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β-ray dosimetry of natural samples by the TLD method
International Journal of Applied Radiation and Iso#olxrS V,ol. 32. pp. 201 to 204, 1981 Printed in Great Britain. All rights reserved
0020,708X/81/040201-04102.00~ Copyright O 1981 PerSmmOn Press Lid
fl-Ray Dosimetry of Natural Samples by the TLD Method JIRI KVASNI(~KA Power Research Institute, Bajkaiski 27, 884 03 Bratislava, Czechoslovakia (Received 21 Auoust 1980; in revisedform 30 September 1980) Thermoluminescent LiF powder was used to estimate the ~-ray dose of homogenous sources with " known concentrations of uranium, thorium and potassium. An influence of the thickness of the LiF layer on the measured r-ray dose was also established. A simple approach was designed for establishing the B-ray dose in natural thick sources and also the ~ray dine in a soft-tissue from radionuclides of reactor effluents.
Introduction
Exl~rimental
/~-R^Y DOSIMETitYof radionuclides within solid,liquid and gaseous samples is useful in nuclear medicine, thermoluminescent dating and also in radiation monitoring of reactor effluents in the environment. Differences which still exist between theoretical calculations and experimental results vary because of final dimensions of detectors and a different composition of detector and the medium in which the r-ray dose has to be established. To measure the ~-ray dose of low ~ activity in a sample it is necessary to use a low-level counting technique and to establish the background of the method. In case of natural samples the r-ray dose is measured in a mixed radiation field of =-, ~,- and cosmic-rays. Thermoluminescent dosimeters (TLD's) have also been in use for several years in this field: al Applying integral TLD's in ~-ray dosimetry of natural samples most of the problems mentioned above are t o be taken into consideration, it is necessary to establish the influence of the final thickness of TL material and the influence of an absorption material needed for absorption of ~,-particles of uranium and thorium series inside natural samples. Correction on the TL response to 7-rays of radionuclides in the sample has to be taken into account. The stopping power ratio of TLD and the source medium which implies the dose ratio in TLD and the medium has to be included in the dose calculation.
Samples of granite, trachyte and basalt with known equilibrium activities of uranium, thorium and potassium were used in our experiments (Table 1~ Samples were crushed and homogenized beforehand, so that the maximum dimensions of grains were less than 7/an. These samples were placed inside lucite containers.The container was a ring I c m high, the outer and inner diameters of which were 3.2 and 2.5 cm. The upper and lower covers of the ring containers were polyethylene foils 8 mg-cm -~ thick and served as a-particle absorbers and enclosed the samples hermetically. The samples inside the containers were pressed down and after 30 days, when the secular equilibrium in the uranium series radionuclides ('26Ra and its daughters) was restored, LiF powder was placed on polyethylene foils of the containers. LiF layers had a thickness of about 20-60 mg.cm-2. The distance of the edge of the colimated TL phosphor layer was about 0.5 cm from the inner edge of the ring container. Under such circumstances the edge effect of p-particle irradiation can be ignored. TL phosphor and container with the sample was covered by a polyethylene foil and a lucite board 1 cm thick. To lower background (terrestrial 7-rays and cosmic-rays) the irradiation of TLD phosphor with natural /~-radiation was arranged inside a lead box. This type of background as well as spurious TL were established by TLD's. To fix the response of LiF to dose
TASLE 1. The concentrations of uranium, thorium and potassium in granite, trachyte and basalt
Granite Trachyte Basalt A.ILI. 32 4 - - a
U (ppm)
Th (ppm)
(%)
20.0 ± 0.2 4.4 + 0.1 1.4 + 0.1
44.1 + 0.4 19.0 + 0.3 5.5 + 0.2
5.36 + 0.06 3.36 + 0.07 1.20 + 0.03
201
K
202
J. Kvasni~ka
150
"--.....
35(
3OO
A )00
| ~ranit
:
....... basalt
zl.iF(rag FIG. I. Dependences of the year /~-ray doses in LiF layers on the LiF layer thickness placed on the
surfaces of semi-infinite natural sources with equilibrium activities of uranium, thorium and potassium. Between LiF layer and the source was polyethylene foil 8 rag. cm- = thick.
unit. TL powder was irradiated by several doses of O°Co 7-rays and were also placed inside the lead box with the other TLD's. After about 6 months TLD's were read on a laboratory TL device constructed for measurement of low doses of radiation. The TL response was read from the TL peak which exists at a heating regimen at 220"C. The average TL response was calculated from four measurements of LiF samples weighing about 7 rag. The ~-ray dose was then calculated from the response to LiF to the ~-rays on the top of the rock samples, considering a background TL response and response to a dose unit of 7-radiation of 6°Co.
Results
Dose calibration of LiF was made by 7-ray irradiation of LiF powder inside cylindrical lucite containers with a cavity diameter 0.3 cm and the wall 0.6 cm thick. The dose was calculated according to Burlin's theory by the simple formula TM ~)¢n.
DI.iF = 0 . 8 6 9 X e - " x (i[(Vl.iF en
(rad)
(I)
(/-L' p ),,it
where X is the exposure in r. the constant 0.869 rad/r. the exponential is a correction for 7-ray absorption in the wall of the container. The ratio of mass energy absorption coefficients in LiF and air was taken from Attix et al. TM It was stated that the TL response of LiF is under given experimental conditions linear, at least from 20 mrad to 200 mrad.
The average ~-ray dose dependences in LiF layer on the "thickness of the layer at the surface of semiinfinite sources are given in Fig. 1. A polyethylene foil 8 mg.cm--" thick was placed between the surface of the source material and the LiF layer. The #-ray dose rate on the surface of the semi-infinite source can be calculated by the equation /)ffi 1/21.6"10-S~N~J.iEi
(rad's -1)
(2)
i
where Nj is a number of atoms of a given radionuclide in 1 g of the source. ,:.~is its decay constant. E~ is the average energy of ~-particle emitted by radionuclide i. Supposing that the equilibrium activity is in the uranium and thorium series, the equation a) can be rewritten in the form == 1/2(13.1 c~ + 2.51CTh + 79.7 c K ) [ m r a d ' y r - t] (3) The average/~-ray energies and decay constants were taken from Martin and Blichen-Toft. ('j Concentrations of uranium and thorium are in ppm (1 ppm = 10~ g.g-~) and the concentration of potassium is in Oo. The isotope is supposed to be contained 100°o in the natural mixture of uranium. According to equation (3) the /~-ray dose rate is calculated in m r a d s - y r - I The surface /~-ray dose rates of given rock samples are shown in Table 2. Also included are the average energies of ~-particles emitted by natural radionuclides in the samples. The depth dependence of ~-dose rates in the semiinfinite air-water media (air is considered as a source
203
#-Ray dosimetry of natural samples by the TLD method TABLE 2 (mrad.yr -t) Granite Trachyte Basalt
400 + 6 186 + 6 63.9 + 2.8
(mrad'yr -t) 333 156 52.1
f , - 2 D//)*(O)
(MeV)
(ern2 .g -I)
2.40 2.38 2.45
0.511 0.533 0.537
8.67 8.05 7.61
I) is #-ray dose rate calculatedaccording to equation (3). D*(0) is #-ray dose rate in LiF layer which thickness approaches zero and was established by_extrapolation dependences at Fig. 1. En is the average #-particle energy emitted by radionuclides in the samples. /~ is absorption coefficient of beta particles in LiE emitted from the surfaces of rock
samples.
of homogenous activity and water as a target) was theoretic~ly solved by Berger: s) Roesch ~6) had used a simple age-diffusion calculation according to which the depth dependence of dose rate has the form /)(:) =/)(0)exp -
z) dz
(4)
where ." is the depth below the boundary (in g. cm-2), /)(0) is the/i-ray dose rate at the depth z -- 0, and ~(z) is the absorption coefficient which is generally depth dependent. If we suppose that in the depth :---* 0, /z = constant the equation (4) can be rewritten in the form
D(z) = ~O)(l
-
~.z)
(5)
Equation {5) was further applied to experimental results (/i-ray doses with respect to LiF layer thicknesses on the surfaces of semi-infinite sources with natural radionuclides). Before TL reading the LiF powder was homogenized by mixing and so the average ~-ray doses in LiF layers were measured. The average/i-ray dose rate/J*(0, z) in a layer of thickness (: - 0) can be calculated from the equation (between the LiF layer and the source the polyethylene foil has been inserted)
b.f0) I : (1 - # - z ) d :
D*(0.: )
=
do
f]d:. :
On these assumptions a line was drawn up through experimental points. By extrapolation the dose rate /)*(0) in a LiF layer which thickness approaches zero can be deduced (Table 2). From equation (6) the average absorption coefficients of beta panicles in LiF were calculated. Conclusion
By T L method the/i-ray doses can be established in LiF on the surface of the foil covering a semi-infinite source. The dose rate /)*(0) relates to the dose rate
inside the source following this relation (which is ira. portant for a better understanding of the problem) ffi
L*
l
(7)
where L ' and ~Lir are the average stopping powers of /i-rays in the source and LiF. They have to be averaged with respect to real /i-ray spectrum at the boundary of the source and target media. It is supposed that the /i-ray spectrum near the boundary approaches the spectrum in the source media. In this relation there is also included the correction factor for absorption of/i-rays in the foil ~ f is the absorption coefficient in polyethylene foil and z / i s the foil thickheSS). S is a correction factor on multiple scattering. Supposing the absorption properties o f rocks differ only insignificantly from SiO2 we can establish the ratio of average stopping powers in equation 7 as 1.04.°) These considerations resulted from calculations of /i-ray spectra on the surface of the thick natural sources with homogeneous concentration 2ssu, 232Th and 4°K.(S) To insert an average absorption coefficient of the polyethylene foil (we suppose that it is about 25~o higher than the absorption coefficient in LiF) the absorption correction of the polyethylene foil 1.09 was calculated and inserted into equation (7). Multiple scattering correction S = 1.06 was then calculated from the equation (7). This factor S also includes a y-dose of radionuclides inside natural samples. As to the T L response of LiF to y-rays of radionuclides in the samples we can deduce that in our experimental conditions the y-ray response is not higher then a few percents of the TL response of LiF to /i-radiation from the same samples. The sample is semi-infinite with respect to /i-rays but far from a semi-infinite source with respect to natural y-radiation. To calculate the #-ray dose rate in a source from the dose rate measured in LiF layer of known thickness, firstthe dose rate/)*(0) is to be calculated from equation {6) by infering the average absorption coefficient ~ = 8.1 cm 2 g-1. Then the /i-ray dose rate in source medium/), is calculated by multiplying D*{0) by average factor f = 2.41 (Table 2). All this pro-
204
J. Kvasni(ka
cedure can be used only in case the chemical composition and concentration ratios of uranium, thorium and potassium in the unknown sample approach the rock samples used in the experiment. These assumptions are fulfilled with a sufficient accuracy in case of ceramic samples and in many rocks and minerals which are used in connection with thermoluminescent dating. From our experimental results it may be inferred the TL method is sensitive enough to be used in monitoring//-ray doses of radionuclides from reactor effluents. In this case //-ray dose rates or integral doses in soft-tissue have to be established. From the fl-ray dose measured in a LiF layer below the polyethylene foil, the dose in the soft-tissue (in the same layer as LiF layer and in depth given by foil thickness) can be calculated with fair accuracy by multiplying the LiF dose by average ratio ~,i~,,,/~LiF. The background of this method is the ~-ray dose of natural and man-made radionuclides and the second-
ary cosmic-ray dose. The kind of background can be stated by parallel exposure of TLD's in a container which absorbs fl-rays. For routine application of TL method in the scope indicated above it will be necessary to use TLD's which have a thin sensitive layer of TL phosphor solidly connected with a fixed dosimeter pad.
References 1. MVJDAm. V. Archaeometry 11, 99 (1969). 2. BURLINT. E. Br. J. Radiol. 39, 727 (1966). 3. ATTIXF. H. et al. Radiation Dosimetry, 2nd edn, Vol. 3 (Academic Press. New York. 1968). 4. M ~ N M. J. and BUC~RT-TOFT P. H. Nuclear Data Tables, AS, pp. 1-198 (1970). 5. B~oE~ M. J. HIth Phys. 26, I (1974). 6. ROI~SCH W. C. General Electric Hartford Atomic Products, Operation Report, HW 3212 (1954). 7. PAGESL. et al. Atomic Data 4, 1-127 (1972). 8. MINATOS. et al. HIth Phys. 34, 6 (1978).
0020,708X/81/040201-04102.00~ Copyright O 1981 PerSmmOn Press Lid
fl-Ray Dosimetry of Natural Samples by the TLD Method JIRI KVASNI(~KA Power Research Institute, Bajkaiski 27, 884 03 Bratislava, Czechoslovakia (Received 21 Auoust 1980; in revisedform 30 September 1980) Thermoluminescent LiF powder was used to estimate the ~-ray dose of homogenous sources with " known concentrations of uranium, thorium and potassium. An influence of the thickness of the LiF layer on the measured r-ray dose was also established. A simple approach was designed for establishing the B-ray dose in natural thick sources and also the ~ray dine in a soft-tissue from radionuclides of reactor effluents.
Introduction
Exl~rimental
/~-R^Y DOSIMETitYof radionuclides within solid,liquid and gaseous samples is useful in nuclear medicine, thermoluminescent dating and also in radiation monitoring of reactor effluents in the environment. Differences which still exist between theoretical calculations and experimental results vary because of final dimensions of detectors and a different composition of detector and the medium in which the r-ray dose has to be established. To measure the ~-ray dose of low ~ activity in a sample it is necessary to use a low-level counting technique and to establish the background of the method. In case of natural samples the r-ray dose is measured in a mixed radiation field of =-, ~,- and cosmic-rays. Thermoluminescent dosimeters (TLD's) have also been in use for several years in this field: al Applying integral TLD's in ~-ray dosimetry of natural samples most of the problems mentioned above are t o be taken into consideration, it is necessary to establish the influence of the final thickness of TL material and the influence of an absorption material needed for absorption of ~,-particles of uranium and thorium series inside natural samples. Correction on the TL response to 7-rays of radionuclides in the sample has to be taken into account. The stopping power ratio of TLD and the source medium which implies the dose ratio in TLD and the medium has to be included in the dose calculation.
Samples of granite, trachyte and basalt with known equilibrium activities of uranium, thorium and potassium were used in our experiments (Table 1~ Samples were crushed and homogenized beforehand, so that the maximum dimensions of grains were less than 7/an. These samples were placed inside lucite containers.The container was a ring I c m high, the outer and inner diameters of which were 3.2 and 2.5 cm. The upper and lower covers of the ring containers were polyethylene foils 8 mg-cm -~ thick and served as a-particle absorbers and enclosed the samples hermetically. The samples inside the containers were pressed down and after 30 days, when the secular equilibrium in the uranium series radionuclides ('26Ra and its daughters) was restored, LiF powder was placed on polyethylene foils of the containers. LiF layers had a thickness of about 20-60 mg.cm-2. The distance of the edge of the colimated TL phosphor layer was about 0.5 cm from the inner edge of the ring container. Under such circumstances the edge effect of p-particle irradiation can be ignored. TL phosphor and container with the sample was covered by a polyethylene foil and a lucite board 1 cm thick. To lower background (terrestrial 7-rays and cosmic-rays) the irradiation of TLD phosphor with natural /~-radiation was arranged inside a lead box. This type of background as well as spurious TL were established by TLD's. To fix the response of LiF to dose
TASLE 1. The concentrations of uranium, thorium and potassium in granite, trachyte and basalt
Granite Trachyte Basalt A.ILI. 32 4 - - a
U (ppm)
Th (ppm)
(%)
20.0 ± 0.2 4.4 + 0.1 1.4 + 0.1
44.1 + 0.4 19.0 + 0.3 5.5 + 0.2
5.36 + 0.06 3.36 + 0.07 1.20 + 0.03
201
K
202
J. Kvasni~ka
150
"--.....
35(
3OO
A )00
| ~ranit
:
....... basalt
zl.iF(rag FIG. I. Dependences of the year /~-ray doses in LiF layers on the LiF layer thickness placed on the
surfaces of semi-infinite natural sources with equilibrium activities of uranium, thorium and potassium. Between LiF layer and the source was polyethylene foil 8 rag. cm- = thick.
unit. TL powder was irradiated by several doses of O°Co 7-rays and were also placed inside the lead box with the other TLD's. After about 6 months TLD's were read on a laboratory TL device constructed for measurement of low doses of radiation. The TL response was read from the TL peak which exists at a heating regimen at 220"C. The average TL response was calculated from four measurements of LiF samples weighing about 7 rag. The ~-ray dose was then calculated from the response to LiF to the ~-rays on the top of the rock samples, considering a background TL response and response to a dose unit of 7-radiation of 6°Co.
Results
Dose calibration of LiF was made by 7-ray irradiation of LiF powder inside cylindrical lucite containers with a cavity diameter 0.3 cm and the wall 0.6 cm thick. The dose was calculated according to Burlin's theory by the simple formula TM ~)¢n.
DI.iF = 0 . 8 6 9 X e - " x (i[(Vl.iF en
(rad)
(I)
(/-L' p ),,it
where X is the exposure in r. the constant 0.869 rad/r. the exponential is a correction for 7-ray absorption in the wall of the container. The ratio of mass energy absorption coefficients in LiF and air was taken from Attix et al. TM It was stated that the TL response of LiF is under given experimental conditions linear, at least from 20 mrad to 200 mrad.
The average ~-ray dose dependences in LiF layer on the "thickness of the layer at the surface of semiinfinite sources are given in Fig. 1. A polyethylene foil 8 mg.cm--" thick was placed between the surface of the source material and the LiF layer. The #-ray dose rate on the surface of the semi-infinite source can be calculated by the equation /)ffi 1/21.6"10-S~N~J.iEi
(rad's -1)
(2)
i
where Nj is a number of atoms of a given radionuclide in 1 g of the source. ,:.~is its decay constant. E~ is the average energy of ~-particle emitted by radionuclide i. Supposing that the equilibrium activity is in the uranium and thorium series, the equation a) can be rewritten in the form == 1/2(13.1 c~ + 2.51CTh + 79.7 c K ) [ m r a d ' y r - t] (3) The average/~-ray energies and decay constants were taken from Martin and Blichen-Toft. ('j Concentrations of uranium and thorium are in ppm (1 ppm = 10~ g.g-~) and the concentration of potassium is in Oo. The isotope is supposed to be contained 100°o in the natural mixture of uranium. According to equation (3) the /~-ray dose rate is calculated in m r a d s - y r - I The surface /~-ray dose rates of given rock samples are shown in Table 2. Also included are the average energies of ~-particles emitted by natural radionuclides in the samples. The depth dependence of ~-dose rates in the semiinfinite air-water media (air is considered as a source
203
#-Ray dosimetry of natural samples by the TLD method TABLE 2 (mrad.yr -t) Granite Trachyte Basalt
400 + 6 186 + 6 63.9 + 2.8
(mrad'yr -t) 333 156 52.1
f , - 2 D//)*(O)
(MeV)
(ern2 .g -I)
2.40 2.38 2.45
0.511 0.533 0.537
8.67 8.05 7.61
I) is #-ray dose rate calculatedaccording to equation (3). D*(0) is #-ray dose rate in LiF layer which thickness approaches zero and was established by_extrapolation dependences at Fig. 1. En is the average #-particle energy emitted by radionuclides in the samples. /~ is absorption coefficient of beta particles in LiE emitted from the surfaces of rock
samples.
of homogenous activity and water as a target) was theoretic~ly solved by Berger: s) Roesch ~6) had used a simple age-diffusion calculation according to which the depth dependence of dose rate has the form /)(:) =/)(0)exp -
z) dz
(4)
where ." is the depth below the boundary (in g. cm-2), /)(0) is the/i-ray dose rate at the depth z -- 0, and ~(z) is the absorption coefficient which is generally depth dependent. If we suppose that in the depth :---* 0, /z = constant the equation (4) can be rewritten in the form
D(z) = ~O)(l
-
~.z)
(5)
Equation {5) was further applied to experimental results (/i-ray doses with respect to LiF layer thicknesses on the surfaces of semi-infinite sources with natural radionuclides). Before TL reading the LiF powder was homogenized by mixing and so the average ~-ray doses in LiF layers were measured. The average/i-ray dose rate/J*(0, z) in a layer of thickness (: - 0) can be calculated from the equation (between the LiF layer and the source the polyethylene foil has been inserted)
b.f0) I : (1 - # - z ) d :
D*(0.: )
=
do
f]d:. :
On these assumptions a line was drawn up through experimental points. By extrapolation the dose rate /)*(0) in a LiF layer which thickness approaches zero can be deduced (Table 2). From equation (6) the average absorption coefficients of beta panicles in LiF were calculated. Conclusion
By T L method the/i-ray doses can be established in LiF on the surface of the foil covering a semi-infinite source. The dose rate /)*(0) relates to the dose rate
inside the source following this relation (which is ira. portant for a better understanding of the problem) ffi
L*
l
(7)
where L ' and ~Lir are the average stopping powers of /i-rays in the source and LiF. They have to be averaged with respect to real /i-ray spectrum at the boundary of the source and target media. It is supposed that the /i-ray spectrum near the boundary approaches the spectrum in the source media. In this relation there is also included the correction factor for absorption of/i-rays in the foil ~ f is the absorption coefficient in polyethylene foil and z / i s the foil thickheSS). S is a correction factor on multiple scattering. Supposing the absorption properties o f rocks differ only insignificantly from SiO2 we can establish the ratio of average stopping powers in equation 7 as 1.04.°) These considerations resulted from calculations of /i-ray spectra on the surface of the thick natural sources with homogeneous concentration 2ssu, 232Th and 4°K.(S) To insert an average absorption coefficient of the polyethylene foil (we suppose that it is about 25~o higher than the absorption coefficient in LiF) the absorption correction of the polyethylene foil 1.09 was calculated and inserted into equation (7). Multiple scattering correction S = 1.06 was then calculated from the equation (7). This factor S also includes a y-dose of radionuclides inside natural samples. As to the T L response of LiF to y-rays of radionuclides in the samples we can deduce that in our experimental conditions the y-ray response is not higher then a few percents of the TL response of LiF to /i-radiation from the same samples. The sample is semi-infinite with respect to /i-rays but far from a semi-infinite source with respect to natural y-radiation. To calculate the #-ray dose rate in a source from the dose rate measured in LiF layer of known thickness, firstthe dose rate/)*(0) is to be calculated from equation {6) by infering the average absorption coefficient ~ = 8.1 cm 2 g-1. Then the /i-ray dose rate in source medium/), is calculated by multiplying D*{0) by average factor f = 2.41 (Table 2). All this pro-
204
J. Kvasni(ka
cedure can be used only in case the chemical composition and concentration ratios of uranium, thorium and potassium in the unknown sample approach the rock samples used in the experiment. These assumptions are fulfilled with a sufficient accuracy in case of ceramic samples and in many rocks and minerals which are used in connection with thermoluminescent dating. From our experimental results it may be inferred the TL method is sensitive enough to be used in monitoring//-ray doses of radionuclides from reactor effluents. In this case //-ray dose rates or integral doses in soft-tissue have to be established. From the fl-ray dose measured in a LiF layer below the polyethylene foil, the dose in the soft-tissue (in the same layer as LiF layer and in depth given by foil thickness) can be calculated with fair accuracy by multiplying the LiF dose by average ratio ~,i~,,,/~LiF. The background of this method is the ~-ray dose of natural and man-made radionuclides and the second-
ary cosmic-ray dose. The kind of background can be stated by parallel exposure of TLD's in a container which absorbs fl-rays. For routine application of TL method in the scope indicated above it will be necessary to use TLD's which have a thin sensitive layer of TL phosphor solidly connected with a fixed dosimeter pad.
References 1. MVJDAm. V. Archaeometry 11, 99 (1969). 2. BURLINT. E. Br. J. Radiol. 39, 727 (1966). 3. ATTIXF. H. et al. Radiation Dosimetry, 2nd edn, Vol. 3 (Academic Press. New York. 1968). 4. M ~ N M. J. and BUC~RT-TOFT P. H. Nuclear Data Tables, AS, pp. 1-198 (1970). 5. B~oE~ M. J. HIth Phys. 26, I (1974). 6. ROI~SCH W. C. General Electric Hartford Atomic Products, Operation Report, HW 3212 (1954). 7. PAGESL. et al. Atomic Data 4, 1-127 (1972). 8. MINATOS. et al. HIth Phys. 34, 6 (1978).