Summary of doctoral thesis of Materials science: Assessment of natural radioactivity in some building materials used in Laos PDR

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The objectives of the thesis is: Determination of the concentration of the Naturally Occurring Radioactive Materials (NORM) in some building materials commonly used in Lao PDR such as cement, sand, etc. by gamma spectrometers using NaI(Tl) and HPGe detectors.

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MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ---------------------------- SONEXAY XAYHEUNGSY PROJECT NAME: ASSESSMENT OF NATURAL RADIOACTIVITY IN SOME BUILDING MATERIALS USED IN LAOS PDR Major: ATOMIC AND NUCLEAR PHYSICS Code: 9440106 SUMMARY OF DOCTORAL THESIS OF MATERIALS SCIENCE HANOI - 2019
The doctoral thesis was completed at Institute of Physics, Graduate University of Science and Technology Supervisors: Prof. Dr. Le Hong Khiem Reviewer 1: …………………… Reviewer 2: …………………… Reviewer3: …………………… This doctoral thesis will be defensed at Graduate University of Science and Technology, Vietnam Academy of Science and Technology on … hour…, date…. month … year… The dissertation can be referred at: National Library of Vietnam
LIST OF PUBLISTIONS 1. Sonexay Xayheungsy, Le Hong Khiem. Measurement of natural radioactivity in some cements of Lao PDR by using NaI(Tl) gamma-ray spectrometer, Advance in applied and engineering Physics IV, Publishing House for Science and Technology,2016, 231 2. Sonexay Xayheungsy, Le Hong Khiem, Phương pháp xác định hoạt độ của các nguyên tố phóng xạ tự nhiên bằng phổ kế gamma dùng detector NaI(Tl), Advance In Applied And Engineering Physics V, Publishing House for Science and Technology, 2018, 295 3. S. Xayheungsy, L.H. Khiem, L.D. Nam, Radiation dose estimation of cement samples used in Lao PDR, Communications in Physics, 27, No. 3, 2017,193-203. 4. Sonexay Xayheungsy, Le Hong Khiem, Le Dai Nam. Assessment Of The Natual Radioactivity And Radiological Hazards In Lao Cement Samples. Radiation Protection Dosimetry, 2018, Vol. 181, No. 3, 208–213. 5. Sonexay Xayheungsy, Le Hong Khiem. Natural Radioactivity In The Soil Of Thoulakhom District In Vietiane Province, LaoPDR, Tạp Chí Phát Triển Khoa Học Và Công Nghệ- Đại Học Quốc Gia TP. HCM, ngày 21 tháng 3 năm 2018. 6. X.Sonexay, L.H.Khiem, L.D.Nam, Assessment of Natural Radioactivity Levels and Radiation Hazards of Building Materials of Lao PDR. International Journal Of Modern Engineering Research (IJMER), 14.04.2018 7. Sonexay Xayheungsy1,3, N.C.Thanh2, L.D.Nam2, V.H.Giang2 and L.H.Khiem2,3*, Measurement of natural radioactivity in some sand and brick in Vietiane province, Lao PDR. IJRDO - Journal of Applied Science, Volume-4, Issue, 11, Nov, 2018.
INTRODUCTION 1. Thesis necessity There are various sources that contain radiation, especially in the earth, rocks with different amounts. An amount of radiation that is higher than the safety threshold can be a cause of many diseases including cancer, which is dangerous for people. Building materials such as cement, brick, sand, soil, etc. are mainly made from raw materials such as soil and rock. As a result, they can break down into radioactive gas radon. According to statistics of the UN, a person spends 70% his lifetime in-door (houses, offices, or public buildings, etc.). If the construction materials contain an extremely high amount of radiation, it will be hazardous. For the safety of humankind, The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) has given a radiation safety threshold for building materials. In most countries, it is mandatory to check radioactivity of the materials for construction before they are used. In Laos PDR , up to now there has not been any inspection of radiation carried out (due to lack of skilled personnel). Laos has officially become a member of the IAEA since 2011. Since then, Lao government have requested Vietnam to give a hand in training highly qualified personnel in the field of radioactive control in construction materials. The objective of this thesis is to understand the method of assessment of natural radioactivity in some building materials for better implementation of constructions in Laos. 2. Objectives of the study The objectives of the thesis is: - Determination of the concentration of the Naturally Occurring Radioactive Materials (NORM) in some building materials commonly used in Lao PDR such as cement, sand, etc. by gamma spectrometers using NaI(Tl) and HPGe detectors. - To assess the radiological hazard associated with the natural occurring radioactive isotopes in the building materials used in Laos PDR. These data are extremely important for the radiation dose assessment for residents, and making proper warning and necessary recommendations to production facilities so that they can make necessary adjustments to ensure the absolute safety in radioactive aspects for construction materials used in the market. 3. Main research contents of the thesis - The research is to analyze the amount of concentration of natural occurring radioactive isotopes including 238U, 235U, 232Th and 40K in the building materials used in Laos PDR by using gamma-ray spectroscopy technique. For our measurements, both NaI(Tl) and HPGe detectors have been used for gamma-ray detection. - For analyzing the gamma-ray spectra obtained with NaI(Tl) detector, a mathematical method has been used for determining the areas of overlapping spectral regions due to the poor energy resolution of NaI(Tl) detector. - To evaluate the radiological hazard of the natural radioactivity, the radium equivalent activity, the air absorbed dose rate, the annual effective dose rate, the representative index and the values of both external and internal hazard indices 1
have been calculated based on obtained concentration of the natural occurring radioactive isotopes of the investigated of the building materials. - Several computer programs have been developed for automatic analysis of gamma-ray spectra obtained with NaI(Tl), HPGe detectors and for routinely determining the values of the quantities related to radiological hazard due to the natural occurring radioactive isotopes in the building materials. CHAPTER 1. OVERVIEW OF NORM IN BUILDING MATERIAL 1.1. Origin of natural radiation and its connection to building materials 1.1.1. The decay series of natural radioactive isotopes Naturally occurring radioactive materials, under certain conditions, can reach radiologically hazardous levels. The natural radioactivity in soil comes mainly from the radionuclides in the U-238 and Th-232 series, and K-40. The radiological implication of these radionuclides is external radiation exposure by gamma rays and internal exposure due to inhalation of radon and its daughters. The decay schemes of these series are listed below. a) The uranium series 238U Beginning with naturally occurring uranium-238, this series includes the following elements: astatine, bismuth, lead, polonium, protactinium, radium, radon, thallium, and thorium. All are present, at least transiently, in any natural uranium-containing sample, whether metal, compound, or mineral. The series terminates with lead-206. The decay scheme of this series is presented in Figure 1.1 238 (1) U 4,468×109 y năm ↓α (2) 234Th 24,1 ngày ↓β 234 (3) Pa 1,17 phút ↓β 234 (4) U 2,455×105 năm ↓α 230 (5) Th 7,538 ×104 năm ↓α 226 (6) Ra 1600 năm ↓α 222 (7) Rn 3,8232 ngày ↓α 218 (8) Po 3,094 phút ↓α 214 (9) Pb 26,8 phút ↓β 214 (10) Bi 19,9 phút ↓β 214 (11) Po 162,3 giây 2
↓α 210 (12) Pb 22,3 năm ↓β 210 (13) Bi 5,013 ngày ↓β 210 (14) Po 138,4 ngày ↓α 206 Pb Figure 1.1. The decay scheme of the 238U series. Nuclides underlined are measurable by gamma-ray spectrometry. b) The actinium series - 235U Beginning with the naturally-occurring isotope U-235, this decay series includes the following elements: actinium, astatine, bismuth, francium, lead, polonium, protactinium, radium, radon, thallium, and thorium. All are present, at least transiently, in any sample containing uranium-235, whether metal, compound, ore, or mineral. This series terminates with the stable isotope lead-207. The decay scheme of this series is shown in Figure 1.2. 235 (1) U 1,7×108 năm ↓α 231 (2) Th 25,52 giờ ↓β 231 (3) Pa 3,276 ×104 năm ↓α 227 (4) Ac 21,772 năm ↓β 227 (5) Th 18,718 ngày + α (1,38 %) to 223Fr 22 phút then β ↓α 223 (6) Ra 11,43 ngày ↓α 219 (7) Rn 3,96 giây ↓α 215 (8) Po 1,781 giay ↓α 211 (9) Pb 36,1 phút ↓β 211 (10) Bi 2,14 phút ↓α 207 (11) Tl 4,77 phút + β (0,273%) 211Po 516 giây then α ↓β 207 Pb Figure 1.2. The decay scheme of the 235U series. Only 235U is measurable by gamma-ray spectrometry. 3
c) The thorium series 232Th Beginning with naturally occurring thorium-232, this series includes the following elements: actinium, bismuth, lead, polonium, radium, radon and thallium. All are present, at least transiently, in any natural thorium-containing sample, whether metal, compound, or mineral. The series terminates with lead-208. The decay scheme of this series is shown in Figure 1.3. 232 (1) Th 1,405 ×109 năm ↓α 228 (2) Ra 5,75 giờ ↓β 228 (3) Ac 6,15 giờ ↓β 228 (4) Th 1,9127 năm ↓α 224 (5) Ra 3,627 ngày ↓α 220 (6) Rn 55,8 giây ↓α 216 (7) Po 150 giây ↓α 212 (8) Pb 10,64 giờ ↓β 212 (9) Bi 60,54 phút ↓ β (64,06%) ↓ α (35,94%) 212 208 (10) Po 0,3 giây Tl 3,06 phúg ↓α ↓β 206 Pb Figure 1.3. The decay scheme of the 232Th series. Nuclides underlined are measurable by gamma-ray spectrometry. 1.1.2. Radon loss 1.1.3. Natural disturbance of the decay series 1.2. Effects of radiation hazards from building material to health body 1.3. Research condition of radiation in building material in the world In most countries, the inspection and assessment of the level of radioactivity in building materials are mandatory. To understand more about this issue, we have listed some recent works about natural radioactivity in different types of building Materials conducted by scientists in some countries in the world. The available data of specific radio-activities of some common building materials in some countries taken from literatures are presented in the tables numbered as 1.1, 1.2 and 1.3 below. 4
Table 1.1. The activity concentration (Bq.kg-1) Portland cement samples for different countries in the world. Activity concentration (Bq.kg-1) Countries 226 232 40 References Ra Th K Greece 92 31 310 [12] Austria 26.7 14.2 210 [13] Bangladesh 60.5 64.7 952.2 [14] China 56.50 36.50 173.2 [15] Egypt 134 88 416 [16] Pakistan 31.3 26.8 51.3 [17] Turkey 40.5 26.1 267.1 [18] Ghana 61.63 25.96 451.30 [19] India 37.0 24.1 432.2 [20] Malaysia 34.7 32.9 190.6 [21] Brazil 61.7 58.5 564.0 [22] Lao PDR 41.12 16.60 141.48 [23] Table 1.2. Comparison between the activity concentrations of our building materials with that of other countries of the world Activity concentration (Bq.kg- Raeq S. 1 Countries materials ) (Bq.kg-1) References No 226 232 40 Ra Th K brick 41 89 681 220,71 [24] 1 Australia Soil 62.9 162.8 403.3 326.76 [24] Sand 3.7 40 44.4 64.32 [24] brick 124.7 28.9 390.2 196.07 [25] 2 China Soil 44.6 86.7 352.8 195.75 [26] Sand 40.7 21.5 302.6 96.4 [15] brick 24 24.1 258 78.33 [27] 3 Egypt Soil 13 6 433 54.92 [28] Sand 9.2 3.3 47.3 17.56 [29] brick 16.2 70 76 122.15 [30] 4 Brazil Soil 30 67 112 134.43 [31] Sand 35.3 74 315 165.38 [30] brick 43.2 53.7 631.2 168.59 [17] 5 Pakistan Soil 42.4 56.2 565.3 166.29 [17] Sand 21.5 31.9 519.6 107.13 [17] brick 63.74 38.6 313.71 143.09 [32] 6 India Soil 116.1 43.51 300.07 201.44 [32] Sand 90.27 101.67 280.71 257.27 [32] brick 35 30 400 [33] World- 7 Soil 35 30 400 [33] wide Sand 35 30 400 [33] 5
Table 1.3. The specific radio-activities of 40K, 226Ra and 232Th in building materials used in Ha Noi S. Activity concentration Building materials No. K-40 Ra-226 Th-232 1 Black sand 515 ± 23 24.4 ± 1,4 36,2 ± 1.0 2 khuyến lương Sand 483 ± 15 53,5 ± 3,7 46 ± 3.6 3 yellow sand 651 ± 21 25,5 ± 0,9 32,3 ± 0.6 4 Hà Bắc yellow sand 357 ± 2 12,4 ± 2,5 20 ± 2,4 5 Hải Phòng cement 73 ± 9 28,6 ± 2,5 32,3 ± 2,8 6 Hoàng Thạch cement 196 ± 2 65,9 ± 3,7 27,8 ± 2,8 7 X77 cement 205 ± 2 69,6 ± 3,7 32,2 ± 2,8 8 Gravel 389 ± 8 23,5 ± 5 23 ± 4 9 Rock 46 ± 21 25,5 ± 5 19 ± 4 10 Brick 665 ± 0 84,0 ± 15 85 ± 4 11 Tiles 385 ± 5 39 ± 8 34 ± 4 12 Plaster 525 ± 5 44 ± 4 37 ± 4 13 Rock dust < 10 12,4 ± 2,5 6,8 ± 2,4 14 Tro xỉ hồ chứa 626 ± 3 122 ± 9 100 ± 15 Fly ash 788 ± 7 164 ± 13 126± 1 1.4. Investigation of Radioactivity in the building materials in Laos PDR In recent years, the economy of Laos has continuously grown and developed in a stable speed, with GDP increasing by an average of 7.6%; Per capita income has reached nearly 1,700 USD in the period 2013-2014. These achievements facilitate the Lao Government to successfully implement the 7th Socio-Economic Development Plan this year as well as the Millennium Development Goals. Along with economic development, the demand for construction is rising significantly, leading to the establishment of various construction materials companies. Nevertheless, because the scientific level of the Lao People's Democratic Republic is still at a very modest level and lack of human resources to undertake, the inspection of natural radioactivity in construction materials so far has not been conducted. The researchers were also encouraged to choose any topic that is related to natural radioactivity survey in Building Materials, which aims to widely expand this research direction in Laos PDR. This thesis may be considered as the first work in this direction in Laos PDR. 6
CHAPTER 2 GAMMA SPECTROCOPY USING EITHER HPGe AND NaI(Tl) SCINTILLATION DETECTOR 2.1. Physics foundation of gamma-ray detection with scintillation and HPGE Detectors 2.1.1. Interaction Of Gamma Radiation With Matter 2.1.2. Photoelectric effect 2.1.3. Compton Scattering 2.1.4. Pair Production 2.1.5. Attenuation of Gamma Radiation with matter 2.2. Configuration and gamma ray spectroscopy of NaI(Tl) and HPGe detector principles 2.3. HPGe Detector: Gamma-ray spectrum structure 2.3.1. Operational principles of HPGe detectors 2.3.2. Configurations of HPGe detectors 2.3.3. Gamma ray spectroscopy with HPGe detector 2.4. Scintillation detector: Gamma-ray spectrum structure 2.4.1. Configuration of Scintillation detectors 2.4.2. Gamma ray spectroscopy with Scintillation Detector CHAPTER 3 EXPERIMENTAL METHODS 3.1. Selection of sampling point of building materials Four kinds of building materials commonly used in Laos PDR including cement, sand, brick and soil have been chosen in this thesis. 3.1.1. Cement samples collection Figure 3.1. The map of Lao PDR showing the local famous cement factories in Lao PDR (from which the cement samples were collected). 7
Table 3.1. The labels of the analyzed cement samples. Position S. Type of Symbol Map icon Latitude (°N) Longitude No cement (°E) 1 1V1 2 1V2 3 1V3 Porland 4 1V4 cement 5 1V5 (1V) 6 1V6 7 1V7 A 18°56'7.6"N 102°27'7.0"E 8 2V1 9 2V2 10 2V3 Mixed 11 2V4 cement (2V) 12 2V5 13 2V6 14 2V7 15 1VT1 Mixed 16 1VT2 cement (1VT) 17 1VT3 18 2VT1 B 18°6'27.3"N 102°47'7.9"E 19 2VT2 Porland 20 2VT3 cement (2VT) 21 2VT4 22 1K1 Porland 23 1K2 cement 24 1K3 (1K) 25 1K4 C 17°24'19.8"N 105°12'58.2"E 26 2K1 27 2K2 Mixed 28 2K3 cement (2K) 29 2K4 30 1SV1 Porland 31 1SV2 cement 32 1SV3 (1SV) 33 1SV4 D 15°50'39.1"N 106°23'16.4"E 34 2SV1 35 2SV2 Mixed 36 2SV3 cement (2SV) 37 2SV4 8
3.1.2. Soil sample selection Figure 3.2. The map of Lao PDR showing the Thoulakhom district and the soil and sand sampling locations were indicated as P1, P2, …, P10. Table 3.2. The labels of the analyzed soil samples. S. Position Symbol Village No Latitude (°N) Longitude (°E) 1 1P1 2 1P2 Ban Dong (P1) 18°16'52.5" N 102°40'51.5"E 3 1P3 4 2P1 5 2P2 Ban PhaThao (P2) 18°19'40.5" N 102°39'56.5"E 6 2P3 7 3P1 8 3P2 Ban Nam Ang (P3) 18°22'23.9" N 102°36'5.4"E 9 3P3 10 4P1 Ban Nanokkhoum 11 4P2 18°17'18.2" N 102°41'35.8"E (P4) 12 4P3 13 5P1 Ban Phonmouang 14 5P2 18°20'15.7" N 102°40'51.4"E (P5) 15 5P3 16 6P1 17 6P2 Ban NaKang (P6) 18°20'42.0" N 102°39'40.4"E 18 6P3 19 7P1 20 7P2 Ban Naxanglek (P7) 18°21'54.5" N 102°37'48.8"E 21 7P3 22 8P1 Ban Keun (P8) 18°21'51.2" N 102°35'13.3"E 9
23 8P2 24 8P3 25 9P1 26 9P2 Ban Hatnoi (P9) 18°22'58.6" N 102°33'52.5"E 27 9P3 28 10P1 Ban Boungphao 29 10P2 18°20'49.3" N 102°33'59.6" (P10) 30 10P3 3.1.3. Sand samples preparation Figure 3.3. Map of Vientiane capital showing the Mekog river and locations of sand samples discussed in this preliminary study Figure 3.4. Photo of river sand in Mekong driver in Vientiane capital Figure 3.5. River sand Namngeum in Thoulakhom district, Vientiane province. 10
Table 3.3. The labels of the analyzed cement samples. Position S. No Symbol Village Latitude (°N) Longitude (°E) 1 1NK1 2 1NK2 Ban HuayYai 3 1NK3 18°56'7.6"N 102°27'7.0"E (NK1) 4 1NK4 5 1NK4 6 2Nk1 7 2NK2 Ban 18°6'27.3"N 102°47'7.9"E 8 2Nk3 HuayHom(NK2) 9 2Nk4 10 3NK1 11 3NK2 Ban 17°58'22.7"N 102°30'8.9"E 12 3NK3 NongDa(NK3) 13 3NK4 14 4N1 15 4NK2 Ban Don 17°57'57.0"N 102°35'47.3" 16 4NK3 Chan(NK4) 17 4NK4 18 5NK1 19 5NK2 Ban Hom1(NK5) 17°50'10.8"N 102°35'58.8" 20 5NK3 21 5NK4 22 6NK1 23 6NK2 Ban Hom2(NK6) 17°51'16.5"N 102°35'37.8" 24 6NK3 25 6NK4 26 1NG1 27 1NG2 Ban Keun (P11) 18°21'30.7"N 102°34'19.3"E 28 1NG3 29 NG4 30 2NG1 31 2NG2 Ban Pakchan (P12) 18°22'15.1"N 102°32'10.7"E 32 2NG3 33 2NG4 11
Figure 3.6. Square flame of 100cm × 100cm. 3.1.4. Brick sample selection 3.2. Preparation of sample for analysis Before analysis, the collected samples have to be prepared for measurement. The sample preparation procedure is presented below in figure 3.6. Figure 3.6. The schematic of the process of sample preparation. Figure 3.7 is a picture for illustration of the sample preparation process. A mortar and pestle for crushing and homogenizing and a standard sieve of 0.2 mm mesh size have been used for sample preparation. The prepared building materials finally were filled in the beakers sealed with plastic tape to prevent the escape of airborne radionuclides. The pictures of some prepared samples are presented in figure 3.8. 12
Figure 3.7. A mortar and pestle for crushing and homogenizing. A standard sieve of 0.2 mm mesh zize. Figure 3.8. A prepared building materials were filled in the beaker sealed with plastic tape to prevent the escape of airborne radionuclides. 3.3. Reference materials Figure 3.9. Picture of Three reference materials, obtained from the International Atomic Energy Agency (IAEA: RGU-1, RGTh-1 and RGK-1). For determination of the specific radioactive concentrations of the materials, the relative method has been used. For this, the reference materials obtained for IAEA have been used. The picture of these reference materials including RGU-1, RGTh-1 and RGK-1 is shown in figure 3.9 together with their data listed in Table 3.4. Table 3.4. The table shows the data of reference material used. Sample Mass (g) Density (g/cm3) Mass acivity (Bq/kg) IAEA-RGK-1 340,91 1,8 14000±400 IAEA-RGU-1 378,82 1,94 4940±30 IAEA-RGTh-1 309,01 1,736 3250±90 13
3.4. Method of Determination of activity concentrations of natural radionuclides from gamma-ray spectra with Scintillation detectors Figure 3.10 is the pictures of the gamma-ray spectrometers used in our work. On the left panel is the spectrometer using NaI(Tl) detector while on the right panel is the spectrometer using HPGe detector. Fig. 3.10. Picture of gamma-ray spectroscopy using Scintillation Detector. For determination of activity of the naturally occurring radioactive isotopes using NaI(Tl) detector, we have used a method for overcoming the poor energy resolution of NaI(Tl) detector. The method is based on the characteristics of the IAEA reference materials used in our investigation. Firstly, we need to measure the spectra of background, RGU-1, RGTh-1 and GRK-1 reference samples. These spectra are presented in figure 3.11. Fig. 3.11. a) Background Spectrum, obtained in a collecting time for 52700 second. b) Spectrum of IAEA RGU-1 was collected for 13942 second. c) Spectrum of IAEA-RGTh-1 was collected for 18190second. d) Spectrum of IAEA-RGK-1 was collected for 17215 second. Based on these spectra, we defined the energy region of interest (ROI) for our interested isotopes, which is written in table 3.5. 14
Table 3.5. Energy windows for determination of concentration of naturally occurring radioactive isotopes using the gamma spectrometer with NaI(Tl) detector. Parent Gamma ray energy Energy window Daughter isotope isotope (keV) (keV) 238 214 1 U Bi 1764,49 1632 – 1897 232 208 2 Th Tl 2614,53 2418 – 2811 40 40 3 K K 1460,8 1351 - 1570 The following algorithm was used to determine the concentration of radioactive isotopes, which is explained below. The net count rate in the ith Roi of a calibration standard j (with i and j equal to 1, 2 and 3 denoting the ROIs, and the calibration standards of K, U and Th, respectively) is proportional to the activity An,j of each investigated nuclide n (n=1,2 and 3 for 40K, 238U and 232Th, respectively) according to: ∑ (3.1) Where is the counting efficiency in the ith. ROI for the nuclide n. the net count rate is given by N    Ri , b i, j i, j (3.2) t j Thus, AK, ATh và AU can be obtained by solving the system of simultaneous equations:  e A e A e A K 1,1 K 1, 2 U 1,3 Th (3.3)  e A e A U 2, 2 U 2, 3 Th  e A e A Th 3, 2 U 3,3 Th From the RGK-1 standard, on has:   1,1 e 1,1 (3.4) A 1,1 From the RGU-1 standard:   1, 2 e1, 2 A 2, 2 (3.5)   2, 2 e 2, 2 A 2, 2 And from the RGTh-1 standard:   1, 3  A 1, 2 A 2,3 e1,3  2, 2 A 3, 3 (3.6) 15
  2,3  A 2, 2 A 2,3 e 2,3  2,3 A 3, 3 The other constant can be obtained by combining the count rates for the U and Th standards in the third ROI:   3, 2 e 3, 2 A 2, 2 (3.7)   A A 3, 3 3, 2 2,3 e  2, 2 3, 3 A 3, 3 Giá trị của các hoạt độ trong các mẫu chuẩn của IAEA là: A11=9869 Bq, A12=129.55 Bq, A13=0.07 Bq, A22=3527 Bq, A23=18 Bq và A33=2298 Bq. Table 3.6. Counting efficiency values, determination from spectrum of reference materials (IAEA) e11 e12 e13 e22 e23 e32 e33 7,216327 x 1,033662 x -2,413112 x 7,927624 x -4,421488 x -2,433944 x 1,29643 10-4 10-4 10-4 10-4 10-4 10-5 x 10-3 238 232 40 The concentration of U, Th and K isotopes are calculated using the following equations:   U Th e e A e e 2, 2 3, 2 Th (3.8)  2,3 3, 3 e e 2, 2 3, 2  e A   A U 2,3 (3.9) U Th e e 2, 2 2, 2  e e A   A A K 1, 2 1, 3 (3.10) K U Th e e e 1,1 1,1 1,1 The standard uncertainty on the activity values, can be calculate as  A  e N  tR  1 1/ 2 1 1,b K t 1,1  A  e N  t R  1 1/ 2 (3.11) 2 2, b U 2, 2 t  A  e N  1  t R3,b 1/ 2 Th 3 3, 3t A computer program has been written to determine these coefficients. Its flow chart is shown in the in Figure 3.12. 16
Fig. 3.12. Computer flow chart showing the automatic determination of activity concentrations of natural radionuclides from gamma-ray spectra with NaI(Tl) detector. 3.5. Determination of activity concentrations of natural radionuclides from gamma-ray spectra with HPGe detectors Two method for measurement of radioactive concentration: Relative method and absolute method. Before measurement of radioactivity concentration in the samples, we have to perform some calibration including energy, resolution and efficiency calibrations. 3.5.1. Data analysis when used relative method of determination of the specific activity for the natural radioactive isotopes 17