Giacomo Clementi
email: giacomo.clementi@femto-st.fr

Giulia Lombardi

Samuel Margueron

Miguel Angel Suarez

Eric Lebrasseur

Sylvain Ballandras

Joël Imbaud

Franck Lardet-Vieudrin

Ludovic Gauthier-Manuel

Bernard Dulmet

Joel Imbaud

Ludovic Gauthier- Manuel

Mickael Lallart

Ausrine Bartasyte

LiNbO3 films -a low-cost alternative lead-free piezoelectric material for vibrational energy harvesters

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

Introduction

In recent years, a strong research effort has been devoted to harvest the energy available in the environment and use it as an electrical power source to power IoT (Internet of Things) applications. Some examples include wheel sensors, structural health monitoring, wearable and portable healthcare devices, distributed wireless sensor networks in smart agriculture, home and industry smart automation, and everywhere where reliable and long-lasting primary electrical energy source (i.e., conventional batteries) cannot be used (for example due to difficult access or harsh environment). Energy harvesting (EH) from vibrations has become a focus of interest during the past decades in line with the advent of very low (< 100 µW) power and portable electronics. Over the last decade, miniaturization of harvesters using MEMS technology with piezoelectric films or nano-composites came into the focus of interest in order to harvest energy from vibrations and to power small systems such as wireless nodes and sensors [START_REF] Spreeman | Electromagnetic Vibration Energy Harvesting[END_REF][START_REF] Beeby | Energy harvesting vibration sources for microsystems applications[END_REF]. Hence, a particular interest has been placed on the possibility of integrating the transducer with the electronic part on the same wafer.

At present, many different ferroelectric (PbZr1-xTixO3 (PZT), BaTiO3 (BTO), K1-xNaxNbO3 (KNN), etc.) and non-ferroelectric (AlN, ZnO, etc.) piezoelectric materials in the form of films, nanostructures and ceramic/crystals bonded on wafers are explored for the fabrication of Piezoelectric Vibration Energy Harvesters (PiViEHs). Obtaining high power output from piezoelectric harvesters in many applications requires a significant electromechanical coupling, k; this resulted in the preference and common use of bulk PZT in piezoelectric harvesters. Recently, it was demonstrated that it was possible to generate an output power of 1.2 mW (at resonance of 250 Hz from a base excitation) vibration sources by using six advanced 5 x 5 cm² PZT bimorph beams [START_REF] Yeo | Strongly (001) Oriented Bimorph PZT Film on Metal Foils Grown by rf-Sputtering for Wrist-Worn Piezoelectric Energy Harvesters[END_REF]. Nevertheless, the large scale of global deployment for IoT applications requires to consider the piezoelectric material grey energy, abundance, recyclability and toxicity (ROHS compliance, REACH regulation). Therefore, in future, PZT has to be replaced by lead-free materials [START_REF] Tian | A Review of MEMS Scale Piezoelectric Energy Harvester[END_REF], whatever its form and shape. Non-ferroelectric piezoelectric materials such as ZnO and AlN and their derivatives, have much lower k factor than PZT (by one order of magnitude, typically), but offer compatibility with conventional integrated circuit technology fabrication process. Recently, it was shown that the transverse piezoelectric coefficient and the figure of merit of the well-known piezoelectric film material AlN (001) increase considerably by partially substituting Al by Sc [START_REF] Matloub | Piezoelectric Al1-xScxN thin films: A semiconductor compatible solution for mechanical energy harvesting and sensors[END_REF][START_REF] Akiyama | Influence of scandium concentration on power generation figure of merit of scandium aluminum nitride thin films[END_REF]. Further effort is done to increase Sc concentration within the films to achieve electromechanical coupling coefficients similar to that of PZT. One of the highest power density values (1.6 mW.cm -3 ) among the micro-PiViEHs with wide bandwidth of 253 Hz was achieved by EH based on lead-free KNN films [START_REF] Van Minh | High Performance Nonlinear Micro Energy Harvester Integrated with (K, Na)NbO3/Si Composite Quad-Cantilever[END_REF]. However, synthesis of KNN films is still far from being a routine due to difficulty to control alkaline oxide composition [START_REF] Wu | Potassium-sodium Niobate Lead-Free Piezoelectric Materials: Past, Present, and Future of Phase Boundaries[END_REF], preventing their commercial application as energy harvesters which remains a niche market.

On the other hand, lithium niobate (LiNbO3) crystal is an industrially produced piezoelectric material easily accessible, rare-earth and toxic-element-free, cheap, available in form of wafers (with diameter up to 6 inches), widely exploited for developments of acoustics and optical devices [START_REF] Bartasyte | Toward High-Quality Epitaxial LiNbO3 and LiTaO3 Thin Films for Acoustic and Optical Applications[END_REF], and presenting similar efficiency in energy harvesting as commonly used PbZr1-xTixO3 (PZT) [START_REF] Tian | A Review of MEMS Scale Piezoelectric Energy Harvester[END_REF]. The major advantages of LiNbO3 over PZT are: (i) extremely chemically inert material; (ii) very high Curie temperature (> 1150 °C) thus compatible with EH at high temperatures (PZT limit < 150 °C). However, the LiNbO3 applications in acoustics are limited to 300 °C by the increased losses at high temperatures due to ionic conductivity. It is important to note that the requirements in terms of losses are much lower in the case of energy harvesting applications. Although the implementation of LiNbO3 crystals as hightemperature transducers (up to 1000 °C [START_REF] Baba | High temperature ultrasonic transducer up to 1000°C using lithium niobite single crystal[END_REF]) and preliminary investigations as energy harvesters (at least up to 500 °C [START_REF] Le Boulbar | Study of Y-cut LiNbO3 (010) Crystal Under Oscillated Vibration at High Temperature for Energy Harvesting in Hostile Environment[END_REF]) were demonstrated, further studies are needed to confirm the suitability of LiNbO3 for high-temperature applications in actuators and energy harvesters, especially when considering application-oriented designs. The piezoelectric energy harvesting demonstration was investigated so far by using industrially available LiNbO3 wafers with thickness of 500 ÷ 1000 m [START_REF] Funasaka | Piezoelectric Generator Using a LiNbO3 Plate with an Inverted Domain[END_REF][START_REF] Bedekar | Comparative Study of Energy Harvesting from High Temperature Piezoelectric Single Crystals[END_REF][START_REF] Vidal | Low-frequency vibration energy harvesting with bidomain LiNbO3 single crystals[END_REF]. However, LiNbO3 presents dielectric constant much lower than those of piezoelectric ceramics (unconstrained ε T 33/ε0 = 28.85 and ε T 11/ε0 = 84.45 [START_REF] Kovacs | Improved material constants for LiNbO3 and LiTaO3[END_REF]). In the case of micro-energy harvesters where lateral dimensions are limited, such thick wafers cannot be used due to issues in impedancematching with EH circuits as well as structural compatibility with the substrate. Moreover, bulk LiNbO3 crystals are very brittle and only low displacement can be attained. Therefore, LiNbO3 film technology has to be implemented in vibrational energy harvesting to overcome such issues and provide realistic operations. Despite their promising properties, the application of LiNbO3 films in piezoelectric vibrational energy harvesting is still very little studied and considerable efforts have to be done towards their integration in the conventional processing of MEMS and EH devices.

In this paper, we experimentally demonstrate a suitable microfabrication process and the successful application of vibrational energy harvesters based on thick (10 to 30 µm) single-crystal LiNbO3 films bonded on Si substrates. The capacitance, electromechanical coupling and power density were studied analytically and designed with respect to the target application, while resonant frequencies, voltage and displacement response of studied structures were simulated by Finite Element Method.

Hence, the potentials of LiNbO3 piezoelectric films for EH are confirmed, showing comparable and even higher power densities than conventional Pb-based and Pb-free energy harvesters.

Theoretical Considerations

LiNbO3 belongs to 3m point group, showing three plane-mirror symmetry. Moreover, it is also a part of the space group R3c, where crystals show threefold rotation along c-axis, or [0001] direction. To investigate the material properties of LiNbO3, we started from a reference system where the crystallographic c-axis is parallel to Z-axis in the standard orthogonal direction. Then, to model a specific orientation cut for LiNbO3, we have to consider a plate where the X-axis is parallel to a-axis, and the perpendicular Y-axis is in the same plane. In this configuration we can improve the electromechanical coupling of the material starting from a standard 90° (YXl) or ZX plate (orientation defined according IEEE Std-176 convention [16]). To model the piezoelectric element orientation, we used the matrix notation where i, j = 1,2,3 are defined as in Fig. 1a. In order to increase the piezoelectric response, we considered the rotated piezoelectric tensor for a beam that was oriented along the rotated Z'-axis of LiNbO3, while the electrical displacement of the charges was rotated along the Y'-axis. The orientation study is implemented using a rotation around X-axis for a given angle parameter ѱ. An example of LiNbO3 piezoelectric tensor anisotropy is represented in 3D tensor form for the specific orientation (YXl)/36° (Fig. 1b) that is considered in the present study. In this representation, we can see both positive and negative piezoelectric coefficient values (absolute value is ranging from 0 to 38 pC/N) of the tensor when a rotation is performed with ѱ = 36°. The obtained properties for this given single crystal orientation will be discussed in the simulation section in comparison with PZT-5A and other selected Pb-free materials. Before introducing the concept of electromechanical coupling, we shall use the following set of two equations for investigating the direct and converse piezoelectric effect:

{ 𝑆 = 𝑠 𝐸 𝑇 + 𝑑 𝑡 𝐸 𝐷 = 𝑑𝑇 + 𝜀 𝑇 𝐸 (1)
where S is the strain, T the stress, d the piezoelectric coefficient, s E the elastic compliance at constant electric field, ε is the permittivity at constant stress, E the electric field, and D the dielectric displacement.

When the cantilever undergoes bending deformation, the strain on the piezoelectric element gives an orthogonal displacement of charges; this configuration of the harvester is called transverse mode. For a given piezoelectric material, we define the material electromechanical coupling coefficient k, as the ratio between stored electrical energy and input mechanical energy, which is generally expressed as:

k ij =√ d ij 2 s jj E ε ii T (2)
Here, we assumed the most common transverse mode configuration. For the case of ceramics, we would consider k31, where '3' indicates the polarization direction, and '1' the deformation direction, where d31 is the piezoelectric coefficient, s11 the compliance and ε33 the permittivity for the given configuration. Two important figures of merit for piezoelectric materials are the one discussed in detail in [START_REF] Roscow | Modified energy harvesting figures of merit for stress-and strain-driven piezoelectric systems[END_REF][START_REF] Rödig | A Survey on Piezoelectric Ceramics for Generator Applications[END_REF]. These are defined respectively for stress-driven (FoM T ) and strain-driven (FoM S ) piezoelectric generators. The former is defined as:

FoM T = d ij 2 ε ii T (3)
which for a constant stress load does not depend on the compliance of the piezoelectric material.

Differently, in the case of strain-driven harvesters, it is necessary to take into account the fact that most of the times, the transducers do not work in open circuit conditions, therefore we have to consider the compliance in short circuit condition, finally FoM S is defined as:

FoM S = d ij 2 s jj E s jj D ε ii T (4)
Where s jj D is the compliance at constant electric displacement field. These two figures of merit are showing how for different excitation types, it is possible to maximize the output electrical energy and are useful to make a comparison between different materials. In general, it is clear that in both cases a high value of kij is required in order to design an efficient harvester.

When considering a high-level analysis of the system, the piezoelectric device can be modeled as a single degree of freedom oscillator resonating near one of its resonance frequencies. Consequently, the structure can be modeled as a spring-mass-damper system dynamically excited by an external force (or equivalently an acceleration), and generating a voltage V from the deformation displacement u. The system can then be described by the following set of dynamic equations:

{ F = Mü+ Cu̇+ K E u + αV I = αu̇-C 0 V ̇ (5)
where F is the external force, KE the open-circuit stiffness of the system, M the dynamic mass, α is the electromechanical force factor, I the current, C the viscous damping and C0 the clamped capacitance.

The electromechanical equivalent circuit for the piezoelectric transducer is presented in Fig. 2, in which the coupling term is represented by a transformer. The external force applied on the mechanical branch of the circuit generates a base velocity 𝑢̇ that is equivalent to a current in the electrical model, then the transformer with α ratio is converting the mechanical velocity into current in the electrical branch of the circuit. In this approximation, we can calculate the electromechanical coupling factor for the structure, k eff 2 defined as:

k eff 2 = α 2 C 0 K E + α 2 (6)
which represents the effective coupling of the structure during the energy conversion process.

Furthermore, the quality factor of the structure can be found as:

Q = √ MK E C (7)
In this paper, we will discuss how to tailor the material electro-mechanical coupling factor in order to have realistic impedance-matching between the piezoelectric transducer and the electronic interface, while for the structural coupling we will present the value measured for our given device.

Typically, the output voltage from our piezoelectric generator will be sinusoidal, whereas in order to power a sensor node, as per our application, a DC voltage supply is needed. Hence, the rectification circuit designed for our prototype is a half-bridge rectifier (Fig. 3). In this configuration we used two diodes and two smoothing capacitors Cr connected to an equivalent resistive load Rl. This interface can rectify and double the voltage amplitude degraded by the threshold voltage of the diodes. Eventually, VDC generated at resonance frequency f0, can be expressed as a function of the displacement magnitude uM as:

V DC = 2α f 0 R l f 0 R l C 0 +1 𝑢 M (8)
The harvested power from the rectified VDC voltage, is simply

P = V DC 2 R l
, giving the following equation:

P = 4α 2 f 0 2 R l (f 0 R l C 0 +1) 2 u M 2 (9)
In the experimental section, more details will be given regarding the electronic interface, along with a comparison between the theoretical and experimental harvested power.

Material and Methods

A commercial 500 µm thick (YXl)/36° LiNbO3 wafer (from Roditi) was used to fabricate thick film on Si substrate (Fig. 4). 200 nm thick Au layers with Cr adhesive layers, were deposited on one side of the LiNbO3 wafer and on one side of a 500 µm thick Si wafer. The Si wafer presented thermal oxide with thickness of 0.5 µm. Then, the LiNbO3 and Si wafers were bonded by means of mechanical compression of Au layers (EVG wafer bonder [START_REF] Baron | Temperature compensated Radio-Frequency Harmonic Bulk Acoustic Resonators Pressure Sensors[END_REF]). The LiNbO3 wafer was subsequently thinned by lapping steps to an overall thickness of 32 µm, which was followed by a micro-polishing step. Then, the Si wafer was polished down to 360 µm thickness. Aluminum electrodes with thickness of 300 nm were structured on the LiNbO3 surface by lift-off process using UV lithography and evaporation deposition technique. The

Simulations

To achieve some predictive results concerning the voltage output and the displacement response of our system, finite element modeling (FEM) was carried out with COMSOL Multiphysics software in different dynamic conditions. We modeled the structure in 3D as a unimorph bender with silicon substrate and LiNbO3 as piezoelectric element. Euler angles were used to implement the oriented cut.

Resonant frequency, vibrational modes and material properties were simulated thereafter by FEM.

In particular, the material properties of (YXl)/36° LiNbO3 cut, were simulated with both FEM software and analytical model. The values obtained for a rotation of 36° around X-axis were 65. For dynamic modeling, we used the same 3D model and proceeded to simulate the voltage response and displacement of the structure, based on the proposed design. The investigations were done at different acceleration levels in order to have a reference and to countercheck the cantilever response and the expected results. In Fig. 5 are shown the results of the simulations, with the acceleration levels were ranging from 0.1 g to 3.6 g. The study was performed in the frequency domain, considering the bending resonance frequency of 1.163 kHz, and studying the displacement and voltage response in open circuit conditions. The peak displacement, taking as a reference the free-end edge of the cantilever, is plotted for each considered acceleration. The low entity of the tip displacement is the result of the silicon substrate stiffness, which was modeled considering Si (100) orientation. We acknowledged that the displacement was measured approximately around the free end of the cantilever, so that the simulated value reached a maximum of 26.4 µm. On the right-hand side of the figure, the voltage response is presented. In this case, considering the piezoelectric coupling given by (YXl)/36° LiNbO3 orientation, the peak voltage simulated is reaching a maximum of 23.9 V. Also, at lower acceleration levels (1 g), the voltage response is in a useful range of values, with the peak voltage around 6.4 V. The results are given using the isotropic loss-factor approximation for the structure. As we expected for a simple cantilever, both displacement and voltage are evolving linearly when increasing the acceleration levels.

The 3D insets in the graph of Fig. 5 are representing the response at the simulated resonance frequency for the structure at 3.4 g, in order to compare with the experimental results.

Experimental Results and Discussion

During tests, the piezoelectric beam was clamped on a 3D-printed sample holder, while the top and bottom electrodes were put on a PCB board for the connection to the energy extraction circuit as well as monitoring the voltage output. The samples were characterized with a HP4194A network analyzer in order to investigate the capacitance and electromechanical coupling of the fabricated cantilevers. The structural electromechanical coupling factor, k eff 2 , and the quality factor, Q, were estimated from measured resonance and anti-resonance frequencies [16]. The dynamic characterization of voltage response and displacement was carried out separately. The associated experimental setup was composed of a shaker providing a base excitation, controlled by a waveform generator and a power amplifier. An oscilloscope was used for monitoring the voltage output of the piezoelectric sample through a high impedance probe (Fig. 6a).

As previously mentioned, the thickness of the piezoelectric transducer has to be adjusted in order to attain minimum necessary capacitance (nF order of magnitude) to ensure realistic impedance matching conditions. The dependence of clamped capacitance on the thickness of the lithium niobate layer with active surface area of 46 mm 2 is presented in Fig. 6b. The thickness of about 32 µm was selected for the experimentally studied structure as a trade-off between voltage magnitude, capacitance value, impedance matching conditions and structural (global) electromechanical coupling coefficient (i.e., taking into account the Si layer). The clamped capacitance, C0, of (YXl)/36° LiNbO3 layer measured through an impedance analyzer was 0.79 nF (at 2 kHz), which was very close to the expected simulated value (0.83 nF). The frequency dependence of impedance modulus of the 32 µm thick piezoelectric (YXl)/36° LiNbO3 crystal orientation in free conditions is presented in the inset of Fig. 6b.

According to the equivalent lumped circuit, the structural coupling k eff 2 of the structure was equal to 0.013. The Q-factor of the complete device, including the clamping system, estimated from the experimental data, was 23. This parameter can be improved changing the clamping system by means of thicker and heavier materials, which can lower the energy dissipation during the vibration cycles at the cost of size and weight.

The displacement and resonance frequency of the cantilevered (YXl)/36° LiNbO3/Si beam tip were measured by means of an optical vibrometer (Polytec MSA-500). For this purpose, the beam was driven with a periodic, slowly varying chirp focused around the first resonance bending mode. The mechanical response of the cantilever as a function of frequency is given in Fig. 6c. The measured resonance frequency value f0 was 1.14 kHz. Finite element simulations for this multilayer structure were also carried out, resulting in a first bending resonance mode at 1.16 kHz (Fig. 6c inset), in good agreement with the frequency found experimentally. The slight discrepancy was acceptable (5 % difference), and can be attributed to the perfect clamping conditions in simulation, fluctuations on the thickness value ( 2 µm) in the experimental apparatus and tolerance on the material elastic constants of both LiNbO3 and Si.

After the characterization of the structure, we proceeded to test the device under constant excitation with the shaker, in order to investigate the piezoelectric harvesting possibility. In Fig. 7a Vrms was approximately 15.8 V, giving a difference from the experimental value of 0.9 V. The reason behind the experimental and FEM values discrepancy (Table 2), is mostly due to a slight difference in terms of coupling and quality factors of the cantilever, as a result of using isotropic loss factor that was just an approximation of the real damping for the structure. This aspect can influence the displacement magnitude and thus the voltage response. Eventually, from the measured values we could estimate the force factor α, defined as α =

V pp u pp C 0 , giving 0.882 mN.V -1 , and displacement magnitude uM = 18.9 µm.

Finally, in order to validate the power that can be extracted from the (YXl)/36° LiNbO3/Si beam driven by a monochromatic excitation at the vibration frequency f0, a half-bridge circuit followed by a load, Rl , was connected to the piezoelectric material. The circuit is essentially composed by two 1N4148 diodes (Fast Switching Diode) and two smoothing capacitors, Cr, (each of 220 µF, resulting in an equivalent capacitor of 110 µF). Fig. 7b depicts the extracted experimental and theoretical (Eq. ( 7))

powers as function of load. The maximum power of 380 W was attained experimentally for a 500 k load impedance. Experimental results showed good agreement with the theoretical predictions (400 W maximum power); although a slight difference can be noted probably due to some losses in the diodes (not taken into account in the theoretical model). According to the results, an experimental power density of 8.26 µW.mm -2 has been measured. This value is consistent with the best results for high-power piezoelectric generators (Table 3). It is important to note that the LiNbO3/Si structures studied in this work were stiff and thus required high acceleration values in order to attain sufficient strain for high power densities. For the purpose of a fair comparison between our work and the state of the art, high frequency Si benders were taken into account. The table shows that even with normalized power density with respect to acceleration levels and frequency, the value of power of our device is comparable and even higher than other typical unimorph PZT and lead-free benders. In general, the power density is strongly correlated to the presence of a tip mass. For this reason, we adapted our finite element simulation to a smaller scale device in such configuration. The results for a micro mechanical transducer with silicon substrate are compared to the state of the art. The simulated device dimensions are 5 mm x 2 mm x 0.03 µm, with a tip mass of 250 µm, where the thickness of the piezoelectric film is reduced to 10 µm. The results show an instantaneous power output of 5.5 µW, that gives a very high normalized power density compared to other harvesters on silicon. Furthermore, with this simulation we can see how the presence of a proof mass lowers the resonance frequency while increasing the power density.

Finally, as an application example, the piezoelectric material and its electrical harvesting interface have

Conclusion

This paper reported the implementation of LiNbO3 layers as Pb-free piezoelectric transducers for a complete vibrational energy harvesting application. It was shown that commercially available (YXl)/36°

LiNbO3 oriented wafers can be successfully implemented in the form of thick single-crystal films on Si substrate and effectively used by adjusting the thickness of the piezoelectric layer and consequently the capacitance, and by using a proper electronic configuration for energy harvesting. Results showed that the reported system yielded performances close to those of PZT materials. We would like to stress out that such performance of micro-transducers cannot be attained by using bulk LiNbO3 wafers, due to impedance-matching issues. In fact, for bulk single crystals, the low value of the capacitance yields delicate interfacing with typical electrical circuit, while in this paper we are providing a more global approach towards energy harvesting applications. In terms of power density, experimental tests yielded 71 µW.cm -2 .g -2 by using the proposed composite structure vibrating at resonance frequency of 1.14 kHz, that is among best values even compared to lead-based (and other lead-free) materials commercially available. Moreover, FEM simulations showed promising performances for MEMS scale devices based on LiNbO3. Therefore, this result opens promising outcomes for lead-free energy harvesting solutions and their fast implementation. The fabrication of flexible structures based on thick LiNbO3 layers will be considered in future to attain this efficiency at low frequency and acceleration values [START_REF] Tian | A Review of MEMS Scale Piezoelectric Energy Harvester[END_REF]. Although one finds some examples of high frequency resonating beams (Table 3), we will consider lowering the resonance frequency in order to match frequency spectra available abundantly in the environment, and design and fabricate bimorph structures to further increase the generated power. Concerning the coupling factors, we tailored the properties of the material in order to optimize the electro-mechanical coupling of the material, but future steps will also consider the optimization of the structural coupling in order to have maximum energy efficiency for our device.

List of Tables Table 1. Comparison of dielectric and piezoelectric properties of (YXl)/36° LiNbO3 with bulk materials. harvester system (downswing in the waveforms correspond to transmission events).

List of Figures

  cantilevers were diced mechanically from (32 µm)LiNbO3/(400 nm)Au-Cr/(1 µm)SiO2/(360 µm)Si structure by means of a dicing saw. The final dimensions of the cantilevers, without considering the clamping, were 20 mm in length and 5 mm in width. The electrode was partially covering the structure, resulting in an active surface of 46 mm 2 . The Cr/Au layer used for wafer bonding was also acting as bottom electrode of the device. We show on Fig.4(e) the cross-section of the cantilever. The photograph was taken with optical microscope from a lateral side, we could clearly see the Cr/Au bottom electrode, while the upper layer was LiNbO3, and the bottom one the Si/SiO2 substrate. Finally, Fig.4(f) presents the cantilever after dicing.

  are shown sinusoidal voltage and displacement signals measured under 3.4 g base acceleration at resonance frequency. The peak voltage amplitude obtained was Vp = 21.1 V, which corresponded to a tip displacement value of up = 21.2 µm, measured with the vibrometer. The root mean squared value of voltage at the resonance frequency was 14.9 V. After comparison with experimental data, FEM simulations results showed a slight overestimation of the voltage and displacement response. In fact, compared to the measured value, FEM overestimated the tip displacement by 3.3 µm. The simulated

  been connected to a custom sensor node (low-power Microchip PIC 16F15313 microcontroller driving an EnOcean PTM 330 node [26], Vmin = 2.5 V -Fig. 8(a)). Fig 8(b) shows the voltage waveforms as well as the available energy on a 110 µF equivalent capacitor in such a configuration. As it can be deduced from Fig 8(b), the harvesting capabilities of the device allowed starting the sensor node (from zero energy initial conditions) after 9 seconds and then maintaining the possibility of sending data every 2 seconds (each transmission event consuming approximately 420 µJ) under continuous excitation.

Fig. 1 .

 1 Fig. 1. (a) Reference system for simulation of (YXl)/36° LiNbO3 orientation study. (b) Typical anisotropy of piezoelectric tensor of LiNbO3 after rotation, both positive and negative values of the coupling are represented.

Fig. 2 .

 2 Fig. 2. Equivalent circuit for the piezoelectric transducer.

Fig. 3 .

 3 Fig. 3. LiNbO3 generator connected to voltage doubler circuit and resistive load Rl.

Fig. 4 .

 4 Fig. 4. Microfabrication process flowchart for (YXl)/36° LiNbO3/Cr/Au/Cr/SiO2/Si heterostructure: (a) 200 nm of Cr/Au were sputtered on the surface of both Si and LiNbO3. (b) The two wafers were bonded together by mechanical compression and then thinned down by lapping. (c) The photoresist was spin-coated on the surface of LiNbO3, and then exposed to UV light though a mask. (d) After evaporation of 300 nm of Al, the top electrode was patterned by lift-off. (e) Optical microscope cross-section photograph for the layer structure after dicing. (f)Eventually, the structures were mechanically diced in cantilever shape with an active surface of 46 mm².

Fig. 5 .

 5 Fig. 5. Displacement and peak voltage results from FEM simulation at different acceleration levels. (insets) Deformation and voltage response of cantilever at resonance for 3.4 g.

Fig. 6 .

 6 Fig. 6. (a) Photograph of setup for dynamic measurements testing. (b) Thickness dependence of parallel plate capacitor based on (YXl)/36° LiNbO3 with active area of 46 mm 2 (b, inset) and frequency response of impedance modulus. (c) Displacement predicted by FEM simulation and measured experimentally by using optical vibrometer, of the studied (32 μm) (YXl)/36° LiNbO3/Au/SiO2/(360 μm)Si heterostructure. (c, inset) The simulated cantilever deformation (increases from blue to red) and the photograph of the experimentally fabricated transducer are given in the inset.

Fig. 7 .

 7 Fig. 7. (a) Displacement and generated voltage obtained through dynamic excitation with acceleration of 3.4 g. (b) Experimental and theoretical harvested power as a function of load by using (YXl)/36° LiNbO3/Si harvester.

Fig. 8 .

 8 Fig. 8. (a) Photograph of sensor node featuring PIC 16F15313 micro-controller driving EnOcean PTM 330 RF Transmitter Module. (b) Experimental waveforms of piezoelectric transducer voltage, rectified voltage and available energy by using (YXl)/36° LiNbO3 /Si

  in this way we can compare easily both electromechanical coupling and figure of merit. For stress-driven harvesters, (YXl)/36° LiNbO3 shows comparable FoM T with Pb-free materials and can be further improved by the choice of more suitable crystal cut. On the contrary, for strain-driven harvesters, (YXl)/36° LiNbO3 has the highest figure of merit, achieving the theoretical value of 19.5 kJ.cm -3 .

	relation s jj D = s jj E (1-k ij	2 ),
		3 for relative
	unconstrained permittivity ε r * , and -18.1 pC/N as effective piezoelectric coefficient d 23 * [20]. The results
	on the piezoelectric coupling factor from static FEM analysis gave the same conclusion as the analytical
	model. Although the transverse piezoelectric coefficient of (YXl)/36° LiNbO3 orientation is lower by
	one order of magnitude than that of PZT-5A (d31 = -171 pC/N [21]), its lower relative permittivity
	compared to that of PZT-5A (1700-1800 [22]) yields similar electromechanical coupling coefficient in
	this orientation (k 31 PZT-5A = 34 %, k 23 LiNbO D using the

3 = 32 %), making it a suitable alternative for energy harvesting applications. A comparison between the two coupling factors kij and FoMs is presented in Table

1

. All the materials in the table are bulk materials

[START_REF] Tsubouchi | Zero temperature coefficients SAW devices on AlN epitaxial films[END_REF][START_REF] Lenk | Elektromechanische Systeme, Band 2 Systeme mit verteilten Parametern[END_REF][START_REF] Jaffe | Piezoelectric transducer materials[END_REF]

, and we estimated the value of s jj

Table 2 .

 2 Comparison of measured and simulated parameters for LiNbO3 cantilever beam at 3.4 g.

	Material	(pm².N -1 ) sjj E	(pm².N -1 ) sjj D	εii T /ε0	(pC.N -1 ) dij	kij	(10 -12 m 3 .J -1 ) FoM T	(10 9. J.m -3 ) FoM S	Ref.
	AlN	3.53	3.48	9.5		-2	0.12		0.048	3.87	[23]
	KNN	8.2	7.6	496		-51	0.27		0.59	9.51	[24]
	(YXl)/36°	5.7	5.1	65.3		-18.1	0.32		0.57	19.5	[20]
	LiNbO3
	PZT-5A	16.4	14.5	1700		-171	0.34		1.94	8.17	[21,22]
	ZnO	7.87	7.59	11		-5.2	0.19		0.28	4.65	[25]
			Parameter		f0 (Hz)	up (µm)		C0 (nF)	Vrms (V)
			Measured	1140	21.2		0.79	14.9
			FEM		1163	24.5		0.83	15.8

Table 3 .

 3 Comparison of piezoelectric high power density (PD) generators. The works selected represent the state of the art for high frequency silicon based devices. The power is normalized with respect to the active area, acceleration level and frequency.

	Material	Mass Tip	(µW) Power	(mm 2 ) Area	(g) 𝑎 ⃗	(Hz) Frequency	(µW/cm 2 /g 2 ) Areal PD	(10 -2 µW/cm 2 /g 2 /Hz) Areal NPD	Ref.
	PZT	Yes	1.4	0.32	2	870	109	12.6	[27]
	PZT	Yes	22	120	4	1300	1	0.09	[28]
	PZT	No	3.4e-4	2.5	1	9275	0.014	1.5e-4	[29]
		Yes	13	2.5	1	2300	520	22.6
	KNN	No	1.1	56.1	1	1036	2	0.19	[30]
	KNN	Yes	0.731	0.21 1.02	1509	335	22.2	[7]
	ZnO	Yes	0.98	0.48 1.02	1300	196	15.1	[31]
	AlN	Yes	0.8	0.32	2	1495	63	4.18	[32]
	AlN	Yes	3.78	2.25	3	1041.4	19	1.79	[33]
	AlN	Yes	34.78	27.3	2	572	32	5.57	[34]
	AlN	No	0.003	3.21	0.4	4150	0.52	0.0126	[35]
		Yes	0.006	3.21 0.06	1140	52	4.56
	This work -(YXl)/36° LiNbO3
	(*)	No	380	46	3.4	1140	71	6.27	--
	(**)	Yes	5.5	2	1	684	275	40.2	--

(*) Experimental values for device without tip mass; (**) Simulated MEMS scale device with tip mass.

Acknowledgments

This research was funded by European MSCN-ITN-ENHANCE program grant number 722496, French RENATECH network and EUR EIPHI program grant number ANR-17-EURE-0002.


Maria A Kokh
email: kokh@uni-potsdam.de

Béatrice Luais
email: luais@crpg.cnrs-nancy.fr

Laurent Truche
email: laurent.truche@univ-grenoble-alpes.fr

Marie Christine Boiron

Chantal Peiffert
email: chantal.peiffert@univ-lorraine.fr

Aimeryc Schumacher
email: aimeryc@crpg.cnrs-nancy.fr

Quantitative Measurement of Rare Earth Elements in Brines: Isolation from the Charged Matrix Versus Direct LA-ICP-MS Measurements, a Comparative Study

Keywords: rare earth elements, brine, cation-exchange resin, ICP-MS, LA-ICP-MS

The quantification of the REEs in natural rocks and fluids is important not only for the sustainable use of geological resources but also for fundamental geological research. Due to significant improvements in experimental, modeling and analytical techniques, it was discovered that the REEs could be efficiently mobilized and transported by hydrothermal fluids.

Thus, analyzing the REEs in fluids, especially in highly saline solutions, is a prerequisite to understand their fate in hydrothermal fluids. An analytical methodology was established to determine the trace quantities of the REEs in aqueous solutions with compositions typical to seawater and brines. The developed protocol was applied for the REEs quantification in experimental sodium-rich carbonate-bearing hydrothermal solutions. For this purpose, we used two analytical approaches: i) the REEs were chromatographically isolated from the charged matrix and introduced in a single collector quadrupole ICP-MS, and ii) direct analysis of the REEs by LA-ICP-MS contents of experimental solutions loaded into glass capillaries without any additional isolation procedure. Both LA-ICP-MS and solution nebulization ICP-MS analysis after the REEs isolation provide identic data in terms of the REEs concentrations in brines and are consistent within analytical uncertainties. Being an express method, LA-ICP-MS could be recommended for the REEs quantification in brines. At the same time, the REEs' isolation from the charged matrix with subsequent ICP-MS analysis provides higher accuracy and precision, giving additional information for the REEs mass fractions that are below the detection limit of the LA-ICP-MS that was estimated at ~10 ng g-1 level.

Introduction

Geological and industrial significance of precise quantification of the rare earth elements in hydrothermal brines

The rare earth elements (REEs) are crucial in many modern technologies, such as mobile phones, screens, hard drives, electric vehicles, and play a key role in the development of techniques related to the renewable carbon-free energy industry. The rise of demand for many items that require rare earth metals induced an increase in metal mining and stimulated significant industrial efforts for their efficient recovery and recycling, as well as prospection of new deposits. The quantification of the REEs in natural rocks and fluids is important not only for the sustainable use of natural resources but also for the fundamental geological research: the rare earths are widely used as redox conditions proxies (e.g., Bau 1991, González-Álvarez and[START_REF] González-Álvarez | REE and HFSE mobility due to protracted flow of basinal brines in the mesoproterozoic Belt-Purcell Supergroup, Laurentia[END_REF], geothermobarometers (e.g., [START_REF] Gratz | Monazite-xenotime thermometry. III. Experimental calibration of the partitioning of gadolinium between monazite and xenotime[END_REF][START_REF] Heinrich | Monazite-xenotime miscibility gap thermometry. 1. An empirical calibration[END_REF][START_REF] Pyle | Monazite-xenotime-garnet equilibrium in metapelites and a new monazite-garnet thermometer[END_REF], geochronometers using the 147 Sm-143 Nd and 146 Sm-142 Nd (e.g., [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF]Hart 2005, Boyet andCarlson 2006), 138 La-138 Ce (Tanaka and Masuda 1982) systems, and geochemical tracers of various petrogenetic processes occurring in mantle, crust and seafloor hydrothermal systems (e.g., [START_REF] Luais | Comparative behavior of Sr, Nd and Hf isotopic systems during fluid-related deformation at middle crust levels[END_REF][START_REF] Schmidt | Rare earth element distribution in 400°C hot hydrothermal fluids from 5°S, MAR: The role of anhydrite in controlling highly variable distribution patterns[END_REF][START_REF] Cole | Rare earth elements as indicators of hydrothermal processes within the East Scotia subduction zone system[END_REF][START_REF] Mercadier | Origin of uranium deposits revealed by their rare earth element signature[END_REF][START_REF] Doucelance | What coupled cerium and neodymium isotopes tell us about the deep source of oceanic carbonatites[END_REF][START_REF] Chavagnac | Sulfate minerals control dissolved rare earth element flux and Nd isotope signature of buoyant hydrothermal plume (EMSO-Azores, 37°N Mid-Atlantic Ridge)[END_REF].

For a long time, magmatism and sedimentary processes were considered as two main forces controlling the distribution of the REEs on the Earth. However, during the last thirty years, due to significant improvements in experimental, modeling and analytical techniques (e.g., [START_REF] Wood | The aqueous geochemistry of the rare-earth elements and yttrium: 2. Theoretical predictions of speciation in hydrothermal solutions to 350°C at saturation water vapor pressure[END_REF][START_REF] Bau | Rare-earth element mobility during hydrothermal and metamorphic fluid-rock interaction and the significance of the oxidation state of europium[END_REF], Ghazy et al. 1993), it was found that the REEs could be efficiently mobilized and transported by hydrothermal fluids as a result of both regional or contact metamorphism (e.g., [START_REF] González-Álvarez | REE and HFSE mobility due to protracted flow of basinal brines in the mesoproterozoic Belt-Purcell Supergroup, Laurentia[END_REF]Kerrich 2010, Richard et al. 2013) and postmagmatic hydrothermal events (Banks et al. 1994, Salvi and[START_REF] Salvi | Alteration, HFSE mineralisation and hydrocarbon formation in peralkaline igneous systems: insights from the Strange Lake Pluton, Canada[END_REF]. These later processes may lead to their redistribution, fractionation and/or focused concentration.

Geothermal brines were even considered as a potential source of the REEs for future industrial extraction [START_REF] Smith | On the extraction of Rare Earth Elements from geothermal brines[END_REF].

Hydrothermal mobilization and transport of the REEs (as well as of other metals) from a parent magmatic body or metal-bearing rock is provided by water, preferentially in the form of aqueous complexes with the most abundant ligands in the crust. The knowledge about this complexation is a key for the understanding of the transporting capacities of hydrothermal fluids (e.g., Seward et al. 2014 and refs. therein). The first studies of the REEs solubilities in hydrothermal fluids implied their complexation with chloride, fluoride and sulfate anions (e.g., Banks et al. 1994, Salvi and[START_REF] Salvi | Alteration, HFSE mineralisation and hydrocarbon formation in peralkaline igneous systems: insights from the Strange Lake Pluton, Canada[END_REF], later acetate anions and hydrocarbons were found to be important for some specific geological environments (e.g., [START_REF] Lecumberri-Sanchez | Transport of rare earth elements by hydrocarbon-bearing brines: Implications for ore deposition and the use of REEs as fluid source tracers[END_REF]; finally, there is growing evidence that carbonate ligands could be also involved into the hydrothermal mobilization of the REEs (Fan et al. 2004, Liu et al. 2018, Vasyukova and Williams-Jones 2018).

In our particular case, we study the role of carbonate and bicarbonate ligands in the hydrothermal transport of the REEs. During this research, we carried out autoclave experiments and faced the necessity of determining the trace quantities of the REEs in experimental products, including solutions with high mass fractions of sodium comparable with those in seawater (up to 3.0 % m/m). Another area of our study is focused on monazite interaction with hydrothermal brines with high concentrations of alkali and alkali earth metals originating from seawater evaporites. These two types of experiments have led us to seek the best method for the REEs quantification in solutions in terms of implementation time, cost of analyzes as well as accuracy, precision and limits of detection. Here, we compare two different strategies that could be applied for the REEs quantification using ICP-MS: direct liquid microvolume analysis using the LA-ICP-MS versus the chromatographic separation of a sample matrix followed by pneumatic nebulization ICP-MS analysis.

Overview of ICP-MS methods for REE quantifications in geological samples

2.1.

ICP-MS for quantification of the rare earth elements in natural samples -alternatives,

advantages, and choice of mass-spectrometer configuration

Since the development of inductively-coupled plasma-mass-spectrometry (ICP-MS) in the early 1980s [START_REF] Houk | Inductively coupled plasma as an ion source for mass spectrometric determination of trace elements[END_REF]Date andGray 1981, 1983), this method is widely used to determine the REEs in natural samples. As an alternative to the MS, the trace quantities of REE could be also measured using inductively coupled plasma-atomic emission spectroscopy (ICP-AES), instrumental neutron activation analysis (INAA) and high-performance ion chromatography (HPIC). Another way of sample ionization, except for ICP that is commonly used for the REEs analyses, is thermal ionization, in particular, isotope dilution-thermal ionization mass spectrometry (ID-TIMS). Details about the advantages and negative aspects of the listed techniques could be found elsewhere (e.g., [START_REF] Ishikawa | Determination of rare-earth elements in rock samples by an improved high-performance ion chromatography[END_REF]. Briefly, ICP-MS is a method of choice for the REEs quantification if: i) a precise quantification of all the REEs including the monoisotopic (Pr, Tb, Ho, and Tm) is needed, ii) the REEs mass fractions in samples are expected to be at the level of 1 µg g-1 and below, iii) samples are unique and limited quantities of material are available for analyses, and iv) the nuclear reactor facilities are not accessible: nowadays INAA is practically replaced by ICP-MS due to its complexity and associated costs.

In our case, we used a single collector quadrupole based ICP-MS unit either coupled with a laser ablation unit, or equipped with traditional nebulization and spray chamber, in order to compare the results of the REEs measurements with the two different ways of sample solution introduction into ICP. Here, we compare the direct laser ablation of experimental solutions loaded into glass capillaries and the classical injection of experimental solutions aerosols after their matrix isolation using column chromatography with strong cation-exchange.

Alternative ICP-MS systems, such as sector-field (sf-ICP-MS) or time of flight (TOF) systems that both can have either single or multiple collector detection system (e.g., Sindern 2017) are out of the scope of the present study.

By using single collector quadrupole ICP-MS we assume, that the ratio of stable isotope of the REEs in our samples have a chondritic isotope composition, thus, only one isotope of each REE can be acquired to obtain the element concentration in a sample. However, we measured a few isotopes of the same REE (where available) during ICP-MS analysis to verify any biais due to uncorrected interferences.

Sample preparation of rocks, minerals and natural fluids applied for ICP-MS analyses of the Rare Earth Elements

During previous studies of the REEs quantification by ICP-MS, two main analytical issues were identified: 1) low abundances of the REEs in some natural objects that approach the detection limits of ICP-MS method (e.g., sub ng g-1 level in residual ultramafic rocks; Nakamura and Chang 2007; [START_REF] Ulrich | Accurate measurement of rare earth elements by ICP-MS after ion-exchange separation: application to ultra-depleted samples[END_REF], and 2) a strong matrix effect. High concentrations of matrix elements in solutions (essentially Si, F and NaCl-rich solutions obtained from digested quartz after crush-leach procedures) induce an enhancement or a suppression of the analytical signal, (Ghazy et al. 1993). For example, [START_REF] Eaton | Application of flow injection sample introduction to inductively coupled plasma-mass spectrometry for geological analysis[END_REF] detected a progressive signal suppression as the salt (NaCl) concentration in the sample solution was increased. These findings determined the main sample preparation procedures for the REEs analysis by ICP-MS: matrix elimination and target elements preconcentration followed by an introduction of sample solution into ICP.

The ion exchange resins are commonly used in chromatography and ICP-MS analysis for element separations. Conventional ion exchange resins consist of a cross-linked polymer matrix with a relatively uniform distribution of ion-active sites. A cross-link is a bond that links one polymer chain to another. The degree of cross-linking (DC), expressed quantitatively as the mole percent, relates to the number of groups that interconnect the polymerization mixture.

The DC affects the kinetics of the cation-exchange process [START_REF] Michaud | The role of cross-linking in ion exchange resins[END_REF], Kołodyńska et al. 2019). The resin AG 50W® is commonly used for REEs isolation from the matrix. It is composed of sulfonic acid functional groups attached to a styrene-divinylbenzene (S/DVB) copolymer lattice: the strands of polystyrene (S) are held together by DVB and X8 or X12 means DC = 8% or DC = 12%, respectively (here, the mole percent of DVB in the (S/DVB) copolymer lattice). [START_REF] Luais | Precise and accurate neodymium isotopic measurements by plasma-source mass spectrometry[END_REF] used a column of strong cation-exchange resin AG 50W®X12 in HCl acid media for high-precision isotope ratios measurements of neodymium and samarium in basalt samples (Reunion Island, Indian Ocean) using a multiple collector ICP-MS (MC-ICP-MS). This method allowed to isolate Heavy Rare Earth Elements and Yttrium (HREEs+Y) from the light and medium REEs (LREEs+MREEs). In the subsequent studies the REEs separation protocol mentioned above was combined with the other procedures of element separation to study the behavior of multiple isotopic systems during fluid-related deformation zone of leucogranite from the French Massif Central [START_REF] Luais | Comparative behavior of Sr, Nd and Hf isotopic systems during fluid-related deformation at middle crust levels[END_REF]) and metamorphic dehydration-hydration in eclogite and amphibolite samples from the Western Gneiss Region in Norway [START_REF] Martin | Behavior of trace elements in relation to Lu-Hf and Sm-Nd geochronometers during metamorphic dehydration-hydration in the HP domain of Vårdalsneset, Western Gneiss Region, Norway[END_REF].

Cation exchange resins methods before REE+Y measurements using ICP-MS techniques is required in some specific cases for precisely and accurately determine REE+Y contents, such as accurate measurements of geological reference materials (JGb2 leucogabbro and JR3 peralkaline rhyolite from the Geological Survey of Japan) [START_REF] Shishido | Determination of lanthanoids and yttrium in JGb2 and JR3 by inductively coupled plasma-mass spectrometry after cation-exchange pretreatment[END_REF]. This also ensures a pre-concentration of REE in highly depleted lithologies, such as ultra-depleted in REEs peridotites [START_REF] Ulrich | Accurate measurement of rare earth elements by ICP-MS after ion-exchange separation: application to ultra-depleted samples[END_REF]. or REE separation from highly charged matrix such as salts (Steinman et al. 2001). Halizc et al. (1996) similarly, developed an on-line preconcentration method for ICP-MS to quantify the REEs in seawaters and highly saline brines.

Here, on the basis of previous analytical developments acquired for solid samples in CRPG (Nancy, France) and ISTerre (Grenoble, France) laboratories, we customize an offline isolation protocol for brines, with highly-charged matrix, typical to our experimental systems.

LA-ICP-MS as a tool for express quantification of the REEs in solutions

LA-ICP-MS analyses of the REEs in minerals and fluid inclusions have already been performed successfully to tackle scientific issues such as abundance and fractionation of the REEs in natural minerals and fluid inclusions [START_REF] Leisen | Analyse chimique des inclusions fluides par ablation laser couplée à l'ICP-MS et applications géochimiques[END_REF], genesis of uranium deposits [START_REF] Mercadier | Origin of uranium deposits revealed by their rare earth element signature[END_REF][START_REF] Lach | In situ quantitative measurement of Rare Earth Elements in u²ranium oxides by Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry[END_REF], geochronometric dating of rocks and minerals using the radioactive REE isotopes 138 La, 147 Sm and 176 Lu (Sindern 2017), mineralogy of the REEs in coal fly ash [START_REF] Thompson | Analysis of rare earth elements in coal fly ash using laser ablation inductively coupled plasma mass spectrometry and scanning electron microscopy[END_REF], partial resettling of the U-Th-Pb geochronometers during monazite recrystallization [START_REF] Grand'homme | Mass transport and fractionation during monazite alteration by anisotropic replacement[END_REF], adsorption of the REEs on aluminum and iron (oxy)-hydroxides in bauxites [START_REF] Mondillo | Rare Earth Elements (REE) in Al-and Fe-(Oxy)-hydroxides in bauxites of Provence and Languedoc (Southern France): implications for the potential recovery of REEs as by-products of bauxite mining[END_REF]) and variety of fluids origin in iron oxidecopper-gold ore deposits revealed by the REEs signatures in fluorites [START_REF] Schlegel | Fluorite as indicator mineral in iron oxide-copper-gold systems: explaining the IOCG deposit diversity[END_REF].

LA-ICP-MS is widely used in geosciences due to the unique combination of its spatial resolution, fast acquisition of results and low detection limits which are supported by reasonable analytical costs. Spatial resolution is critical for some minerals and fluid inclusion assemblages that have micrometer to millimeter scale, overgrowths and zoning of minerals related to successive geological events. Thus, a spatially resolved analysis at an appropriate scale is the only way to determine the evolution of the mineral composition through time and thereby decipher multiple processes related to geochemical evolution during single crystal growth (e.g., [START_REF] Lach | In situ quantitative measurement of Rare Earth Elements in u²ranium oxides by Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry[END_REF].

The use of LA-ICP-MS for solutions historically originates from the challenging studies of mineral fluid inclusions, that are complicated by very small quantities of solution in individual fluid inclusions typically ranging from 10 -13 to 10 -6 g [START_REF] Roedder | Fluid inclusions[END_REF]). However, it was shown that this method could be also used for a small quantity of any aqueous solution (e.g., standard

or experimental) loaded into pure silica capillary that could be then ablated by laser like a fluid inclusion (Leisen et al. 2012a,b, Harlaux et al. 2015[START_REF] Grand'homme | Mass transport and fractionation during monazite alteration by anisotropic replacement[END_REF]. The matrix effects for elemental analyses using LA-ICP-MS were widely discussed in literature (e.g., [START_REF] Günther | Quantitative analysis of major, minor and trace elements in fluid inclusions using laser ablationinductively coupled plasma mass spectrometry[END_REF][START_REF] Velásquez | Situ Determination of Au and Cu in Natural Pyrite by Near-Infrared Femtosecond Laser Ablation-Inductively Coupled Plasma-Quadrupole Mass Spectrometry: No Evidence for Matrix Effects[END_REF], Leisen et al. 2012a[START_REF] Grand'homme | Mass transport and fractionation during monazite alteration by anisotropic replacement[END_REF].

Liquid samples can be quantitatively analyzed by their introduction into glass capillaries without any additional chemical treatment using NIST SRM glasses as reference materials and precisely quantified sodium concentrations as an internal standard [START_REF] Günther | Quantitative analysis of major, minor and trace elements in fluid inclusions using laser ablationinductively coupled plasma mass spectrometry[END_REF]. This procedure, which uses solid reference materials to quantify the REEs mass fractions in aqueous solution, is carefully validated in this study.

Experimental

Experimental conditions and setup of hydrothermal reactors

The solubilities of the REEs were studied in the following carbon-bearing and carbonfree systems at 100, 150, 200, and 250°C and at pressures ranging from 20 to 150 bar (Table 1).

Hydrothermal reactors were developed to combine injection and sampling of solutions in a multi-phasic system at high temperatures and pressures with the monitoring of pH in-situ. The detailed description of the experimental setup could be found elsewhere (e.g., [START_REF] Truche | Direct measurement of CO2 solubility and pH in NaCl hydrothermal solutions by combining in-situ potentiometry and Raman spectroscopy up to 280°C and 150 bar[END_REF]. Briefly, we used commercial bolt-closure reactors (Parr Instrument©) made of pure titanium (grade 3). The body and the head of the reactors were sealed with a PTFE gasket. The maximum working temperature and pressure of the reactors were 300°C and 200 bar, respectively. The internal volumes of the vessels varied from 250 to 500 ml. The temperature was monitored using an immersed thermocouple and was held constant within ±1°C by an electric furnace. The vessel was equipped with several connections that enabled regular sampling and injection of fluids, as well as adjustment of the working pressure.

Table 1. Summary of the experiments with the REE oxides conducted in this study.

The reactors were filled to two-thirds of their volume with an experimental solution.

The solution and the pressure vessel were bubbled and flushed with argon for half an hour to remove dissolved nitrogen and oxygen. After flushing with argon, the autoclaves were leak checked at ambient temperature at a pressure of 60 bar. The experimental solutions and solids were stirred at 200 rpm by an impeller driven by an external magnetic driver. Aliquots of solution (2-3 g) were regularly sampled during the experiments. The first sample during one sampling session served to remove the dead volume from the sampling tubes and to measure the pH at ambient conditions. The second sample was filtered through a 0.2 μm PTFE filter and acidified with 2 wt. % HNO3 solution (dilution factor 10) for the subsequent ICP-OES analyses of sodium and determination of the REEs using LA-ICP-MS and ICP-MS.

Chemical reagents used for the hydrothermal experiments

The initial solid phases of the REEs used for the hydrothermal experiments were the following oxide powders: yttrium oxide Y2O3 (Rare Earth Products Ltd., 99.999 % m/m, CAS № 1314-36-9), lanthanum oxide La2O3 (Sigma-Aldrich, 99.99 % m/m, CAS № 1312-81-8), cerium oxide CeO2 (Prolabo Rhône-Poulenc Ltd., 99.9 % m/m, CAS № 1306-38-3), praseodymium oxide Pr2O3 (Rhône-Poulenc Industries, 99.99%, CAS № 12036-32-7), neodymium oxide Nd2O3 (Sigma-Aldrich, 99.9 % m/m, CAS № 1313-97-9), samarium oxide Sm2O3 (Sigma-Aldrich, 99.9 % m/m, CAS № 12060-58-1), europium oxide Eu2O3 (Rhône-Poulenc Industries, 99.99 % m/m, CAS № 1308-96-9), gadolinium oxide Gd2O3 (Sigma-Aldrich, 99.9 % m/m, CAS № 12064-62-9), dysprosium oxide Dy2O3 (Sigma-Aldrich, 99.99 % m/m, CAS № 1308-87-8), erbium oxide Er2O3 (Sigma-Aldrich, 99.99 % m/m, CAS № 12061-16-4), ytterbium oxide Yb2O3 (Sigma-Aldrich, 99.99 % m/m, CAS № 1314-37-0). The mass of each oxide powder loaded into the autoclave was ~100 mg in all the experiments. Experimental solutions were prepared using the following salts:

Na2CO3 (Roth, ≥99,5 % m/m, ACS, anhydrous, CAS № 497-19-8) and NaHCO3 (Sigma Aldrich, ≥99.7 % m/m, ACS, anhydrous, CAS № 144-55-8). An aqueous solution of HNO3 (2 % m/m) was prepared from a bi-distilled acid.

Certified reference materials (CRM) used for ICP-MS, LA-ICP-MS and ICP-OES analyses and standard solutions preparation

All chemical procedures were carried out in clean room conditions. Preparation of reactants, standard solutions, and dilutions were performed by weight and using high purity

Chromatographic isolation and ICP-MS analyses of the REEs in experimental solutions

Polypropylen columns (Triskem® 10 cm high and 1.5 cm internal diameter) were filled with AG 50W ® cation-exchange resin (200-400 mesh, hydrogen form) with a degree of crosslinking of 8 mol % (or 12 mol % for some calibration tests). Considering the large amount of matrix with respect to the REEs contents (~60 g l-1 of chloride salts vs ~60 mg l-1 of the REEs for the calibration tests), a resin volume of 20 ml was used in order to avoid resin saturation. The matrix-rich REE standard solutions and sampled experimental solutions were slowly evaporated to dryness at 90°C in Savillex ® PTFE vials. The residue was dissolved in 5 ml of HCl (2.0 mol l-1) and loaded onto resin pre-cleaned with alternately HCl (6 mol l-1) and MQ water and conditioned by 20 ml of HCl (2 mol l-1). After complete elution of sodium (or complete elution of Na, Mg, K, and ~75 % m/m of Ca for the case of calibration tests) with 90 ml HCl solution (2.0 mol l-1), the fraction containing the REEs was collected in Savilex® Teflon vials with 155 ml of HCl solution (6.0 mol l-1). The REEs fraction was evaporated to dryness at 90°C and redissolved in 10 ml HNO3 2 % m/m solution for the subsequent ICP-MS analyses. All chromatographic isolation and evaporation steps were made in cleanroom conditions.

The REEs mass fractions in solutions were measured using the quadrupole ICP-MS X-

Series 2 ThermoScientific at CRPG laboratory (Nancy, France) (Table 2). The selected isotopes for REE quantification, and corresponding instrumental detection and quantification limits obtained after ten parallel measurements of matrix solution HNO3 (2 % m/m) are reported in Table 3. Detection limits for all the REEs were determined as the mass fraction equivalent of three times the standard deviation of the procedural blank. They range from 0.1 pg g-1 for Lu to 5 pg g-1 for La and 20 pg g-1 for Y, and are better than published values published, e.g., from 1 to 120 pg g-1 [START_REF] Ulrich | Accurate measurement of rare earth elements by ICP-MS after ion-exchange separation: application to ultra-depleted samples[END_REF]. Our detection limits are significantly lower relative to the REE mass fractions of all the experimental solutions analyzed in this work and are systematically lower than the REE contents determined in procedural blanks after the use of the chemical protocol that is described below (Table 6).

Table 2. Instrumental operating parameters for ICP-MS.

Table 3. The detection limits (DL, 3σ) and the quantification limits (QL, 10σ) for the ICP-MS analyses of the REEs, reported in pg g-1. (reference material and sample), the background was measured for 30 s, and the overall signal acquisition was recorded for 100 s. The glass reference materials NIST SRM 610 and NIST SRM 612 [START_REF] Jochum | Determination of Reference Values for NIST SRM 610-617 Glasses Following ISO Guidelines[END_REF] were used as reference materials, whereas sodium concentrations in solutions preliminary quantified using ICP-OES were used as an internal standard (for details see section 2.3). The spot size of 60 μm was used. The data reduction (quantification and limits of detection) was carried out using Iolite software [START_REF] Paton | Iolite: Freeware for the visualisation and processing of mass spectrometric data[END_REF] based on the equations developed by [START_REF] Longerich | Laser ablation inductively coupled plasma mass spectrometric transient signal data acquisition and analyte concentration calculation[END_REF]. More details on instrumental operating parameters are reported in Table 4.

LA-ICP-MS analyses of experimental solutions

Table 4. Instrumental operating parameters for LA-ICP-MS.

Results

Calibration tests and choice of the cation-exchange resin, validation of analytical protocol of off-line sample preparation for ICP-MS analysis of the REEs

Seven tests of column calibration on standard solutions were performed during this study. The off-line protocol for the REEs separation from sodium-rich matrix, e.g., type of resin, concentrations and volumes of acids, was established from calibration tests with simulated Na-K-Mg-Ca-rich standard solutions (Table 3). Using these solutions, we selected the type of cationexchange resin, as well as molarities and volumes of HCl acids used for subsequent elution of matrix and the REEs. The cation exchange columns were calibrated to obtain the best yields (100±7%) for the REEs using minimal volumes of acids during the elution process (Fig. 1). The two AG 50W® resins (200-400 mesh) with 8 and 12 mol % cross-linkage were tested for this purpose. The AG50W-X8 resin (8 mol % in DVB) was chosen because the use of AG50W-X12 (12 mol % in DVB) required more than 225 mL of HCl 6.0 mol l-1 solution to quantitatively collect all the REEs from the column, rising issues concerning procedural blanks, sample throughput and reactive consumption.

Here we report only the result of the last calibration with complete isolation of the REEs. A volume of 5 ml of the standard solution in HCl (2.0 mol l-1), containing MgCl2 5.18 g l-1, CaCl2 10.01 g l-1, NaCl 15.93 g l-1, KCl 25.38 g l-1, lanthanides and Sc 3.85 mg l-1, and Y 8.27 mg l-1, was loaded into the column. This matrix composition was chosen to simulate a composition of typical natural brine that always contains high concentrations of the alkaline and alkaline earth elements (see chapter 1.1 for details). Sodium, magnesium, and potassium were completely removed from the resin after the elution with 90 ml of HCl solution (2.0 mol l-1), whereas calcium was removed incompletely (76%) (Table 5, Fig. 1c). In our experimental study with carbonates, only sodium needed to be carefully isolated from the REEs, because its preferential ionization compared with other elements can disturb their ionization, thus, so we have not further refined the presented extraction protocol. The elution of the REEs with HCl solution (6.0 mol l-1, 155 cm 3 ) was complete during the final calibration, in the order HREEs (~40 ml), MREEs (~25 ml), and finally LREEs (~90 ml), with the REEs yields in the uncertainty range of 100±7% (Table 3). A complete Ca extraction of calcium could be reached by an increasing the HCl 2.0 mol l-1 volume of matrix elution, but not by increasing HCl molarity to 2.5 mol l-1 that would induce early elution of HREEs in the matrix fraction. Blank solutions of high purity 18.2 MΩ cm water and aqueous solutions of NaCl (1 mol l-1) were treated like experimental samples to quantify the procedural blanks. The obtained mass fractions of the REEs in the blank solutions varied from 2 to 650 pg g-1 (Table 6) depending on the REE and could not affect the outcome of our analytical results that are at the 10 ng g-1 level, with the exception of the lowest mass fractions of Ce, La, and Nd analyzed during this study. The obtained mass fractions of these elements were corrected for procedural blank levels.

Table 6. The REEs mass fractions in blank and standard solutions after the use of a cation exchange resin column, reported in pg g-1.

The analytical protocol for REEs separation from sodium for the subsequent ICP-MS analyses established during this study includes the following procedures:

i) weighing of the sample solutions;

ii) evaporation of solutions to dryness at 90°C and residue dissolution in 5 ml of HCl 2.0 mol l-1;

iii) preparation of the cation exchange resin columns filled with 10 cm 3 volume resin (AG® 50W-X8 200-400 mesh); iv) conditionning of the resin with HCl 2.0 mol l-1 (20 ml) v) loading of the prepared samples vi) add 90 ml of HCl 2.0 mol l-1 in each column for matrix elution vii) add 155 ml of HCl 6.0 mol l-1, for complete REE elution, and collection into Teflon vials .

viii) evaporation of the HCl 6.0 N REE-bearing fraction to dryness, at 90°C on a hot plate.

ix) redissolution of the dry residue in 10 ml of HNO3 2 % m/m (ultrasonic bath);

x) weighing of the obtained HNO3 solutions and calculation of dilution factors.

In order to estimate the accuracy of our off-line analytical protocol for the REEs separation from saline matrix described above, REE-bearing standard solutions doped with high contents of sodium, potassium, magnesium, and calcium (Table 6) were treated in the same manner as our experimental samples. The measured concentrations of the REEs are in a reasonable agreement with the REEs concentrations of prepared standard solutions, with an accuracy estimated within ±10% (3 SD) for the mass fraction range between 25 and 100 ng g-1.

This is similar to the calibration test performed for standard solution (±7%) (Table 5) for ~1 to ~10 µg g-1 REEs mass fractions. Our analytical protocol is validated for the lanthanides and yttrium measurements with a ±10 % accuracy, within a mass fraction range from ~10 ng g-1 to ~10 µg g-1. The reported accuracy estimation is comparable with the repeatability of the ICP-MS analysis for the same solution, whereas RSD for an individual analysis typically varied between 3 and 5%. 7. Typical relative standard deviations (RSD, %) for an analytical signal obtained on standard solutions during LA-ICP-MS measurements were found to be below 20% for the mass fraction range from 100 ng g-1 to 10 µg g-1 for all the REEs and about 50-60% for a standard solution containing 10 ng g-1 of the REEs. Accuracy and repeatability between measurements obtained by multiple ablations of the same standard solutions are illustrated in Fig. 3 and are reported in the Electronic Supplementary Material. Analyses of standard solutions with the REEs mass fractions lower than 1 µg g-1 are less accurate, with deviation from the regression line towards lower measured values. values for some standard solutions with REE mass fractions lower than 1 µg g-1.

Accuracy and repeatability of LA-ICP-MS analyses of the

The both reference materials -NIST SRM 610 and NIST SRM 612 -were measured twice before and after each analytical session. The NIST SRM 612 glass was quantified for the REEs as a sample: certified sodium concentration in NIST SRM 612 glass served as an internal standard and NIST SRM 610 glass served as a calibrator. The average error between the two quantifications of the REEs in NIST SRM 610 and NIST SRM 612 reference materials vary from 0,1 to 7% for all the REEs in both glasses (Electronic Supplementary Material).

Discussion

Comparison of the REEs quantification in experimental solutions with two introduction systems for quadrupole ICP-MS measurements: laser ablation and pneumatic nebulization after matrix purification

The mass fractions of rare earth elements (including Y) in the experimental solutions obtained using direct LA-ICP-MS and ICP-MS with pneumatic nebulizer (hereafter, pn-ICP-MS) after matrix isolation are reported in Tables 8-11 and graphically presented in Fig. 4.

As a whole, the mass fractions of the REEs measured in acidified experimental solutions (Fig. 4) are in a very good agreement with pn-ICP-MS for the case of Ce, Pr, Eu, Er and Yb within associated analytical uncertainties (~18-22%). Yttrium, Nd, Sm and Dy were well quantified within their typical RSD and reproducibility values (~25-30%, Tables 891011), whereas the data obtained for La and Gd are much less accurate (~47 and ~41% of the pn-ICP-MS values, respectively).

There are however few outliers for Ce. Indeed, few low Ce-samples (10-70 ng g-1)

show LA-ICP-MS mass fractions systematically lower than those obtained by pn-ICP-MS, with, however, similar typical analytical uncertainties in terms of 3RSD (%) for both methods (Tables 891011). Such deviation towards low Ce mass fractions is also seen for LA-ICP-MS Ce analyses of standard solutions of same concentration range (Fig. 3). Then, it is improbable that for the low concentrations, cerium mass fractions are overestimated by pn-ICP-MS analyses after matrix separation of sample solutions and blank correction. The calculated Ce mass fractions of those samples by LA-ICP-MS, using the regression line equation in Fig. 4, would be in the range of (12-85 ng g-1). Then, the observed discrepancy is more likely due to Ce concentrations being close to the detection limit of the LA-ICP-MS.

Table 8. Fluid compositions of experimental samples in the H2O-NaHCO3-REEs system. LA-ICP-MS data. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

Table 9. Fluid composition of experimental samples in the H2O-NaHCO3-REEs system. ICP-MS after ion-exchange resin Na-isolation. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

Table 10. Fluid composition in the H2O-Na2CO3-REEs system. LA-ICP-MS data. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

Table 11. Fluid composition in the H2O-Na2CO3-REEs system. ICP-MS after ion-exchange resin Na-isolation. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

Analyzing REEs in solutions by LA-ICP-MS

The current practice of LA-ICP-MS analyses of the REEs in solutions using NIST SRM glasses as reference materials and sodium as an internal standard was further verified in the present study. Three types of matrix were ablated for the REEs analyses: synthetic silicate RM glasses NIST SRM 610 and NIST SRM 612, NaCl-rich neutral brines and NaNO3-rich acidified experimental solutions. The obtained results show that the presence of matrix effects for the REEs analyses in solutions could not be totally excluded for using NIST SRM glasses standardization, at least for the MS configurations with nanosecond laser. In NaCl-rich neutral brines all the REEs mass fractions analyzed with NIST SRM glasses are systematically underestimated by 4 to 40% compared to the REEs mass fractions in prepared standard solutions (Fig. 3). At the same time, for the case of acidified NaNO3-rich experimental samples the obtained results are systematically overestimated if we assume the data of nb-ICP-MS preceding by off-line sample preparation as real values (Fig. 4, Tables 891011). Thus, the concentrations of the REEs in solutions could be both systematically overestimated and underestimated by LA-ICP-MS depending on the nature of the sample (here, essentially presence of Si, Cl, N matrix elements and pH of analyzed solution).

The matrix effects on some REEs observed in this study sometimes exceed the analytical uncertainties reported both in terms of RSD (%, 3σ confidence level), reproducibility of multiple ablations of the same solution and cross-analysis of the two NIST SRM glasses using sodium as an internal standard. For example, the analyzed mass fractions of Er in NaCl-rich neutral brines are systematically underestimated by ~40% of the values known from the preparation procedure of the standard solutions (Fig. 3). Such a high discrepancy for Er exceeds both the estimated values of RSD (~30%, 3σ confidence level) and reproducibility (~30%) from parallel LA-ICP-MS analyses, at least for the mass fractions above 100 ng g-1. However, for the same analytical session, the matrix effects for Nd, Sm and Gd are undistinguishable within the reported analytical uncertainties.

The solution matrix effects for the REEs vary in a very individual manner: the same REE could be well analyzed in one type of matrix using NIST SRM reference materials and be subjected to the matrix effect in another type of matrix as could be seen for Gd and Er (Table 12). Thus, the NIST SRM calibration method works, but some systematic variations that were observed in the present study encourage us to recommend an additional calibration using the REEs standard solutions with adjusted matrix type, loaded in glass capillaries. The precision of analyses could be further improved by adding an isotope spike of a single element (e.g., Sm or Nd) to sample solutions by weight and quantifying a single element with isotope dilution after LA-ICP-MS. Then this element can be used as precisely known internal standard to correct all other REEs for matrix effects.

Conclusions

The key points of this study are the following:

The established analytical protocol for the REEs quantification by ICP-MS in brines after matrix isolation with cation-exchange resin provides robust data for the REEs mass fractions as low as the 1 ng g-1 level.

LA-ICP-MS analyses of solutions loaded into capillaries and classical pneumatic nebulization ICP-MS analyses after saline matrix isolation with cation exchange resin provide consistent results for the REEs quantification in brines in a range of mass fractions between 10 ng g-1 and 10 µg g-1 within reported analytical uncertainties (RSD from 15 to 30% of a value for LA-ICP-MS). The precision level acquired during this study by LA-ICP-MS technique is acceptable and sufficient enough for the purposes of the experimental hydrothermal geochemistry.

LA-ICP-MS, being an express method, could be highly recommended for the REEs quantification in brines: in a single day of LA-ICP-MS analyses it is possible to measure up to 100 capillaries with REE solution, while it takes one month of cleanroom REE isolations to produce these analyses with classical ICP-MS with pneumatic nebulizer. At the same time, the REEs isolation from the charged matrix with subsequent ICP-MS analysis provides more precise results (±10% a value within 3SD confidential level), and is required for the REEs mass fractions that are below the quantification limit of the LA-ICP-MS that was estimated at the ~100 ng g-1 level. These results provide a framework for the selection of analytical methods in future studies, depending on the required accuracy of REE quantification.

-----------------------------------------------N/A---------------------------------------------------- 3-9 0.
±25 - ±20 ±20 ±20 ±25 ±20 ±25 ±25 ±25 ±25

903

"bdl" -below detection limit; N/A -not analyzed. The samples N 3-12, 3-13, and 3-14 were not analyzed 904 because of the low concentration of sodium that was used as an internal standard for LA-ICP-MS. The 905 results of measurements with an unexploitable signal during laser ablation are not reported (-).

906 907

18. 2

 2 MΩ cm MQ water (Elga Chorus system®) was used through this study. HCl and HNO3 acids were purified by double distillation using a Savillex™ DST-1000 sub-boiling distillation system (Savillex, USA).Calibration curves for the REEs analyses by ICP-MS were established relative to standard solutions containing 1, 10, 25 and 50 ng g-1 of the REEs in HNO3 matrix (2 % m/m).These standard solutions were prepared by weighting the certified CRM standard solution REE mix TraceCERT® Co. LLC Sigma-Aldrich, 16 elements, 50 mg l-1 in 2 % m/m nitric acid. Standard solutions containing 100 and 500 ng g-1 of the REEs were also prepared and analyzed as additional standards to check the linearity of the obtained calibration curves, which was useful for analyses of the most concentrated samples.Standard solutions with high contents of matrix elements (sodium, potassium, magnesium and calcium) were prepared to establish the off-line quantification protocol for the REEs separation from а charged matrix using cation-exchange resin. The following salts were weighted with the REE mix and yttrium CRM solutions and Milli-Q water: MgCl2•6H2O (Prolabo), CaCl2•2H2O (Merck), NaCl (99.5 % m/m, Acros Organics), KCl (99.5 % m/m, Roth pa ACS ISO Reagent). The prepared standard solutions were analyzed for major cations in SARM (CRPG, Nancy) using ICP-OES Thermo Fischer ICap 6500. An analytical signal calibration of sodium during ICP-OES analyses was performed using the sodium CRM for ICP (TraceCERT® Co. LLC Sigma-Aldrich, 1000 mg l-1 Na in 2 % m/m nitric acid).Standard solutions containing 10 ng g-1, 100 ng g-1, 1 µg g-1 and 10 µg g-1 of the REEs in the matrix of aqueous NaCl solution (1 mol l-1) were prepared to test the accuracy of LA-ICP-MS analyses. These standard solutions were prepared from the diluted REEs CRM (TraceCERT® 16 elements mentioned above) and NaCl salt (99.5 % m/m, Acros Organics). Sodium was added into the standard solutions to be used as an internal standard for all LA-ICP-MS analyses.Sodium concentrations in standard solutions and in experimental samples were measured by ICP-OES in SARM (CRPG, Nancy). The standard solutions with known amount of Na were loaded into glass capillaries.The CRM glasses NIST SRM 610 and NIST SRM 612 (matrix composition SiO2 72 % m/m, Na2O 14 % m/m, CaO 12 % m/m, Al2O3 2 % m/m) were used as calibrators for LA-ICP-MS. These glasses are certified for a limited number of elements by NIST. Thus, following ISO guidelines and the protocol of the International Association of Geoanalysts, the reference values for the REEs in NIST SRM 610 and NIST SRM 612 were taken from[START_REF] Jochum | Determination of Reference Values for NIST SRM 610-617 Glasses Following ISO Guidelines[END_REF].

Fig. 1 .

 1 Fig. 1. a) Photo of cation exchange resin; a) schematic illustration of a cation-exchange process

  REEs in solutions with simulated matrix loaded in glass capillaries, reproducibility of NIST SRM glasses analyses The accuracy of LA-ICP-MS analyses was verified by using standard solutions prepared by weighing (see section 2.3). Typical time resolved LA-ICP-MS signals and the REEs responses during capillary ablation are shown in Fig. 2. Limits of detection for each REE, as well as chosen isotopes, are reported in Table

Fig. 2 .

 2 Fig. 2. LA-ICP-MS analyses of the REEs in standard solutions.

Fig. 3 .

 3 Fig. 3. Results of the REEs analyses in standard solutions obtained using LA-ICP-MS (results for

Fig. 4 .

 4 Fig. 4. Comparison of the mass fractions of the REEs in solutions obtained using LA-ICP-MS and

  Blank MQ -REE-free Milli-Q solution treated like a sample; Blank salt -REE-free 1 mol l-1 NaCl solution treated like a sample; Standard 1, reference mass fractions: REEs (lanthanides and Sc) 25.1 ng g-1, Y 50.9 ng g-1;Standard 2, reference mass fractions: REEs (lanthanides and Sc) 51.0 ng g-1, Y 103.3 ng g-1.N/A -not analyzed; *Sc mass fractions were tentatively checked in blanks and standard solutions (yield 75-77%).

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. ICP-MS profiles of the REEs during the ablation of standard solutions in glass capillaries.

Fig. 3 .Fig. 4 .

 34 Fig.3. REEs analyses of standard solutions obtained using LA-ICP-MS (for other REEs see Electronic Supplementary Material). Analytical uncertainties (2SD) are expressed in the symbols' sizes. Solid lines and corresponding equations represent the linear fits of the analytical results obtained for the prepared by weight standard solutions, whereas analyses of the NIST SRM glasses (610 and 612) used as calibrators are plotted for information.

  LA-ICP-MS analyses of experimental solutions were carried out at the GeoRessources laboratory (Nancy, France). The LA-ICP-MS setup is composed of a 193 nm GeoLas Excimer laser (ArF, Microlas, Göttingen, Germany), with a microscope for sample observation and laser beam focus onto the sample, and an Agilent 7500c quadrupole ICP-MS. The experimental solutions were loaded into pure silica capillaries (320 µm int Ø, 435 µm ext Ø, ®Polymicro-Technologies).For each experiment, the lanthanides, 89 Y, and 23 Na were analyzed. Data were collected with an integration time of 0.01 s per channel for 23 Na, 28 Si, 29 Si, 0.02 s for 89 Y, 139 La, 140 Ce, 141 Pr, 146 Nd, 147 Sm, 153 Eu, 0.03 s for 157 Gd, 159 Tb, 163 Dy, 165 Ho, 166 Er, 169 Tm, 172 Yb, and 175 Lu. Data were acquired as raw counts per second (cps) using the time-resolved mode. For each analysis

Table 5 .

 5 Results of the final calibration of cation-exchange resin column AG 50W®X8 (200-400 mesh).

Table 7 .

 7 Mean values of detection (DL) and quantification (QL) limits acquired on standard solutions during one analytical LA-ICP-MS session, in ng g-1. Note that for individual analyses, the best DL values could rich ~10 ng g-1.

Table 1 .

 1 Summary of the experiments with the REE oxides conducted in this study.

	Tables

Table 2 .

 2 Instrumental operating parameters for ICP-MS. 139 La, 140 Ce, 141 Pr, 143 Nd, 146 Nd, 147 Sm, 149 Sm, 151 Eu, 153 Eu, 157 Gd, 159 Tb, 161 Dy, 163 Dy, 165 Ho, 166 Er, 167 Er, 169 Tm, 171 Yb, 172 Yb, 175 Lu

	ICP-MS model	X-Series 2 ThermoScientific
	Type	Quadrupole
	RF Power	1400W
	Cool gas flow rate	13.5 l min -1 Ar
	Auxilary gas flow rate	0.82 l min -1 Ar
	Sample gas flow rate	0.97 l min -1 Ar
	CeO/Ce	<0.03
	Ba ++ /Ba	<0.035
	Nebuliser	Microflow PFA
	Spray chamber	PC 3 ESI Peltier Chiller, cooled to 2°C
	Torch	Quartz glass torch
	Sample Cone	Ni 4450
	Skimmer Cone	Ni PS8R
	Detector mode	Dual (pulse and analogue counting)
	Dwell time / mass	Variable (10-15 ms)
	Mass resolution	Standard
	Solution uptake	peristaltic pump 12 rpm
	Acquisition Mode	Peak Jumping
	Number of sweeps	55
	Channels	5
	Number of repeats	3
	Calibration	Indium as internal standard with on-line injection
		Standard solution control every five measurements
	Isotopes	89 Y,

Table 3 .

 3 The detection (DL) and quantification (QL) limits for the ICP-MS analyses, in pg g-1. 89 Y 139 La 140 Ce 141 Pr 143 Nd 146 Nd 147 Sm 149 Sm 151 Eu 153 Eu 157 Gd Tb 161 Dy 163 Dy 165 Ho 166 Er 167 Er 169 Tm 171 Yb 172 Yb 175 Lu

	DL, 3σ 21 4.5	0.6	1.0	4.7	1.9	1.7	28	0.6	0.6	1.2
	QL, 10σ 37 11.4 1.3	1.8	9.6	4.5	3.6	43	1.5	1.3	2.8
	159 DL, 3σ 0.21 0.9	0.6 0.12 0.15 1.5	0.16 0.9	0.7 0.08
	QL, 10σ	0.48 1.8	1.3 0.28 0.38 2.9	0.36 2.2	1.8 0.21

Table 4 .

 4 Instrumental operating parameters for LA-ICP-MS. 89 Y, 139 La, 140 Ce, 141 Pr, 146 Nd, 147 Sm, 153 Eu, 157 Gd, 159 Tb, 163 Dy, 165 Ho, 166 Er, 169 Tm, 172 Yb, 175 Lu

	Laser type	GeoLas Excimer
	Wavelength	193 nm
	Laser frequency	5Hz
	Fluence	7 J cm -2
	Ablation cell	Internal diameter 5.5 cm, useful volume 24 cm 3
	Ablation spot size	60 µm
	ICP-MS model	Agilent 7500cs
	Type	Quadrupole
	RF Power	1550W
	Carrier gas flow rate	0.92 l min -1 Ar
	Vector gas flow rate	0.50 l min -1 He
	ThO/Th	<0.3
	Th/U	0.98-1
	Torch	Quartz glass torch
	Sample Cone	Ni G1820-65238 made for Agilent by Spectron, Inc.
	Skimmer Cone	Ni G3270-65024 for 7500ce/cx, Agilent Technologies
	Sampling depth	5 mm
	Detector mode	Dual (pulse and analogue counting)
	Dwell time / mass	depending on the mass, see text
	Background	30 s
	Acquisition time	40 s (200 pulses)
	Total time (1 analysis)	100 s
	Number of repeats	6-7
	Calibration	Calibrator (NIST SRM 610,), internal ( 23 Na)
	Isotopes	23 Na,

Table 5 .

 5 Results of the cation-exchange resin column calibration, chemical yield (%).

	Element	Y La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Mg	Ca	Na	K
	Loaded, µg 43 20 20 20 20 20 20 20 20 20 20 20 20 20 20 6 879 18 810 32 608 69 246
	Measured, µg 42 19 19 19 21 20 19 20 19 19 20 19 20 19 20 6 640 14 217 37 416 72 133
	Yield, %	99 97 96 93 106 102 93 101 97 97 99 97 99 95 99 97	76	115	104
	Chemical composition of solution used for calibration (prepared by weighting of certified standard solution
	and salts): MgCl2 5.18 g l-1, CaCl2 10.01 g l-1, NaCl 15.93 g l-1, KCl 25.38 g l-1, lanthanides and Sc 3.85
	mg l-1, Y 8.27 mg l-1. Volume: 5.2 ml.

Table 6 .

 6 The REEs mass fractions in the blank solution (in pg g-1) and standard solutions (in ng g-1) after the chemical treatment using the cation exchange resin AG ® 50W-X8 (200-400 mesh) column.

	Sample/REE	Y	La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Sc*
	Blank MQ-0, pg g-1 32 446 648 104 258 39 179 19 N/A 8 N/A 6 N/A 15 N/A N/A
	Blank MQ-1, pg g-1 51 426 474 61 234 44 106 48 5.2 32 7.6 26 5.2 19 5.3 591
	Blank MQ-2, pg g-1 164 89 278 41 195 41 18 42 4.3 38 8.3 24 4.3 24 5.2 500
	Blank salt-1, pg g-1 47 427 469 52 195 52 88 41 2.2 26 2.9 33 2.2 65 2.4 684
	Blank salt-2, pg g-1 167 114 313 41 221 43 22 45 3.6 41 8.2 28 3.6 25 4.9 454
	Standard 1, ng g-1	48 24 24 23 25 24 24 24 23 24 23 24 23 24 23 19
	Standard 2, ng g-1 106 47 48 46 54 50 48 50 51 50 51 48 51 50 52 39

Table 7 .

 7 Mean values of detection and quantification limits (DL and QL) acquired on standard solutions 898 during one LA-ICP-MS measurement session, in ng g-1. 899 89 Y 139 La 140 Ce 141 Pr 143 Nd 146 Nd 147 Sm 149 Sm 151 Eu 153 Eu 157 Gd Tb 161 Dy 163 Dy 165 Ho 166 Er 167 Er 169 Tm 171 Yb 172 Yb 175 Lu

	DL, 3σ	N/A 28	32	24	N/A	140	250	N/A	N/A	37	180
	QL, 10σ N/A 93	110	78	N/A	470	820	N/A	N/A	120	590
	159 DL, 3σ 49	N/A	75	31	55	N/A	24	N/A	88	23
	QL, 10σ	160	N/A	250	100	182	N/A	80	N/A	293	78
	*N/A -not analyzed. Note, that for individual analyses, the best DL values rich ~10 ng g-1
	900

Table 8 .

 8 Fluid compositions of experimental samples in the H2O-NaHCO3-REEs system. LA-ICP-MS 901 data. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

	902
	Sample	Na,	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Dy	Er	Yb
	number	mol/kg soln						ng g-1
	3-0	0.63	6 845	-	3.6	43	421 1 827 4 447 17 695 2 460	325	1 523
	3-1	0.62	15 525 -	5.7	29	147	958 2 982 10 080 9 500	960	4 160
	3-2	0.65	53 945 -	12	132	228	706 3 412 6 315 37 360 13 865 55
	3-3	0.65	59 250 -	16	466	505 1 747 3 300 7 400 43 345 32 965 97
	3-4	0.63	55 510 -	12	240	344 1 472 3 323 7 665 40 905 33 605 750
	3-5	0.65	19 135 -	8.4	419	142	490	980 2 245 8 850 26 300 000
	3-6	0.67	14 380 -	bdl	287	90	361	852 2 059 8 620 21 620 067
	3-7	0.67	14 270 -	bdl	186	66	296	814 1 896 9 180 17 635 86
	3-8	0.60	-

Table 9 .

 9 Fluid composition of experimental samples in the H2O-NaHCO3-REEs system. ICP-MS after 909 ion-exchange resin Na-isolation. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

	910
	Sample	Na,	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Dy	Er	Yb
	number	mol/kg soln							ng g-1
	3-0	0.63	4 760	16	13	31	345 1 391 3 472 11 530 1 902	257	1 297
	3-1	0.62	11 199 32	48	28	150 890	2 758 7 073	8 059	841	3 620
	3-2	0.65	41 722 31	22	136 216 669	3 241 4 630 32 623 12 856 49 461
	3-3	0.65	43 725 121	26	448 479 1 560 3 038 5 479 36 748 29 437 82 370
	3-4	0.63	41 003 36	20	212 298 1 203 2 794 5 416 33 000 28 155 80 257
	3-5	0.65	15 180 65	11	397 136 434	895	1 653	8 012 22 954 131 423
	3-6	0.67	12 174 57	12	270	99	342	816	1 479	7 423 18 559 86 114
	3-7	0.67	11 972 38	10	182	69	279	750	1 350	7 660 14 707 68 387
	3-8	0.60	11 665 36	10	200	80	414	863	1 650	7 576 12 558 58 247
	3-9	0.53	6 168	16	9.5	42	41	164	337	671	3 091	5 697	26 684
	3-10	0.52	5 913	26	11	78	58	192	395	745	3 225	5 560	22 027
	3-11	0.48	6 803	27	13	80	93	240	518	901	3 800	6 527	28 166
	3-12	0.0051	946	22	19	22	22	43	96	188	643	508	997
	3-13	0.0004	1 415	51	12	85	66	185	384	778	1 668	791	1 174
	3-14	0.0058	149	13	15	2.7	11	12	24	41	73	37	58
	3-15	0.71	5 102	86	32	383 393 869	1 292 2 158	5 394	5 440	16 476
	3RSD,	±15	±20	±10 ±10	±10 ±10 ±10	±10	±15	±15	±15	±15
	%

Table 11 .

 11 Fluid composition in the H2O-Na2CO3-REEs system. ICP-MS after ion-exchange resin Na-914 isolation. Uncertainty (measurement repeatability) is expressed in terms of 3RSD.

	915
	Sample	Na,	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Dy	Er	Yb
	name	mol/kg soln						ng g-1
	2-0	1.1	88 822 5 354 293 2 035 1 527 2 574 262 86 202 52 10 635 5 649
	2-1	1.2	146 901 2 649 268 1 627 2 287 13 812 1 329 154 630 63 13 355 6 708
	2-2	1.2	159 758 1 431 223 940 1 800 11 543 1 277 129 638 55 12 359 6 033
	2-3	1.2	175 187 1 067 173 705 1 471 9 590 1 061 108 748 55 12 923 5 876
	2-4	1.2	111 903 221 16 168	365 1 690 172 26 350 55 74 528 65 916
	2-5	1.2	30 144	391 11 548 1 383 3 773	87	13 543 18 29 911 30 458
	2-6	1.2	20 157	269 12 362	593 7 712	85	10 900 12 24 360 27 326
	2-7	1.2	25 312	492 11 685 1 137 7 097 135 15 367 16 27 925 32 613
	2-8	1.1	21 505	430 9.4 800 1 125 4 576 123 12 594 13 25 760 32 363
	2-9	1.2	19 782	322 6.6 939	893 2 623	87	7 919 11 25 041 37 734
	2-10	1.2	19 700	128 5.3 559	659 1 712	67	5 424	9 446 26 070 42 697
	2-11	1.2	11 772	45	9.2 202	155	376	37	1 068	4 341 15 432 29 245
	2-12	0.7	3 496	66	6.6	87	90	301	18	1 009	1 277 2 500 2 915
	2-13	1.3	16 478	6.2 8.5	29	78	370	68	1 360	5 986 13 694 13 121
	3RSD, %	±15	±20	±10 ±10 ±10	±10	±10	±10	±15	±15	±15	±15
	916

Table 12 .

 12 Quantitative estimation of matrix effects observed on solutions during LA-ICP-MS.

	917
	Matrix effect, %	Matrix salt	La Ce Pr Nd Sm Eu Gd Dy Er Yb
	Underestimated vs prepared NaCl 3.0 mol l-1 pH = 5.5	4	13 17	3 2 26 6 36 41 30
	Overestimated vs pn-ICP-MS NaNO3 0.06-0.11 mol l-1 pH = 1.0 47 22 18 30 26 16 41 30 19 22

Acknowledgments

This work was funded by the French National Research Agency through the "Investissements d'Avenir" National Research program (ANR-10-LABX-21-LABEX RESSOURCES21). M. Kokh acknowledges postdoctoral fellowship granted by Floralis UGA during the manuscript preparation. We thank D. Cividini (CRPG), D. Yeghicheyan (SARM, CRPG), S. Bureau (ISTerre) for their professional help with tedious sample preparations and ICP-OES chemical analyses. Special thanks go to Dr. Y. A. Kostitsyn (GEOKHI RAS) and Dr. S. M. Chernonozhkin (University Ghent) for the fascinating discussions of the trace elements quantification techniques in solutions, minerals and fluid inclusions. We are grateful to Dr. R. Mertz-Kraus for the handling of the manuscript and to the two anonymous reviewers that highly improved the quality of the present article.