Ioana Nuta
email: ioana.nuta@grenoble-inp.fr

Francois Virot

Evelyne Fischer

Christian Chatillon

Thermodynamic assessment of RuO 4 oxide

Keywords: RuO 4, Ru-O, Entropy, Formation enthalpy

RuO 4 oxide appears much less stable than RuO 2 (s) in the Ru-O binary system with a melting point close to room temperature and a certain propensity to vaporize or decompose at low temperatures. Ab initio simulations in the framework of density functional theory (DFT) on RuO 4 (s) are performed to analyze the cubic and monoclinic structures and to evaluate the heat capacities at low temperatures. Then, a critical evaluation of thermodynamic data from calorimetry and vapor pressure determinations -was carried out coupled with ab-initio calculations to propose new thermodynamic data: the entropy, S° (RuO 4, s, cubic, 298K) = 132.7 J•K -1 mol -1 and formation enthalpy,  f H° (RuO 4 , s, cubic, 298K) = -252.4  5.5 kJ mol -1 .

Introduction

In the event of a hypothetical severe accident in a nuclear power plant, the potential release of highly radiotoxic fission products (FPs), such as ruthenium, is of particular concern [START_REF] Thoma | Phase diagrams of nuclear reactor materials[END_REF][START_REF] Garisto | Thermodynamic behaviour of ruthenium at high temperatures[END_REF][START_REF] Motojima | Removal of Ruthenium from PUREX Process[END_REF][START_REF] Eichler | Volatilization and deposition of ruthenium oxides in a temperature gradient tube[END_REF][START_REF] Mun | Review of Literature on Ruthenium Behavior in Nuclear Power Plant Severe Accidents[END_REF][START_REF] Auvinen | Progress on ruthenium release and transport under air ingress conditions[END_REF]. RuO 4 (g) shows a high volatility at low temperatures and many groups suspect that it is the source of ruthenium transport in a carrier gas flowing over organic or aqueous solutions used in nuclear effluent treatment. [START_REF] Auvinen | Progress on ruthenium release and transport under air ingress conditions[END_REF][START_REF] Holm | Interactions of RuO4 (g) with different surfaces in nuclear reactor containments[END_REF][START_REF] Holm | Deposition of RuO4 on various surfaces in a nuclear reactor containment[END_REF][START_REF] Beuzet | Ruthenium release modelling in air and steam atmospheres under severe accident conditions using the MAAP4 code[END_REF][START_REF] Swain | Separation and recovery of ruthenium: a review[END_REF][START_REF] Kato | Study on volatilization mechanism of ruthenium tetroxide from nitrosyl ruthenium nitrate by using mass spectrometer[END_REF][START_REF] Lefebvre | Addressing Ruthenium speciation in tri-n-butyl-phosphate solvent extraction process by Fourier transform infrared, extended X-ray absorption fine structure, and single crystal X-ray diffraction[END_REF][START_REF] Kajan | Interaction of ruthenium tetroxide with surfaces of nuclear reactor containment building[END_REF]. In previous studies -(i) we proposed new thermodynamic data for RuO 2 (s) [START_REF] Chatillon | Chemical thermodynamics of RuO2(s)[END_REF] i.e. heat capacity, entropy and enthalpy of formation, -(ii) we revised the standard formation enthalpies as well as the entropies of RuO 4 (g), RuO 3 (g), RuO 2 (g) and RuO(g) [START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF] and compared them with calculations from the SSUB database [START_REF] Sgps(sgpsbase | SGTE Pure substances database[END_REF] and with the ab-initio data given by Miradji [START_REF] Miradji | Thermodynamic Properties of Gaseous Ruthenium Species[END_REF]. The low temperature region of the Ru-O phase diagram is not accurate and some data are missing. The compound RuO 4 (s) exists in the binary system in oxygen-rich compositions and in the low temperature range since it melts at 298.65 K according to Debray and Joly [START_REF] Debray | Recherches sur le Ruthénium: acide hypzerruthènique[END_REF] and at 298.55 K according to Nikol'skii [START_REF] Nikol'skii | Existence of two modifications of Ruthenium tetroxide[END_REF]. The enthalpy of formation of this compound was determined by calorimetry by Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] and by Mercer and Farrar [START_REF] Mercer | Heats of Formation of RuO4 and RuO 4 2and Related Compounds[END_REF]. The boiling point (1 atm) of RuO 4 (l) was determined by Koda [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] at T eb = 402.75 ± 0.2 K. The vapor pressure in the range 273 to 363 K -probably in the form of the RuO 4 (g) molecule mainly if no decomposition occurs -was studied by Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF]. These data gives access to the enthalpy of formation of the solid or liquid by using the independently determined enthalpy of formation of the gaseous RuO 4 (g) molecule from a thermodynamic cycle, as already done by Cordfunke and Konings [START_REF] Cordfunke | Thermochemical data for reactor materials and fission products[END_REF]. Despite the important applications of the molecular crystal ruthenium tetroxide compound as an organic oxidant [START_REF] Piccialli | Ruthenium tetroxide and perruthenate chemistry. Recent advances and related transformations mediated by other transition metal oxo-species[END_REF] as well as its interest in the field of nuclear safety, some of its properties remain uncertain or are no longer reported in literature. There are currently no experimental data concerning the specific heat at low and high temperatures for the compound RuO 4 (s, or liq). Using original data we recalculate the thermodynamic functions to improve the description proposed in the last compilation performed in 1990 by Cordfunke and Konings [START_REF] Cordfunke | Thermochemical data for reactor materials and fission products[END_REF].

Results and discussions

Thermal functions

There is no experimental data for the low and high temperature heat capacities. In Appendix A we present our method for DFT calculations performed to obtain the heat capacity C°p at low temperature, and the deduced entropy and Gibbs energy function (free energy function referred to 0 K) for the RuO 4 (s, cubic) crystal. Hence, we propose the following relation, reliable in the 10 -298.6K range. The entropy value calculated by integration of C°p as 132.7 J K -1 mol -1 is compared with those proposed in literature (see Appendix I, Table A-2). Acceptable agreement is obtained with data extracted from the online database [26] while those published in the 1990s are excluded [START_REF] Cordfunke | Thermochemical data for reactor materials and fission products[END_REF]. In the absence of low temperature specific heat C°p experimental data, the entropy could be also estimated by Latimer's rule [START_REF] Kubaschewski | Materials Thermochemistry[END_REF][START_REF] Latimer | Methods of Estimating the Entropies of Solid Compounds[END_REF][START_REF] Latimer | Polarity and ionization from the standpoint of the lewis theory of valence[END_REF] from the ionic contributions to entropy at 298 K for oxides and compounds (see Appendix B). The so-estimated entropy which is 132.5 J K -1 mol -1 it is in agreement with the DFT based value.

Finally, the entropy retained in this work is, For the liquid phase, after melting at 298.6K, the heat capacity is considered to be constant and equal to the value of the solid at melting (298.6K), i.e. C°p = 91.598 J K -1 mol -1, a value given by the least squares adjustments as proposed in Appendix I.

Enthalpy and entropy of melting are discussed in more detail with the vapor pressure data from Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF]. Free energy function for the condensed phases, calculated in this way, is presented in figure 1.

Enthalpy of formation

Bomb calorimetry

As in this work we recalculate all intermediate relations, the presentation will be in kcal (1 cal = 4.184 J) to allow the reader to compare with the original Russian publication (reference [START_REF] Nikol'skii | Existence of two modifications of Ruthenium tetroxide[END_REF]). Table 1 also reproduces directly the original publication. Final results are presented in kJ.

In 1964, Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] prepared RuO 4 (s) by transport and condensation in a glass ampoule stored at liquid nitrogen temperature. The ampoule is introduced into a calorimeter filled with NH 3 at high pressure. The reaction between RuO 4 (s, or l) and the NH 3 gas was studied in a calorimetric bomb under 10 and 5 atm of NH 3 and for temperatures close to the melting of the oxide. Two simultaneous reactions are assumed to occur, 3 RuO 4 (s, or liq.)

+ 4 NH 3 (g) = 3 RuO 2 (s) + 6 H 2 O (l) + 2 N 2 (g) Q 2 (R2)
3 RuO 4 (s, or liq.)

+ 8 NH 3 (g) = 3 Ru (s) + 12 H 2 O (l) + 4 N 2 (g) . Q 3 1 (R3)
These reactions were confirmed by XRD and chemical analysis of the solid residue. The authors [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] did not detect any NO x molecules in the produced gas phase meanwhile they did not mention their analytical tool. The proportions of solids for each reaction -expressed as mole fraction "a" -are determined by analysis of the residue after each combustion experiment. The reactions are carried out either with RuO 4 (l) at 26°C or with RuO 4 (s) at 24°Cthe temperature of the bomb calorimeter. In parallel, water as a reaction product reacts with ammonia -this could be a dissolution forming a solution of NH 3 in water. Previously, the authors determined the heat of reaction between water and ammonia at 10 atm (proposed as 8.53 ± 0.1 kcal mol -1 ) and 5 atm (4.65 ± 0.1 kcal mol -1 ). Note that the above reactions assume that there is no dissolution of solids in water, particularly for RuO 4 whose solubility in water is discussed below.

The authors [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] combine reactions (R2) and (R3) to derive the value of the difference Q 3 -Q 2 mentioned in their relation [START_REF] Eichler | Volatilization and deposition of ruthenium oxides in a temperature gradient tube[END_REF], that corresponds to the reaction

3 RuO 2 (s) + 4 NH 3 (g) = 3 Ru (s) + 6 H 2 O (l) + 2 N 2 (g). Q 3 -Q 2
with a heat balance calculated from the standard enthalpies of the compounds as proposed,

Q 3 -Q 2 =-(ΔH°3 -ΔH°2) = 147.4 kcal.
This relationship allows the calculation of the enthalpy ΔH°i or the heat determined at constant pressure. As written, the two values Q 3 and Q 2 are therefore no longer considered as heats that the calorimeter receives at constant volume (or internal energy received by the calorimeter bomb and lost by the system) but as heats at constant pressure (enthalpies). The minus sign in front of the enthalpies confirms that the heats Q are those received by the calorimeter 2 .

On the basis of n init moles of RuO 4 (s, or l) and with a mole fraction "a" calculated from the chemical analysis according to reaction (R2) and "(1-a)" to reaction (R3), the authors expressed the total energy at constant volume released by these two simulated reactions alone, a heat that the calorimeter receives, . Therefore, the heat exchanged by the chemical system at constant volume is related to the enthalpy at constant pressure for any reaction by: dQ = dH -VdP.

It is this heat dQ supplied by the constant volume system that will be received by the calorimeter for each reaction (R2) and (R3) i.e. Q 2 and Q 3 as mentioned in their paper. Calculation of the thermal effect received by the calorimeter must be related to the enthalpies ΔH 2 and ΔH 3 at constant pressure given by the authors or from our original data selection. Relation (5) will become:

Assuming an ideal gas, the term Vdp is a function of the number of moles, Vdp = RT dn dn being the variation in the number of moles between the two terms of the reaction. For reaction (R2) dn = -2, and for reaction (R3) dn = -4. Indeed, the heats mentioned by Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] Q 2 and Q 3 are equal to,

Q 2 = -(ΔH°2 +2RT) Q 3 = -(ΔH°3 + 4RT)
and relation [START_REF] Mun | Review of Literature on Ruthenium Behavior in Nuclear Power Plant Severe Accidents[END_REF] of Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] becomes, .

This relationship is the one proposed by Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] with Q 2 and Q 3 the measured calorimetric values. With our reference for the enthalpy of formation values Δ f H(RuO 2 ,s) = -74.58 kcal [START_REF] Chatillon | Chemical thermodynamics of RuO2(s)[END_REF] and JANAF tables [START_REF] Chase | NIST-JANAF Thermochemical Tables[END_REF] Δ f H(NH 3 ,g) = -10.97 kcal and Δ f H(H 2 O,liq)= -68.315 kcal, the heat becomes .

The quantity Q above corresponds only to the two reactions mentioned (2) and (3) when they are stoichiometric. However, the amount of heat measured must also take into account the mixing reaction between the initial NH 3 phase and the created H 2 O phase, an amount that was evaluated by the authors in a preliminary calorimetric experiment.

The thermodynamic calculation at 298. as the authors we deduce the relationship .

At 10 atm, using our references, the calculated enthalpies are:

and at 5 atm, .

These last two equations we use with our chosen values for NH 3 (g). In the case where NH 3 is liquid, the relations (4) and (5) become The uncertainties listed here are standard deviations and they are directly related to the reproducibility of the experiments.

Q 3 -Q 2 = -(ΔH°3 -ΔH°2) =
Table 1. Comparison between the Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] calorimetric data as recalculated from their published relationships and with our new reference values.

*Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] are different for the solid because they results included the heat of fusion (from their vapor pressures: see section 1.3).

Initial mix RuO 4 + NH 3 RuO 2 product ΔH f (RuO 4 ) liq
Rel. ( 11),( 12) Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] This work The values for solid RuO 4 (s) can be deduced from our analysis (section 1.3.1.) of the vapor pressures measured on RuO 4 , or Δ f H°(RuO 4 , s, 298K) = -239.7 ± 7.5 kJ mol -1 Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] take into account of NH 3 dissolution in the created aqueous phase but neglected the RuO 4 (s) dissolution studied later by Nikol'skii [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF]. This dissolution reaction probably exothermic competes with the combustion for the heat received by the calorimeter. This heat contribution should be deduced from the measured Q value by the calorimeter as done for NH 3 dissolution and same effect is attended: the deduced formation enthalpy would slightly decrease. [START_REF] Watt | The Interaction of ruthenium tetroxide and ammonia[END_REF] observed frank ignition when they mixed NH 3 (g) with RuO 4 (s) at -70°C. To avoid this ignition, they added small increments of NH 3 (g) under 10 -3 Torr to RuO 4 (s) starting at -70°C. They observed some reactions detected by a black coloration of the solution formed turning brown at -50°C. No reaction products were found by X-ray analysis. Using thermogravimetric analysis (TGA) and a temperature ramp of 3°C/min, an explosion occurred at 206°C. From the infrared absorption analysis, they proposed the formation of the compound Ru 4 N 11 O 12 H 33 since similar absorption bands were observed with the compound Os. The authors believe that Nikol'ski and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] actually measured other reactions by calorimetry. However, since Nikol'ski and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] analyzed all their reaction products by XRD and chemical analysis to determine the RuO 2 (s) / Ru(s) ratio, we believe that the bomb calorimetric reactions observed under NH 3 (g) high pressure remain very different from those observed by Watt and McMordie. [START_REF] Watt | The Interaction of ruthenium tetroxide and ammonia[END_REF] This is probably due to the actual operating temperature range of the bomb as well as the higher pressure of NH 3 . [START_REF] Mercer | Heats of Formation of RuO4 and RuO 4 2and Related Compounds[END_REF] [START_REF] Mercer | Heats of Formation of RuO4 and RuO 4 2and Related Compounds[END_REF] performed dissolution calorimetry measurements in an aqueous medium. Firstly, the authors carried out a reaction between Br 2 (liq.) and Ru(s) powder dispersed in a solution of NaOH (1 mol l -1 ): the bromine is enclosed in a bulb that is immersed in soda. After reaching thermal equilibrium in the calorimeter, the ampoule is broken and a thermal effect is recorded. Two main reactions that take place simultaneously are proposed,

Thermal analysis In 1965 Watt and McMordie

Dissolution in water Calorimetry

Ru(s) + 3 Br 2 (liq.) + (a NaOH, b H 2 O) = [Na 2 RuO 4 , 6 NaBr, (a-8) NaOH, (b+4) H 2 O] ΔH 1 3 Br 2 (liq.) + (a NaOH, b H 2 O) = [5 NaBr, NaBrO 3 , (a-6) NaOH, (b+3) H 2 O]. ΔH 2
The square brackets indicate an aqueous solution. The total heat or enthalpy observed is, relationship where f D is the fraction of Br 2 entering the two reactions (called disproportion) in relation to the total introduced. This factor is calculated from the analysis of the concentration of RuO 4 2-ions formed (analysis of the Na 2 RuO 4 content). A linear fit of the observed enthalpy to the factor f D gives the enthalpies ΔH 1 and ΔH 2 . The authors found that the deduced enthalpy ΔH 2 and that proposed in an NBS report agree and this result confirms the two competing reactions cited. Next, three other reactions in solution are used to obtain the enthalpy of formation of sodium ruthenate Na 2 RuO 4 in the basic solution. Note that two approximations are made in the summation, i.e. for the heats of formation of NaBr(aq) and water in the pure state. From the heat of formation of Na + (aq) at infinite dilution, the heat of formation of the RuO 4 2-(aq) ion is -109.4 ± 1.0 kcal mol -1 (-457.7 ± 4.2 kJ mol -1 ) that the authors estimate to be close to the standard enthalpy of formation.

Nine other dissolution reactions using numerous intermediate compounds (BaCl 2 , NaIO 4 , NaIO 3 ) in the acid phase (HClO 4 ) make it possible to precipitate the compound RuO 4 (liq. at 26°C) and to determine its enthalpy of formation from 19 enthalpies: six of these enthalpies of dissolution come from the calorimetric investigations of the authors, the others are known reactions. The final value proposed by the authors is: Δ f H°(RuO 4 ,liq, 299K) = -238.5 ± 4.6 kJ mol -1 The uncertainties quoted by the authors largely overlap with those existing for the many intermediate reactions used and quoted. Perhaps the authors take into account their three approximations in the uncertainty domain. The present calorimetric determination overlaps with the determination of Nikol'ski and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] determination within the limits of their overall uncertainties.

Mercer and Farrar [START_REF] Mercer | Heats of Formation of RuO4 and RuO 4 2and Related Compounds[END_REF] quote an enthalpy of formation for the RuO 4

2-(aq) ion = -109.4 ± 1.0 kcal mol -1 (-457.7 ± 4.2 kJ mol -1 ) being more negative than the final product RuO 4 (s. or liq. 299K) proposed by Nikol'skii and Ryabov [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF]. However, as RuO 42-(aq) ion is formed by dissolution of RuO 4 in water, the difference between these two studies in the proposed enthalpy of formation of RuO 4 (s, or l) may arise from the dissolution in this medium that is produced in bomb calorimetry experiments.

1.3 Volatility of RuO 4 (s, or l)

Determination of vapor pressures

Nikol'skii (1963) [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] determined the total saturated vapor pressure using a Bourdon gauge constructed with glass (Pyrex) in the temperature range 22°C to 91°C (295-364K). The Bourdon gauge is immersed in a thermostatically controlled liquid bath regulated at ± 0.02°C. Another series of measurements were carried out in the low temperature range from 0.4 to 50°C by calibrated radiometry by cross-checking with the previous results. The temperature is reported to be known within ± 0.1°C. This work is presented in figure 2.

Figure 2 Total vapor pressure as measured on RuO 4 (s, or liq.) according to literature [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] more recently determined the boiling point of RuO 4 (l) at 1 atm. This pressure is in agreement with the extrapolated experimental data of Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF]. We also detail very old data from Debray and Joly (1888) [START_REF] Debray | Recherches sur le Ruthénium: acide hypzerruthènique[END_REF]. These authors observed a certain instability of the RuO 4 as it easily decomposes into black RuO 2 (s) under atmospheric pressure with probably a release of oxygen. The higher pressure boiling point data from Koda [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] assumes that no decomposition of the oxide occurs in a closed system when atmospheric pressure is not operating.

In Nikol'skii's experiments [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] the preparation of the compound RuO 4 (s) takes place "in situ" by sublimation/condensation of a high-temperature input vapor phase composed mainly of RuO 4 (g) and O 2 (g) molecules. During the condensation process, oxygen is removed by pumping. Other gaseous oxides such as RuO 3 (g) are probably in very small amounts in the initial vapor phase -see previous analysis by Nuta et al. [START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF] on the gas phase in the Ru-O binary system -and their condensation in the deposit may form an orange RuO 4 (s) oxide with excess O 2 (g) rather than the RuO 2 (s) -RuO 4 (s) diphase that quickly turns grey or black.

The ionization potentials determined by Dillard and Kiser [START_REF] Dillard | Ionization and Dissociation of Ruthenium and Osmium Tetroxides1[END_REF] in the mass spectrometric observation of the vapor phase of RuO 4 (l) introduced directly into an ion source confirm the hypothesis that the RuO 4 (g) molecule is major in the saturated vapor phase since they identify only the RuO 4 (g) parent molecule by the RuO 4

+ molecular ion and possibly some traces of RuO 3 (g). Thus, the vapor pressure determined by Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] is rich in RuO 4 (g), although in the RuO 2 (s) -RuO 4 (s, or liq) two-phase domain, there is also an equilibrium pressure of O 2 (g). This could be lower than RuO 4 (g) although higher than that calculated in the Ru(s) -RuO 2 (s) domain ≈ 1.4 10 -44 bar at 298 K.

Brittain and Hildenbrand [START_REF] Brittain | Gas phase reaction of Ruthenium Tetroxide with Nitrogen Oxides[END_REF] observed the evaporation of RuO 4 (s) with a quadrupole mass spectrometer using a two-compartment effusion cell constructed of Pyrex. The lower compartment, loaded with RuO 4 (s) and maintained at a temperature between -30 and -78°C, is connected by a tube and a monel valve to the upper compartment maintained at a temperature between 20 and 130°C. The connection tube is fitted with a Pt baffle at the entrance to the upper cell to impose sufficient collision (and thermal equilibrium) in the upper compartment fitted with the effusion orifice. The lower compartment is kept at a constant temperature throughout the experiment (under high vacuum) to supply the upper compartment with a constant molecular flow or inlet pressure. With the upper compartment at 20°C, the authors first observed the O 2 + ion (from oxygen) for at least one hour when the connecting valve was opened, and, then, the RuO 4 + (molecular ion of RuO 4 (g)) appeared and remains stable, i.e. at constant pressure "although O 2 + is still present in the vapor (sic)". After experiment, the authors observed a black deposit in the whole effusion device and they propose a first passivation of the wall materials by RuO 2 (s) deposits. These observations mean that the commercial RuO 4 (s) material began to decompose during storage (although kept at -5°C) and during introduction of the device into the mass spectrometer. However, the authors point out that the oxygen pressure remains stable when RuO 4 (g) was detected and this means that decomposition occurred in parallel with the production of RuO 4 (g) in the upper cell. In a second specific experiment, the upper compartment was heated up to 130°C while the lower compartment remains at a constant temperature assuming a constant inlet flow and pressure in the upper compartment. Such an experiment therefore allows the decomposition of RuO 4 (g) into e.g. RuO 3 (g), RuO 2 (g), RuO(g), Ru(g) and O 2 (g) to be observed. The authors observed a 20% decrease in the intensity of RuO 4 + and its disappearance at 190°C, whereas the other molecules were not observed. It can be seen that for a constant applied pressure of RuO 4 (g) in the upper compartment, according to the Knudsen relation, the increase in temperature produces a decrease in the Knudsen flow to the mass spectrometer ion source. According to Knudsen's relation, .

with a constant pressure the decrease in relative flow rate (as detected by the ion source) between 20 and 130°C is, This value, close to that observed in spectrometry, suggests that RuO 4 (g) does not decompose in this temperature range -at least in the sensitivity range of their quadrupole. Indeed, the disappearance of the RuO 4 + ion at 190°C may also be due to a poor sensitivity of the quadrupole. Note also that the authors encountered significant difficulties in their measurement technique: -(i) black deposits of RuO 2 (s) in the ion source, requiring frequent disassembly and cleaning of the ionization source, -(ii) poor resolution of the true molecular beam with respect to multiple re-evaporations of the volatile RuO 4 (g), due to the design of their shuttering device, as evidenced by a residual shuttering effect, as explained in figure 3. + observed by Brittain and Hildenbrand [START_REF] Brittain | Gas phase reaction of Ruthenium Tetroxide with Nitrogen Oxides[END_REF] in mass spectrometry upon introduction of NO 2 (g) and, then, activation of the molecular beam shutter. First, the introduction of NO [START_REF] Garisto | Thermodynamic behaviour of ruthenium at high temperatures[END_REF]

(g) into the effusion cell decreases the pressure of RuO 4 (g) at the black arrows (probably the interaction of some decomposition reaction). Then, the shutter movement shows successively a first instantaneous decrease due to the occultation of the real molecular beam coming directly from the effusion orifice (measurement of the real partial pressure of RuO 4 (g)), followed by a re-vaporization of the stable RuO 4 deposits in the ionization box, and, finally, some residual pressure of RuO 4 (g) is detected in the background in relation with the capacity of the pumping device and the ambient temperature.

In conclusion, after an initial heterogeneous reaction between RuO 4 (g) and the Pyrex or platinum walls producing a deposit of RuO 2 (s), the decomposition of RuO 4 (g) in the gas phase seems to be limited in the temperature range corresponding to the Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] vapor pressure experiment but the relative proportion between O 2 + and RuO 4 + has not been evaluated -and consequently their pressure ratio -. Furthermore and as a confirmation, a low rate of decomposition into RuO 2 (s) + O 2 (g) was measured by [START_REF] Ortner | Research and development studies on waste storage process[END_REF] [START_REF] Ortner | Research and development studies on waste storage process[END_REF] in the range 100 -160°C. These authors give an Arrhenius law preceded by an incubation time. Finally, a net decomposition occurred above 1025°C, analyzed by Thermogravimetry. These observations confirm that the probable vapor phase is relatively pure RuO 4 (g) in the Nikol'skii experiments but with an unknown proportion of oxygen. This proportion of oxygen may be reduced due to the in-situ elaboration of RuO 4 (s) during pumping and storage at liquid nitrogen temperature, but could increase during the experiment performed in a closed Bourdon gauge.

Standard Enthalpy of melting by second law

The vaporization enthalpy of RuO 4 (s, or liq.) assuming the vapor is composed mainly of RuO 4 (g) species can be calculated by the second and third laws of thermodynamics. The enthalpy of fusion is deduced from the enthalpies of sublimation and vaporization calculated from the slopes (second law) as shown in Figure 2 using Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] total pressure data for the solid and liquid. The latter set is in agreement with Koda's [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] boiling point that is retained it in this work. The second law calculations give an enthalpy of vaporization for the liquid of 41.74 ± 0.29 kJ mol -1 , and for the solid, 54.9 ± 1.3 kJ mol -1 , the uncertainties quoted being the standard deviations. The enthalpy and entropy of fusion of RuO 4 at 298.6 K are then deduced: 14 Δ fusion H°(RuO 4 , s→liq, 298.6K) = 13.3 ± 0.9 kJ mol -1

Standard Enthalpy of Vaporization

Assuming that the main vaporization reaction of solid or liquid RuO 4 produces the single species RuO 4 (g) in the vapor phase, the free enthalpy of the vaporization reaction of the RuO 4 (s, or liq) is written, relation where the activity From this relationship, the standard enthalpy of vaporization at 298.15 K (presently sublimation) can be calculated by applying the third law of thermodynamics,

The second term, usually called the free energy (or Gibbs) function, is calculated from the entropies of each reactant at 298K and their heat capacities: The function for RuO 4 (g) comes from Nuta et al. [START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF] while the functions for RuO 4 (s), RuO 4 (liq) and melting come from this work. The treatment by the third law is presented in table 2. [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] and Koda [START_REF] Koda | Boiling points and ideal solutions of ruthenium and osmium tetraoxides[END_REF] The third law values are practically constant as a function of the measurement temperature (see table 2) and are in agreement with those obtained by the second law. This means that the entropy proposed for RuO 4 (s) as well as that calculated for the liquid do not introduce any bias in the calculations of the third law. Moreover, the assumption of the main vapor RuO 4 (g) in the Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] experiments seems reliable.

Table 2. Third law sublimation enthalpy of the solid RuO 4 at 298 K and comparison with the results of the 2 nd law of Nikol'skii

1.5 Enthalpies of formation of RuO 4 (s, or liq.)

The enthalpies of formation analyzed in this work are summarized in table 3, compared with previous compilations. Also included are the solid and gaseous species that were used as references in the thermodynamic cycles leading to the standard enthalpy of formation of RuO 4 (s, or liq.). *Note that these values should decrease due the dissolution of RuO 4 (s) in the produced water phase that is not entered in the combustion process.

The thermodynamic cycle using vapor pressure gives an enthalpy value that does not match the calorimetric results. As the calculation of the third law is based on the main gas species RuO 4 (g) in equilibrium with the RuO 4 (s, or liq), this assumption may be wrong. Following the various studies on the decomposition of this oxide -either in storage or during transport in the gas phase under vacuum (cf. Brittain and Hildenbrand [START_REF] Brittain | Gas phase reaction of Ruthenium Tetroxide with Nitrogen Oxides[END_REF] ) -the gas phase on RuO 4 (s, or liq) could be a mixture RuO 4 (g) + O 2 (g). Thus, another hypothesis may be that a vapor richer in oxygen than RuO 4 (g) and the decomposition occurs according to the main reaction, RuO 4 (s) = RuO 2 (s) + O 2 (g).

If the pressure on RuO 4 (s, or l) determined by Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] using a closed Bourdon gauge is mainly composed of oxygen, the equilibrium constant of this reaction at 298.6 K -the melting point of RuO 4 (s) -leads directly to the standard enthalpy of formation of RuO 4 (s) using the known enthalpy of RuO 2 (s) [START_REF] Chatillon | Chemical thermodynamics of RuO2(s)[END_REF]:

and with a total pressure (assumed = p(O 2 ), at 293K (20°C) according to Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] p = 0.0106 bar,

(J mol -1 )
The enthalpy of formation of RuO 4 (s) would be -358.1 kJ mol -1 , a value far away from the proposed calorimetric values or those deduced from thermodynamic cycles based on RuO 4 (g).

The Gibbs energies of mixing -calculated for RuO 4 (s) with the current ab-initio entropy -are shown in figure 4, highlighting the instability of the RuO 4 (s) compound because it is located above the RuO 2 (s) -½ O 2 (g) line, except for the calculation based on the assumption of lone oxygen in the vapor phase that is located along the line and thus RuO 4 (s) would be an ideal solution between RuO 2 (s) and oxygen. Higher values would explain its propensity to decompose during storage or temperature rises into RuO 2 (s) deposits and oxygen release. The equilibrium oxygen pressure calculated with the current free enthalpy values is presented in table 4. With the enthalpy deduced from the vapor pressure of oxygen alone in the Nikol'skii experiments, we obviously find the original pressure introduced in the calculations.

For other enthalpy values, the oxygen pressures being very high, this is a good indicator of the instability of the RuO 4 (s or liq.) compound compared with RuO 2 (s). Thus, it would explain that some experimenters in the past had explosions during temperature increase ramps. This also justifies that the RuO 4 (s, or g) is able to release oxygen during storage with low decomposition kinetics as studied for example by Ortner et al. [START_REF] Ortner | Infrared spectrum and thermodynamic properties of ruthenium tetroxide[END_REF]and by Mun et al. [START_REF] Mun | Study of RuO 4 decomposition in dry and moist air[END_REF]. As a partial conclusion, relatively large differences in the enthalpies of formation cannot be clearly explained although calorimetric determinations and vapor pressure measurements with saturated RuO 4 (g) vapor give enthalpies in the same range. Compared to the calorimetric results, the vapor pressure measurements with the only RuO 4 (g) performed by Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] can be used as the best saturation pressure for the pure compound RuO 4 (s, or liq) (reference activity = 1), especially in view of the following thermodynamic analysis of RuO 4 behavior in solution. However, the vaporization of complex gaseous oxides -even in a closed vessel -may be delayed (low vaporization kinetics) and therefore the vapor pressures will be underestimated in the experiments due to an evaporation coefficient < 1. Indeed, from the above pressure values mentioned in table 4, the experimental vapor pressures of Nikol'skii [START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] should be increased by a factor of ≈ 44 to reach his calorimetric result [START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] corresponding to an evaporation coefficient ≈1/44 = 0.027, as a quite plausible value for the vaporization of complex oxides. This value for an evaporation coefficient is less probable if the solid RuO 4 (s) is considered as RuO 4 entities bonded by intramolecular forces.

Conclusion

In this work values for thermodynamic functions for RuO 4 solid and liquid are summarized in table 5. For the calorimetric determinations of the enthalpy of formation of the RuO 4 (s) oxide, the dissolution of RuO 4 (s) in water will probably made the two calorimetric values quoted compatible. They remain far from the enthalpies resulting from the thermodynamic cycles involving the vapor phase when the latter is mainly composed of RuO 4 (g) gas on the condensed oxide. The determination of the vapor pressure is in agreement with DFT calculations of the sublimation enthalpy, and for this reason we propose to retain the third law enthalpy obtained from vapor pressure experimental values. , ab-initio data are useful to select the more accurate value. Furthermore, when RuO 4 (s, or liq.) is dissolved in a more or less concentrated acidic environment or with added salts, a vaporization of RuO 4 (g) will occur. This vaporization is largely dependent on pH, as the activity of dissolved RuO 4 (s) may vary considerably. With Ru nitrate salts, there is also some decomposition of the nitrate producing other molecules than RuO 4 (g) in the gas phase. When dissolved in CCl 4 (liq.), the activity of dissolved RuO 4 (liq.) is very low, resulting in low volatilization of RuO 4 (g). These volatilization phenomena have been observed in the treatment of nuclear effluents by dissolution in aqueous solutions or solvents, as in the distillation process.

where E elec is the electronic energy at 0 K whereas ΔZPE and Δ(H 298 -H 0 ) correspond to the difference between gaseous and solid phase of the zero-point energy and enthalpy increment, respectively.

Table A-2. Entropy, enthalpy of sublimation and enthalpy of formation of RuO 4 compound calculated within harmonic approximation for the cubic crystal structure compared to published ones in thermodynamic databases. Theoretical values from Material Project [START_REF] Jain | Commentary: The Materials Project: A materials genome approach to accelerating materials innovation[END_REF] and OQMD [START_REF] Kirklin | The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies[END_REF] and databases are computed at 0K and do not includes the zero point energy whereas all other values are calculated at 298.15K. Our uncertainty on  f H  corresponds to the one of heat of formation of RuO 4 (g) evaluated in Ref. [START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF]. S°2 98 RuO 4 (s) / J K -1 mol -1 OQMD database [START_REF] Kirklin | The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies[END_REF] -418 --MP database [START_REF] Jain | Commentary: The Materials Project: A materials genome approach to accelerating materials innovation[END_REF] -576 --Cordfunke et al [START_REF] Cordfunke | Thermochemical data for reactor materials and fission products[END_REF] -243 ± 7 54.8 ± 2.4 137.3 ± 8 Online database [26] -239. The computed sublimation enthalpy (Table A-2) is close to published values in accordance to evaluated uncertainty of Ref. [START_REF] Cordfunke | Thermochemical data for reactor materials and fission products[END_REF]. From sublimation enthalpy, the standard heat of formation of crystal can be deduced by: ) relation where the standard heat of formation of RuO 4 (g) is taken from recent critical assessment (-197.65.5 kJ/mol [START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF]). Usually, the standard heat of formation is computed from elements under their most stable states: Ru (c) , O 2(g) for ruthenium tetroxide.

Unfortunately, this approach is excluded in the present work because the overbinding of GGA functional in the O 2 molecule as expected [START_REF] Wang | Oxidation energies of transition metal oxides within the GGA+U framework[END_REF] would approximately induce an error of about 200 kJ/mol on the standard heat of formation. Furthermore, this calculation scheme would involve species having too different chemical binding leading to an additional bias. These statements could explain the huge gap between our value and those coming from DFT databases [START_REF] Jain | Commentary: The Materials Project: A materials genome approach to accelerating materials innovation[END_REF][START_REF] Kirklin | The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies[END_REF], the fact that their DFT methodologies do not include long range interactions additionally induces differences. Finally, present approach tends to get the most accurate theoretical heat of formation: Δ f H  = -251.0  5.5 kJ/mol. The application of the original Latimer's rule for RuO 2 (s) shows that this rule largely underestimates the contribution of oxygen (3.2 instead of 8.8 deduced from reliable experimental RuO 2 entropy value). Thus, the Latimer's value applied to RuO 4 (s) entropy could be underestimated as presented in the second raw. Correction based on known RuO 2 (s) produces an entropy that agrees with the DFT value.

Figure 1 .

 1 Figure 1. Gibbs (or free) energy function referred to 298 K for RuO 4 (s) and RuO 4 (liq) calculated from solid and liquid heat capacities, entropy at 298 K and enthalpy of fusion.

Figure 3 .

 3 Figure 3. Different ionic intensities of RuO 4+ observed by Brittain and Hildenbrand[START_REF] Brittain | Gas phase reaction of Ruthenium Tetroxide with Nitrogen Oxides[END_REF] in mass spectrometry upon introduction of NO 2 (g) and, then, activation of the molecular beam shutter. First, the introduction of NO 2 (g) into the effusion cell decreases the pressure of RuO 4 (g) at the black arrows (probably the interaction of some decomposition reaction). Then, the shutter movement shows successively a first instantaneous decrease due to the occultation of the real molecular beam coming directly from the effusion orifice (measurement of the real partial pressure of RuO 4 (g)), followed by a re-vaporization of the stable RuO 4 deposits in the ionization box, and, finally, some residual pressure of RuO 4 (g) is detected in the background in relation with the capacity of the pumping device and the ambient temperature.

  7 ± 7.5 from[START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF]* -252.4 ± 5.5 of[START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] with RuO 4 (g) vapor -358.1 of[START_REF] Nikol'skii | Saturated Vapour Pressure of Ruthenium Tetroxide[END_REF] with O 2 (g) vapor assumption -251.0 ± 5.5 from DFT (

Figure 4 .

 4 Figure 4. Gibbs's energies of mixing of compounds in the Ru-1/2 O 2 binary system .To check the consistency of the deduced values, we calculated the equilibrium pressures of oxygen existing on the two-phase mixture RuO 4 (s) -RuO 2 (s) via the equilibrium constant of the reaction, RuO 4 (s) = RuO 2 (s) + O 2 (g) corresponding to the release of oxygen with the black RuO 2 (s) deposit as observed by many researchers.

  2 (s) entropy value; ** calculated from the average of the two extrapolations in Figure B-1.

Figure B- 1 .

 1 Figure B-1. Application of Latimer's rule to estimate the contribution of the O 2-ion in a compound with several oxidation states.

The heats Q 2 and Q 3 are heats at constant pressure produced by the

	ΔQ is not a state function while ΔH and ΔU are. According to the fundamental definition of
	heat (Prigogine [31] p. 24), the enthalpy of reactions (R2) and (R3) is expressed as a function
	of the internal energy E (or U) and the work by this relation :
	H=U+pV.
	Using the first principle (Prigogine [31] p. 19) written as
	dU = dQ -pdV,
	the differential of H becomes,
	dH = (dQ -pdV) + Vdp + pdV = dQ + Vdp.
	two
	reactions and received by the calorimeter (thermal effect). The RT terms correspond to the
	work, i.e. with VdP = dn RT, produced at constant volume in the calorimeter when the
	number of gaseous moles dn created or lost in the two reactions is taken into account and
	changes the pressure. Finally, the authors propose,
	.
	The pressure variation in the calorimetric bomb must be taken into account, that makes the
	calculation of the heat at constant volume difficult and problematic. The main question is how
	to transform heat at constant pressure, ΔH, into heat at constant volume, ΔU, knowing that

The heat of reaction Q is in principle the total heat measured by the calorimeter bomb, i.e. at constant volume.

  All parameters of the experiments w, Δr , n and a, are given by Nikol'skii and Ryabov[START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] in their table allowing us to recalculate the enthalpy of formation of RuO 4 (s, or liq, 298K) as presented in table 1. Our re-calculations reproduce those of Nikol'skii and Ryabov[START_REF] Nikol'skii | Determination of the Heat of Formation of Ruthenium Tetroxide[END_REF] and, furthermore, new data are obtained with theses references. The average values calculated for the RuO 4 liquid are, Δ

	Experiments with NH 3 (liq) performed under 10 atm:
	From reaction (R3) with NH 3 liquid,
		from our references
	By importing the enthalpy values ΔH°3 of reaction (R3) we obtain the relationship
		.
		109.38 kcal with our references
	with
	then	.

f H°(RuO 4 , liq, 298K) = -226.4 ± 7.5 kJ mol

-1

  determination of the total pressure.The present 3 rd law results lead to the standard enthalpy of formation for RuO 4 (s) at 298 K derived from Nuta et al.[START_REF] Nuta | Gaseous phase above Ru-O system: A thermodynamic data assessment[END_REF] selected enthalpy of formation of RuO 4 (g), i.e. -197.6 ± 5.5 kJ mol. -1 Δ f H°(RuO 4 , s, 298K) = -252.4 ± 5.5 kJ mol-1

			-To be continued-
	T/K T/K	log 10 p/bar log 10 p/bar	RLn p / J K -1 mol -1 RLn p / J K -1 mol -1	∆ vap Fef° 298 / J K -1 mol -1 ∆ vap Fef° 298 / J K -1 mol -1	∆ subl H°(298K) / kJ K -1 mol -1 ∆ subl H°(298K) / kJ K -1 mol -1
	273.55 330.57	-2.735 -1.127	-52.363 -21.572	147.894 144.017	54.8 54.7
	277.05 331.05	-2.543 -1.124	-48.677 -21.528	148.132 143.969	54.5 54.8
	278.35 341.55	-2.572 -0.908	-49.237 -17.382	148.217 142.916	55.0 54.7
	283.25 349.25	-2.378 -0.768	-45.528 -14.699	148.519 142.162	55.0 54.8
	293.15 349.65	-2.069 -0.777	-39.607 -14.876	149.040 142.123	55.3 54.9
	293.35 350.03	-1.995 -0.773	-38.189 -14.804	149.049 142.086	54.9 54.9
	294.05 350.19	-1.975 -0.766	-37.814 -14.673	149.082 142.071	55.0 54.9
	297.35 353.65	-1.878 -0.713	-35.963 -13.651	149.226 141.737	55.1 55.0
	297.45 353.91	-1.893 -0.708	-36.236 -13.560	149.230 141.712	55.2 55.0
	297.65	-1.866	-35.732	149.238	55.1
	295.11 363.59	-1.940 -0.545	-37.150 -10.426	149.129 140.795	55.0 55.0
	297.15 363.95	-1.897 -0.546	-36.323 -10.457	149.217 140.761	55.1 55.0
	297.97 Boiling point of Koda	-1.871	-35.814	149.251	55.1
	Melt 399.45	0.005823753	0.048	137.590	54.9
	298.65	-1.862	-35.651 3 rd average value law 147.391	54.7 54.8
	303.15 303.55	-1.741 -1.711	-33.340 Standard deviation 146.899 -32.750 146.856 2 nd solid law**	0.2 54.6 54.5 54.9
	307.95 313.15	-1.632 -1.495	-31.243 Standard deviation 146.381 -28.617 145.826 2 nd liquid law**	1.3 54.7 54.6 41.6*
	313.75	-1.489	-28.514 Standard deviation 145.763	54.7 0.1
	318.25	-1.371	-26.251	145.289	54.6
	321.15	-1.277	-24.454	144.986	54.4
	323.45	-1.270	-24.308	144.747	54.7
	299.01	-1.846	-35.334	147.351	54.6
	301.05	-1.803	-34.520	147.128	54.7
	303.45	-1.711	-32.750	146.867	54.5
	303.61	-1.723	-32.981	146.849	54.6
	305.61	-1.676	-32.093	146.633	54.6
	308.05	-1.615	-30.917	146.370	54.6
	309.87	-1.589	-30.429	146.175	54.7
	310.23	-1.535	-29.379	146.137	54.5
	311.53	-1.539	-29.455	145.998	54.7
	311.67	-1.529	-29.266	145.983	54.6
	319.85	-1.336	-25.576	145.121	54.6
	321.45	-1.294	-24.775	144.955	54.6
	321.63	-1.308	-25.041	144.936	54.7
	327.15	-1.190	-22.785	144.366	54.7

*If the enthalpy of fusion is added, the result is 54.9 kJ mol

-1

, corresponding exactly to the solid. ** Corrections for average temperatures are not applied as these temperatures are close to 298.15K.

Table 3 .

 3 Comparison of different published standard enthalpies of formation at 298 K with our present results.

	Compound or molecules	Δ Cordfunke and	Calorimetry	This work
		Könings	Experiences	/ kJ mol -1
		compilation [24].	/ kJ mol -1
		/ kJ mol -1
	RuO 2 (s)	-314.2 ± 0.5	-305. 1	-312.3 ± 1.6 of [14]
				as a reference

f H°(RuO x , s/g, 298K)-Standard enthalpy of formation at 298 K

Table 4 .

 4 Oxygen pressure calculated on the two-phase RuO 4 (s) + RuO 2 (s) at 298K from different proposed formation enthalpies of RuO 4 (s). All other thermodynamic functions for RuO 2 (s) and RuO 4 (s) are those used in this work.

	RuO 4 (s) = RuO 2 (s) + O 2 (g)
	∆ form H°(298K) reference for RuO4(s)	∆ r G °(298K) / kJ mol -1	ln p(O 2 )/bar	p(O 2 ) / bar
	Nikol'ski calorimetry [20]	-103.236	30.810	2.40 •10 13
	corrected (this work)
	Cordfunke and Konings [24]	-93.286	27.840	1.23 •10 12
	Mercer and Farrar [21]	-91.136	27.199	6.49 •10 11
	Nikol'ski [23] RuO steam 4	-90.536	27.020	5.43 •10 11
	(g)
	Nikol'ski [23] steam O 2 (g)	15.164	-4.526	1.08 •10 -2

Table 5 .

 5 Thermodynamic functions retained in this work for RuO 4 (s) and RuO 4 (liquid).However, the further calculation of vapor pressures with our proposed data is only valid in the presence of freshly prepared RuO 4 (s, or liq) oxide discarding the presence of oxygen produced during storage. Indeed, due to the thermodynamic instability of RuO 4 (s) compared to RuO 2 (s) and O 2 (g), RuO 4 (s, or liq) decomposes at room temperature, and may "explode" when the temperature exceeds 200°C, producing RuO 2 (s) and O 2 (g). The kinetics of this decomposition suggest a low decomposition rate at low temperatures. As the entropy and heat capacity of the RuO 4 (s) compound have not been determined experimentally, we recommend a value obtained by ab-initio calculations. Facing the scattered values for enthalpies of formation of RuO

	Function	Values for RuO 4 (s or liq)
	Cp° (RuO 4 , s, cubic) / J K -1 mol -1	(10 to 298K)
	S° (RuO 4 , s, cubic,298K) / J K -1 mol -1	132.7
	 f H° (RuO 4 , s, cubic, 298K) / kJ mol -1	-252.4  5.5
	 sub H°(298K) / kJ mol -1	53.4  5.5
	T fusion / K	298.6  0.1
	 fus H° / kJ mol -1	13.3 ± 0.9
	Cp° (RuO 4 , liquid) / J K -1 mol -1 	91.598

  [START_REF] Eichler | Volatilization and deposition of ruthenium oxides in a temperature gradient tube[END_REF]

Table B -

 B 1. Latimer rule estimation and comparison with selected experimental data.

	Origine	S°2 98 Ru	S°2 98 O

2- S°2 98 RuO 2 (s) S°2 98 RuO 4 (s)

	Latimer table[27, 28]	53	3.2	59.4	140.7
	Experimental Ru[20] + Latimer for O 2-	28.614	3.2	35.014	116.3
	Re-calculated	28.614	8.768*	46.15	132.5**

* calculated contribution O 2-from experimental RuO

N.B. Quantities Q

and Q

quoted here are the heats received by the calorimeter.

The authors mentioned in their relation (4) a value of Q

-Q 2 =147.4 kcal. From the enthalpies mentioned in their paper, we calculate a value of Q 3 -Q 2 = -147.36 kcal. The difference in sign clearly confirms that the constant volume heats, Q 2 and Q 3 , mentioned by the authors first, are indeed the thermal effects that the calorimeter receives. In contrast, the enthalpies are related to chemical reactions. A value of Q 3 -Q 2 = -(ΔH°3 -ΔH°2 ) = 142.265 kcal was recalculated using the enthalpy of formation of RuO 2 (s) that we critically retained in a previous work[START_REF] Chatillon | Chemical thermodynamics of RuO2(s)[END_REF] and the JANAF[START_REF] Chase | NIST-JANAF Thermochemical Tables[END_REF] tables for gaseous ammonia and liquid water.

Acknowledgements

I.N. ,C.C., E.F. thank IRSN (France) for the financial support (contract number IRSN-LS20317). The authors would like to thank Sidi Souvi, Bénédicte Michel and Marc Barrachin for their helpful discussions and comments on this work. This work was made possible by the HPC resources of the CCGT/CCRT.

Appendix A: Thermodynamic data for low temperature solid RuO 4

Computational method

All calculations are performed in the DFT framework as implemented in the Quantum Espresso package [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF]. The Perdew-Burke-Ernzerhof [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] function constructed in the generalized gradient approximation (GGA) is used to calculate the exchange and correlation energies. Ultra-soft pseudopotentials are used to model the ionic nuclei while only valence electrons are explicitly considered (semi-core electrons are included in the pseudopotentials). To ensure the cohesion of the crystal, especially during the lattice optimization step, Van der Waals corrections are necessary as ruthenium tetroxide exhibits a molecular crystal behavior. In this work, long-range interactions are taken into account using the DFT-D [START_REF] Barone | Role and effective treatment of dispersive forces in materials: Polyethylene and graphite crystals as test cases[END_REF]. The convergence threshold on forces has been set at 7.2× 10 -4 eV/Å whereas the default value is considered on energy. In addition, the criterion for the residual pressure during the cell optimization is set at 0.05 kbar. The Brillouin zone (BZ) sampling and plane wave cut-off energy were adjusted to satisfy a convergence criterion of 2 meV/f.u on electronic energy. The BZ grids were extended to 2 × 2 × 2 and 2 × 3 × 2 for cubic and monoclinic crystal stacks, respectively. The plane wave cut-off energy is fixed at 1142 eV for both cells. The vibrational properties of ruthenium tetroxide are calculated from phonon data computed with the finite displacement method as implemented in the Phonopy [START_REF] Togo | First principles phonon calculations in materials science[END_REF] tool. The sizes of primitive cells are large enough to accurately calculate the phonons at Γ for the cubic cell while a 1 × 2 × 1 supercell is used for the monoclinic cell. Two different arrangements are studied, a cubic and a monoclinic crystal structure. The cubic unit cell is described by an arrangement of 8 RuO 4 patterns while only 4 units describe the monoclinic crystal structure (see Ref. [START_REF] Pley | Two crystalline modifications of RuO4[END_REF] for more details on crystallographic data as well as the initial atomic coordinates). In a complementary way, the RuO 4 molecule is also briefly studied with a similar approach to obtain the sublimation enthalpy. In this case, the calculation is performed in a 15 Å cubic cell and the plane wave cut-off energy is set to 1224 eV.

Results

Comparison of the total energies of the two crystal structures shows that the cubic structure is the more stable at 0 K, although the energy difference is extremely small (0.18 kJ/mol f.u. or 1.9 meV/f.u., including ZPE). Taking into account the effect of temperature in the harmonic approximation, the Helmotz vibrational energies remain degenerate up to room temperature. Therefore, the phase stability cannot be definitively stated and the present results tend to confirm the crystal polymorphism of ruthenium tetroxide in accordance with the most recent experimental study [START_REF] Pley | Two crystalline modifications of RuO4[END_REF]. Thermodynamic properties such as standard entropy (S  (T)), heat capacity, enthalpy increment (H(T) -H(0)) and Gibbs energy function can be calculated from the vibrational data. The first properties are mandatory for a critical evaluation of the experimental calorimetric results, in particular the Gibbs energy function Φ(T), of each species concerned. This property is expressed as follows:

(A.1) The obtained data are fitted with the following function:

where T is given in Kelvin. The heat capacity can be expressed as:

Comparison of calculated heat capacity at both constant volume (harmonic) and constant pressure(quasi-harmonic) for the cubic crystal (cub.) as well as heat capacity at constant volume for the monoclinic one (mono). Calculated Gibbs energy function () is computed for the cubic crystal of ruthenium tetraoxide whitin harmonic approach. Straight lines correspond to the interpolation with Equation 1 and 2 of computed data (dashed lines and dots).

The quasi-harmonic calculation showed no deviation from the harmonic approximation in the interval 0 K to room temperature interval (highlighted by the heat capacity property, see figure A-1), so it can be assumed in this case that the harmonic approximation gives an acceptable evaluation of the vibration data. The parameters obtained for the two functions are summarized in Table A-1.

Table A-1. Parameters of the Gibbs energy function (Eq. 1) and the heat capacity (Eq.2) for the cubic crystal of ruthenium tetraoxide. Parameters lead to properties given in J/mol/K.

--These sets of thermodynamic functions complete the missing thermodynamic data needed to interpreting calorimetric experiments.

The difference in enthalpy between the gas and the solid, the sublimation enthalpy, is calculated using the properties of the solid and the gas according to the formula:

Appendix B. Estimated entropy via Latimer's rule

In the absence of experimental data on the specific heat at low temperature C°p, another conventional method was used to estimate the entropy. Moreover, it was used as a cross check for ab initio calculations as well as an indication of the general uncertainty for the entropy. The estimate can be done from the Latimer 's rule [START_REF] Kubaschewski | Materials Thermochemistry[END_REF][START_REF] Latimer | Methods of Estimating the Entropies of Solid Compounds[END_REF][START_REF] Latimer | Polarity and ionization from the standpoint of the lewis theory of valence[END_REF] based on ionic contributions to entropy at 298 K for oxides and compounds. In Table B-Erreur ! Source du renvoi introuvable.1 we mention the calculations with Latimer's rule at beginning for RuO 2 (s), whose experimental value is known and can be used for scaling, and, then, an evaluation is made for the RuO 4 (s) from the Latimer contribution for O 2-with a cation of degree +8. For the later degree, in figure B-1 two types of smoothing are used to obtain the contribution of each oxygen for a +8 charge of the Ru cation.


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The provisioning territory through middle and upper palaeolithic : between prehistorics' and prehistorians' perceptions

Solène Caux, Erwan Vaissié, Jean-Philippe Faivre

To cite this version:

Solène Caux, Erwan Vaissié, Jean-Philippe Faivre. During the Palaeolithic, the cultural territory is traditionally represented for each prehistoric group by the area containing all sites where evidences of this material culture occur. Inside this large cultural territory we could attempt to identify provisioning territories by studies focused on one single site or by regional synthesis showing the relations between several places. However, some studies highlight that provisioning territories and cultural territories do not always fit. How to interpret such results?

Here we present a cross-study of four French sites from both Middle and Upper Palaeolithic in order to compare the classical model and the outsider results. We will first synthesis the results of Combe-Grenal (Lot; Middle Palaeolithic) and l'abri Pataud (Dordogne; Upper Palaeolithic) that fit with the classical model and show clearly all the well-known differences regarding provisioning territories between these two phases. Then we will detail two other cases that show significant differences between provisioning and cultural territories: Baume-Vallée (Haute-Loire; Middle Palaeolithic) and le Pigeonnier (Gironde; Upper Palaeolithic). Finally, we will discuss the interpretation of these results on various levels questioning:

-our own concepts: what is a cultural territory and how do we define the share of knowledge through space?

-on what data are we basing the comparisons to support the cultural territory expansion? -and finally the palethnological implications of these outsider cases for both Middle and Upper Palaeolithic: could we precise the management of raw materials between direct (nomadism) or indirect (trade) provisioning by the study of resources and/or groups mobility?

04098616 THE PROVISIONING TERRITORY THROUGH MIDDLE AND UPPER PALAEOLITHIC: BETWEEN PREHISTORICS' AND PREHISTORIANS' PERCEPTIONS

	Solène Caux 1 , Erwan Vaissié 1 , Jean-Philippe Faivre 1 1 De la Préhistoire à l'Actuel : Culture, Environnement et Anthropologie (PACEA) -UMR
	5199 ; Université de Bordeaux

The provisioning territory through middle and upper palaeolithic : between prehistorics' and prehistorians' perceptions. 24th EAA Annual Meeting, Sep 2018, Barcelone, Spain. hal-


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