Constantinos Hatzoglou

Solène Rouland

Bertrand Radiguet

Auriane Etienne

Gérald Da Costa

Xavier Sauvage

Philippe Pareige

François Vurpillot

Preferential evaporation in atom probe tomography: an analytical approach

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Atom probe tomography (APT) is a three-dimensional (3D) characterization technique that is nowadays commonly used to visualize and quantify the microstructure of materials at atomic scale.

This technique is widely used in materials sciences. More details on this technique can be found in [START_REF] Lefebvre | Atom probe tomography: put theory into practice[END_REF][START_REF] Gault | Atom Probe Microscopy[END_REF][START_REF] Miller | Atom Probe Tomography: Analysis at the Atomic Level[END_REF].

APT is based on the field evaporation of atoms located at the surface of the specimen. The elemental nature of each evaporated atom is obtained by time-of-flight mass spectrometry. Such measurement requires a precise control of the field evaporation (FE) process. This is done by superimposing to the constant voltage (

) applied to the specimen, short pulses that trigger the field evaporation and, at the same time, these pulses trigger time of flight measurements. If some atoms are FE between pulses, their time of flight is unknown, and they are not considered for the composition quantification. This phenomenon is called preferential evaporation (PE) [START_REF] Tsong | Atom-Probe Field Ion Microscopy: Field Ion Emission, and Surfaces and Interfaces at Atomic Resolution[END_REF][START_REF] Miller | Atom Probe Tomography: Analysis at the Atomic Level[END_REF][START_REF] Miller | Atom probe Field Ion Microscopy[END_REF][START_REF] Miller | Atom probe Field Ion Microscopy[END_REF] when this bias is element specific. PE may degrade significantly the composition measurement accuracy in APT.

The probability for an atom to be FE is linked to many parameters such as the temperature of the sample, the electric field at the sample surface and the evaporation field of the considered atoms.

Evaporation field is defined as the required field for an atom to be evaporated from the specimen surface [START_REF] Tsong | Atom-Probe Field Ion Microscopy: Field Ion Emission, and Surfaces and Interfaces at Atomic Resolution[END_REF]. At defined conditions of temperature and electrical field, if atoms of a compound have similar evaporation field then their probability to be FE at is similar. In this case the global number of atoms evaporated out of pulses follows the actual composition of the specimen, and the composition measurement made from atoms collected on pulses is not biased.

However, if the evaporation field between atoms is significantly different, some species exhibit a higher probability to be FE out of pulses. This generates some deficit of these species and the composition measurement can be significantly biased. Indeed, since the evaporation probability is not the same out of pulses, it affects then the residual proportion of atoms that can be evaporated on pulses.

These biases have been already observed and studied by many authors in different materials such as FeCu [START_REF] Takahashi | Comparison of the quantitative analysis performance between pulsed voltage atom probe and pulsed laser atom probe[END_REF], cemented tungsten carbide [START_REF] Peng | Evaluation of Analysis Conditions for Laser-Pulsed Atom Probe Tomography: Example of Cemented Tungsten Carbide[END_REF], GaAs [START_REF] Russo | Field-Dependent Measurement of GaAs Composition by Atom Probe Tomography[END_REF], ODS steel [START_REF] Hatzoglou | Experimental artefacts occurring during atom probe tomography analysis of oxide nanoparticles in metallic matrix: Quantification and correction[END_REF] or ZnO [START_REF] Amirifar | Quantitative analysis of doped/undoped ZnO nanomaterials using laser assisted atom probe tomography: Influence of the analysis parameters[END_REF]. It has been determined that the measured elemental composition depends on the APT analysis conditions. In some cases, for example ZnO or GaAs, the situation is even more complex due to molecular ion dissociation [START_REF] Blum | Dissociation of Molecular Ions During the DC Field Evaporation ZnO in Atom Probe Tomography[END_REF][START_REF] Zanuttini | Simulation of field-induced molecular dissociation in atom-probe tomography: Identification of a neutral emission channel[END_REF][START_REF] Saxey | Correlated ion analysis and the interpretation of atom probe mass spectra[END_REF] or because of detection limitations like for tungsten carbide [START_REF] Bacchi | Spatial and Compositional Biases Introduced by Position Sensitive Detection Systems in APT: A Simulation Approach[END_REF][START_REF] Meisenkothen | Effects of detector dead-time on quantitative analyses involving boron and multi-hit detection events in atom probe tomography[END_REF].

It is generally accepted that quantitative analyses are preferably obtained under low specimen temperature, high-pulse fraction (ratio of the pulses amplitude over the DC voltage) and high pulse repetition rate. Unfortunately, these optimal conditions also increase the sample failure probability [START_REF] Prosa | A Study of Parameters Affecting Atom Probe Tomography Specimen Survivability[END_REF]. A solution would be to develop an analytical model to better predict such phenomena. This model would provide the more favourable analysis conditions while maintaining high measurement accuracy and low bias. A first model was proposed by Takahashi et al. [START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]. This model explains the sample temperature dependence on the apparent composition of solute element, whereas the dependence on the pulse fraction and pulse frequency is not completely predicted.

In this study, a new analytical model of the PE for an electrical pulse APT is proposed. This model was applied to the experimental biases observed in three model alloys studied at different APT analysis conditions. More than reproducing the influence of all the studied parameters (temperature, pulse fraction and repetition rate), the model can also provide some valuable information about energetic constant directly linked to energy barrier, required to FE atom from the sample surface.

The analytical model

In APT, several biases may arise as low FE occurs at the DC voltage (i.e. between two pulses). For a given material, the number of atoms FE between pulses may be estimated with respect to the number of atoms evaporated on pulses. In voltage mode APT, atoms evaporated on pulses have higher kinetic energy, and are identified on the mass spectrum. Atoms FE between pulses and detected without any correlation with pulses, are identified as background noise events [START_REF] Lefebvre | Atom probe tomography: put theory into practice[END_REF].

For an alloy composed of chemical species, the number of atoms (among the elements) FE on pulses, can be calculated, regarding its own evaporation pulse width (ns range) and assuming that its rate of evaporation ( ) is defined by an Arrhenius expression,:

(1)

with the evaporation rate of atoms during the pulse, the surface atoms vibration frequency, the total number of atoms FE per unit of time, the Boltzmann constant, the analysis temperature, and the energy barrier for an atom at a defined field . is the total electric field above atoms at the pulse maximum:

(2)

with the electric field at the DC voltage and the pulse electric field.

Close to the evaporation field, the expression of the energy barrier is given by the common expression:

(3) with an energetic constant of the atoms and its evaporation field [START_REF] Lefebvre | Atom probe tomography: put theory into practice[END_REF][START_REF] Forbes | Field evaporation theory: a review of basic ideas[END_REF][START_REF] Miller | Atom probe Field Ion Microscopy[END_REF].

The agreement of this last equation with experimental measurement is correct, if we assume an energetic constant in the range 1-3 eV for refractory metals [START_REF] Kellogg | Measurement of activation energies for field evaporation of tungsten ions as a function of electric field[END_REF][START_REF] Ernst | Experimental investigation on field evaporation of singly and doubly charged rhodium[END_REF][START_REF] Wada | On the thermally activated field evaporation of surface atoms[END_REF]. Experimentally, the linearity of is approximately observed in the range of 0.8 to 0.95 for some materials [START_REF] Kellogg | Measurement of activation energies for field evaporation of tungsten ions as a function of electric field[END_REF]. Deviations exist out of this region but there will be neglected in a first approach. The energetic constant is a projection of at a field close to the evaporation field according to the linear approximation of .

In this range, the linear tendency has also been observed with ab initio calculation by Sanchez et al. [START_REF] Sánchez | Field-evaporation from first-principles[END_REF]. Note that the experimental estimation of equal to predicted by the Muller-Schottky model is poor as discussed by different authors (with the energy barrier without field in the Muller-Schottky description of the field evaporation) [START_REF] Muller | Gas-Surface Interactions and Field-Ion Microscopy of Nonrefractory Metals[END_REF].

The number of atoms evaporated on one pulse is then:

(4)
Similarly, the number of atoms evaporated between two pulses is:

(5) with the time interval between two pulses (10 s at 100 kHz) and the ratio between the total and pulse electric field (i.e.

). This ratio is related to the pulse fraction ( ), commonly used experimentally. The pulse fraction is the ratio between the pulsed electric field and the field at the DC voltage (i.e.

) and is so linked to the ratio by:

(6)

The apparent composition measured by APT could be estimated by writing a conservation law that assumes that the number of evaporated atoms over a complete cycle of evaporation, (DC + pulse) is constant. Considering the initial composition of atoms , , ( with the number of atoms evaporated over a complete cycle of evaporation), and the equations ( 4) and ( 5), this conservation law can then be written as:

(7)
with a constant.

It is important to stress that the electric fields above atoms at are not identical according to their chemical nature. In fact, due to the steep nature of the evaporation rate with the electric field, at the top of the voltage pulse, the electric field is very close to the evaporation field of each element. It is thus introduced with a small value ( << 1). It will be then considered as negligible and so that . It is thus possible to correlate the evaporation rate at the DC voltage ( ) and the one at the pulse ( ).

(

) 8
By combining this last equation and the equation ( 7), the evaporation rate on the pulse ( ) is thus equal to:

(9)

Considering a gaussian shape electrical pulse, (Fig. 1), with a FWHM , the FE pulse FWHM (i.e. )

is expressed as follows:

(10)

This equation is obtained from the evaporation rate ( , Fig. 1), equal to , with a temporal evolution of the normalized field ( ) equal to , with regarding the gaussian pulse shape. In this study the pulses width ( ) is 1 ns since a LEAP 4000 HR has been used. The FE pulse width is temporally much narrower than the electrical pulse one (Fig. 1).

As a function of their energetic constant ( ), the evaporation pulse duration seen by the atoms is not the same (Fig. 1). This equation restricts the study to a certain range of analysis conditions, since must be lower than 1. However, as it will be demonstrated later, this limitation range is very far from the commonly used experimental conditions. The ratio can be expressed as a function of APT parameters and is then equal to with the pulse frequency and the pulse width. The apparent composition in atoms measured in APT ( ) is the ratio between the number of those atoms (

) and the total number of atoms both evaporated during the pulses. Considering, the expression of those numbers (equation 1), the apparent composition can be written as:

(11)
Considering the expression of the evaporation rate of the atoms at the pulse (expression 9), the apparent composition in atoms measured in APT eventually becomes:

(12)
The influence of the analysis conditions ( , and ) on the apparent composition ( ) is not obvious, due to the complexity of equation ( 12). For this purpose, the evolution of the apparent composition for an equiatomic alloy (A/B, i.e. = = 50 at.%) was computed as a function of the different parameters of equation ( 12) (Fig. 2). close to ), it is required to increase pulse frequency ( ) or the pulse contribution, (and so the pulse fraction ), or by decreasing the base temperature. This behavior is well known experimentally, and analysis conditions must be tested to calibrate every new material [START_REF] Lefebvre | Atom probe tomography: put theory into practice[END_REF].

For any new material, the knowledge of the different energetic constants allows us to predict the apparent chemical composition as a function of the experimental parameters set by users ( , and

), those depending on the APT used ( ) and the studied material ( ). In this study, energetic constants values were determined for different alloys by fitting the predicted apparent compositions to the experimentally measured ones under different analysis conditions. The deviation between the calculated and experimental values was minimized using least square method.

APT analysis conditions and measurement procedure

Materials

Three different metallic alloys were analyzed by APT using a broad range of analysis conditions. The first alloy is composed of Ni and Cu in the same proportion (50 at.% of Ni and 50 at.% of Cu). This alloy has been chosen due to the significant difference of theoretical evaporation field between copper (ECu = 30 V/nm) and nickel (ENi = 35 V/nm) [START_REF] Tsong | Atom-Probe Field Ion Microscopy: Field Ion Emission, and Surfaces and Interfaces at Atomic Resolution[END_REF] [START_REF] Takahashi | Comparison of the quantitative analysis performance between pulsed voltage atom probe and pulsed laser atom probe[END_REF][START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF][START_REF] Shu | Multi-technique characterization of the precipitates in thermally aged and neutron irradiated Fe-Cu and Fe-Cu-Mn model alloys: Atom probe tomography reconstruction implications[END_REF].

APT analysis conditions

Three parameters are known to play a major role in the composition measurements accuracy by APT [START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]: the analysis temperature, the pulse repetition rate and the pulse fraction. In this study, a Cameca Local Electrode Atom Probe (LEAP) 4000 HR has been used for all the alloys. The influence of the sample temperature (T) has been studied in the range 20-90 K. The pulse repetition rate (f) influence has been studied in the range 25-250 kHz. The last parameter is the pulse fraction (fp). fp influence has been studied in the range 2.5-30 %. For all the analyses, the detection rate was between 0.3 to 0.5%/pulse. Though we do not present the data, we also performed analyses varying only the detection rate (from 0.1 to 10%) to ensure that this parameter does not influence the apparent composition, as already observed by Takahashi.

For each set of analysis condition, an average of 0.6×10 6 impacts were collected. This value is sufficiently high to obtain a relatively low statistical uncertainty on the composition measurements (around 2 = 0.14 at.% for the NiCu system for example) and sufficiently low to avoid a significant morphological change of the sample during series of measurements (in particular the radius of curvature of the specimen).

Measurement procedure

In the NiCu case, Ni and Cu atoms are mainly evaporated as Ni 2+ , Cu 2+ and Cu + . There is a very small amount of Ni + ions (less than 0.7% of Ni ions). This can be well understood considering the Kingham post ionization theory [START_REF] Kingham | The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states[END_REF][START_REF] Haydock | Post-Ionization of Field-Evaporated Ions[END_REF]. The same behavior for FeCu is observed where Fe and Cu atoms are mainly evaporated as Fe 2+ , Cu 2+ and Cu + . In the case of FeCrNi, almost all atoms are evaporated as double charged ions (i.e. Fe 2+ , Cr 2+ and Ni 2+ ).

It has to be noticed that O and N atoms were also detected for the NiCu alloy. Regarding the small amount (less than 0.3 at.%), only Ni and Cu atoms will be considered in the following. For the FeCu alloy, a small amount of C, P, O, Al, Cr, Mn and N atoms was detected (total amount less than 0.3 at.%). In this case, only Fe and Cu atoms will be considered. For the FeCrNi alloy, a small amount of C, O, N and Al atoms (less than 0.5 at.%) was also detected and similarly will not be taken into account in this study.

After identification of the peaks of interest in the mass spectra, the background into each peak was removed according to the background level from both sides of the peak as defined in [START_REF] Lefebvre | Atom probe tomography: put theory into practice[END_REF]. To estimate the chemical composition, the overlaps of 54 Fe 2+ with 54 Cr 2+ and 58 Fe 2+ with 58 Ni 2+

were considered (FeCrNi alloy). This was done considering the natural abundance of isotopes. There is no isotopic overlap for the NiCu and the FeCu alloys.

The atoms located in the center of crystallographic poles were also not considered in the composition measurements. This region, which exhibits commonly a low atomic density, is prone to electrical field fluctuations, inducing chemical biases and significant detection bias due to the rapid evaporation of last atoms situated on a low index pole center. Moreover, the chemical bias is not the same from one crystallographic direction to another, as already been observed by [START_REF] Gault | Impact of directional walk on atom probe microanalysis[END_REF].

If ions spatially and temporally give rise to close impacts the detector (so-called multi-hits events), an additional selected loss induced by detector loss of efficiency may occur and can induce chemical composition measurements biases [START_REF] Meisenkothen | Effects of detector dead-time on quantitative analyses involving boron and multi-hit detection events in atom probe tomography[END_REF]. This composition bias was not considered in our model; therefore, a multi-hits correction was applied to experimental data following the procedure described in [START_REF] Angseryd | Quantitative APT analysis of Ti(C,N)[END_REF][START_REF] Thuvander | Quantitative atom probe analysis of carbides[END_REF]. Fig. 3 represents the results of such correction, applied to the FeCrNi alloy and the uncertainty corresponds to the standard deviation. The multi-hits correction magnitude is lowest at high temperature, as seen in Fig.

3.

As also observed by field evaporation simulation [START_REF] Gruber | Field evaporation: A kinetic Monte Carlo approach on the influence of temperature[END_REF], detection issues, that could bias the apparent composition, are lower at higher temperature. So, considering only multi-hits detection issues, analyses at high temperature were preferred for quantitative chemical composition measurements.

Results

NiCu

The pulse frequency influence has been studied using two different temperatures and pulse fractions (fig. 4.a). Whatever the conditions, the apparent composition of Cu decreases when decreasing the pulse frequency. In the studied range of pulse repetition rate, this trend is more pronounced at high temperature. The measured Cu composition decreases from 45.5 ± 0.2 at.% at 200 kHz pulse repetition rate to 27.0 ± 1.1 at.% at 25kHz at temperature of 92 K and a pulse fraction of 20 %.

Whereas, at lower temperature (45 K) and a lower pulse fraction (10%), it decreases only from 45.9 ± 0.1 at.% to 42.1 ± 0.2 at.%. This influence of the pulse repetition rate can be easily interpreted in term of time interval between pulses. Indeed, as the pulse frequency increases, the duration during which PE can occur decreases, since the time interval between pulses becomes shorter. This explains why at high pulse repetition rate (200 kHz), the apparent composition is closer to the nominal (Fig.

2.d).

The influence of the pulse fraction has been also studied at two temperatures ( The estimation of the model parameters has been done considering that the exact Cu composition was 48 at.% (small deviation to the nominal 50at.% probably due to composition fluctuations in the material). The values of the constant CCu and CNi determined from the adjustment (Fig. 4) are not function of the temperature nor the electric field. The electric field has been estimated using the Kingham curves, based on the charge state ratio [START_REF] Kingham | The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states[END_REF][START_REF] Haydock | Post-Ionization of Field-Evaporated Ions[END_REF],

FeCrNi

Since the pulse fraction and the analysis temperature are the main parameters influencing the apparent composition, the study was focused on these 2 parameters (Fig. 2). The influence of the Reducing the pulse fraction down to a threshold value induces a decrease of the apparent Cr composition (and inversely for the Ni) since Cr is the element with the lowest evaporation field. Like in the NiCu alloy, evaporation at DC voltage becomes important at very low pulse fractions for all elements, whatever their energetic constant and their evaporation field are. As a consequence, the measured composition tends toward the real one. Since the FE probability is linked to the temperature, the pulse fractions for which PE of Cr is observed, and the pulse fraction for which all elements evaporate at DC voltage are higher at higher temperatures.

Conversely to the previous analysis (i.e. NiCu) where it was well known, here the composition depends on the studied phase (i.e. austenite or ferrite) and is only approximatively known from EDS measurements. Since the nominal composition is not perfectly known, the average one measured at high pulse fraction (> 10 %) was used. It corresponds to a nominal composition of Cr and Ni respectively equal to 18.6 and 9.5 at.%. These values are used to perform the adjustment of the analytical model (Fig. 5.a and Fig. 5.b, straight lines). In this case, the analytical model reproduced very well the experimental values and their associated evolution as a function of the analysis temperature and the pulse fraction.

Regarding the values of the energetic constant of Fe, Cr and Ni obtained from the analytical model, it is observed that : -(i) they are constant whatever the APT analysis conditions are (only 10% of deviation between extremum compared to the mean value) as for the NiCu case and -(ii) the highest constant of energy is for Ni and the lowest for Cr (like their respective theoretical evaporation fields [START_REF] Tsong | Atom-Probe Field Ion Microscopy: Field Ion Emission, and Surfaces and Interfaces at Atomic Resolution[END_REF]). Since there is no influence of APT analysis conditions, the average values are: 1.13 ± 0.03 eV for Fe (CFe), 1.05 ± 0.03 eV for Cr (CCr) and 1.17 ± 0.03 eV for Ni (CNi). It appears that the average value of the energetic constant of Ni (CNi) is not the same in the case of the NiCu alloy (CNi = 0.76 ± 0.04 eV) and in the case of FeCrNi steel (CNi = 1.17 ± 0.03 eV). This point will be discussed later.

FeCu

For the FeCu alloy, only the influence of the temperature at constant pulse fraction (fp = 20%) and pulse frequency (f = 200 kHz) was studied. As the temperature increases, the apparent Cu composition decreases (Fig. 6). The experimental trend is very well reproduced with the model (Fig. 6). Indeed, as the temperature increases, the evaporation probability increases, at the pulse and also at the steady voltage, inducing an increase of the PE probability (Fig. 2.c). So, it leads to a significant loss of Cu since it is the low field element.

The fit of the data also shows a slight increase of the apparent Cu composition for a temperature higher than 90 K. Indeed, continuing to increase the temperature, the evaporation probability of Fe between pulses may become significant so that it could balance the PE of Cu. This gives rise to an increase of the apparent Cu composition.

Regarding

Discussion

Regarding the results presented above, the analytical model reproduces relatively well all experimental measurements. The model reproduces the evolution of the apparent composition as a function of APT analysis conditions: temperature, pulse fraction and pulse repetition rate. This is already a big step forward as compared to the analytical model proposed by Takahashi et al. [START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]

Optimal analysis conditions

As mentioned in the introduction, one of the main objectives of this study was to determine the optimal APT analysis conditions. For a specific alloy, at a defined temperature and pulse frequency, the pulse fraction from which there is no PE is the one from which the apparent composition is constant and is chosen as the optimal APT analysis conditions (Fig.

Energetic constant and extrapolation to other materials

The average energetic constants (Ci) of Fe, Cr, Ni and Cu, obtained with the analytical model applied to different alloys are reported in the table 1. All values obtained are in the order of eV (from 0.35 to 1.17 eV). Comparing these values with those of the literature is difficult because only few results are available. From data obtained by Ohnuma [START_REF] Ohnuma | Surface Diffusion of Fe and Cu on Fe (001) Under Electric Field Using First-Principles Calculations[END_REF] using DFT calculation, under intense electrostatic field, it can be roughly estimated that the energetic constant of Fe in FeCu alloy is lower than 2 eV. To the authors' knowledge, it is the only study related to the materials studied here. Using the same approach (DFT calculation, under intense electrostatic field), Carrasco et al. [START_REF] Carrasco | Modeling field evaporation degradation of metallic surfaces by first principles calculations: A case study for Al, Au, Ag, and Pd[END_REF] and Peralta et al. [START_REF] Peralta | Mapping energetics of atom probe evaporation events through first principles calculations[END_REF] have estimated that the constant energy of Al is respectively equal to 0.5 eV in pure Al and 1.1 eV in Al3Sc phase. These DFT results are very similar to our experimental results on several points: (i) the range of energetic constant (few tenth of eV) and (ii) the energetic constant is linked to the studied phase. For example, the energetic constant of Fe is equal to 1.13 eV in FeCrNi and equal to 0.38 eV in FeCu (Table 1). This can be easily understood since the energetic constant of an element is a fraction of its energy barrier without field ( ) [START_REF] Kreuzer | Field evaporation[END_REF] which is linked to its binding-energy with the surrounding element [START_REF] Gomer | Theory of Field Desorption[END_REF][START_REF] Ashton | Ab initio Description of Bond-Breaking in Large Electric Fields[END_REF]. The energetic constants must be determined before and for each phase in order to be able to estimate the optimal analysis conditions. These values of energetic constant can be obtained, as done in this study, by varying the APT analysis conditions and by then adjusting the apparent composition with the analytical model. Another possibility would be to obtain these values by DFT calculation.

However, it must be first confirmed that DFT calculations provide quantitative energetic constant corresponding to those obtained experimentally. It must be noted that the present experimental work allows for the first time the measurement of these energetic constants for alloys. Indeed, to date, these values were only obtained experimentally on pure materials, such as W [START_REF] Kellogg | Measurement of activation energies for field evaporation of tungsten ions as a function of electric field[END_REF] or Rh [START_REF] Ernst | Experimental investigation on field evaporation of singly and doubly charged rhodium[END_REF].

Since the energetic constants are tabulated values for a specific material, the values obtained in this study for the FeCu alloy (Fe-1.05Cu at.%) were applied to experimental measurements obtained by close to those of this study (Table 1). In addition, the values thus obtained are not constant as a function of the pulse fraction (Table 2) and tend towards the values of this study (Table 1) when the pulse fraction increases. This evolution probably results from the data treatment procedure of Takahashi. Indeed, in their study, they tried to develop an analytical model of the PE considering the noise level in the mass spectrum. Thus, the background noise in the apparent composition measurement was included, while it was corrected in our study. This explains why our values do not reproduce the experimental data of Takahashi (Fig. 8.a). As Takahashi also observed, when the pulse fraction increases, the noise level decreases drastically, explaining why the values obtained on the adjustment of these data tends towards those of this study at high pulse fraction, as the noise level is the lowest his influence on the measures is the lowest. 20 and 25%). Experimental data (dots) have been extracted from [START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]. Full lines are obtained from the analytical model of this study using energetic constants of Fe and Cu reported in (a) table 1 and (b) table 2.

Fig. 1 :

 1 Fig. 1: Temporal (ns) evolution of the normalized field () at the sample apex during a gaussian shape electric pulse (FWHM = 1 ns) and its associated evaporation rate ( ). The evaporation rate has been plotted for two different energetic constants ( ): 1 (red line) and 0.3 eV (red dash line), at a temperature of 80 K and a pulse fraction of 20 %.

Fig. 2 :

 2 Fig. 2: Evolution of the apparent composition of B ( in at.%) for an equiatomic alloy (A/B) as a function of : (a) the pulse fraction ( in %) for different B energetic constants ( in eV), (b) also the pulse fraction but for different analysis temperatures ( in K), (c) the temperature for different pulse fraction and (d) the pulse frequency ( in Hz) for different pulse fractions

Fig. 3 :

 3 Fig. 3: Measured composition of Fe, Cr and Ni (at.%) in the FeCrNi alloy at high pulse fraction (25%) at 3 different temperatures (27, 57 and 92K) : composition measured from the raw data (Raw) and the one with multiple hits correction (Corrected).

  92 and 57 K) for a constant repetition rate of 200 kHz(fig.4.b). Whatever the temperature, a similar trend is experimentally observed. The apparent composition of Cu decreases when the pulse fraction decreases. However, at a very low pulse fraction (5%) and high temperature, measured Cu amount goes up. At high pulse fractions, which means at low electric field between pulses, the evaporation probability of Ni and Cu atoms between pulses is relatively low, explaining that the apparent composition is close to the nominal. Reducing the pulse fraction means increasing the electrical field induced by the DC voltage, his tends to increase the evaporation probability between pulses. Since the evaporation field of Cu is lower than that of Ni, the probability to evaporate Cu between pulses is higher than Ni. This explains the PE of Cu and thus the decrease of the apparent Cu composition. By continuing to decrease the pulse fraction (and so increasing the electrical field at the DC voltage), the probability to evaporate Ni at the DC voltage increases significantly which balances the PE of Cu. It induces an increase of the apparent Cu composition (Fig.2.b).

Fig. 4 :

 4 Fig. 4: Measured Cu composition (at.%) (Ni in balance) as a function of (a) the pulse frequency f (kHz) and (c) the pulse fraction fp (%) for different APT analysis conditions.

  pulse fraction at three temperatures (27, 57 and 92 K) for a constant pulse frequency of 200 kHz is reported on Fig. 5.a and Fig. 5.b. Whatever the temperature, a similar trend is observed. The apparent Cr composition decreases when the pulse fraction decreases (Fig. 5.a), and inversely for the apparent Ni composition (Fig. 5.b). It should be highlighted that the apparent Fe composition is not constant and follows a similar trend like Ni. The model (Fig. 5.a and Fig. 5.b) reproduces well this trend. At high pulse fraction, the apparent compositions of Cr and Ni are close to the expected one.

Fig. 5 :

 5 Fig. 5: Measured Cr (a) and Ni (b) compositions as a function of the pulse fraction (fp in %). Fe is in balance of the sum of these 2 graphs. Full lines are results of the analytical model.

  the values of the energetic constant of Fe and Cu obtained from the model, it is observed that the highest constant of energy is for Fe and the lowest is for Cu. The values are: CFe = 0.38 ± 0.02 eV and CCu = 0.34 ± 0.02 eV. The value of the energetic constants of Fe (CFe) in FeCu is not the same than in the FeCrNi alloy (CFe = 1.13 ± 0.03 eV) and the value of the energetic constant of Cu (CCu) in FeCu is not the same than in the NiCu alloy (CCu = 0.65 ± 0.03 eV).

Fig. 6 :

 6 Fig. 6: Measured Cu composition as a function of temperature (K). In all cases, Fe is in balance and full line is the result of the analytical model. The pulse fraction and frequency are 20% and 200 kHz respectively.

Fig. 7 :

 7 Fig. 7: Maximum analysis temperature (T in K) as a function of the pulse fraction (fp in %) at different pulse frequency (f in kHz) for which there is no PE, for different alloys: (a) NiCu, (b) FeCrNi and (c) FeCu.

Takahashi

  et al. (Takahashi & Kawakami, 2014) on a very similar material (Fe-1.2Cu at.%). In their study, they measured the apparent composition of Cu as a function of the analysis temperature (35 -100K) at different pulse fractions (15, 20 and 25%) using an energy-compensated 3DAP with a largeangle reflectron (Oxford Nanoscience Ltd.) at a pulse frequency of 20 kHz and a pulse width ( ) of 10 ns. Their measurements are reported in Fig. 8. Using the energetic constants obtained in this study for the Fe (0.38 eV) and Cu (0.34 eV, table 1) in the FeCu alloy does not reproduce the evolution of the apparent composition of Cu as a function of the APT analysis conditions (Fig. 8.a). In table 2, the values of the energetic constants of Fe and Cu obtained by fitting the experimental data of Takahashi with the analytical model of this study (Fig. 8.b) are reported. First of all, the values obtained are

Fig. 8 :

 8 Fig. 8: Cu compositions (at.%) as a function of the analysis temperature (K) for different pulse fractions fp(15, 20 and 25%). Experimental data (dots) have been extracted from[START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]. Full lines are obtained from the analytical model of this study using energetic constants of Fe and Cu reported in (a) table 1 and (b) table 2.

  . The second one is a Fe based metal composed of Cr and Ni with the following nominal chemical composition: 19.5 at.% of Cr and 11.7 at.% of Ni (Fe is in balance). This alloy is composed of 80% of austenite and 20% of ferrite. The by the large number of studies of Fe based metals utilizing APT. It remains some interrogations about the APT quantitative measurements of Cu composition in Fe matrix. This last case was chosen regarding the large number of former studies focused on the understanding on experimental APT biases. This case is historically a model case for preferential evaporation investigations

austenite is enriched with Ni (12 at.% of Ni and 18 at.% of Cr) and the ferrite is enriched with Cr (10 at.% of Ni and 20 at.% of Cr), according to EDS measurements. The third alloy is also a Fe based metal with a nominal composition of 1.05 at.% of Cu. The choice of the last two alloys (FeCrNi and FeCu) was motivated

Table 1 :

 1 Energetic constant (Ci in eV) of Fe, Cr, Ni and Cu as a function of the alloys of this study: NiCu, FeCrNi and FeCu. The uncertainty corresponds to the standard deviation.

		Fe	Cr	Ni	Cu
	NiCu	-	-	0.76 ± 0.06	0.65 ± 0.04
	FeCrNi	1.13 ± 0.03	1.05 ± 0.03	1.17 ± 0.03	-
	FeCu	0.38 ± 0.02	-	-	0.34 ± 0.02

Table 2 :

 2 APT analysis conditions (T, fp, and f) applied to the Fe-1.2Cu (at.%) alloy[START_REF] Takahashi | A quantitative model of preferential evaporation and retention for atom probe tomography[END_REF]. The values of CFe and CCu (eV) obtained from the adjustment of the experimental results by the analytical model developed in this study are also reported.

	T (K)	fp (%)	f (KHz)	CFe (eV)	CCu (eV)
	40 → 105	15	20	0.51	0.32
	40 → 105	20	20	0.44	0.30
	40 → 105	25	20	0.38	0.31

Acknowledgments

A part of this work has been performed on the Genesis platform. Genesis is supported by the Région Haute-Normandie, the Métropole Rouen Normandie, the CNRS via LABEX EMC3 and the French

Conclusions

An analytical model is proposed that enables to quantify and predict the preferential evaporation.

The validity of the model is supported by experimental measurements, on three different alloys (NiCu, FeCrNi and FeCu). The strong influence of the analysis temperature and of the pulse fraction on the apparent composition has been confirmed and to a lesser extent the influence of the pulse frequency. Those influences are well reproduced by the model. Thus, the model can estimate the best analysis conditions, avoiding PE and leading to quantitative composition measurements.

Even more, the model can also provide some valuable information about the energetic constant linked to the evaporation process. They are tabulated values for a defined phase. In this study, they have been obtained from experimental measurements. The next step will be to confirm the values of those energetic constants, with some numerical approach (such as DFT), and thus to be able to predict the best APT analysis conditions for any kind of phase.


domain: sde sdu

text:
P Blanc
email: p.blanc@brgm.fr

A Burnol

N Marty

J Hellal

V Guérin

V Laperche

METHYLMERCURY COMPLEXES: SELECTION OF THERMODYNAMIC PROPERTIES AND APPLICATION TO THE MODELLING OF A COLUMN EXPERIMENT

Keywords: Methylmercury, reactive transport, percolation, sulfate reduction

Complexation with methyl groups produces the most toxic form of mercury, especially because of its capacity to bioconcentrate in living tissues. Understanding and integrating methylation and demethylation processes is of the utmost interest in providing geochemical models relevant for environmental assessment. In a first step, we investigated methylation at equilibrium, by selecting the thermodynamic properties of different complexes that form in the chemical system Hg-SO3-S-Cl-C-H2O. The selection included temperature dependencies of the equilibrium constants when available. We also considered adsorption and desorption reactions of both methylated and non-methylated mercury onto mineral surfaces. Then we assessed the kinetics of methylation by comparing a dedicated column experiment with the results of a geochemical model, including testing different methylation and demethylation kinetic rate laws. The column system was a simple medium: silicic sand and iron hydroxides spiked with a mercury nitrate solution. The modelling of methylmercury production with two different rate laws from the literature is bracketing the experimental results. Dissolved mercury, iron and sulfate concentrations were also correctly reproduced. The internal evolution of the column was also correctly modeled, including the precipitation of mackinawite (FeS) and the evolution of dissolved iron. The results validate the conceptual model and underline the capacity of geochemical models to reproduce some processes driven by bacterial activity.

Introduction

Mercury (Hg) is among the most toxic elements, and has many natural sources. Human activity, especially mining and the burning of coal, has increased the mobilization of mercury into the environment. For about 200 years, anthropogenic emissions have been greater than natural emissions (UNEP, 2013). Mercury occurs in various chemical forms. Most atmospheric Hg is gaseous elemental mercury (Hg 0 ). In surface water and soils it occurs as elemental mercury (droplets of liquid mercury) and as Hg(II) complexes [START_REF] Kim | Mercury Speciation by X-ray Absorption Fine Structure Spectroscopy and Sequential Chemical Extractions: A Comparison of Speciation Methods[END_REF].

Hg-containing minerals, such as cinnabar and metacinnabar (two polymorphs of HgS) and montroydite (HgO), can control its solubility [START_REF] Kim | Mercury Speciation by X-ray Absorption Fine Structure Spectroscopy and Sequential Chemical Extractions: A Comparison of Speciation Methods[END_REF]. Much human exposure to mercury is through the consumption of fish and other marine foods, since mercury is mainly introduced into the food chain as methylmercury (MeHg). In soils, the presence of MeHg results from a balance between different competing processes [START_REF] Skyllberg | Chemical Speciation of Mercury in Soil and Sediment[END_REF]: methylation and demethylation [START_REF] Cossa | A Michaelis-Menten type equation for describing methylmercury dependence on inorganic mercury in aquatic sediments[END_REF] reactions, formation of aqueous complexes and gaseous species and adsorption/desorption reactions onto inorganic and organic substrates.

The balance between those different mechanisms determines bioaccumulation and MeHg transportation.

Researchers have begun to use geochemical modelling to assess the fate of mercury in the environment. [START_REF] Bessinger | Reactive Transport Modeling of Subaqueous Sediment Caps and Implications for the Long-Term Fate of Arsenic, Mercury, and Methylmercury[END_REF] have proposed a comprehensive model to reproduce mercury and arsenic speciation in sediment caps and how it changes over time, including MeHg. [START_REF] Leterme | A reactive transport model for mercury fate in soilapplication to different anthropogenic pollution sources[END_REF] also developed geochemical modelling of a conceptual soil, to assess the relative proportion of mercury release in the atmosphere or transported through the soil column or trapped, either onto mineral surfaces or as minerals precipitated along the profile. [START_REF] Leterme | A reactive transport model for mercury fate in soilapplication to different anthropogenic pollution sources[END_REF] explained that in spite of being an important tool, geochemical modelling suffers from the lack of well characterized sites. Actually, the counterpart of being able to reproduce detailed reactive mechanisms is that those models may require an important input dataset, including site-specific parameters. Even if determined, the values may suffer from variability and heterogeneities. As an alternative, we propose building a model to reproduce the results of a less complex column experiment. The model itself would include all the complexity governing MeHg fate, including methylation/demethylation reactions, the formation of aqueous complexes and gaseous species and surface complexation reactions. [START_REF] Johannesson | Geochemical cycling of mercury in a deep, confined aquifer: Insights from biogeochemical reactive transport modeling[END_REF] conducted a comprehensive set of measurements in groundwater along a 13 km flowpath located within a confined aquifer in southeastern Texas, USA. Their biogeochemical model was able to highlight the main mechanisms (mineral dissolution and sorption onto oxide surfaces) responsible for the speciation of total Hg.

The aim of this study is to test geochemical modelling in a more controlled context like the column experiment performed by [START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF]. The geochemical calculations on Hg fate can then be somehow constrained or compared with respect to those experimental results. In addition, taking advantage of the analyses performed by [START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF], the calculations are especially focused on methylmercury fate (methylation/demethylation and transportation), allowing testing of the methylation/demethylation rates available to date in the literature. Before comparing the calculations with the experimental results, we include a critical selection for MeHg complexes, consistent with the database built up by [START_REF] Leterme | A reactive transport model for mercury fate in soilapplication to different anthropogenic pollution sources[END_REF] for Hg-bearing species. The selection extended to surface complexation reactions and methylation/demethylation rates, following the review and case study proposed by [START_REF] Bessinger | Reactive Transport Modeling of Subaqueous Sediment Caps and Implications for the Long-Term Fate of Arsenic, Mercury, and Methylmercury[END_REF] and [START_REF] Cossa | A Michaelis-Menten type equation for describing methylmercury dependence on inorganic mercury in aquatic sediments[END_REF].

Selection of thermodynamic properties for methylmercury aqueous complexes

Methylmercury is a strongly toxic complex that accumulates in the muscles and various living tissues of living organisms. After [START_REF] Thomassin | Le mercure et ses composés . Comportement dans les sols, les eaux et les boues de sédiments[END_REF], the methylation of mercury is favored in anoxic environments by the presence of sulfate-reducing bacteria and of sulfur.

Generally speaking, the methylation reaction proceeds this way:

                  (1)
Dimethyl products are found as both aqueous complexes (in basic solutions) and in gaseous form. Methylation of mercury is reversible. We selected MeHg species using thermodynamic data processed according to guidelines describes by [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF] and consistent with the previous selection by [START_REF] Leterme | A reactive transport model for mercury fate in soilapplication to different anthropogenic pollution sources[END_REF]. The thermodynamic parameters associated with complexation reactions have been collected and discussed from [START_REF] Erni | Relaxationskinetische Untersuchungen von Methylquecksilberübertragungsreaktionen[END_REF], [START_REF] Alderighi | Co-ordination chemistry of the methylmercury(II) ion in aqueous solution: a thermodynamic investigation[END_REF], [START_REF] Loux | An assessment of thermodynamic reaction constants for simulating aqueous environmental monomethylmercury speciation[END_REF] and [START_REF] Skyllberg | Chemical Speciation of Mercury in Soil and Sediment[END_REF], for various chemical systems, at 25°C. [START_REF] Loux | An assessment of thermodynamic reaction constants for simulating aqueous environmental monomethylmercury speciation[END_REF] are especially important, resulting from an extrapolation to infinite dilution of large experiment datasets. [START_REF] Alderighi | Co-ordination chemistry of the methylmercury(II) ion in aqueous solution: a thermodynamic investigation[END_REF] have measured, by calorimetry, the heat exchanged during various complexation reactions involving methylmercury. From these measurements, we were able to calculate the entropy of complexes, which are reported in Table 1. Actually, they provided Sr for reactions involving CH3Hg + as primary specie. In order to use these measurements, we have considered the reaction:

H Hg CH CH Hg 3 aq 4,         (2)
It was converted into an isocoulombic equilibrium using Ca++ and Ca(OH)+ species:

O H Ca Hg CH CaOH CH Hg 2 3 aq 4,             (3)
The third law entropy was calculated considering the one term approximation method from [START_REF] Gu | A one-term extrapolation method for estimating equilibrium constants of aqueous reactions at elevated temperatures[END_REF] and entropies from the Thermoddem database [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF]. The result allows obtaining the third law entropies from [START_REF] Alderighi | Co-ordination chemistry of the methylmercury(II) ion in aqueous solution: a thermodynamic investigation[END_REF] measurements. The whole results are reported in Table 1. In addition to the aqueous complexes we have included a gas phase, Hg(CH3)2,g which represents an extreme stage of the methylation process [START_REF] Thomassin | Le mercure et ses composés . Comportement dans les sols, les eaux et les boues de sédiments[END_REF].

(2) CH3HgSH

CH3Hg + + HS -= CH3HgSH 14.50

(2) (CH3)2Hg 2CH3Hg + = (CH3)2Hg + Hg ++ 13.00

(1) CH3HgCO3 - CH3Hg + + HCO3 -= CH3HgCO3 -+ H + -4.23

(2)

CH3HgHCO3 CH3Hg + + HCO3 -= CH3HgHCO3 2.60 (2) CH3HgSO4 - CH3Hg + + SO4 --= CH3HgSO4 - 2.64 (2) (CH3Hg)2OH + 2CH3Hg + + H2O = (CH3Hg)2OH + + H + -2.15 167.62 (2), (3) (CH3Hg)2S a CH3Hg + + CH3HgS -= (CH3Hg)2S 20.32
(2) Hg(CH3)2,g Hg ++ + 2CH4,aq = Hg(CH3)2,g + 2H + 8.82 306.00 (4) (1) [START_REF] Erni | Relaxationskinetische Untersuchungen von Methylquecksilberübertragungsreaktionen[END_REF]; (2) Loux ( 2007); (3) recalculated using reaction entropy from [START_REF] Alderighi | Co-ordination chemistry of the methylmercury(II) ion in aqueous solution: a thermodynamic investigation[END_REF]; (4) [START_REF] Wagman | NBS Tables of Chemical Thermodynamic Properties: Selected Values for Inorganic and C1 and C2 Organic Substances in SI Units[END_REF] a. Not selected (see text)

For the selection, we followed the approach promoted by [START_REF] Stumm | Aquatic chemistry: chemical equilibria and rates in natural waters[END_REF] where the methyl group is represented by the CH3 -anion. This formally identifies the methylated complexes and easily separates the inorganic and organic chemical system when required.

The selection was integrated in the Thermoddem database [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF] in order to use it with geochemical codes GWB (Bethke, 2004) and PhreeqC [START_REF] Parkhurst | User's guide to PHREEQC (Version 2) : a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF].

A first test of the database consisted in calculating the production of methyl complexes which would arise from the speciation model detailed in Table 1. After [START_REF] Leterme | Literature Review: Mercury fate and transport in Soil Systems[END_REF], the amount of MeHg in waters in contact with soil systems is usually close to 2%. A speciation calculation is conducted, using PhreeqC-2 with the above database and considering a solution with [NaCl] = with 10 -3 M and [Hg] = 10 -9 M. This amount was reached applying two different corrections:

-by modifying reaction (2) equilibrium constant from log10K = 3 to 2.5 when reactions from Table 1 a written with CH4,aq as primary specie -or by modifying CH4,aq = CH3 -+ H + equilibrium constant from log10K = -46 to -52.5 when reactions from Table 1 a written with CH3 -as primary specie.

Actually, we did not expect the relation between organic and inorganic carbon to be driven by thermodynamic equilibrium. The correction considered in the first test is still of small extent, especially because the value originally given by [START_REF] Erni | Relaxationskinetische Untersuchungen von Methylquecksilberübertragungsreaktionen[END_REF] was calculated and not measured and the uncertainty can be larger in that case. In addition, the fact that the results obtained for MeHg speciation may depend on the way the database is written is to be underline. For the rest of the calculations, we no longer consider the equilibrium between organic and inorganic reduced carbon. However it is important to note that when the database uses CH4,aq or CH3 -complexes as primary specie for the methylation reactions, this allows considering also the methylation for other metals like Sn or Pb [START_REF] Stumm | Aquatic chemistry: chemical equilibria and rates in natural waters[END_REF], jointly with Hg methylation. The database in Table 1 was also tested using activity diagrams of which examples are displayed in Figure 1 The database set up previously is now tested by modeling the MeHg rate obtained experimentally by [START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF] in a companion. To our knowledge, such comparison is rather unique for Hg methylation, up to now.

Only a brief description is given here and the reader referred to [START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF] for additional details. The experiment design is reported in Figure 2. The lower half the column is filled with sterile sand and the upper half with a sterile mixture of sand and iron oxides, initially enriched with Hg(+2). The column is inoculated with a bacterial consortium and the inflowing solution is supplemented with magnesium sulfate and sodium lactate to enhance the growth and activity of sulfate-reducing bacteria (SRB). The water flow is ascendant. Five septa set regularly along the columns enable water sampling from the different layers of the column without perturbing water flow or in situ experimental conditions. After an abiotic rinsing period, the system is inoculated with a bacterial consortium, and physical, chemical and microbial parameters are monitored in time and space, up to 143 days.

Model development

A specific reactive transport model was developed to reproduce the experimental conditions.

Methylation is described in the model following a suite of chemical reactions described in Figure 3, where MeHg formation arises from a rather complex process including different steps:

-a first step corresponds to the reduction of Fe(+3) from the dissolution of ferrihydrite.

It is reproduced using the model developed by [START_REF] Poulton | Sulfide oxidation and iron dissolution kinetics during the reaction of dissolved sulfide with ferrihydrite[END_REF] -meanwhile, sulfate undergoes a reduction induced by the activity and growth of SRB bacteria. The reduction is modeled using a first order rate law which rate constant is extracted from [START_REF] Bharati | A study on efficiency of five different carbon sources on sulfate reduction[END_REF] experiment (Table 2)

-both Fe(+2) and S(-2) are consumed to precipitate mackinawite (FeS,cr)

-cobaltihexamine (CoB-CH3) complexes with mackinawite surfaces, the methyl group CH3 -is released and combines in solution with dissolved mercury Hg ++ to form eventually the methylmercury complex CH3Hg + . Two rate laws were tested, a first order proposed by [START_REF] Bessinger | Reactive Transport Modeling of Subaqueous Sediment Caps and Implications for the Long-Term Fate of Arsenic, Mercury, and Methylmercury[END_REF] and a second law based on the work by [START_REF] Heyes | Mercury methylation in estuaries: Insights from using measuring rates using stable mercury isotopes[END_REF] (Table 2) and which rate corresponds to a balance between both methylation and demethylation rates.

The possible formation of complexes at the ferrihydrite surface is implemented, using capacity of ferrihydrite, using the [START_REF] Dzombak | Surface complexation modeling: hydrous ferric oxide[END_REF] model and database. Numerical modelling uses PhreeqC-2 code [START_REF] Parkhurst | User's guide to PHREEQC (Version 2) : a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] and the Thermoddem database [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF]. The conceptual model is based on 1D-cartesian geometry, as displayed in Figure 4. A tracer test has been successfully simulated to verify the hydrodynamic set of parameters used.

Surface complexation

Ferrihydrite surface

                1)H (z FeOX X OH Fe 1)H (z FeOX X OH Fe 1) (z w 1) (z s z z X z = Fe ++ ,

Results and discussion

The results were first verified at the column breakthrough point (Figure 5) and along the column (Figure 6) for the longest reaction time (143 days). The reduction of sulfates was correctly reproduced, globally. In that regard, [START_REF] Bharati | A study on efficiency of five different carbon sources on sulfate reduction[END_REF] experiment was selected because they were performing sulfate reduction by using lactate as substrate and carbon source, as in our case. However, sulfate reduction appears somewhat underestimated by the model, especially concerning sulfide production. The redox conditions in the column (and departure to equilibrium conditions) could be questioned in that regard.

Dissolved Fe(+2) at the outlet was quite correctly predicted and calculations corresponding to the concentrations measured in the different septa even matched the abrupt increase observed in the ferrihydrite-loaded part of the column. Such increase happens during a period when calcite precipitates. It also corresponds to the precipitation of Mackinawite, observed in the experiments by [START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF], using Raman spectroscopy. From the reaction displayed in Table 2, mackinawite precipitation happens to consumes protons which increases pH and can lead induce the precipitation of carbonates.

For dissolved mercury (Figure 5), the total concentrations were correctly predicted.

Methylmercury concentrations analyzed were somewhat bracketed by the calculation performed with the model proposed by [START_REF] Bessinger | Reactive Transport Modeling of Subaqueous Sediment Caps and Implications for the Long-Term Fate of Arsenic, Mercury, and Methylmercury[END_REF] and [START_REF] Heyes | Mercury methylation in estuaries: Insights from using measuring rates using stable mercury isotopes[END_REF] (Model 1 and Model 2 in Figure 5, and from the thermodynamic dataset. In addition, it enhances possible connections between inorganic and organic dissolved carbon forms, from the point of view of methylation processes. Such relations do probably not involve equilibrium reaction. There is a strong need for additional experiment data to test such hypotheses, including measurements that does not seems to be related, at first sight, like dissolved CH4 concentrations, for instance.

Figure 1 -

 1 Figure 1 -Stability relation between MeHg aqueous complexes at 25°C: A -for the carbonate sub-system; B -depending on sulfide and chloride activity; C -depending on sulfide activity and pH

  experiment[START_REF] Hellal | Mercury mobilization and speciation linked to bacterial iron oxide and sulfate reduction: A column study to mimic reactive transfer in an anoxic aquifer[END_REF]

Figure 2 -

 2 Figure 2 -Experimental design developed by Hellal et al. (2015)

Figure 3 -

 3 Figure 3 -Main reactions involved

Ferrihydrite

  S(+6) and S(-2) Fe decoupled into Fe(+2) and Fe(+3)

Figure 5 -

 5 Figure 5 -Concentration in dissolved elements analysed at the outlet of the column

Table 1 -

 1 Selection for thermodynamic properties of MeHg-bearing species

	Specie CH3 -	Equilibrium CH4,aq = CH3 -+ H +	Log10K (298.15 K) -46.00	S° (J/mol.K)	References (1)
	CH3Hg +	CH4,aq + Hg ++ = CH3Hg + + H +	3.00	65.91	(1), this work
	CH3HgCl	CH3Hg + + Cl -= CH3HgCl	5.45	142.91	(2), (3)
	CH3HgOH	CH3Hg + + H2O = CH3HgOH + H +	-4.53	110.71	(2), (3)
	CH3HgS -	CH3Hg + + HS -= CH3HgS -+ H +

Table 2 -

 2 Main parameters for reactive transport modeling

	Minerals	Chemical system

Table 2

 2

	respectively). The lowest concentrations

ACKNOWLEDGEMENTS

Financial support from the French Geological Survey (BRGM, Geomer Project) and from the EU through the Snowman IMAHg project is gratefully acknowledged. The authors would like to thank for BA Bessinger for his kind help.


Alexandre Y Goudreault

Daniel M Walden

Daniel L Nascimento

Adrian G Botti

Stephan N Stein- Mann

Carine Michel

Deryn E Fogg

Hydroxide-Induced Degradation of Olefin Metathesis Catalysts: A Challenge for Metathesis in Alkaline Media

Keywords: olefin metathesis, catalyst decomposition, N-heterocyclic carbene, water, aqueous metathesis, hydrogen-bonding, chemical biology

Hydroxide ion is shown to be a potent disruptor of Ru-catalyzed olefin metathesis, in a study of the Hoveyda cata- lyst HII. Addition of [N n Bu4][OH] immediately terminates metathesis via HII, an effect traced to formation of bis(hydroxide) complex HII-OH. The latter was synthesized for direct study. HII-OH initiates very slowly on reaction with olefins, and decomposes in the first cycle of metathesis. Computational analysis reveals rapid bimolecular coupling between HII-OH and its four-coordinate methylidene derivative. Importantly, fully decomposed catalyst also accelerates decomposition of HII-OH. The H-bonding capacity of the hydroxide ligand is proposed as a powerful driving force for decomposition.

Ruthenium-catalyzed olefin metathesis offers exceptionally powerful methodologies for the assembly of carbon-carbon bonds. 1 In many applications in total synthesis, [START_REF] Cossy | Metathesis in Natural Product Synthesis: Strategies, Substrates and Catalysts[END_REF][START_REF] Furstner | Metathesis in Total Synthesis[END_REF] pharmaceutical manufacturing, 4 and chemical biology, [START_REF] Bhushan | Genetic Incorporation of Olefin Cross-Metathesis Reaction Tags for Protein Modification[END_REF][START_REF] Isenegger | Concepts of Catalysis in Site-Selective Protein Modifications[END_REF][START_REF] Lin | The Allylic Chalcogen Effect in Olefin Metathesis[END_REF] metathesis is carried out on densely-functionalized substrates bearing polar functional groups, in the presence of variable amounts of water. We speculated that hydroxide ion might pose a common, unrecognized challenge to catalyst function under such conditions. At the extreme is the metathetical modification of proteins in water buffered to pH >7, a forefront application that necessitates use of the Ru complex in high stoichiometric excess. [START_REF] Isenegger | Concepts of Catalysis in Site-Selective Protein Modifications[END_REF] While clever strategies have been designed to accelerate metathesis relative to catalyst degradation, [START_REF] Lin | The Allylic Chalcogen Effect in Olefin Metathesis[END_REF] the basis of the problem remains ambiguous. Understanding the unintended, non-metathetical reactivity of the Ru=CHR bond under such conditions is thus of both fundamental and practical importance. The present work was aimed at assessing the impact of hydroxide on the productivity and fate of the second-generation Hoveyda catalyst HII, an exemplary, widely used metathesis catalyst.

Prominent among the decomposition pathways now known to disrupt Ru-catalyzed metathesis are those enabled by nucleophiles and Bronsted base (Scheme 1). Nucleophiles have been shown to attack the methylidene carbon of Ru-1, [START_REF] Botti | Nucleophilic amines can abstract the alkylidene ligand, as shown in Scheme 1a[END_REF][START_REF] Mcclennan | Nucleophilic phosphines can likewise abstract the [Ru]=CHR carbon. For a mechanistic study demonstrating this pathway for broad range of PR3-stabilized benzylidene and indenylidene metathesis precatalysts[END_REF] while Bronsted bases readily deprotonate the metallacyclobutane (MCB) intermediate Ru-2. [START_REF] Bailey | Decomposition of Olefin Metathesis Catalysts by Brønsted Base: Metallacyclobutane Deprotonation as a Primary Deactivating Event[END_REF][START_REF] Ireland | Decomposition of a Phosphine-Free Metathesis Catalyst by Amines and Other Nitrogen Bases: Metallacyclobutane Deprotonation as a Major Deactivation Pathway[END_REF] The potential engagement of hydroxide ion in either manifold was antici-pated. [START_REF] Sinha | Precedents for nucleophilic attack by hydroxide ion on ligands at Ru centres are found in contexts ranging from the water-gas shift reaction (WGSR) in aqueous alkaline media, to catalyst synthesis, to water oxidation catalysis[END_REF][START_REF] Camm | An important difference should be noted between decomposition by hydroxide itself, vs. hydroxide in methanol (a medium once widely used for metathesis in biologically-relevant contexts, the impact of which was discussed[END_REF][START_REF] Osman | As noted by a referee, exchange of chloride for fluoride also has a deactivating effect, which can be countered by addition of (TMS)2O to remove fluoride anions[END_REF] Unexpectedly, however, a potent new decomposition pathway was identified, which appears unique to Ruhydroxide species. Here we describe transformation of HII into bis-hydroxide complex HII-OH, and bimolecular decomposition of HII-OH during the first cycle of metathesis. Our attention was first drawn to the potential of hydroxide ion to hinder metathesis in studies of the impact of Bronsted base on metathesis productivity. [START_REF] Bailey | Decomposition of Olefin Metathesis Catalysts by Brønsted Base: Metallacyclobutane Deprotonation as a Primary Deactivating Event[END_REF][START_REF] Santos | Overcoming Catalyst Decomposition in Acrylate Metathesis: Poly-phenol Resins as Enabling Agents for Phosphine-Stabilized Metathe-sis Catalysts[END_REF] Yields were negatively affected by the presence of strongly basic enolate anions, [START_REF] Bailey | Decomposition of Olefin Metathesis Catalysts by Brønsted Base: Metallacyclobutane Deprotonation as a Primary Deactivating Event[END_REF] but dropped even further when water was added as a sacrificial proton source. [START_REF] Santos | Overcoming Catalyst Decomposition in Acrylate Metathesis: Poly-phenol Resins as Enabling Agents for Phosphine-Stabilized Metathe-sis Catalysts[END_REF] (In contrast, sacrifical phenols restored metathesis activity). Likewise suggestive was a preliminary survey of the impact of common contaminants on metathesis productivity. These experiments examined the impact of additives on turnover numbers (TON) in cyclization of diethyl diallylmalonate (DDM, A; Figure 1), with the rationale that any agents capable of disrupting this exceptionally facile ring-closing metathesis (RCM) reaction merit attention. As shown in Figure 1a, either water or morpholine C (a basic contaminant present in technical grade toluene) [START_REF] Nicola | First Scale-Up to Production Scale of a Ring Closing Metathesis Reaction Forming a 15-Membered Macrocycle as a Precursor of an Active Pharmaceutical Ingredient[END_REF] caused TONs to drop by approximately half, but a 50% further decrease occurred when both water and morpholine were present.

The premise that hydroxide ion might be responsible was tested via a knockdown experiment, in which [N n Bu4][OH] (a THF-soluble source of hydroxide ion) 17 was added during RCM. Metathesis activity immediately ceased (Figure 1b; red line), even at catalyst loadings 20x higher than those used in the original screen. To assess whether this drop reflects attack on the active species Ru-1 or Ru-2, or on the precatalyst HII, a second experiment was carried out, in which hydroxide was added prior to substrate. RCM activity (blue line) was completely suppressed. This suggests that hydroxide ion attacks HII to yield a ruthenium product that is either completely inactive, or decomposes in the first cycle of metathesis. Synthesis of the putative hydroxide complex was undertaken for closer examination. Accordingly, aqueous [N n Bu4][OH] was added to a solution of HII in THF (Scheme 2). [START_REF] Wappel | The ammonium salt was used, as reaction with excess KOH yielded an equilibrium mixture. Similar behaviour was reported in salt metathesis with KBr and KI[END_REF] As use of 1 equiv hydroxide per Ru resulted in 50% consumption of HII, a 2:1 stoichiometry was employed. A colour change from green to red occurred over the time of mixing, and 1 H NMR analysis revealed a new singlet for the benzylidene proton at 14.04 ppm (cf. 16.72 ppm for HII). Reaction was complete in <10 min even on 200 mg scale, and bishydroxide HII-OH was isolated in ca. 85% yield. Complete selectivity for salt metathesis was evident, as expected from reactions of related Ru alkylidenes with aryloxide ion, [START_REF] Catecholates | Electronic Effects of the Anionic Ligand in Ruthenium-Catalyzed Olefin Metathesis[END_REF] but in contrast with reactions of hydroxide with Ru-CO complexes, which yield Ru formates via attack on the carbonyl ligand. 12a,b With the exception of the Ru=CHAr signal, the chemical shifts and multiplicities of all proton signals for HII-OH accord closely with those for HII. An additional singlet was observed for the Ru-OH protons at 1.1 ppm, the assignment of which was confirmed by exchange with degassed D2O. [START_REF] Addison | Tau parameter analysis reveals a distorted trigonal bipyramidal geometry for Ru-1, as compared to distorted square pyramidal for HII (tau = 0.61 or 0.39, respectively; cf. values of 0 for a perfect square pyramid, and 1 for a perfect trigonal bipyramid)[END_REF] The structure depicted for HII-OH in Scheme 2 is that predicted by density functional theory (DFT) analysis: specifically, a distorted trigonal bipyramidal geometry, 21 with an HO-Ru-OH angle of 139.1° (Table S2). In comparison, the Cl-Ru-Cl angle for HII is nearly 20° larger (computed: 155.1°; crystallographic: 22 156.5°).

Scheme 2. Synthesis of HII-OH.

Consistent with the knockdown behaviour seen in Figure 1b, HII-OH proved unreactive toward DDM. Even with 10 mol% of HII-OH at 60 °C, <3% RCM was evident after 2 h (cf. 100% within 15 min at RT with 1 mol% HII as catalyst). Slow initiation of HII-OH is not surprising, given the inductive withdrawal of electron density from the Ru center by the oxygen ligands. The compressed HO-Ru-OH angle may also be relevant, as Ru metathesis catalysts with cis-anionic geometries are known to initiate very slowly. [START_REF] Kotyk | Geometric and Electronic Structure of a C1-Symmetric Ru-Aryloxide Metathesis Catalyst: An Experimental and Computational Study[END_REF] Computational analysis of the initiation step, undertaken using ethylene as a model olefin (Scheme S4a), [START_REF] Ashworth | Olefin Metathesis by Grubbs-Hoveyda Complexes: Computational and Experimental Studies of the Mechanism and Substrate-Dependent Kinetics[END_REF] revealed a higher energy barrier to cycloaddition for HII-OH, relative to HII (20.9 kcal/mol, vs. 16.7 kcal/mol). The resulting metallacyclobutane is trigonal bipyramidal in both cases, but intramolecular H-bonding of the OH ligands (ca. 2 Å) stabilizes a cis-anionic geometry for HII-OH, in contrast with the trans-anionic geometry seen for HII (Scheme S4b).

While this energy difference accounts for slower reaction of HII-OH, it does not account for the complete loss of metathesis activity. We infer that HII-OH is considerably more susceptible to decomposition. In examining the relevant pathways, we first considered those established for HII and related catalysts (see Introduction). Nucleophilic attack by hydroxide on the benzylidene carbon (cf. Scheme 1a) is expected to liberate the aldehyde HC(O)Ar (Ar = o-C6H4-O i Pr). [START_REF]Also established in sterically congested first-generation catalysts of the Grubbs class is alkylidene deprotonation by bound aryloxide, liberating the phenol and generating a Ru carbyne[END_REF] This aldehyde is indeed detected, but in minor, variable amounts, depending on rates of mixing. [START_REF] Kim | Small, variable proportions of water may also be relevant. Formation of benzaldehyde was earlier reported in a mass spectrometric study in which GII was exposed to water, and was attributed to nucleophilic attack by water on the benzylidene carbon[END_REF] The alternative possibility, in which a hydroxide ligand deprotonates the MCB Ru-3 (cf. Scheme 1b), is unlikely given the ca. 41 kcal/mol barrier calculated by DFT analysis (Scheme S5). A potent new decomposition pathway thus appears to be operative. Given that the sole difference between HII and HII-OH lies in the nature of the anionic ligands (and given that related Ru(OAr)2 and Ru(k 2 -O2C6R4) exhibit notably high metathesis productivity), [START_REF] Catecholates | Electronic Effects of the Anionic Ligand in Ruthenium-Catalyzed Olefin Metathesis[END_REF] the hydroxide groups appears to play a critical, negative role.

To gain deeper insight, we reacted HII-OH with ethylene, using a sealed NMR tube to retain any volatile products (Scheme 3). Loss of the [Ru]=CHAr signal for HII-OH was complete within 24 h. Unexpectedly, however, only ca. 50% of the HII-OH complex had participated in metathesis, as judged from the combined yields of styrenyl ether D (Scheme 3a) and propenes E/E' (Scheme 3b). These propenes are presumed to form via b-elimination from the MCB Ru-3, a well-established decomposition pathway for HII 27,[START_REF] Nizovtsev | Metathesis Catalysts Stability And Decomposition Pathway[END_REF] and other metathesis catalysts. [START_REF] Bailey | Bimolecular Coupling as a Vector for Decomposition of Fast-Initiating Olefin Metathesis Catalysts[END_REF] The computed barrier to elimination of E/E' from Ru-3 is comparable to that for cycloreversion (15.9 vs. 17.0 kcal/mol, respectively).

The fact that these organic products account for only 50% of the starting HII-OH is puzzling. As Ru(OH) complexes are known to form hydroxy-bridged dimers with remarkable facility, [START_REF] Nelson | Hydroxide Complexes of the Late Transition Metals: Organometallic Chemistry and Catalysis[END_REF][START_REF] Roesky | Organometallic Hydroxides of Transition Elements[END_REF] we queried whether bimolecular coupling might consume HII-OH prior to metathesis. We recently reported that HII and related metathesis catalysts decompose via dimerization of RuCl2(H2IMes)(=CH2), Ru-1. [START_REF] Bailey | Bimolecular Coupling as a Vector for Decomposition of Fast-Initiating Olefin Metathesis Catalysts[END_REF] In the case of HII-OH, slow initiation limits the concentration of the corresponding hydroxo complex Ru-4. This disfavours homo-coupling of two Ru-4 molecules, but opens the door to hetero-coupling with the large excess of HII-OH present (Figure 2 DFT calculations indicate that hetero-coupling of HII-OH is indeed thermodynamically favoured relative to ethylene binding. The latter is endergonic by 13.3 kcal/mol. Because these calculations are based on gas-phase entropies, however, they greatly exaggerate the entropic penalty to dimerization. If we adopt one proposed correction factor, and add 50% of the gas-phase entropy to account for the change from perfect gas to perfect solution, 33 the heterodimer is -12.4 kcal/mol more stable than HII-OH + Ru-4, whereas the ethylene complex lies at +14.9 kcal/mol. Hetero-dimerization is thus greatly favoured relative to ethylene binding (the requisite first step for formation of D and Ru-4). Consistent with this picture, kinetics experiments indicate that decomposition is first order in [Ru] (Figure S2). That is, formation of Ru-4 is rate-limiting. Two conformers of the anticipated [START_REF] Bailey | Bimolecular Coupling as a Vector for Decomposition of Fast-Initiating Olefin Metathesis Catalysts[END_REF]34,[START_REF] Leitao | Kinetic and Thermodynamic Analysis of Processes Relevant to Initiation of Olefin Metathesis by Ruthenium Phosphonium Alkylidene Catalysts[END_REF] heterodimer are predicted to be thermodynamically favoured with respect to HII-OH + Ru-4. These are transoid-and cisoid-Ru-6, of which the former is the more stable (DG -4.0 kcal/mol). Liberation of styrenyl ether D from transoid-Ru-6 is inhibited by the relative disposition of the two ylidene groups on opposite sides of the Ru2(µ-OH)2 plane. Precedents from the chloride system 29 suggest that elimination of D from cisoid-Ru-6 could be feasible, if the methylidene ligand can adopt the conformation shown in cisoid-Ru-6' (inset, Figure 2). However, the proportion of D liberated via the sum of metathesis and decomposition should then approach 100%. The observed 40% yield of D argues against such an elimination pathway. Instead, the cumulative data suggest that while bimolecular coupling is thermodynamically favoured relative to metathesis, C=C coupling and elimination is inhibited. To confirm that decomposed Ru-OH species can trap HII-OH, we added fresh catalyst to a solution of the decomposed material (Figure 3). Disappearance of the fresh HII-OH was indeed much faster than in the control reaction of HII-OH under N2.

(As expected, however, it is slower than decomposition of HII-OH under ethylene). Importantly, the corresponding experiment with HII caused negligible decomposition of fresh HII (Figure S3). The H-bonding capacity of the hydroxide ligands thus appears to be critical in promoting attack of decomposed Ru-OH species on fresh catalyst. While coupling of HII-OH with Ru-4 is thus plausible, we were unable to detect the alkylidene protons of Ru-6 by NMR analysis, or to observe agglomerated species by DOSY-NMR. This, as well as the steady degradation in NMR signal-to-noise ratios over the 24 h timescale of decomposition (Figure S11) is consistent with rapid transformation of Ru-6 into paramagnetic products. Paramagnetism may result from the versatile coordination modes and redox properties of the hydroxide ligand, [START_REF] Nelson | Hydroxide Complexes of the Late Transition Metals: Organometallic Chemistry and Catalysis[END_REF][START_REF] Roesky | Organometallic Hydroxides of Transition Elements[END_REF] although multisite alkylidene binding is also feasible. [START_REF] Carty | Ru4(CO)10(C=CHPri)(OH)(PPh2): A Tetranuclear Ruthenium Carbonyl Cluster with µ4-Vinylidene and Face-Bridging Hydroxo-Groups; X-Ray Crystal Structures Of Ru4(CO)10(C=CHPr i )(OR)(PPh2) (R = H or Et)[END_REF][START_REF] Hahn | Transition Metal Complexes Containing Bridging Alkylidene Ligands[END_REF] The foregoing demonstrates that hydroxide ion is an unexpectedly potent disruptor of Ru-catalyzed olefin metathesis.

Termination is traced to the slow initiation and rapid decomposition of the bis(hydroxide) complex HII-OH. A notable feature is the capacity of the decomposed Ru species to sequester and decompose the precatalyst HII-OH, behaviour that arises from the H-bonding capacity of the hydroxide ligand. These results highlight previously unrecognized challenges to metathesis under conditions that can generate hydroxide, and more particularly metathesis in alkaline water.

ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website. PDF file: experimental and computational details, NMR spectra xyz files: computed xyz coordinates and energies

  Scheme 1. Decomposition of Metathesis-Active Species by (a) Nucleophiles; (b) Bronsted Base. L = H2IMes; Red Arrows Indicate Sites of Attack.

Figure 1 .

 1 Figure 1. Impact of additives on RCM. (a) Water, morpholine C, or both. (b) [N n Bu4][OH] (2 equiv vs Ru).

32 Schemea

 32 Scheme 3. Products Generated in the First Cycle of Metathesis. (a) Via Metathesis Exchange. (b) Via MCB Decomposition. a a Path (a) is quantified from the yield of D; Path (b) from the yield of E+E' (4% each).

Figure 2 .

 2 Figure 2. Competing reaction pathways for HII-OH: ethylene binding, vs. hetero-coupling with Ru-4. Gibbs free energies (kcal/mol) computed at the PBE-D3M(BJ)/cc-pVQZ+ECP28MDF/PCM(Benzene)// M06L/cc-pVDZ+ECP28MDF) level of theory. The free energy for the heterodimer is underestimated, owing to exaggeration of the entropic penalty to dimerization: see text.

Figure 3 .

 3 Figure 3. Accelerating effect of decomposed catalyst on the decomposition of HII-OH. Black: (left) Decomposition of HII-OH under C2H4; (right) impact of decomposed HII-OH on fresh precatalyst. Green: proportion of D formed during experiments indicated with black lines).

AUTHOR INFORMATION

Corresponding Authors *dfogg@uottawa.ca, carine.michel@ens-lyon.fr

ACKNOWLEDGMENT

The University of Ottawa, CNRS, and ENS Lyon are thanked for support via the International Associated Laboratory 'Fundamental Catalysis for Green Chemistry' (FUNCAT). The Natural Sciences and Engineering Research Council of Canada (NSERC), the SYSPROD project and AXELERA Pôle de Compétitivité for financial support (PSMN Data Center) are thanked for financial support.