Ian Colliard

Clement Falaise

May Nyman

Bridging the Transuranics with Uranium(IV) Sulfate Aqueous Species and Solid Phases

Isolating isomorphic compounds of tetravalent actinides (i.e., Th IV , U IV , Np IV , and Pu IV ) improve our understanding of the bonding behavior across the series, in addition to their relationship with tetravalent transition metals (Zr and Hf) and lanthanides (Ce). Similarities between these tetravalent metals are particularly illuminated in their hydrolysis and condensation behavior in aqueous systems, leading to polynuclear clusters typified by the hexamer [M IV 6O4(OH)4] 12+ building block. Prior studies have shown the predominance and coexistence of smaller species for Th IV (monomers, dimers, and hexamers) and larger species for U IV , Np IV , and Pu IV (including 38-mers and 70-mers). We show here that aqueous uranium(IV) sulfate also displays behavior similar to that of Th IV (and Zr IV ) in its isolated solid-phase and solution speciation. Two single-crystal X-ray structures are described: a dihydroxide-bridged dimer (U2) formulated as U2(OH)2(SO4)3(H2O)4 and a monomer-linked hexamer framework (U-U6) as (U(H2O)3.5)2U6O4(OH)4(SO4)10(H2O)9. These structures are similar to those previously described for Th IV . Moreover, cocrystallization of monomer and dimer and of dimer and monomer-hexamer phases for both Th IV (prior) and U IV (current) indicates the coexistence of these species in solution. Because it was not possible to effectively study the sulfate-rich solutions via X-ray scattering from which U2 and U-U6 crystallized, we provide a parallel solution speciation study in low sulfate conditions, as a function of the pH. Raman spectroscopy, UV-vis spectroscopy, and small-angle X-ray scattering of these show decreasing sulfate binding, increased hydrolysis, increased species size, and increased complexity, with increasing pH. This study describes a bridge across the first half the actinide series, highlighting U IV similarities to Th IV , in addition to the previously known similarities to the transuranic elements.

INTRODUCTION

Large tetravalent M IV cations (six-coordinate ionic radius = 0.85-1.1 Å), including transition metals (Zr IV and Hf IV ), lanthanides (Ce IV ), and actinides (Th IV , U IV , Np IV , and Pu IV ), exhibit rich polynuclear speciation in water, leading to the assembly of molecular nanoclusters,(1-6) inorganic frameworks, and metal-organic frameworks (MOFs, with added linkers). [START_REF] Yuan | Stable Metal-Organic Frameworks with Group 4 Metals: Current Status and Trends[END_REF][START_REF] Dolgopolova | Actinide-based MOFs: a middle ground in solution and solid-state structural motifs[END_REF][START_REF] Jacobsen | The first water-based synthesis of Ce(IV)-MOFs with saturated chiral and achiral C4-dicarboxylate linkers[END_REF] This aqueous behavior is due to the strong Lewis and Brønsted acidity that promotes hydrolysis and condensation processes, even at pH < 2. For all of these metals, the most commonly observed species in solution and in the solid state is a hexamer; its core is generally formulated as [M IV 6O4(OH)4] 12+ . The hexamer is also the core building unit for M IV O2 with fluorite topology. To isolate the hexamer as a solid, the appropriate capping groups are required, which include acetates and amino acids (molecular clusters), [START_REF] Hennig | Solution Species and Crystal Structure of Zr(IV) Acetate[END_REF][START_REF] Takao | First Hexanuclear UIV and ThIV Formate Complexes -Structure and Stability Range in Aqueous Solution[END_REF][START_REF] Knope | Plutonium(IV) cluster with a hexanuclear [Pu6(OH)4O4] 12+ core[END_REF] ditopic carboxylate linkers (MOFs), [START_REF] Yuan | Stable Metal-Organic Frameworks with Group 4 Metals: Current Status and Trends[END_REF][START_REF] Dolgopolova | Actinide-based MOFs: a middle ground in solution and solid-state structural motifs[END_REF][START_REF] Jacobsen | The first water-based synthesis of Ce(IV)-MOFs with saturated chiral and achiral C4-dicarboxylate linkers[END_REF] or sulfates (frameworks or clusters). [START_REF] Sun | Aqueous Isolation of 17-Nuclear Zr/Hf Oxide Clusters during the Hydrothermal Synthesis of ZrO2 /HfO2[END_REF](12)(13) While the M IV hexamer has been isolated numerous times, understanding the reaction steps from the dissolved M IV monomer to the hexamer via solution and solid-state characterization provides an opportunity to better control or redirect the reaction toward new synthons and to understand the aqueous behavior of metal cations in natural systems. Defining aqueous hydrolysis/olation/oxolation and coordination chemistry of the tetravalent actinides Th IV , U IV , Np IV , and Pu IV (the most common oxidation state of the early actinides) presents an opportunity to develop a better description of their bonding behavior. It is hypothesized that crossover of the 5f and 6d frontier orbitals on the energy scale underlies the rich redox and coordination chemistry of the actinide series.(14-17) Thus, the early actinides are more similar to the transition metals, while the late actinides resemble the lanthanides. Beyond the An IV -monomer cation, an oxo-or hydroxyl-linked dimer is the simplest subunit of the hexamer and also represents very early nucleation of AnO2 from An IV (H2O)n (n = 8-10). As an example, a hydroxyl or an oxo bridge between the metal centers is formed by the following fundamental steps for M IV : [START_REF] Henry | Aqueous Chemistry of Metal Cations: Hydrolysis, Condensation and Complexation[END_REF] (1) [START_REF] Knope | Solution and Solid-State Structural Chemistry of Actinide Hydrates and Their Hydrolysis and Condensation Products[END_REF] (3) Dimers are commonly bridged by two or more hydroxyls. Th IV is considered to be the "softest" of the An IV series, and thus the least acidic. The dihydroxide-and trihydroxide-bridged Th2 dimers have been isolated numerous times with various coordinating ligands.(2) More relevant to this current study, the sulfate-capped Th IV dimers have been observed in solution and isolated in the solid state. [START_REF] Knope | Synthesis and characterization of thorium(IV) sulfates[END_REF][START_REF] Albrecht | The crystal chemistry of four thorium sulfates[END_REF][START_REF] Hu | Understanding the Ligand-Directed Assembly of a Hexanuclear ThIV Molecular Cluster in Aqueous Solution[END_REF] Recently, several intricate thorium sulfate frameworks that feature monomers, dimers, and hexamers have been structurally characterized,(12,13) suggesting the coexistence of these species in solution. In addition, a Th3 trimer has recently been isolated. [START_REF] Wacker | Monomeric and Trimeric Thorium Chlorides Isolated from Acidic Aqueous Solution[END_REF] On the other hand, the higher acidity of Pu IV promotes the formation of larger molecular clusters, including Pu16,(23) Pu22, [START_REF] Sigmon | Extension of the Plutonium Oxide Nanocluster Family to Include {Pu-16} and {Pu-22}[END_REF] and Pu38, [START_REF] Soderholm | The structure of the plutonium oxide nanocluster[END_REF] in addition to the ubiquitous hexamer as isolated clusters [START_REF] Knope | Plutonium(IV) cluster with a hexanuclear [Pu6(OH)4O4] 12+ core[END_REF] and, more recently, within a MOF framework.(25) Different from thorium, the diplutonium(IV) dihydroxide bridged dimer is more elusive, isolated only once, with nitrate ligands,(26) and, more recently, singly bridged via an oxo ligand also with nitrate ligands.(27) On the basis of large isolatable clusters including U38(28-30) and Np38 [START_REF] Martin | {Np-38} clusters: the missing link in the largest poly-oxo cluster series of tetravalent actinides[END_REF] (in addition to numerous examples of hexamers, i.e., refs [START_REF] Tamain | Coordination of Tetravalent Actinides (An═Th(IV), U(IV), Np(IV), Pu(IV)) with DOTA: From Dimers to Hexamers[END_REF] and (32-35), the polymerization of U IV and Np IV appear to be more similar to Pu IV than Th IV . Unlike Pu38, Np38 and U38 isolation required organic media that slow olationoxolation reactions. [START_REF] Yue | Unexpected Roles of Alkali-Metal Cations in the Assembly of Low-Valent Uranium Sulfate Molecular Complexes[END_REF] In addition, neither the Np IV 2 nor U IV 2 dimer has been isolated, from either water or organic media. In 1973, however, the dihydroxide-bridged U2 dimer was proposed in Xray scattering analysis of uranium(IV) perchlorate solutions. [START_REF] Pocev | An X-ray Investigation of the coordination and the hydrolysis of the uranium(IV) ions in aqueous perchlorate solutions[END_REF] Motivations to study U IV aqueous chemistry go beyond understanding periodic table and f-element trends. It has been mined for more than a century, initially for isolation of radium, second for production of weapon-grade uranium and plutonium, and then by production of fuel for nuclear energy. Fuel fabrication, reprocessing, separations, storage and disposal, retroactive treatment of legacy wastes, and environmental contamination motivate continued studies of uranium speciation. There is particular focus on aqueous and solid-state uranium(IV) sulfate chemistry in the industrial realm. Sulfuric acid is commonly used for in situ leaching, leading to the formation of postmining alteration minerals. [START_REF] Uhrie | In situ immobilization of heavy metals associated with uranium leach mines by bacterial sulfate reduction[END_REF] Additionally, sulfate-and iron-reducing bacteria in nature and in the laboratory promote U VI -to-U IV reduction, by the formation of either U IV complexes or UO2 nanoparticles,(39) with sizes similar to that of U38. Recently, we have shown that simply combining uranium(IV) sulfate in water with transition-metal or lanthanide countercations leads to larger cluster forms (including U84 and U70) and heterometallic oxysulfate frameworks. [START_REF] Colliard | Supramolecular Assembly of U(IV) Clusters and Superatoms with Unconventional Countercations[END_REF][START_REF] Colliard | U IV 70(OH)36(O)64] 4oxocluster frameworks with sulfate, transition metals[END_REF] In these intricate assemblies, the U6 hexamer remains the core building unit.

Here we expand the library of uranium(IV) sulfate species with the description of two new phases by single-crystal X-ray diffraction, as well as solution characterization studies. U-U6 is a U IVmonomer-linked hexamer framework, and U2 is the "missing" U IV 2 dimer, providing another metric in the aqueous tetravalent actinide series, bridging the Th2 [START_REF] Knope | Synthesis and characterization of thorium(IV) sulfates[END_REF][START_REF] Albrecht | The crystal chemistry of four thorium sulfates[END_REF][START_REF] Hu | Understanding the Ligand-Directed Assembly of a Hexanuclear ThIV Molecular Cluster in Aqueous Solution[END_REF] dimer to the Pu2(26) dimer. Because U-U6 and U2 crystallize from heated solutions at 0.5 M H2SO4 concentration, it was not feasible to study their assembly pathways or solution speciation by benchtop X-ray scattering. Instead, we dissolved U(SO4)2 in water and control hydrolysis reactions via a pH increase. Raman spectroscopy and small-angle X-ray scattering (SAXS) show increasing size of polynuclear uranium(IV) oxyhydroxysulfate and decreasing sulfate ligation, corresponding with increasing pH instead of heat. Size and size distribution analysis of the SAXS data suggest mixtures of monomers, dimers, hexamers, and monomer/dimer-decorated hexamers; species similar to those isolated from sulfate-rich solutions. Powder X-ray diffraction (PXRD) of bulk solids from which single crystals of U2 and U-U6 are isolated show cocrystallization of monomers, dimers, and monomer-hexamer frameworks. Likely the coexistence of these species in their parent reaction solutions suggests a competition between strongly coordinating ligands with flexible binding modes (sulfate) and strong hydrolysis chemistry of acidic U IV , which drives complexity. The dihydroxide-bridged U2 dimer presented here provides a missing link in aqueous U IV chemistry as the first step of hydrolysis chemistry that leads to the predominant hexamer. Moreover, the coexistence of phases featuring monomers, dimers, and hexamers provides a bridge from Th IV to the transuranics. Specifically, the uranium(IV) sulfate behavior documented here is akin to thorium(IV) sulfate chemistry, while prior U IV speciation studies show behavior more similar to the transuranics with the self-assembly of larger polynuclear clusters.

EXPERIMENTAL SECTION

Caution! Although we are using depleted uranium (DU), it still possesses some radioactivity and it is a toxic heavy metal, so precautions with suitable care and protection for handling each substance have been followed.

Materials

UO2(CH3COO)2, concentrated H2SO4 (98% Macron Fine Chemicals), and Millipore-filtered water with a resistance of 18.2 MΩ•cm was used as received in all reactions.

Synthesis of U(SO4)2

The uranium(IV) sulfate starting material was synthesized as previously described. [START_REF] Colliard | Supramolecular Assembly of U(IV) Clusters and Superatoms with Unconventional Countercations[END_REF][START_REF] Colliard | U IV 70(OH)36(O)64] 4oxocluster frameworks with sulfate, transition metals[END_REF] Briefly, 5.0 g (0.01 mol) of uranyl acetate was dissolved in 75 mL of anhydrous ethanol. Concentrated sulfuric acid (25 mL) was added dropwise. After complete dissolution of the uranyl acetate, the solution was placed under UV light (390-400 nm, 15 W) for 24-48 h. The uranium was reduced and precipitated as uranium sulfate. The green/purple powder was vacuum-filtered and washed with four 50 mL aliquots of ethanol. It is X-ray amorphous and has a formula of approximately U(SO4)2•4H2O. The powder was then stored in a desiccator. Raman (cm -1 ): sulfate and U-O, 420, 448, 491, 592, 616, 656; sulfate, 987 (shoulder), 1011, 1043. IR (cm -1 ): sulfate and U-O, 580, 649; sulfate, 950, 1127. The percent yield was ∼95% based on uranium (5.6 g).

Synthesis of U2(OH)2(SO4)3(H2O)4 (U2)

U(SO4)2 (0.1.g) was dissolved in 0.5 mL of 0.5 M H2SO4 in a 2 mL screwcap vial to give a concentration of 0.46 M U IV . The vial was capped, placed in a sand bath, and heated at 75 °C in an oven for 24 h. During the hydrothermal treatment, crystals of U2 grew. The crystals were then filtered and washed with 2 mL of 0.5 M HCl to remove any soluble material, followed by repeated washing of 2 mL of water. The crystals were left to dry in vacuo. Raman (cm -1 ): sulfate and U-O, 270, 420, 440, 597, 620; sulfate, 1013 (shoulder), 1028. IR (cm -1 ): sulfate and U-O, 491, 591; sulfate, 1030, 1093; H2O, 3000-3500 (broad), 1600. Percent yield was ∼67% based on uranium (0.07 g).

Synthesis of (U(H2O)4.5)2U6(OH)4(O)4(SO4)10(H2O)9 (U-U6)

U(SO4)2 (0.2 g) was dissolved in 0.5 mL of 0.5 M H2SO4 in a 2 mL screwcap vial to give a concentration of 0.92 M U IV . The vial was capped, placed in a sand bath, and heated at 75 °C in an oven for 24 h. During the hydrothermal treatment, crystals of U-U6 grew. The crystals were then filtered and washed with 2 mL of 0.5 M HCl to remove any soluble material, followed by 2 mL of water. The crystals were left to dry in vacuum. Raman (cm -1 ): sulfate and U-O, 232, 260, 364, 436, 449, 493, 621, 633; sulfate, 1021, 1038, 1071. IR (cm -1 ): sulfate and U-O, 444, 595; sulfate, 1027, 1050; H2O, 3000-3200 (broad), 1600. The percent yield was ∼45% based on uranium (∼0.1 g).

Spectroscopic Monitoring of U(SO4)2 Solutions

A solution of sulfuric acid (H2SO4; 0.5 M) was saturated with tetravalent uranium sulfate. Typically, around 1 g of U(SO4)2(H2O)n was dissolved in 13.5 mL of diluted sulfuric acid, with a uranium concentration of around 0.15 M. A total of 200 μL of the U IV /SO4 solution were mixed with 800 μL of distilled water ([U IV ] ∼ 30 mM). Then a NaOH solution (12.5 wt %) was added to the diluted U IV /SO4 solution (50, 100, 150, 175, 200, 225, and 250 μL). The pH values of the resulting solutions are respectively 1.78 (initial), 1.92, 1.95, 2.15, 2.25, 2.40, and 2.60. Raman spectroscopy and UV-vis spectroscopy were recorded for each solution.

Crystallographic Studies

U-U6 crystals were collected on a Bruker DUO-APEX II CCD area detector at 173 K using Cu radiation (λ = 1.54178 Å). Data reduction was accomplished using SAINT V8.34a. U2 was collected on a Rigaku Oxford Synergy S at 100 K equipped with a PhotonJet S Cu source (λ = 1.54178 Å) and a hyPix-6000HE photon counting detector. All images were collected and processed using CrysAlisPro, version 171.40_64.53 (Rigaku Oxford Diffraction, 2018). After integration, both (analytical) absorption and empirical absorption (spherical harmonic, image scaling, and detector scaling) corrections were applied.( 42) All structures were solved by the intrinsic phasing method from SHELXT, [START_REF] Sheldrick | SHELXT -Integrated space-group and crystal-structure determination[END_REF] developed by successive difference Fourier syntheses, and refined by fullmatrix least squares on all F 2 data using SHELX [START_REF] Sheldrick | A short history of SHELX[END_REF] via the OLEX2 interface. [START_REF] Dolomanov | OLEX2: a complete structure solution, refinement and analysis program[END_REF] Several A-level alerts resulted from strong absorption of the crystal. Empirical absorption correction was applied before frame scaling. Several other methods were employed before ultimately using analytical absorption correction for U2 and "Multi-scan" for U-U6 using the SCALE3 ABSPACK.(45) This gave an Rint value after absorption correction for U2 of 9.43% (from 10.20%) and for U-U6 of 6.98% (from 8.56%). Nevertheless, a large residual electron density of less than 1 Å away from the U atoms remained. For U2, the largest residual peak is -5.1 Å -3 , 0.930 Å from the U site, and for U-U6, the largest residual peak is 3.7 Å -3 , 0.644 Å away from U1B. All non-H atoms were refined anisotropically with the exception of the aqua ligands on U1B for the U-U6 structure because of the positional disorder of the monomer. This resulted in large prolated O atoms that could not be modeled independently, even from data collected at 173 K, used to limit thermal motion. Crystallographic information and additional structural information are provided in Table 1. Supporting information is available in CIF format for U2 and U-U6.

SAXS

SAXS data were collected on an Anton Parr SAXSess instrument utilizing Cu Kα radiation and line collimation. Data were recorded on an image plate in the range of 0.008-2.5 Å -1 . The sampleto-image plate distance was 26.1 cm. Solutions were measured in 1.5 mm glass capillaries. Water was used as the background, and scattering was measured for 30 min. SAXSQUANT software was used for data collection and processing (normalization, primary beam removal, and background subtraction). All other data analyses were carried out with the IRENA macros within IGOR Pro. [START_REF] Ilavsky | Irena: tool suite for modeling and analysis of small-angle scattering[END_REF] Simulated scattering data were calculated using SolX.( 47)

Fourier Transform Infrared (FT-IR) Spectroscopy

IR spectra were recorded in attenuated reflectance mode using a Thermo Scientific Nicolet iS10 FT-IR spectrometer.

Raman Vibration Spectroscopy

Raman spectra were recorded on a Thermo Scientific DXR spectrometer (fine laser power: powercontrolled and reported at samples in 0.1 mW increments) with a 760 nm laser source, between wavelengths of 100 and 1200 cm -1 .

Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray Spectroscopy (EDXS)

Electron micrographs and atomic ratios (%) of the crystalline materials were obtained from a Quanta 600F instrument (FEI) combining a scanning electron microscope and an energydispersive X-ray spectrometer.

RESULTS and DISCUSSION

Synthesis and Characterization of U2 and U-U6

Two new uranium sulfate structures were isolated and characterized by single-crystal X-ray diffraction in this study. From a solution of ∼0.5 M U IV and 0.5 M H2SO4, heated at 75 °C (see the Experimental Section for details), we isolated crystals of the dihydroxide-bridged dimer U2. U2 is fully formulated as U2(OH)2(SO4)3(H2O)4 and crystallizes in the centrosymmetric monoclinic space group C2/c (Table 1). The structure adopts a three-dimensional (3D) framework (Figure 1b) comprised of a dihydroxide-bridged dimeric U IV core [U2(OH)2(H2O)4] 6+ (Figure 1a), analogous to previously reported dihydroxide-bridged thorium dimers. We note that U2 has a transition-metal isostructural counterpart, Zr2(OH)2(SO4)3(H2O)4, [START_REF] Mcwhan | The Crystal Structure of Zr2(OH)2(SO4)3(H2O)4[END_REF] although the ionic radius of M IV differs significantly (0.86 and 1.04 Å for Zr IV and U IV , respectively), suggesting that it is likely possible to isolate analogues with tetravalent M IV of intermediate ionic radii (e.g., Hf IV , Ce IV , Np IV , and Pu IV ). Another related compound is the dihydroxide-bridged M IV 2 dimer M IV (OH)2SO4 composed of infinite chains of dihydroxidebridged [MO8] (M = Zr,(49) Hf,(50) Th, [START_REF] Knope | Synthesis and characterization of thorium(IV) sulfates[END_REF] and U(51)). All of these hydroxide-bridged metal(IV) sulfate analogues exhibit 3D inorganic networks and are isolated by the hydrothermal treatment of aqueous metal(IV) sulfate solutions.

By doubling the U IV concentration to ∼1 M (see the Experimental Section) in the reaction, we obtained the monomer-linked hexamer framework U-U6. The U-U6 structure, fully formulated as (U(H2O)3.5)2U6O4(OH)4(SO4)10(H2O)9, crystallizes in the noncentrosymmetric tetragonal space group I4̅ 2d (Table 1). The structure (Figure 2) is comprised of the well-known U IV S2) of the U sites indicate good agreement with the U IV oxidation state for the two sites within the hexamer (4.0 and 4.1), but the value is slightly higher for the disordered monomer site (4.5). The geometry of the monomer and the reaction conditions do not support pentavalent uranium, and thus this apparent "overbonding" of the U IV monomer is attributed to the disorder. U-U6 can be compared to the U6 framework reported in 1955 by Lundgren.(52) In the U6 framework, the U6 units are linked directly to each other via sulfates, without the monomer bridge. Each U6 has a scaffold of 4 bridging sulfates and 12 terminal sulfates, linking to 12 additional U6 units in an approximately closest-packed array of U6 "superatoms". The monomer unit of U-U6 opens up the framework, with only four neighboring hexamers per U6 unit, and the U1 units increasing the spacing between hexamer units. Channels are observed down the c axis (∼7 Å diameter; Figure 2C). Because no strong peaks are located in this space, we assume it contains delocalized water molecules.

Raman spectra of solids U2 and U-U6 are shown in Figure 3 for both the sulfate resonances between 950 and 1200 cm -1 and additional low-energy vibrations at 200-700 cm -1 , which could be interpreted as either additional sulfate stretches and/or U-O bond vibrations (Figure 3, inset, discussed later). The highest-intensity peaks between 1000 and 1050 cm -1 for both U2 and U-U6 were previously assigned as A1-symmetric stretches of sulfate by Schnaars and Wilson, while the broader peaks at >1050 cm -1 were assigned as T2-asymmetric sulfate stretches. [START_REF] Schnaars | Uranium(IV) sulfates: investigating structural periodicity in the tetravalent actinides[END_REF] Both phases also exhibit intense peaks at lower frequency (inset), which were previously attributed to sulfate. [START_REF] Schnaars | Uranium(IV) sulfates: investigating structural periodicity in the tetravalent actinides[END_REF] In all polyoxometalate (POM) systems, this region in IR and Raman spectra is attributed to M-O stretches of the metal-oxo clusters, where vibrational frequencies increase with decreased bond length. Therefore, it is reasonable to expect U-O vibrations in this low-frequency region as well. For these peaks, as well as the sulfate peaks, the U-U6 spectrum exhibits more complexity than U2, consistent with the higher number of crystallographically unique U IV sites (one for U2 and three for U-U6). The corresponding IR spectra of U2 and U-U6 are shown in Figure S1. These also exhibit greater complexity for the U-U6 phase in the strong sulfate vibrations (centered around 1000 cm -1 ) and U IV -O vibrations. The unique stretch at 750 cm -1 for U2 is tentatively attributed to vibration of the unique U-(OH)2-U unit. In addition, the OH stretch of the bridging hydroxide is distinctive for U2.

Aqueous Speciation of Uranium(IV) Sulfate in Low-Ionic-Strength Solutions

The high uranium and sulfate concentrations with commensurate high X-ray attenuation of the optimized U2 and U-U6 crystallization solutions, the required heating, and the poor solubility of species in these solutions precluded analysis by SAXS or Raman, either prior to heating or postprecipitation of the solid phase(s). Therefore, we carried out a separate solution-phase study to spectroscopically monitor the evolution of uranium sulfate species with changing pH. The isolated solids provide models to characterize solution species, and it becomes evident that similar species could exist in both the high-and low-ionic-strength solutions, discussed later. With constant U(SO4)2 concentration (30 mM), we varied the pH by adding NaOH (see the Experimental Section). With a starting pH of 1.7 (without added base), the solution was titrated up to 2.8, in approximately eight steps. Raman and UV-vis spectra were recorded. By Raman spectroscopy (Figure 4b), we observe two free sulfate stretches designated as HSO4 -(1050 cm -1 ) and SO4 2-(980 cm -1 ), plus two U-SO4 stretches at 1000 cm -1 (terminally bound or bridging) and 960 cm -1 (bidentate). These stretches are very similar and are assigned based on prior solution-phase studies of hafnium sulfate speciation.( 54) Interestingly, the equivalent SO4-bound uranium peak positions identified in the solid state (discussed above) are shifted ∼50 cm -1 to lower frequency in solution. This is attributed to extensive hydrogen bonding of the U-SO4 species with their solvation shells in solution, lengthening the S-O bonds. With increasing pH, the chelating U═O2SO2 decreases in intensity and the terminally bound U-O-SO3 increases. These changes evidence increasing hydrolysis of U IV , as U-OH -/O 2-bonds replace uranium-sulfate bonds, which promotes oligomer formation. In conjunction, we observe deprotonation of HSO4 -with pH, as this peak disappears. UV-vis spectroscopy showed the typical four bands for U IV , indicating a purity of the oxidation state. The term symbols are labeled for the pH 1.7 solution in Figure S2, following prior assignments of uranium(IV) sulfate solutions(55) and U IV in deuterated perchloric acid.(56) Ligand-field effects and speciation alter the intensity of these peaks but not the positions. However, with increasing hydrolysis and assembly of larger species (dimers, hexamers, etc., discussed below) with increasing pH, the 1 I6 peak broadens and splits, and the 3 P0 and D2 peaks increase in intensity. This latter change was previously noted for the ingrowth of polynuclear complexes of uranium sulfate.(55) SAXS (Figure 5A) data recorded for three pH values revealed strong and distinctive scattering of polynuclear forms. The flat low-q (<0.2 Å -1 ) region indicates no aggregation for all three solutions. At pH 1.8 (without added base), a comparison of the experimental scattering data to simulated scattering [START_REF] Zuo | X-ray diffraction "fingerprinting" of DNA structure in solution for quantitative evaluation of molecular dynamics simulation[END_REF] indicates that the dimer form dominates this solution. However, the dissolved species are smaller than the dimer observed in the U2 solid, with terminally bound and bridging sulfates (Figure 5B). Instead, the simulated scattering of either a H2O/OH --terminated species or a hypothetical dimer (created by Avogadro) [START_REF] Hanwell | Avogadro: an advanced semantic chemical editor, visualization, and analysis platform[END_REF] with mixed chelating sulfates and/or H2O/OH - ligands provided a close match to the experimental data. Although simulated scattering of the dimer without sulfates also provided an excellent match to the experimental data, the Raman data suggest that U IV with chelating sulfate is abundant in these solutions, in agreement with the proposed dimer species with mixed ligands (Figure 4B). We also simulated scattering data of a monomer with various numbers of sulfates, and two monomers bridged by a sulfate, but these did not provide as close a match as the two dimer forms. We can further solidify this interpretation by comparison to prior high-energy X-ray scattering (HEXS) studies of zirconium [START_REF] Hu | Understanding the role of aqueous solution speciation and its application to the directed syntheses of complex oxidic Zr chlorides and sulfates[END_REF] and hafnium(59) sulfate solutions. Increasing the sulfate concentration increased species containing bidentate sulfate, but the zirconium sulfate monomer that precipitates from these solutions does not contain bidentate sulfate.(58) Similarly, HEXS provided strong evidence for bidentate coordination to hafnium, whereas no isolated solids contain this binding mode. We too observe evidence for bidentate-coordinated sulfate (by Raman and SAXS) in solution.

With increasing pH, the uranium(IV) sulfate species grow, as evidenced by the shift in the Guinier elbow to lower q (q ∼ 0.3-0.8 Å -1 for pH 1.8 and q ∼ 0.1-0.5 Å -1 for pH 2.6). The pair distance distribution functions (PDDFs, probability distribution maps of the scattering vectors through the clusters) of the three solutions (Figure 5C) indicate that the maximum diameters observed are 9, 14, and 24 Å, respectively, with increasing pH. On the basis of a comparison to simulated scattering, the pH 2.6 solution is dominated by species with the approximate size and shape of the hexamer decorated with four tetrahedrally arranged monomers, as observed in U-U6 (Figures 2A and5B). The intermediate solution (pH 2.4) scattering does not precisely match any subunits of the described phases, but intermediate sizes observed in both the scattering data and PDDF suggest a mixture of hexamers capped with varying numbers of U1 monomers and/or sulfate groups and possibly some dimer species. The PDDF profiles are all complex and could be interpreted in different ways. The pH 1.8 solution exhibits the classic profile of a "dumbell" shape with a short dimension of ∼2.5 Å (maximum of the first peak) and a long dimension of 8.5 Å [maximum linear extent of PDDF, where the probability, P(r), goes to 0]. Both the profile shape and dimensions are exactly consistent with a dihydroxide-bridged dimer, either with all H2O/OH -termination or with chelating sulfates (both shown in Figure 5B). The PDDFs of the pH 2.4 and 2.6 solutions indicate some complexity, suggesting some polydispersity of these uranium(IV) sulfate solutions, as discussed previously. In Soderholm's zirconium sulfate study, they also employed SAXS, which showed increasing species size up to 0.5 M sulfate, followed by decreasing species size up to 2 M sulfate. This was interpreted as the well-known Zr18 sulfate species dominating the 0.5 M sulfate solution, whose assembly is inhibited as sulfate replaces oxo/hydroxyl bridges as sulfate is increased to 2.0 M.(58) Soderholm's study and prior studies by Clearfield et al. [START_REF] Clearfield | Nature of hydrous zirconia and sulfated hydrous zirconia[END_REF] show that, even in very acidic conditions, large species such as Zr18 containing abundant OH -/O 2-ligands can be crystallized. Despite high acid and sulfate concentrations, hydrolysis/olation/oxalation reactions leading to these species are not inhibited. This highlights the very strong Bronsted and Lewis acid behavior of these tetravalent metals.

The above-described solutions are optimized for studying solution speciation, and we have identified species consistent with those crystallized in this study and prior studies. The identified solution species are mainly mixtures of monomers, dimers, and hexamers, with both sulfate and H2O/OH -/O 2-ligation. However, the low acidity and low ionic strength promotes gelation rather than crystallization. Therefore, the synthesis of crystalline solids was optimized in 0.5-1.0 M H2SO4 and 0.5-1.0 M U(SO4)2 (see the Experimental Section). Because species evidenced in lowacid, low-sulfate solutions are similar to those crystallized from high-acid, high-sulfate solutions, this raises the question, what are the roles of the acid and sulfate? We suggest three specific roles. First, the high H + retains a positive charge on the species formed by hydrolysis/olation/oxolation reaction, preventing them from aggregating and precipitating neutral forms, also previously suggested by Clearfield et al. [START_REF] Clearfield | Nature of hydrous zirconia and sulfated hydrous zirconia[END_REF] Second, sulfate capping the growing species also prevents uncontrolled precipitation. Third, the sulfates are important for crystallization, both capping and bridging the M IV species of U2 and U-U6 of this study and numerous other sulfate-capped oxo clusters isolated in prior studies that are usually cationic, but in rare cases, anionic.(61) In our study and prior studies, sulfate-chelating M IV seems important to retain solubility, but bridging modes are prevalent in crystallized forms because infinite lattices of solution species grow via sulfate bridging.

PXRD of bulk materials from synthesis experiments usually indicated cocrystallization of two (or more) phases. In general, lower H2SO4 and higher uranium concentration yielded larger species such as hexamers (i.e., U-U6), while higher acid and lower uranium concentration favored U2.

From lower uranium concentration targeting U2, this dihydroxide-bridged dimer cocrystallizes with the U(SO4)2•4H2O monomer reported in 1956 (ICSD-24057; Figure 6A, designated as U1 for this discussion).( 62) Meanwhile, optimization of the U-U6 synthesis yielded mixtures of U2 and U-U6 (Figure 6B). Note that cocrystallized U2 and U-U6 suggest the coexistence of monomers, dimers, and hexamers in uranium sulfate reaction solutions, analogous to thorium sulfate.(12,13) This can also be viewed by SEM in Figure 7, where the three different phases are identified by morphology, and composition confirmed by EDXS (Table 2). The experimental U-U6 uranium composition is most similar to that predicted from the X-ray structure, followed by U2 and then U1. We can perhaps attribute this to the symmetry of the phases. U-U6 has the highest symmetry (tetragonal) and U1 the lowest (monoclinic). Higher symmetry means that the various crystal faces analyzed by EDXS present a more similar composition at the surface.

CONCLUSIONS

The tetravalent actinides Th IV , U IV , Np IV , and Pu IV with their common oxidation state and similarities to Zr IV , Hf IV , and Ce IV provide rich opportunities to understand the hydrolysis of metal cations across the periodic table. Here we described by single-crystal X-ray diffraction a dihydroxide-bridged U IV dimer, capped and bridged by sulfate into a 3D framework, and a uranium(IV) sulfate framework of monomer-linked hexamers. These phases along with the apparent coexistence of monomers, dimers, and hexamers as solids and in solution exhibit behavior very similar to that previously described in thorium(IV) sulfate solutions and solids, whereas prior examples of isolated clusters (containing 38-70 metal centers) suggested that U IV is more similar to Np IV and Pu IV . From the perspective of a periodic trend, we indeed expect more extensive polymerization with decreasing metal-cation size, commensurate with increased acidity across the actinide series. This study, showing the similarity between U IV and Th IV chemistry, provides a bridge between thorium and the transuranics to contribute to our global understanding of the actinide series.

  [START_REF] Knope | Synthesis and characterization of thorium(IV) sulfates[END_REF][START_REF] Albrecht | The crystal chemistry of four thorium sulfates[END_REF] There is one crystallographically unique U IV center that is eight-coordinate, bound to four sulfates [U-OSO3 = 2.33(1)-2.37(1) Å], two hydroxides [U-OH = 2.21(1)-2.36(1) Å], and two terminal water molecules [U-OH2 = 2.40(1)-2.42(1) Å]. The dimers are aligned approximately along the (101) direction, and the 3D lattice is created by sulfate bridging between dimers. There are two crystallographically unique sulfates: S(1) bridges three dimers, denoted as μ3-SO4, and S(2) bridges two dimers, μ2-SO4 (Figure1b). Each dimer bridges to neighboring dimers by eight sulfates, four for each U center: three S(1)O4 2-and one S(2)O4 2-. There is no disorder in this simple structure. Bond-valence-sum (BVS) calculations (TableS1) readily distinguish hydroxyl (BVS = 1.27) from water (BVS ∼ 0.5) ligands and are consistent with a tetravalent oxidation state of uranium (BVS = 4.3).

Figure 1 .

 1 Figure 1. (A) Ball-and-stick representation of the [U2(OH)2] core. U IV is green, bridging OH -is red, H2O is blue, oxo of μ3-SO4 is orange, and oxo of μ2-SO4 is turquoise. (B) Polyhderal representation of the extended framework, viewed down the b axis. U IV is green, μ3-SO4 is orange, and μ2-SO4 is turquoise.

Figure 2 .

 2 Figure 2. Representations of U-U6. (A) Ball-and-stick representation of the connectivity between the hexamer and monomer units via a disordered sulfate. For the U6O4(OH)4 unit, U IV are green spheres, O 2-are red spheres, and OH -are blue spheres. The monomer U IV is purple, and S (disordered over two half-occupied sites) of bridging SO4 2-are yellow spheres. (B) Illustration of the tetrahedral arrangement of the monomers around the U6 unit. Purple polyhedra are the U IV monomers, green polyhedra are the U IV of the hexamer, and yellow polyhedra are sulfates. (C) Framework view down the c axis. The color scheme is the same as that in part B.

Figure 3 .

 3 Figure 3. Raman spectra of solid U2 and U-U6, emphasizing the sulfate vibrations and U-O/sulfate vibrations (inset).

Figure 4 .

 4 Figure 4. UV-vis (A) and Raman (B) spectra of 30 mM U(SO4)2, with increasing pH from 1.7 (bottom) to 2.8 (top). Inset: Raman spectra showing two modes of sulfate bonding to U IV : chelating (blue box) and terminal/bridging (red box).

Figure 5 .

 5 Figure 5. SAXS data and analyses. (A) log-log plot of the experimental (data points) and simulated (lines) scattering data. (B) Structures used for scattering data simulations. The frame matches the simulated scattering curve in part A. In the red box is precisely the dimer unit of U2 with all terminal/bridging sulfates, the solid black box shows the dimer with only H2O/OH - ligands, the broken black frame shows a hypothetical dimer capped with chelating sulfates, and the lavender box shows the core unit of U-U6, a hexamer with tetrahedrally arranged monomer caps. (C) PDDF representation of three scattering curves. r is the distance from the edge of the scattering particle, and P(r) is the probability of the scattering vector of length r (Å).

Figure 6 .

 6 Figure 6. PXRD of bulk material for the optimized synthesis of (A) U2 (with U1(61)) and (B) U-U6 (mixed with U2). Simulated diffraction patterns are from the single-crystal X-ray diffraction structures.

Figure 7 .Table 2 .

 72 Figure 7. SEM images of the U1/U2 (left) and U2/U-U6 (right) mixtures.

Table 1 .

 1 Crystallographic Information for U2 and U-U6

	identification code	U2	U-U6
	CCDC	2015781	2015780
	empirical formula	H10O18S3U2	O128S20U16
	molecular formula	U2(OH)2(SO4)3(H2O)4	(U(H2O)3.5)2U6O4(OH)4(SO4)10(H2O)9
	fw	870.32	6497.68
	temperature/K	100(2)	172(2)
	cryst syst	monoclinic	tetragonal
	space group	C2/c	I4̅ 2d
	a/Å	13.5620(2)	21.2076(5)
	b/Å	6.78250(10)	21.2076(5)
	c/Å	15.5926(2)	11.9257(3)
	α/deg	90	90
	β/deg	95.6200(10)	90
	γ/deg	90	90

PXRD

Samples for PXRD were prepared by filtering and washing freshly synthesized crystals of the mixed products. The crystals of each sample were ground in a mortar and pestle. PXRD patterns were collected from 3 to 50° 2θ at a rate of 1.5°/min, using a Rigaku Miniflex with Cu Kα radiation (λ = 1.54056 Å).

  hexameric core, [U6O4(OH)4] 12+ arranged tetrahedrally in 3D space, bridged by four U IV monomers that surround the U6 core in a tetrahedral arrangement. The core exhibits no O/OH disorder that is typical of isolated molecular clusters;(32) the rigid framework enforces ordering. The hydroxides and oxides are readily distinguished by BVS (TableS2). Each monomer bridges two U6 units, and all U1-U6 bridges are via sulfates. Each U

IV center in the hexamer is bonded to two μ3-O [U-O = 2.24(2)-2.28(2) Å] and two μ3-OH [U-OH = 2.46(2) Å] of the core U6O4(OH)4 unit, plus four bridging sulfates [U-OSO3 = 2.39(2)-2.42(2) Å] and one water molecule [U-OH2 = 2.62(2)-2.86(2) Å], completing a nine-coordinate, capped square-antiprismatic geometry. Per the U6 unit, there are 8 fully occupied bridging sulfates and 4 half-occupied (disordered) sites (shown in Figure 2a) for a total of 10 per formula unit. The monomer has considerable disorder in its ligand coordination and is, on average, eight-coordinate. The monomer bridges two hexamers. To each hexamer, the monomer links via one half-occupied sulfate [U-OSO3 = 2.55(1) Å] and two fully occupied sulfates [U-OSO3 = 2.20(1) Å]. In addition to these six bonds to the uranium monomer, it is surrounded by eight partially occupied water positions [U-OH2 = 2.21(2)-2.62(2) Å]. BVS calculations (Table

ACKNOWLEDGMENTS

This work was supported by the Department of Energy, National Nuclear Security Administration, under Award DE-NA0003763. We acknowledge the Murdock Charitable Trust (Grant SR-2017297) for acquisition of the single-crystal X-ray diffractometer.


Germercy Paredes

Grégory Seine

Robin Cours

Florent Houdellier

Hatem Allouche

Thierry Ondarçuhu

Fabrice Piazza

Marc Monthioux

Synthesis and (some) applications of carbon-nanotube-supported pyrolytic carbon nanocones

come

I. Introduction

All-graphene carbon cones with nanosized apex can be obtained by means of high temperature pyrolytic carbon deposition process using methane and hydrogen as gaseous feedstock and individual carbon nanotubes (CNTs) as deposition substrates 1,2 . Aside the cones with smooth surface, micrometer-sized carbon beads (Figures 1b and1c) or fiber segments (Figures 1a and1c) are deposited meanwhile, which are a key morphological component for allowing handling and mounting the carbon cones and then using them for various applications.

II. Synthesis and growth mechanisms

CNTs are grown first, using iron nanoparticles as catalyst combined with a regular chemical vapor deposition process (CCVD) in which a CH4 + H2 feedstock is cracked at 1000-1100°C 2 .

Then catalyst-free conditions (CVD) involving temperatures in the 1300-1500°C range and a modified H2/CH4 ratio are used to deposit pyrolytic carbon onto each CNT, which spontaneously adopt the complex morphologies as shown in Figure 1 while aligning more or less periodically along the CNTs [1][2][3][4] . A deposition mechanism which requires both the presence of small carbon radicals and the transient formation of pitch-like (i.e., containing polyaromatic hydrocarbon molecules (PAHs) and lighter hydrocarbons) droplets in the gas phase is proposed, based on both the literature and experimental evidences 4 (Figure 3). At the beginning of the deposition process, radicals cannot chemisorb onto the CNTs because of the lack of active sites. Therefore, based on ref. 4 , the proposed mechanism for the early deposition step is related to the wettability of the substrate (the primary nanotube surface) by the carbon species (PAH-containing droplets) where the deposition and carbonization processes take place. Because of the substrate geometry (non-planar), two situations of partial wetting define the way droplets are deposited onto the nanofilament. These situations depend on the nanotube over droplet diameter ratio. Should the droplets exhibit diameters smaller than the CNT diameters (5-10 nm), they would deposit on the filament surface as they would onto a planar surface, corresponding to the first situation. The second situation occurs when the carbon nanotubes have smaller diameters than droplets. In such a case, each PAHrich droplet is deposited onto the carbon nanotube surface forming a double meniscus (Figure 3b). The primary droplet deposition event is assumed to be somewhat periodic following the Plateau-Rayleigh instability 5 . These double menisci are responsible for forming the primary double nanocones observed in short duration experiments (step C in Figure 3) 4 . Indeed, The PAHs from the liquid double meniscus align parallel to the nanotube because of capillary forces and surface tension and then carbonize as concentric graphenes (step C in Figure 3).

The cones continue growing the same way until a threshold value of about 100 nm for the diameter at the cone base is reached. At the reached threshold value, the deposition of the droplets continues at the base of the double cones now following situation 1 abovementioned, because at that time, the radius of curvature of the substrate surface has become long enough for the droplets to deposit on it as they would do onto a flat substrate. From this moment, the graphenes resulting from the carbonization of the PAHs no longer align well, because the effect of surface tensions no longer prevails, producing morphologies with rough surface. Rough surface sub-morphologies can be bead-like or fiber-segment-like (Figure 1) probably depending on the number of droplets in the gas phase. Once this step is reached, the cones and the beads/fiber segments continue to grow simultaneously, but now driven by a competition between the two carbon deposition modes: the chemisorption of radicals onto the active sites present at the cone surface and the physisorption of PAH-rich droplets mostly onto the bead/fiber-segments, respectively.

III. Application of carbon cones as electron emitters

The concentric texture and the graphene perfection of the carbon cones are likely to provide them with the physical properties of large multiwall CNTs, typically, high electrical and thermal conductivities, high current density, and high flexural resilience, yet with an apex in the ~5-10 nm range only. Therefore, carbon cones were successfully tested as electron emitters instead of the usual W emitter, in cold-field emission guns (CFEG) (Figure 4a), the best current electron sources for electron microscopes. Results overpassed the expectations, and the carbon cone emitter revealed to be able to provide 5 times higher reduced brightness and better coherence than any commercial electron source for TEM [6][7][8] . They also are better than pristine CNTs, because of the conical shape which provides sufficient mechanical stability to prevent the tip from vibrating while emitting.

Overall, the carbon cone electron source exhibits much better time stability than the best CFEG on market (Figure 4b), presumably because much fewer active sites are present at the cone surface (Figure 2a) with respect to the tungsten crystal, leaving the residual species present in the ultravacuum atmosphere with little opportunity to adsorb and thereby preventing the current from dropping. Indeed, as the cones are made of concentrically displayed perfect graphenes, the only active sites at the cone surface are the graphene edges, which occurrence is in the range of one every 7-10 nm on the cone side (Figure 2a) and 2-3 nm in the vicinity of the cone apex (Figure 5b). On the opposite, for a chemically-etched singlecrystal tungsten-tip, every surface atom is under-coordinated, hence is reactive towards the residual species, which makes one active site every 2-3 Angströms at the tip surface. Carbon cones were then patented for this application [START_REF] Monthioux | European Patent (pub. EP 2-617-049-B1)[END_REF] .

IV. Application of carbon cones as probes for scanning probe microscopy

The aspect ratio and electrical conductivity property (which is expected from the perfect nanotextural quality, see Figure 2) make the carbon cones presumably suitable as probes for various modes of near field microscopy. The carbon nanocone shape have a length L in the range of (2-7 µm) and a base-width W of about up 700 nm, and a very sharp apex angle noted 2α. The smallest the cone radius W/2, the closest to zero the cone angle. This very small angle can be estimated by the following equation:

Tan α = α = W/(2 * L) (1)
this leads to:

2α = W/L (2)
For W = 700 nm; L = 6 µm (maximum value) as depicted in Figure 5a, the cone angle 2α takes the value of 0.12°.

Figure 5. Main geometrical characteristics of a nanocone tip. (a) SEM image showing the length, width and angle parameters. (b) High resolution transmission electron microscopy (HRTEM) image of the cone apex. (Photo credit: R. Wang, CEMES-CNRS).

Carbon cone morphologies such as shown in Figure 1a were glued onto tailor-made AFM cantilevers (obtained from AppNano) following either a micro-manipulation procedure under optical microscope as initially proposed by Dai et al. for CNTs 10 , or the same focused electron beam-induced welding techniques as carried-out for mounting the cones as electron emitters 6,7 . In the latter case, the mounting process was conducted using a Scanning Electron Microscope (SEM Zeiss 1540 XB) equipped with a dual Focused Ion Beam (FIB) Electron Beam system and a micromanipulator (clamps) as depicted in Figure 6. Subsequently, tests of the probes for different conductive and non-conductive SPM modes were conducted.

Figure 6. Mounting a carbon nanocone tip as SPM probe by focused electron-beam-induced metal deposition. (a) A carbon nanocone morphology is grabbed by micromanipulator clamps; (b) The carbon nanocone morphology is placed into the groove of a specially-designed Si-doped cantilever; (c) The carbon nanocone tip (welded onto the cantilever) is ready to be used for different AFM tests: the yellow colour represents a Si doped cantilever, the purple colour, the carbon cone tip morphology, and the red parts correspond to the platinum metal deposit used for welding.

Carbon nanocones exhibit better resolution than standard AFM Si tips when used for AFMtapping mode topography images (Figure 7). The images parameters of a scan size area of 500 nm width with a speed scan of 2hz and 256 X 256 scan pixels allowed distinguishing the background of a silicon wafer surface as well as the separation between two gold nanoparticles which are clearly delimited thanks to the tip sharpness of the carbon cone tip (Figure 7b). Thanks to their carbon nature, these conical tips are also suitable for near-field modes requiring conducting probes, such as conducting AFM, charge injection, and Kelvin force microscopy, for which they have already shown a promising behaviour [START_REF] Paredes | Proc. of The World Conference on Carbon 'Carbon-2018[END_REF] . Other conductive modes such as C-AFM, Scanning Tunnel Microscopy (STM), and non-conductive ones such as Peak-Force Quantitative Nanomechanical Mapping (PFQN AFM)-are currently tested, and work in this area is in progress.

V. Conclusions

In summary, we have shown that unique carbon conical morphologies can be produced from pyrolytic carbon deposition onto nanoscale substrates (carbon nanotubes) during a thermal CVD process. The fact of synthetizing micro-nano morphologies made up of smooth nanocones as well as rough bead or fiber segments, suggest (at least under experimental conditions of high temperature and atmospheric pressure) a pyrolytic carbon deposition driven by two different mechanisms. This can be explained by the coexistence (in the gas phase) of carbon radicals, which provide the needed active sites, in addition to PAH-containing droplets which randomly deposit wherever onto the substrate surface.

On the other hand, it was demonstrated that the well-controlled geometrical characteristics (i.e. aspect ratio, tip radius) of the synthesized morphologies, and their excellent physical properties (i.e. good electrical conductivity, mechanical strength) as well as their relatively easy mounting, allow them to have the potential to equip electron sources with unprecedented performances, and to be unique, presumably durable, multi-mode probes for various kinds of near-field microscopy.

Figure 1 .

 1 Figure 1. (a) Morphology of a "carbon nanocone" with a fiber segment. (b) Morphology of a "carbon nanocone" with an isolated carbon bead. C) Co-existence of different "carbon

Figure 2 .

 2 Figure 2. Carbon nanocone texture and nanotexture. (a) High resolution transmission electron microscopy (HRTEM) image showing a perfect orientation of the nanocone graphene layers with respect to the cone axis (primary carbon nanotube). As indicated (see arrows) the cone surface is made of graphene edges, each of them being a preferred site for adsorption. (b) Display of the constituting graphenes within the conical part (model by I. Suarez-Martinez, Curtin University, Australia).

Figure 3 .

 3 Figure 3. sketch of the formation mechanisms of the carbon nanocone-bearing morphologies seen in Figure 1. A: growth of the primary CNTs; B: deposition of pitch-like (PAH-containing) droplets onto the CNTs, forming double meniscus; C: PAHs align parallel to the CNT axis upon surface tension forces and then subsequently carbonise, forming bicones; D: Growth of the cones mostly from C radicals, while the short fiber segments (or beads) form mostly from droplets.

Figure 4 .

 4 Figure 4. (a) Carbon cone W-welded by focused ion beam onto a regular yet truncated W tip emitter. (b) comparison of the current stability with time for (b-1) the carbon cone emitter; (b-2) a regular W tip emitter. Such a stability is unprecedented for CFEG electron source (from ref. 8 ).

Figure 7 .

 7 Figure 7. (a) AFM image obtained from a commercial Si probe on gold nanoparticles deposited on a Si wafer; (b) Same area as (a) using a carbon cone probe.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Carbon nanocone texture and nanotexture. (a) High resolution transmission electron microscopy (HRTEM) image showing a perfect orientation of the nanocone graphene layers with respect to the cone axis (primary carbon nanotube). As indicated (see arrows) the cone surface is made of graphene edges, each of them being a preferred site for adsorption. (b) Display of the constituting graphenes within the conical part (model by I. Suarez-Martinez, Curtin University, Australia).

Figure 3 .

 3 Figure 3. sketch of the formation mechanisms of the carbon nanocone-bearing morphologies seen in Figure 1. A: growth of the primary CNTs; B: deposition of pitch-like (PAH-containing) droplets onto the CNTs, forming double meniscus; C: PAHs align parallel to the CNT axis upon surface tension forces and then subsequently carbonise, forming bicones; D: Growth of the cones mostly from C radicals, while the short fiber segments (or beads) form mostly from droplets.

Figure 4 .

 4 Figure 4. (a) Carbon cone W-welded by focused ion beam onto a regular yet truncated W tip emitter. (b) comparison of the current stability with time for (b-1) the carbon cone emitter; (b-2) a regular W tip emitter. Such a stability is unprecedented for CFEG electron source (from ref.8 ).

Figure 5 .

 5 Figure 5. Main geometrical characteristics of a nanocone tip. (a) SEM image showing the length, width and angle parameters. (b) High resolution transmission electron microscopy (HRTEM) image of the cone apex. (Photo credit: R. Wang, CEMES-CNRS).

Figure 6 .

 6 Figure 6. Mounting a carbon nanocone tip as SPM probe by focused electron-beam-induced metal deposition. (a) A carbon nanocone morphology is grabbed by micromanipulator clamps;(b) The carbon nanocone morphology is placed into the groove of a specially-designed Si-doped cantilever; (c) The carbon nanocone tip (welded onto the cantilever) is ready to be used for different AFM tests: the yellow colour represents a Si doped cantilever, the purple colour, the carbon cone tip morphology, and the red parts correspond to the platinum metal deposit used for welding.

Figure 7 .

 7 Figure 7. (a) AFM image obtained from a commercial Si probe on gold nanoparticles deposited on a Si wafer; (b) Same area as (a) using a carbon cone probe.

Acknowledgments

The Pontificia Universidad Católica Madre y Maestra (Santiago, Dominican Republic) is thanked for providing the grant for GP. The LabEx NEXT is thanked for funding the "CarboProbe" project and mutual visits.

Abstract

Graphene-based cones with nanosized apex can be obtained by means of high temperature pyrolytic carbon deposition process using methane and hydrogen as gaseous feedstock and single carbon nanotubes as deposition substrates. Aside the cones, micrometer-sized carbon beads or fibre segments are deposited meanwhile which are a key morphological component for allowing handling and mounting the carbon cones and then using them for various applications. Based on both the literature dealing with pyrolytic carbon deposition processes and experimental observations, a peculiar deposition mechanism is proposed, involving the transient formation of pitch-like liquid phase droplets which deposit onto the individual carbon nanotubes. In this picture, it is believed that a key parameter is the ratio between the droplet and the nanotube diameters, respectively. The cone concentric texture and perfect nanotexture are shown by high resolution transmission electron microscopy, which allows interesting mechanical and conducting properties to be predicted. Correspondingly, applications of the carbon nanocones as electron emitters for cold-field electron sources on the one hand, and as probes for various modes of near-field microscopy on the other hand, have been tested.


E Armengaud

C Augier

A S Barabash

F Bellini

G Benato

Alain Benoit

A Benoît

M Beretta

L Bergé

J Billard

Yu A Borovlev

Ch Bourgeois

V B Brudanin

P Camus

L Cardani

N Casali

A Cazes

M Chapellier

F Charlieux

D Chiesa

M De Combarieu

I Dafinei

F A Danevich

M De Jesus

T Dixon

L Dumoulin

K Eitel

F Ferri

B K Fujikawa

J Gascon

L Gironi

A Giuliani
email: andrea.giuliani@ijclab.in2p3.fr

V D Grigorieva

M Gros

E Guerard

D L Helis

H Z Huang

R Huang

J Johnston

A Juillard

H Khalife

M Kleifges

V V Kobychev

Yu G Kolomensky

S I Konovalov

A Leder

P Loaiza

L Ma

E P Makarov

P De Marcillac

R Mariam

L Marini

S Marnieros

D Misiak

X.-F Navick

C Nones

E B Norman

V Novati

E Olivieri

J L Ouellet

L Pagnanini

P Pari

L Pattavina

B Paul

M Pavan

H Peng

G Pessina

S Pirro

D V Poda

O G Polischuk

S Pozzi

E Previtali

Th Redon

A Rojas

S Rozov

C Rusconi

V Sanglard

J A Scarpaci

K Schäffner

B Schmidt

Y Shen

V N Shlegel

B Siebenborn

V Singh

C Tomei

V I Tretyak

V I Umatov

L Vagneron

M Velázquez

B Welliver

L Winslow

M Xue

E Yakushev

M Zarytskyy

A S Zolotarova

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The CUPID-Mo experiment at the Laboratoire Souterrain de Modane (France) is a demonstrator for CUPID, the next-generation ton-scale cryogenic 0νββ experiment. It consists of a 4.2 kg array of 20 enriched Li2 100 MoO4 scintillating bolometers to search for the lepton number violating process of 0νββ decay in 100 Mo. With more than one year of operation (2.16 kg×yr of physics data), no event in the region of interest and hence no evidence for 0νββ is observed. We report a new limit on the half-life of 0νββ decay in 100 Mo of T 1/2 > 1.5 × 10 24 yr at 90% C.I. The limit corresponds to an effective Majorana neutrino mass m ββ < (0.3-0.5) eV, dependent on the nuclear matrix element in the light Majorana neutrino exchange interpretation.

The discovery that neutrinos are massive particles through the evidence of neutrino flavor oscillations [1] would have a tremendous impact on our vision of Nature, implying the violation of the total lepton number L as well as for the matter-antimatter asymmetry in the Universe [6], see also review [7].

The distinction between Dirac and Majorana behavior is an extreme experimental challenge. Neutrinoless double-beta (0νββ) decay is the traditional and the most sensitive tool to probe the Majorana nature of neutrinos. This process is a nuclear transition consisting in the transformation of an even-even nucleus into a lighter isobar containing two more protons and accompanied by the emission of two electrons and no other particles, with a change of the lepton number L by two units [8][9][10][11]. An observation of this rare process would establish that neutrinos are Majorana particles [12]. The current most stringent limits on 0νββ decay half-lifes are at the level of 10 26 yr in 136 Xe and 76 Ge [13,14].

0νββ decay can be induced by a variety of mechanisms [9,11,15,16]. Among them, the so-called mass mechanism -consisting in the exchange of a virtual light Majorana neutrino -represents a minimal extension of the Standard Model. In this mechanism, the 0νββ decay rate is proportional to the square of the effective Majorana neutrino mass m ββ , a linear combination of the three neutrino mass eigenvalues which fixes the absolute neutrino mass scale. Present limits on m ββ are in the range of (0.06 -0.6) eV [11], assuming that the axial charge g A is not quenched and equal to the free nucleon value of 1.27 [17][18][19].

The distinctive signal of 0νββ decay is a peak in the total energy spectrum of the two emitted electrons at the total available energy Q ββ of the 0νββ transition, enlarged only by the finite detector energy resolution. Besides 0νββ decay, candidate nuclei undergo standard two-neutrino double-beta (2νββ) decay where two anti-neutrinos are emitted along with the two electrons [20]. 2νββ conserves the lepton number L and as anti-neutrinos escape detection, the two-electron energy spectrum is a continuum extending from zero to Q ββ . This process has been observed in several nuclei with half-lives in the 10 18 -10 24 yr range [21,22]. Among the 35 natural double-beta emitters [23], only a few of them are experimentally relevant because of their high Q ββ (> 2 MeV) with high decay probability, typically favorable backgrounds at higher energy and their high natural isotopic abundance and/or technically feasible isotopic enrichment.

Low-temperature calorimeters, often named bolometers, are the detectors of choice for several experimental efforts, including the one reported here. Featuring high energy resolution, high efficiency, and flexibility in detector-material choice [24][25][26], bolometers are perfectly tailored to 0νββ search. These detectors consist in a single crystal that contains the 0νββ source coupled to a temperature sensor. The signal is collected at very low temperatures 20 mK for large (0.1-1 kg) bolometers and consists of a thermal pulse registered by the sensor.

A detector embedding a candidate with Q ββ > 2615 keV is an optimal choice in terms of background control, as the bulk of the γ natural radioactivity ends at 2615 keV, corresponding to the energy of the 208 Tl line in the 232 Th decay chain. However, the energy region above ∼ 2.6 MeV is dominated by events due to surface radioactive contamination, especially energy-degraded α particles [27,28], as shown by the results of CUORE, the largest 0νββ bolometric experiment currently under way.

A method to reject α events in bolometers exploits light emission -scintillation or Cherenkov -from certain detector materials [25,26,[29][30][31][START_REF] Azzolini | CUPID-0)[END_REF][START_REF] Azzolini | CUPID-0)[END_REF][34]. Since the γ and β light yield is appreciably different from the α light yield at equal deposited energy, while the bolometric thermal response is almost equivalent, the simultaneous detection of light and heat can effectively reject the surface α background.

The detector technology of CUPID-Mo has been developed by the LUMINEU Collaboration [35,[START_REF] Poda | AIP Conf. Proc[END_REF] and is described together with the experimental setup in [START_REF] Armengaud | [END_REF]. The isotope of interest 100 Mo features a Q ββ of (3034.40±0.17) keV [38] and a natural abundance of 9.7% making large scale enrichment viable by gas centrifuge isotopic separation. In CUPID-Mo, it is embedded into scintillating Li 2 100 MoO 4 (LMO) crystals by a double lowthermal-gradient Czochralski crystallization process [39] from enriched Mo previously used in the NEMO-3 experiment [START_REF] Arnold | NEMO-3)[END_REF]. A total of twenty cylindrical ∼ 210 g crystals are stacked into 5 towers which results in a 100 Mo mass of (2.258 ± 0.005) kg with an average 100 Mo isotopic abundance of (96.6 ± 0.2)%. Bolometric Ge light detectors (LDs) complement each LMO detector module, such that all but the top LMO elements of the 4-crystal tower see a LD at both the top and bottom. The LMO crystals as well as the LDs are instrumented with Neutron-Transmutation-Doped (NTD)-Ge sensors [41]. The towers are installed with a mechanical decoupling inside the EDELWEISS cryogenic infrastructure [42,43] at the Laboratoire Souterrain de Modane in France.

The data of the present analysis have been acquired over a 380 day period between March 2019 and April 2020 at operation temperatures of 20.7 and 22 mK. 82 % of the time was devoted to the 0νββ search, split into 240 days of physics data and 73 days of calibration data.

We only consider 213 out of the 240 days of physics data, split into 7 datasets for which we also have calibration data with high statistics and hence a precise knowledge of the energy scale.

We further exclude periods of temperature instabilities, disturbances in the underground laboratory and periods of excessive noise on the individual detectors reducing the physics exposure by 6%. We reject one of the twenty LMO bolometers that shows an abnormal performance [START_REF] Armengaud | [END_REF] and obtain a physics exposure of 2.16 kg×yr (Li 2 100 MoO 4 ). All data are acquired as a continuous stream with 500 Hz sampling frequency and analyzed with a software package developed by the CUORE [44] and CUPID-0 [START_REF] Azzolini | CUPID-0)[END_REF] Collaborations, first used in CUPID-Mo in [START_REF] Armengaud | [END_REF]46]. We use an optimum filter based analysis chain with 3 s long pulse traces for both the LMO and LD channels. The data were re-triggered offline using the optimum filter [28,47]. This resulted in significantly lower trigger thresholds with 90% efficiency values attained at typical (median) energies of 9.4 keV / 0.5 keV for the LMOs / LDs. The LMOs analysis and coincidence thresholds have been set at 45 keV, well above this efficiency turn on. For each signal on an LMO detector we evaluate the resolution weighted average light signal of the two (one) adjacent LDs to discriminate α events, exhibiting ∼20% of the light yield of γ&β events of the same energy [START_REF] Armengaud | [END_REF]. Furthermore, the energy difference of the upper and lower LDs, corrected for geometrical light collection efficiencies is computed to extend the identification of near surface decays. We developed a new pulse shape analysis procedure for the signal of the LMO detector to remove remaining spikes and pulser-induced cross-talk events from the data. As described in detail in [48] a principal component analysis (PCA) is used to establish a characteristic shape of a pulse as the leading PCA component(s). We then compute the reconstruction error defined as the square-root of the variance from a pulse with respect to its projection onto the leading PCA component(s). The reconstruction error shows a linear energy dependence and a constant spread over our γ&β data which makes it ideally suitable for the 0νββ analysis where it needs to be extrapolated to Q ββ of 100 Mo at 3034 keV. Together with this very simple energy dependence we gain a ∼ 9% efficiency increase compared to the analysis presented in [46]. Lastly we calibrate the response of the LMO detectors with a 2nd order polynomial using the U/Th calibration data as in [46] and cross-calibrate the LD against the LMO signals.

We adopt a blinding strategy removing all events in a ±50 keV window around Q ββ to avoid any bias in the optimization of our analysis procedures and consider the following event selections. For events

• to be contained in a single crystal and in anticoincidence with a triple module trigger and energy deposit in the muon-veto system [49] based on a 100 ms time window;

• to have a single trigger in each 3-s pulse window;

• to have a flat pre-trace with a slope of less than 15 median absolute deviations;

• to have a pulse shape compatible with the principal components established by the PCA. This cut is optimized using calibration data by maximizing a hypothetical discovery sensitivity for a 0νββ process equal in half-live to the previous best limit [START_REF] Arnold | NEMO-3)[END_REF], see also [48];

• to have the expected light yield for γ&β events and no difference in top and bottom LDs. Both of these cuts are set to obtain close to full coverage at ±3 σ each, based on a Gaussian fit of the light yield in calibration data. The energy dependence of the cut was modeled with a linear function after we observed an excess broadening of the recorded light yield with respect to the photon statistics model discussed in [START_REF] Armengaud | [END_REF]. The excess width is associated with an under-sampling of the faster LD pulses and is presently under further investigation.

(3) (4) (5) ( The resulting spectra summed over 19 LMO detectors and the entire data taking period are shown in Fig. 1.

The physics data exhibit an extended 2νββ component, associated with the short 2νββ half-life (high rate) of 100 Mo [START_REF] Arnold | NEMO-3)[END_REF]51], which dominates the spectrum from 0.5 to 3 MeV. Above this component only a limited number of γ peaks from remaining natural radioactivity in the experimental setup are visible. The most prominent γ peaks in our data are 208 Tl, 40 K, 60 Co and an activation γ peak from 99 Mo, visible for a short time after a neutron irradiation of the detectors. For more details we refer to a prior characterization of the backgrounds in this setup by the EDELWEISS Collaboration in [42]. The four labeled γ peaks in the scaled calibration spectrum in Fig. 1 are used for the calibration of each data-set.

We optimize the 0νββ search window for a Poisson counting process in the low background regime. We consider the current exposure of 2.16 kg×yr as a first unblinding of the full data of the now completed CUPID-Mo experiment. For the definition of the signal region of interest (ROI) we hence optimize using the full expected exposure and consider detector and data-set based resolutions and a preliminary background index evaluated from the current data release.

The detector resolutions are extracted from a data-set based, simultaneous unbinned extended maximum likelihood fit of the 208 Tl 2615 keV peak in calibration data.

The fit is performed with individual parameters for the detector resolutions, peak amplitudes and position and with common parameters for the peak-background ratio [46]. Limited by the statistics in physics data we estimate a global scaling factor (common to all data-sets and detectors) that is used to project the individual calibration resolutions to Q ββ . We report the more conservative value of an extrapolation considering the preferred scaling described in [46] as well as the polynomial fit used in [27,28]. This results in a characteristic resolution of (7.6 ± 0.7) keV FWHM at Q ββ for the overall data taking. We note that the estimation of the scaling factor does have some sensitivity to non-Gaussian tails in calibration data, leading to an excess systematic error of 2%.

The accuracy of the energy scale is further investigated based on the mean position of the 352, 583, 609, 1461 and 2615 keV peaks in our physics spectrum (Fig. 1). A 2nd order polynomial fit in reconstructed-to-expected peak position results in an energy bias at Q ββ compatible with zero: E Q ββ bias = (-0.2 ± 0.4) keV. We note that we excluded the prominent peaks from 60 Co, due to a known spatial non-uniformity, and 99 Mo, due to its time dependence.

The background index has been evaluated from the still blinded data with a phenomenological fit model that contains an exponential to approximate both the high energy part of the 2νββ spectrum as well as tails from U/Th contaminants in the setup, and a constant as a conservative estimate for the coincident detection of two 2νββ events in the same crystal, remaining unvetoed muon events and close contamination from the high energy beta decays in the natural U/Th chains. The result of an unbinned extended maximum likelihood fit is strongly dependent on the initial and final fit range. For a fit with the start range varied from 2.65-2.9 MeV and the final fit range from the upper end of the blinded region to 4 MeV we obtain a background index of 2 × 10 -3 counts/(keV×kg×yr) to 6×10 -3 counts/(keV×kg×yr) in a 10 keV window around Q ββ . This background estimate is consistent with the results from a preliminary Geant4-based reconstruction of the γ&β backgrounds, similar to the ones described in [START_REF] Azzolini | CUPID-0)[END_REF][START_REF] Alduino | CUORE-0)[END_REF]53].

Considering the large remaining uncertainty we round the background index for the ROI optimization to b = 5 × 10 -3 counts/(keV×kg×yr). We model the background as locally flat, consider detector and data-set based resolutions, and simulate the 0νββ peak containment in our Geant4 Monte Carlo model. We maximize the mean limit setting sensitivity of a Poisson process

S 90 = ∞ i=0 P (i, b) • S 90 (i)
with the sum running over the product of the Poisson probability P (i, b) of obtaining i background events for a background index b times the expected 90% confidence exclusion limit S 90 (i). We transfer this maximization from the optimization of the energy range for a peak search in 19 (detectors) times 7 (data-sets) to the optimization of a single parameter by splitting the simulated smeared 0νββ peaks into 0.1 keV bins and ranking each bin associated with a triplet (detector, data-set, energy) in Signal-Background (B/S) likelihood space. The optimal cutoff parameter (B/S) cutof f results in a ROI that is on average (exposure weighted) 17.9 keV wide. It has a mean signal containment of 75.8% with a spread of ±1.0%. The ROI width corresponds to an average 2.7 σ Gaussian coverage with the loss of 0νββ decay events in the full energy peak dominated by Bremsstrahlung loss from events close to the surface of the crystals. The optimization exhibits only a mild dependence on the background index or the knowledge of the resolution, with the overall containment changing by ±0.7% for a 50% change in b (2.2 keV wider, 1.5 keV narrower ROI). We truncate the computation of the mean limit setting sensitivity after the first three terms as the probability of 3 or more background events is negligible for the considered ROI.

We used two independent analyses to extract a limit or potential signal on the rate of 0νββ events. We present results from a likelihood analysis of the 100 keV wide blinded analysis region. This analysis has been implemented in the framework of the Bayesian Analysis Toolkit (BAT) [54], but we note that we obtained compatible results from a Poisson counting analysis. In the BAT analysis we consider both the signal region as well as the sidebands in our likelihood function

L = 3 i=1 e λi λ ni i n i ! ,
which is the product over three Poisson terms with observed events n i and expected events λ i . The mean number of expected events λ i is computed considering the phenomenological background model described above and a Gaussian signal contribution in which we leave the strength of the signal and flat background component free by using uninformative flat priors. After defining all analysis steps we unblind and obtain the spectrum in Fig. 2. We observe no event in the signal region and a single event (cyan) in the right-hand side region. The corresponding marginalized posterior distribution for the number of signal events has a most probable value of zero with an upper limit of 2.4 events at 90% C.I., resulting in a half-life limit for 0νββ decay in 100 Mo of T 0ν 1/2 > 1.4 × 10 24 yr (90% C.I.). The posterior for the flat background is non-zero with a 1 σ interval of 3 +7 -3 ×10 -3 counts/(keV×kg×yr) and the posterior distributions for the parameters of the exponential are compatible with priors from a fit of the 2νββ spectrum in the 2650-2980 keV interval. We repeat the same fit for the approximation of a Gaussian signal with a locally flat background over the 100 keV analysis region. The limit on 0νββ decay of 100 Mo is unaffected. Nuisance parameters are summarized in Table I. Uncertainties on the detector response, in particular the energy scale and resolutions, are included in the simulation of 0νββ events. They are hence covered in the resulting containment in the optimized central ROI on a detector and data-set basis and not considered independently. The only remaining uncertainty for the detector response (Index 3) is based on a potential non-gaussianity of the 0νββ peak. In this analysis we estimate this contribution based on the shape of the 2615 keV calibration peak. We observe evidence for non-gaussian tails, which are dominated by unrejected pile-up events caused by the high trigger-rate in calibration data. Given the much lower trigger-rate in physics data we believe that the containment reduction of up to 5%, obtained for pulse shape cuts that are representative of the ones used in physics data, is a very conservative estimate.

The second nuisance parameter on the containment (Index 2) accounts for the Geant4 modeling uncertainty of Bremsstrahlung events. Reported accuracies for the Geant4 Bremsstrahlung production of a few MeV electrons in thick targets [55,56] of ∼10% result in a systematic uncertainty in the containment of 1.5% for our crystal geometry, which we include as a multiplicative factor with a Gaussian prior.

The inclusion of the analysis efficiency = (90.6 ± 0.4 (stat.) +0.8 -0.2 (syst.))% is split into two parts. For the evaluation of the mean value and its statistical uncertainty (Index 4), we make use of the two independent signals in the LDs and LMOs to evaluate cut efficiencies on a clean sample of signal events in the 1.3 MeV to 2 MeV 2νββ spectrum or from the 210 Po peak [46]. Energy independent cuts are evaluated directly from the ratio between passed and total events with binomial uncertainty. The pulse shape analysis efficiency is extracted from a linear fit extrapolated to Q ββ in order to account for the energy dependence in the reconstruction error.

The systematic uncertainty associated with the excess broadening of the light yield cut has been evaluated considering either the applied linear cut and linear energy dependence or a modified statistical behavior with arbitrary a 0 where the width of the light yield band is σ

(E) = σ 2 0 + (a 0 √ E) 2 .
The quantification with a set of pseudo-experiments results in a likely underestimate of the signal acceptance which is reflected in our limit setting as a multiplicative factor with uniform prior in 0.998-1.008 (Index 5). Lastly, we include the subdominant uncertainty in the number of 100 Mo atoms of 0.2% (Index 1). All of these nuisance parameters are considered in the limit of our blind analysis T 0ν 1/2 > 1.4 × 10 24 yr (90% C.I.). We further refined our analysis after unblinding, implementing a cut designed to reject high energy β events from the 212 Bi = 183 s, 5 MeV Q-value). Similar to previous analyses with scintillating bolometers [29,[START_REF] Azzolini | CUPID-0)[END_REF][START_REF] Azzolini | CUPID-0)[END_REF] we tag 212 Bi α candidates with energies in the 6.0-6.3 MeV range, and veto any decay in the same crystal in a 10 half-life period (1832 s). This cut has a negligible impact on the life-time (0.02%) accidentally rejecting 2:10000 events, while being fully efficient in rejecting any tagged true 212 Bi α -→ 208 Tl β -→ 208 Pb event. It rejects the event highlighted in cyan in Fig. 2. The energy of the preceding α candidate is consistent with the Q-value of 212 Bi within 10 keV and the time difference between the events is 113 s. We report a final 0νββ limit that is 1.3% stronger and rounds to T 0ν 1/2 > 1.5 × 10 24 yr (90% C.I.).

The posterior for the flat background of the bayesian fit in this case is peaked at zero with a 90% C.I. of 1.1 × 10 -2 counts/(keV×kg×yr). We interpret the obtained half-life limit in the framework of light Majorana neutrino exchange using g A = 1.27, phase space factors from [57,58] and nuclear matrix element calculations from [59][60][61][62][63][64][65][66]. The resulting limit on the effective Majorana neutrino mass of m ββ <(0.3-0.5) eV is the fourth most stringent limit world wide, obtained with a modest 100 Mo exposure of 1.19 kg×yr. It is the leading constraint for 100 Mo, exceeding the previous best limit from by 30% with almost 30 times lower 100 Mo exposure. The technology of CUPID-Mo has proven that it can be operated reliably, reaches high efficiency for 0νββ search of 68.6% (containment × analysis efficiency) and a resolution of 0.11% (1σ) at Q ββ . Together with a preliminary estimate of the background in the ROI at the few 10 -3 counts/(keV×kg×yr) level, this results in an excellent sensitivity to 0νββ decay for the present and future experiments. Further analyses will be focused on precisely reconstructing remaining backgrounds, comparing to the best reported background index for a cryogenic 0νββ search [START_REF] Azzolini | CUPID-0)[END_REF] and to optimally design and use the technology of the CUPID-Mo experiment in CUPID [START_REF] Armstrong | CUPID Interest Group), CUPID pre-CDR[END_REF].

The help of the technical staff of the Laboratoire Souterrain de Modane and of the other participant laboratories is gratefully acknowledged. This work has been partially performed in the framework of the LUMINEU program, funded by ANR (France). This work was also supported by

FIG. 1 .

 1 FIG. 1. Physics spectrum (blue) for 2.16 kg×yr of data and calibration spectrum (red) scaled to match the 2615 keV counts from 208 Tl. A ± 50 keV region around Q ββ has been blinded (gray). The most prominent γ-peaks in the physics and calibration data are the following: (1) 208 Tl 2615 keV, (2) 40 K 1461 keV, (3) 60 Co 1173 and 1332 keV, (4) 214 Bi 1764, 1120 and 609 keV, (5) 212 Pb 239 keV, (6) 99 Mo 142 keV.

  CEA and IN2P3, by P2IO LabEx with the BSM-Nu project, by Istituto Nazionale di Fisica Nucleare, the Russian Science Foundation (Russia), the National Research Foundation (Ukraine), the US Department of Energy (DOE) Office of Science, the DOE Office of Science, Office of Nuclear Physics, the National Science Foundation (USA), by the France-Berkeley fund, the MISTI-France fund, and by the Chateaubriand Fellowship of the Office for Science & Technology of the Embassy of France in the United States. Individuals have received support from the National Academy of Sciences of Ukraine and P2IO LabEx managed by the ANR (France). This work makes use of the DIANA data analysis software which has been developed by the Cuoricino, CUORE, LUCIFER, and CUPID-0 Collaborations.

TABLE I .

 I Physics spectrum for 2.16 kg×yr of data after unblinding. No event is observed in the detector and dataset based ROI. A single event, highlighted in cyan has been observed in the analysis region. In a further refinement of the analysis it was identified as a β-candidate out of the 212 Bi→ 208 Tl→ 208 Pb part of the natural decay chain (see text). For visualization the exposure weighted mean ROI for 0νββ decay (17.9 keV wide) has been indicated with solid black lines. Nuisance parameters included in the analysis and their implementation with Flat or Gaussian prior in the Bayesian Parameters 2 and 5 are multiplicative scaling factors instead of absolute uncertainties, see text for details.

	Counts / keV		Tl 208	ROI evts 208 Tl evts → Bi 212 Analysis region Mean ROI Sideband evts
	10
	1
	2500	2600	2700	2800	2900	3000	Energy (keV) 3100 3200
	FIG. 2. Systematic			Index	Value		Prior
	Isotopic enrichment		1	0.966 ± 0.002 Gauss
	0νββ containment MC		2	1.000 ± 0.015 Gauss
	0νββ cont. detector response	3	0.95-1.00	Flat
	Analysis efficiency a		4	0.906 ± 0.004 Gauss
	Light yield selection a		5	0.998-1.008	Flat

a Data-set dependent; exposure weighted mean value presented.