J.-E Groetz
email: jegroetz@univ-fcomte.fr

N Ounoughi

C Mavon

A Belafrites

M Fromm

Conception and realization of a parallel-plate free-air ionization chamber for the absolute dosimetry of an ultrasoft X-ray beam

Conception and realization of a parallel-plate free-air ionization chamber for the absolute dosimetry of an ultrasoft X-ray beam

I. INTRODUCTION

Ultrasoft X-rays (USX) have been and still are extensively used to refine and gain new insights into the radiobiological mechanisms that underline cellular inactivation and more generally cellular damage. [1][2][3][4][5][6] In recent years, such low energy X-rays have also been employed to evaluate the efficacy of both USXs and secondary Low Energy Electrons (LEEs) at damaging DNA 7,8 . There are basically two main ways to use USX beams; access to a synchrotron radiation facility 3,9,10 or to use a laboratory X-ray generator. 5,6,11,12 Laboratory bench X-ray sources consist of two possible types; hot-cathode 13 or cold-cathode X-ray tubes. Cold cathode discharge tubes are attractive due to some unique characteristics, as they can operate in a rough vacuum using an inexpensive high voltage supply. 14 Most of the recent studies in which lab-bench USX beams where used are based on the use of coldcathode devices. We designed and developed a well-tailored cold cathode USX generator to deliver Al Kα photon beams (1486.295 eV, 1.5 keV). 15 Intensity of such USXs is dramatically reduced in air (i.e. a 4.8 mm thickness corresponds to 50% attenuation in standard conditions) and their dosimetry must therefore be particularly well-adapted. In order to properly characterize the generators dosimetry, an original millimeter-sized free-air ionization chamber was designed specially for this purpose, to measure the air kerma rate. On the other hand, commercial Gafchromic dosimetric films (HD-810) were used in order to map the spatial dose distribution of the beam (not shown in details herein). 15 Design of both the cold cathode USX generator and free-air ionization chamber were optimized by means of specific simulation tools: FLUKA 16,17 and PENELOPE 18 calculation codes for Monte-Carlo simulation of electron and photon transport and COMSOL 19 , a multiphysics simulation software environment for defining the geometry, meshing, solving and visualizing electric field lines in the devices. In this article, we report the main characteristics of the USX cold cathode generator, we describe the free-air ionization chamber design as well as its operation in terms of dosimetry, and we characterize the capabilities of the generator in terms of USX photons fluence rate delivery, notably for future radiobiological experiments.

Prior to a full description of its geometry, we describe the way in which the dimensions of the chamber have first been optimized and validated. With a free air ionization chamber, if the ion-collecting gas volume is precisely known, the chamber can be considered as an absolute dosimeter. 20,21 Nevertheless, the precise determination of the air kerma rate necessitates an additional set of correction factors to be determined. 22 We show how those different correction factors where determined using both bibliographic references and computer simulations.

Finally, kerma rate measurements make it possible to determine the photon fluence rate.

II. MATERIALS AND METHODS

The conception of the generator used in this work is based on a design first proposed by Lea 23 in the early forties and revisited in the sixties by Neary et al. 11 and Solomon and Baun 14 , Hoshi et al. 24 and Folkard et al 25 in the eighties. Additionally, the generator and the characterization of its beam have been the object of a recent article. 15 Briefly described, the generator is a cold-cathode source in which, when high voltage is applied, under given internal pressure conditions, an electric discharge appears between the electrodes and the electric current is stabilized. This Townsend discharge is sustained by multiplication of electron flow through ion impact on the cathode when a critical value of the electric field strength is reached, which depends on the gas density. Electrons interact with the atoms of the aluminum foil giving rise to the emission of characteristic Kα (1.5 keV) USXs accompanied by the emission of bremsstrahlung radiation. Depending on the parameters set (accelerating voltage, current and pressure) during operation, the bremsstrahlung can be suppressed or not: to produce a Kα peak with our cold-cathode USX generator, the accelerating voltage must be set between 2 and 2.5 kV. 15

A. Free-air ionization chamber

Parallel-plate free air ionization chambers are widely used for the absolute measurement of air kerma beams of hard and soft X-ray. Figure 2 represents the general diagram of such an ionization chamber. [20][21][22]26 The photon beam passes through an aperture diaphragm, then between two parallel metal plates where an appropriate voltage (V C ) is applied in order to collect the charges created by the interaction of the photons with the atomic components of air. The guard plates are used to ensure uniformity of the electric field lines in the volume of collection. The collection electrode is used for measuring the electric current.

The air kerma rate for a free-air ionization chamber with a measuring volume V m is

K = I ρ air V m × W eff e × 1 1 -g ∏ i k i ( 1
)
where I (A) is the measured ionization chamber current, ρ air is the density of dry air under measured temperature and pressure conditions (at standard conditions 293.15 K and 101.33 hPa, ρ air = 1.2048 kg.m -3 with relative uncertainty 0.01%, as defined by NIST),

W eff is the effective mean energy necessary to create an electron-ion pair in dry air (W eff must be calculated for the Al Kα X-rays, i.e. for 1.5 keV photons, 27,28 detailed in section III B) ; e is the elementary charge; g is the mean fraction of the secondary electron energy lost to bremsstrahlung radiation which is negligible when ultrasoft X-rays are absorbed in air 21,29 and ∏ i k i is the dimensionless product of all necessary chamber correction factors. 21,22,27,28,[30][31][32][33] Some of these correction factors are straightforward to determine, while others must be assessed with specific calculations. In this work, the following correction factors have been used:

• k at , the attenuation factor in air along the distance d between reference and measurement plane 22 (see Fig. 1.); since this factor depends on the density of air in the ambient conditions of temperature and pressure, it was calculated with these corrections; 34

• k TP , the mass correction factor for taking account of the pressure and temperature variations. 35 This factor has a low sensitivity to ambient pressure variations, but it is more sensitive to ambient temperature variations. In our case, an artificial weathering chamber is used to circulate dry or humid air in the irradiation chamber, to control both temperature and hygrometry;

• k H , the factor applied to correct the variation in the air hygrometry

• k R is the factor for correcting the initial recombination in the collection volume, determined according to the two-voltage method; 36,37 for small volume chambers, the general recombination is negligible; 38 k R is determined based on a set of two electrical current measurements I 1 and I 2 at two different voltages V 1 and V 2 :

k R = 1 + (I 1 /I 2 -1)/(V 1 /V 2 -I 1 /I 2 )
• k p is the polarization factor calculated using direct (I + ) and inverse (I -) chamber

currents 21 : k p = (|I + | + |I -|)/(2|I -|)
• k Exc the factor to correct the excess charge due to the ion pairs produced by the initial photon interaction in air, 22,27 calculated with the following relation k Exc = 1-1/N ion = 1 -W (T )/(E × µ en /µ); at E = 1500 eV, µ en and µ are very close (0.25% difference) and W(T) is equal to 34.36 eV (see section III B);

• k Field the factor to correct the distortion of the electric field in the collection volume; 39 ,

• k e and k s are respectively the correction factors for electron-loss and coherently scattered and fluorescence photons; 30 those factors are generally determined with Monte-Carlo simulations.

The values used in the present work and which have been easily calculated based on the relationships found in the literature are presented in Table 1. Uncertainties associated to the kerma rate measurements were calculated using the formula for propagation of uncertainties.

The factors k Field , k e and k s have been computed using COMSOL TM and FLUKA calculation codes (see respectively section III.C. and section III.D).

B. Electric field simulations

COMSOL TM has been used for optimizing the ionization chamber dimensions and operating parameters, using the AC/DC module which provides an environment for the simulation of electrostatic phenomena. Parallel-plate free-air chambers must have a uniform electric field between their plates to ensure that the dimensions of the ion-collection volume and the length of the volume are accurately known.

C. Particle physics Monte-Carlo simulations -FLUKA and PENELOPE codes

FLUKA is a multipurpose Monte-Carlo simulation code, mainly dedicated to high energy physics and radiation dosimetry. 16,17 Now, its use has been extended to nuclear medicine dosimetry and hadrontherapy, 40,41 and it can be used to determine, with accuracy, the correction factors for the electron losses, photon scattering and photon fluorescence in a free-air ionization chamber. Energy cut-off for transport of primary electrons and photons is 1 keV, but this parameter can be lowered to 0.1 keV for secondary photons. Fluorescence emission for K and L lines are well considered, and for charged particle transport such as electrons, a single scattering approach could be specified through the MULSOPT option.

Since the aluminum foil (X-ray source) and the ionization chamber are close together, we must be aware of the beam divergence of our system. 15 Beam divergence can be specified with the appropriate angular distribution.

PENELOPE is a Monte-Carlo code system for simulation of electron and photon transport. 18 Both detailed simulations (hard events or analog histories) and multiplescattering approaches (soft events with the Continuous Slowing Down Approximation -CSDA) are possible. These transport algorithms are controlled by several parameters, C 1 , C 2 , W CC and W CR . The C 1 and C 2 parameters refer to the average angular deflection and the maximum average fractional energy loss between consecutive hard elastic events (we set C 1 = C 2 = 0.05). W CC and W CR relate to the cutoff energy loss for hard inelastic collisions and hard bremsstrahlung emission (W CC = W CR = 1 keV in our case). The lower absorption energy was set to 50 eV, which is the allowed minimal value.

III. FEATURES OF THE IONIZATION CHAMBER AND CORRECTION FACTOR CALCULATIONS

A. Design of the free-air ionization chamber

The design of an ionization chamber requires the choice of sizes and materials depending on the quality of the beam and the area of interest. Based on the schematic diagram of Fig. 1, a parallel-plate ionization chamber suitable for measuring the air kerma of USXs (typically < 5 keV) has been developed (Fig. 2). The use of such an ionization chamber requires that the measurement volume (V m ) satisfies the condition of charged-particle equilibrium (i.e.

the number of charged particles of each type, leaving a volume are equal to the number entering). 20 This is ensured by the fact that the distance between the reference plane and the plane of measurement (see Fig. 1) is greater than the maximum range R air of the secondary electrons created by photons in air. From the CSDA, the value R air is estimated at 2.40 mm for 10 keV photons (with ESTAR 42 and PENELOPE) and at 0.15 mm for 2 keV photons (with PENELOPE calculations, since ESTAR calculates the CSDA range down to 10 keV). For the secondary electrons created in the volume V m , which dissipate their energy before being collected, it is a necessary condition that the distance from the latter to the electrodes remains greater than R air . Two possible distances d (corresponding to 6.5 and 10.5 mm starting from the reference plane) for the collector electrodes (see Fig. 2(a) and 2(b)) are available with our IC. For this application, only the electrodes at 6.5 mm were used, because the attenuation factor in air at 10.5 mm is too large, leading to values for the current too low to be measured. Both diaphragm and aperture (see Fig. 2) define the size of the X-ray beam entering the chamber. The mass attenuation coefficient for copper at 1.5 keV (the energy of the Al Kα line) is 4.42 × 10 3 cm 2 /g. The copper diaphragm machined for the ionizing chamber is actually 3 mm thick which ensures a complete attenuation of the considered photons. Copper is also used to machine the electrodes and guard plates, all maintained by polystyrene plates.

Table II presents the sizes of the ionizing chamber. It should be noticed that this chamber is intended to measure air kerma rates of USXs (i.e. with energies less than 5 keV) and therefore, we can consider that R air < 2.4 mm. As for the diameter of the copper diaphragm aperture, we have chosen a 8 mm value due to the fact that we envisage the use of the X-ray source mainly to irradiate nanometer-scaled DNA layers 43 in order to obtain data of radiobiological importance. Briefly, the DNA deposition method developed recently by our group 43 consists of a droplet of constant volume, being deposited on a hydrophobic graphite surface, which ensures a constant area (with diameter = 8 mm) is created, this is why we selected the above mentioned area for the ionization chamber aperture.

B. Determination of W eff

The effective value of the energy expended in air per electron-ion pair must be calculated from the spectrum of secondary electrons generated, in our case, by 1.5 keV photons. Within the chosen operating parameters, we can consider that the beam is monoenergetic. For photons of energy E, W eff is defined by the following relation: 27

W eff (E) = ∫ Emax 0 ( dϕ dt ) T dT ∫ Emax 0 ( dϕ dt ) T W (T ) dT (2)
where E max is the maximum energy transfered to electrons, dϕ/dt is the spectral fluence of electrons liberated by photon interactions in air and W (T ) is the mean energy required to create an ion pair in air by an electron with a kinetic energy T .

Buhr et al. 28 used a parameterization of the W value based on a fit to experimental values, which yields to:

W (T ) = W air 1 -(T /A 1 ) A 2 +A 3 T (3)
with A 1 = 14.636 eV, A 2 = -0.828 and A 3 = -3.8 × 10 -5 eV -1 (this last parameter is defined for electron energies T > A 1 , meaning that no ion pairs are created by electrons with energies below A 1 ).

For this study, the PENELOPE-2011 18 code was used to determine the electron spectral fluence generated by the 1.5 keV photons in air, which simulates photoionizations for K-shells and L-shells and relaxations including Auger electrons down to 100 eV. Figure 3 illustrates the spectral fluence of electrons from the Kα Al X-rays calculated with PENELOPE-2011.

These simulated results of dϕ/dt and parameterization of W (T ) (Eq. ( 3)) were implemented in Eq. ( 2) to assess W air . This leads to a value of W air /e for 1.5 keV photons equal to 35.50 ± 0.01 J/C. This value is in good accordance with the evolution of W eff as proposed in Bermann et al. 27 In our case, the W eff is not corrected directly by the excess charge, as Buhr et al. proposed in their model. 28 Therefore the excess charge factor k Exc was used for that correction. ). This will allow the penetration of a beam of large dimension in the chamber, thus generating larger signals that increase the sensitivity. 33 The value of V C /2 will be used in further work and the correction factor k Field is determined using this particular voltage. The determination of the correction factor k Field is based on the method described in detail in a report of the CIPM (International Committee for Weights and Measures) metrology portal. 39 In brief, a digitized picture of the field lines in the collection volume of the ionization chamber (see for example Fig. 4(b)) is used to determine the parameters in Eq. ( 4). The field lines that pass through the center of the gap between the guards and collector are followed until they cross the central axis of the chamber. Using the intersection of this field line with the central axis, the offsets of the field lines along this axis (x) are determined.

Fig. 5 illustrates the method. The correction factor k Field is calculated using 39 :

k Field = 1 + 2∆x L el + L g (4)
Parameters L el and L g are implicit values depending on the design of the chamber; in the present study: L el = 1 mm and L g = 50 µm. The numerical values determined using the above-mentioned method are ∆x = 0.06 mm and ∆x = 0.04 mm, leading to an average value of 0.05 mm. The correction factor accounting for field effects in the collection volume of the chamber is thus k Field = 1.095 ± 0.10%.

D. Correction factors k e and k s

In this part, the collection and detection volumes must be carefully described. The collection volume matches the volume of air inside the ionization chamber. As to the detection volume, it corresponds to the electrodes, the air space between the inner side and the collection volume (in the plane YZ), the wall surrounding the collection volume and the collection volume itself.

Figure 6 shows the different regions used in FLUKA, corresponding to the different volumes:

• collection volume: region C31 (air)

• air space between inner side and collection volume: region C34 (upper) and region C35 (lower)

• IC wall : region C30 (epoxy)

• IC wall surrounding the collection volume : region C36 (epoxy)

• electrodes : upper region C32 and lower region C33 (copper)

• air (excluding the air regions above) : region C10

In our case, the detection volume is made up of regions C31, C32, C33, C34, C35 and C36, while the collection volume corresponds to region C31.

The correction factor k e is used to take into account the energy loss due to the primary electrons reaching the IC electrodes, the inner wall or the air space, and a partial energy deposition in the collection volume. It can be defined as 30 :

k e = E det E coll = E elec + E vol + E coll E coll (5)
where E det is the energy deposited in the detection volume, E elec is the energy deposited 260 in the electrode plates (regions C32 and C33), E vol is the energy deposited in the air space between the inner sides and the collection volume (regions C34 and C35) and E coll is the energy deposited in the collection volume by primary electrons.

The correction factor k s is defined for the scattered radiation producing additional electrons, which occurs when incident photons scatter on the diaphragm edge or when photons 265 are produced by fluorescence. This factor k s is calculated as 30 6) where S coll is the energy deposited by secondary electrons from scattered and fluorescence photons.

k s = E coll S coll (
Both correction factors were calculated at various distances, corresponding to the range of use of the ionization chamber: 10, 12, 15, 20, 25 and 30 mm between the aluminum foil and the shielding box diaphragm (Fig. 7). From these results, we can deduce the average values and associated standard deviations k e = 1.001 ± 0.001. and k s = 0.999 ± 0.001.

IV. RESULTS AND DISCUSSION

A. Air kerma rate

Aimed at determining the photon fluence rate φ in radiobiology experiments, the chamber provides air kerma rate K measurements. In case the distance between the USX source and the chamber must be varied, a step by step motor is used to move the chamber at the required distance. Air kerma rate K measurements were performed at various distances from the source (plane of the aluminum foil) of our lab-bench cold cathode generator in dry air (2.4 kV and 3 mA). The dose is also calculated using FLUKA at the same distances, with special attention given to the angular distribution of the beam (Gaussian divergence at 0.7 rad). 15 Concerning FLUKA calculations it should be noticed that the electronic equilibrium being established in the ionization chamber volume, absorbed dose in air and air kerma are identical. In Fig. 8, measurements and calculations are compared, where FLUKA results are expressed as air kerma per primary photons. Both results show a very good accordance with the distance source-ionization chamber. Experimental errors are sometimes shorter than the black dots and can therefore not be seen on the plot.

B. Photon fluence rate

In the special case where the USX beam is of a mono-energetic character (under specific operating conditions, our cold-cathode USX generator acts as a mono-energetic source, see

Ref. 15 for more details), the measured kerma rate can be converted to a photon fluence rate using:

φ = K × [ E × ( µ en ρ ) air ] -1 ( 7
)
where E is the mean photon energy and (µ en /ρ) air is the mass energy-absorption coefficient for 1.5 keV X-rays in dry air, equal to 1.188 × 10 3 cm 2 .g -1 . At constant acceleration voltage, the measured photon fluence rate increases linearly with the generators current. 15

We measured the photon flux through a detector Si (PIN)-type XR-100 CR Amptek TM with a sensitive area of 6.72 mm and a beryllium shielding foil having a thickness of 12.5 µm (the correction due to the attenuation in the beryllium foil was taken into account).

Operating conditions for the USX generator were 2 kV and 1.5 mA, in order to minimize pulse pile-up and radiation damages to the detector, as well as taking maximum benefit of highest beam purity (96%). Measurements were also performed for distances to the aluminum foil remaining beyond 50 mm for the same reasons. The decreasing exponential fit shows a good correlation for both detectors. Nevertheless, it should be difficult to have a perfect correlation, due to the beam geometry and that of both measuring systems. Indeed the spatial fluence distribution of the beam is not homogeneous close to the aluminum foil (in the IC distance range of measurement), and becomes more homogeneous away from the source. 15 Moreover, measurements carried out by the IC are averaged over an area of 50 mm 2 (aperture area), while those performed using the Si (PIN) are averaged over an area of 6.75 mm 2 (sensitive surface of the detector).

V. CONCLUSION

We have successfully designed an original millimeter-sized parallel plate free air ionization chamber specially intended to determine the photon fluence rates of a mono-energetic USXs The measured absolute kerma rate in air compared to Monte-Carlo simulations have shown good agreement within the experimental uncertainties range. The evolution of fluence rates related to the distance from the source were also performed with the IC and a Si-diode and have shown a good correlation. Further work will consist in strictly validate the photon fluence rate with a suitable and calibrated diode.

The ionization chamber developed herein will allow considerable time savings in future radio-biological experiments, where DNA layers with nanometer-scaled thicknesses will be exposed to USXs in order to generate low energy photo-electrons (0-10 eV) from a graphite substrate. Additionally, such an ionization chamber may provide useful in research areas

where Ultra-Soft X-rays are used. Lastly, the work presented in this paper completes the energy domain of application of parallel plate free air ionization chambers, which to our knowledge, were used, up to now, solely for the dosimetry of hard and soft X-rays.

FIG. 1 .

 1 FIG. 1. Schematic diagram of a parallel-plate free-air ionization chamber, d represents the distance between the reference plane and the measurement plane.

  calculated by 22 :

1 FIG. 2 .

 12 FIG. 2. Free-air ionization chamber: (a) 3D COMSOL TM representation of the chamber showing electrodes and guard plates (in black); (b) Picture of the design of the chamber without shielding box, where the welding points of the CMS resistances that connect consecutive guard plates are visible. Collector electrodes with connections are on the front side; (c) Picture of the final design with a cylindrical shielding box containing the copper diaphragm (8 mm diameter aperture) and electric insulation made up of black High-Density Poly-Ethylene (HDPE).

FIG. 3 .

 3 FIG. 3. Electron fluence spectrum from 1.5 keV photons in air calculated with PENELOPE-2011

1 FIG. 4 .

 14 FIG. 4. Distribution of electric field lines in the ionization chamber. The black rectangle between electrodes represents the limits of the collection volume. (a) Field lines when the copper shielding box (in white color) is plugged to the ground; (b) Simulation corresponding to the case where the shielding box is polarized at V C /2. (c) Radial cross-sectional view of the field lines when the shielding box is at V C /2.

FIG. 5 .

 5 FIG.5. Schematic representation of the parameters ∆x, L el and L g used in Eq. (4) for the determination of k Field .

1 FIG. 6 .

 16 FIG. 6. 2D representation of the ionization chamber: (a) 2D section in ZX with the IC walls in blue and the shielding box in brown; 2D section with the different regions corresponding to the collection and detection volumes in ZX, also with the region C32 showing the upper electrode (b); in ZY (c) and in XY (d).

1 FIG. 7 .

 17 FIG. 7. (a) 2D representation of the deposed energy (normalized to GeV/cm 3 /primary) in the IC. (b) Correction factors k e and k s as a function of the distance source-shielding box diaphragm.

FIG. 8 .

 8 FIG.8. Air kerma rate measurements with the ionization chamber at distances between 11 and 19 mm from the foil source (left axis), as compared to air kerma FLUKA calculation (right axis).

FIG. 9 .

 9 FIG.9. Photon fluence rate measurements with the ionization chamber at distances between 11 and 15 mm from the foil source and with the Si diode from 50 to 65 mm.

Fig. 9

 9 Fig. 9 presents the photon fluence rate measured with the IC and the Si diode in their range of distances (between 11 and 15 mm for the IC, from 50 to 65 mm for the diode).

  photons in the collection volume.

TABLE I .

 I Corrections factors used in this work to calculate air kerma and which have been collected in the references listed above. U is the relative uncertainty in %.

	Correction factor Value U (%)	Specific conditions
	k at	2.498 1.44
	k TP	1.024 0.68	300 K and 1013,25 hPa
	k H	0.998 0.10 between 20% and 80% of hygrometry
	k R	1.026 0.30
	k p	1.010 1.50
	k Exc	0.977 0.12

TABLE II .

 II Free-air ionization chamber geometrical parameters.

	Chamber parameters	Dimensions (mm)
	Aperture diameter of copper diaphragm	8.00 ± 0.02
	Air path length (d)	6.50 ± 0.02
	Collecting length	12.000 ± 0.005
	Electrode separation	15.00 ± 0.02
	Collector width	1.000 ± 0.005
	Guard plate width	1.000 ± 0.005
	Measuring volume (mm 3 )	52.78 ± 0.36

ACKNOWLEDGMENTS

This work was partially funded through a CNOUS France-Algeria financial support (PROFAS). The authors would like to acknowledge Dr. Wassim Ksouri and Dr. Jean-Marc Bordy from the French National Henri Becquerel Laboratory (LNHB) for their valuable comments, hints and support during the conception of the Parallel-Plate Free-Air Ionization Chamber.

Chem. C 115, 21291 (2011).


Pierre Le Goff

Jean-Marie Duda

Philippe Guétat

Pauline Rambaud

Christophe Mavon

Laurent Vichot

Pierre-Marie Badot

Michel Fromm

Pierre Le Goff
email: pierre.legoff@cea.fr

Measurement of tritium in the free water of milk : spotting and quantifying some biases and proposing ways of improvement

Keywords:

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Among the unstable isotopes released by the nuclear industry, the quantities of tritium reaching the environment are usually small and generally fit easily with regulatory limits. As tritium was massively released during the atmospheric nuclear tests between 1945 and1980, it has become widely dispersed in the environment and in food chains. Its quantity in the atmosphere peaked in 1963 and has been decreasing ever since. It is now mainly localized in the water of oceans (about 99 %) [START_REF] Jacobs | Sources of tritium and its behaviour upon release to the environment[END_REF][START_REF] Weaver | Tritium in the environment from Nuclear Powerplants[END_REF] [START_REF] Unscear | Sources and effects of ionizing radiation (Report to the General Assembly)[END_REF].

Nevertheless, tritium, along with 14 C and noble gases remain the dominant radionuclides released into the atmosphere by the nuclear industry. The main anthropic sources are weapon facilities, nuclear power plants, reprocessing facilities, the production and use of labelled compounds for medical use, research or even self-powered lighting products and research facilities for nuclear fusion [START_REF] Guétat | Tritium and the environment: Sources, measurement and transfer[END_REF][START_REF] Irsn/Dei | Le tritium dans l'environnement -Synthèse des connaissances[END_REF].

Being an isotope of hydrogen, tritium can be incorporated into almost all components of biological systems: water (HTO) or organic molecules [START_REF] Diabaté | Organically bound tritium[END_REF] (so-called Organically Bound Tritium or OBT). When dealing with OBT, two categories of atomic bonds are generally distinguished:

binding to a nitrogen, oxygen or sulphur atom, i.e. labile bonds. It can easily be exchanged with labile hydrogen of other functional groups or molecules in its near vicinity, especially water; this fraction is called exchangeable Organically Bound Tritium (eOBT).

binding to a carbon atom. Such covalent bounds are stable and therefore hydrogen atoms (or isotopes) are incorporated in the metabolic cycle of each molecule with more or less complex and lengthy features. This latter type of bound tritium is known as non-exchangeable Organically Bound Tritium (neOBT).

Exposure of individuals depends on the type of the tritiated molecule(s) incorporated as well as on its/their metabolism. When tritium originates from tritiated water release and is further integrated in the food chain by, for example, going through photosynthesis (see further details in [START_REF] Boyer | Tritium in plants: a review of current knowledge[END_REF], some simplifications are considered to define a single "dose per unit intake factor" (ICRP 1989(ICRP , 1997)):

considering exchangeable/non exchangeable proportions to be equal, -considering an average biological half-life of 40 days for all non-exchangeable tritium of all organic molecules.

When using liquid scintillation counting, measurements of tritium specific activity on water allow the lowest decision threshold to be reached. Laboratories that measure tritium in environmental samples frequently use a same protocol:

extraction of the free water of the sample and measure (Free Water Tritium), then on the one hand: oxidisation of the dry fraction resulting in the production of combustion water, then measurement of total organic tritium (i.e. the sum of eOBT and neOBT), -on the other hand: isotopic exchange of hydrogen isotopes by washing the dry fraction with tritiated water, thus a second extraction of water to measure (if possible) eOBT and oxidisation of the "washed" and dried fraction to measure the neOBT as combustion water.

Frequently, eOBT is not measured but deduced from the following simple relation:

eOBT = OBT -neOBT (1)
Every isotope or inaccuracy effect in every step of the procedure may induce errors in the measurement of the specific activity of extracted free water and of OBT [START_REF] Baumgärtner | Isotope effects in the equilibrium and non-equilibrium vaporization of tritiated water and ice[END_REF][START_REF] Kim | Tritium fractionation in biological systems and in analytical procedures[END_REF].

Usually, water is extracted from fresh samples or after isotopic rinsing by at least one of the following four techniques:

filtration: it allows quick and easy recovery of the main part of the dry matter, except soluble molecules which are in the filtrate. The bias induced depends on the filtration technique (i.e. characteristics of the filter) and on the nature of the sample. Retentate and distillate both need further treatment prior to measurement.

distillation: it is performed under atmospheric pressure or under reduced pressure, it allows the recovery of almost pure water. Under reduced pressure, it is possible to completely distil at lower temperature (which induces less degradation of organic samples), to prevent the risk of contamination of extracted water by pyrolitic products [START_REF] Wood | Tritium sampling and measurement[END_REF] and to limit the isotopic effect during evaporation. the influence of the mass of sample: as each water removal technique has a specific dead volume and a specific geometry, the global yield of dehydration 7/32 can be influenced and thus be the origin of a bias in the measurement of specific activity.

the influence of the final degree of dehydration: if isotopic fractionation occurs during water removal, the final level of dehydration will influence the specific activity measured.

Materials and Methods

Water was extracted from nineteen aliquots of the same milk sample (collected in the vicinity of the Valduc Centre of the French Atomic Agency) using three different dehydration techniques. The experiments were completed with twenty-one measurements performed on milks collected for our routine activity. Each time, weights of fresh milk, of dry matter and of collected water were noted.

Analytical method

Specific tritium activities were measured by liquid scintillation counting (PerkinElmer Tri-Carb 2910 TR) with an overall precision (2σ) of ± 17 %. The scintillator used was Ultimagold LLT (Packard). Quenching effects of the measuring system were carefully examined and the results measured corrected accordingly.

Storage of samples

The commercially available source water Volvic is considered to have very low levels of tritium. It is commonly used in laboratories as a blank. In order to check if storage of samples in Valduc induced biases in the measurement of the specific activity, samples of Volvic water were stored in different conditions and their specific activity was been measured after 6 h, 16 h, 24 h, 48 h, 96 h, 1 week, 2 weeks, 3 weeks or 30 days of storage.

Modifications in the conditions of storage were performed to test the influence of the temperature and the type of bottle in which the samples were stored.

Four sets of nine samples of 50 mL of Volvic water were stored in 150 mL polyethylene bottles at -25°C, 3°C, 20°C and 40°C. 1 L of Volvic water was also stored in an open 1.5 L bottle. 10 mL were sampled after 6 h, 16 h, 24 h, 48 h, 96 h, 1 week and 2 weeks of storage. This experiment was shorter than the others since there was no water left in the bottle after the seventh sampling (due to evaporation and aliquot removal).

9/32

The results presented below are the means of four repetitions.

Techniques of water removal

Comparison of common techniques

Three commonly used techniques of dehydration were compared pairwise:

distillation under reduced pressure using a distillation bridge with a Liebig condenser distillation under reduced pressure with a rotating evaporator (Buchi Rotavapor R200 or Buchi Rotavapor RE 121 equiped with Buchi 471 Oil bath) -freeze drying using a Heto Drywinner PL3000.

Equal quantities of samples were used in each group of paired samples. In the first technique, the sample was introduced in a 1 L Erlenmeyer flask in a water bath at 55°C. The flask was fitted with a splash head (to prevent or limit the sample from spurting in the apparatus during distillation). The distillate was collected from a Liebig condenser containing a flow of 3°C thermostated water. Its dead volume was 0.69 mL ± 0.25 mL. The distillation bridge was connected to a Vacuubrand ME 2C pump working at full capacity. The condensate was recovered in an Erlenmeyer also at in a water bath at 3°C. At the end of dehydration, the first water bath was heated to 70 °C.

Distillation under reduced pressure was also conducted using rotating evaporator. This technique differs from the previous one by the apparatus used. One of the major differences between them is the geometry of the condenser: a rotating evaporator is equipped with a diagonal spiral condenser which has a dead volume of about 7 mL. Samples are introduced in a 1 L flask which is then connected to a rotating evaporator (Buchi Rotavapor R200 or Buchi 10/32

Rotavapor RE 121 equiped with Buchi 471 Oil bath) connected to a pump (Vacuubrand ME 2C) which is also used at its full capacity. Condensed vapours are recovered in a flatbottomed flask. As with the previous technique, the water bath was thermostated first at 55°C

and then at 70°C. The water flowing in the condenser was thermostated at 3°C.

Freeze drying was performed with a modified Heto Drywinner PL 3000. Samples were introduced in acrylic pots connected to a manifold which is connected to a glass insert. The insert was placed in the cold trap of the Heto Drywinner PL 3000 (temperature: -55 °C) to allow the required decontamination of the cold trap between samples thus avoiding "memory effects". The manifold was also connected to the pump (Adixen Pascal 1005) used for general vacuum applications. Pressure in the system was < 0.5 hPa. After complete dehydration of the samples, the glass insert was removed from the system and immediately sealed to avoid contamination of the extracted water with atmospheric moisture until the ice has completely thawed.

Dehydration techniques were compared by pairwise to improve the power of the statistic tests (9 repetitions to compare freeze drying and rotating evaporator and 8 for freeze drying vs.

distillation bridge and 8 for rotating evaporator vs. distillation bridge).

Test of the reliability of freeze drying and distillation

The specific activity of tritiated pure water (type 3 produced by RiOs 3 Water Purification System (Merck Millipore)) were measured in three cases:

without other treatment, -after being distilled under reduced pressure using a distillation bridge (as described above), -after being freeze-dried (in the conditions described above). For each case, 3 aliquots of 49.9 g ± 0.1 g were prepared. Empty freeze drying: Drywinner Heto PL 3000 was used empty three times for 5-7 days at Valduc Centre. A commercial bubbling system (MARC 7000-SDEC France) was used to monitor the atmospheric tritium levels during the third repetition. After the end of freeze drying, the mass of the cold trap was measured and compared to its mass when empty. Then, 10 mL of non-tritiated water was inserted into the cold trap to recover possible traces of water trapped during freeze drying. The specific activity of the water in the cold trap was measured, taking into account the dilution and compared to the specific activity of the water in the pots of the bubbling system.

Influence of ambient atmosphere on freeze drying

Sample mass

12/32

To test the influence of the quantity of the sample on the reliability of measures, 6 masses were considered (about 15, 30, 60, 120, 240 and 480 g) and samples were treated by two of the three previously presented methods: distillation under reduced pressure using a distillation bridge or a rotating evaporator. Most of the sets were composed of two samples prepared with the distillation bridge and one with the rotating evaporator. The central point at 30-38 g was composed of three more samples treated with the rotating evaporator. The highest mass was only composed of one measurement since in other repetitions milk spurted throughout the apparatus until there was none left.

State of dehydration

The weight of fresh milk before treatment, and of dry matter and water after dehydration on the other hand, provide correlation between the mass of water extracted from milk and the specific activity measured.

"Sequential distillations" of milk were performed. The apparatus used in these experiments is illustrated in Fig. 1. A sample of about 300 mL was introduced in a 1 L Erlenmeyer flask in a 55°C bath. The flask was connected to a splash head to prevent or limit the sample from spurting into the apparatus during distillation. When the system is under reduced pressure, vapours flow to a condenser at 3°C and connected to a Vacuubrand ME 2C pump working at full capacity. The condensed vapour then falls into a dropping funnel. Each 10-30 mL (23 mL on average), it is opened to let the water flow into a 50 mL Erlenmeyer. Once the dropping funnel is empty, it is closed to collect the next aliquot and the water is collected from the 50 mL Erlenmeyer and weighed. The experiment is pursued until the sample is completely dry.

When possible, the dry matter of the sample is freeze-dried to collect any water which could remain. The specific activity of each aliquot is measured. Sequential distillations were carried out on four different milks collected for our routine measurements.

Results and discussion

Influence of samples storage

Only one set of samples showed any significant change in its specific activity during storage:

the Volvic water stored in an open bottle (Fig. 2). The specific activity of the water increased until it reached equilibrium with the atmospheric water vapour (178.5 ± 133.0 Bq L -1 ) after two weeks. All the other results of the experiments remained below the decision threshold (2.8 Bq L -1 ) during storage.

This proves that storage in well closed plastic or glass bottles is able to prevent the marking of the samples from the laboratory environment even in the case of the relatively tritiated atmosphere of a nuclear centre. Nevertheless, to avoid any cross contamination, we decided to store samples at -20°C (to preserve organic matter during storage) and in double packaging (bottle + sealed vinyl pocket or double sealed vinyl pocket) to avoid any unintentional marking.

15/32

Influence of the technique of dehydration

Comparison of three common techniques

The specific activity of water extracted from milks using the three techniques previously described was measured (mean: 60.4 g). The three techniques were not performed on each of the collected milk samples. Fig. 3 shows how the results are distributed. On the one hand, both methods of distillation (distillation bridge and rotating evaporator)

gave similar median concentrations but the rotating evaporator technique showed a standard deviation 22 % higher than the distillation bridge. On the other hand, the measured specific activities of water extracted by freeze drying were 40% higher when compared to the results obtained with a rotating evaporator.

Three experiments were performed to explain these results.

Reliability of distillation and freeze drying

The specific activity of pure water was measured with or without a complementary treatment Distillation had no significant incidence on the measured specific activity of extracted water (+ 2.9 %) whereas freeze drying led to a clear increase (+ 42.9 %).

Influence of ambient atmosphere on freeze drying

First, to test the effect of ambient air during freeze drying, two sets of three 50 g-aliquots of the same milk sample were freeze-dried, one set in Besançon and one in the Valduc Centre.

Freeze drying in both the Valduc Centre and Besançon led to almost complete extraction of the water, i.e. 88% of the weight of the total sample without any significant difference between samples (standard deviation: 0.09 %). Nevertheless, the comparison of the specific activities of the two sets of samples did show significant differences (see Fig. 5). This difference can only be explained by a (de)marking of the extracted water by the condensation of atmospheric water vapour. This phenomenon can occur during freeze drying by leaks in the apparatus, or before freeze drying by condensation of atmospheric water on the frozen sample or even after freeze drying when the vacuum is broken to recover the condensed water. Note that the observed deviation after freeze drying in Besançon is high regarding the little difference of specific activities between atmospheric water (< 5.8 Bq L -1 ) and free water of milk (about 20 Bq L -1 ).

The apparatus used in the Valduc Centre avoided the risk of exchange during melting of frozen condensate but this was not the case in Besançon. This can explain why the impact of condensed atmospheric vapour was so significant in Besançon whereas the differences in specific activities remained small. In laboratories specifically equipped for measurement of tritium (for example with a small cold trap which can be isolated from the atmosphere while the condensed water is recovered), the biases would be, at worst, in the measurement uncertainty interval.

Secondly, empty freeze dryings were run in the Valduc Centre. They showed recovery of water with a significant specific activity. The results are presented in Table 1. The results of the first and third freeze dryings fit well with the results presented in Fig. 4. For example, 0.8 mL of "parasite" water with a specific activity of 257 Bq L -1 can explain an overestimation of the specific activity of about + 4 Bq L -1 in a sample of 47.5 mL in which the specific activity is about 23 Bq L -1 .

Nevertheless, the mass of water collected during freeze drying appears variable, as does its specific activity. This indicates that an intermittent mechanism (most probably depending on atmospheric conditions) leads to the pollution phenomenon.

In the third repetition, the specific activity of the recovered water was about 257 Bq L -1 where the specific activity of atmospheric vapour measured by bubbling during freeze drying was only 90.8 Bq L -1 . This means in our opinion that, in addition to a possible leak in the apparatus (before the cold trap), four other ways of contamination might be suspected:

as the sample is frozen before freeze drying, atmospheric water is able to condense at its surface in the time lapse between storage and introduction into the freeze drying system; -the water vapour in the air present in the freeze drying system (about 6 L in the case of the Heto Drywinner PL 3000) is prone to condense starting from the moment when the cold trap is at its set-point temperature to the instant when vacuum is established in the system; -the water vapour in air that fills the freeze drying system when the vacuum is broken at the end of freeze drying can also condense in the cold trap; -some exchanges may occur from the atmosphere to the condensed water while the water melts in the cold trap for recovery.

It appears that during the different steps of a freeze drying process, some atmospheric water can be condensed or exchange and therefore be mixed to the extracted free water of the samples. The efficiency measured in water recovery is of the order of 97 %. The mass of external water cannot be identified in the different tests because it surely compensates sample water which is lost at the same time. This phenomenon was fortunately discovered due to the ambiance in the Valduc Centre that is sufficiently tritiated to be measured. Nevertheless, marking of extracted water during freeze drying may occur in other laboratories with very low 19/32 tritiated atmosphere. In that case, the water extracted would be "demarked" with non-tritiated water, even if it is within the uncertainty interval of measure.

One way to limit the deviation due to this pollution of the extracted water would be to freeze dry larger samples to dilute the effect in the water extracted from the sample or to operate freeze drying in a dry atmosphere.

Influence of the mass of sample in distillation techniques

The free water of nineteen aliquots from the same milk sample was extracted by distillation using a rotating evaporator or a distillation bridge. The results of this series of experiments are presented in Fig. 6. As expected, the nineteen specific activities measured are well described by a Gaussian distribution. Uncertainties ranged from 14 % for higher specific activities to 17 % for lower specific activities.

Fig. 6: Specific activity of extracted water as a function of the mass of treated samples and normality of the distribution of density of measured specific activities Small samples (< 60 g) and large samples (60 g) present almost the same average value, respectively 22.3 Bq L -1 and 22.8 Bq L -1 , but different standard deviations: 2.17 Bq L -1 and 0.88 Bq L -1 . The variation of these average values may be explained by differences in the proportions of water extracted in each case (respectively 84.4% vs. 85.9 %).

Treating very large samples (> 100 g) is not easy: experimentally we observe that the milk is boiling and spurting very rapidly after the beginning of each repetition. This phenomenon is prone to contaminate both extracted and condensed water. Treating small samples allowed the use of larger vessels compared to the sample volume: a difference of a factor of 5 between the volumes of the Erlenmeyer flask and the sample is sufficient to limit spurting.

Each distillation technique also showed its own limitations with regard to the mass of the samples treated. While the rotating evaporator efficiently dehydrates only samples between 100 g and 400 g, the distillation bridge is efficient for a larger range of sample volumes (only one dehydration was not complete as it was interrupted to soon) (Fig. 7).

In these experiments, distillations of 60-100 g milk samples under reduced pressure using a distillation bridge gave the best results with a limited dispersion of the measured specific activities.

Influence of the state of dehydration

The specific activities measured were viewed with respect to the state in which each experiment was ended. The results are presented in Fig. 8. The specific activity appears to increase slightly with the degree of dehydration but neither Spearman's nor Student's correlation tests revealed a correlation between the two parameters. Isotopic fractionation during distillation is generally described by means of the Rayleigh equation that was first derived for fractional distillation of mixed liquids [START_REF] Rayleigh | On the distillation of binary mixtures[END_REF].

))

1 1 ln( ) (ln( 1 1 ) ln( 0 0 0 X X X X n n          (2)
where: n 0 : is the initial number of all moles of all species in the sample n: is the number of all moles of all species in the residual sample X 0 : is the initial mole fraction of HTO in the sample 22/32 X: is the mole fraction of HTO in the residual sample α: is the vapour-liquid fractionation factor [START_REF] Kim | Tritium fractionation in anomalous water bound to environmental samples[END_REF] reported that tritium enrichment on distillation of pure HTO/H 2 O can be calculated using the Rayleigh formula taken under the following form (3):

 1 .           r o o o r r V V V A V A
(3)

Where:

A r : is the specific activity of residual water A 0 : is the initial specific activity of the water sample V r : is the volume of residual water V 0 : is the initial volume of water in the sample  α: is the vapour-liquid fractionation factor Under equilibrium vaporization conditions, may be equivalent to the vapour pressure isotope effect (VPIE) that can be calculated theoretically ( [START_REF] Hook | Vapor pressures of the isotopic waters and ices[END_REF] or determined experimentally [START_REF] Baumgärtner | Isotope effects in the equilibrium and non-equilibrium vaporization of tritiated water and ice[END_REF]) under given approximations. The VPIE corresponds to the definition provided in (4) and is considered equivalent to the separation factor ignoring the corrections accounting for both a non-ideal liquid and gas phases (Jancso and [START_REF] Jancso | Condensed phase isotope effects (especially vapor pressure isotope effects)[END_REF][START_REF] Kakiuchi | Distribution of isotopic water molecules, H 2 O, HDO and D 2 O, in vapor and liquid phase in pure water and aqueous solution systems[END_REF]:

V H T L H T HTO O H X X X X P P VPIE ) / ( ) / ( 2     (4)
23/32 P H2O and P HTO are the vapour pressures of pure water and pure tritiated water, respectively, X T and X H stand respectively for the molar fractions of HTO and water, in the liquid (L) and vapour (V) phase.

In order to fit with our experiments, residual volume (V r ) and specific activity (A r ) were replaced in (3) by extracted volume (V e ) and specific activity (A e ) using relations ( 5) and ( 6). Equation ( 7) is thus obtained:

r e V V V   0 (5) r r e e V A V A A V   0 0 . ( 6
)
By considering (3):

                         1 0 0 0 0 1 e e e V V V V A A V (7)
Lastly, each aliquot sampled during the distillation has a specific activity (A (1-2) ) which is the mean value of (7) between V 1 and V 2 , respectively the volume of water extracted at the beginning and at the end of the extraction of the given aliquot (8): Conversely, with samples of milk, at percentages of free water extracted higher than  95 %, ( 7) and ( 8) generally fail at modelling the observed experimental behaviour of the relative activity of extracted water, due to the drastic increase in relative activity measured at the end of the water extraction process (Fig. 9). When most of the water is extracted from the milk, the remaining part of the sample in the boiler is likely to behave as a non-ideal solution. It is thus necessary to introduce a correction in (7) and thus in (8). Such a correction may be obtained in two main ways: a complete theoretical description of the sources of non-ideality or a blind parameterization of the observed effect. As for the theoretical description, in its simplest form a model may at least take account of two kinds of water, cosphere (hydration) water in the immediate neighbourhood of solute particles or molecules and bulk water which retains the properties of the pure solvent [START_REF] Jancso | Condensed phase isotope effects (especially vapor pressure isotope effects)[END_REF]. In this part of the study, we will try to parameterize the observed effect and confine our work to the consequences of this behaviour on the metrology of tritium specific activity.

                   
To take account of the drastic increase observed at the end of the water extraction, equation ( 7) is parameterized by introducing two dimensionless free parameters p and β in the following manner:

                                    1 0 1 0 0 0 1 . 1 . 1 1 V V p V V p V A A V ext ext ext ext (9)
The specific activity of an aliquot is thus given by (10):

                                            
The experimental data presented in Fig. 9 can be modelled using relation (10). The best values for p, α, and β (which are respectively 0.04, 1.14, 11.7) were estimated by a function in the R software (R Core Team, 2012) which carries out minimization of a function (f) using a Newton-type algorithm. In R software, this function is called nlm. Each first aliquot of the different repetitions has a variable specific activity as compared to the mean final specific activity of the set. This is most probably an artefact linked to the experimental conditions. It is noticeable in Fig. 10 that this value has a perceptible impact on the mean specific activity of, say the 4-5 first aliquots. Using the model based on relation ( 9) we learn that even with a (hypothetically) perfect dehydration apparatus, if the dehydration is interrupted when 10% of water remains (a situation that may happen if the temperature is too low, the pressure too high or the dehydration simply is uncompleted); the measured specific activity of the extracted water should thus be underestimated by about 9 %.

The dead volume, an example of a combination of sources of biases

In light samples (ranging from 15 g to 60 g), the measured specific activities of water extracted with a rotating evaporator were systematically lower than those obtained with a distillation bridge. Additional experiments were performed to explain this particular point.

The rotating evaporator condenser indeed has a dead volume estimated to be 7.0 mL ± 1.2 mL. In other words, 7 mL must reach the condenser before the first drop of distillate is observed and 7 mL remain in the condenser at the end of distillation. A model of the timecourse of the specific activities in the condenser and in the distillate during distillation based on an isotopic fractionation was set up.

Let us now consider the following assumptions as axiomatic: 26/32 as described above isotopic fractionation exists, in the condenser of the rotating evaporator, equilibrium between vapour and condensed phase is instantaneous, each mass of vapour that flows up from the boiler to the condenser gets rid of the same mass of condensed vapour to the distillate. Now, introducing the subscript "cond." to denote the activity (or the mass) in the condenser;

from the beginning of the distillation to the extraction of a mass of water equal to the mass of water in the dead volume, we have:

i ext i cond A A . .  (11)
As soon as the dead volume of the condenser is filled:

        1 1 1 . .           i i cond i i i i cond cond i cond V V V V V A A V A ( 12
)
We consider that no water flows into the distillate until the dead volume of the condenser is full and introduce the subscript "dist." to denote a specific activity of the distillate, thus:

   i dist i i i cond i dist i dist i disti V V V A A V A . 1 . 1 .. 1 . .         (13)
This model was tested on the different data sets of our results as well as with an experiment where the condenser was first saturated with untritiated water before distilling tritiated water.

All sets of results are well-fitted by the present model. It shows how the measured specific activity (measured in the distillate) is modified by the loss of water in the dead volume (Fig. 12) for a known dead volume (7 mL in this example). This influence depends on the mass of the sample and on its specific activity (Fig. 13). For samples of milk lower than 10 g, the bias is less than 3 %. Actually, as there is only 8.7 g of water in 10 g of milk and the dead volume of the condenser being estimated to 7 mL (7 g), the few drops that flow out from the condenser has a specific activity that is fully representative of water extracted from the sample. For samples with 15 g ≤ M ≤ 75 g, the underestimation of the specific activity is about -6 %. The latter is in good agreement with the results presented in Fig. 8 which represents how specific activities of different samples are distributed as a function of their final rate of dehydration. Lastly, using samples larger than 200 g is a necessary condition to obtain a deviation that remains below 3 % when using a rotating evaporator.

Conclusion

In this study we show that each methodological aspect tested (water removal technique, mass of sample and final state of dehydration) is able to induce a bias in the specific activity measured in the extracted water. In most environmental monitoring situations, these biases 28/32 remain close to the uncertainty of measurement when liquid scintillation is used in the usual conditions (i.e. about 15% when measuring a sample of 10 mL with an activity of 20 Bq.L -1 water mixed with 10 mL of UltimaGold LLT [START_REF] Pointurier | Determination of organically bound tritium background level in biological samples from a wide area in the south-west of France[END_REF] for 200 minutes).

Nevertheless, some of these biases can produce systematic underestimations of the actual specific activity. First, it was shown that in the conditions of this study the water extracted by freeze drying had a specific activity significantly higher than the water extracted using a distillation technique based on the same milk sample. This is explained by a pollution of the extracted water by atmospheric water before, after or during the freeze drying process. This particular behaviour became apparent due to the fact that atmospheric water in the Valduc centre is has slightly elevated ambient levels of tritium. Caution must thus be taken to avoid marking during freeze drying, especially when the specific activity of the sample is not of the same order of magnitude as the specific activity of the atmospheric vapour. An easy and economic way to prevent this phenomenon would be to freeze dry larger samples (at least 100 g) which would dilute the effect of atmospheric water condensation. A more suitable way nevertheless would be to operate freeze drying in a dry atmosphere and to break the vacuum with dry gas.

When dehydration is performed by distillation under reduced pressure, the dead volumes of the devices (especially those of the condenser) have to be limited as they can induce a bias in the estimation of the mass of extracted water as well as and in the measurement of specific activities. It appears that using a distillation bridge suits a wider range of samples masses than a rotating evaporator, the latter should be preferred for large samples (> 300 mL).

Lastly, in this study a fractionation effect during dehydration proved to be more significant than expected. This shows the necessity to perform dehydration until there is no water left in the sample. When a fraction of water cannot be extracted without taking the risk of damaging the dry matter, the residual fraction of water should be estimated and the specific activity measured corrected using formula (9) proposed in this work.

The effects of the different sources of biases must be summed. For instance, if a distillation using a rotating evaporator (dead volume of 7 mL) of a sample of 20 mL of milk is interrupted when 10 % of water remains in the matrix, the measured specific activity would be about 91 % of the real specific activity and the standard deviation of this result would be 11 % additionally increase by the uncertainty of measure (about 15 % in usual conditions).

Overall, this would lead to a global underestimation of about 10 % and an uncertainty of ± 26 %.

In the literature, VPIE has been shown to decrease while temperature increases without differences being measured between vaporization and sublimation [START_REF] Baumgärtner | Isotope effects in the equilibrium and non-equilibrium vaporization of tritiated water and ice[END_REF]. It has also been shown that a link exists between isotopic fractionation during extraction of water and a three-layer model for bound water [START_REF] Kim | Tritium fractionation in anomalous water bound to environmental samples[END_REF] (described by Drost-Hansen). The results gathered herein using milk samples show fractionation behaviour which can be described by a two-component formula, each component being based on specific Rayleigh distillation processes. These results bring to mind the features of two fractions of water that coexist in milk: the first one (96%) that acts as pure water (free water) and the second (4%) which presents an isotopic separation factor β equal to 11.7 much higher than that of pure water;  = 1.14. The fraction described here by the isotope separation factor β may be bound water.

-

  azeotropic distillation extracts water at lower temperatures than distillation. As it uses organic compounds, it is more difficult to perform and it can additionally induce contamination of the dry matter by hydrocarbons. 6/32 -Freeze drying: i.e. extraction of water via sublimation; it has the same advantages as distillation under reduced pressure. The size of the apparatus, the temperature of the cold trap (usually > -20°C) and the time required to completely extract the water may induce biases by condensing atmospheric vapour before starting or during the process. Repetition of measurements performed in our laboratory on the free water of a given tritiated milk obtained by distillation under reduced pressure or by freeze-drying, have shown certain systematic errors and dispersion of the values beyond the basic uncertainties of the measurements. The reasons underlying these differences have been sought and improvements of the reliability of tritium measurements are proposed. Four possible hypothetical origins of the observed differences in measured specific activities were identified: -the influence of sample storage: as ambient levels of tritium at the Valduc Centre of the French Atomic Agency can be higher than those of the environment where the samples were collected, they may become significantly more tritiated during their storage. -the influence of the technique of water extraction: the usual techniques of dehydration differ from each other by their conditions of pressure, temperature and the apparatus used. These different factors may lead to biases in the measurement.

Five

  other sets of nine samples of Volvic were stored in different kind of bottles: -50 mL of Volvic water in 150 mL high density polyethylene (HDPE) bottles, -150 mL of Volvic water in the same kind of bottles, -50 mL of Volvic water in the same bottles placed in double welded vinyl bags, -20 mL of Volvic water in 20 mL glass bottles, -20 mL of Volvic water in 20 mL HDPE bottles (usually used for scintillation counting)

  To detect possible external contamination, two kinds of experiments were performed: Measurement of the specific activity of water extracted by freeze drying in two different ambient atmospheres: one in the Valduc Centre (in the conditions described above) and one in Besançon (25-France) where the specific activity of the atmosphere in HTO is below the decision threshold. The milk was separated into 7 samples of 51.23 g ± 0.45 g. They were frozen in Valduc in plastic bottles inserted in double welded vinyl bags. Three were freezedried in Valduc, three in Besançon and one was distilled using a distillation bridge in the Valduc Centre in the conditions described above. Freeze drying at Besançon was performed in a Cosmos 20k (Cryotec). Vaccum was generated by a pump (Adixen Pascal 2005-Ci) working at full capacity. After the end of freeze drying, the water was recovered by heating the condenser. The specific activity of each recovered water sample was measured in the Valduc Centre and compared.

Fig. 1 :

 1 Fig. 1: Apparatus used for "sequential distillations"

Fig. 2 :

 2 Fig. 2: Specific activity of Volvic water stored in an open bottle versus duration of storage. The first point having a specific activity under the limit of detection was plotted as having a specific activity of 0 Bq L -1 .

Fig. 3 :

 3 Fig. 3 : Comparison of the distributions of measured specific activities of water extracted using the three different methods described in this study. Central boxes represent the values from the lower to upper quartile.Middle lines represent the median. Vertical lines extend from the minimum to the maximum value of each population, which are represented by horizontal lines at their extremity. The specific activity of the water extracted by freeze drying is significantly higher than the specific activity of the water extracted by each of the two distillation methods tested (Wilcoxon test, p < 0.01). Differences between the two techniques of distillation were not significant.

Fig. 4 :

 4 Fig. 4 : Comparison of specific activities measured on water with and without treatment (distillation or freeze drying)

Fig. 5 :

 5 Fig. 5 : Specific activities of water extracted from milk by means of freeze drying performed in Besançon and in the Valduc Centre.

Fig. 7 :

 7 Fig. 7: Proportion of water extracted (in % of weight of total sample) versus mass of sample treated. The mean proportion of free water obtained was evaluated by measuring the dry mass of each sample remaining after 5 h in a forced-air oven at 102°C.

Fig. 8 :

 8 Fig. 8 : Specific activity of extracted water versus the degree of dehydration The line shows the same relationship modelled by relation (10) with p = 0.04, α = 1.14, and β = 11.7.

Fig. 9 :

 9 Fig. 9 : Specific activity of aliquots of extracted water versus the proportion of water extracted The line plots the variation modelled with equation (11) with p = 0.04, α = 1.14, and β = 11.7. Each type of label represents a set of repetition. Four repetitions were performed on one sample of milk (squares), two on a second sample (triangles) and lozenges represent a set performed on a third sample. Mean specific activity of extracted water = 1.

Fig. 10 :

 10 Fig. 10 : Mean specific activity versus proportion of water extracted. The solid line was computed using relation (10) with p = 0.04, α = 1.14, and β = 11.7. Each type of label represents a repetition set. Four repetitions were performed on one sample of milk (squares), two on a second (triangles) and lozenges represent a set performed on a third. Mean specific activity of extracted water = 1

Fig. 11 :

 11 Fig. 11 : Extraction of HTO during distillation of pure HTO/H 2 O versus proportion of free water extracted Lines are calculated by equations (7) and (9). Triangles and circles correspond to experimental values. Mean specific activity of extracted water = 1

Fig. 12 :

 12 Fig. 12: Modelled evolution of specific activity of water in different compartments during the distillation of a 20 g sample of milk (Mean specific activity of extracted water = 1).

Fig. 13 :

 13 Fig. 13: Bias due to the rotating evaporator versus mass of sample. The model described above was tested with different masses of sample (from 7 g to 10 000 g) to determine how the modelled bias induced by the dead volume of the condenser   theoric measured theoric A A A /  evolves in this range of mass.

Table 1 : Mass and specific activity of water recovered after empty freeze dryings performed in the Valduc

 1

	Centre
	Duration of freeze drying		Specific activity of the
		Mass of recovered water (g)
	(h)		recovered water (Bq L-1)
	168	0.4	200
	168	0.0	No measurement
	146	0.8	257

Acknowledgements

30/32

The authors would like to thank to the Conseil Régional de Bourgogne (France) for the 688 financial support of this study. 689

Equation ( 8) fits experimental data provided by distillation of pure HTO/H 2 O (Fig. 11). In these experiments,  was evaluated at 1.14 which is 6.7 % higher than expected in our experimental conditions [START_REF] Baumgärtner | Isotope effects in the equilibrium and non-equilibrium vaporization of tritiated water and ice[END_REF]. This difference may be explained by the specificities of the apparatus used which seem to increase the height by the equivalent of a theoretical plate (HETP) and thus α [START_REF] Fukada | Tritium isotope separation by water distillation column packed with silica-gel beads[END_REF] .

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