrode. A similar attribution can be made also for the first three components identified for the Sn K-edge spectra. Component 4, necessary only in the case of Sn, represents the formation of an intermediate Sn species which reaches its maximum at the end of the first plateau of the electrochemical curve (see dotted line, Fig. 4). From previous studies this suggests its attribution to a form of amorphous metallic Sn. [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF][START_REF] Xiao | High capacity, reversible alloying reactions in SnSb/C nanocomposites for Na-ion battery applications[END_REF] The reconstructed pure components were fitted in the traditional way, starting from the known structures. The results of the EXAFS fit for Sn and Sb K-edge, see S.I., are reported in Tab. 1 and 2, respectively. Optimum fit for component 1 of Sn was achieved using 3 Sn-Sn(Sb) shells corresponding to the published structure of SnSb. For the second component the optimum fit was obtained using 3 Sn-Na shells, similar to the structure published for Na 15 Sn 4 , whereas fits with other sodiated tin phases (e.g. Na 9 Sn 4 ) did not lead to satisfactory results. For the third component best fit was achieved using a single shell of Sn-Sn(Sb) which corresponds to an amorphous form of SnSb (or Sn) with lower coordination and quite short bond distances. Fitting of the 4th component is somewhat similar involving solely one Sn-Sn shell corresponding to an amorphous Sn with bond distance at 2.94 Å, somehow in between those reported for α and β-Sn, and a coordination number of 4, identical to that of αtin. It is interesting to notice that tetragonal β-tin, also known as white tin, is the stable polymorph of tin at ambient conditions, and is characterised by a coordination number of 6, corresponding to a distorted octahedron with two different bond distances (4 neighbours at 3.02 Å and 2 neighbours at 3.18 Å). The α-Sn allotrope, on the other hand, is known as grey tin, has a highly symmetric diamond-like structure with a perfect four-fold coordination shell at 2.81 Å, and is usually stable only below 13.2 • C. [START_REF] Silver | A systematic investigation of the Mössbauer parameters of some intermetallic compounds and electroplated alloys of tin[END_REF][START_REF] Stevens | Isomer shift reference scales[END_REF] Component 1 of the Sb K-edge spectra, representing pristine SnSb is fitted in the identical way as the Sn K-edge spectrum, starting from the crystal structure of the pure compound.

The fitting of component 2 can be performed using the first two Sb-Na shells of hexagonal Na 3 Sb. It is noteworthy that unlike our previous study in which we were able to identify both cubic and hexagonal Na 3 Sb, 30 such a distinction is impossible in this study since we only see the first shell of next neighbours. Such limited range in R-space renders the two polymorphs indistinguishable from an EXAFS viewpoint, hence we observe an average of the two phases. Finally, component 3 can be fitted by using simply the first coordination shells of Sb metal, with a significant decrease of the average Sb-Sb distance and half the number of nearest neighbours of Sb metal. The presence of a tri-coordinated Sb-Sb shell with a Sb-Sb interatomic distance lower than in Sb metal reminds of the long known structure of amorphous "explosive" antimony, synthesized by Krebs et al. via electrolysis of antimony chloride. [START_REF] Krebs | Neubestimmung der Nahordnung im glasigen Selen, im explosiven Antimon und im beta-und gamma-Arsen[END_REF] The proposed structural model for this phase is based on a disordered network of antimony, where all antimony atoms are bonded to three other ones with a Sb-Sb distance sensibly lower than in Sb metal. A large range of coordination angles results in the total disappearance of the spectral contributions beyond the first nearest neighbour shell, and an absence of long-range order. It is important to notice that such interpretation is in complete agreement with the totally flat X-ray diffraction pattern observed at the end of the charge process, previously published. [START_REF] Darwiche | Facile synthesis and long cycle life of SnSb as negative electrode material for Na-ion batteries[END_REF] Table 1: EXAFS fitting parameters of MCR-ALS components of Sn K-edge Now, it is important to notice that, from these analyses, no intermediate Na-Sb species could be evidenced. This result is somehow in contradiction not only with the work of Baggetto et al., [START_REF] Baggetto | Intrinsic thermodynamic and kinetic properties of Sb electrodes for Li-ion and Na-ion batteries: experiment and theory[END_REF] who suggested the formation of an amorphous form of NaSb as an intermediate phase during the discharge, but also with more recent results that we obtained by operando Pair Distribution Function (PDF) and ex situ [START_REF] Conte | BPO4]1-x composites as negative electrodes for lithium ion cells: Comparison with amorphous SnB0.6P0.4O2.9 and effect of composition[END_REF] Na Solid State Nuclear Magnetic Resonance analysis in the case of pure Sb. [START_REF] Allan | Tracking Sodium-Antimonide Phase Transformations in Sodium-Ion Anodes: Insights from Operando Pair Distribution Function Analysis and Solid-State NMR Spectroscopy[END_REF] In that work, two different electrochemically formed intermediates were identified: (i) amorphous Na 3-x Sb (with x ≈ 0.4 to 0.5), having a local structure similar to crystalline Na 3 Sb but with a significant number of sodium vacancies and a limited correlation length, and (ii) amorphous Na 1.7 Sb, with a highly amorphous structure featuring some Sb-Sb bonding. Even though the first of these two phases seems to form during the first sodiation, the second one is expected to appear only during the following desodiation. It is important to notice that such phases, even though mostly amorphous, can be identified by PDF in the direct space using the series of peaks from 2 to about 10 Å. Contrary to PDF, in the EXAFS spectra measured during the operando processes, only the first coordination shell is visible due to the amorphous nature of the samples, with the notable exception of pristine SnSb where also the second coordination shell is visible. This limit of EXAFS compared to PDF is inherent to the nature of the probe: scattered electrons and X-rays in EXAFS and PDF, respectively, which have different diffusion path lengths in the materials. Therefore, even though EXAFS is more sensitive to the nature of the neighbouring atoms, and Sb atoms can thus be distinguished from the Na ones in the fits, the analysis remains restricted to the neighbours corresponding to only the first peak of the PDF signal, and is probably not sufficient to differentiate among many possible amorphous phases characterised by similar nearest-neighbours distances, which is the case of the intermediates proposed by Allan et al. [START_REF] Allan | Tracking Sodium-Antimonide Phase Transformations in Sodium-Ion Anodes: Insights from Operando Pair Distribution Function Analysis and Solid-State NMR Spectroscopy[END_REF] A parallel study on the sodiation/desodiation of Sb performed in the same way proves exactly the same inability of spotting intermediate species, confirming that EXAFS is not the appropriate probe to identify such phases. (ref submitted to journal)

Component Shell N R theo [ Å] R f it [ Å] σ 2 [ Å] 2 S 2 0 M-
The Sn and Sb K-edge EXAFS spectra of the initial phases are very similar in shape, and Sn K-edge spectra of the 3rd component (EOC) of amorphous SnSb are very similar (see S.I.), whereas here the difference in intensity leads to slightly different coordination numbers. However, practically the same bond distance and σ 2 are obtained while fitting.

The similarity of the Sb and Sn K-edge of the EOC phase is in line with the reformation of the SnSb alloy. We would like to point out that the phase obtained at the EOC is different from the amorphous tin metal intermediate, which is formed during the first plateau and reaches its maximum concentration at the plateau limit, see dotted line in Fig. 4.

119 Sn Mössbauer spectroscopy

Evolution of the operando 119 Sn Mössbauer spectra during the first discharge along with corresponding electrochemical curve are shown in Fig. 5. In the pristine state, the Mössbauer plot reveals a dominant feature at 2.4-2.8 mm s -1 which loses its intensity upon discharge. second minor contribution is identified as nanosized SnO 2 stemming from surface oxidation of Sn, with a share of ≈5%, obtained via weighing absorption area ratio with Lamb-Mössbauer factor.

In the case of MCR#2, a single spectral contribution with an isomer shift of 1.93 mm s -1 is observed. Such an isomer shift cannot be attributed to any known sodiated tin Na x Sn species. In fact, all sodiated phases have isomer shifts above 2.17 mm s -1 , which corresponds to the sodiated tin phase with the highest Na content, i.e., Na 15 Sn 4 , 34 see S.I. for Mössbauer spectra of reference samples. On the other hand, such a low isomer shift value does not correspond to that of the thermodynamically expected β-Sn phase, but rather resembles to that of the grey α-Sn allotrope (vide supra, Sec. 3.1). The formation of an amorphous Sn phase similar to α-Sn during the first discharge plateau is supported by the operando XAS data presented above (cf. Sec. 3.1), which also indicate the formation of an intermediate with structural parameters (bond distance and coordination number) similar to those of α-Sn that undergoes sodiation mainly during the second discharge plateau. The formation of thermodynamically unexpected phases is not uncommon in electrochemical processes and has been previously reported for several other conversion and alloy reactions. [START_REF] Darwiche | Better cycling performances of bulk Sb in Na-ion batteries compared to Li-ion systems: an unexpected electrochemical mechanism[END_REF][START_REF] Villevieille | NiSb2 as negative electrode for Li-ion batteries: An original conversion reaction[END_REF][START_REF] Sougrati | TiSnSb a new efficient negative electrode for Li-ion batteries: mechanism investigations by operando-XRD and Mössbauer techniques[END_REF] Towards the end of the discharge the signal-to-noise ratio becomes very small, see Fig. 5, testifying the formation of new tin-containing species with small Lamb-Mössbauer factors. This result is not surprising, since an elastic softening of the alloys upon increasing sodiation is expected for tin as well as for antimony. [START_REF] Allan | Tracking Sodium-Antimonide Phase Transformations in Sodium-Ion Anodes: Insights from Operando Pair Distribution Function Analysis and Solid-State NMR Spectroscopy[END_REF][START_REF] Mortazavi | Elastic softening of alloy negative electrodes for Na-ion batteries[END_REF] In order to increase the Lamb-Mössbauer factor of the obtained phases, an ex situ variable temperature Mössbauer spectroscopy study was carried out on two selected electrodes, which were put in test batteries and stopped after the reaction of 3 mol of Na per mol of Sn, and at the end of the first discharge, respectively.

The spectra of these two samples measured at room temperature and at 12 K are shown in The spectrum of the electrode stopped after the reaction of 3 mol Na, i.e. at about 3/4 of the first plateau, contains (at least) two spectral components with quite similar intensity: the first one corresponds to the spectrum of pristine SnSb, whereas the second component is characterised by an isomer shift of 1.98(2) mm s -1 at 12 K, corresponding to about 1.9 mm s -1 at ambient temperature. Such a spectrum corresponds well to the presence of both pristine SnSb and the amorphous Sn phase similar to α-Sn detected in the operando spectra. The presence of minor amounts of sodiated tin phases cannot be excluded, since a minor signal of such species could be hidden in between these two major contributions. It is interesting to notice that the relative amounts of the two spectral components vary very little between ambient conditions and 12 K, indicating that the two phases are characterised by similar Debye temperatures Θ D .

Discussion

With these combined spectral information in mind, it is now possible to follow the evolution of the different phases during the sodiation/desodiation/sodiation processes shown in Fig. 4. The electrochemical reaction mechanism during sodiation (discharge) can be written as a two-step process, as resumed in Eq. 1 and 2, being well in line with the hypothesis of Xiao et al., [START_REF] Xiao | High capacity, reversible alloying reactions in SnSb/C nanocomposites for Na-ion battery applications[END_REF] but in partial contradiction with other works, which suggested the direct formation of sodiated tin phases without the formation of tin intermediates. [START_REF] Baggetto | The reaction mechanism of SnSb and Sb thin film anodes for Na-ion batteries studied by X-ray diffraction, 119Sn and 121Sb Mössbauer spectroscopies[END_REF] These authors, however, proposed a sodiation mechanism based mainly on ex situ 119 Sn Mössbauer spectra measured solely at room temperature and on relaxed samples. Unfortunately, these spectra could not be fitted in an unequivocal way and thus provided only an incomplete sketch of the whole mechanism.

During the first part of the reaction, Sb is sodiated to form almost pure Na 3 Sb, along with amorphous metallic tin resembling to α-Sn. It is important to note that, during the first discharge, XAS also indicates the temporary formation of amorphous SnSb. This is in partial analogy to the reaction of SnSb vs. Li reported in the literature in which Li 3 Sb and β-Sn are formed. [START_REF] Zhou | Microwaveassisted selective preparation and characterization of Li 21Si5 and Li17Sn4[END_REF] Contrary to the lithiation, however, the tin and antimony species formed in the electrochemical reaction vs. Na are mostly amorphous. The subsequent reaction step involves the sodiation of Sn leading to the formation of Na 15 Sn 4 . This mechanism is very distinct from sodiation process of Sn metal and from the lithiation mechanism of SnSb, for which several intermediate steps involving successive crystalline phase transitions have been reported. [START_REF] Du | Investigation of the reversible sodiation of Sn foil by ex-situ X-ray diffractometry and Mössbauer effect spectroscopy[END_REF][START_REF] Stratford | Investigating Sodium Storage Mechanisms in Tin Anodes: A Combined Pair Distribution Function Analysis, Density Functional Theory, and Solid-State NMR Approach[END_REF][START_REF] Antitomaso | SnSb electrode for Li-ion batteries: electrochemical mechanism and capacity fading origins elucidated by Operando techniques[END_REF] The fact that the nano-confined, amorphous metallic tin phase shows high electrochemical reversibility in this system is in accordance with our previous study in which we highlighted these prerequisites. [START_REF] Jahel | Exceptionally highly performing Na-ion battery anode using crystalline SnO 2 nanoparticles confined in mesoporous carbon[END_REF] It is noteworthy that the sodiation reaction of SnSb is often incomplete due to a voltage drop caused by overpotentials arising from kinetic limitations or ohmic resistances which reduces the reversible capacity obtained.

Upon desodiation (charge) the processes and potentials are inverted. After one complete cycle an amorphous "SnSb"-like species is dominating, see Eq: 3, which is distinct from the pristine starting material. This result reminds of the phenomena of nanostructuring of electrode materials observed for alloy and conversion type materials in lithium batteries, such as, for instance, the ternary intermetallic TiSnSb. [START_REF] Fehse | In-Depth Analysis of the Conversion Mechanism of TiSnSb vs Li by Operando Triple-Edge X-ray Absorption Spectroscopy: A Chemometric Approach[END_REF] SnSb + 3N a

Conclusion

The sodiation mechanism of SnSb was thoroughly investigated under operando conditions using Sn and Sb K-edges XAS and 119 Sn Mössbauer spectroscopy. The collected XAS and Mössbauer spectra were analyzed using a chemometric approach including PCA and MCR-ALS. Our findings confirm that SnSb undergoes a two-step alloying reaction upon sodiation in which firstly Sb is sodiated, ensuing the sodiation of Sn. We successfully identified sodiated species of Na 3 Sb and Na 15 Sn 4 as well as an amorphous Sn metal intermediate phase resembling metallic α-Sn, as confirmed by in situ and ex situ 119 Sn Mössbauer spectroscopy.

Nevertheless, no intermediate Na-Sb nor Na-Sn species could be identified. The concentration profile of the identified species were monitored throughout the electrochemical reaction, and it was possible to link the prominent features of the electrochemical signature to specific reaction steps. Furthermore, EXAFS fingerprints prove that SnSb formed after one complete cycle is distinct from pristine SnSb. Our findings show that sodiation process of SnSb is distinct from alloying of individual elements Sn and Sb, but also from the lithiation process of SnSb. The chemometric approach pursued in this study clearly illustrates that

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 10

Figure 1 :

 1 Figure 1: (a) Electrochemical signature of subsequent sodiation/desodiation and sodiation at C/3 rate of SnSb during operando XAS acquisition. (b) Typical electrochemical cycling curve of SnSb vs. Na and its derivative (inset) at C/2.

Figure 2 :

 2 Figure 2: Operando Sn (left) and Sb (right) K-edge EXAFS spectra collected upon sodiation/desodiation and further sodiation process of a SnSb electrode. Dotted line marks the end of first discharge (#53), dashed line marks the end of first complete cycle (#79).

Figure 3 :

 3 Figure 3: Variance plots obtained by PCA analysis for Sb (×) and Sn (•). The dashed lines indicates the 99% threshold below which the origin is considered as experimental noise. Three and four components have to be taken into consideration for reconstructing the full data set of Sb and Sn, respectively.

Figure 4 :

 4 Figure 4: Evolution of the concentrations of the MCR-ALS spectral components for Sb (top) and Sn (bottom) K-edges during subsequent sodiation, desodiation and sodiation.

Figure 6 :

 6 Figure 6: Evolution of concentrations of the MCR-ALS spectral components of the Mössbauer signal during a discharge(sodiation) of SnSb.

Fig. 7 ,

 7 Fig. 7, while the hyperfine parameters obtained from their fitting are shown in Tab. 3. The spectrum of the electrode stopped at the end of the first discharge indicates the presence of a dominant spectral contribution centred at ≈ 2.2 mm s -1 , corresponding to the formation of a majority of Na 15 Sn 4 , 34 together with some residual unreacted SnSb. The low Debye temperature Θ D derived from the temperature dependence of the intensity of the Na 15 Sn 4 spectral component underlines the loss of rigidity upon sodiation and explains why the intensity of the signal decreases strongly along the sodiation reaction.

Figure 7 :

 7 Figure 7: Ex situ 119 Sn Mössbauer spectra measured at 12 K (top) and at ambient temperature (bottom) of two SnSb electrodes recovered at the end of the first discharge (EOD, left) and after the reaction of 3 mol of Na per mol of SnSb (3Na, right), and fit results

1 ) 4 α

 14 High voltage plateau-----------→ α Sn + N a 3 Sb (Sn + 15N a Low voltage plateau -----------→ N a 15 Sn 4(2)4SnSb + 27N a1 st Reduction -------→ 4N a 3 Sb + N a 15 Sn 4 Subsequent cycle ←--------→ 4"SnSb" + 27N a (3)

Table 2 :

 2 EXAFS fitting parameters of MCR-ALS components of Sb K-edge values without error have been fixed during the fit ** all goodness of fit values are lower than 0.02 (R values) see S.I.. The small differences observed can be ascribed to slightly different S 2 0 amplitude reduction factors observed experimentally for the two metals which originate from the ball milling induced disorder. Since Sn or Sb neighbours are indistinguishable from an EXAFS point of view on both Sn and Sb K-edge spectra, similar spectra indicate the presence of virtually identical neighbours around two metal centres. This is reflected by EXAFS fitting results, showing very similar bond distances and σ 2 , see Tab. 1 and 2. In the same way Sb

	Component	Shell	N R theo [ Å] R f it [ Å]	σ 2 [ Å] 2	S 2 0
		M-Sn/Sb 6	3.113	2.944(7) 0.013(1) 0.80(6)
	1	M-Sn/Sb 6	4.379	4.13(4)	0.021(8) 0.80(6)
		M-Sn/Sb 6	4.426	4.30(3)	0.016(5) 0.80(6)
		M-Na	3	3.093	3.04(3)	0.010(4)	0.80 *
	2	M-Na	2	3.171	3.18(4)	0.007(4)	0.80 *
		M-Na	6	3.481	3.62(6)	0.030(7)	0.80 *
	3	M-Sn/Sb 3	3.113	2.850(5) 0.0063(3)	0.80 *

*

Table 3 :

 3 119 Sn Mössbauer parameters of the components derived from the MCR-ALS analysis of the operando spectra and of the ex situ samples measured at variable temperatureComponent ∆ [mm s -1 ] δ * [mm s -1 ] Γ [mm s -1 ] Area [%] Θ D Isomershift values are given relative to CaSnO 3 at RT ** Errors in the determination of the Debye temperatures are currently of ≈ 10 K. In order to compare the values of the low temperature measurement with those acquired at RT, the second order Doppler shift arising from the difference in temperature between source and absorber has to be taken into account, which leads to a difference of the IS values of ≈ 0.1 mm s -1 .[START_REF] Stievano | Solid Mater. Heterog. Catal[END_REF]

	** [K]

* *** Nota bene:

Acknowledgments

S. Belin and V. Briois are gratefully acknowledged for their expert advice on beamline operation, Synchrotron Soleil (France) for providing beamtime at the beamline SAMBA. Alistore-European Research Institute is gratefully acknowledged for financial support through the postdoc grant to M. F. The research group Catalyse, Réactivité de Surface et Rayonnement Synchrotron (GDR CNRS 3590) is gratefully acknowledged for its information and supporting activity for the application of the chemometric approach in the analysis of spectroscopic data.

Starting from spectra 5 a new signal centered at about 2 mm s -1 arises and disappears around spectra #11 again. The spectra #13 and #14 were lost due to instrumental problems. After recovery of the signal, only a very weak spectral feature is visible in spectrum #15, which continues to decrease upon further sodiation. In order to avoid over-and misinterpretation of the data set a PCA + MCR-ALS approach was pursued. Three orthogonal independent components were identified via PCA (see S.I.) and reconstructed into real spectral components using MCR-ALS. To follow the evolution of these components upon sodiation, MCR-ALS was applied using only two components, while the third one was considered as inherent, representing the flat spectrum at EOD state. The evolution of their relative intensities upon one complete discharge is shown in Fig. 6. The concentration profile depicts that before discharge there is one single component (named MCR#1) which decreases upon sodiation while a second component (called MCR#2) rises and reaches its maximum around spectrum #8 before starting to slowly fade away. In the final four spectra only small residue of MCR#1 is present.

The reconstructed pure Mössbauer components were fitted in a traditional way, see S.I.. The obtained parameters are presented Tab. 3. MCR#1 can be fitted using two subspectra: a dominant spectral component which can be unambiguously attributed to SnSb, while a the formation of sodiated phases occurs in a gradual and decoupled way by firstly sodiating Sb and subsequently Sn. This induces a stepwise and steady increase in volume change which is less harmful to the electrode integrity than an abrupt formation of highly sodiated compounds, as observed in the case of lithiation. Moreover the strong amorphization upon sodiation, which is much more pronounced than for lithiation of SnSb, together with the elastic softening of tin and antimony alloys through sodiation provide a cushion for the volume expansion. Therefore we have strong evidence to believe that the combination of these unique cycling characteristics are the key to the enhanced capacity retention and cycle life.

Supporting Information Available

FT and k-space EXAFS data obtained via PCA MCR-ALS on operando SnSb are presented along with the fit in R-space of the components. Furthermore Mössbauer spectra of sodiated tin reference samples and the variance plot and pure spectra components of PCA MCR-ALS on operando Mössbauer spectra are shown. This material is available free of charge via the Internet at http://pubs.acs.org/.


M L L Strandet

A Weiss

C De Breuck

D P Marrone

J D Vieira

M Aravena

M L N Ashby

M. S M S Bethermin

C M M Bothwell

Bradford

A Weiß

M Béthermin

C M Bradford

J E Carlstrom

S C Chapman

D J M Cunningham

Chian-Chou Chen

C D Fassnacht

A H Gonzalez

T R Greve

B Gullberg

C C Hayward

Y Hezaveh

K Litke

J Ma

M Malkan

K M Menten

T Miller

E J Murphy

D Narayanan

K A Phadke

K M Rotermund

J S Spilker

J Sreevani

ISM PROPERTIES OF A MASSIVE DUSTY STAR-FORMING GALAXY DISCOVERED AT Z ∼ 7

Keywords: galaxies, high-redshift -galaxies, star formation -early universe

published or not. The documents may come

INTRODUCTION

Searches for the most distant galaxies have now reached as far back as the first billion years in the history of the Universe, and are peeking into the epoch of reionization (EoR) at 6 < z < 11 (Planck Collaboration et al. 2016). Some of the most important questions in observational cosmology concern the time scale over which the reionization of the Universe took place, the identification of the objects providing the ionizing photons and the enrichment of galaxies with metals. It is expected that star-forming galaxies play a major role in the reionization, so to understand the evolution of the Universe from its neutral beginning to its present ionized state we must study the galaxies in the EoR (see reviews by Stark 2016;Bouwens 2016). How galaxies formed and evolved in the EoR is unknown. Galaxies in this era are currently being found from rest-frame ultraviolet (UV) surveys (e.g. Ouchi et al. 2010). Most of these systems, however, are low-mass star-forming galaxies for which the enrichment of the cold ISM is difficult to study even in long integrations with the Atacama Large Millimeter/submillimeter Array (ALMA) (Bouwens et al. 2016, b).

Massive dusty star-forming galaxies (DSFGs) (Casey et al. 2014) are not expected to be found into the EoR because it is difficult to produce their large dust masses within a few hundred Myr of the Big Bang (Ferrara 2010;Mattsson 2015). Recent wide-area Herschel and optical QSO surveys, however, have revealed dusty galaxies out to z ∼ 6 -7 (e.g., Venemans et al. 2012;Riechers et al. 2013). These systems offer the unique opportunity to study extreme cases of metal/dust enrichment of the ISM within the EoR in the most massive over-densities at these redshifts.

Here we present the DSFG SPT-S J031132-5823.4 (hereafter SPT0311-58) discovered in the South Pole Telescope (SPT)-SZ survey (Carlstrom et al. 2011;Vieira et al. 2013). SPT0311-58 is the highest redshift millimeter-selected DSFG known to-date, located well into the EoR at a redshift of z = 6.900 ± 0.002. With this source, we take a step of almost 100 Myr closer to the Big Bang than the previously most distant DSFG at z = 6.34 found by Riechers et al. (2013), bringing us ∼760 Myr away from Big Bang. Throughout the paper, we assume a ΛCDM cosmology with H 0 =70 km s -1 Mpc -1 , Ω Λ = 0.7 and Ω M = 0.3.

OBSERVATIONAL RESULTS

Determining the redshift

The redshift search for SPT0311-58 was performed in ALMA band 3 by combining five tunings covering 84.2 -114.9 GHz (project ID: 2015.1.00504.S; see Weiß et al. 2013;Strandet et al. 2016, for further details on the observing setup). The observations were carried out on 2015 December 28 and 2016 January 2 in the Cycle 3 compact array configuration. The number of antennas varied from 34 to 41, with baselines up to 300 m yielding a synthesized beam size of 2. 2-3. 0. Typical system temperatures for the observations were T sys = 50 -80 K (SSB). Flux calibration was done with Uranus, bandpass calibration with J0334-4008, and phase calibration with J0303-6211 and J0309-6058. The on-source time varied between 60 seconds and 91 seconds per tuning, accounting for a total of 6 minutes and 10 seconds. The data were processed using the Common Astronomy Software Application package (CASA, McMullin et al. 2007).

We created a cleaned 3 mm continuum image combining all 5 tunings. This yields a high signal to noise ratio (SNR) detection of ∼35. We also generated a spectral cube using natural weighting with a channel width of 19.5 MHz (50 -65 kms -1 for the highest and lowest observing frequency, respectively), which gives a typical noise per channel of 0.9 -1.7 mJy beam -1 .

The ALMA 3 mm spectrum of SPT0311-58 was extracted at the centroid of the 3 mm continuum emission (α: 03 h 11 m 33. s 142 δ: -58 • 23 33. 37 (J2000)) and is shown in Figure 1. We detect emission in the CO J = 6 -5 and 7 -6 lines and the [C I] 3 P 2 -3 P 1 line (in the following 2 -1) and their noise-weighted line frequencies yield a redshift of z = 6.900 ± 0.002. We also see hints of H 2 O(2 11 -2 02 ) and CH + (1-0), but these are not formally detected in this short integration.

The line and continuum properties are given in Table 1. For the fit to the CO(7-6) and [C I](2-1) lines we fix the line width to the mean value derived from the unblended lines. Their uncertainties include the variations of the line intensities for a fit where the line width is a free parameter.

Observations of CO(3-2) and [C II]

We used the 7 mm receivers of the Australia Telescope Compact Array (ATCA) to observe the CO(3-2) line (project ID: CX352). Observations were carried out with the hybrid H214 array, which yields a beam size of 5-6 at the observing frequency of 43.77 GHz. The line is detected with a SNR of 5.0 at a frequency and line width consistent with the ALMA derived redshift and line profiles.

In addition, we used the Atacama Pathfinder Exper- The line parameters derived from Gaussian fits to the data are given for both transitions in Table 1; the spectra are shown in Figure 1.

FIR dust continuum

Table 1 (right) summarizes the dust continuum observations of SPT0311-58.

With seven broadband continuum detections between 3 mm to 250 µm, the far-infrared spectral energy distribution (SED) of SPT0311-58 is thoroughly covered.

The SPT 1.4 and 2.0 mm flux densities were extracted and deboosted as described by Mocanu et al. (2013). We obtained a 870 µm map with APEX/LABOCA (project ID: M-091.F-0031-2013). The data were obtained, reduced, and the flux extracted following Greve et al. (2012). Using Herschel/SPIRE, we obtained maps at 250 µm, 350 µm and 500 µm (project ID: DDT mstrande 1). The data were obtained and reduced as described by Strandet et al. (2016).

From our photometry, we derive an apparent farinfrared (FIR) luminosity (integrated between 40-120 µm rest) of L FIR = 4.1 ± 0.7 × 10 13 L (see Figure 2).

CHARACTERIZING THE ISM IN SPT0311-58

3.1. Source properties from high resolution imaging ALMA high spatial resolution imaging (angular resolution of 0.3 × 0.5 ) of the [C II] line in SPT0311-58 shows that the system consists of two galaxies in close proximity (Marrone et al. in prep.). Only the western source is significantly gravitationally magnified and this source dominates the apparent continuum luminosity (> 90% of the restframe 160 µm continuum flux density is emitted by the western source). In the following, we assume that the contribution from the eastern source is negligible and model the system as a single object, using the system magnification of µ = 1.9 (Marrone et al. in prep.).

Radiative Transfer Models

We use the FIR photometry and the line luminosities from Table 1 to simultaneously model the dust continuum, CO spectral line energy distribution (SLED), and the [C I](2-1) line following the radiative transfer calculation presented in Weiß et al. (2007). In this model, the background radiation field is set to the cosmic microwave background (CMB) for the dust and to the CMB plus the dust radiation field for the lines. The line and dust continuum emission are further linked via the gas column density in each component that introduces the turbulence line width as a free parameter in the calculation (see Eq. 7 in Weiß et al. 2007). The gas column density calculated from the line emission together with the gas to dust mass ratio (GDMR) then determines the optical depth of the dust.

The calculations treat the dust and the kinetic temperature as independent parameters, but with the prior that the kinetic gas temperature has to be equal to or higher than the dust temperature. Physically, this allows for additional sources of mechanical energy (e.g. shocks) in the ISM in addition to photo-electric heating.

The chemical parameters in our model are the CO and [C I] abundances relative to H 2 and the GDMR. We use a fixed CO abundance of 8 × 10 -5 relative to H 2 (Frerking et al. 1982), but keep the [C I] abundance and the GDMR as free parameters. For the frequency dependence of the dust absorption coefficient we adopt κ d (ν) = 0.04 (ν/250 GHz) β [m 2 kg -1 ] (Krügel & Siebenmorgen 1994), which is in good agreement with κ 870µm = 0.077 m 2 kg -1 used in other work (see Spilker et al. 2015, and references therein), for our best-fitting β.

Model solutions are calculated employing a Monte-Carlo Bees (Pham & Castellani 2009) algorithm which randomly samples the parameter space and gives finer sampling for good solutions (as evaluated from a χ 2 analysis for each model). In total, we sample ∼ 10 7 models. Parameter values and uncertainties were calculated using the probability-weighted mean of all solutions and the standard deviations.

Model results

Figure 2 shows the CO SLED, the continuum SED, and [C I] flux density. From the figure, it is apparent that the dust continuum SED cannot be modeled with a single temperature modified blackbody, so we instead fit two components. Since we have no information on the high-J CO transition, we use the shape of the CO SLED of Arp220 (Rosenberg et al. 2015) and HFLS3 (Riechers et al. 2013) as priors. With this choice, we compare the moderately excited CO SLED of Arp220 (see Rosenberg et al. (2015) for a comparison of Arp220 to other local ULIRGs) to the more extreme case of HFLS3 where the CO SLED stays high up to the J up =9 level (see Fig. 2). The use of the priors mainly affects the parameters of the warm gas and therefore only has a small effect on our derived gas mass (see below). Table 2 lists the parameters obtained from the radiative transfer calculations for the Arp220 prior, not corrected for magnification.

For both priors, the warm dust component dominates the peak of the CO SLED and the short wavelength part of the dust spectrum and therefore the FIR luminosity. Its size is small compared to the cold gas with an area ratio of ∼ 6 (r 0 = 1.7±1.4 kpc where r 0 is the equivalent radius defined as r 0 = D A Ω s /π (Weiß et al. 2007)) for HFLS3 and slightly smaller for Arp220) which implies that the region of intense FIR continuum emission is significantly smaller than the overall gas distribution. Due to a lack of observations of CO transitions beyond (7-6), its properties are mainly driven by the assumed shape of the CO SLED for the high-J transitions. But the models for both priors indicated consistently that the warm gas has a substantial density (of order 10 5 cm -3 ), a dust temperature of ∼ 100 K and a kinetic temperature in excess (but consistent within the errors) of the dust temperature (T kin =180 ± 50 K when using Arp220 priors).

The cold dust component is required to fit the CO(3-2) and [C I] line emission, and the long wavelength part of the dust SED. Due to its large extent and relatively high density (r 0 =3.7 ± 1.3 kpc, log(n(H 2 )=3.7 ± 0.4)), it carries ≈ 90% of the gas mass. The abundance of neutral carbon in this gas phase is [C I]/[H 2 ] = 6.0 ± 1.4 × 10 -5 in agreement with other estimates at high redshift and in nearby galaxies (e.g. Weiß et al. 2005, and references therein). For both priors, the cold gas dominates the CO(1-0) line luminosity. As for the warm gas, we find that the kinetic temperature is above the dust temperature (T dust =36 ± 7 K, T kin =58 ± 23 K), which may suggest that the ISM in SPT0311-58 experiences additional mechanical energy input e.g., via feedback from stellar winds or AGN driven outflows. This is also supported by the large turbulent line width of order 100 km s -1 and super-virial velocity gradients (κ vir > 1, see note b in Table 2) we find for both components and priors.

We use the kinematic parameters (dv turb and κ vir ) together with the source size and the H 2 density for each component (see Eq. 8 in Weiß et al. 2007) to derive a total apparent gas mass of M gas =(6.3 ± 3.7) × 10 11 M (including a 36% correction to account for the cosmic He abundance). For the HFLS3 prior, the gas mass is ∼ 30% higher.

DISCUSSION

Gas mass conversion factor

With the independent gas mass estimate from the radiative transfer models in-hand we can also derive the gas-to-dust mass ratio (GDMR) and the CO-to-H 2 conversion factor (α CO ) for SPT0311-58. Since the CO(1-0) transition has not been observed, we use the flux density from the radiative transfer model which predicts I CO(1-0) =0.10 ± 0.03 Jy km/s. In our models, we assume that each gas component has the same GDMR and we find GDMR=110 ± 15. Due to the different physical conditions in each gas component, there is a specific α CO value for each component. For the cold dust component, we find α CO = 5.5 ± 4.0 M (K km s -1 pc 2 ) -1 and for the warm dust component α CO = 3.1 ± 2.5 M (K km s -1 pc 2 ) -1 . Combining both gas components we find for SPT0311-58 α CO = 4.8 ± 2.9 M (K km s -1 pc 2 ) -1 .

When calculating gas masses for ULIRGs, a factor of α CO = 0.8 M (K km s -1 pc 2 ) -1 is typically assumed (Downes & Solomon 1998), significantly below our estimate. The difference can easily be explained by the much higher densities we find in both components compared to the models from Downes & Solomon (1998) in which most of the CO(1-0) luminosity arise from a diffuse inter-cloud medium. Since the bulk of the gas mass of this source is in the dense component, it is vital to include the higher-J CO transitions in the calculation of α CO .

A similar two-component analysis was done for the broad absorption line quasar APM08279+5255 at z = 3.9 (Weiß et al. 2007), where the dense component was

[C I]/[H 2 ] (6.0 ± 1.4)×10 -5 (1.7 ± 2.3)×10 -5 M dust M (5.7 ± 0.8)×10 9 µ -1 (5.2 ± 0.7)×10 9 µ -1 (4.8 ± 0.7)×10 8 µ -1
Mgas M (6.3 ± 3.7)×10 11 µ -1 (5.7 ± 3.8)×10 11 µ -1 (5.3 ± 3.8)×10 10 µ -1 α CO M /K km s -1 pc 2 4.8 ± 2.9 5.5 ± 4.0 3.1 ± 2.5

L FIR L (4.1 ± 0.7) ×10 13 µ -1 (1.2 ± 1.1) × 10 13 µ -1 (2.9 ± 0.7) × 10 13 µ -1 SFR c M yr -1 (4100 ± 700) µ -1 t dep Myr 150 ± 90
Note-The values here are apparent values. Intrinsic values can be calculated using µ = 1.9.

a r 0 = D A Ωs/π b dv/dr=κ vir × 3.1 n(H 2 )/1e4; we calculate the velocity gradient for virialized clouds (κ vir = 1, Goldsmith 2001) but also consider nonvirial, unbound motions (κ vir > 1, Greve et al. 2009). c using SFR=10 -10 × L FIR based on a Chabrier initial mass function (Kennicutt 1998;Chabrier 2003) d Fitted in the radiative transfer calculation but set to be the same for both components.

found to dominate the CO(1-0) line by 70%. They find a high conversion factor of α CO ∼ 6 M (K km s -1 pc 2 ) -1 , similar to what we find in the dense gas component. A similar reasoning for higher CO conversion factors owing to the presence of dense gas was put forward by Papadopoulos et al. (2012) based on the CO SLED in local (U)LIRGs.

[C II]

From our [C II] detection, we derive a L [CII] /L FIR ratio of (7.3 ± 0.1)×10 -4 . Figure 3 shows that this puts SPT0311-58 into the lower region of the L [CII] /L FIR ratio observed in a larger sample of SPT-DSFGs (Gullberg et al. 2015). Similarly, low L [CII] /L FIR ratios are found for the z = 6.3 star-forming galaxy HFLS3 (Riechers et al. 2013) and for the z = 7.1 QSO host galaxy J1120+0641 (Venemans et al. 2012).

The L [CII] /L CO(1-0) ratio in SPT0311-58 is similar to what is observed in the SPT sample (4300 ± 1300 compared to 5200 ± 1800 Gullberg et al. 2015), and HFLS3 (∼3000, Riechers et al. 2013). This is consistent with the picture in which the [C II] emission stems from the surface of dense clouds exposed to the strong UV field from the intense starburst in SPT0311-58 (Stacey et al. 2010;Gullberg et al. 2015;Spilker et al. 2016).

The larger [C II] deficit together with the decreasing L [CII] /L CO(1-0) ratio of SPT0311-58 and other high redshift sources compared to local galaxies may be un-

Concluding remarks

Both our radiative transfer model and fine structure line results indicate that SPT0311-58 resembles typical DSFGs, just at z ∼ 7. This is also supported by its extreme SFR surface density of Σ SFR ∼ 600 M yr -1 kpc -2 (derived using the size of the warm gas component that dominates the FIR luminosity) which approaches the modeled values for radiation pressure limited starbursts (10 3 M yr -1 kpc -2 Thompson et al. 2005) and is comparable to what is found in other starburst like Arp220, HFLS3 and other SPT-DSFGs (Scoville 2003;Riechers et al. 2013;Spilker et al. 2016). Future observations of this source will explore its spatial structure, physical conditions, formation history, and chemical evolution in great detail as it is one of very few massive galaxies known at z ∼ 7 MLS was supported for this research through a stipend from the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. MA acknowledges partial support from FONDECYT through grant 1140099. JDV, DPM, KCL, JSS and SJ acknowledge support from the U.S. National Science Foundation under grant No. AST-1312950. BG acknowledges sup-

Figure 1 .

 1 Figure 1. The lower part of the figure shows the ALMA 3 mm spectrum of SPT0311-58 spanning 84.2 -114.9 GHz. The spectrum has been binned to best show the lines. Transitions labeled in black are detected and grey labels indicate where other transitions should be. The red line indicate the zeroth order baseline. The sub-panels above the spectrum show, from left to right, the continuum-subtracted spectra of: ATCA CO(3-2), ALMA CO(6-5), ALMA CO(7-6) and CI(2-1), and APEX [C II] with ALMA [C II] overlaid as a solid black histogram. Gaussian fits to the spectra are shown in red.

Figure 2 .

 2 Figure 2. Results of simultaneous fitting of the CO SLED (left), SED (middle) and [C I] (right) line flux. The CO line intensities are plotted as filled circles, the continuum fluxes as open circles and the [C I]flux as an asterisk. The blue dashed line and squares show the cold component, the red dotted line and triangles show the warm component, the black solid line and circles (in right panel) show the combination of the two components. In grey is shown similar data for HFLS3 (dots and dotted line) and Arp220 (crosses and solid line), normalized to the CO(6-5) flux of SPT0311-58 for the CO-SLED and to the peak of the continuum SED of SPT0311-58 for the SED. The line fluxes and continuum properties fitted are listed in Table 2. Left: Two component CO-SLED. Middle: Two component SED fitting based. Right: The contribution of each of the two components to the [C I](2-1) line and predictions for the [C I](1-0) line.

Figure 3 .

 3 Figure 3. L [CII] /LFIR vs L [CII] /L CO(1-0) with PDR models and samples adapted from Gullberg et al. (2015). The red star shows how SPT0311-58 falls within the larger SPT DSFG sample. The typical error bar for the low redshift sample is presented by the black cross.

Table 1 .

 1 Observed properties of SPT0311-58

			Line properties		Continuum properties
	Transition	SdV	dV a	L	L	Wavelength	Sν
		[Jy km/s]	[km/s]	×10 11 [K km/s/pc 2 ] ×10 8 [L ]	[µm]	[mJy]
	CO(3-2)	0.96 ± 0.15 790 ± 150	1.52 ± 0.24	2.01 ± 0.32	3000	1.30 ± 0.05
	CO(6-5)	2.10 ± 0.33 720 ± 140	0.83 ± 0.13	8.8 ± 1.4	2000	7.5 ± 1.3
	CO(7-6)	2.78 ± 0.80	750 b	0.81 ± 0.11	13.6 ± 1.8	1400	19.0 ± 4.2
	[C I](2-1)	1.29 ± 0.80	750 b	0.37 ± 0.10	6.4 ± 1.8	870	32.0 ± 5.0
	[C II]APEX	22.1 ± 5.1	890 ± 260	1.16 ± 0.27	254 ± 59	500	52.0 ± 8.0
	[C II]ALMA	25.88 ± 0.65		1.36 ± 0.03	298.1 ± 7.5	350	38.0 ± 6.0
						250	29.0 ± 8.0
	a FWHM b fixed from CO(3-2) and CO(6-5).

Table 2 .

 2 ISM parameters of SPT0311-58 from the radiative transfer calculation

	Parameter	unit	overall	cold component	warm component
	Equivalent radius a	pc	(4000 ± 1700) µ -1/2	(3700 ± 1300) µ -1/2	(1500 ± 1200) µ -1/2
	T dust	K		36 ± 7	115 ± 54
	T kin	K		58 ± 23	180 ± 51
	log(n(H 2 ))	cm -3		3.7 ± 0.4	5.1 ± 1.9
	dv turb	km s -1		130 ± 17	100 ± 4
	κ vir	b			1.9 ± 1.9	3.1 ± 2.5
	GDMR			110 ± 15 d
	β				1.91 ± 0.05 d

port from the ERC Advanced Investigator programme DUSTYGAL 321334. The Flatiron Institute is supported by the Simons Foundation. Partial support for DN was provided by NSF AST-1009452, AST-1445357, NASA HST AR-13906.001 from the Space Telescope Science Institute, which is operated by the Association of University for Research in Astronomy, Incorporated, under NASA Contract NAS5-26555, and a Cottrell College Science Award, awarded by the Research Corporation for Science Advancement. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Herschel is a European Space Agency Cornerstone Mission with significant participation by NASA. APEX is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The SPT is supported by the National Science Foundation through grant PLR-1248097, with partial support through PHY-1125897, the Kavli Foundation and the Gordon and Betty Moore Foundation grant GBMF 947.