Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams

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Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams. The noise level of the temperature measurement system was approximately 0.08 mK (peak to peak). The temperature of the core part rose by approximately 8.6 mK at 800 MU (monitor unit) for 6-MV Xray beams, and it increased as X-ray energy increased. The temperature rise showed less spread when it was normalized to the accumulated charge, as measured by an external monitoring chamber.
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Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams. The noise level of the temperature measurement system was approximately 0.08 mK (peak to peak). The temperature of the core part rose by approximately 8.6 mK at 800 MU (monitor unit) for 6-MV Xray beams, and it increased as X-ray energy increased. The temperature rise showed less spread when it was normalized to the accumulated charge, as measured by an external monitoring chamber..

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  1. N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 Available online at ScienceDirect Nuclear Engineering and Technology journal homepage: www.elsevier.com/locate/net Original Article Building a Graphite Calorimetry System for the Dosimetry of Therapeutic X-ray Beams In Jung Kim*, Byoung Chul Kim, Joong Hyun Kim, Jae-Pil Chung, Hyun Moon Kim, and Chul-Young Yi Korea Research Institute of Standards and Science, 267 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea article info abstract Article history: A graphite calorimetry system was built and tested under irradiation. The noise level of the Received 11 November 2016 temperature measurement system was approximately 0.08 mK (peak to peak). The tem- Accepted 5 January 2017 perature of the core part rose by approximately 8.6 mK at 800 MU (monitor unit) for 6-MV X- Available online 11 February 2017 ray beams, and it increased as X-ray energy increased. The temperature rise showed less spread when it was normalized to the accumulated charge, as measured by an external Keywords: monitoring chamber. The radiation energy absorbed by the core part was determined to High Energy X-ray have values of 0.798 J/mC, 0.389 J/mC, and 0.352 J/mC at 6 MV, 10 MV, and 18 MV, respectively. Absorbed Dose These values were so consistent among repeated runs that their coefficient of variance was Graphite Calorimeter less than 0.15%. Calorimetry © 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/). 1. Introduction The radiation therapy dose is calibrated in terms of the water absorbed dose (unit: Gy) [4e6]. The water absorbed dose Radiation therapy using high energy X-rays generated by is a physical quantity that is defined as the amount of radia- medical linear accelerators has already been a major tool for tion energy absorbed by water of a unit mass [4e6]. Water cancer treatment. Approximately 30% of patients with cancer absorbed dose measurement can be realized with water are undergoing radiation treatment [1], and 197 medical linear calorimetry or by graphite calorimetry. Primary standard accelerators are currently operating in Korea [1e3]. Thus, ra- dosimetry laboratories use these types of calorimetry for pri- diation therapy quality control and assurance is very impor- mary dosimetry standards. tant for cancer treatment. The world’s first graphite calorimetry system was devel- Radiation dosimetry is the most important indicator for oped by S.R. Domen at the National Bureau of Standards in the quality control and assurance. When the irradiation is accu- 1970s [7]. Compared to water calorimetry, graphite introduces rately performed at the prescribed dose, cancer cell death is additional uncertainty owing to the necessity of converting maximized, whereas normal cell death is minimized. For this the graphite absorbed dose to the water absorbed dose. purpose, the International Commission on Radiation Units & However, the graphite method still has advantages over water Measurement recommends that the radiation dose measure- calorimetry. One is that graphite has a specific heat capacity ment uncertainty should not exceed 5% [4]. lower than that of water, which leads to a greater rise in * Corresponding author. E-mail address: kimij@kriss.re.kr (I.J. Kim). http://dx.doi.org/10.1016/j.net.2017.01.015 1738-5733/© 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
  2. N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 811 temperature than is the case for water at the same absorbed dose. Another is that graphite has no thermal [8,9]. The sensitive volume or sensitive medium of a graphite calorimeter is called a core. Thermal isolation of the core from the environment is very important because the temperature at the core increases by only a few milliKelvins when a graphite calorimeter is irradiated by therapeutic X-rays. Thus, the core is usually covered with many layers of jackets in vacuum. In the core, there are one or more thermometers and heaters. The thermometer(s) is needed to measure the tem- perature rise of the core at irradiation. The heater(s) is needed for the calibration of the temperature rise to the energy absorbed in the core. The calibration is performed by comparing the temperature rise at irradiation to the temper- ature rise caused by known amounts of electric heat or energy. Thermistors, or resistive thermometers, are used for tem- Fig. 1 e Schematic layout of the graphite calorimeter core perature measurements at the core as well as for heating. (C1505-4). Thermistors have poor linearity and poor stability; however, they have sensitivity to temperature and are not affected by irradiation up to megaGrays [10]. In addition, thermistors are available in very small sizes, which is helpful for minimizing impurities in the core. resistances of 20 kU at room temperature; they contained To ensure the repeatable measurement of the core tem- nickel alloy lead wires (0.101 mm thick). Hollow Kapton tubes perature, the calorimeter must run under a quasi-adiabatic were used to support the core. Epoxy resin was used to glue all condition [11,12]. Under this condition, thermal transfer of the components of the core together. During the integration from the core to the inner jacket is kept nearly constant, and of the core, the core was weighed at each step to detect im- the temperature rise at the core is always proportional to the purities (nongraphite ingredients). The jackets were prepared energy absorbed during its runs. A French group recently in the same manner as the core, but they were not weighed. achieved this condition by introducing thermal feedback The inner surfaces of the jackets were lined with thin alumi- [13,14] to the inner jacket. In this study, a similar type of nized Mylar foils to reduce radiative heat transfer. The outer thermal feedback was developed and applied to achieve this jacket used a Manganin wire (LakeShore, OH, U.S.A.) (diam.: quasi-adiabatic condition. 0.202 mm) as a heater, instead of using thermistors. In this study, a graphite calorimetry system was built to After all parts were built, the thermistors were calibrated measure the high energy X-ray absorbed dose. Experiments for temperature in a high precision water bath (7008, Fluke). were performed to investigate system properties, and the re- The parts were separately placed in thin and watertight sults are discussed. In Section 4, the uncertainties of some polyethylene bags (100 mm thick) and placed in the water bath. values are given, but details are not provided as to how they The temperature of the bath was measured using an SPRT were evaluated, because that is outside the scope of this (Standard Platinum Resistor Thermometer, 5187SA, Tinsley). article. The resistance of the thermistors and the SPRT was read using a high precision half-bridge (1595A, Fluke). Calibration was 2. Materials and methods performed within a range of 20e30 C at each degree Celsius. 2.1. Apparatus 2.1.2. Electronics and external monitoring chambers Wheatstone bridges were built to measure the temperature of 2.1.1. Building graphite calorimeter the core and of the inner jacket. High precision standard re- The graphite calorimeter (C1505-4) adopted a pan-shaped sistors and decade resistors were used to build the bridges. A vacuum housing and double-layered jackets as in the design high precision voltage calibration source (3350A, Transmille) of the GR9 of the French group [13]. The core was covered with was used to supply the excitation voltage to the bridges. two layers of jackets and graphite mediums, and then placed Nanovoltmeters (34420A; Agilent, CA, U.S.A.) were used to in a vacuum housing and a graphite phantom. All of the read the voltage difference across gaps in the bridges. graphite parts were composed of a batch product of high- An electric heating and power measurement circuit was density pyrolytic graphite (M507; Morgan Korea, Daegu, built, as shown in Fig. 2. In the figure, Vx represents the voltage South Korea), whose density was separately determined to be drop across the heating thermistor of the core. Rs and Vs (1.8154 ± 0.0014) g/cm3. represent the resistance of a standard resistor and the voltage The core was 16 mm in diameter and was 3 mm thick, with drop across the resistor, respectively. Then, the electric power three sensing thermistors, one heating thermistor and three dissipated at the heating thermistor, Px, is given as Px ¼ VxVs/ supports, as shown in Fig. 1. NTC-type thermistors with micro Rs. Electric power was fed by a multichannel dc power supply glass beads (diam.: 0.3 mm) were used (AB6B4-BR11KA103; GE (2230-30-1, Keithley) to the heating thermistor. A precision Measurement & Control, U.S.A.). The thermistors had resistor (SRL-10k; IET Labs., MA, U.S.A.) was used as the Rs; its
  3. 812 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 core and the inner jacket from the bridges, and used thermal feedback to control the temperature difference. The second module interfaced with the electric heating and power mea- surement circuit so that the circuit could control the electric power fed to the core and measure it. The third module interfaced with the external monitoring chamber system to read the accumulated electric charge of the ionizing current. Through the platform, all data points were acquired every 0.6 s. The temperature of the outer jacket was controlled separately using a standalone-type automatic temperature controller (350, Lakeshore). A temperature analysis tool was coded using Mathematica 9.0.1. When it opened a file of the measured temperature data, Fig. 2 e Diagram of a circuit for electric heating of the core it automatically found heating events (irradiation or electric and for measurement of electric power. heating) and analyzed the magnitude of the temperature rise. This tool used the interpolation function, provided by Math- ematica 9.0.1, to enhance the capability of finding heating events. Heating events were easily recognized from the time resistance was 9,999.2 ± 0.3 U. The voltage drop across the Rs derivative plot of interpolated points of the temperature data. and the heating thermistor was measured by two nano- The magnitude of the temperature rise was determined by voltmeters (34420A, Agilent), whose calibration coefficients linearly fitting the points, as shown in Fig. 3. The analysis was were 1.00005 ± 0.00002 and 1.00001 ± 0.00002. automatically performed, but required a manual input for An external monitoring chamber system consisted of a set initialization; this input was a roughly estimated value of the of two thimble-type ion chambers (0.53 cm3) and a high pre- time width, that is, the period of events heating the calorim- cision electrometer. The chambers (Exradin A2, Standard eter by electric power or irradiation. Imaging) were held at 660 mm from the target, between the multileaf collimators and the calorimeter, and were separated by 125 mm in the cross-line direction. For the sake of buildup, 2.2. Experiments the chambers were covered with high density pyrolytic graphite cylinders (inner diam.: 12.8 mm; outer dia.: 25 mm), 2.2.1. Experimental set and connected in parallel to the electrometer (6517B, Keith- The calorimeter was mounted on a precision stage. The stage ley). Bias voltage at e300 V was applied to the ion chambers. was moved so that the center of the core was placed 1,000 mm The room temperature and pressure were also measured to from the target of the accelerator; this accelerator was an correct their effects on the ionization current measurement. Elekta Synergy Platform (Elekta, Stockholm, Sweden). The calorimeter was covered with graphite slabs, which made the 2.1.3. Calorimeter operation and temperature analysis mass thickness of graphite from the entrance of X-ray beams An operation platform was built using the LabVIEW program to the center of the core equal to approximately 10 g/cm2. (National Instruments, TX, U.S.A.). The platform consisted of The mass thickness was separately determined to be three modules. The first module read the temperature of the (9.951 ± 0.008) g/cm2. Fig. 3 e Temperature rise analysis at the core.
  4. N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 813 The temperature of the outer jacket was maintained at 26 C. Table 1 e Measured mass of the core components (C1505-4). The Wheatstone bridges were activated at 0.8 V, and the heater Value (g) ustd (g) urel (%) Mass fraction thermistor of the inner jacket was also activated at 1.0 V to Graphite disk 1.098188 0.000006 0.0005 0.9952 warm it up. When the temperatures of the core and the jackets Supports (Kapton) 0.000763 0.000002 0.20 0.0007 were equilibrated, the temperature difference between the core Thermistor beads 0.001748 0.000060 3.4 0.0016 and the inner jacket was set (at approximately 21 mK), and the Thermistor lead wires 0.001826 0.000086 4.7 0.0017 thermal feedback was turned on. Then, the calorimeter was Glue (Epoxy) 0.000943 0.000002 0.17 0.0009 prepared for operation in the quasi-adiabatic mode. Total 1.10347 0.00011 0.0095 1 2.2.2. Electric heating and irradiation The calorimeter’s response to the electric energy dissipation Table 2 e Estimation of heat capacity of the core (C1505-4) to the core was investigated. Electric energy was fed to the based on the measured mass of components. core for 140e172 s within a range of 6e8 mJ. Specific heat Heat capacity The calorimeter was irradiated at 800 monitor units (MU) Value ustd Value ustd using 6-MV, 10-MV, and 18-MV X-rays at 300 MU/min, 410 MU/ (J/kg/K) (J/kg/K) (J/K) (J/K) min, and 350 MU/min, respectively. It took approximately 140e172 s to complete an irradiation of 800 MU for each X-ray Graphite [17] disk 706.9 0.6 0.7763 0.0007 Supports (Kapton) [18] 1,090 e 0.0008 e beam. Prior to or between every irradiation, electric heat was Thermistor beads [17] 600 200 0.0010 0.0004 also provided to the core to compare the core’s response to Thermistor lead wires [17] 900 200 0.0016 0.0004 irradiation and to electric heating Glue (Epoxy) [17] 1.800 300 0.0017 0.0003 Total e 0.7815 0.0009 3. Results and discussion Table 3 e Results of thermistor temperature calibration. The measured mass values of the core components are shown Parameters in Table 1. The total mass values of the core and its impurities A (10e6) B (10e6) C (10e9) were 1.10347 ± 0.00011 g and 0.00528 ± 0.00011 g, respectively. Core (C1505-4) 440 ± 11 247.9 ± 1.5 108.5 ± 4.0 Thus, the portion of the core that consisted of impurities was Inner jacket 332.8 ± 7.8 253.9 ± 1.0 90.3 ± 2.7 0.48%, which was as good as the number reported by the Outer jacket 516.9 ± 1.0 253.38 ± 0.14 98.89 ± 0.42 French group (GR-09, 0.59%; GR-10, 0.90%; GR-11, 0.35%) [14,15] Here, Te1 ¼ A þ B  ln(R) þ C  (ln(R))3, or by the Japanese group (1.5%) [16]. Based on the measured where T is temperature given in K and R is resistance given in U. mass of the core components, the heat capacity of the core was expected to be as shown in Table 2. According to the Fig. 4 e Measured temperature change of the core (T_core) and the inner jacket (T_jac).
  5. 814 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 measured mass and the known values of specific heat, the uncertainty of the temperature measurement (>0.9%), the core heat capacity was estimated to be 0.7815 ± 0.0009 J/K. ambiguity of the cited specific heat values or thermal loss Thermistors were calibrated to temperature by applying from the core to the inner jacket. the SteineHart model equation [19], as shown in Table 3. The The intercept (0.056 mK) of the fit was not ignorable uncertainty of the fitting parameters for the core was slightly compared with its uncertainty (0.023 mK), but it was suffi- large. According to the error propagation equation, the un- ciently small compared with the noise level (0.08 mK). Thus, it certainty of the temperature rise by 10 mK at 26 C was ex- was determined that the intercept could be ignored for the pected to be 0.9%. Furthermore, it is known that Wheatstone calibration of the temperature rise to the energy absorbed in bridges with DC excitation voltage are not very stable [16], the core. So, the effective heat capacity of the core was ob- which means that the uncertainty of the absolute value of the tained at every run as the ratio of electric energy dissipation to temperature rise will be larger than 0.9%. the temperature rise. The coefficient of variance of the effec- The temperature of the core and the inner jacket rose, as tive heat capacity was approximately 0.2%, which was mainly shown in Fig. 4, under irradiation and electric heating. The attributable to the uncertainty of the determination of the noise level at the Wheatstone bridge was about 0.3 mVpp (peak electric energy dissipated in the core. to peak), which corresponded to approximately 0.08 mK in Under irradiation, the temperature rise of the core showed temperature. The core temperature rose by approximately good correlation with the accumulated charge of the external 8.6 mK at 800 MU for 6-MV X-ray beams; core temperature increased as X-ray energy increased. It was possible to very accurately measure the electric power dissipated in the core (ustd ¼ 0.015%) because of the small uncertainties of the resistance and of the voltmeters. However, owing to the poor time resolution of the data sampling (0.6 s), it was expected that the amount of electric energy dissipated might have a larger spread. Assuming a uniform distribution, uncertainty of time might be 0.35 (¼0.6/√3) s, which would cause the determined electric energy to spread by 0.2%. The calorimeter’s response to the electric energy dissipa- tion at the core is shown in Fig. 5. It was very linear, within 6e8 mJ (R2 ¼ 0.9997), with a slope of 1.242 ± 0.003 K/J. The in- verse of the slope (0.805 J/K) corresponded to the effective heat capacity of the core, but it was larger by 3% than the heat capacity, which was expected according to the data shown in Table 2. This discrepancy might be attributable to the Fig. 6 e Correlation between temperature rise of the core Fig. 5 e Plot of core temperature rise according to electric and accumulated charged of the external monitor chamber energy dissipation. at 6-, 10-, 18-MV X-ray beams.
  6. N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 815 monitoring chamber. If the internal monitoring chamber of rise of the core should be normalized to the accumulated the accelerator had been sufficiently accurate to monitor the charge of the external monitoring chamber. Also, the co- X-ray beams, the temperature rise of the core should have efficients of variance of the temperature rise were around shown no correlation with the accumulated charge of the 0.2% or 0.3%, but dropped by approximately 0.1% when they external monitoring chamber, because all irradiation was were normalized to the accumulated charge of the external performed at 800 MU. However, the measured temperature monitoring chamber. The measured temperature rise rise showed obvious correlations for the 6-MV and 10-MV X- normalized to the external monitoring chamber (hereafter ray beams, as shown in Fig. 6. Even at 18 MV, the data points, called “the normalized temperature rise”) was as shown in except those measured on June 30, 2016 still showed good Fig. 7. correlation. The reason for the anomaly that surfaced on June The amount of radiation energy absorbed by the core was 30 is not understood yet, but will be further investigated. In determined by taking the product of the normalized tempera- any case, the overall correlation coefficients at 6 MV, 10 MV, ture rise and the effective heat capacity. The results are as and 18 MV (excepting the abnormal data points) were 0.64, shown in Fig. 8. The mean energy absorbed by the core had 0.94, and 0.47, respectively. Thus, it was convincingly values of 0.798 J/mC, 0.389 J/mC, and 0.352 J/mC at 6 MV, 10 MV, and demonstrated that, to achieve better data, the temperature 18 MV, respectively. These values were so consistent among runs that their coefficient of variance was less than 0.15%. Fig. 7 e Measured temperature rise of the core by irradiation. The temperature rise was normalized to Fig. 8 e Determined energy absorbed by the core under accumulated charge of the external monitoring chamber. irradiation at 800 MU. Error bars represent standard error.
  7. 816 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 4. Conclusion references In this study, a graphite calorimetry system was successfully built and showed good repeatability among repeated runs. [1] S.H. Lee, Current status and future prospect of regulation for The calorimeter demonstrated good linearity of the core’s radiation safety in medicine, 2015 Winter meeting of The temperature rise to electric energy of heating within a range of Korean Association for Radiation Protection, 5 Feb. 2015 (in Korean). 6e8 mJ. The effective heat capacity of the core was deter- [2] J.S. Yang, Development of requirements for quality mined at every run. The coefficient of variance of the effective assurance of radiation therapy, 2015 Radiation Security heat capacity was approximately 0.2%; this value was mainly Symposium, Daejeon, 9 Sep. 2015 [in Korean]. attributable to the poor time resolution of the electric power [3] KINS, Radiation Safety Information System [Internet].[cited measurement system. Thus, it was expected that the mea- July 2016]. Available from: http://rasis.kins.re.kr (in Korean). surement uncertainty of the effective heat capacity could be [4] ICRU, Determination of absorbed dose in a patient irradiated by beams of X or gamma rays in radiotherapy procedures, reduced if the electric power could be measured with better ICRU Report No. 24, MD, 1976. time resolution. [5] ICRU, Dosimetry of high-energy photon beams on standards Under irradiation, the temperature of the core rose and of absorbed dose to water, ICRU Report No. 64, MD, 2001. showed a good correlation with the accumulated charge of the [6] IAEA, Absorbed dose determination in external beam external monitoring chamber. Thus, the temperature rise of radiotherapy: an international code of practice for dosimetry the core was normalized to the accumulated charge of the based on standards of absorbed dose to water, TRS 398, external monitoring chamber, and it showed better results. Vienna, 2000. [7] S.R. Domen, P.J. Lamperti, A heat-loss-compensated The amount of radiation energy absorbed by the core was calorimeter: theory, design, and performance, J. Res. Natl. determined by taking the product of the measured effective Stand. Sect A 78A (1974) 595e610. heat capacity and the normalized temperature. All results [8] S.R. Domen, Advances in calorimetry for radiation were so consistent among runs that their coefficient of vari- dosimetry, in: K.R. Kase, B.E. Bjarngard, F.H. Attix (Eds.), The ance was less than 0.15%. Dosimetry of Ionizing Radiation, Vol. II, Academic Press, Inc., In this study, it was demonstrated how the system worked London, 1985, pp. 245e320. and how repeatable its working was. However, more experi- [9] J. Chavaudra, B. Chauvenet, A. Wambersie, Medicine and ionizing radiation: metrology requirements, C.R. Phys 5 ments are necessary to understand the system better and to (2004) 921e931. enhance the repeatability. Also, the current results are pre- [10] M.R. McEwen, D.T. Burns, A.J. Williams, The use of liminary. The final purpose of the system is to determine the thermistors in the NPL electron-beam calorimeter, NPL water absorbed dose of the X-ray beams of the accelerator. For Report RSA(EXT) 41, London, 1993. that purpose, more studies are needed to determine param- [11] J.P. Seuntjens, A.R. Dusautoy, Review of calorimeter based eters such as the effective mass of the core, the graphite-to- absorbed dose to water standards, in: Proceedings of International Symposium on Standards and Codes of water absorbed dose conversion factor, and the nonunifor- Practice in Medical Radiation, Vienna, Nov. 2002, IAEA-CN- mity correction of the X-ray dose distribution. Results of these 96-3, Vol. 1 (2003) 37e66. kinds of studies will be reported and discussed soon. [12] J. Witzani, K.E. Duftschmid, Ch. Strachotinsky, A. Leitner, A graphite absorbed-dose calorimeter in the quasi-isothermal mode of operation, Metrologia 20 (1984) 73e79. [13] A. Ostrowsky, J. Daures, The construction of the graphite Conflict of interest calorimeter GR9 at LNE-LNHB, Rapoort CEA-R-6184, LNE- LNHB, 2008. The full description of the procedures used in this paper re- [14] J. Daures, A. Ostrowsky, B. Rapp, Small section graphite quires the identification of certain commercial products and calorimeter (GR-10) at LNE-LNHB for measurements in small their suppliers. The inclusion of such information should in no beams for IMRT, Metrologia 49 (2012) S174. way be construed as indicating that such products or suppliers [15] S. Dufreneix, J.-M. Bordy, J. Daures, F. Delaunay, A. Ostrowsky, are endorsed by the authors, or are recommended by the au- Construction of a large graphite calorimeter for measurements in small fields used in radiotherapy, 16th thors, or that they are necessarily the best materials, in- International Congress of Metrology, Paris, Oct. 2013, pp. 1e4. struments, software, or suppliers for the purposes described. [16] Y. Morishita, M. Kato, N. Takata, T. Kurosawa, T. Tanaka, N. Saito, A standard for absorbed dose rate to water in a 60Co Acknowledgments field using a graphite calorimeter at the National Metrology Institute of Japan, Radiat. Prot. Dosim. 154 (2013) 331e339. This work was supported by the Korea Research Institute of [17] S. Picard, D.T. Burns, P. Roger, Determination of the specific Standards and Science under the project “Establishment of heat capacity of a graphite sample using absolute and differential methods, Metrologia 44 (2007) 294e302. Measurement Standards of Ionizing Radiations” grant 16011037. [18] Dupont, Kapton® HN technical Data Sheet [Internet].[cited 1 The full description of the procedures used in this paper re- August 2016]. Available from: http://www2.dupont.com/ quires the identification of certain commercial products and Kapton/en_US/assets/downloads/pdf/HN_datasheet.pdf. their suppliers. The inclusion of such information should in no [19] J.S. Steinhart, S.R. Hart, Calibration curves for thermistors, way be construed as indicating that such products or suppliers Deep-Sea Res. Oceanogr. Abstr. 15 (1968) 497e503. are endorsed by KRISS or are recommended by KRISS or that they are necessarily the best for the purposes described.

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