Gaseous phase above Ru–O system: A thermodynamic data assessment

Highlights

• New gaseous phase thermodynamics of Ru–O is performed.

• Accurate thermal functions for RuO₄(g), RuO₃(g), RuO₂(g), RuO(g) are proposed.

• Third law calculation for RuO₃(g) and RuO4(g) give reliable formation enthalpies.

• Non-equilibrium experimental conditions are highlighted for RuO₂(g) and RuO(g).

• Born-Haber cycles give more reliable RuO₂(g) and RuO(g) formation enthalpies.

Abstract

The present study is a critical assessment of thermochemical data for gaseous ruthenium oxides based on available experimental data. A full critical analysis and a reinterpretation of data are presented with a proposition for new accurate standard formation enthalpies values: Δ_f H°₂₉₈(RuO₄, g) = −197.6 ± 5.5 kJ mol⁻¹, Δ_f H°₂₉₈(RuO₃, g) = −53.0 ± 10 kJ mol⁻¹, Δ_f H°₂₉₈(RuO₂, g) = 158 ± 20 kJ mol⁻¹ and Δ_f H°₂₉₈(RuO, g) = 301 ± 28 kJ mol⁻¹.

Introduction

Knowledge of the gas phase thermodynamic properties of the Ru–O binary system is important for at least three main applications: - (i) the corrosion behavior of Ru electrodes or RuO₂(s) catalytic coatings – (ii) the evaporation of some Ru species above 373 K during nitric acid treatment of the Ru containing burned nuclear fuels that have been supposed containing mainly RuO₄(g) or related molecules, or - (iii) in severe nuclear accident releases.

In the Ru–O₂ system, there exists two condensed oxides:

• RuO₂(s) the thermodynamic properties of which have been recently compiled and assessed by Gossé et al. [1] and Chatillon et al. [2];

• RuO₄(s) that melts at room temperature and vaporizes with significant total vapor pressure at low temperature as determined by Nikol'ski (1964) [3].

The gas phase composition of the Ru–O system has been studied only above the Ru–RuO₂ range where the molecules of RuO₄(g), RuO₃(g), RuO₂(g) and RuO(g) are identified by independent spectroscopic methods and by quantum chemistry and their structure is given. In the last compilation made in 1990 by Cordfunke and Konings [4] the free energy functions have been only estimated because a lack of experimental values concerning the structural data of the molecules.

The present work improve this first selection of thermodynamic properties by taking into account more complete experimental data sets. In the first step of this study, a literature review of the structural properties of the gaseous molecules of Ru–O system and their thermodynamic functions is made. Then, starting with these selected values, new third law calculations are performed to propose more accurate values than those proposed in the last compilation [4].

First step in the thermodynamic knowledge of gaseous molecules is the determination of the structural properties of the molecules: their geometry (i.e. interatomic distances and bond angles), vibration frequencies, rotational constants as well as their electronic states.

Interatomic Ru–O distances in the gaseous molecules as well as methods of measurement and/or calculations come from Hameka et al. [5], Siegbahn [6], Miradji et al. [7], Zhou et al. [8], Krauss et Stevens [9], Schäfer et al. [10] and Scullman and Thelin [12]. Distances in the two varieties of RuO₄(s) solid crystal published by Pley and Wickleder [11] are considered (see Table I-1 in Appendix I).

Molecular parameters of RuO₄(g) as proposed in literature and used throughout this work are presented in Table I–2 in Appendix I. The selected structure is a tetrahedral molecular structure, strictly regular (T_d), in agreement with that proposed by Greene et al. [13]. Pley and Wickleder [11] by X-ray diffraction of RuO₄(s) crystal showed that the crystal is formed of tetrahedral entities with Ru–O distances ranging from 1.695 Å (cubic structure) to 1.701 Å (monoclinic structure).

Normally, the gaseous molecule has a more relaxed structure because there are no nearest neighbors, thus, RuO₄(g) would be similar to the most relaxed solid entity, i.e. the monoclinic. The geometry of the RuO₄(g) molecule was analyzed by Braune and Stute [14] by electron diffraction from molecular beam on the basis of a regular tetrahedron structure and then more recently by Schäfer et al. [10] with an improved technique. In the present study, the retained interatomic distance value for Ru–O in RuO₄ (g) is set as proposed by Schäfer et al. [10] (i.e. r _Ru–_O with 1.7058 ± 0.003 Å) because it is considered as slightly relaxed (0.3%) as for the condensed phase when a monoclinic crystal structure is considered. Quantum calculations (see Table I–2 in Appendix I) give smaller values resulting in higher vibration frequencies (mainly verified with the normal symmetric vibration ν₁). Several authors determined the ν₃ (anti-symmetric) vibration frequency using IR spectroscopy (Table I–2 in Appendix I): experimental measurements are in agreement, around 920 cm⁻¹, meanwhile ab-initio calculations gave higher values ranging from 923 to 974 cm⁻¹. Generally, frequencies obtained by quantum or ab-initio calculations are higher than those measured because the calculated equilibrium interatomic distance is smaller than the measured one and these are related to a slightly greater force constant. After analysis of the band contours in spectroscopy, the complete set of experimental vibration frequencies proposed by McDowell et al. [15] is retained in this work with the only vibration frequencies resulting from Ar matrix isolation. Indeed, those measured in the presence of Ne are discarded because they might be influenced by Van Der Vaals interactions in the case of this rare gas with higher molar mass. The ab-initio frequency set calculated by Hameka et al. [5] and Miradji et al. [7] confirms the present experimental selection while being slightly higher in relation with an interatomic Ru–O distance calculated shorter than from our selected experimental values. The selected ground electronic state is the one calculated by Miradji et al. [7] ¹A₁ with a triplet state at an electronic level 14210 cm ⁻¹ (1.76 eV).

Molecular parameters of RuO₃(g) as proposed in literature and used throughout this work are presented in Table I–3 in Appendix I. The structure of the RuO₃(g) molecule is planar type one with 120° angle (D_3h). The only measured vibration frequency ν₃ by Kay et al. [16] is rather confirmed by ab-initio calculations of Miradji et al. [7] with some shift. The comparison of Ru–O interatomic distances between RuO₄(g) and RuO₃(g) (see Table I–3 in Appendix I) obtained by various quantum chemistry calculations shows that there is no (or very little) hybridization of the released electrons with those in other orbitals. Thus, the RuO₃(g) molecule keeps the same interatomic distance as in the saturated RuO₄(g) molecule. Consequently, in this study, the experimental interatomic distance proposed for RuO₄(g) was retained for the RuO₃(g) molecule and farther for RuO₂(g). The ground electronic state of RuO₃(g) selected is that calculated by Miradji et al. [7] ¹A₁ with a triplet state at an electronic level 5183 cm ⁻¹ (0.64 eV).

Molecular parameters of RuO₂(g) as proposed in literature and used throughout this work are presented in Table I-4 in Appendix I. Two experiments of IR spectroscopy ([8,16]) are in relative agreement and propose a C_2v type structure with a 150 ± 2° angle. Vibration frequencies (symmetric and anti-symmetric in the axis of the bonds) that was experimentally measured are in relative agreement, while ab-initio calculations give some higher symmetrical frequencies. These higher values reflect the downward trend in frequency measured when molecules are trapped in Ar or Ne matrix. The general trend shows small difference between the two experimental symmetrical frequencies ν₁ and anti-symmetric ν₃ - particularly determined by Kay et al. [16] – in agreement with ab-initio work of Miradji and al [7]. Given this agreement and because the bending frequency ν₂ was not experimentally determined, the present study retains the value of ν₂ calculated by Miradji et al. [7]. To be consistent between frequencies and interatomic distance, the value proposed by Miradji et al. [7] is proportionally adjusted with the average ratio deduced from frequencies ν₁ and ν₃. For the electronic state, the basic one is a singlet sigma ¹A₁ type and, as proposed by two quantum calculations, there exists a triplet state at 334 cm⁻¹ level. Since no other available experimental information exists, this study retains these values for the electronic states.

Molecular parameters of RuO(g) as proposed in literature and used throughout this work are presented in Table I–5 in Appendix I. This study retains the values from atomic emission spectroscopy obtained by Scullman and Thelin [12], who already corrected the data of Raziunas et al. [20]. Ab-initio calculations of Miradji et al. [7], more refined than other previous calculations give interatomic distance and vibration frequency close to experimental values. The calculated Ru–O distance in the molecule RuO(g) shows a weakened bond due to the presence of non-bonding orbitals, which probably play a "repulsive" role (anti-bonding). This bond length is consistent with spectroscopic results (Table I–1 and Table I–5 in Appendix I). The ground electronic state selected takes into account the first level observed by spectroscopy.

Thermodynamic studies of the Ru–O system gas phase stability have been carried out: - (i) using transpiration or transport methods mainly for the study of RuO₄(g) and RuO₃(g) molecules, - (ii) using mass spectrometry for the study of RuO₂(g) and RuO(g) molecules.

Schäfer et al. [[24], [25], [26]] carried out three kinds of experiments:

• Heating a Ru filament in a controlled oxidizing atmosphere (the so-called “incandescent filament technique”) with evaluation of the filament mass loss by weighing before and after heating

• Continuous weighting with a thermo-balance of Ru samples subjected to oxidation and H₂ reduction cycles to evaluate the volatility of Ru oxides in relation to the Ru loss of the initial sample

• Total pressure measurement by a static method i.e. manometry at cold point (room temperature at walls).

In the incandescent filament technique, Ru loss of the filament is performed at two oxygen pressures for the same temperature (pyrometric monitoring of filament surface). Some experiments are carried out in sealed glass ampoules followed by a heat treatment. Ru mass losses allows the authors to determine the main vaporization reactions from the different proportions of Ru losses related to the O₂(g) pressure according to the following reactions,

$$\text{Ru}\left(\text{s}\right)+3/2{\text{O}}_2\left(\text{g}\right)={\text{RuO}}_3\left(\text{g}\right)$$

$${\text{RuO}}_2\left(\text{s}\right)+{\text{½ O}}_2\left(\text{g}\right)={\text{RuO}}_3\left(\text{g}\right)$$

$${\text{RuO}}_2\left(\text{s}\right)+{\text{O}}_2\left(\text{g}\right)={\text{RuO}}_4\left(\text{g}\right)$$

At low temperature, the proportionality observed between the mass losses and the pressure p(O₂) (reaction (3)) indicates that RuO₄(g) molecule is in equilibrium with RuO₂(s) and that this molecule is predominant in the gas phase. Conversely, at high temperature RuO₃(g) predominates since the mass loss is proportional to pressure p(O₂)^3/2 on Ru(s) and to pressure p(O₂)^1/2 on RuO₂(s).

Schäfer et al. [26] have published two tables (on pages 50 and 51) with the partial pressures of RuO₄(g) and RuO₃(g) and the equilibrium constants of reactions (2) and (3). Schäfer et al. [26] selected two measurements at two temperatures – 1069K for RuO₄(g) – 1477K for RuO₃(g) - to deduce reaction (2) and (3) enthalpies. They estimated entropies of RuO₂(s) and Cp of RuO₃(g) and RuO₄(g) gaseous molecules to deduce enthalpies of reactions (2) and (3) at 298 K, then enthalpies of formation.

Bell and Tagami [27] confirm, by varying the oxygen content at different temperatures in a transpiration device, that the vapor is mainly composed of RuO₃(g) and RuO₄(g). Then, quantitative experiments are performed by method of transpiration under O₂ flow at 1 atm with a RuO₂(s) sample doped by a radiotracer. The mass transport of total Ru is performed by radiometric analysis of deposit at the output. It is assumed that the total transport is proportional to the sum p(RuO₃) + p(RuO₄) according to reactions (2) and (3). The authors [27] estimated the proportions of RuO₃(g) and RuO₄(g) in the vapor from these mass losses according to relation,

$$p_{Ru{O}_3}+p_{Ru{O}_4}=A{e}^{C/T}+B{e}^{D/T}$$

in the temperature range 1075 - 1776 K and by an iterative method they determine all constants. These four constants are related to the enthalpies and entropies of reactions (2) and (3) and their fit is a general treatment based on 2nd law of thermodynamics that determines the enthalpy and entropy values of the two reactions at mean temperature.

Penman and Hammer [28] performed a transpiration experiment with an oxygen carrier gas on a sample of RuO₂(s). The pressure of the oxygen, which is fed counter-currently in the furnace shell to the evaporation chamber, is determined by means of a mercury manometer, while the vapors of the gaseous oxides of Ru escape through a capillary tube and then condense in a glass wool. Deposits are then dissolved to analyze the transported amount of Ru by scintillation. Different capillary tube diameters are used to certify that the extracted gas is saturated within a flow range of a factor 10. However, the authors [28] do not give any indication on the differences observed nor on the determination of a plateau as a function of the carrier gas flow rate as is usually done in the transpiration method: constant determined pressure values correspond at least to part of the usual plateau. Based on the experiments of Schäfer et al. [[24], [25], [26]] and a constant temperature test with different oxygen pressures, the authors proposed a vapor mainly composed of RuO₄(g) in their low temperature range i.e. 726 - 996 K.

Tagirov et al. [29] vaporized RuO₂(s) in quartz effusion cells between 980 and 1190 K and measure the O₂ pressure by mass spectrometry without detecting any other Ru-based gaseous species, probably due to insufficient mass spectrometry sensitivity. Indeed, according to Schäfer et al. [26] and Bell and Tagami [27] RuO₃(g) and RuO₄(g) would have a proportion ≈ 10⁻³ to 10⁻⁴ relatively to oxygen pressure, a proportion that can be measured in the usual detection range of mass spectrometry using effusion cells.

To circumvent the sensitivity requirements of the mass spectrometer and promote the dissociation of complex gaseous oxides, Norman et al. [23] carried out a mass spectrometric study using an effusion cell equipped with an O₂ gas flow inlet to stabilize the oxygen potential by compensating for the preferential oxygen lost by effusion. For low temperature studies (<1500 K), the sample is pure Ru placed in a quartz cell, and for higher temperatures the authors [23] use an alumina cell. The O₂(g) pressure in the cell has been set at about 10⁻⁴ bar (this 10⁻⁴ bar, we assume, must be the usual upper pressure limit for the effusion method) according to the authors’ [23] estimates and they can vary it by a factor 10 (probably below 10⁻⁴ bar). The authors [23] analyzed the slope of the measured ionic intensities of RuO₃⁺, RuO₂⁺ and RuO ⁺ at low temperature as a function of the variation in the oxygen potential p(O₂) ≈ intensity (O₂⁺) and they observed a break indicating the transformation of the sample from Ru(s) to RuO₂(s). In the low temperature range, they study the following reactions that produce RuO₃(g) which is the main detected gaseous species,

Ru(s) + 3/2 O₂(g) = RuO₃(g) (1295–1538 K) (1)

$$K_p\left(1\right)=\frac{{\text{p}}_{Ru{O}_3}}{a_{Ru}{\text{np}}_{O_2}^{3/2}}\approx \frac{I_{Ru{O}_3^{+}}T}{1\text{n}{\left(I_{O_2^{+}}\text{n}T\right)}^{\frac{3}{2}}}\approx I_{Ru{O}_3^{+}}\text{n}{T}^{-1/2}$$

RuO₂(s) + 1/2 O₂(g) = RuO₃(g) (1147–1228 K) (2)

$$K_p\left(2\right)=\frac{{\text{p}}_{Ru{O}_3}}{a_{Ru{O}_2}{\text{np}}_{O_2}^{1/2}}\approx \frac{I_{Ru{O}_3^{+}}T}{1\text{n}{\left(I_{O_2^{+}}\text{n}T\right)}^{\frac{1}{2}}}\approx I_{Ru{O}_3^{+}}\text{n}{T}^{1/2}$$

These reactions correspond to two different slopes over the entire temperature range when working at a constant ion intensity I(O₂⁺). These slopes (Fig. 2 of Norman et al. [23]) give the enthalpies (2nd law method) of reactions (2) and (3).

At higher temperature, using an alumina cell, the molecule RuO₃(g) is totally decomposed - disappearance of the RuO₃⁺ ion intensity in the mass spectrum - and the authors [23] observe the evolution of RuO₂⁺, RuO⁺ and Ru⁺ ion intensities as a function of the oxygen potential followed by the O⁺ coming from the dissociation of oxygen at high temperature according to the reaction,

$$O_2\left(\text{g}\right)=2\text{ O}\left(\text{g}\right)$$

As the proportion of O(g) varies with temperature, the authors [23] monitor the main reactions involving O₂(g) (i.e. O₂⁺ ionic intensities) which can be maintained at a constant value when the flow of incoming oxygen is adjusted. Indeed, maintaining the intensity of O₂⁺ as a constant value at a given temperature does not allow determining the sensitivity of the mass spectrometer for this species. Based on the assumption of a constant O₂⁺ ion intensity, the slopes reflect the following main vaporization reactions,

Ru(s) + O₂ (g) = RuO₂(g)

$$K_p\left(7\right)=\frac{{\text{p}}_{Ru{O}_2}}{a_{Ru}\text{n}{p}_{O_2}}\approx \frac{I_{Ru{O}_2^{+}}T}{1\text{n}{I}_{O_2^{+}}T}\approx I_{Ru{O}_2^{+}}$$

Ru(s) + ½ O₂ (g) = RuO(g)

$$K_p\left(9\right)=\frac{p_{RuO}}{a_{Ru}\text{n }{p}_{O_2^{+}}^{1/2}}\approx \frac{I_{Ru{O}^{+}}T}{1\text{n}{\left(I_{O_2^{+}}\text{n}T\right)}^{1/2}}\approx I_{Ru{O}^{+}}\text{n}{T}^{1/2}$$

Oxygen potential p(O₂) remains fixed at 10⁻⁴ bar (estimated by the authors) whatever the temperature, and the 2^nd law (slope) gives the enthalpies of the above reactions.

The parent ion Ru⁺ (measured at an ionization voltage of 10 V to eliminate any contribution of dissociative ionization of the gaseous oxide species) is not sensitive to oxygen pressure as long as RuO₂(s) is not formed. Indeed, its origin is only due to the vaporization of the sample Ru(s) as Ru(g) with an oxygen solubility in Ru(s) considered negligible (see Chatillon et al. [2]). The authors registered the logarithm of the products $I_{R{u}^{+}}\text{n}T$ (in mass spectrometry, these products are proportional to the pressure of Ru) with respect to the inverse of temperature and, then, calibrated their spectrometer on the known pressure of pure Ru to obtain the mass spectrometer sensitivity related to Ru(g). Further, sensitivities for oxides are calculated using the maximum ionization cross-section (at 75 V) as proposed by Otvos and Stevenson [30] - but applied to their measurement at very low potentials i.e. close to the ionization threshold - and have estimated the efficiency of the multiplier (efficiency(yield) ≈ 1/√Molar Mass of the ion). They not provide any of their estimated values to re-calculate their sensitivity. However, the use of the maximum ionization cross-sections for such very low ionization potentials can lead to large uncertainties (≈2 to 5 times the value of the ion ratios between the different species). Their calibration of the spectrometer leads to the evaluation of the equilibrium constants K_p (not published) and consequently the published Gibbs energies which allow the calculation of the reaction entropies at medium temperature by the relation,

$${\text{n}}_r{S}_T^{°}=\text{R}\ln K_p+\frac{{\text{n}}_r{H}_T^{°}}{\text{T}}.$$

using their published 2^nd law reaction enthalpies ${\text{n}}_r{H}_T^{°}$.