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Non-uniform polonium distribution in lead-bismuth eutectic revealed by evaporation experiments

B. Gonzalez Prieto1,2, J. Lim1, A. Mariën1, K. Rosseel1, J.A. Martens2, J. Van den Bosch1, J. Neuhausen3, A. Aerts1,*

1SCK•CEN (Belgian Nuclear Research Centre), Boeretang 200, 2400 Mol, Belgium

2Centre for Surface Chemistry and Catalysis, KU Leuven, Kasteelpark Arenberg 23, 3001 Heverlee, Belgium

3 Laboratory for Radio- and Environmental Chemistry, Paul Scherrer Institute, Villigen PSI, CH-5232 Villigen

1.  Evaporation experiments in pure Ar

The effect of the presence of hydrogen in the flowing gas was studied by performing time dependent release experiments in pure Ar. The results expressed as partial polonium pressures, together with the results in Ar/5%H2 at corresponding temperatures, are shown in Fig. OR1. The experiments in Ar also initially showed a high partial pressure which at longer experiment times decreased towards values expected from the high temperature correlation. Compared to the results obtained in Ar/5%H2, the results in Ar showed more scatter, but the general trends were similar.

Fig. OR1 Corresponding evolution of the Po partial pressure after different heating times, at various temperatures in: (a) Ar/5%H2 and (b) pure Ar. Dotted horizontal lines indicate the calculated partial pressures of Po according to the high-temperature correlation (Eq. (1) and Henry's law)

2.  First-order model of Po evaporation from LBE

Consider an evaporation tube loaded with a small sample of Po-doped LBE of mass mlbe (see Fig. OR2). The concentration of Po is very low so the mass of Po is negligible compared to the sample mass, mPo(lbe) < mlbe.

Fig. OR2 Sketch of the transpiration tube containing a Po doped LBE sample during evaporation experiments.

Through the tube carrier gas flows with volumetric flow rate V. When the carrier gas flows over the sample, it picks up Po(g) that evaporates from the sample, reaching a partial pressure pPo. The Po(g) vapors are transported downstream of the sample through advection only (diffusive transport is considered negligible). This assumption is expected to be valid under the experimental conditions of the current paper (flow of carrier gas at 100 mL min-1 at STP), as suggested by flow-rate dependent evaporation experiments reported in Ref.[1]. The same set of experiments indicated that the evaporation equilibrium is closely approximated.

Assuming Po(g) behaves as an ideal gas, the rate of transport of polonium vapors, and, by conservation of mass, the rate at which the LBE sample looses Po is given by:

dnPolbedt=–pPoVRT (OR_1)

where nPo(lbe) is the molar amount of Po dissolved in LBE and pPo is the partial pressure of (monoatomic) Po vapor species [Pa] above the LBE sample.

Since Po is present in a very low concentration in liquid LBE, it was further assumed that the equilibrium partial pressure of Po depends directly on Po concentration on the bulk of the LBE sample, according to Henry's law:

pPo= KPo(lbe)xPo(lbe)= KPo(lbe)nPo(lbe)Mlbemlbe(0) (OR_2)

where KPo(lbe) is the Henry constant [Pa], xPo(lbe) is the mole fraction of Po dissolved in LBE, mlbe(0) is the initial mass of LBE sample [g] and Mlbe is the molecular weight of LBE (208.2 g mol-1). We confirmed the validity of Henry's law in the mole fraction range xPo(lbe)=10-13 to 10-11 [2]; by comparison with literature data Henry's law seems to be valid up to at least 10-8 mole fraction.

Substitution of Eq. (OR_2) in (OR_1) and subsequent integration gives an expression for the decrease of the amount of Po in the LBE sample during time-dependent evaporation experiments:

nPolbetnPolbe0=exp–KPo(lbe)MlbeVmlbe0RTt (OR_3)

Eq. (4) of the manuscript is a linear combination of two of these equations.

Finally, diffusion transport limitations of Po in the bulk of the LBE sample to the surface are not included in the model of Eq. (OR_3). For bulk polonium, these were however found to have a negligible influence on evaporation under the conditions of the present paper according to the results in Ref. [1]. Still, the influence of diffusion on the evaporation of the fraction of surface polonium may be different to that of the bulk polonium. Currently we assume that the surface polonium is incorporated in a solid oxide layer floating on top of the liquid LBE. Because it is solid, diffusion of polonium in this layer should be very slow, so if diffusion is controlling the evaporation rate of surface polonium, it would certainly not result in the observed very high evaporation rates. Therefore, we believe other, currently unknown, mechanisms are dominating the observed evaporation behavior of the surface polonium. The model of Eq. (4) does probably not accurately describe the evaporation mechanism of the surface polonium, but it provides a means to quantify the observed phenomena and allows for comparison to the better-known bulk evaporation behavior.

References

[1] Gonzalez Prieto B, Marino A, Lim J, Rosseel K, Martens JA, Rizzi M, Neuhausen J, Van den Bosch J, Aerts A (2014) Use of the transpiration method to study polonium evaporation from liquid lead-bismuth eutectic at high temperature. Submitted to Radiochim Acta

[2] Gonzalez Prieto B, Van den Bosch J, Martens JA, Neuhausen J, Aerts A (2013) Equilibrium evaporation of trace polonium from liquid lead-bismuth eutectic at high temperature. J Nucl Mater. Doi: http://dx.doi.org/10.1016/j.jnucmat.2013.06.037