Bifunctional Amidophosphonate Molecules for Uranium Extraction in Nitric Media

Keywords: Solvent extraction, bifunctional extractant, uranium extraction, nitric media

Bifunctional amidophosphonate derivatives, already known as efficient ligands in uranium extraction from phosphoric media, have been evaluated and compared to the conventional trin-butyl phosphate (TBP) for uranium extraction from nitric medium. The efficiency of U extraction and its selectivity towards competing elements such as Th, Zr, Mo, Fe and V was evaluated with various ligand structures. It was found that extractant molecules containing a monosaponified phosphonate moiety instead of phosphonate moieties are less effective and selective. Furthermore, it was observed that alkylation of the methylene bridge linking the two functional groups prevent the formation of precipitates during the uranium loading. Effects of acidity as well as ligand concentration were also investigated to estimate the loading capacity of the molecules. More detailed stoichiometry and transfer energy were further determined by the slope analysis method and a thermodynamic study. The possible uranium recovery from the organic phase has finally been demonstrated thanks to stripping steps at low nitric acid concentration.

Introduction

The refining plants of natural uranium concentrates rely on a solvent extraction process to produce uranium at so-called "nuclear" purity. Purification of uranium is obtained from yellow cake thanks to an organic phase containing the well-known extractant molecule tri-n-butyl phosphate (TBP). [START_REF] Kumar | A Brief Review on Solvent Extraction of Uranium from Acidic Solutions[END_REF] This organic phase is further washed to recover pure uranium which is exploited to produce 10% of the annual global electricity consumption. [2] Despite the extensive application of TBP at industrial scale, it is still of research interest to find optimized and highly efficient systems. Higher selectivity towards Zr or Mo, optimized loading capacity, and a minimized extractant loss due to solubilization in aqueous phase are some of the targeted optimizations. Several research groups have proposed alternatives to TBP, [START_REF] Shen | Extraction of U(VI), TH(IV) and some fission-products from nitric-acid medium by sulfoxides and effect of gamma-irradiation on the extraction[END_REF][START_REF] Wang | Extraction of uranium(VI) and thorium(IV) ions from nitric acid solutions by N,N,N',N'-tetrabutyladipicamide[END_REF][START_REF] Han | Solvent extraction of uranium (VI) by N-octanoylpyrrolidine in toluene[END_REF] among them monoamide derivatives [START_REF] Manchanda | Amides and diamides as promising extractants in the back end of the nuclear fuel cycle: an overview[END_REF][START_REF] Mccann | Comparing Branched versus Straight-chained Monoamide Extractants for Actinide Recovery[END_REF][START_REF] Pathak | N-Dialkyl amides as extractants for spent fuel reprocessing: an overview[END_REF][START_REF] Condamines | The Extraction by N.N-Dialkylamides. II. Extraction of Actinide Cations[END_REF] exhibit high potential as well as carbamides which have been studied very recently. [START_REF] Berger | Coordination Structures of Uranium(VI) and Plutonium(IV) in Organic Solutions with Amide Derivatives[END_REF][START_REF] Berger | Extraction of Uranium(VI) and Plutonium(IV) with Tetra-Alkylcarbamides[END_REF] Another approach consists of designing multifunctional molecules, various multi-functional compounds have shown promising properties, for example, iminomethylenediphosphonic acids (phosphorus and nitrogen functions) [START_REF] Ali | Synthesis under Microwave Irradiation, Characterization and Application of Alkyliminodimethylenediphosphonic Acids in Solvent Extraction of Uranium (VI)[END_REF] or amidosulfoxide structures (sulfur and nitrogen functions) [START_REF] Gamare | Extraction Studies of Uranium(VI), Plutonium(IV) and Americium(III) from Nitric Acid Using the Bi-functional Carbamoyl Methyl Sulfoxide Ligands[END_REF] have been proposed for uranium extraction and purification from diluted or concentrated nitric acid solutions. Taking into account the potential of this approach, a new series of N, P bifunctional extractants was patented and showed excellent properties in nitric media in terms of affinity for uranium extraction. [START_REF] Pellet-Rostaing | Use of bifunctional compounds with phosphonic acid / phosphonate and amino functions for extracting uranium (VI) from aqueous nitric acid solutions[END_REF] N,P bifunctional extractants such as carbamoylalkylphosphonates involving an amido and a phosphorus functionality and especially the butyl-1-[N,N-bis(2-ethylhexyl)carbamoyl]nonyl phosphonic acid, called DEHCNPB, have shown unprecedented extraction properties for uranium from phosphoric media. [START_REF] Turgis | Uranium extraction from phosphoric acid using bifunctional amido-phosphonic acid ligands[END_REF][START_REF] Turgis | Carbamoylalkylphosphonates for Dramatic Enhancement of Uranium Extraction from Phosphates Ores[END_REF][START_REF] Turgis | Carbamoylalkylphosphonates type ligand for uranium extraction from phosphates ores[END_REF][START_REF] Miguirditchian | Development of a new solvent extraction process based on butyl-1-N,N-bis(2ethylhexyl)carbamoyl nonyl phosphonic acid for the selective recovery of uranium(VI) from phosphoric acid[END_REF][START_REF] Leydier | Recovery of uranium (VI) from concentrated phosphoric acid using bifunctional reagents[END_REF] So far, DEHCNPB efficiency has never been evaluated for uranium extraction from nitric media, and the patented N, P bifunctional family has not been investigated in the literature for this media. In the present study, two amidophosphonates, are therefore studied and compared to both DEHCNPB and TBP as reference extractants. As illustrated in Figure 1, these two molecules differ by the alkylation of the methylene bridge between the amido and the phosphonate functions:

Materials and methods

Synthesis of amidophosphonate

Amidophosphonates were synthesized as described in references. [START_REF] Turgis | Uranium extraction from phosphoric acid using bifunctional amido-phosphonic acid ligands[END_REF][START_REF] Turgis | Carbamoylalkylphosphonates for Dramatic Enhancement of Uranium Extraction from Phosphates Ores[END_REF] The synthesis is illustrated in Scheme 1.

Scheme 1. Synthesis of amidophosphonate extractant involved in this study

Butyl-1-[N,N-bis(2-ethylhexyl)carbamoyl]nonyl phosphonic acid 3 (DEHCNPB) was synthesized in four steps with an overall yield of 81%.

-Amidation (step A) of N,N-ethylhexylamine with chloroacetyl chloride in the presence of K2CO3 in dichloromethane afforded an amide intermediate.

-Subsequently this intermediate is engaged in an Arbusov reaction (step B) with tributylphoshite to afford, with an overall yield of 90%, the Dibutyl N,N di(2ethylhexyl)carbamoylmethylphosphonate (DEHCMPDB) named extractant 1 in the following.

-C-alkylation of extractant 1 (step C) using 1-iodooctane and sodium hydride in order to introduce an octyl group on the methylene bridge afforded the Dibutyl N,N di(2ethylhexyl)carbamoylnonylphosphonate (DEHCNPDB) with an overall yield of 86% (extractant 2).

-The corresponding amido-monophosphonate (extractant 3) was finally obtained by mono-saponification with an aqueous sodium hydroxide solution (step D).

Extraction experiments

The organic phases were prepared by dissolving each extractant in n-dodecane. Aqueous solutions at desired acidity were obtained using uranyl nitrate, thorium nitrate (Th(NO3)4), iron nitrate (Fe(NO3)3), molybdenum oxide (MoO3), zirconyl nitrate (ZrO2(NO3)2) in their salt form (from Sigma Aldrich), and vanadium from Inductively Coupled Plasma ICP standard from SCP Science (aqueous solution of NH4VO3 1000 µg/mL in HNO3 4%). The desired concentrations were prepared by dilution in ultrapure water (MilliQ, Millipore, 18 MΩ.cm -1 ). Acidities (HNO3 0.1 to 8 M) were adjusted with 69% nitric acid. Solvent extraction experiments were carried out in 2 or 15 mL vials. Organic phases were pre-equilibrated with an aqueous phase at the same acidity as the extraction step without cations in a thermostated shaker (Infor-ht® ecotron) at 25°C and 400 rpm for 30 min. The volume ratio of organic to aqueous phases was O/A=1/3. The concentration of nitric acid was kept constant for the extraction experiments carried out thereafter. The aqueous and organic phases were separated by centrifugation at 19017 rcf for 10 min (Rotina 380R or Eppendorf centrifuge 5417R).

The pre-equilibrated organic phases were then contacted with an equal volume of aqueous acidic stock solution of cations (O/A = 1) in a thermostated shaker at 25°C and 400 rpm for 1 h, (this time is sufficient to reach thermodynamic equilibrium). [START_REF] Pellet-Rostaing | Use of bifunctional compounds with phosphonic acid / phosphonate and amino functions for extracting uranium (VI) from aqueous nitric acid solutions[END_REF] Phases were separated after centrifugation at 19017 rcf for 10 minutes. The acid concentration in the aqueous and organic phases before and after extraction was analyzed by titration with NaOH 0.1M or 0.01M (Fluka analytical) using a Metrohm 809 Titrando.

The concentrations of metals in aqueous phase were measured by inductively coupled plasma/atomic emission spectroscopy (ICP/OES Spectro Arcos -AMETEK Materials Analysis). The ICP calibration samples were prepared from 1000 ±4 mg/L uranium, thorium, iron, molybdenum, zirconium and vanadium standard solution (SCP Science PlasmaCal).

Uncertainties relating to the metal concentration were determined by repeated measurement of different samples of the same concentration. These uncertainties were estimated to be of the order of ±5%.

As commonly defined in liquid-liquid extraction, the distribution coefficient DM of an element M corresponds to the ratio between the concentrations of this element in the organic and aqueous phases at equilibrium. The metal concentration in the organic phase, [M]org, was estimated by the difference between the initial concentration in the aqueous phase, [M]aq,ini, and the concentration at equilibrium,[M]aq,eq, such as the following relation for a volume ratio of organic to aqueous phases O/A=1:

DM = [Morg]/[Maq] = ([M]aq,ini]-[M]aq,eq)/[M]aq,eq (1)
Additionally, the separation factor for a specific metal towards another metal is defined by the ratio of the distribution coefficient such as:

SFM1/M2 = DM1/DM2 (2)
The concentrations of the elements in the organic phase were also confirmed after a backextraction step. The previous organic phase loaded with cations was contacted with a stripping aqueous solution typically a HNO3 0.05 M acidic solution. When the back-extraction is total, the concentration of the element in the aqueous phase is equal to the concentration in the initial loaded organic phase. The efficiency of the back-extraction was estimated thanks to ICP/AES.

The amount of organic phase transferred in the aqueous phase was determined by measuring the Total Organic Content (TOC) using a Shimadzu TOCVCSH analyser based on a 680°C combustion catalytic oxidation/NDIR method.

Results and discussion

Extraction studies

Separation factors

The efficiency of amidophosphonate 1, 2 and 3 to selectively extract uranium from an aqueous phase containing competitive metals was compared to TBP. The extraction profile of the extractants was established for U(VI), Fe(III), Mo(VI), V(III), Zr(IV) and Th(IV), which are metals potentially present in uranium refining solutions.

Extraction experiments were carried out by contacting an equal volume (Vorg = Vaq) of a 4 M nitric acid aqueous phase consisting of a 1 mM of each cation (U(VI), Fe(III), Mo(VI), V(III), Zr(IV) and Th(IV)) with an organic phase containing 0.2 M of extractants in dodecane. The results are summarized in Table 1 for the distribution coefficients and in Figure 2 for the separation factors for the extraction of U(VI).

U]=[Th]=[Zr]=[Mo]=[V]=[Fe]=1 mM, [HNO3]=4 M. U/Th U/Zr U/V U/Mo U/Fe
[U]=[Th]=[Zr]=[Mo]=[V]=[Fe]=1mM, [HNO3]=4 M -separation factors
As shown in Table 1 and Figure 2, extractant 3 exhibits the highest distribution coefficients for all the elements, leading to poor separation factors for U towards Th, Zr and Mo. However, when the unsaponified amidophosphonates 1 and 2 are used, the extraction of competitive metals is much lower and comparable to those achieved with TBP, while the distribution coefficient for uranium is much higher (DU >16 for amidophosphonate compared to 5.24 for TBP).

These results show that the unsaponified amidophosphonates 1 and 2 display interesting features for the specific extraction of uranium (VI). At the same time, extractant 3 shows low separation factors and high distribution coefficients (which suggests potential issues for back extraction), indicating that it cannot be considered for a uranium refining process in nitric media.

Subsequently, the extraction capacities and the parameters of the extraction processes of the two amidophosphonates 1 and 2 have been compared to TBP. The influence of the alkyl chain grafted on the methylene bridge has been studied with regards to the solubility in the aqueous phase and the uranium loading capacity.

Extractant solubility in the aqueous phase

Solubility of extractants 1 and 2 in aqueous phase was evaluated by contacting an organic phase containing 0.5 M of the extractant in dodecane, with an aqueous phase of 4 M nitric acid with A/O = 3. After centrifugation, the organic and aqueous phases were separated and the Total Organic Carbon concentration (TOC) of the aqueous phase was measured by COT meter. Table 2 shows the mass percentages of carbon solubilized in the aqueous phase obtained from total organic carbon concentration analysis. The solubility of each extractant was determined by taking into account the volume ratio involved, the concentration and molar mass of the extractant and by considering that dodecane solubility is negligible. [START_REF] Velavendan | Studies on solubility of TBP in aqueous solutions of fuel reprocessing[END_REF] As expected, due to the presence of a lipophilic alkyl chain on the methylene bridge it appears that the mass loss of extractant 2 is lower than for extractant 1. This difference in solubility is coherent with higher lipophilicity due to the alkylation of the molecule, log P = 11 vs. 7.63, respectively, for extractants 2 and 1 (log P estimated from ACDlab2015 -Percepta software).

In comparison to data obtained from literature [START_REF] Velavendan | Studies on solubility of TBP in aqueous solutions of fuel reprocessing[END_REF] , extractants 1 and 2 have lower solubility than TBP, with an interesting result for extractant 2 .

It should be noticed that the carbon concentration measured in the aqueous phase may come from degradation products of the extractants as well as from impurities. However, the analyses after pre-equilibration and/or successive contact suggests that the carbon concentration probably does not come from impurities. A degradation study of the molecules 1 and 2 as well as of the solubility of the possible degradation products should be performed in the future.

Influence of uranium (VI) loading on uranium extraction

The uranium (VI) loading capacity of the extractants was investigated by extraction experiments carried out contacting the organic phases (0.2 M of extractant 1, 2 or TBP in dodecane) with increasing concentrations of uranium from 10 to 300 mM in 4 M nitric acid.

[U] aq,init (mM) The loading capacity of extractant 1 in dodecane reached 52 mM when the aqueous phase used had a concentration of 100 mM in uranium and decreased for higher concentration because of the formation of precipitates. This result demonstrates the importance of the alkyl chain in order to prevent the apparition of precipitates.

As plotted in Figure 3 up to 90 mM (> 21 g/L) of uranium(VI) can be loaded into the organic phase when the extractant 2 is used. At its maximum loading capacity with 0.2M of extractant 2 in dodecane, neither third-phase nor precipitate formation were observed. From these results, an extractant/U molar ratio of about two is estimated at saturation in these conditions, which suggests that two molecules of extractant 2 are necessary to extract uranium(VI) into the organic phase at saturation. This result was correlated by applying the slope analysis method which enables determining complementary information regarding the number of extractant molecules in the extracted complex.

Therefore, extractant 2 allows a higher loading capacity than TBP (70 mM in the same conditions). This measured value is also consistent with the relationship experimentally found by B. Narasimha Murty et al. with TBP diluted in kerosene [START_REF] Murty | Determination of percentage saturation of uranium in TBP samples from uranium extraction plant[END_REF] :

Y = 3.9753 X + 0.10143 (3)
where Y represents the concentration of uranium saturation in g/L and X the volume percentage of TBP in the organic phase. From this equation and considering our operating conditions, a uranium saturation concentration of 77 mM in the organic phase can be assumed.

Thermodynamic studies

Slopes analysis

To analyze the effect of the concentration on the extraction efficiency, a range of extractant concentrations was engaged in the same extraction conditions. The concentration in extractant 1, 2 or TBP was varied from 0.025 to 0.2 M. The organic phase was subsequently contacted with an aqueous phase containing 1 mM of U(VI) in 4 M nitric acid media. The logarithm of the distribution coefficient of uranium is plotted as a function of the logarithm of free extractant concentration in Figure 4. Considering a solvation mechanism of extraction with TBP, 1 and 2, uranium extraction can be described by the following equation:

𝑈𝑂 2 2+ + 2𝑁𝑂 3 -+ 𝑥𝐿 ̅ ↔ 𝑈𝑂 2 (𝑁𝑂 3 ) 2 𝐿 𝑥 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ (4)
where x represents the number of extractants required for the transfer of one uranyl from the aqueous phase to the organic phase. The overbar refers to species in the organic phase, and the absence of the overbar denotes aqueous species.

𝐾 𝑒𝑥 = [𝑈𝑂 2 (𝑁𝑂 3 ) 2 𝐿 𝑥 ] ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ [𝑁𝑂 3 -] 2 . [𝑈𝑂 2 2+ ]. [𝐿 ̅ ] 𝑥 . 𝛾̅ 𝑈𝑂 2 (𝑁𝑂 3 ) 2 𝐿 𝑥 𝛾̅ 𝐿 𝑥 . 𝛾 𝑈𝑂 2 2+ . 𝛾 𝑁𝑂 3 - 2 (5)
If the ratio of activity coefficients is considered constant (which is acceptable in such diluted solutions and with a constant nitric acid concentration), the following equation can be established:

[𝐿 ̅ ] 𝑓𝑟𝑒𝑒 𝑥 = 𝐷 𝑈 . 1 𝐾 𝑒𝑥 . [𝑁𝑂 3 -] 2 (6)
Considering a constant nitrate concentration, log-log plots of distribution ratios vs. total concentration of the extractant indicate the number of free extractants in the extracted complex (Figure 4).

𝑙𝑜𝑔(𝐷 𝑈 ) = 𝑥 𝑙𝑜𝑔([𝐿 ̅ ] 𝑓𝑟𝑒𝑒 ) + 𝑙𝑜𝑔(𝐾 𝑒𝑥 ) + 2𝑙𝑜𝑔([𝑁𝑂 3 -]) (7)
The [𝐿 ̅ ] 𝑓𝑟𝑒𝑒 can be calculated from the ligand concentration after subtracting the part of extractant complexed with uranium and the part of ligand complexed with nitric acid:

[𝐿 ̅ ] 𝑓𝑟𝑒𝑒 = [𝐿 ̅ ] 𝑖𝑛𝑖 -𝑥. [𝑈] 𝑜𝑟𝑔𝑎 -[𝐻𝑁𝑂 3 ] 𝑜𝑟𝑔𝑎 (8)
Acid titration demonstrated that very little nitric acid was extracted into the organic phase, therefore the free ligand concentration was obtained from the following equation:

[𝐿 ̅ ] 𝑓𝑟𝑒𝑒 = [𝐿 ̅ ] 𝑖𝑛𝑖 -𝑥. [𝑈] 𝑜𝑟𝑔𝑎 (9)
Concentrations of free extractants were calculated by iteration considering x values from 1 to 5 with the assumption that the fraction of extractants protonated or associated with nitric acid can be neglected.

The plot of the logarithm of distribution ratio is linear with the logarithm of the concentration of extractant with a slope between 1.5 and 1.75. It suggests that uranium is similarly extracted by the three molecules investigated. The stoichiometry of complexation between the extractant and uranium is expected to be 2:1. For extractant 2, this result is consistent with the molar ratio obtained at saturation. Also, these values are similar to those that can be encountered in the literature for this type of bifunctional molecule in the context of the extraction of uranium from phosphoric acid. [START_REF] Pecheur | Uranium Extraction by a Bifunctional Amido-Phosphonic Acid: Coordination Structure and Aggregation[END_REF] The value found for TBP is also in agreement with that reported by Stas and coworkers. [START_REF] Stas | Extraction of uranium (VI) from nitric acid and nitrate solutions by tributylphosphate/kerosene[END_REF]

Temperature dependency of uranium extraction

Uranium distribution ratio was determined for various temperatures from 25 to 55°C at 4 M of nitric acid containing 1 mM of U(VI) and with 0.2 M of extractant in dodecane. The results point out the exothermic nature of the extraction process with a decreasing D-value with increasing temperature for each extractant. Uranium extraction was measured for various temperatures to estimate different thermodynamic parameters, which can provide trends regarding the complexation of U with the various extractants.

If we consider the direct proportionality between DU and Kex, van't Hoff's law enables calculation of the different free enthalpies related to the extraction of uranium.

𝐿𝑛𝐾 𝑒𝑥 = - Δ𝐻 𝑒𝑥𝑡 0 𝑅 . 1 𝑇 + Δ𝑆 𝑒𝑥𝑡 0 𝑅 (10)
The logarithm plot of the distribution coefficient vs. the inverse of the absolute temperature (Figure 5) produces a straight line function, from which enthalpy can be calculated with the slope of the linear regression plot. The value of the thermodynamic parameters (ΔH, ΔS, and ΔG) are provided in the Table 3. Negative values of free enthalpies indicate that each compound reacts spontaneously to extract uranium through an exothermic reaction. Also, the Gibbs free energy values (-ΔG) for the extractants follow the order: -ΔG(1) ≥ -ΔG(2) > -ΔG(TBP), which suggests that uranium extraction is thermodynamically more favorable for the amidophosphonates than for TBP.

Furthermore, the similar values obtained for the amidophosphonates 1 and 2 show that the complexes formed with the two bifunctional extractants have a similar stability.

Stripping of uranium

Influence of the nitric acid concentration in the aqueous phase

The effect of nitric acid concentration on the uranium extraction was investigated for all three extractants. Extractions were carried out using organic phases containing 0.2 M of extractants and with aqueous phases containing 5 mM of uranium(VI) at nitric acid concentrations ranging from 0.1 to 8 M.

Figure 6 shows uranium distribution ratio as a function of nitric acid concentration. For the three extractants tested, distribution values increase sharply with low nitric acid concentrations and reach a saturation plateau. No difference is observed between extractants 1 and 2, and both amido-phosphonates exhibit higher distribution ratios than TBP over the whole range of nitric acid tested. Figure 6 also shows a clear correlation between nitric acid concentration and extraction efficiency, which is in accordance with a solvating mechanism during the extraction.

At low acidity the distribution coefficient of uranium is lower than one, suggesting a possible efficient back-extraction with a decrease of concentration in nitric acid.

Uranium back-extraction by nitric acid

Given the low extraction performance of the compounds at low nitric acid concentration, the possibility of carrying out the back-extraction step was investigated for the purpose of quantitatively stripping uranium from the organic phases. After the extraction step (0.2 M of extractant in dodecane was contacted with 4 M nitric acid solution containing 5 mM of uranium) the loaded organic solution was then engaged in the back-extraction step which was performed by three successive contacts of the organic phase with 0.05 M HNO3. Uranium stripping appears less efficient with extractant 1 and 2 than with TBP, suggesting that the uranium complexes in the organic phase may be more stable with the amidophosphonates than with TBP. This behavior is coherent with the thermodynamic study described earlier. It was shown for extractant 1 and 2 that the octyl chain on the methylene bridge between the functions implies a decrease of the extractant solubility in the aqueous phase and a significant increase of uranium loading capacity. This alkylation also prevents the appearance of the third phase and precipitate formation at high uranium concentration. In comparison to TBP, it was also found that the bifunctional extractant 2 improves uranium loading capacity by a factor of ca 1.3 and presents a slightly lower solubility in the aqueous phase.

As for TBP, uranium extraction is favored for high nitric acid concentrations, which suggests also that a back extraction at low acidity would be possible. This was confirmed in this study that up to 80% of uranium can be back extracted after 3 contacts of an organic phase (loaded with 5 mM of uranium) with an aqueous phase of 0.05 M nitric acid. The stoichiometry of the extracted complex has been determined by the slope method. As for TBP, two bifunctional molecules are necessary to extract one uranyl. The free energy (ΔG), enthalpy (ΔH) and entropy Additional experiments, in particular on real solutions, would be useful to validate such promising ligand for uranium extraction at the front end of the nuclear fuel cycle.

Complementary experiments such as a study on the degradation of the extractant, on the impact of degradation products on the extraction performance, the development of a process diagram and a study on a semi-industrial scale, would however be necessary before proposing amidophosphonate 2 as an alternative to TBP for the industrial process.

List of Figures

[U] aq,init (mM)

List of Schemes

Scheme 1. Synthesis of amidophosphonate extractant involved in this study *data for TBP extrapolated from literature [START_REF] Velavendan | Studies on solubility of TBP in aqueous solutions of fuel reprocessing[END_REF]

List of Tables

Figure 1 .

 1 Figure 1. Structure of extractants TBP, DEHCMPDB (1), DEHCNPDB (2), and DEHCNPB (3) involved in this study.

Figure 2 .

 2 Figure 2. Extraction result for compounds 1, 2, 3 and TBP diluted at 0.2 M in dodecane -Aqueous phase:

Figure 3 .

 3 Figure 3. Loading uranium extraction isotherm-Aqueous phase: [U] = 10 mM to 300 mM, [HNO3] = 4 M; Organic phase: 1, 2 or TBP extractant at 0.2M in dodecane; (Vorg = Vaq).

Figure 4 .

 4 Figure 4. Slopes analysis of uranium extraction as a function of free ligand concentration Logarithm of the distribution ratio of uranium (VI) as a function of free extractant [L]free: log DU = f(log[1]): y = 1.505(±0.026)x + 2.432(±0.033), R 2 = 0.999 log DU = f(log[2]): y = 1.736(±0.063)x + 2.667(±0.096), R 2 = 0.995 log DU = f(log[TBP]): y = 1.726(±0.036)x + 1.947(±0.041), R 2 = 0.998 Aqueous phase: [U] = 1 mM, [HNO3] = 4 M; Organic phase: 1, 2 or TBP extractant from 0.025 to 0.2 M in dodecane; (Vorg = Vaq), 25°C.

Figure 5 .

 5 Figure 5. Influence of the temperature on uranium extraction (25 -55 °C). Logarithm of the distribution ratio DU as a function of the reverse of the temperature T: log Kex(1) = f (1/T): y = 1364(±202) x + 2.400(±0.647); R 2 = 0.958 log Kex(2) = f (1/T): y = 1594(±161) x + 1.635(±0.514); R 2 = 0.980 log Kex(TBP) = f (1/T): y = 714(±53) x + 3.898(±0.170); R 2 = 0.989 Aqueous phase: [U] = 1 mM, [HNO3] = 4 M; Organic phase: 1, 2 or TBP extractant at 0.2 M in dodecane; (Vorg = Vaq).

Figure 6 . 1 M to 8 M

 618 Figure 6. Uranium distribution coefficient versus the initial acidity in aqueous phaseaqueous phase: [U] = 5 mM with 0.1 M to 8 M of nitric acid; organic phase 1, 2 or TBP extractant at 0.2 M in dodecane.

Figure 7

 7 shows the uranium concentration in organic phase as a function of the number of nitric acid backextractions. The results highlight that the uranium concentrations in organic phases gradually decrease after the different back-extraction steps from uranium concentration of 5 mM to less than 2 mM. Back-extraction of uranium appears possible with a simple [HNO3] decrease, however at least two back-extraction contacts are required.

Figure 7 .

 7 Figure 7. Back-extraction of uranium -aqueous phases: [HNO3]=0.05M O/A=1 ; organic phase: 1, 2 or TBP extractant at 0.2 M in dodecane loaded with [U]=5 mM.

(

  ΔS) were estimated showing an exothermic and spontaneous reaction for the extraction process. Extractions at different temperatures showed that the bifunctional molecules form slightly more stable complexes, which is consistent with the easier stripping of uranium in TBP.All these results demonstrate the potential use of the alkylated amidophosphonate 2 for the selective extraction of uranium from nitric acid solution. This extractant molecule has interesting extraction properties. Indeed, it extracts more uranium than TBP, induces a very low extractant loss due to its solubility in the aqueous phase, provokes no third-phase nor precipitate problems and allows a possible back-extraction of uranium by [HNO3] decrease.

Figure 9 .

 9 Figure 8. Structure of extractants TBP, DEHCMPDB (1), DEHCNPDB (2), and DEHCNPB (3) involved in this study.

Figure 10 .

 10 Figure 10. Loading uranium extraction isotherm-Aqueous phase: [U] = 10 mM to 300 mM, [HNO3] = 4 M; Organic phase: 1, 2 or TBP extractant at 0.2M in dodecane; (Vorg = Vaq).

Figure 11 .Figure 12 .

 1112 Figure 11. Slopes analysis of uranium extraction as a function of free ligand concentration Logarithm of the distribution ratio of uranium (VI) as a function of free extractant [L]free: log DU =f(log[1]): y = 1.505(±0.026)x + 2.432(±0.033), R 2 = 0.999 log DU =f(log[2]): y = 1.736(±0.063)x + 2.667(±0.096), R 2 = 0.995 log DU =f(log[TBP]): y = 1.726(±0.036)x + 1.947(±0.041), R 2 = 0.998 Aqueous phase: [U]= 1mM, [HNO3]=4 M; Organic phase: 1, 2 or TBP extractant from 0.025 to 0.2M in dodecane; (Vorg = Vaq), 25°C.

Figure 13 . 1 M to 8 MFigure 14 .

 131814 Figure 13. Uranium distribution coefficient versus the initial acidity in aqueous phaseaqueous phase: [U]=5 mM with 0.1 M to 8 M of nitric acid; organic phase 1, 2 or TBP extractant at 0.2 M in dodecane.

Table 5 .Extractant 1

 51 Aqueous phase: [U]=[Th]=[Zr]=[Mo]=[V]=[Fe]=1 mM, [HNO3]=4 M.Solubility of the extractant molecules in the aqueous phase (0.5 M in dodecane) 0.141 ± 0.007 0.27 0.45 ± 0.01 Extractant 2 (0.5 M in dodecane) 0.044 ± 0.002 0.065 0.11 ± 0.01

Table 1 .

 1 Distribution

			extractant
		1	2	3	TBP
	D U	22	16	238	5.2
	D Th	9.4	0.35	492	0.13
	D Zr	2.5	0.08	162	>0.01
	D V	0.01	0.01	0.16	>0.01
	D Mo	1.2	1	30	0.95
	D Fe	0.01	0.01	0.58	>0.01
		Aqueous phase: [

coefficients for 1, 2, 3 and TBP compound diluted at 0.2 M in dodecane

Table 2 .

 2 Solubility of the extractant molecules in the aqueous phase

	Extractant	[C]aq (g/L)	Mass loss (%)	[L]aq (mM)
	TBP (0.5 M in dodecane)*			0.6*
	Extractant 1 (0.5 M in dodecane)	0.141 ± 0.007	0.27	0.45 ± 0.01
	Extractant 2 (0.5 M in dodecane)	0.044 ± 0.002	0.065	0.11 ± 0.01

*data for TBP extrapolated from literature

Table 3 .

 3 Thermodynamic parameters (ΔH, ΔS, and ΔG) for the extraction of uranium with 1, 2 and TBP

			extractants
		H (kJ/mol)	S (J/mol/K)		G (kJ/mol)
				313 K	323 K	333 K
	1	-11.34 ± 1.68	19.95 ± 5.38	-17.59 ± 3.36	-17.79 ± 3.42	-17.98 ± 3.47
	2	-13.25 ± 1.34	13.59 ± 4.27	-17.51 ± 2.68	-17.64 ± 2.72	-17.78 ± 2.76
	TBP	-5.94 ± 0.44	32.41 ± 1.41	-16.08 ± 0.88	-16.40 ± 0.90	-16.73 ± 0.91

Aqueous phase: [U] = 1 mM, [HNO3] = 4 M; Organic phase: 1, 2 or TBP extractant at 0.2 M in dodecane; (Vorg = Vaq).

Table 4 .

 4 Distribution coefficients for 1, 2, 3 and TBP compound diluted at 0.2 M in dodecane

			extractant
		1	2	3	TBP
	D U	22	16	238	5.2
	D Th	9.4	0.35	492	0.13
	D Zr	2.5	0.08	162	>0.01
	D V	0.01	0.01	0.16	>0.01
	D Mo	1.2	1	30	0.95
	D Fe	0.01	0.01	0.58	>0.01

Acknowledgement

This research was supported financially by CEA. We thank Beatrice Baus Lagarde, Fabrice Giusti and Bruno Corso for the help in ICP, synthesis and SAXS experiments.


A L Serra

T Vogel

G Lefevre

S Petzold
email: stefan.petzold@tu-darmstadt.de

N Kaiser
email: nico.kaiser@tu-darmstadt.de

G Bourgeois

M C Cyrille

L Alff

C Trautmann
email: c.trautmann@gsi.de

C Vallée

D Sylvain

C Charpin-Nicolle

G Navarro

E Nowak

Heavy Ions Radiation Effects on 4kb Phase-Change Memory

Keywords: Radiation hardness, radiation effects, phase-change memory, PCM, Ge2Sb2Te5, Ge-rich GeSbTe, interfacial layer PCM

In this work we analyze, thanks to both material and 4kb memory arrays characterization, the different effects of heavy ion radiation at high fluences on Ge2Sb2Te5 and Ge-rich GeSbTe based Phase-Change Memory (PCM).

I. INTRODUCTION

HASE-Change Memory (PCM) is considered today the most mature and promising resistive memory technology, as demonstrated by recent commercialization for Storage Class Memory market, because of its scalability and proven reliability [START_REF] Cheng | 3D cross-point phase-change memory for storageclass memory[END_REF]. Its functionality is based on the reversible transition of a chalcogenide material that can be switched theoretically infinite times between the amorphous and the crystalline phase. The crystalline phase is ordered and low resistive, whereas the amorphous phase is disordered and highly resistive. The temperature at which the transition takes place, called crystallization temperature (T C ), can be tuned by engineering the material composition [START_REF] Navarro | Phase-Change Memory:Performance, Roles and Challenges[END_REF]. This enables the improvement of the PCM thermal stability, in particular targeting automotive application which requires strict reliability specifications at high temperature [START_REF] Arnaud | Truly Innovative 28nm FDSOI Technology for Automotive Micro-Controller Applications embedding 16MB Phase Change Memory[END_REF]. In a PCM device, the programming is achieved thanks to the voltage (i.e. current) induced Joule heating of the phase-change material that enables the phase transition. Dependently on the programming electrical pulse parameters (i.e. intensity, duration etc.), the phase-change material can be melt-quenched in the amorphous phase (RESET state), or gradually recrystallized (SET state). The most common used phase-change material is Ge 2 Sb 2 Te 5 (GST), featuring a fast phase transition and a high resistance The work leading to this publication has received funding within the ECSEL Joint Undertaking project WAKeMeUP in collaboration with the European Union's H2020 Framework Program (H2020/2014-2020) and National Authorities, under grant agreement number 783176. Funding by the Federal Ministry of Education and Research (BMBF) under contract 16ESE0298 and by the DFG grant AL 560/21-1 is gratefully acknowledged. The irradiation experiments for this publication were performed at the UNILAC X0 beam line at the GSI Helmholtz Center for Heavy Ion Research, Darmstadt (Germany), based on a UMAT experiment in the frame of FAIR Phase-0. window (i.e. ratio between the amorphous and the crystalline resistivity). However, GST has a T C of ~ 150 °C, not compatible with automotive requirements. Recent material engineering leaded to the development of a Ge-rich GeSbTe (GGST) alloy capable of high temperature amorphous stability, that made PCM suitable also for automotive applications [START_REF] Zuliani | Engineering of chalcogenide materials for embedded applications[END_REF]. Since the discovery of phase-change materials and PCM [START_REF] Ovshinsky | Radiation Hardness of Ovonic Devices, Energy Conversion Devices[END_REF], being the storage mechanism not based on charge storage (like in flash memory technology), a high radiation tolerance was foreseen. Indeed, the first studies on the radiation tolerance of PCM arrays demonstrated the PCM device radiation hardness to different kind of ion beams, highlighting that degradation is mainly given by the impact on the CMOS selector device, due to charges trapped in the gate [START_REF] Wrachien | Total Ionizing Dose Effects on 4 Mbit Phase Change Arrays[END_REF] [7] [START_REF] Gerardin | Present and Future Non-Volatile Memories for Space[END_REF]. Nevertheless, further studies described some possible degradation mechanisms due to radiation that could impact the PCM depending on its device structure, in particular in highly scaled devices [START_REF] Gerardin | Single Event Effects in 90-nm Phase Change Memories[END_REF] [START_REF] Gerardin | Upsets in Phase Change Memories Due to High-LET Heavy Ions Impinging at an Angle[END_REF]. The aim of this work is to investigate the heavy-ion radiation effects in state-of-the-art "Wall-based" PCM devices [START_REF] Serra | Outstanding Improvement in 4Kb Phase-Change Memory of Programming and Retention Performances by Enhanced Thermal Confinement[END_REF] comparing standard GST with GGST. Firstly, morphological evolution of both amorphous and crystalline phases of the chalcogenide material under heavy ion irradiation at different fluences are analyzed by X-ray diffraction (XRD) and TEM/EDX analyses. Then, SET and RESET states evolution under different irradiation fluences in 4kb arrays is presented demonstrating a higher radiation tolerance of GGST wrt GST. Finally, a standard PCM stack is compared with an innovative interfacial layer PCM stack (IL-PCM) [START_REF] Navarro | Innovative PCM+OTS Device with High Sub-Threshold Non-Linearity for Non-Switching Reading Operations and Higher Endurance Performance[END_REF], showing the higher radiation tolerance of IL-PCM, likely due to its nm-scale active region.

II. RADIATION EFFECTS ON GESBTE ALLOYS STRUCTURE

The evolution of amorphous (as-deposited) and crystalline (obtained by annealing at 450 °C for 15 min) structures of phase-change layers under ion beam irradiation was investigated by XRD and TEM/EDX analyses. The 100 nm thick films were deposited on Si substrate and protected from air exposure by a 10 nm SiN encapsulation layer. The samples were irradiated with Au ions with an energy of 1.635 GeV at different fluences (from 10 9 up to 10 13 ions/cm 2 ) with a constant flux of 3  10 8 ions/(cm 2 s). Heavy-ion irradiation experiments were performed at the beam facility of GSI Darmstadt (Germany).

A. Amorphous layers analysis

The evolution of the GST and GGST structures with increasing beam fluence is reported in Fig. 1. The analysis shows a crystallization of GST toward a cubic phase between 5  10 10 and 10 12 ions/cm 2 (Fig. 1 (a)). The crystallization Fig. 3 XRD patterns of GST (a) and GGST (b) crystalline layers (after annealing at 450 °C 15min) before (REF) and after irradiations at increasing fluence (reported in the spectra in ions/cm 2 ). XRD peaks corresponding to the GST hexagonal phase (h,GST) are highlighted in (a) and GST cubic (c,GST) and Ge cubic (c,Ge) phase in (b). triggered at high fluences is confirmed by TEM and nano-diffraction patterns analyses reported in Fig. 2, revealing the growth of large crystals in the system, compatibly with the sharpness of the XRD peaks detected. We think that two main mechanisms are competing in the material structure under ions irradiation: i) the breaking of crystalline bonds; ii) a localized temperature increase that could induce nucleation and growth phenomena (if the temperature reached is higher than the T C ). XRD results for GST seems to confirm that the second mechanism is predominant at the investigated fluences. In GGST, on the contrary, the amorphous phase is preserved even at high fluences, confirming the higher thermal stability of the material. 3 shows the XRD patterns of GST and GGST layers annealed at 450 °C. The annealing brings the GST in the hexagonal phase (h) that is preserved (Fig. 3 (a)) up to high fluences. However, at 5×10 12 ions/cm 2 we observe a broadening and shift of the hexagonal peaks, confirming the competition between bonds breaking and recreation. In GGST (Fig. 3 (b)), from 10 12 ions/cm 2 , we observe a gradual vanishing of the Ge and GST cubic peaks present after the annealing (known to induce phase separation in GGST).

TEM/EDX analysis (Fig. 4) performed on the irradiated samples confirms the preservation of the segregated morphology of GGST even after irradiation. However, almost no crystalline patterns are detected. By pushing nano-diffraction patterns analysis at its limit, we can highlight few and low signal nm-scale features, confirming a residual polycrystalline nature of both Ge and GeSbTe phases, extremely impacted by irradiation at high fluences. The preserved short range order in the layer, can be the origin of the XRD feature observed between 25° and 35°, present also in several chalcogenide amorphous layers. The impact of irradiation on GGST crystalline samples, can be interpreted as a confirmation of the higher bonds breaking rate wrt nucleation and growth rates in this layer, being the crystallization slower in GGST wrt standard GST (i.e. at the origin of GGST higher thermal stability).

III. RADIATION EFFECTS ON 4KB PCM

We studied the radiation effects on state-of-the-art wall-based PCM devices [START_REF] Serra | Outstanding Improvement in 4Kb Phase-Change Memory of Programming and Retention Performances by Enhanced Thermal Confinement[END_REF] embedded in the Back-End-Of-the-Line (BEOL) fabrication of 4kb arrays integrated in LETI Memory Advanced Demonstrator (MAD) based on 130 nm CMOS technology. The behavior of both GST and GGST-based PCM are investigated and compared before and after irradiations at different fluences. Moreover, the standard GST stack is compared in terms of radiation tolerance with an innovative IL-PCM [START_REF] Navarro | Innovative PCM+OTS Device with High Sub-Threshold Non-Linearity for Non-Switching Reading Operations and Higher Endurance Performance[END_REF]. PCM arrays programmed in both SET and RESET state are read after irradiation experiments at fluences of 10 9 , 5  10 10 and 10 12 ions/cm 2 , with same experimental conditions described in previous chapter. All the arrays irradiated at 10 12 ions/cm 2 showed the impossibility to access to the PCM cells after the experiment, due to the strong impact of heavy ions on the addressing circuitry. It is important to note that in this work the use of high fluences in a short time induces a higher damage of CMOS devices and external circuitry wrt a harsh radiation environment situation where the fluence is generally smaller [START_REF] Gasperin | Analysis of Proton and Heavy-Ion Irradiation Effects on Phase Change Memories With MOSFET and BJT Selectors[END_REF]. All the data are then reported for the two lower fluences used.

A. GST vs GGST

The median and ±σ for the SET and RESET distributions measured in GST and GGST arrays are reported in Fig. 5 and Fig. 6. The analysis is performed on devices with an electrode GST SET area of 10 -3 µm 2 . The SET state in GST faces a structural relaxation at a fluence of 10 9 ions/cm 2 , highlighted by the increase of the resistance, whereas it shows a reduction (i.e. recrystallization) at a resistance comparable with the initial one at 5  10 10 ions/cm 2 . This is in agreement with the incoming crystallization observed in the material analysis at high fluences. The loss of the programmed state is more evident in the GST RESET resistance value that decreases with increasing fluence, due to the incoming crystallization of the amorphous phase. On the contrary, both SET and RESET states in GGST show only structural relaxation (known to be higher wrt GST) at both fluences. The higher thermal stability of GGST hinders the crystallization phenomena and the loss of information even at a fluence of 5×10 10 ions/cm 2 . Indeed, both the resistance window and the amorphous phase in the RESET state result to be preserved.

B. GST vs IL-PCM

Finally, we compared the radiation tolerance of a standard GST stack with an innovative IL-PCM stack integrated in wall devices featuring an electrode area of 3  10 -3 µm 2 . The advantageous lower programming current in IL-PCM is highlighted in Fig. 7, achieved thanks to the intrinsic active volume reduction in this structure. IL-PCM shows a higher radiation tolerance wrt GST (Fig. 8). Indeed, while the SET state remains stable in both stacks at all fluences, the RESET state shows a complete recrystallization at 5  10 10 ions/cm 2 with the loss of the resistance window in standard GST stack. IL-PCM on the contrary preserves a good resistance window even at the highest fluence. Indeed, a higher thermal stability is expected in reduced amorphous chalcogenide volumes, due to a reduced nucleation rate. Moreover, the reduced electrode effective surface of an IL-PCM, makes the device less sensible to local heating phenomena that could be induced by ion interactions with the electrode/phase-change material interface [START_REF] Gerardin | Upsets in Phase Change Memories Due to High-LET Heavy Ions Impinging at an Angle[END_REF] [START_REF] Gerardin | Present and Future Non-Volatile Memories for Space[END_REF].

IV. CONCLUSIONS

We compared radiation tolerance of GST and GGST phase-change materials. From physico-chemical analyses on irradiated amorphous and crystalline layers, we highlighted the two main competitive mechanisms induced by irradiation: bonds breaking and crystallization induced by local temperature increase. In GST we observe a dominant crystallization at high fluences, while GGST, being more thermally stable, features a higher structural relaxation and a gradual reduction of the long range order, demonstrated by the gradual loss of the crystalline structure. Thanks to state-of-the-art 4kb PCM array analysis, we demonstrated the higher radiation tolerance of GGST devices, showing no recrystallization of the amorphous phase (RESET) even at high fluence of 5  10 10 ions/cm 2 . Finally, we report the radiation hardness of the IL-PCM stack solution wrt standard GST, confirming the benefit of a reduced PCM device size against heavy ion irradiation impacts.

Fig. 1

 1 Fig.1XRD patterns of GST (a) and GGST (b) amorphous layers before (REF) and after irradiations at increasing fluence (reported in the spectra in ions/cm 2 ). XRD peaks corresponding to GST cubic phase are highlighted.

Fig. 4

 4 Fig.4TEM/EDX and nano-diffraction patterns analyses of crystalline GGST after irradiation at a fluence of 7  10 12 ions/cm 2 . We observe the Ge segregation, induced by annealing, remained unchanged after irradiation (left). The main irradiation impact is on the crystalline morphology with the reduction at nm scale of the crystals size, as evidenced by few and low intensity nano-diffraction patterns identified (right).

Fig. 2

 2 Fig. 2 TEM (left) and nano-diffraction patterns (right) analyses of as-deposited amorphous GST after irradiation at a fluence of 10 13 ions/cm 2 . It evidences the creation of a crystalline structure with large crystalline grains.

GGST 3 B

 3 . Crystalline layers analysis Fig.

Fig. 5

 5 Fig. 5 Median and ±σ for SET and RESET distributions in GST 4kb arrays before and after irradiations at increasing fluences.

Fig. 6

 6 Fig. 6 Median and ±σ for SET and RESET distributions in GGST 4kb arrays before and after irradiations at increasing fluences.

Fig. 7

 7 Fig. 7 Resistance-vs-Current characteristics comparing a standard GST device with an IL-PCM. IL-PCM shows a high current reduction wrt GST in devices featuring same critical dimension (electrode area ~ 3  10 -3 µm 2 ).

Fig. 8

 8 Fig. 8 Median and ±σ for SET and RESET distributions in GST and IL-PCM 4kb arrays before and after irradiations at increasing fluences.


Marie-France Robbe

Etienne A Thévenot

Markus Stoeckli

Alfons Hester

Andreas Roempp

Andriy Kharchenko

Jean-Pierre Both

Olivier Gal

Serge Haan

Mass Spectrometry Imaging visualization tools developed during the Computis European project

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

  Mass spectrometry imaging visualization tools developed during the Computis European project Marie-France Robbe a , Etienne Thévenot a , Markus Stoeckli b , Alfons Hester c , Andreas Roempp c , Andriy Kharchenko d , Jean-Pierre Both a , Olivier Gal a , Serge Haan a BioMap imzML standard data format XML file based on mzML format and validated by HUPO-PSI, including an extension of the mzML vocabulary for imaging specific parameters + Binary file for mass spectral data (external file for faster access and processing time) Version 1.1.0 RC1 developed by the COMPUTIS project (2006-2009) and announced on 31 August 2009 at the IMSC conference in Bremen a CEA, LIST, Laboratoire d'Outils d'Analyse des Données, Gif-sur-Yvette cedex, F-91191, France, marie-france.robbe@cea.fr b NOVARTIS, Lichstraβe 35, WSJ-507.1101, CH-4002 Basel, Switzerland c Justus Liebig University, Schubertstraβe 60, Building 16, D-35392 Giessen, Germany d FOM/AMOLF, Kruislaan 407, NL-1098 SJ, Amsterdam, The Netherlands Comparison of the functionalities of 4 software tools developed or upgraded during the COMPUTIS project on a rodent urinary bladder image. Easy MSI Interface and images Interface, spectra and images imzML enables reading data from all MSI equipments by external post-processing software. Mass spectrometry imaging technology is an operational and matured technology. The goal of the Computis European project was to develop a standard format and efficient tools for processing and visualization of large size and complex datasets to answer the users' needs. www.computis.org BioMap A well-known free platform for MALDI MSI and MRI analysis, adapted to the needs of proteomic and biologist teams. Running under Windows and Linux. IDL virtual machine free setup necessary. Export/Import of multiple formats including DICOM, Analyze, imzML, jpg, tiff, mp4, avi and text. Visualization based on multiplanar analysis. Spectrum and image display with numerous colour tables, zooming and intensity adjustment. Multi-image display (simultaneous view of all images of a dataset, display of an image stack shifted and partially overlaid). Geometrical transformations (translation, rotation, flipping and resizing of images). Possibility to download and process only part of a dataset to manage large datasets with limited memory. Selection and processing of multiple ROIs with annotation of images. Statistical and histogram analysis. Geometrical operations. Movie creation. Co-registration to superimpose several images and compare the position of patterns appearing at different m/z. Easy MSI A platform for visualization and interpretation of MALDI and SIMS images. Full raw data loading and processing Running under Windows and Linux. Import of Analyze, GRD, Bruker Flex and imzML formats. Export in jpg, tiff, bmp, csv, postscript and svg formats. Spectrum and image display with several colour tables, zooming, peak and pixel picking, intensity tuning. Spectrum processing (wavelet denoising, baseline subtraction). Data reduction (binning, subimage). Selection of Region Of Interest (ROI) with display of the associated spectrum. Indicators highlighting peaks of interest in the spectra to guide data interpretation (relative variance, Moran index). Correlation matrix of the image, and correlation spectrum of a given m/z with the other m/z. Spatial and spectral classification with 4 clustering methods (K-means, fuzzy, hierarchical, diffusion map). Parametric peak extraction for faster interrogation of biological databases Image registration with EasyReg2D software. authors gratefully acknowledge the financial support from the European Commission (FP6 STREP project LSHG-CT-2005-518194) Several offline software tools are at users' disposal for processing mass spectrometry images. Next step is molecular characterization and quantification. imzML specifications, imzML converters and MSI software are available on www.maldi-msi.with MALDI, SIMS and DESI techniques, and processing high mass resolution images under Windows. Xcalibur installation necessary. Import of imzML , JLU internal and Thermo Fisher raw formats. Export in bmp, tif and jpeg formats. Display with zooming of pixel spectrum and total spectrum as histogram. Total ion count display as rotating hypercube. Image display with an automatic selection of the best images, based on general image criteria, mass lists and individually given parameters. Manual intensity adjustment and legend options for images. Data management and processing organized as projects with saving. Analysis guided by the user-interface. Comparison of MS images with complementary imaging techniques (optical, PCA, …) through arithmetic operations. Masks to keep aside unwanted data (m/z, regions, shots, runs) and process larger datasetsfriendly tool to provide an easy spectral and spatial exploration of imaging MALDI and SIMS datasets under Windows. Import of imzML and FOM internal formats. Export in png and csv formats. Total spectrum display with zooming Image display with a manual greyscale tuning to improve image contrast. Selection of Regions Of Interest (ROI) with the display of the associated spectra. "Self-organizing map" function to classify images according to pixel intensity and to select automatically a given number of images as different as possible. The classification method used is unsupervised competitive learning, also known as the Kohonen neural network. Interface Region Of Interest and spectrum Self-organizing map


Clara Maurel

Patrick Michel

J Michael Owen

Richard P Binzel

Megan Bruck-Syal

G Libourel

Simulations of high-velocity impacts on metal in preparation for the Psyche mission

In 2026, the NASA Discovery mission Psyche will orbit the asteroid (16) Psyche, the largest known metal-rich asteroid in the main belt. To estimate relative ages of the surface, identify re-surfacing events and better constrain Psyche's history, impact craters will be counted and characterized. No spacecraft has ever visited a metal-rich small body; therefore, laboratory-scale impact experiments and numerical simulations will play an important role in the interpretation of the mission's data.

However, the planetary applications of high-velocity impacts have so far mostly been studied for silicate targets. Limited attention has been drawn to planetary objects predominantly made of metal, and more laboratory experiments and numerical calibrations are needed. As part of this effort, we present a suite of numerical simulations using an adaptative smoothed particles hydrodynamics numerical code (ASPH) reproducing a high-velocity impact experiment conducted on a steel target. This work primarily focuses on the influence of the chosen equation of state and initial distribution of flaws in the material on the estimated crater dimensions, damage and temperature. We find that changing the EOS and initial flaw distribution affects the crater dimensions, though for a vast majority of cases the dimensions remain within 20% of the experimental values. The target is in most cases only locally weakened but not fully damaged, independently from the EOS chosen. Finally, temperatures at the impact point and around the forming crater can reach values above the melting point of iron at < 100 GPa, which is in agreement with experimental observations. These results allow us to speculate on the differences expected between the surfaces of visited silicate-rich asteroids and that of the metal-rich target of the Psyche mission.

Introduction

In 2026, the NASA Discovery mission Psyche will orbit the ~200-km asteroid ( 16) Psyche [START_REF] Elkins-Tanton | Asteroid (16) Psyche: visiting a metal world[END_REF]. The asteroid bulk density estimate of 3990 ± 260 kg m -3 [START_REF] Viikinkoski | Psyche: A mesosiderite-like asteroid?[END_REF] is consistent with that of stony-iron meteorites. The high radar albedo of Psyche (0.37 ± 0.09) also strongly suggests the presence of metal in abundance at its surface [START_REF] Shepard | Radar observations and shape model of asteroid 16[END_REF]. This makes Psyche the largest known metal-rich asteroid in the main belt. The leading hypothesis to explain the nature of Psyche is that the asteroid is the metallic core of an ancient planetesimal, whose silicate mantle was stripped away by one or several grazing, hit-and-run impacts [START_REF] Asphaug | Mercury and other iron-rich planetary bodies as relics of inefficient accretion[END_REF]. This idea remains challenged, for example, by the possibility that Psyche accreted from a metal-rich reservoir in the proto-planetary disk [START_REF] Weisberg | A new metal-rich chondrite grouplet[END_REF].

The instruments on board the spacecraft will use different approaches to constrain the history of the asteroid, with the objective to elucidate Psyche's nature. One of these approaches is to count and characterize impact craters. The recent radar-derived shape model of Psyche has already allowed the identification of two large depressions in the topography of the asteroid, interpreted as being two craters larger than ~20 km in diameter [START_REF] Shepard | Radar observations and shape model of asteroid 16[END_REF]. Although unresolved by this shape model, it is expected that hundreds of > 100-m craters will be observed over the course of the mission based on collisional evolution models of the main belt [START_REF] Marchi | Hypervelocity impact experiments in metallic targets: Implications for the NASA Psyche mission[END_REF]. Craters on small bodies and planets constitute an important source of information to estimate 1) the age of the asteroid relative to other planetary bodies, 2) the chronology of events that shaped the asteroid, 3) the environment in which the body evolved and 4) the composition and strength of its subsurface.

Psyche poses an additional challenge compared to other small and planetary bodies studied in situ since no spacecraft has ever visited a metallic asteroid. Also, most numerical and smallscale experimental studies of planetary impacts have been carried out on silicates. Since both the size and shape of craters are affected by the nature of the asteroid's surface [START_REF] Jutzi | Modeling asteroid collisions and impact processes[END_REF][START_REF] Marchi | The missing large impact craters on Ceres[END_REF], calibrations against well-known crater size distributions may not apply optimally to Psyche. An important effort in understanding cratering processes in metallic material, through a combination of impact experiments and simulations, is therefore crucial for the interpretation of the mission's data.

For decades, industrial and military applications of high-velocity impacts on metals provided data for the development of several strength models and equations of state [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF][START_REF] Johnson | Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures[END_REF][START_REF] Tillotson | Metallic equation of state for hypervelocity impacts[END_REF][START_REF] Thompson | Improvements in the Chart D radiation-hydrodynamic CODE III: Revised analytic equations of state[END_REF]. Although limited attention has been drawn to the planetary-scale applications of high-velocity impacts on such materials, some impact experiments have been carried out on iron meteorites-possible analog to Psyche's surface-or alloyed irons with comparable mechanical properties [START_REF] Matsui | On the brittle-ductile behavior of iron meteorites' new experimental constraints[END_REF][START_REF] Katsura | Impact experiments on collisional evolution of iron regolith[END_REF][START_REF] Ogawa | The effect of temperature and impact velocity on crater shape on the surface of iron bodies[END_REF][START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF][START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF][START_REF] Marchi | Hypervelocity impact experiments in metallic targets: Implications for the NASA Psyche mission[END_REF].

For example, [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF] and [START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF] carried out a suite of impact experiments on Cr-Mo alloy steel (SCM 435) and the iron meteorite Gibeon at the Institute of Space and Astronautical Science (ISAS) in Japan. The objective of the present study is to calibrate the adaptive smoothed particle hydrodynamics (ASPH) computational package Spheral++ [START_REF] Owen | Adaptive smoothed particle hydrodynamics: Methodology. II[END_REF] against the high-velocity impact experiments carried out by these authors. Relying on the well-established Steinberg-Guinan strength model for steel [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF] we are interested in understanding the effect on crater dimensions of 1) the equation of state (EOS), and 2) the dynamic fracture model (initial distribution of flaws in the material). We compare the outcomes of 86 simulations obtained with the Tillotson EOS [START_REF] Tillotson | Metallic equation of state for hypervelocity impacts[END_REF] and ANEOS (Thomson and Lauson, 1972) with the same initial conditions using different initial flaw distributions characterized by a pair of Weibull parameters, with the objective to identify those that best fit the experimental data. We also compare the damage caused to the target in all cases, and in selected simulations we analyze the evolution of the target's temperature.

Numerical framework

We use the computational package Spheral++, which employs the adaptative smooth-particle hydrodynamics method (ASPH; [START_REF] Shapiro | Adaptive smoothed particle hydrodynamics, with application to cosmology: Methodology[END_REF][START_REF] Owen | Adaptive smoothed particle hydrodynamics: Methodology. II[END_REF]. ASPH replaces the scalar smoothing scale of SPH [START_REF] Monaghan | Smoothed particles hydrodynamics[END_REF] with a symmetric tensor, such that the resolution around each point is represented by an arbitrary ellipsoidal volume allowed to follow the local anisotropies in the particle distribution. This improves the locally Lagrangian approximation of ASPH in that each material points volume can follow the Lagrangian deformation of the local fluid element more faithfully than the simple volume adaptation of SPH. The SPH smoothing scale approximation is really only appropriate for locally isotropic volume changes. In practice it means that ASPH allows the local resolution scale to follow while point distributions are stretched or compressed anisotropically. That way, both numerical stability as well as efficiency can be improved when resolution is needed in preferential directions. More details about Spheral++ can be found in the literature [START_REF] Owen | Adaptive smoothed particle hydrodynamics: Methodology. II[END_REF][START_REF] Owen | A tensor artificial viscosity for SPH[END_REF][START_REF] Owen | A compatibly differenced total energy conserving form of SPH[END_REF]; here we describe the parameters and models used and investigated in our simulations. These include the equation of state (materialdependent equation that relates the pressure to the density and either directly the temperature or the internal energy), the strength model (which takes into account the mechanical reaction and the possible plastic deformations of the material) and the damage model (initial distribution of incipient flaws that may evolve in fractures under a given amount of stress).

Equations of state

The equation of state (EOS) relates the pressure of a system to its density and temperature or internal energy. This equation must be added to the equations of conservation and motion for a complete characterization of the system's dynamics. It is material-dependent, and typically consists in a set of interpolation parameters derived to match experimental data in the range of pressure, temperature and density of interest. The effect of two different equations of state is examined in this study: the Tillotson EOS [START_REF] Tillotson | Metallic equation of state for hypervelocity impacts[END_REF] and ANEOS (Thomson and Lauson, 1972).

The Tillotson parameters for pure iron have been published by [START_REF] Melosh | Impact cratering: a geologic process, Research supported by NASA[END_REF] and are implemented as default values for iron in Spheral++. The main parameters for steel have also been published [START_REF] Nesterenko | Dynamics of heterogeneous materials[END_REF]. Both sets of parameters (Table 1) were compared by conducting two otherwise identical simulations, and no fundamental difference was found between the evolution in time of the crater's dimensions (Fig. 1). Therefore, we chose to perform the rest of the simulations using the Tillotson parameters for pure iron, since they have been more widely used and the other EOS studied (ANEOS) has only been parameterized for pure iron.

No detailed work has recently been published on the ANEOS of pure iron since the original publications, unlike for example SiO2 [START_REF] Melosh | A hydrocode equation of state for SiO2[END_REF]. Two versions of ANEOS are available for pure iron, accounting for different phases and phase transitions (Melosh, private communication).

The version adapted from the original ANEOS library matches experimental data for the solidsolid phase transition at ~13 GPa. This version, however, lacks a distinct liquid phase. Another version accounts for the liquid phase but not the solid-solid transition [START_REF] Thompson | ANEOS analytic equation of state for shock physics codes input manual[END_REF]; recent experimental work has shown the limitation of this version for very high pressures (~500 GPa; [START_REF] Kraus | Impact vaporization of planetesimal cores in the late stages of planet formation[END_REF]. Both versions of ANEOS would equally benefit from being re-evaluated in the light of new available experimental data.

The approximate pressure expected in the target during the compression phase of an impact was derived by [START_REF] Mizutani | New scaling laws on impact fragmentation[END_REF]:

𝑃 ~ 𝑃 0 ( 𝐷 𝑃 𝑟 ) 3 (1)
where the initial peak pressure 𝑃 0 is defined as:

𝑃 0 ~𝜌0,𝑡 𝐶 𝑡 𝑣𝜁 2 (1 + 𝑣𝑠 𝑡 𝜁 2𝐶 𝑡 ) where 𝜁 = 2 [1 + ( 𝜌 0,𝑡 𝐶 𝑡 𝜌 0,𝑝 𝐶 𝑝 ) 1/2 ] -1 (2)
In eqs. ( 1) and (2), subscripts 𝑡 and 𝑝 denote target-and projectile-related quantities. 𝐷 𝑃 (m) is the impactor diameter, 𝑟 (m) is the distance from the closest point located on the sphere of radius 𝐷 𝑃 below the impact point, 𝜌 0 (kg m -3 ) is the initial density, 𝐶 (m s -1 ) is the bulk sound velocity in the material, 𝑣 (m s -1 ) is the impact velocity, 𝑠 is a constant equal to 1.92 [START_REF] Mizutani | New scaling laws on impact fragmentation[END_REF]. Using eqs.

(1) and ( 2), initial densities of 2700 and 7800 kg m -3 , bulk sound velocity of 3500 and 5200 m s -1 for basalt and iron, respectively, we find a peak pressure of ~75 GPa and up to ~45 GPa at 0.45 cm below the crater (i.e., the depth of the final crater, see section 4). Given that the pressure involved in the area of interest during the impact can be much higher than 13 GPa, and that based on the experiments partial melting of the target is expected, we chose the version of ANEOS accounting for a liquid phase to compare to the suite of simulations carried out with the Tillotson EOS.

Strength model

The response of a system to an applied force strongly depends on the strength model implemented and it is crucial to choose the model most adapted to the simulated material. The Steinberg-Guinan strength model [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF] describes the evolution of both the shear modulus and yield strength as a function of temperature, pressure and density-as opposed to the Johnson-Cook strength model, also commonly adopted for metals, which does only provide the yield strength.

This model assumes that both shear modulus and yield strength are independent from the strain rate, which is only valid if the strain rate is higher than ~10 5 s -1 . During an impact, the compressive strain rate 𝜀̇ is approximately:

𝜀̇ ~ 𝑣 𝑃 𝑟 𝑃 𝑟 2 (3)
where 𝑣 𝑃 is the impact velocity, 𝑟 𝑃 the radius of the projectile and 𝑟 is the distance [START_REF] Melosh | Dynamic fragmentation in impacts: hydrocode simulation of laboratory impacts[END_REF]). In our case, with 𝑣 𝑃 = 6.9 km s -1 , 𝑟 𝑃 = 1.9 mm (Section 3) and 𝑟 = 1 cm (i.e., approximatively twice the size of the final crater; Section 4.1), we find 𝜀̇ ~ 1.3×10 5 s -1 , which is above the model's validity threshold. The fitting parameters used for steel are summarized in Table 2.

Damage model

The tensile stress applied during the impact yields the activation and propagation of flaws in the material, which irreversibly damage it (i.e., reduce its strength) up to an eventual breaking point.

In Spheral++, the damage of a node is modeled by a tensor 𝐷, and the stress tensor applied to a node will be scaled down by 𝐼-𝐷, where 𝐼 is the identity matrix. Because the yield strength of a metrial is directly related to the stress applied by the Steinberg-Guinan model [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF]), a damaged node will decrease in strength until it is fully damaged. It is then treated as a strengthless material. To quantify the damage of a node, we look at the maximum eigenvalue of the damage tensor calculated for this node.

The accumulation of damage in the material is modeled with the widely-used Grady-Kipp fragmentation theory [START_REF] Grady | Continuum modelling of explosive fracture in oil shale[END_REF] adapted to SPH by [START_REF] Benz | Impact simulations with fracture. I. Method and tests[END_REF]. This

theory relies on the existence of incipient flaws in the material-naturally occurring due to, for example, crystal defects. Each flaw possesses its own stress threshold above which it starts to grow in order to release part of the stress applied to the material. When the target is initialized, Spheral++ distributes incipient flaws with different threshold stresses and assigns several flaws to each node.

The distribution of these incipient flaws follows the Weibull statistics:

𝑁(𝜎) = ( 𝜎 𝜎 𝑁 ) 𝑚 (4)
where 𝑁 is the number of flaws that activate at or below a stress 𝜎 for a given volume. The parameters 𝑚 and 𝜎 𝑁 (called shape and scale parameters, respectively) are material dependent and can be experimentally determined-although so far a limited number of materials have been calibrated. Eq. ( 4) is also commonly found in the form 𝑛(𝜀) = 𝑘𝜀 𝑚 , where 𝑛 is the number density of activated flaws at a strain 𝜀, and:

𝑘 = 1 𝑉 ( 𝐸 𝜎 𝑁 ) 𝑚 (5)
where 𝑉 and 𝐸 are the volume and the Young's modulus of the target, respectively [START_REF] Nakamura | Weibull parameters of Yakuno basalt targets used in documented high-velocity impact experiments[END_REF].

One objective of this study is to determine numerically the range of values of Weibull parameters 𝑚 and 𝜎 𝑁 (or equivalently 𝑘) that best reproduce the impact experiment carried out by [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF], and evaluate the dependence of the final crater dimensions on these parameters. None of them has been experimentally measured for SCM 435 steel, and no clear values of 𝑚 and 𝜎 𝑁 were identified in the literature for stainless steel. We selected the range of values investigated for 𝜎 𝑁 using the fact that this parameter is related to the mean fracture stress (𝜎 ̅) of the material by:

𝜎 𝑁 ~ 𝜎 ̅ Γ(1 + 1/𝑚) (6)
where Γ is the gamma function [START_REF] Bergman | On the variability of the fracture stress of brittle materials[END_REF]. Taking 𝜎 ̅ equal to the tensile strength of the SCM 435 steel (since flaws activate in tension), 𝜎 𝑁 should fall in the range 650-950 MPa for values of the shape parameter 𝑚 between 2 and 30. Regarding an estimate of 𝑚, [START_REF] Asphaug | Asteroid interiors[END_REF] mention that metals could be approximated by 𝑚 ~ 8 (for reference, a value of 9.5 is often adopted for basalt). The authors do not provide additional information or reference. Accounting for the uncertainties of these parameters, we conducted a suite of simulations spanning a broad range of values of 𝑚 (2, 5, 8, 10, 12, 15 and 30) and 𝜎 𝑁 (0.05, 0.2, 0.5, 0.8, 0.9, 1.1, 1.5, 2.0 and 3.0 GPa).

The equivalent values of the parameter 𝑘 are given in Table 3.

Note that the Grady-Kipp fragmentation theory was developed to model failure in a brittle material, while steel and iron meteorites are both ductile at room temperature. However, [START_REF] Grady | Investigation of explosively driven fragmentation of metals-two-dimensional fracture and fragmentation of metal shells: progress report II[END_REF] applied this theory to fragmentation of ductile metals explaining that although some stress may be accommodated by ductile deformation, this dissipation process is relatively limited and represents a minor contribution to the final outcome of high-strain rate events. Moreover, impact experiments comparing steel, Fe-Ni alloy and iron meteorites targets found no significant difference in crater shape between impacts above and below the brittle-ductile transition temperature [START_REF] Matsui | On the brittle-ductile behavior of iron meteorites' new experimental constraints[END_REF][START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF]. Therefore, we assumed the Grady-Kipp theory could reasonably be applied to model high-velocity impacts in steel targets.

Selected experiment

We replicated a high-velocity impact experiment conducted by [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF]. In the experiment, the target was a cylinder of SCM 435 steel, with a diameter of 6 cm and a height of 3-4 cm. In the simulation, the target is a parallelepiped of 6 × 6 × 3 cm. The projectile is a 80-mg sphere of basalt (i.e., with a radius of 1.92 mm, assuming a density of 2700 kg m -3 ) impacting vertically at 6.89 km s -1 under Earth gravity (9.81 m s -2 ). It is initially located three radii above the target's surface (5.76 mm). The target is simulated with a resolution of 0.5 mm, which represents ~866,000 SPH particles. The impactor is made of ~93,800 SPH particles; this number is calculated the mass per SPH particle is the same in the target and impactor. We also conducted two selected runs with a resolution of 0.2 mm to verify the convergence of the results with increasing resolution and also analyze the target's temperature. The SPH particles were assigned an EOS (Tillotson or ANEOS) and a strength according to the Steinberg-Guinan model for steel (Section 2.2). We carried out simulations with both EOS for 43 pairs of Weibull parameters 𝑚 and 𝜎 𝑁 (Section 2.3).

We applied a plastic yield model with constant shear modulus 𝐺 0 = 22.7 GPa and yield strength 𝑌 0 = 3.5 GPa to characterize the projectile's strength and used Weibull parameters published for basalt (𝑚 = 9.5 and 𝑘 = 10 30 cm -3 ; [START_REF] Asphaug | Asteroid interiors[END_REF].

Comparison with the impact experiment

Crater dimensions

In the replicated experiment [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF], a crater diameter of 9.8 mm was measured at the original level of the target's surface and a depth of 4.5 mm was measured from this original level down to the bottom-center of the crater. We measured both quantities the same way at the end of the simulations (10 µs); at this time, all the craters had their final dimension. We considered the spatial resolution of our simulation (0.5 mm) as the uncertainty in the dimensions of the simulated craters; this corresponds to a 10% uncertainty for both diameter and depth.

With the Tillotson EOS, we find that only 58% of the diameters and 30% of the depths obtained in the simulations are within ±10% of the experimental values, though all diameters and almost all depths (95%) remain within ±20% (Fig. 2A). Both depth and diameter vary monotonically with the Weibull scale parameter 𝜎 𝑁 : for a given shape parameter 𝑚, the dimensions decrease inversely to 𝜎 𝑁 (except for 𝑚 = 2, where they are approximately constant). In most cases, the higher 𝜎 𝑁 , the closer the dimensions to experimental values. However, we do not observe significant differences when 𝜎 𝑁 is kept constant and 𝑚 varies. Both results are not surprising if we consider the cumulative distribution function of the Weibull distribution (Fig. 3). When 𝜎 𝑁 increases, a larger applied stress is necessary for the same amount of nodes to fail, yielding a smaller crater. If 𝑚 increases, the simulated material becomes more homogenous, but the amount of stress needed to fail ~2/3 of the nodes (definition of 𝜎 𝑁 ) is the same, explaining why varying 𝑚 has less effect than 𝜎 𝑁 . Interestingly, the pairs (𝑚, 𝜎 𝑁 ) = (8, 0.8-0.9 GPa) are among the best fits when accounting for both diameter and depth. This is in agreement with our preliminary calculations for 𝜎 𝑁 (Section 2.3), and with the value suggested by [START_REF] Asphaug | Asteroid interiors[END_REF] for 𝑚, and corresponds to a value of 𝑘 of ~10 17 cm -3 .

With ANEOS, the diameters and depths are overall closer to experimental values with 77% and 51% within ±10%, respectively (Fig. 2B). We observe a similar monotonic trend with 𝜎 𝑁 as with the Tillotson EOS, with more spread in depth than diameter as a function of 𝜎 𝑁 . Note that the pairs (𝑚, 𝜎 𝑁 ) = (8, 0.8-0.9 GPa) also reproduce well the experimental values.

Target damage

Because the strength of a material decreases with accumulating damage, any area within the target with non-zero damage will be irreversibly and proportionally weakened. [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF] imaged a section of the crater with scanning electron microscopy (SEM) and observed deformations of the target and minor cracks within ~1 mm around the crater edge and up to several mm directly below the crater. Cracks < 0.2-mm wide were also observed down to about 2 mm underneath the bottom of the crater, indicating the material had marginally failed. Given the resolution of the nominal simulations (0.5 mm), it was expected that such cracks would not be resolved, but that a possible partial damage of the target could be found.

For 𝑚 > 5, the cases where 𝜎 𝑁 = 0.05 GPa produce near-global failure of the target, with a majority of nodes damaged at 100%. This is also the case for 𝑚 = 30 and 𝜎 𝑁 = 0.2 GPa. The cases where 𝑚 = 2 leave the target completely undamaged. In all other cases and with both EOS, the first layer of SPH particles surrounding the crater is only partially damaged by the impact (Fig. 4A-B).

Increasing 𝑚 from 5 to 30 increases the maximum damage (typically near the impact point) of ~10% and the thickness of material damaged below the impact point by a factor of 2 to 3. Not surprisingly, increasing 𝜎 𝑁 yields less damaged nodes because the average threshold stress of the incipient flaws shifts toward higher values. Globally, the smaller this scale parameter, the thicker and more damaged the layer of material below the crater. The Tillotson EOS yields on average a maximum that is about 10% smaller than the same simulation conducted with ANEOS. However, the EOS does not have a significant influence on the amount of damaged material below the crater (Fig. 4B). For the cases where the crater dimensions are within 10% the experimental values, the layer of damaged material below the crater does not exceed 2 mm, which is in agreement with experimental observations.

For comparison, we performed one simulation with the same initial setup, the Tillotson EOS and a basaltic target (Fig. 5A-B). We used the Weibull parameters of basalt (𝑚 = 9.5 , 𝑘 = 10 30 cm -3 ) and the strength model developed by [START_REF] Collins | Modeling damage and deformation in impact simulations[END_REF] for rock materials. The impact resulted in a crater 1.5 times larger in diameter and depth after 10 µs (end of the simulations with a steel target). We observed a more important damage (between 0 and 10%) affecting larger regions of the target, as opposed to the very localized, minor damage of the steel target. This illustrates the importance of the nature of the target in the characterization of impact craters.

Temperatures in the target

The temperature in the target was not measured during the experiments by [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF].

However, the authors found numerous metal beads embedded in the ejecta and in the quenched impactor melt that was deposited at the surface of the target or infiltrated in cracks, suggesting that the metal reached at least locally melting temperatures. Similarly, immiscible emulsion of silicate and Fe-Ni metal liquid were observed at the bottom of the crater on the Gibeon iron meteorite [START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF], showing the target had experienced temperatures above the melting point of Fe-Ni metal.

We recorded the evolution of the temperature in the target for two simulations (one for each EOS) with 0.2-mm resolution and the Weibull parameters (𝑚, 𝜎 𝑁 ) = (8, 0.9 GPa). The Tillotson EOS relates the pressure and density to the internal energy of the system, not directly to the temperature, which is calculated assuming a constant specific heat capacity. Because of this approximation, the simulations with the Tillotson EOS may provide less reliable temperatures than with ANEOS, which directly relates the temperature to the other quantities.

During crater formation (t = 1 µs, Fig. 6A-B), a >2-mm heated zone surrounds the crater.

In particular, the temperature of the upper half layer of the heated zone exceeds ~2600°C, the liquidus for iron at pressures ~70 GPa (maximum pressure in the target; [START_REF] Ahrens | Shock temperatures and the melting point of iron[END_REF]. This confirms that liquid metal is formed during the impact, as expected from the presence of spheroidal metal blebs in crater and ejecta [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF], or by metal-silicate liquid immiscibility in craters [START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF]. At the end of the simulation when the crater is in steady state (t = 10 µs, Fig. 6C-D), a zone heated above 100°C remains between 1 and ~3 mm (on the sides and below the crater, respectively). The maximum temperatures are reached in the uppermost layer in the crater, which is right at the liquidus temperature for SCM 435 steel at room pressure (~1500°C)

and therefore could still contain melted residues. Remarkably, the temperatures both at 1 µs and 10 µs do not drastically differ between the case with the Tillotson EOS and ANEOS. In our case, the Tillotson EOS seems to provide a relatively reliable approximation of the temperature in the target. In both cases, we suspect that the highest temperatures (≫ 2600°C) could be artifacts due to the still relatively coarse resolution of the simulations. Note that the Tillotson EOS has a continuous analytic solution for internal energy (and therefore temperature), whereas for ANEOS, a grid of temperatures accessible to the EOS must be created. This is due to the fact that Spheral++ evolves the model in terms of the specific thermal energy, while ANEOS works in temperature.

For efficiency, Spheral++ accommodates this difference by computing lookup tables converting the energy to temperature (as a function of density) and using bilinear interpolation to go between the two. This increases the computation speed at the expense of a certain discreteness in the resulting temperatures. In the simulations, the resolution for the ANEOS case was ~50°C, which explains why small temperature differences cannot be resolved (Fig. 6A-D).

Discussion

Tillotson EOS versus ANEOS

Overall, in the conditions of the experiment we replicated, the influence of the EOS on the outcomes of the simulations remains limited and always depends on other parameters such as the initial flaw distribution. In terms of crater dimensions, ANEOS cases are overall closer to the experimental values than the Tillotson cases. However, for the Weibull shape parameter 𝑚 = 8 found in the literature [START_REF] Asphaug | Asteroid interiors[END_REF] and reasonable values of the scale parameter 𝜎 𝑁 (0.8-0.9 GPa) estimated by simple calculation (Section 2.3) both EOS yield accurate dimensions. In terms of temperature recorded in the target, we do not find a significant difference between ANEOS and the Tillotson EOS, which in this case provides reliable temperature estimates despite the approximation of a constant specific heat capacity. Finally, except for extreme values of the Weibull scale parameter 𝜎 𝑁 < 0.2 GPa where the target fails with ANEOS but is only widely damaged with Tillotson, there is no notable difference in the amount of material damaged between the two EOS. The simulations with ANEOS globally result in a damage ~10% higher that with Tillotson, though in both cases the target is only marginally affected (damage below 40%).

Steel versus meteoritic metal

Iron meteorites-possible analog to Psyche's surface material-are made of a Fe-Ni alloy that was most often very slowly cooled (a few degrees per million years), yielding the formation of very specific structures characteristic of meteoritic alloys. One of the most striking example is the formation of the Widmanstätten pattern, a mm-scale intergrowth of two Fe-Ni phases called kamacite (Ni-poor) and taenite (Ni-rich) that gives iron meteorites their recognizable geometric pattern when etched [START_REF] Buchwald | Handbook of iron meteorites[END_REF]. With such exceptional cooling conditions and resulting heterogeneities, differences may be expected between the mechanical behavior of iron meteorites and that of man-made steels. The limited number of impact experiments and strength tests carried out on iron meteorites had companion experiments made on various steel targets [START_REF] Matsui | On the brittle-ductile behavior of iron meteorites' new experimental constraints[END_REF][START_REF] Katsura | Impact experiments on collisional evolution of iron regolith[END_REF][START_REF] Ogawa | The effect of temperature and impact velocity on crater shape on the surface of iron bodies[END_REF][START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF]. Tensile tests carried out on the iron meteorite Gibeon measured a yield strength at room temperature of ~310 MPa [START_REF] Johnson | A new interpretation of the mechanical properties of the Gibeon meteorite[END_REF], similar to that of the SCM 435 steel (~350 MPa). [START_REF] Matsui | On the brittle-ductile behavior of iron meteorites' new experimental constraints[END_REF] performed high-velocity impact experiments on 1020 steel (yield strength ~300 MPa), pure iron and three iron meteorites. They found that crater size and shape (lip) were very similar for each type of target. [START_REF] Matsui | On the brittle-ductile behavior of iron meteorites' new experimental constraints[END_REF] also reported evidence of failure on most iron meteorites, with cracks propagating along the Widmanstätten discontinuities. Similar observations (lip and cracks along boundaries) were made by [START_REF] Libourel | Hypervelocity impacts as a source of deceiving surface signatures on ironrich asteroids[END_REF] after comparison between impacts on Gibeon and on SCM 435 steel. This difference likely emerges from the contrast between a relatively isotropic steel and highly anisotropic iron meteorites. The similarities between the craters in steel and in meteorite show the relevance of modeling steel targets, for which more data are available. On the other hand, the failure observed on meteorites away from the crater suggests that the Weibull distribution for incipient flaws may have to be adapted for iron meteorites and should not necessarily be assumed to be similar to steel, because of the weaker interfaces of the meteoritic Widmanstätten structure. However, whether such heterogeneities are relevant for planetary-scale impacts remains to be investigated.

Possible implications for impact craters on Psyche

The results of our simulations allow us to compare and contrast what impacts into targets of different compositions might be like. For a given set of initial conditions, iron targets are almost never fully damaged but rather experience a minor and very localized weakening, whereas a basaltic target is more widely weakened. Crater size gives us another way to examine these trends.

In the experiment simulated here, the crater to projectile diameter ratio is 2.6 (and varies between 2.2 and 2.9 for other experiments conducted by [START_REF] Ganino | Impact-induced chemical fractionation as inferred from hypervelocity impact experiments with silicate projectiles and metallic targets[END_REF] for velocities between 3.39 and 6.88 km s -1 ). In comparison, impacts at 6.9 km s -1 into aluminum targets yield a ratio of 4.8 [START_REF] Hörz | Cratering and penetration experiments in aluminum and teflon: Implications for space-exposed surfaces[END_REF]. Both these values are smaller than the value of 8 calculated from scaling laws for intact basalt [START_REF] Holsapple | A crater and its ejecta: An interpretation of Deep Impact[END_REF][START_REF] Marchi | The cratering history of asteroid (2867) Steins[END_REF].

Scaling laws tested against experiments on silicate targets predict that the threshold for catastrophically destroying the target, and therefore activating flaws, will decrease as the target's size increases [START_REF] Housen | Scale effects in strength-dominated collisions of rocky asteroids[END_REF]. This dependence is in particular controlled by the shape parameter 𝑚. Since the value of this parameter estimated in this study (𝑚 = 8-10) bracket that estimated for basalt (𝑚 ~ 9.5), it is expected that, like a silicate object, an iron-rich object of increasing size will get weaker.

However, in the case of cratering, we have seen that the strength of the target influences the crater size. Therefore, despite the fact that both silicate-rich and metal-rich targets would weaken at larger scale, the threshold for failure for iron will always be higher than that for silicate. The implication is that for equivalent impacts, much larger or faster projectiles would be necessary to cause a similar crater on a metal-rich surface as that inflicted to a silicate one. As a consequence, a comparison between impact experiments or simulations and the size-frequency distribution of craters measured on Psyche combined with models of the main belt population may allow us to glean insights into the composition and strength of Psyche's surface relative to other asteroid surfaces. A different crater to projectile diameter ratio on Psyche than that measured on other main belt asteroids would also mean that scaling laws derived for objects dominated by silicates could not optimally apply to this asteroid.

This study focused on modeling non-porous, pure-iron targets. It is probable that Psyche's surface and subsurface will rather be made of a mixture of iron with silicates, possibly hydrated [START_REF] Takir | Detection of water and/or hydroxyl on asteroid (16) Psyche[END_REF], and possibly micro or macroporous. Moreover, we only focused on vertical impacts, even though oblique impacts would more realistically occur in nature [START_REF] Pierazzo | Understanding oblique impacts from experiments, observations, and modeling[END_REF]. With confidence that vertical impacts on pure iron can be well replicated, a next step could be to introduce complexities such as oblique impacts, along with varying microporosity and macroporosity of the target. Further simulating layered or rubble-pile-like silicate-iron mixtures, in comparison with experiments on stony-iron meteorites and alloyed mixtures, will allow us to explore the effects of surface heterogeneities on the fate of impact craters.

Conclusion

Understanding the outcomes of impact processes on iron alloys and iron meteorites, as well as their scaling to planetary-like events is crucial for the optimal interpretation of the cratering data of the forthcoming NASA Discovery mission Psyche. Moreover, verifying the reliability of numerical models applicable to metals against simple experiments is an essential step toward more general investigations of planetary processes involving metallic or differentiated bodies. This work aims at better characterizing the influence of numerical parameters in the modeling of high-velocity impacts in steel targets, and possibly iron meteorites, using the ASPH package Spheral++. For a given strength model of stainless steel, we investigated the influence of the equations of state (Tillotson EOS and ANEOS), as well the influence of the Weibull distribution of incipient flaws in the material. The crater dimensions are within 10% of the experimental value in more cases with ANEOS than the Tillotson EOS. However, for reasonable Weibull parameters estimated from the literature or simple calculations, both EOS yield craters similar to the experimental one. In a majority of cases and independently from the EOS, the target does not fail and is only marginally damaged (damage <40% within 1 to 2 mm around the crater). Finally, the recorded temperatures are not significantly affected by the choice of the EOS and reach locally values above the melting point of iron at pressure <100 GPa, which is in good agreement with experimental observations of melted metal beads coming from the target. This work highlights the importance of specifically studying impacts in Psyche-like targets, because crater formation differs from what would be observed with a silicate target in similar impact conditions. Differences might therefore be expected between the crater size distribution of Psyche (if metal is dominating the surface and subsurface)

and other asteroids of similar size orbiting in the main belt. The NASA Psyche mission will for the first time image impact craters on a metal-rich asteroid and predictions arising from experimental and numerical work will be valuable during data interpretation.

Figures

Fig. 1. Depth versus diameter of a crater formed after an impact at 6.89 km s -1 by an impactor ~1.9mm in radius, for two different sets of Tillotson parameters: pure iron [START_REF] Melosh | Impact cratering: a geologic process, Research supported by NASA[END_REF] and steel [START_REF] Nesterenko | Dynamics of heterogeneous materials[END_REF]. Apart from their EOS parameters (given in Table 1), the targets were identical.

The simulations lasted 10 µs and both craters had their final shape at the end of the simulation.

Squares and circles represents 0.5-µs time steps. [START_REF] Melosh | Impact cratering: a geologic process, Research supported by NASA[END_REF] and steel [START_REF] Nesterenko | Dynamics of heterogeneous materials[END_REF].

Parameters a, b, A, B, E 0 are material-specific, α, β are fitting parameters and E IV , E CV are the energy of incipient and complete vaporization, respectively. Because the values of E IV and E CV for steel were not provided by [START_REF] Nesterenko | Dynamics of heterogeneous materials[END_REF], we used the same values as pure iron. parameter 𝜎 𝑁 . The combinations showed with a gray cell were not investigated. These values were obtained using the equation 𝑘 = 1/𝑉(𝐸/𝜎 𝑁 ) 𝑚 [START_REF] Nakamura | Weibull parameters of Yakuno basalt targets used in documented high-velocity impact experiments[END_REF], where 𝑉 is the volume of the target (108 cm 3 in the simulations) and 𝐸 the Young modulus of the target material (~200 GPa).

Parameter

Fig. 2 .Fig. 3 .

 23 Fig. 2. Crater dimensions as a function of the Weibull shape parameter 𝑚 for the simulations with

Fig. 6 .

 6 Fig. 6. Temperature in the target after 1 µs (A-B) and 10 µs (C-D). Simulations use the Tillotson

Table 1 .

 1 Tillotson parameters published for pure iron

		5	128	105	9.5×10 6	5	5	2.4×10 6 8.67×10 6
	Steel	0.55 0.62	117	55	17.5×10 6	5	5	2.4×10 6 8.67×10 6

Table 2 .

 2 Parameters of the Steinberg-Guinan strength model for stainless steel[START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF]. Y 0 is taken equal to the yield strength of the SCM 435 steel used in the experiment.

	𝑮 𝟎 (MPa) 𝒀 𝟎 (MPa) 𝑨 (MPa -1 )	𝑩 (K -1 )	𝜷	𝒏	𝒀 𝐦𝐚𝐱
	Stainless steel
	7.7×10 5	350	2.26×10 -6 4.55×10 -4	43 0.35 2.5×10 3
	(except 𝒀 𝟎 )

Table 3 .

 3 Corresponding values of the Weibull parameter 𝑘 for a given shape parameter 𝑚 and scale

Acknowledgements

We are very grateful to Dr. Dawn Graninger for her help with the ANEOS package in Spheral++, and to Dr. William F. Bottke and Dr. Simone Marchi for their comments on the manuscript. The simulations presented in this paper were performed on the Engaging cluster located at the Massachusetts Green High Performance Computing Center (MGHPCC). C.M. thanks the NASA Discovery program (Psyche mission) for financial support. P.M. acknowledges funding support from the French space agency CNES and from Academies of Excellence: Complex systems and Space, environment, risk, and resilience, part of the IDEX JEDI of the Université Côte d'Azur. The work of M.B.S. and J.M.O. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.