Fanny Cattani

Pierre-Yves Gillot

Xavier Quidelleur
email: xavier.quidelleur@u-psud.fr

Anthony Hildenbrand

Jean-Claude Lefèvre

Claire Boukari

Frédéric Courtade

Jean- Claude Lefevre

Fréderic Courtade

In-situ K-Ar dating on Mars based on UV-Laser ablation coupled with a LIBS-QMS system: Development, calibration and application of the KArMars instrument

Keywords: in-situ K-Ar dating, Mars, UV laser ablation, laser-induced breakdown spectroscopy, LIBS, Quadrupole Mass Spectrometry, QMS

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

Introduction

Knowledge of the Martian chronology yet relies on relative dating based on impact craters density (e.g., [START_REF] Bibring | Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data[END_REF]. From this approach, 80% of the Martian surface would have been formed during the first 2 billion years after initial planetary accretion. It corresponds to the Hadean and the Archean epochs on Earth, which ended around 2.5 Ga, and represent less than 2% of the present-day Earth's surface rocks. Thus, studying the surface of Mars provides insight into the conditions and early evolution of the primitive Earth.

Nevertheless, timing of Mars evolution remains poorly constrained yet, showing cratering rates and ages that can vary by a factor of four [START_REF] Doran | Mars chronology: Assessing techniques for quantifying surficial processes[END_REF][START_REF] Hartmann | Martian cratering 8: Isochron refinement and the chronology of Mars[END_REF]. A critical goal of the forthcoming Mars 2020 mission will be to collect a batch of samples for their possible future return to Earth and subsequent radiometric dating [START_REF] Witze | NASA plans Mars sample-return rover[END_REF].

Potassium-Argon dating method is particularly suitable for such purpose. It is based on the radioactive decay of the 40 K, a major element universally distributed in rocks and minerals. Its daughter, 40 Ar, is a noble gas, which accumulates as a function of time and remains in minerals of undisturbed rocks [START_REF] Boynton | Concentration of H, Si, Cl, K, Fe, and Th in the low-and mid-latitude regions of Mars[END_REF][START_REF] Mcdougall | Geochronology and thermochronology by the 40 Ar/ 39 Ar method[END_REF]. It is thus possible to obtain an age from combined measurements of K and Ar contents from a single crystal phase. This, however, requires accurate determination of the mass of the mineral on which both analyses are achieved.

Recently, several experimental settings based on spot laser analyses have been developed to investigate the feasibility of in-situ K-Ar dating [START_REF] Cattani | Realization of a collection of reference minerals to develop a technique for in situ dating of the Martian rocks[END_REF][START_REF] Cho | Dating igneous rocks using the Potassium-Argon Laser Experiment (KArLE) instrument: A case study for ~380 Ma basaltic rocks[END_REF][START_REF] Cho | An in-situ K-Ar isochron dating method for planetary landers using a spot-by-spot laser-ablation technique[END_REF][START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF][START_REF] Solé | In situ determination of K-Ar ages from minerals and rocks using simultaneous laserinduced plasma spectroscopy and noble gas mass spectrometry[END_REF]. These preliminary studies have brought promising perspectives, but yet suffer important limitations. The main difficulties in performing accurate K-Ar dating are i) to perform the total extraction and quantification of the number of 40 Ar atoms from a given amount of sample, and ii) to accurately estimate its potassium content. In order to reach these objectives, we present here KArMars, an instrumental setting based on UV-laser ablation, K measurement by Laser-Induced Breakdown Spectroscopy (LIBS), and argon analysis by quadrupole mass spectrometer (QMS). Initiated by [START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF], this setting has been fully redrawn here in order to optimize the LIBS and argon isotopic measurements, and to accurately determine the mass of mineral ablated by UV-laser. For this purpose, we have qualified a set of minerals and rocks selected as Martian analog reference materials. Finally, the KArMars instrument has been validated using a set of terrestrial analogue samples dated as unknowns.

In-situ K-Ar dating of Mars surface

Principle and applicability

Potassium is an essential constituent of many major rock-forming minerals, such as micas, amphiboles, feldspars, clay minerals [START_REF] Heier | The geochemistry of the alkali metals[END_REF], most of which are also present on Mars [START_REF] Bibring | Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data[END_REF][START_REF] Morris | Silicic volcanism on Mars evidenced by tridymite in high-SiO 2 sedimentary rock at Gale crater[END_REF]. Potassium has three natural isotopes, 39 K (93.2581 ± 0.0029 %), 40 K (0.0117 ± 0.00004 %) and 41 K (6.7302 ± 0.0029 %) [START_REF] Garner | Absolute Isotopic Abundance Ratios and the Atomic Weight of a Reference Sample of Potassium[END_REF]. 40 K is radioactive and decays into stable 40 Ca and 40 Ar* with a half-life of 1.249×10 9 years [START_REF] Renne | Joint determination of 40K decay constants and 40Ar * /40K for the Fish Canyon sanidine standard, and improved accuracy for 40Ar/39Ar geochronology[END_REF]. Therefore, the K-Ar geochronometer is suitable to date geological materials ranging in age from a thousand and less [START_REF] Gillot | The Cassignol technique for potassium-Argon dating, precision and accuracy: Examples from the Late Pleistocene to Recent volcanics from southern Italy[END_REF] to several billions of years. Potassium is an alkali metal and a solid element, while argon is a chemically inert noble gas. They occur as different phases and are easily separated during geological processes (melting, metamorphism or alteration, and diagenesis). Because Ar is an inert gas, the liquid magma degasses into the atmosphere when erupting at the surface. When the lava has solidified, the K-Ar chronometer starts to accumulate radiogenic 40 Ar ( 40 Ar*). In minerals, the amount of radiogenic argon is thus a function of time and K content. Thus, K-Ar measurement allows to determine the age of eruption if the system remained closed, i.e., if it calculated according to the following equation:

t = × ln × * . . + 1 . (1)
Where λ = 5.543x10 -10 yr -1 and λe = 0.581x10 -10 yr -1 are the total decay constant of 40 K, and the decay constant of 40 K to 40 Ar*, respectively [START_REF] Steiger | Subcommission on geochronology: convention on the use of decay constants in geo-and cosmochronology[END_REF]. 40 K is the radioactive isotope K [atoms] and 40 Ar* is the radiogenic argon produced [atoms].

The amount of 40 K (in atoms) is deduced from the K content ( % ) obtained by LIBS, according to the following equation:

. = % × 0.0001167 × × ! " # $ %. ( 2
)
Where Na is Avogadro's number, ma is the ablated mass (in gram), and MK is the atomic weight of K (39.09834 g.mol -1 ). 40 Ar* is defined from the QMS 40 Ar measurement. Mars surface is expected to comprise mostly old rocks, which have accumulated a large amount of radiogenic argon (> 99%).

Therefore, because blanks resulting from laser ablation are very small, we can assume that all the measured argon is radiogenic, while the amount of atmospheric argon is negligible [START_REF] Gillot | The K/Ar dating method: principle, analytical techniques, and application to holocene volcanic eruptions in Southern Italy[END_REF].

The error on the age determination (Δt) is calculated following: [ . ] % ².

(3)

Measurements of K and 40 Ar can be used for dating as long as the sample mass from which they were extracted is known.

Using equation (2) into equation (3) yields the equation from which the derivative is calculated to determine uncertainty on age determination of this work: ] :

∆' = 1 5 )1 -+
; + 7 ∆[ % ] [ % ] : ; + 7 ∆[< = ] [< = ] : ; . (4)
KArMars age determination relies on several ablations, which could have contrasted K and Ar contents depending on the minerals hit by the laser spot. Therefore, as previously proposed [START_REF] Cho | An in-situ K-Ar isochron dating method for planetary landers using a spot-by-spot laser-ablation technique[END_REF][START_REF] Cho | Dating igneous rocks using the Potassium-Argon Laser Experiment (KArLE) instrument: A case study for ~380 Ma basaltic rocks[END_REF][START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Solé | In situ determination of K-Ar ages from minerals and rocks using simultaneous laserinduced plasma spectroscopy and noble gas mass spectrometry[END_REF], the best way to calculate the age of a given sample is to rely on the isochron approach. Indeed, spot-by-spot UV laser ablations provide a sufficient range of K contents to obtain relatively well-defined isochron slopes. Then, in order to obtain a precise age from a single sample, we use the following equation:

89 . = 89 . > + ( ? ( % . )+ (--1.,. (5)
where 40 Ari represents the number of 40 Ar atoms of sample that where not formed by decay of 40 K since closure of the rock or mineral (i.e., the possible excess of 40 Ar described by [START_REF] Bogard | 39Ar-40Ar dating of the Zagami Martian shergottite and implications for magma origin of excess 40[END_REF]. Nevertheless, K-bearing phases coexisting in the same sample are supposed cogenetic and thus may have comparable 40 Ari. Moreover, such rapidly-cooled coexisting phases have the same K-Ar age [START_REF] Faure | Principles of isotope geology[END_REF]. Therefore, the equation 5 represents a family of straight lines in coordinates of 40 Ar and 40 K, where the intercept on the y axis is A = 89

Hence, the isochron approach allows to reduce the total uncertainty applied on spot-by-spot ages (equation 6) by considering only uncertainty on the slope of the isochron line determined by least squares fitting [START_REF] Mahon | The New "York" Regression: Application of an Improved Statistical Method to Geochemistry[END_REF]

Previous attempts

Although different radiometric techniques have been considered for in-situ dating planetary surfaces [START_REF] Anderson | Dating the Martian meteorite Zagami by the 87Rb-87Sr isochron method with a prototype in situ resonance ionization mass spectrometer[END_REF][START_REF] Morgan | Instrumentation Development for In Situ 40 Ar/ 39 Ar Planetary Geochronology[END_REF][START_REF] Riedo | Highly accurate isotope composition measurements by a miniature laser ablation mass spectrometer designed for in situ investigations on planetary surfaces[END_REF], the K-Ar technique appears as the most suitable to date rocks from the Martian volcanic surface [START_REF] Boynton | Concentration of H, Si, Cl, K, Fe, and Th in the low-and mid-latitude regions of Mars[END_REF][START_REF] Cho | An in-situ K-Ar isochron dating method for planetary landers using a spot-by-spot laser-ablation technique[END_REF][START_REF] Cho | Dating igneous rocks using the Potassium-Argon Laser Experiment (KArLE) instrument: A case study for ~380 Ma basaltic rocks[END_REF][START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF][START_REF] Farley | A double-spike method for K-Ar measurement: A technique for high precision in situ dating on Mars and other planetary surfaces[END_REF][START_REF] Mcdougall | Geochronology and thermochronology by the 40 Ar/ 39 Ar method[END_REF][START_REF] Solé | In situ determination of K-Ar ages from minerals and rocks using simultaneous laserinduced plasma spectroscopy and noble gas mass spectrometry[END_REF][START_REF] Talboys | In situ radiometric dating on Mars: Investigation of the feasibility of K-Ar dating using flight-type mass and X-ray spectrometers[END_REF].

During MSL mission, a first in-situ dating experiment was conducted on a sedimentary rock sampled at the surface of Mars. A mudstone, from the floor of the Gale crater, was cored and degassed under high vacuum (900°C, 25 minutes) [START_REF] Mahaffy | The Sample Analysis at Mars Investigation and Instrument Suite[END_REF] in order to extract and analyze argon using a QMS into Sample Analysis at Mars instrument (SAM) instrument [START_REF] Mahaffy | The Sample Analysis at Mars Investigation and Instrument Suite[END_REF]. The whole rock K2O content was estimated by identification of the different minerals (feldspars, glass, clays, etc.) and their relative abundance by CheMin (Xray diffraction; [START_REF] Vaniman | Mineralogy of a Mudstone at Yellowknife Bay, Gale Crater[END_REF] which allows to roughly estimate a whole-rock mean K% content [START_REF] Farley | In Situ Radiometric and Exposure Age Dating of the Martian Surface[END_REF]. From the total Ar measurement, the authors estimated a K-Ar age of 4.21 ± 0.35 Ga, which suggests that K-Ar dating is actually possible on Mars [START_REF] Farley | In Situ Radiometric and Exposure Age Dating of the Martian Surface[END_REF]. However, because it was obtained from a sedimentary rock containing a mixture of detrital and authigenic minerals, such value cannot be unambiguously interpreted as the age of the rock formation.

During the last ten years, analytical systems including a laser have been developed for in-situ K/Ar dating. Laser ablation appears as the most suitable approach for creating a plasma in order to determine K content and to extract Ar simultaneously [START_REF] Cattani | Realization of a collection of reference minerals to develop a technique for in situ dating of the Martian rocks[END_REF][START_REF] Cho | An in-situ K-Ar isochron dating method for planetary landers using a spot-by-spot laser-ablation technique[END_REF][START_REF] Cho | Dating igneous rocks using the Potassium-Argon Laser Experiment (KArLE) instrument: A case study for ~380 Ma basaltic rocks[END_REF][START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF][START_REF] Solé | In situ determination of K-Ar ages from minerals and rocks using simultaneous laserinduced plasma spectroscopy and noble gas mass spectrometry[END_REF]. For example, to extract 99% of 40 Ar from a shergottite feldspar, a furnace has to be maintained between 900 and 1000°C for 3 to 30 h [START_REF] Bogard | K-Ar dating of rocks on Mars: Requirements from Martian meteorite analyses and isochron modeling[END_REF]. The same result can be obtained by using laser ablation, which requires much less energy.

Previous laser ablation-based systems [START_REF] Cho | An in-situ K-Ar isochron dating method for planetary landers using a spot-by-spot laser-ablation technique[END_REF][START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF][START_REF] Solé | In situ determination of K-Ar ages from minerals and rocks using simultaneous laserinduced plasma spectroscopy and noble gas mass spectrometry[END_REF] display various instrumental designs and analytical methods, but most are based on: i) the laser induced breakdown spectroscopy technique, using an optic spectrometer with a resolution high enough to observe both emission lines of K (766.49 and 769.89 nm); ii) a QMS to analyze the abundance and composition of Ar released by laser ablation; and iii) an ablated mass determination obtained generally by the profilometry technique. These studies present K-Ar ages, obtained from K-rich phases, with relative uncertainty between 5 and 25%, depending on the sample age and K content of the mineral phase analyzed.

Methods

New instrument development and calibration

Calibration of the LIBS and QMS, as well as improved quantification of the ablated mass are here investigated through the development of a collection of reference samples with chemistry and 40 Ar* yields determined independently.

UV laser ablation and LIBS method

The laser Induced Breakdown Spectroscopy (LIBS) technique allows a spectral analysis of the plasma light through the characteristic emission wavelength of various major elements present in the sample, such as O, Na, Mg, Al, Si, K, Ca, and Fe. In order to determine elemental compositions from LIBS spectra, two techniques are applied: univariate analysis and partial least squares technique (PLS). The univariate technique correlates, for each element, the LIBS signal to a known concentration using calibration curves based on standards analyses [START_REF] Fabre | In situ calibration using univariate analyses based on the onboard ChemCam targets: First prediction of Martian rock and soil compositions[END_REF]. This technique needs to preprocess the signal before analysis in order to control parameters that affect the precision and accuracy of measurement such as laser fluctuation, atmosphere above sample, chemical and physical matrix effects, self-absorption, etc. [START_REF] Cremers | Handbook of Laser-Induced Breakdown Spectroscopy[END_REF]. The signal is then normalized by the total intensity, the total area, or using an internal standard [START_REF] Aragon | Improvements in Quantitative Analysis of Steel Composition by Laser-Induced Breakdown Spectroscopy at Atmospheric Pressure Using an Infrared Nd:YAG Laser[END_REF][START_REF] Body | Optimization of the spectral data processing in a LIBS simultaneous elemental analysis system[END_REF][START_REF] Fabre | In situ calibration using univariate analyses based on the onboard ChemCam targets: First prediction of Martian rock and soil compositions[END_REF][START_REF] Mosier-Boss | Field Demonstrations of a Direct Push FO-LIBS Metal Sensor[END_REF][START_REF] Sallé | Comparative study of different methodologies for quantitative rock analysis by Laser-Induced Breakdown Spectroscopy in a simulated Martian atmosphere[END_REF][START_REF] Tucker | Calibrating ChemCam: Preparing to Probe the Red Planet[END_REF]. The second technique, the PLS technique, commonly used for LIBS, is a multivariate analysis method [START_REF] Clegg | Multivariate analysis of remote laser-induced breakdown spectroscopy spectra using partial least squares, principal component analysis, and related techniques[END_REF][START_REF] Tucker | Optimization of laserinduced breakdown spectroscopy for rapid geochemical analysis[END_REF]. It overcomes chemical matrix effects to a certain extent [START_REF] Guezenoc | Variables selection: A critical issue for quantitative laser-induced breakdown spectroscopy[END_REF], but needs an accurate and complete standard database. The LIBS technique has been used for 30 years for elementary analyses [START_REF] Coche | Laser-Enhanced Ionization Detection in a Laser-Produced Plasma at Atmospheric Pressure: Theoretical and Experimental Considerations[END_REF]Cremers andRadziemski, 2006, 1983), and the ChemCam experiment represents the first use of the LIBS technique on another planet [START_REF] Maurice | The ChemCam Instrument Suite on the Mars Science Laboratory (MSL) Rover: Science Objectives and Mast Unit Description[END_REF][START_REF] Perez | The ChemCam instrument for the 2011 Mars Science Laboratory Mission: System Requirements and Performance[END_REF][START_REF] Wiens | The ChemCam instrument suite on the Mars Science Laboratory (MSL) rover: Body unit and combined system tests[END_REF]. The main advantage of LIBS for this study is that it can be performed on a whole-rock or chip sample after slight polishing to flatten the sample.

Fig. 1 presents a schematic diagram of KArMars system. A pulsed UV laser is focused on sample and produce plasma in a vacuum chamber. We use a Nd:YAG laser (Spectra Physics GCR-130) with a quadrupled wavelength of 266 nm in order to perform laser ablation by mechanical impact, while thermal effects around the laser spot remain limited [START_REF] Cabalin | Experimental determination of laser induced breakdown thresholds of metals under nanosecond Q-switched laser operation[END_REF][START_REF] Cho | Development of an in-situ K-Ar isochron dating method using LIBS-QMS configuration[END_REF].

The generated laser pulses have a duration of 14 ns and a frequency of 10 Hz, and power is stabilized at 0.2 W to better than 5% for 300 pulses. The irradiance on the sample is about 2 GW/cm² and the laser spot diameter about 300 µm. A pyroelectric laser energy sensor controls the UV laser power during ablation, and a laser shutter controls its duration. In order to change the direction of the laser beam, a dielectric glass lens is used to refract 60.5% of the UV laser towards a spherical lens that focuses the beam on the sample surface underneath.

The remaining 39.5% un-deviated UV laser is focused on the pyroelectric laser energy sensor surface, which allows monitoring laser power and steadiness. The sample is kept under ultrahigh vacuum (maintained by a turbo-molecular pump at around 10 -8 mbar) by placing it under a fused silica glass window placed 17 cm above the surface of the sample. Such distance minimizes opacification of the window by sublimated particles from the plasma and allows us to use high laser intensity without damaging the window.

An Ocean Optics HR2000+ spectrometer is used in KArMars for LIBS analyses of the minerals chemistry. It has a spectral range from 395 to 830 nm with 2048 pixels, which makes possible the accurate determination of major element concentrations, including K, and a resolution of 0.25 nm, which helps to precisely detect of the two close emission lines of K at 766.49 and 769.89 nm. The optical signal emitted from the laser-produced plasma, with a light emission diameter lower than 2 mm, passes through 1 mm wide optical fiber, and through a 25 µm wide slit. It is located nearly horizontally above the plasma at a short distance (< 5 cm), in order to improve recording of most plasma light via the optical fiber.

Due to the low intensity of the light signal released from the plasma under ultra-high vacuum [START_REF] Effenberger | Effect of atmospheric conditions on LIBS spectra[END_REF], and to fluctuations in laser power (of about 5%), each spectrum is calculated as the average of 10 spectra obtained from an integration time of 500 ms. As each plasma fades in less than 0.1 ms [START_REF] Cremers | Handbook of Laser-Induced Breakdown Spectroscopy[END_REF], and since the laser is operated at 10 Hz frequency, this corresponds to the total light emitted from 5 different plasmas. This allows us to obtain a mean spectrum with a signal/noise ratio optimized each 5 seconds, therefore corresponding to the average of 50 different plasmas (produced from 50 laser pulses). Taking into account that the total ablation time is between 15 and 60 seconds, depending on Ar content released (the lower the Ar content, the longer the ablation needed for a good QMS measurement), LIBS data are thus obtained from a total of 150-600 laser pulses performed at the same location. It can be viewed as performing a depth profile, about 300 µm wide and <500 µm deep, which, therefore, limits this approach to relatively thick minerals. In addition, as the plasma intensity varies during ablation, most likely due to changes in surface conditions between the top and the bottom of the crater as laser ablation excavates the sample [START_REF] Cho | High-precision potassium measurements using laser-induced breakdown spectroscopy under high vacuum conditions for in situ K-Ar dating of planetary surfaces[END_REF], the signal of each element is calculated as its integrated peak area normalized by the whole spectrum integrated emission intensity [START_REF] Cohen | The potassium-argon laser experiment (KArLE): In situ geochronology for planetary robotic missions[END_REF][START_REF] Dyar | Strategies for Mars remote Laser-Induced Breakdown Spectroscopy analysis of sulfur in geological samples[END_REF][START_REF] Fabre | In situ calibration using univariate analyses based on the onboard ChemCam targets: First prediction of Martian rock and soil compositions[END_REF][START_REF] Fabre | Onboard calibration igneous targets for the mars science laboratory curiosity rover and the chemistry camera laser induced breakdown spectroscopy instrument[END_REF][START_REF] Stipe | Quantitative laser-induced breakdown spectroscopy of potassium for in-situ geochronology on Mars[END_REF][START_REF] Wiens | Pre-flight calibration and initial data processing for the ChemCam laser-induced breakdown spectroscopy instrument on the Mars Science Laboratory rover[END_REF]. The LIBS used in KArMars allows simultaneous measurements of several peaks of interests, with characteristic wavelength as determined by NIST database for K (766.49 nm and 769.89 nm), Ca (422.79 nm), Mg (518.51 nm), Si (505.74 nm), Na (589.16 nm) and O (777.41 nm). Fe was not determined here because the analyzed spectral range does not allow.

In this study, we focused more specifically on the K doublet to obtain an accurate determination of K content for sake of dating. However, the other elements are also determined to identify the nature of the ablated mineral, with special emphasis on Mg and Fe contents determinations. Indeed, the strongest K line appears at 766.49 nm, but secondary Mg I and Fe I emissions are present at 765.76 nm and 767.61 nm respectively. Unfortunately, the optic spectrometer resolution (0.25 nm) is not sufficient to separate these peaks [START_REF] Cho | High-precision potassium measurements using laser-induced breakdown spectroscopy under high vacuum conditions for in situ K-Ar dating of planetary surfaces[END_REF]. Therefore, in order to avoid overestimation of the K content, the second strongest K emission line at 769.89 nm is used instead for samples with high Mg content.

In this study, we define the most suitable parameters for K content determinations using LIBS, in order to perform accurate in-situ K-Ar dating using a UV laser and under ultravacuum with reduced matrix and self-absorption effects. For that, we have used reference samples presented below, with characteristics close to the Martian rocks and known ages, and international standards (JA-3, JB-2, SRM278, and AGV-2) with known chemistry.

Quadrupole Mass Spectrometry (QMS)

Before SAM instrument can be used on Mars for absolute dating, it requires a precise calibration in order to determine the correlation between the measured intensity and the number of 40 Ar atoms. Laser ablation provides only a very low amount of 40 Ar*, which directly affects the uncertainty on 40 Ar* measurement. Therefore, using reference samples, we have first investigated the limits of the QMS and the optimal ablation parameters to be used.

This allowed us to define the linearity, the reproducibility, the accuracy and the relationship between measured intensity and number of atoms introduced of our QMS. We have used here a SXP Elite VG QMS upgraded from [START_REF] Rouchon | Nonspiked 40Ar and 36Ar quantification using a quadrupole mass spectrometer: A potential for K-Ar geochronology[END_REF] and [START_REF] Devismes | KArMars: A Breadboard Model for In Situ Absolute Geochronology Based on the K-Ar Method Using UV-Laser Induced Breakdown Spectroscopy and Quadrupole Mass Spectrometry[END_REF]. The QMS performed electron-impact ionization using a thoriated iridium filament source. The (LCD) and a small CD (SCD) for the electron multiplier. From volumetric calculations and calibration by reference minerals (selected and characterized in this study, such as phlogopite 15-yates-1-bio, muscovite 15-limou-1-musc and amphibolite AMP3.8), and available standard minerals GLO [START_REF] Odin | Interlaboratory Standards for Dating Purposes[END_REF] and LP6 [START_REF] Baksi | Intercalibration of 40Ar39Ar dating standards[END_REF], we have determined that a LCD contains 3.05 ± 0.04 x 10 14 atoms of 40 Ar (Fig. 2) and 1.13 ± 0.01 x 10 12 atoms of 36 Ar, which gives a 40 Ar/ 36 Ar ratio of 271 ± 2. The difference to the reference value of 40 Ar/ 36 Aratm = 295.5 [START_REF] Steiger | Subcommission on geochronology: convention on the use of decay constants in geo-and cosmochronology[END_REF] is due to the mass discrimination in the ion source, in the analyzer and the ion detection system, all contributing to the mass dependence of the QMS isotopic ratios [START_REF] Rouchon | Nonspiked 40Ar and 36Ar quantification using a quadrupole mass spectrometer: A potential for K-Ar geochronology[END_REF][START_REF] Schneider | 40Ar/39Ar geochronology using a quadrupole mass spectrometer[END_REF]. Since the tank used for SCD was filled from 1 pipette of LCD, volumetric calculations allowed us to determine that one SCD contains 4.42 ± 0.05 x 10 10 atoms of 40 Ar and 1.63 ± 0.02 x 10 8 atoms of 36 Ar.

Mass spectrometer signal evolution during analysis is function of signal height, which may promote either implantation on the QMS, or release of adsorbed argon from QMS surface during sample measurement (Fig. 3). In order to account for these phenomena, a 2 nd order polynomial regression is performed to obtain the initial value (at t = t0), when the signal is equilibrated into the QMS after isolation from the rest of the line. Linearity and reproducibility of QMS measurements have been tested using increment and decrement of several aliquots of SCD. In addition, comparison between measurement of successive decrements and theoretical data (e.g., [START_REF] Coulié | Exploring the multicollection approach for the 40 Ar/ 39 Ar dating technique[END_REF], calculated from a 1.31 volumetric ratio, highlighted the extended linearity response of the QMS for signals between 0.2 and 71 x10 -11 A.

Before gas introduction and measurement, the line is heated for a few days at about 90°C while pumping, until the pressure decreases below 10 -8 mbar, in order to achieve low blanks.

Such long pumping duration is mainly due to the use of chips samples with natural porosity, which have trapped a large amount of atmospheric gas adsorbed at the surface of the rock.

The analysis of argon is achieved in 3 steps (Fig. 1): i) Measurement of line blanks with laser off. ii) Measurement of the ablation signal with laser power set at 0.2 W and the cell valve closed during ablation, which lasts between 5 and 90 seconds, depending on the mineral analyzed. After 90 seconds, the cell valve is open for 210 seconds of gas purification. Then, argon is expanded in the QMS until pressure is equilibrated (between 20 and 30 seconds), and the QMS valve is closed for measurement of masse 40 in static mode during about 180 seconds. iii) Measurement of a CD aliquot in the same volume and conditions than used for analysis of gas sample in order to quantify the number of 40 Ar atoms released during ablation.

Ablated mass

The ablated mass was first estimated by volume measurements performed by the profilometry technique using a Sensofar 3D Optical Profilers at CNES (Toulouse, France), and the estimated density of the ablated mineral. The craters resulting from ablation were inspected with a scanning electron microscopy (SEM) to characterize their aspect. In addition, another approach has been systematically developed here. It consists in the measurement by QMS of 40 Ar extracted by ablation of a mineral with known amount of radiogenic 40 Ar per gram as deduced from independent K/Ar and 40 Ar/ 39 Ar measurements on mineral separates of the same rock. For such purpose, we developed a dataset of new reference minerals. The use of such a variety of common minerals allows assessing the possible variable response of each of type of mineral to ablation, and to derive a correlation between ablated mass and ablation time (ablation by 10 laser pulses per second).

Development of new reference materials

Observation of thin sections, whole-rock chemistry and Electron microprobe analyses (WDS)

were performed in order to qualify the mineralogy and the stoichiometry of a set of old terrestrial rocks with various textures. A careful mineralogical separation was performed and the K content was measured by flame absorption spectrometry, and Ar was measured with a mass spectrometer following the K-Ar method [START_REF] Gillot | The K/Ar dating method: principle, analytical techniques, and application to holocene volcanic eruptions in Southern Italy[END_REF]. In addition, 40 Ar/ 39 Ar dating was also performed for some samples.

Analogy to Martian samples

The Spirit landing [START_REF] Mcsween | Basaltic Rocks Analyzed by the Spirit Rover in Gusev Crater[END_REF], and the Mars Odyssey Thermal Emission Imaging System (THEMIS; [START_REF] Christensen | Evidence for magmatic evolution and diversity on Mars from infrared observations[END_REF], have identified the occurrence of a wide diversity of igneous materials on Mars. The Alpha Particle X-ray Spectrometer chemical analyses of rocks from Gusev crater are consistent with picritic basalts containing normative olivine, pyroxenes, plagioclase, and accessory Fe-Ti oxides [START_REF] Mcsween | Basaltic Rocks Analyzed by the Spirit Rover in Gusev Crater[END_REF]. Quartzbearing granitoid rocks have also been discovered by THEMIS, revealing that high degree of differentiation has occurred. Currently, the Mars Science Laboratory (MSL) rover Curiosity explores sedimentary rocks within the Gale crater. Some instruments operating on Curiosity, like the Chemistry Camera (ChemCam) or the Chemistry and Mineralogy X-ray diffraction (CheMin), performed textural and compositional analyses. They identified a variety of textures including porphyritic samples with dark grains (likely pyroxene megacrysts) in a fine-grained groundmass containing plagioclase needles, and coarse-grained rocks showing equigranular texture with millimeter size crystals of plagioclases and Fe-Ti oxides (Cousin et al., 2017;[START_REF] Sautter | Igneous mineralogy at bradbury rise: The first chemcam campaign at gale crater[END_REF]. Coarse gravels surrounding Gale crater are dominated by feldspathic (andesine-bytownite) clasts. These observations document a relatively wide magmatic diversity at Gale crater, and describe the first fragments of feldspar-rich lithologies (possibly an anorthosite), that may originate from ancient crust transported from the crater rim and now forming float rocks, coarse gravel, or conglomerate clasts [START_REF] Palucis | Origin and Evolution of the Peace Vallis Fan System that Drains into the Curiosity Landing Area, Gale Crater[END_REF][START_REF] Sautter | Igneous mineralogy at bradbury rise: The first chemcam campaign at gale crater[END_REF][START_REF] Williams | Martian Fluvial Conglomerates at Gale Crater[END_REF]. These studies highlight the ubiquitous presence of feldspars-rich (K-bearing phases) of the Martian crust. Furthermore, lithium, strontium, rubidium, and/or barium enrichments, mainly related to the presence of alkali materials (mica, feldspar, and K-phyllosilicate) due to evolved, or low partial melting, magmatic systems have been reported from Curiosity rover data [START_REF] Payré | Alkali trace elements in Gale crater, Mars, with ChemCam: Calibration update and geological implications[END_REF]. Therefore, in order to define a set of terrestrial analogues to Martian rocks, basaltic, feldspar-rich rocks and micas have been selected in the present study.

Homogeneous mono-crystal samples with well-established stoichiometry were selected to qualify LIBS measurements (Table 1). There are 2 mono-crystals investigated by previous studies: i) a dark mica, 15-yates-1-bio, sampled from a pegmatite at Yates mine, Otter Lake (Quebec, Canada) and dated at 913 ± 7 Ma with the Lu-Hf method on apatites [START_REF] Barfod | Lu-Hf and PbSL geochronology of apatites from Proterozoic terranes: A first look at Lu-Hf isotopic closure in metamorphic apatite[END_REF]; ii) a muscovite, 15-limou-1-musc, sampled from an intrusive pegmatite in Massif Central (Limousin, France) and dated at 309 ± 5 Ma with the U-Pb and 40 Ar/ 39 Ar methods applied on lepidolites and oxides (columbites and tantalites) [START_REF] Cheilletz | 40Ar/39Ar ages of the Beauvoir topaze-lepidolite leucogranite and the Chedeville sodolithic pegmatite (northern Massif Central, France). Petrologic and geodynamic significance[END_REF][START_REF] Melleton | U-Pb dating of columbite-tantalite from Variscan rare-elements granites and pegmatites[END_REF].

Additionally, massive samples composed of different minerals and various textures (Table 1)

were selected to further improve LIBS determination and properly account for different effects (e.g. matrix effect, self-absorption, analyzes of several minerals simultaneously). They will also be used to determine QMS detection limits on rocks with similar 40 Ar yield than Martian basalts. The rocks samples are: i) an amphibolite composed of amphiboles and plagioclases, AMP3.8, from Nuvvuagittuq complex (Canada). The zircons have been dated at 2693 ± 3 Ma by the U-Pb method [START_REF] David | U-Pb ages (3.8-2.7 Ga) and Nd isotope data from the newly identified Eoarchean Nuvvuagittuq supracrustal belt, Superior Craton, Canada[END_REF]; ii) an enderbite (ADB) composed of quartz, plagioclases, pyroxenes, biotites and amphiboles, from Churchill province (Canada).

The zircons have been dated at 1860 ± 15 Ga by the U-Pb method [START_REF] Davis | Datations U-Pb dans les provinces de Churchill et du Supérieur effectuées au JSGL en 2013-2014[END_REF]; iii) a dolerite from Viluy Traps principally composed of clinopyroxenes and plagioclases (30-01), sampled along the Viluy river (Siberian platform, Russia). The plagioclases from this sample show a K content of 0.202 wt.% and are dated at 370 ± 5 Ma using the K-Ar Cassignol-Gillot technique [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF]. 40 Ar/ 39 Ar data obtained on the same mineral separates yield similar results, with plateau ages at 370 ± 2 Ma [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF].

Total chemistry (stoichiometry and composition)

Major elements analyses of metagabbroic minerals have been performed with a Cameca SX100 electron probe microanalyzer (EPMA) at the Laboratoire Magmas et Volcans (Clermont-Ferrand, France). The primary acceleration voltage was 15 kV, a 15 nA beam current and 5 µm beam diameter was used for all mineral analyses. The counting time was 10 s for all elements. The detection limits of this procedure are between 400 and 900 ppm for K.

Quantitative analyses were conducted for multiple spots on multiple grains to assess the variation in K contents within each sample.

The chemical composition of whole-rock and K-bearing phases (phlogopite, muscovite, (Nancy, France). Furthermore, total volatiles were analyzed by loss on ignition (LOI) using the weight difference after ignition at 1000°C; obtained data likely represent a combination of structural H2O and CO2 in the minerals along with some minor organics.

New K-Ar ages on separated minerals

In order to further qualify our reference samples, new K-Ar analyses on separated mineralogical phases were performed in the GEOPS geochronology laboratory (Université Paris-Sud, France). Following thin section examination, careful separations were performed using heavy liquids in a narrow density interval in order to select the main mineral phases and obtain pure and homogeneous mineral preparation.

The determination of K was carried out by flame absorption spectrometry and was compared with reference values for MDO-G [START_REF] Gillot | Two reference materials, trachytes MDO-G and ISH-G, for argon dating (K-Ar and 40Ar/39Ar) of Pleistocene and Holocene rocks[END_REF] and BCR-2 (United States Geological Survey; USGS, [START_REF] Jochum | Chemical Characterisation of the USGS Reference Glasses GSA-1G, GSC-1G, GSD-1G, GSE-1G, BCR-2G, BHVO-2G and BIR-1G Using EPMA[END_REF] standards. For each reference material, an aliquot of minerals (typically between 5 and 30 mg) was used. This technique is suitable to measure the whole range of K compositions in rocks and minerals, from less than 0.1 wt.% to up to 15 wt.%, with a relative uncertainty of 1% in all cases [START_REF] Gillot | The K/Ar dating method: principle, analytical techniques, and application to holocene volcanic eruptions in Southern Italy[END_REF].

Then, using another aliquot of the separated minerals, argon was measured with a mass spectrometer similar to the one described by [START_REF] Gillot | The Cassignol technique for potassium-Argon dating, precision and accuracy: Examples from the Late Pleistocene to Recent volcanics from southern Italy[END_REF]. The air aliquot used to calibrate the 40 Ar measurements is calibrated by routine measurements of the interlaboratory standard HD-B1 [START_REF] Fuhrmann | Examination of some proposed K-Ar standards: 40Ar39Ar analyses and conventional KAr data[END_REF]. This technique is suitable for dating into the last millennia [START_REF] Gillot | The K/Ar dating method: principle, analytical techniques, and application to holocene volcanic eruptions in Southern Italy[END_REF][START_REF] Quidelleur | K/Ar dating extended into the last millennium: Application to the youngest effusive episode of the Teide Volcano (Spain)[END_REF], as well as into the pre-Cambrian [START_REF] Sagna | K-Ar mineral ages and thermal history of magmatic and metamorphic Palaeoproterozoic units from the northern part of Kedougou Kenieba Inlier, West African Craton (Eastern Senegal)[END_REF]. Note that for old samples determination, the total relative age uncertainty is 1.4% and is calculated as the quadratic sum of the 1% uncertainties attached to both the K content determination and the 40 Ar calibration, the radiogenic argon content uncertainty being negligible.

Both K and Ar data were duplicated for all samples. Uncertainties are given at the 1σ level, and decay constants and K isotopic ratios of [START_REF] Garner | Absolute Isotopic Abundance Ratios and the Atomic Weight of a Reference Sample of Potassium[END_REF] have been used throughout this study.

Results

Whole-rock geochemistry of our new reference materials

Analyses of AMP3.8 and Viluy basalts show a LOI lower than 1 wt.%, indicating no significant alteration. Analyses of 15-yates-1-bio (dark mica) and 15-limou-1-musc (muscovite) show a range of LOI between 3 and 6 wt.%, which reflects the high water content of these minerals. EPMA data highlight the large variety of feldspars present in our dataset, ranging from labradorite and bytownite composition (Table 2). It can be noted that bytownite is expected in rocks from the Martian crust [START_REF] Sautter | Igneous mineralogy at bradbury rise: The first chemcam campaign at gale crater[END_REF].

K-Ar ages of our new reference materials

The six new K-Ar ages obtained here (Table 3) range from 310.2 ± 4.4 (15-limou-1-musc) to 2649 ± 38 Ma (amphibole of AMP3.8). Both K and Ar analyses were duplicated for each sample and are consistent at the 1σ level. The K contents, obtained by spectrophotometry, range between 0.29 and 8.49 wt.% (Table 3). The results obtained using both ICP-OES and spectrophotometry appear in fairly good agreement, but flame spectrophotometry is more accurate and has a relative uncertainty of only 1%.

LIBS K data

In order to optimize LIBS calibration for K determinations, 4 basaltic and andesitic standard glasses (JA-3, JB-2, SRM278, and AGV-2 powders, melted into glasses at 1100°C under a pressure of 600 kg/cm 2 in order to obtain homogenous material), and each of our new reference minerals (plagioclase and amphibole from AMP3.8, and dark mica from 15-yates-1bio) were selected. JA-3 and JB-2 were characterized by the National Institute of Advanced Industrial Sciences and Technology (AIST), and AGV-2 and SRM278 by the USGS. Fig. 5 shows the calibration curves obtained for each of the potassium peak (766 nm and 770 nm).

Calibration curves were fitted with a power law with the following parameters: DEE = 0.0431 × H .E IJ , and: (7)

DD = 0.0204 × H .EDE , (8)
where N766 and N770 are the peak areas (determined by a trapezoidal-law applied with the National Instrument LabView software) at 766 nm and 770 nm, respectively, normalized by the total spectrum intensity, and C is the known K content (in wt.%) (Fig. 5 and Table 4).

Note that, in order to obtain K content from LIBS analysis, we have selected the emission line at 766 nm when there is no interference line. In such case, a simple observation of the spectrum helps to define which kind of emission line must be selected.

The overall non-linear trend (Fig. 5), and the increasing uncertainty, can be explained by i) the self-absorption, that is considered to be fostered when the fundamental level is involved in the transition, which is the case of the two potassium lines considered in this study [START_REF] Cho | High-precision potassium measurements using laser-induced breakdown spectroscopy under high vacuum conditions for in situ K-Ar dating of planetary surfaces[END_REF][START_REF] Cho | Dating igneous rocks using the Potassium-Argon Laser Experiment (KArLE) instrument: A case study for ~380 Ma basaltic rocks[END_REF][START_REF] Cremers | Handbook of Laser-Induced Breakdown Spectroscopy[END_REF][START_REF] Guezenoc | Variables selection: A critical issue for quantitative laser-induced breakdown spectroscopy[END_REF]; ii) the decreasing luminosity of the plasma hidden by the walls of the created crater as ablation is going on (for long ablation time, which depends on Ar content); and iii) the matrix effects, which include changes in chemical composition (e.g. mineral zonation) and in physical properties (e.g. hardness, porosity, or grain size; [START_REF] Guezenoc | Variables selection: A critical issue for quantitative laser-induced breakdown spectroscopy[END_REF]. Furthermore, in Narich samples (such as SRM278; Table 4) chemical matrix effect can be observed when ablation time increases. Indeed, the presence of dissolved NaCl that causes an increase of the plasma temperature and the excited atoms, leading to a stronger emission signal of the analytes and results show that K emission lines are dependent on NaCl concentration [START_REF] Cremers | Laser-Induced Breakdown Spectroscopy[END_REF][START_REF] Goueguel | Effect of Sodium Chloride Concentration on Elemental Analysis of Brines by Laser-Induced Breakdown Spectroscopy (LIBS)[END_REF]. The limit of detection (LOD) and the limit of quantification (LOQ) of K determinations are derived from the calibration curves. To avoid the self-absorption, we selected only the lowest concentration (between 0.29-3.45 wt.%) and thus obtained a straight line for the LOD and LOQ determination. Following the approach of [START_REF] Mermet | Limit of quantitation in atomic spectrometry: An unambiguous concept?[END_REF], and using the non-weighted calibration at the 1σ confidence level, the LOD and LOQ for peak area normalized at 766 nm, determined by reference samples, are 0.14 and 0.52 wt.%, respectively. The LOD and LOQ for peak area normalized at 770 nm are 0.05 and 0.19 wt.%, respectively.

In order to assess the accuracy and the precision of the quantification deduced from our calibration, based on standard glasses and minerals (plagioclase, amphibole and phlogopite)

analyses and used to determine K content of crystals, several measurements on Viluy samples (TL18, TL19, 30-01), ADB and AMP3.8 have been performed. Table 5 shows that K contents determined using LIBS analyses range from 0.254 ± 0.090 to 0.401 ± 0.078 wt. K%. These values have relative standard deviations (σ) ranging from 7 to 35%, and are consistent at the 2-σ level with reference K contents determined with spectrophotometry. Note that, although AMP3.8 plagioclase and amphibole crystals were used to obtain the calibration curve shown in Fig. 5, analyses presented in Table 5 for this sample have been obtained from different laser shots, and can be considered as internal checks for our calibration.

The accuracy of the univariate model is characterized by calculating the calibration error called the root-mean-square error prediction (RMSEP in the units of the predicted quantity, i.e. wt.%) of cross validation between the concentrations of the laboratory standards measured and the calculated predictions [START_REF] El Haddad | Good practices in LIBS analysis: Review and advices[END_REF][START_REF] Wiens | Pre-flight calibration and initial data processing for the ChemCam laser-induced breakdown spectroscopy instrument on the Mars Science Laboratory rover[END_REF]. The RMSEP is calculated by the following expression:

LMNOP = / ∑ (2>,S>) T U VWX Y , ( 9
)
where pi is the predicted value, ri is the reference value, and N is the number of samples in the dataset. Based on data from Table 5, the RMSEP, which is calculated for the potassium value obtained from 50 spectra analyzed on a set of reference samples with K contents between 0.2 and 0.5%, is ± 0.1 wt.% (Table 5).

QMS Ar data

As a very small amount of sample is evaporated during ablation (between 10 and 50 µg), 40 Ar and 36 Ar were measured with an electron multiplier (EM). From several analyses on SCD, the EM sensitivity is defined at 1.47x10 -21 A/atom and its quantification limits at 3x10 8 atoms (5x10 -16 moles).

The uncertainty defined by the relative standard deviation on the signal, is lower than 5% for 36 Ar, and lower than 1% for 40 Ar. In addition, taking into account an uncertainty on the argon signal calibration of 1.2% (based on repeated measurements of the calibration dose and standards LP6 and GLO, and reference samples; Fig. 2), the overall relative uncertainty on the number of argon atoms determination is 5.2% for 36 Ar, and 1.6% for 40 Ar.

QMS blank for 36 Ar is 2.9 ± 0.4x10 -17 moles, and is < 3x10 -16 moles for 40 Ar, which precludes the accurate measurement of small 36 Ar signals. Indeed, the signal to noise ratio (S/N) for one SCD is about 10 for the 36 Ar, and does not exceed 1 for the 36 Ar released by a sample ablation. Hence, it cannot be considered as significative, and therefore all the measured 40 Ar is considered as radiogenic. It is important to note that 36 Ar is used here only to check for the absence of anomalous atmospheric contamination produced during the preparation or following unexpected ablation of a vesicle.

Ablated mass determination

Fig. 7 shows ablation craters images obtained by profilometer and scanning electron microscopy (SEM) for phlogopite 15-yates-1-bio and amphibolite AMP3.8. SEM images show the roughness of craters morphology, which renders the accurate volume determination difficult. This is further highlighted by the raw images of profilometry data. Indeed, no measurement (NM in Fig. 7) could be obtained on most of AMP3.8 surface. On the other hand, when applied to single crystals such as phlogopite, profilometry data acquisition was more straightforward. Using a mineral density of 2.8 g.cm -3, a volume of 8.1 ± 0.8 µg was obtained for 15-yates-1-bio for the crater shown in Fig. 7. For both samples, Fig. 8 shows the correlation between the ablated mass obtained by profilometry technique, and the ablated mass determined from 40 Ar content and QMS measurements (see section 3.2.). The correlation appears very good for craters performed on phlogopite (15-yates-1-bio).

Nevertheless, Fig. 8 clearly shows that no correlation exists for amphibolite AMP3.8, probably due to the poor profilometry volume determination for such rock sample.

The mass determination based on the profilometry technique remains unsatisfactorily, because i) the shape of the ablation crater is often irregular and perturbated by ejecta deposits;

ii) ablation may be variable from one spot to the other depending on variable mineral strength; and iii) calculation of the ablated mass is based on an a priori value of the mineral density, which can vary greatly depending on composition; and iv) the surface color (made of single or polyminerals) and the visibility of the bottom of the crater affect the accuracy of the profilometry technique, impacting directly volume and mass determinations. Consequently, we will only rely on the volume determination based on the QMS measurements, which can provide mass measurement from the released amount of 40 Ar with a relative uncertainty as low as 2%. Such approach requires to establish a well-defined correlation between the ablated mass and the ablation time, for all mineralogical facies of interest for Martian dating, and, thus, multiple measurements from different mineral phases are needed.

Several analyses of plagioclase crystals of ADB, AMP3.8 and 30-01 allowed us to define the relation between the ablation time and the ablated mass (Fig. 9). The ablated mass is obtained by comparison between number of atoms measured by QMS and content of 40 Ar* atoms per gram determined by the K-Ar Cassignol-Gillot technique with 11.8x10 14 atoms per gram for plagioclases of ADB (this study), 11.5x10 14 atoms per gram for plagioclases of AMP3.8 (this study), and 1.5x10 14 atoms per gram for plagioclases of 30-01 [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF]. Fig. 9a shows data for each selected plagioclase from each sample in order to obtain the correlation between the ablated mass and the ablation time. Fig 9b shows the data average and the associated uncertainty of these plagioclases for each sample at different ablation time. Finally, Fig. 9c shows the average of ablated mass sample according to ablation time. The uncertainty was defined from the relative dispersion of average data obtained for each sample at given ablation time, and the uncertainty on the slope of 4% is obtained using [START_REF] Mahon | The New "York" Regression: Application of an Improved Statistical Method to Geochemistry[END_REF].

Discussion

K data: Comparison between LIBS and other methods for K determination

Optic spectroscopy (LIBS) K measurements, that are used for in-situ dating with KArMars, have been compared with in-situ Electron micro-analysis (EPMA), spectrometry (ICP-OES), and spectrophotometry achieved on mineral separates (Table 6).

The results obtained by the two different in-situ techniques (EPMA and LIBS) on the amphibole from AMP3.8 are in agreement within uncertainties, while those for plagioclase of the same rock show significant discrepancy. This can be explained by the difference in size of the two spots (EPMA and LIBS), and by the chemical heterogeneity of the plagioclase phenocrysts, which show significant mineral crystal zoning. Indeed, EPMA provide analyses with a beam diameter of 5µm only, which is much smaller than the typical beam size of our U-V laser. While the latter averages different parts of the mineral, including K-rich crystal zoning in their outer rim, and inclusions (e.g., amphiboles as observed in thin section), the very low-K concentration obtained by EPMA indicates that punctual analysis reached a zone depleted in K. In turn, sericite alteration is also present in most plagioclase crystals [START_REF] Mcdougall | Geochronology and thermochronology by the 40 Ar/ 39 Ar method[END_REF]. It induces small-scale re-crystallization of fine-grained muscovite, with K-rich composition, within plagioclase crystals. In contrast, LIBS analyses are performed with a beam diameter of about 300 µm, thereby averaging out these heterogeneities, if present (mineral sizes from this study range between 50 µm and 2 mm).

Nevertheless, the good agreement between the other results obtained from spot-by-spot analyses, at various location in a given sample, shows a relatively even K distribution, taking into account the uncertainty of each analysis.

LIBS K values obtained on AMP3.8 and ADB samples are in good agreement with those obtained by spectrophotometry. This validates the use of these pure mineral standards in order to calibrate our in-situ dating instrument. However, K content obtained for 30-01 sample by LIBS is significantly different from spectrophotometry data. Indeed, the plagioclase phenocrysts (0.5-1 mm) show a lower K content (0.202 wt.%) but yield consistent ages (at the 1 sigma level) with the plagioclase crystals present in the microlite fraction (0.12-0.25 mm; 0.355 wt.% of K) [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF]. Hence, because it is not possible to determine which crystal fraction is hit by the laser spot, LIBS K values range between 0.202 and 0.355 wt.%, which are the K contents of phenocrysts and microcrysts, respectively (Table 6).

LIBS data provide very valuable information for the interpretation of each ablation, and eventually to perform a better data correction. Effectively, major elements LIBS measurements allow to identify which mineral phase was ablated, or if it is a mix between several minerals, and furthermore, if it is suitable for K-Ar dating. The uncertainty of K content determination using LIBS, mainly due to plasma fluctuation during ablation time and the rock heterogeneity at the sub-millimeter scale, is the most limiting factor of the KArMars method because it dominates the uncertainty of K-Ar ages. In order to minimize these fluctuations and the heterogeneity effects, short duration ablations should be preferred.

Using KArMars for in-situ dating

In order to test the KArMars instrument for in-situ K-Ar dating, terrestrial analogues to Martian rocks with a large range of crystals size (supp. Fig. 1), have been selected. UV laser ablations with 150 to 900 laser pulses were performed on amphibolite (AMP3.8) from Nuvvuagittuq, enderbite (ADB) from Churchill Province, and basalts (30-01, TL-18, TL-19, from Viluy Traps (This study; [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF][START_REF] Ricci | Ar / 39[END_REF] used here as unknowns. Results obtained by QMS, LIBS and mass calibration (based on reference samples analyses) are given in supp. Table 2. The main source of age uncertainty is due to the LIBS measurements, as K uncertainties range between 5 and 40% (supp. Table 2). The uncertainty on 40 Ar measurement is about 2% (supp. Table 2), and the uncertainty on mass determination obtained using reference samples, is about 4%. Propagating these independent sources of uncertainty gives a total relative uncertainty on the age between 7 and 40% for a typical single ablation. KArMars ages of these samples have been determined using the isochron approach (Fig. 10) and are compared with the reference K-Ar ages in Table 7.

The results obtained on AMP3.8 show K content between 0.19 and 0.39 wt.% (K% reference of plagioclase: 0.29%; Table 3), and a range of 40 Ar between 5 and 70x10 9 atoms (supp. Table 2). The isochron age obtained for plagioclase minerals is 2218 ± 135 Ma (Fig. 10), which yields an uncertainty of 6% and a difference with the reference age of about 8% (Table 7).

The correlation defined for the determination of the ablated mass on plagioclase was also tested on other mineral phases from sample AMP3.8 (Fig. 10): i) pure amphibole and ii) mixture of amphibole and plagioclase (mix phases), because analysis of pure plagioclase minerals from this sample was not always possible since many crystals have sizes (< 250 µm;

supp. Fig 1) smaller than the laser beam diameter. In addition, amphibole inclusions in some plagioclase crystals are also observed (supp. Fig. 1). The isochron age obtained for amphibole minerals is 2913 ± 292 Ma, with an accuracy of 8% relative to the reference age (Table 7), while an age of 2585 ± 138 Ma is obtained for mixtures of plagioclase/amphibole minerals.

As expected, the later is between the reference ages of 2052 ± 29 and 2649 ± 38 Ma, for plagioclase and amphibole crystals, respectively (Table 7). It can be noted that this rock presents a complex geological history, which will probably not be the case for basalts of the Martian surface formed during the first 2 Ga.

The results obtained on ADB plagioclase show K contents ranging from 0.22 to 0.53 wt.% (K% reference: 0.5%; Table 3), and 40 Ar contents between 4 and 35x10 9 atoms (supp. Table 2). The isochron age is 1382 ± 46 Ma (Fig. 10), showing an uncertainty of 3% and a difference with the reference age of about 6% (Table 7). Such very good agreement has been favored by the size of the plagioclase crystals, which are much larger than the laser beam, thereby reducing the risk to dig through the mineral and ablate a mix between several phases.

Four basaltic samples from the Devonian Viluy Traps [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF][START_REF] Ricci | Ar / 39[END_REF] have also been dated in order to test the limits of KArMars. 30-01, have plagioclase sizes between 250-500 µm, which allow pure minerals to be ablated, while TO-35 has much finer grains.

K contents obtained for 30-01 plagioclase minerals are between 0.26 and 0.30 wt.%, within the range of reference values previously reported [START_REF] Courtillot | Preliminary dating of the Viluy traps (Eastern Siberia): Eruption at the time of Late Devonian extinction events? Earth Planet[END_REF], and 40 Ar content ranging between 1 and 4x10 9 atoms (supp. Table 2). An isochron age of 351 ± 33 Ma is obtained for this sample (Fig. 10). It shows an uncertainty of 10% and a difference with the reference age of about 5% (Table 7). K contents ranging from 0.21 to 1.45 wt.% (K% reference of plagioclase: 0.35%; [START_REF] Ricci | Ar / 39[END_REF], and 40 Ar contents ranging from 1 to 10x10 9 atoms have been obtained for TL-18 (supp. Table 2). It yields an isochron age of 362 ± 15 Ma for TL-18 plagioclases (Fig. 10), displaying an uncertainty of 4% and a difference with the reference age of about 5% (Table 7). Similarly, the age of 358 ± 20 Ma obtained for plagioclases of TL19 (Fig. 10) has an uncertainty of 6%, and a difference with the reference age about 5% (Table 7). It has been obtained from K contents ranging between 0.13 and 0.66 wt.%, and 40 Ar contents between 0.4 and 8x10 9 atoms (supp. Table 2). The correlation line gives an age of 358 ± 20 Ma. Finally, TO-35 shows a range of K content from 0.12 to 0.22 wt.%, and a number of 40 Ar atoms between 0.4 and 3x10 9 (supp. Table 2). As expected from its low K content and texture, the isochron age of 406 ± 210 Ma (Fig. 10) displays a relatively large uncertainty of 52%. However, the difference with the reference age is only 9% (Table 7; Fig. 11).

Finally, the comparison shown in Fig. 11 highlights the accuracy of KArMars ages, which all are within 10% only of their reference age (Table 7). This is even observed for relatively young and low K samples from Viluy basalts, which are at the limit of detection of the instruments composing the KArMars setting.

Conclusions

In this study, we developed and calibrated a new in-situ K-Ar dating instrument (KArMars) based on LIBS for K measurements, QMS for Ar determinations, and analyses of reference samples for calibration of the ablated mass. Note that several components used here in KArMars have already been adapted for planetary exploration. Onboard rover Curiosity, the Sample Analysis at Mars instrument (SAM), includes a QMS suitable for noble gas analyses of Martian rocks, and the ChemCam experiment runs a LIBS instrument.

We have shown that the sample mass released during short duration UV-laser ablation can be successfully determined by QMS analyses of a set of reference samples for which the 40 Ar content has been previously precisely determined.

In-situ K-Ar ages obtained here with KArMars on Viluy basalts, ADB and AMP3.8 samples have been validated by the comparison with their reference ages obtained using classic K-Ar measurements (Fig. 11; Table 7). The expected K and Ar contents on Mars are quite similar than those of amphibolite AMP3.8 and enderbite ADB successfully analyzed here (Fig. 10).

Furthermore, despite the low Ar content of Viluy samples, due to their relative young age, and their small-scale textural heterogeneity, the KArMars instrument was able to provide consistent ages, with less than 15% of uncertainty. Overall, our results clearly show that the KArMars approach can be successfully used for dating a large compositional range of Martian rocks, with uncertainties as low as about 10%, and with accuracy, i.e. difference with the reference age, of only 10%. Furthermore, these results validate our approach based on reference samples for mass determination.

Acknowledgments

This Meslin, for help and advice during the development of KArMars. We wish to thank D. Pinti [START_REF] Odin | Interlaboratory Standards for Dating Purposes[END_REF], LP6 [START_REF] Odin | Interlaboratory Standards for Dating Purposes[END_REF], AMP3.8 [START_REF] David | U-Pb ages (3.8-2.7 Ga) and Nd isotope data from the newly identified Eoarchean Nuvvuagittuq supracrustal belt, Superior Craton, Canada[END_REF], and this study), 15-limou-1musc [START_REF] Melleton | U-Pb dating of columbite-tantalite from Variscan rare-elements granites and pegmatites[END_REF] this study) and 15-yates-1-bio [START_REF] Barfod | Lu-Hf and PbSL geochronology of apatites from Proterozoic terranes: A first look at Lu-Hf isotopic closure in metamorphic apatite[END_REF], and this study). [START_REF] Bibring | Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data[END_REF][START_REF] Boynton | Concentration of H, Si, Cl, K, Fe, and Th in the low-and mid-latitude regions of Mars[END_REF]. 1

  analyzer (VG AN-9N) is composed of a rod system of four 12-mm diameter molybdenum electrodes, and the source conditions are controlled by the original VG SXP-Elite electronics: trap-current control of 0.3 mA (regulates the electron production) and electron energy setting of 47 eV (minimizing double ionization effects). Ion detection is achieved by an electron multiplier (EM under high-voltage of 1300 V) for weak signals, while a faraday cup is used for stronger signals. The output of the EM is measured by a Keithley 6514 picoammeter with an internal noise below 10 -16 A. The QMS volume is about 1 L. The default VG radiofrequency generator ranged in mass from 0 to 50 amu. We adjusted it to be constrained in a flat region between masses 36 and 40. The m/Δm value is 400 at a mass of 40 (resolution at 0.1 amu), which is sufficient as 40 Ar is the only gas present with a mass of 40 amu. The chamber is isolated during ablation and the released gas is purified by a SAES MP-10 Zr-Al getter operating at 400°C before introduction in the QMS. The latter is calibrated by analysis of known atmospheric argon aliquots (doses). Indeed, a reproducible amount of atmospheric argon (calibrated dose, CD) is pipetted to convert the electronic intensity into number of atoms, and hence to calibrate the QMS detectors. For the faraday cup, we use a large CD

  amphiboles and feldspars) was analyzed by inductively coupled plasma optical emission spectrometry (ICP-OES) for major elements, and inductively coupled plasma-mass spectrometry (ICP-MS) for trace elements, at the Centre de Recherches Pétrographiques et Géochimiques -Service d'Analyse des Roches et des Minéraux (CRPG-SARM) facility

Fig. 4

 4 Fig. 4 shows K content plotted as a function of 40 Ar atoms number (in atoms per gram) derived from these analyses. Sample 15-limou-1-musc presents a similar 40 Ar content as the

Fig. 6a shows

  Fig.6ashows the linearity of our QMS response, based on analysis of several successive increments of SCD (from 1 to 5 air pipettes), providing 40 Ar signals between 6 and 30 x 10 -11 A. Similarly, Fig.6bpresents the 3 distinct comparisons between measured 40 Ar signal

  work has been funded by the Centre National d'Etudes Spatiales (CNES; Project "Datation Potassium-Argon sur Mars", grants R-S17/SU-0003-043 and R-S16/SU-0003-043) and the Université Paris Sud (part of F.C. PhD grant). We are grateful to Cécile Fabre for detailed comments that significantly improved the manuscript. We acknowledge the ChemCam team, particularly S. Maurice, O. Gasnault, V. Sautter, A. Cousin and P.-Y.

Fig. 1 :

 1 Fig. 1: Schematic diagram of the experimental setup. 1. UV laser unit and pyroelectric laser energy sensor; 2. ablation unit; 3. purification unit; 4. quadrupole mass spectrometer unit (QMS); 5. pipette unit (a known amount of atmospheric argon to calibrate the QMS detectors); LCD: large air pipette to calibrate the faraday cup; SCD: small air pipette to calibrate the electron multiplier (SEM); 6. standard calibration unit. Ti: titanium foam to purify; Ch: active charcoal to trap; Std: extraction of argon from standard samples for pipette unit calibration.

Fig. 2 :

 2 Fig.2: Determination of number of 40 Ar atoms of a large air pipette (uncertainties on standard age and of measurements are integrated). This determination was calibrated by standard and reference samples with a known number of 40 Ar atoms per gram. i.e. GL-O[START_REF] Odin | Interlaboratory Standards for Dating Purposes[END_REF], LP6[START_REF] Odin | Interlaboratory Standards for Dating Purposes[END_REF], AMP3.8[START_REF] David | U-Pb ages (3.8-2.7 Ga) and Nd isotope data from the newly identified Eoarchean Nuvvuagittuq supracrustal belt, Superior Craton, Canada[END_REF] this study), 15-limou-1musc[START_REF] Melleton | U-Pb dating of columbite-tantalite from Variscan rare-elements granites and pegmatites[END_REF] this study) and 15-yates-1-bio[START_REF] Barfod | Lu-Hf and PbSL geochronology of apatites from Proterozoic terranes: A first look at Lu-Hf isotopic closure in metamorphic apatite[END_REF], and this study).

Fig. 3 :

 3 Fig. 3: Mass spectrometer signal evolution with time as a function of (a) degassing of 40 Ar during a line blank measurement; and (b) During the first 20s, signal 40 Ar increase due to EM equilibration (grey band), then signal of 40 Ar decrease due to ion implantation on the QMS during sample measurement. All signal values are SEM outputs. For each point, 40 Ar is determined by averaging 14s of continuous SEM output. Error bars represent 1σ uncertainties of the SEM output during this measurement time.

Fig. 4 :

 4 Fig. 4: Number of Ar atoms per gram versus K% for reference samples. The grey bar represents expected Martian values[START_REF] Bibring | Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data[END_REF][START_REF] Boynton | Concentration of H, Si, Cl, K, Fe, and Th in the low-and mid-latitude regions of Mars[END_REF].

Fig. 5 :

 5 Fig. 5: Calibration curves for the potassium doublet at 766 nm and 770 nm under high vacuum conditions (10 -8 mbar). The horizontal error bars indicate the standard deviations for the inter-laboratory measurements of references samples (AIST, USGS and this study), while the vertical error bars represent the standard deviations of more than ten LIBS spectra measurements of the same sample.

Fig. 6 :

 6 Fig. 6: QMS linearity, at low intensity values, is highlighted by (a) linear regression obtained from successive introducing of air pipettes (SCD analyses); (b) comparison between data obtained by successive decrements of 3 SCD during a conventional experiment and values calculated from theoretical modelling of a perfect decrement. Intensity measured (in 10 -11 A) decreases linearly with the number of decrement. Uncertainty of each point is less than 1% and is integrated in graphic representation.

Fig. 7 :

 7 Fig. 7: SEM image (right), raw and processed images from profilometry measurement (left) of ablation craters. (a) Images of a crater formed following a 60s long UV-laser ablation on phlogopite 15-yates-1-bio; (b) Image of a crater formed following a 40s long UV-laser ablation on amphibolite AMP3.8. This highlights the rough morphology of craters. The lack of observations by the profilometer is represented by NM (no measurement) on pale yellow.

Fig. 8 :

 8 Fig. 8: Comparison between masses deduced from QMS measurements and those obtained by profilometry on 15-yates-1-bio and AMP3.8.

Fig. 9 :

 9 Fig. 9: Results on plagioclase ablations. (a) Ablated mass versus ablation time for plagioclase ablations from reference samples. (b) Linear regression lines obtain from mass average as a function of ablation time for each sample. (c) Correlation line between the ablated mass obtained via QMS data and the ablation time, defined from average of ablated mass defined from plagioclase minerals of reference sample.

Fig. 10 :

 10 Fig. 10: KArMars results obtained on Nuvvuagittuq amphibolite (AMP3.8), Churchill province enderbite (ADB) and Viluy basalts (30-01, TL-18, TL-19, TO-35) used as unknown samples (1: this work; 2: Courtillot et al., 2010; 3: Ricci et al., 2013).

Fig. 11 :

 11 Fig. 11: Comparison between reference and KArMars ages on AMP3.8, ADB and Viluy

  15-yates-1-bio (dark mica) analyses (by ICP-OES and EPMA are comparable within the range of accuracy and yielded value of 19.2 Si wt.%, 0.3 Ti wt.%, 5.5 Al wt.Si wt.%, 0.3 Ti wt.%, 8.6 Al wt.%, 7.6 Fe wt.%, 4.8 Mg wt.%, 0.2 Mn wt.%, 8.5 Ca wt.%, 1.3 Na wt.% and 0.39 K wt.% (Supp. Table1; Table2).

	K contents of K-bearing minerals (phlogopite, muscovite, feldspar and amphibole) obtained
	by EPMA and ICP-OES are given in Table 2. Overall the dataset shows a large range of
	values, between 0.04 ± 0.02 wt.% (plagioclase from AMP3.8) and 8.74 ± 0.42 wt.%
	(muscovite from 15-limou-1-musc) for EPMA, and between 0.35 ± 0.09 wt.% (amphibole
	from AMP3.8) and 8.49 ± 0.42 wt.% (muscovite from 15-limou-1-musc) for ICP-OES.
	AMP3.8: Both amphibole and plagioclase minerals, and whole-rock of AMP3.8 were
	analyzed. Results obtained by ICP-OES and EPMA on amphiboles are similar, with 22.0 Si
	wt.%, 0.5 Ti wt.%, 4.5 Al wt.%, 11.7 Fe wt.%, 7.3 Mg wt.%, 0.3 Mn wt.%, 7.9 Ca wt.%, 0.7
	Na wt.% and 0.35 K wt.%. This allows to determine the structural formula of
	Ca2[Mg4(Al,Fe 3+ )]Si7AlO22(OH)2, which corresponds to a magnesio-hornblende. Plagioclase
	crystals analyzed by EPMA show a composition between bytownite and labradorite with

%, 8.0 Fe wt.%, 12.2 Mg wt.%, 0.1 Na wt.% and 8.5 K wt.%. This shows a major-elements composition of phlogopite with a structural formula of K(Mg2.5Fe0.5)(AlSi3)O10(OH)2 (Supp. Table

1

; Table

2

).

15-limou-1-musc (white mica) results by ICP-OES and EPM are also comparable within the range of accuracy with value of 21.1 Si wt.%, 0.3 Ti wt.%, 16.6 Al wt.%, 3.1 Fe wt.%, 0.6 Mg wt.%, 0.4 Na wt.% and 8.6 K wt.%. This shows a major-elements composition of muscovite with a structural formula of KAl2(AlSi3)O10(OH)2 (Supp. Table

1; Table 2).

23.1-24.0 Si wt.%, 17.0-16.3 Al wt.%, 11.0-9.8 Ca wt.%, 2.2-2.8 Na wt.% and 0.04-0.05 K wt.%. Whole-rock was measured by ICP-OES and shows a composition between amphibole and plagioclase phases, with 22.9

Table 4 :

 4 LIBS results on standard and reference samples used for calibration. The number of analyzed spectra is indicated on the "N" column. Measurements with longer ablation time were performed to highlight possible variations.

			Ablation time shorter than 15s -Data used to performed calibration curve
	Sample name	Ref. K content ± un. (wt.%)	A/Itot (766.49 nm)	Standard deviation (%)	N	A/Itot (769.89 nm)	Standard deviation (%)	N
	15-yates-1-bio	8.48 ± 0.06	0.166	6%	4	0.081	6%	4
	SRM278	3.41 ± 0.02	0.097	12%	10	0.050	11%	10
	JA3	1.17 ± 0.10	0.049	8%	31	0.024	13%	31
	JB2	0.35 ± 0.01	0.027	10%	31	0.013	13%	31
	AGV-2	2.39 ± 0.09	0.077	7%	31	0.039	8%	31
	plg AMP3.8	0.29 ± 0.01	0.016	18%	6	0.008	12%	6
	amp AMP3.8	0.34 ± 0.00	0.023	12%	18	0.008	18%	18
				Ablation time longer than 15s
	Sample name	Ref. K content ± un. (wt.%)	K% predict (766.49 nm)	Standard deviation (%)	N	K% predict (769.89 nm)	Standard deviation (%)	N
	SRM278	3.41 ± 0.02	5.58	22%	55	5.69	22%	55
	JA3	1.17 ± 0.10	1.42	21%	76	1.42	21%	76
	JB2	0.35 ± 0.01	0.66	23%	76	0.70	35%	76
	AGV-2	2.39 ± 0.09	2.84	12%	76	2.82	11%	76
	plg AMP3.8	0.29 ± 0.01	0.18	18%	8	0.25	12%	8
	amp AMP3.8	0.34 ± 0.00	0.39	9%	48	0.25	19%	48

Table 5 :

 5 LIBS K content analyses for samples TL18, TL19, 30-01 ( a : 0.5 -1 mm, and b : 0.12-0.25 mm size fractions), ADB, and AMP3.8 (Ref.: Reference K content obtained by spectrophotometry; this work;1 : Courtillot et al., 2010; 2 : Ricci et al., 2013; Stdev.: standard deviation; N: number of LIBS analyses performed).

	Sample name	TL18	TL19	30-01	ADB		AMP3.8
	Analyzed crystal	plg	plg	plg	plg	plg	amp	mix phase
	Ref. K content (wt.%)	0.351 2	0.257 2 0.202 a,1 -0.355 b,1	0.500	0.287	0.344 0.287 -0.344
	LIBS K content (wt.%)	0.278	0.254	0.278	0.401	0.306	0.299	0.291
	LIBS Stdev.	± 0.062 ± 0.090	± 0.020	± 0.078 ± 0.075 ± 0.033	± 0.038
	LIBS relative Stdev. (%)	22	35	7	19	25	11	13
	N	9	8	5	8	3	4	10

Table 6 :

 6 Comparison between K content obtained using differents techniques (EPMA, ICP-OES, Spectrophotometry and LIBS).

	Sample name Mineral phases	K content determination using several techniques: EPMA ICP-OES Spectrophotometry LIBS
	30-01	Plagioclase	-	-	0.202 ± 0.002	0.28 ± 0.02
	ADB	Plagioclase	-	-	0.500 ± 0.005	0.40 ± 0.08
	AMP3.8	Amphibole Plagioclase	0.34 ± 0.04 0.05 ± 0.02	0.35 ± 0.09 -	0.344 ± 0.002 0.287 ± 0.004	0.30 ± 0.03 0.31 ± 0.08

Table 7 :

 7 Comparison between KArMars and reference ages (this work;1 : Courtillot et al., 2010; 2 : Ricci et al., 2013). The relative accuracy of KArMars results is given in column A% (in %). *: mean value calculated from plagioclase and amphibole ages.

	Sample name	Analyzed mineral	Reference K-Ar age ± un (Ma)	KArMars age ± un (Ma)	A%
		plagioclase	2052 ± 29	2218 ± 135	8%
	AMP3.8	amphibole	2649 ± 38	2913 ± 292	10%
		mix phases	2351 ± 300*	2585 ± 138	10%
	ADB	plagioclase	1447 ± 21	1382 ± 46	6%
	30-01	plagioclase	369 ± 5 1	362 ± 16	5%
	TL-18	plagioclase	381 ± 5 2	358 ± 20	5%
	TL-19	plagioclase	378 ± 5 2	351 ± 33	5%
	TO-35	plagioclase	374 ± 5 2	406 ± 210	9%

for its help to find old reference samples. We thank J.-B. Sirven for his assistance with LIBS theory. We thank L. Djemel and K. Kateryna for giving us the opportunity to use profilometer and SEM systems, and the Laboratoire Magmas et Volcans for using EPMA. Finally, we acknowledge V. Godard, C. Lanoé, C. Drag and P. Pariset for their help during the instrumental development.