Scholarly article on topic 'Molecular data of mixed metal oxides with importance in nuclear safety'

Molecular data of mixed metal oxides with importance in nuclear safety Academic research paper on "Chemical sciences"

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Abstract of research paper on Chemical sciences, author of scientific article — Attila Kovács, Rudy J.M. Konings

Abstract The gas-phase structural and spectroscopic properties of selected mixed metal oxides (Cs2CrO4, Cs2MnO4, Cs2MoO4, Cs2RuO4, BaMoO4, BaMoO3) have been calculated using Density Functional Theory (DFT). The possible structural isomers have been analyzed and for the found global minima the vibrational (IR, Raman) spectra have been predicted taking into account also anharmonic corrections. The bonding properties have been characterized by means of the Natural Bond Orbital analysis model while the low-lying excited electronic states have been calculated using time-dependent DFT. In order to assess the stability of the target species the dissociation enthalpies have been evaluated.

Academic research paper on topic "Molecular data of mixed metal oxides with importance in nuclear safety"

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Journal of Nuclear Materials

journal homepage: www.elsevier.com/locate/jnucmat

Molecular data of mixed metal oxides with importance in nuclear safety

Attila Kovacs*, Rudy J.M. Konings

European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe, Germany

GRAPHICAL ABSTRACT

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ABSTRACT

Article history: Received 11 March 2016 Received in revised form 4 May 2016 Accepted 6 May 2016 Available online 8 May 2016

The gas-phase structural and spectroscopic properties of selected mixed metal oxides (Cs2CrO4, Cs2MnO4, Cs2MoO4, Cs2RuO4, BaMoO4, BaMoO3) have been calculated using Density Functional Theory (DFT). The possible structural isomers have been analyzed and for the found global minima the vibra-tional (IR, Raman) spectra have been predicted taking into account also anharmonic corrections. The bonding properties have been characterized by means of the Natural Bond Orbital analysis model while the low-lying excited electronic states have been calculated using time-dependent DFT. In order to assess the stability of the target species the dissociation enthalpies have been evaluated.

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The chemistry of the fission product in irradiated fuel is complex due to the numerous chemical reactions that can possibly occur, depending on the local oxygen potential and temperature [1,2]. Thermochemical calculations suggest that cesium could form compounds like CsI, Cs2UO4, Cs2MoO4 and barium compounds like BaZrO3 or BaUO3 [2], but in reality this will strongly depend on the diffusion kinetics of the different elements in the fuel matrix. In Light Water Reactor (LWR) fuels the mobility of most fission products is low and reactions are generally not taking place during normal operation. However, in Fast Reactor (FR) fuels operating at much higher temperatures the formation of fission product phases

* Corresponding author. E-mail address: attila.kovacs@ec.europa.eu (A. Kovacs).

is more common. An oxide phase rich in cesium and molybdenum has been observed in the gap between the pellet and the cladding [3], which may also contain alloying elements from the steel cladding, such as Cr and Mn, and a perovskite Ba(Zr,Pu,Mo,U)O3 phase has been observed in post-irradiation examinations of irradiated fuels [4,5]. Ru is also an abundant fission product [6] and although it is not highly volatile under the conditions in the fuel pin, it can become highly volatile under oxidizing conditions. For example, in the Chernobyl accident the total release of 103Ru was higher than that of 137Cs [7].

Mixed oxide phases such as Cs2MO4 and BaMO4 with M representing transition metals like Cr, Mn, Mo or Ru vaporize congru-ently to form stable gaseous species and thus can contribute to the gaseous releases from defected fuel pins. For example, we have identified Cs2MoO4 in the inhalable aerosol fraction produced by reaction of CsI and Mo in air after a short thermal transient generated by a laser pulse and concluded that it was formed by

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0022-3115/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

condensation of the gaseous phase [8].

Knowledge of the stability of the gaseous species of relevant mixed fission compounds like Cs2MoO4, BaMoO3 and Cs2CrO4 is thus of importance for understanding and modeling the fission product behavior during normal operation and accidental conditions. The vapour pressure of these compounds has been measured in the past [9-14] and from these measurements the enthalpy of formation of the gaseous species can be derived. Such analysis is, however, severely hampered by the absence of reliable thermo-dynamic data (entropy, heat capacity) for the gases. The thermal function can be derived from the molecular parameters but they are poorly known for these species. For that reason we have performed high-level quantum chemical calculations that provide the required information on the molecular structure, vibrational frequencies and electronic ground and excited states. In the present paper we show the computed results on Cs2CrO4, Cs2MnO4, Cs2MoO4, Cs2RuO4, BaMoO4 and BaMoO3. The geometry and harmonic vibrational frequencies Cs2RuO4 have been reported recently [15]. In the present study we extend them with the anharmonic frequencies, low-lying excited states and charge distribution characteristics.

2. Computational details

The DFT calculations were carried out with the Gaussian 09 code [16]. We used the B3LYP exchange—correlation functional [17,18] in conjunction with the small-core quasi-relativistic pseudopotentials of the Stuttgart-Cologne group for the metals (for Mo and Ru ECP28MDF with valence basis 71s56p41d3f2g1h/6s6p5d3f2g1h [19]; for Ba ECP46MDF with valence basis 13s12p6d4f2g,/9s9p6d4f2g [2o]; for Cs ECP46MDF with valence basis 12s11p5d3f2g/8s8p5d3f2g [21]) while the cc-pVQZ all-electron basis set for Cr, Mn [22] and O [23]. The default Finegrid, having 75 radial shells and 302 angular points per shell, was used for integration. The stability of the wave-functions was checked for all the optimized structures. In the case of BaMoO3 and MoO2 both the singlet and triplet spin multiplicities were probed. In order to find the minima on the potential energy surfaces several possible structures of the target molecules (including mono-, bi- and tridentate coordinations, symmetric and asymmetric arrangements) were investigated. The character of the optimized structures was determined by frequency calculations. The study of the bonding properties was based on atomic charges and orbital populations obtained by natural bond orbital analysis [24] using the NBO5.9 [25] code. The thermal corrections to the enthalpies were calculated using the rigid rotor harmonic oscillator approximation by means of a home-made Fortran code.

3. Results and discussion

3.1. Structures and bonding

The minimum structures found on the potential energy surfaces of the target molecules are presented in Fig. 1. The bis-bidentate D2d structures of ground-state Cs2CrO4, Cs2MnO4, Cs2MoO4 and Cs2RuO4 are in agreement with the molecular structures determined by gas-phase electron diffraction for Cs2CrO4 [26], Cs2MoO4 [27] and related compounds (K2CrO4 [28], Rb2MoO4 [29], Cs2SO4 [30], Cs2WO4 [27]). We note that the experimental geometrical parameters from these old studies have generally large experimental uncertainties. Nevertheless, our computated data agree well with the experimental ones for Cs2MoO4, while the deviations are over the given experimental errors for Cs2CrO4.

For BaMoO4 the bidentate C2v structure proved to be the global minimum being lower in energy by 37 and 117 kJ/mol than the C3v tridentate and monodentate local minima, respectively. For BaMoO3 a singlet bidentate Cs structure (close to the planar C2v

saddle-point, cf. Fig. 1) is the global minimum. The triplet bidentate C2v structure of this molecule lies higher in energy by 16 kJ/mol. The other symmetric structures are saddle-points on the singlet and triplet potential energy surfaces showing one or two imaginary frequencies.

The geometrical parameters of the global minima are compiled in Table 1. The MO4 moiety of the four Cs2MO4 molecules shows only slight deviations from the tetrahedral MO4- structure. The change in BaMoO4 is somewhat larger. We note the small deviation of BaMoO3 from the planar arrangement with the terminal oxygen being out of the plane of the MoO2 moiety by 30°. This refers to some steric effects of a lone pair, the presence of which is clarified from the NBO analysis (vide infra).

The NBO data compiled in Table 2 support the strongly ionic character of the molecules. The natural charges of Cs and Ba approach the formal ionic charges of +1 and + 2 e, respectively. In contrast, the natural charges of the oxygens are around -1 e. The bridging oxygens have a somewhat more negative character than the terminal ones in agreement with the strongly electrostatic nature of their bonding with Cs and Ba. The bonding with the central metals (Cr, Mn, Mo, Ru) has a mixed ionic-covalent character. It can be seen in the atomic charges of the metals being between +1 and + 2 e (the formal charge of a hexavalent metal ion is +6 e) and explains the smaller charge of the oxygens (the formal charge is -2 e). In BaMoO3 the central Mo is formally tetravalent. The Lewis model used by the NBO analysis shows a hybrid lone pair consisting of 21% 5s and 79% 4 d electrons. The steric demand of this lone pair is responsible for the tilt of the terminal oxygen from the plane of the MoO2 moiety. We note the smaller positive charges of the first-row transition metals (Cr, Mn) with respect to the second-row ones (Mo, Ru). This is in agreement with the larger electronegativity of the former elements [31] leading to somewhat smaller ionic contribution in their bonding. The extra valence electrons (in addition to the six ones forming the bonds of such hexavalent metals) in Mn and Ru are not localized on a well-defined lone pair orbital. It can be concluded from the symmetric D2d structure that they form molecular orbitals being delocalized over the MO4 moiety.

3.2. Spectroscopic properties

In order to extend the molecular data, we computed the vibra-tional frequencies of the six molecules. The anharmonic frequencies, the IR intensities and Raman intensities corrected for the 514 nm laser line are compiled in Table 3. The harmonic frequencies and uncorrected Raman scattering activities are given as supplementary information. The fundamentals are characterized by the irreducible representations of the given point groups. Visualization of the fundamentals by means of the GaussView 5 code [32] facilitated the determination of their major vibrational components, this assignments is also given in Table 3.

In general, the vibrational frequencies fall in the expected wavenumber ranges. Due to the larger mass and expected weaker force constants of the second-row transition metals with respect to the first-row ones, the frequencies of the former Cs2MO4 molecules are in most cases somewhat smaller than those of the isostructural first-row Cs2MO4. The frequencies decrease generally also along the two rows, in agreement with the stronger metal-oxygen bonds (reflected by the dissociation energies, vide infra) in the closed-shell Cs2CrO4 and Cs2MoO4 molecules. In agreement with the one-side interaction, in BaMoO4 and BaMoO3 there are significant differences in the frequencies of the moieties containing the bridging and terminal oxygens. Regarding the spectral intensities, there are no notable differences in the IR intensities of the studied molecules. In contrast, while five of the molecules (all Cs2MO4, and

Fig. 1. Found minimum structures of the investigated molecules.

Table 1

Geometries3 of the global minima of each studied mixed oxide.

Symmetry Cs2CrO4b Cs2MnO4 Cs2MoO4c CS2RuO4d BaMoO4 BaMoO3

D2d D2d D2d D2d C2v Cs

M-O 1.647 1.68 (1) 1.646 1.775 1.80(3) 1.777 1.854 1.826

M-O' - - - - 1.715 1.711

A-O 2.730 2.85 (4) 2.699 2.780 2.80 (5) 2.764 2.335 2.396

O-M-O 105.5 115(4) 104.4 103.0 105 (4) 102.9 91.9 99.4

O'-M-O' - - - - 112.0 -

O-M-O' - - - - 112.9 125.4

A-O-M 98.5 99.0 98.5 98.4 99.3 92.1

iaibic 5.077-10-132 4.903-10-132 6.614-10-132 6.498 -10-132 4.29-10-133 2.00-10-133

a Bond distances are given in angstroms, bond angles in degrees, the moments of inertia in kg3m6.

b The gas-phase electron diffraction data with experimental errors in parentheses are from Ref. [26].

c The gas-phase electron diffraction data with experimental errors in parentheses are from Ref. [27].

d From Ref. [15].

Table 2

Atomic charges and valence population (e) of the central metal from NBO analysis.

Cs2CrO4 Cs2MnO4 Cs2MoO4 Cs2RuO4 BaMoO4 BaMoO3

M +1.05 + 1.11 +1.83 +1.66 + 1.86 +1.19

A +0.96 +0.96 +0.96 +0.96 + 1.81 +1.73

O -0.74 -0.76 -0.94 -0.89 -1.13 -1.10

O' - - - - -0.70 -0.72

M population 4sa213d4.6f 8 4s0253d559 5sa184d3.94 5s0234d608 5sa174d3.92 5sa594d4.16

BaMoO4) have rather week Raman scattering, BaMoO3 has a few strong (from them two extremely strong) Raman active fundamentals which all belong to the A' irreducible representations.

To our knowledge, experimental spectroscopic studies have been reported for Cs2CrO4, Cs2MoO4 and Cs2RuO4. Nagarantha et al. reported Raman spectra of the matrix isolated Cs2CrO4 and Cs2MoO4 [33], and found the symmetric Cr—O and Mo—O stretchings at 847 and 891 cm-1 in good agreement with the calculated value. Ball et al. [34,35] reported the infrared spectra of matrix isolated Cs2CrO4 and Cs2MoO4, (Cs2CrO4: 890, 867, 427, 407, 184 cm-1; Cs2MoO4:837, 827, 369, 315,163, 143 cm-1), the bands assigned to the B2 and E modes of the Mo—O stretching, O—Mo—O bending and Cs—O stretching. Also these wavenumbers are in very

good agreement with the calculations. The contradiction of the very low computed IR intensity of the lowest-wavenumber band of Cs2MoO4 (143 cm-1 experimental, 150 cm-1 calculation) versus the substantial intensity in the experimental spectrum may be explained by some distortions of the structure in the matrix.

The experimental infrared data on the matrix-isolated vapour phase above Cs2RuO4 are less conclusive. Ball et al. observed three strong bands in the mid-infrared region at 907, 849 and 752 cm-1 (N2 matrix) or 905, 839 and 745 cm-1 (Ar matrix), and a fourth, much weaker, band at 326 (in N2) or 322 cm-1 (in Ar) [36]. In addition, they found two bands at 153.6 and 146.8 cm-1 (Ar matrix) in the far-infrared. Ball et al. assigned these to CsRuO3, formed by decomposition of Cs2RuO4 during evaporation. The RuO3 moiety in

Table 3

Calculated anharmonic frequencies (IR and Raman intensities)3 of the fundamentals.

Character D2d Cs2CrO4 Cs2MnO4 Cs2MoO4 Cs2RuO4 C2v BaMoO4 Cs BaMoO3

Vss MO' - - - - A1 964(171,34) A' 958 (260, 40)

Vas MO' - - - - B2 948 (291, 21) -

Vss MO Ai 879 (0, 62) 851 (0, 63) 887 (0, 63) 829 (0, 94) A1 763 (377, 21) A' 751 (113, 1995)

Vsa MO B2 912 (692, 12) 901 (486, 11) 845 (731, 7) 783 (543, 12) - -

Vas MO E 888 (243, 4) 832 (230, 6) 826 (251, 1) 761 (200, 3) B1 676(185, 11) A'' 744 (154, 2)

ßa MO2 B2 445 (23, 6) 452(15, 6) 379 (76, 3) 279 (217,5) - -

ßs MO2 Ai 404 (0, 59) 403 (0, 78) 365 (0,51) 329 (0, 128) A1 485 (166, 8) A' 392 (59, 2621)

ß MO'2 - - - A1 333 (4, 12) -

g MO2 E 382 (1,3) 344(10, 4) 322 (11,0) 260 (27, 1) B2 316(15, 4) A' 243 (21, 157)

tw MO2 Bi 327 (0, 16) 295 (0, 5) 288 (0, 19) 234 (0, 41) A2 241 (0, 28) A'' 234(1, 1)

Vsa AO B2 189(l35, 0) 192 (126, 0) 166 (94, 0) 159 (65, 0) - -

Vas AO E 178(1,8) 165 (0.2, 3) 150(1,9) 151 (0.1, 9) B1 319(21, 13) A'' 267 (13, 10)

Vss AO Ai 104 (0, 13) 105 (0, 13) 169 (0, 8) 123 (0, 87) A1 202 (22, 61) A' 189 (5,313)

g A E 36(19, 0) 34(17, 0) 49 (14, 0) 34(12, 0) B2 60 (3, 24) -

g MO' - - - B1 182 (1, 15) A' 59 (8, 73)

a The frequencies are given in cm-1, the IR intensities in km/mol, the Raman intensities (corrected for 514 nm laser line) in A4/(amu cm-1). The notations for the fundamentals mean the following: n, stretching; b, in-plane bending, g, out-of-plane bending, tw, twisting; s and a in subscript mean symmetric and asymmetric, respectively, in combination e.g. vsa MO means the symmetric stretching on an MO2 moiety of MoO4, moving asymmetrically with respect to the (symmetrically stretching) other MO2.

the matrix was supported by normal coordinate calculations, while the suggested composition by identification of both Cs2RuO4 and RuO2 in the condensed product after the experiment. Indeed, this observed band pattern in the IR spectrum corresponds much worse to the calculated frequencies of Cs2RuO4, compared to the case of Cs2MoO4 (cf. Table 3).

For calculation of the thermodynamic functions of the gaseous species the low-energy excited electronic states are also important. We calculated the lowest-energy excited states using the time-dependent DFT [37] method. The results are presented in Table 4.

In agreement with the expectations, the singlet Cs2CrO4, Cs2MoO4 and BaMoO4 molecules have no low-lying excited states with notable contribution to the thermodynamic functions. However, the first excited states of Cs2MnO4 (at around 20 kJ/mol) can have considerable contribution to the thermodynamic functions at high temperatures, while some effect can be expected from the next ones. Numerous low-lying excited states are shown by Cs2RuO4 and BaMoO3. Both molecules have scarce excited states below 100 kJ/mol (% and 1Bi of Cs2RuO4 at 52 and 84 kJ/mol, respectively, and 3A1 of BaMoO3 at 16 kJ/mol) with expected considerable contribution to the thermodynamic functions.

3.3. Dissociation enthalpies

The calculated dissociation enthalpies of the reactions XnMOm = XnO + MOm-1 (1)

are given in Table 5. These values can be compared to results from thermodynamic analyses of vaporization studies, which are

Table 5

Dissociation energies and enthalpies (kJ/mol) at 298 K from DFT calculations.

Dissociation reaction De DrH298 Literature data

Cs2CrO4 / Cs2O + CrO3 635 629 671 ± 49a

Cs2MnO4 / Cs2O + MnO3 514 507

Cs2MoO4 / Cs2O + MoO3 685 680 685 ± 32b

Cs2RuO4 / Cs2O + RuO3 434 431

BaMoO4 / BaO + MoO3 574 569 478 ± 17,b 618 ± 32c

BaMoO3 / BaO + MoO2 471 465

a Calculated from the recommended thermochemical data in Ref. [38] in combination with the enthalpy of formation of CrO3 from Ref. [39]. b Calculated from the recommended thermochemical data in Ref. [38]. c Calculated from the enthalpy of formation of BaMoO4(g) derived from the sublimation reaction BaMoO4(cr) = BaMoO4(g) [9,38].

available for Cs2MoO4, Cs2CrO4 and BaMoO4 and have yielded the enthalpies of formation. When we use the enthalpies of formation for all the species involved in the reaction (1) from the assessment by Cordfunke et al. [38], we obtain for the dissociation enthalpy of Cs2MoO4 (685 ± 32) kJ/mol at 298.15 K, in excellent agreement with the value from the DFT calculations, 684.3 kJ/mol. For Cs2CrO4 the agreement is fair, (671 ± 49) kJ/mol, compared to 629 kJ/mol from the calculations. In contrast, the agreement is poor for BaMoO4, (478 ± 17) kJ/mol derived from the experimental results for reaction (1) compared to 573.6 kJ/mol from the calculations. It should be noted here that the thermochemical values for the enthalpy of formation of Cs2MoO4 and Cs2CrO4 are highly reliable, based on several concordant experimental studies. The enthalpy of formation of BaMoO4 is derived from the mass spectrometric work of Pupp et al. [9] and is highly uncertain, as discussed in Ref. [38]. The

Table 4

Lowest-energy excited states3 (kJ/mol) from TD-DFT calculations. Compound Electronic states

Cs2CrO4 0 (%), 198 (3A"), 255 (3A"), 335 (3A0), 349 (%), 353 ^E), 379 (3A0), 391 ^E), 394 (3A"), 413 (%), 415 (%), 419 ^E), 420 (3A")

Cs2MnO4 0 (2B1), 20 (2B1), 87 (4A0), 155 (2A2), 193 (2E), 199 (4A0), 204 (2E), 217 (4A"), 232 (2A2), 261 (4A"), 264 (2A2), 269 (4A0), 289 (4A"), 292 (2B1), 295 (4A0), 302 (2A2), 302

(4A"), 304 (2B2), 306 (2E), 339 (4A0), 340 (2E), 353 (2B2), 353 (4A"), 361 (4A0), 364 (4A"), 391 (4A"), 394 (4A"), 423 (4A") Cs2MoO4 0 (1A1), 347 (3A"), 436 (1A2), 438 (1E), 446 (3A")

Cs2RuO4 0 (3B1), 52 (1A1), 84 (1B1), 144 (3A2), 146 (3B2), 155 (1A2), 203 (3E), 222 (3A1), 229 (1B1), 231 (3B2), 234 (3E), 238 (3B1), 239 (1A2), 249 (3A2), 264 (1E), 321 (3E), 323

(3E), 327 (3A1), 327 (1E), 328 (3E), 329 (3E), 334 (1B1), 335 (1E), 336 (3B2), 340 (3E), 344 (3E), 345 (3B1) BaMoO4 0 (1A1), 321 (3A0), 357 (1B2), 361 (3A"), 374 (3A"), 383 (%), 393 (1A2), 400 (3A0)

BaMoO3 0 (1A0), 16 (3A1), 111 (1A"), 113 (1A0), 135 (3A2), 200 (3B2), 212 (1A0), 222 (3A2), 226 (3A1), 226 (1A0), 231 (1A0), 254 (1A"), 258 (3B2), 262 (1A"), 271 (3A2), 275 (3B1), 284 (1A0), 289 (3B1), 306 (3A1), 318 (3A1), 326 (1A0), 341 (3A2), 344 (3B2), 346 (3B1), 348 (1A0), 363 (3A1)

a Symmetries of the states in parentheses.

direct sublimation reaction measured in that work yielded an enthalpy of formation more negative by 143 kJ/mol, which would correspond to (618 ± 32) kJ/mol for the dissociation energy of BaMoO4. The large uncertainties of the experimental values are principally due to uncertainties of the gaseous oxides, CrO3, MoO3 and MoO2.

4. Conclusions

We reported the gas-phase structural and main spectroscopic properties of the mixed metal oxides Cs2CrO4, Cs2MnO4, Cs2MoO4, Cs2RuO4, BaMoO4 and BaMoO3 being important fission product compounds that can form as a result of chemical reactions in the fuel during accidental conditions. From the possible structural isomers we found the bidentate forms as most stable. We predicted the vibrational spectra for the found global minima including anharmonic vibrational frequencies and wavelength-corrected Raman intensities. The calculated frequencies are generally in very good agreement with experimental data for the matrix-isolated molecules. The lowest-energy excited states were calculated using the TD-DFT method. The ionic character of the bonding interactions is supported by our NBO results. The dissociation enthalpies indicate a high stability of the gaseous species. The computed dissociation enthalpy for Cs2MoO4 compares very well to the thermochemical values based on the experimental enthalpies of formation, that of Cs2CrO4 compares fairly with the experimental value. For BaMoO4 the computed value is in-between two highly uncertain thermochemical values, and we consider the computed value as the most reliable.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jnucmat.2016.05.015 [40—43].

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