MOBILITY DETERMINATION OF LEAD ISOTOPES IN GLASS FOR RETROSPECTIVE RADON MEASUREMENTS

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INTRODUCTION
It is estimated that radon in dwellings accounts up to 2% of ali deaths from cancer in Europe [I].This number is higher in the areas where higher concentrations of the natural uranium exists in the bedrock.To make accurate conclusions of radon induced fatalities it is important to have reliable method for measuring radon concentra tions for a sufficient long time period.Starting from the 238 U the radium decay series acts as a constant source of radioactive decay products.The half life of 1 1 12 = 3.8 d of the radon(222) gas allows 222 R n to diffuse out from the ground and to the dwellings.It is however not the radon itself that causes most of the exposure but the short lived alfa-emitting solid progenies of the inhaled radon [I].
Epidemiological surveys where radon retrospective measurements are used are based on surface traps such as glass [2, 3, 4, 5, 6] for determining the alpha re coil implanted radon progenies.Also substrates like CR-39 or other polymers is widely used for retrospec tive radon measurements, progeny detection and in epidemiolo � ical studies; see [7, 8, 9, 10] for example.
When 22 Rn decays the radium decay series quickly evolves but builds up after about an hour to in 210 Pb.The long half life of t 11 2 = 22 a of the 210 Pb is what enables the retrospective radon measurements when the *Corresponding author: Mikko Laitinen, tel.: +358 14 260 2419; fax: +358 14 260 2465.E-mail address: mikko.laitinen@jyu.fiimplanted 21 0 Pb (or it's progenies) concentrations into the glass can be determined reliably.
Most of the retrospective radon measurements based on the surface trap method does not however take into account the possibility of the diffusion of the 210 Pb.Im plantation depth of 21 0 Pb from alpha decays of 218 Po and 214 Po is very shallow and :'.S 100 nm at the maxi mum [11,12].This can lead to erroneous results if the 210 Pb is mobile and diffuses out from the glass.This is because most of the implanted 210 Pb is concentrated very close to the surface [11,12].
In retrospective radon measurements alpha activities of 2 Bq m-2 of 210 Po can be measured [3].Cal culated from decay constants this polonium activity corresponds to about 4 x 10 7 210 Pb at.cm 2 .The dif fusion processes where only very small concentration ( 10 7 -10 10 at.cm-2 ) of implanted atoms exists can only be studied by the radiotracer technique [13].To measure the diffusion of 21 0 Pb we used 209 Pb as a radiotracer to mimic 210 Pb as from the diffusion perspective they only differ by their mass which can be safely disregarded.This study further investigates the surface escape of the Pb and expands the reliability of the initial study [14] of the low concentration diffusion of Pb in glass.

METHOD
To measure diffusion by radiotracers at low concentra tions the implanted isotopes need to have a half life between �30 min and few tens of hours so that enough statistics from (3 -decays can be collected in short period shows this to be a good approximation to our experimen tal data.When Eq. (I) is integrated it can be represented in the form: where v and xo are taken from the as-implanted Gaussian and N, >., R and B are free parameters.(2) and t is the annealing time.

The temperature dependence of D follows the Arrhe nius equation:
(3) here Do is the so-called pre-exponential factor, H is the activation enthalpy, k is Boltzmann's constant and Tis temperature in Kelvin.to the diffusion data correlation to the fits 2 (Fig. 3), respectively.

The fitted activation enthalpy was 3.2 ± 0.2 eV and Do in the order of 20 m 2 s-1 • The largest uncer tainty factor in the measurements was the background in the foil activity measurement. Background deviation of a few percent in the measurements cause noticeable changes to the diffusion length and this is the main cause of the scatter from a straight line in
The diffusion length at the room temperature for 209 Pb extrapolated over a time period of 50 years is in the order of 10 22 -10 -23 m.This result confirms that 2 10 Pb is immobile in glass.This is a critical assumption in retrospective radon measurement by Samuclssson's method [3].
In contrast to our preliminary study the surface was found to be characteristic of a near-perfect sink (R � -1).This is confirmed by inspection of Fig. 3 where Pb is seen to be depicted in the diffused profiles in the 30 nm closest to the surface.This is not inconsistent with the data in our previous study [14,21].This means that if the 20 9 Pb is diffused to the surface, it will escape from the sample under the conditions studied.Even if this holds true at the room temperature it affects only the very surface l � cr because, as shown above, in the glass 209 p b ( and 2 1 Pb ) is immobile.

CONCLUSIONS
Diffusion coefficients of 20 9 Pb in glass were measured over the temperature range of 470 -620 °C.The ac tivation enthalpy was determined to be 3.2 ± 0.2 eV and the pre-exponential factor Do in the order of 20 m 2 s-1 .Extrapolation of these diffusion parameters to room temperature shows that Pb is completely immobile in the glass over a time scale of 50 years.We also did not 2 Diffusion length error is calculated fr om the error obtained for the diffusion constants Eq.(2).

Radiation
Proleclion Dosimetry Voi.0 No. 0 © Oxford University Press 2007; ali rights reserved of time.At Jyvaskylii a primary energetic beam from the K-130 cyclotron is guided to a solid target at the ion guide isotope separator on-line (IGISOL) [15, 16, 17) where the radioactive products are isotope separated and accelerated to a maximum energy of 40 keV for implan-E tation.After the implantation the sample is thermally o annealed in vacuum to induce diffusion.Subsequently, the concentration profile of implanted 209 Pb was serially sectioned onto thin mylar foils by a sputtering method [18).After sputtering the activity on each section was mea sured and the total crater depth of the sputtered sample determined.For different temperatures the diffusion profiles are determined from the crater depth, number of foils and from the measured activity on each foil.The mathematical form of the diffusion profiles can be deduced from Fick's law [19, 20, 21) (see Eq. 1).Prior to fitting, the measured profiles were corrected for radioactive decay during the measurement.Diffusion equation loo [ ( (x _ x' t) with depth x and time t to the initial, as implanted profile Cpb(x, t = 0).>. is the diffusion length.In eq.(I) the shallow implantation depth from the sur face has been taken account by R ( -1 :S R :S + 1) which describes the surface boundary condition.R = -1 for a perfect sink while R = + 1 corresponds to a per fectly reflecting boundary [21 ].The as-implanted profile Cpb(x,t=O) was taken to have a Gaussian form where xo is the centroid of the as-implanted profile.Fig. 3 Figure 1.A) IGISOL-setup: 1.Primary beam from cyclotron, 2. Target chamber and ion extraction, 3. Mass separation, 4. Experiment setup, 5. Magnet with 2 Penning traps for nu clear measurements 6. Beam dump and concrete shielding.B) Schematic of the experimental setup at point 4 in Fig. 1 A).

Figure 2 .
Figure 2. Photographic montage of the sample during serial sectioning.Incident l ke V ion beam erodes the sample andsputtered flux is collected on a mylar foil.

Fig. 4 .Figure 3 .
Figure 3. Measured as-implanted and annealed profiles.For clarity error bars are shown only in the as implanted profile as they are similar in size for the others.See text for further details.

Figure 4 .
Figure 4. Arrhenius fit to the diffusion coefficients.All data points are used in the fit.