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Online resource
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Non-uniform polonium distribution in lead-bismuth eutectic revealed by
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evaporation experiments
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B. Gonzalez Prieto1,2, J. Lim1, A. Mariën1, K. Rosseel1, J.A. Martens2, J. Van den Bosch1, J.
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Neuhausen3, A. Aerts1,*
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SCK•CEN (Belgian Nuclear Research Centre), Boeretang 200, 2400 Mol, Belgium
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Centre for Surface Chemistry and Catalysis, KU Leuven, Kasteelpark Arenberg 23, 3001
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Heverlee, Belgium
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Laboratory for Radio- and Environmental Chemistry, Paul Scherrer Institute, Villigen PSI,
CH-5232 Villigen
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1. Evaporation experiments in pure Ar
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The effect of the presence of hydrogen in the flowing gas was studied by performing time
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dependent release experiments in pure Ar. The results expressed as partial polonium
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pressures, together with the results in Ar/5%H2 at corresponding temperatures, are shown in
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Fig. OR1. The experiments in Ar also initially showed a high partial pressure which at longer
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experiment times decreased towards values expected from the high temperature correlation.
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Compared to the results obtained in Ar/5%H2, the results in Ar showed more scatter, but the
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general trends were similar.
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Fig. OR1 Corresponding evolution of the Po partial pressure after different heating times, at
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various temperatures in: (a) Ar/5%H2 and (b) pure Ar. Dotted horizontal lines indicate the
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calculated partial pressures of Po according to the high-temperature correlation (Eq. (1) and
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Henry's law)
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2. First-order model of Po evaporation from LBE
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Consider an evaporation tube loaded with a small sample of Po-doped LBE of mass mlbe (see
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Fig. OR2). The concentration of Po is very low so the mass of Po is negligible compared to
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the sample mass, mPo(lbe) << mlbe.
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Fig. OR2 Sketch of the transpiration tube containing a Po doped LBE sample during
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evaporation experiments.
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Through the tube carrier gas flows with volumetric flow rate 𝑉̇ . When the carrier gas flows
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over the sample, it picks up Po(g) that evaporates from the sample, reaching a partial pressure
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pPo. The Po(g) vapors are transported downstream of the sample through advection only
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(diffusive transport is considered negligible). This assumption is expected to be valid under
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the experimental conditions of the current paper (flow of carrier gas at 100 mL min-1 at STP),
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as suggested by flow-rate dependent evaporation experiments reported in Ref.[1]. The same
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set of experiments indicated that the evaporation equilibrium is closely approximated.
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Assuming Po(g) behaves as an ideal gas, the rate of transport of polonium vapors, and, by
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conservation of mass, the rate at which the LBE sample looses Po is given by:
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𝑑𝑛Po(𝑙𝑏𝑒)
𝑑𝑡
=–
𝑝Po 𝑉̇
𝑅𝑇
(OR_1)
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where nPo(lbe) is the molar amount of Po dissolved in LBE and pPo is the partial pressure of
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(monoatomic) Po vapor species [Pa] above the LBE sample.
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Since Po is present in a very low concentration in liquid LBE, it was further assumed that the
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equilibrium partial pressure of Po depends directly on Po concentration on the bulk of the
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LBE sample, according to Henry's law:
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𝑝Po = 𝐾Po(lbe) 𝑥Po(lbe) = 𝐾Po(lbe)
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where KPo(lbe) is the Henry constant [Pa], xPo(lbe) is the mole fraction of Po dissolved in LBE,
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mlbe(0) is the initial mass of LBE sample [g] and Mlbe is the molecular weight of LBE (208.2 g
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mol-1). We confirmed the validity of Henry's law in the mole fraction range xPo(lbe)=10-13 to
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10-11 [2]; by comparison with literature data Henry's law seems to be valid up to at least 10-8
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mole fraction.
𝑛Po(lbe) 𝑀𝑙𝑏𝑒
(OR_2)
𝑚𝑙𝑏𝑒 (0)
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Substitution of Eq. (OR_2) in (OR_1) and subsequent integration gives an expression for the
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decrease of the amount of Po in the LBE sample during time-dependent evaporation
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experiments:
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𝑛Po(lbe) (𝑡)
𝑛Po(lbe)
= exp [–
(0)
𝐾Po(lbe) 𝑀lbe 𝑉̇
𝑚lbe (0)𝑅𝑇
𝑡]
(OR_3)
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Eq. (4) of the manuscript is a linear combination of two of these equations.
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Finally, diffusion transport limitations of Po in the bulk of the LBE sample to the surface are
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not included in the model of Eq. (OR_3). For bulk polonium, these were however found to
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have a negligible influence on evaporation under the conditions of the present paper according
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to the results in Ref. [1]. Still, the influence of diffusion on the evaporation of the fraction of
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surface polonium may be different to that of the bulk polonium. Currently we assume that the
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surface polonium is incorporated in a solid oxide layer floating on top of the liquid LBE.
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Because it is solid, diffusion of polonium in this layer should be very slow, so if diffusion is
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controlling the evaporation rate of surface polonium, it would certainly not result in the
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observed very high evaporation rates. Therefore, we believe other, currently unknown,
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mechanisms are dominating the observed evaporation behavior of the surface polonium. The
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model of Eq. (4) does probably not accurately describe the evaporation mechanism of the
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surface polonium, but it provides a means to quantify the observed phenomena and allows for
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comparison to the better-known bulk evaporation behavior.
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References
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[1] Gonzalez Prieto B, Marino A, Lim J, Rosseel K, Martens JA, Rizzi M, Neuhausen J, Van
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den Bosch J, Aerts A (2014) Use of the transpiration method to study polonium evaporation
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from liquid lead-bismuth eutectic at high temperature. Submitted to Radiochim Acta
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[2] Gonzalez Prieto B, Van den Bosch J, Martens JA, Neuhausen J, Aerts A (2013)
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Equilibrium evaporation of trace polonium from liquid lead-bismuth eutectic at high
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temperature. J Nucl Mater. Doi: http://dx.doi.org/10.1016/j.jnucmat.2013.06.037
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