Water calorimetry for radiation dosimetry

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Water calorimetry for radiation dosimetry

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1996 Phys. Med. Biol. 41 1 (http://iopscience.iop.org/0031-9155/41/1/002) The Table of Contents and more related content is available

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Phys. Med. Biol. 41 (1996) 1–29. Printed in the UK

REVIEW

Water calorimetry for radiation dosimetry C K Ross and N V Klassen Ionizing Radiation Standards, Institute for National Measurement Standards, National Research Council, Ottawa, Ontario K1A 0R6, Canada Received 17 January 1995 Abstract. Calorimetry has a long history as a technique for establishing the absorbed dose, and graphite calorimetry has often been used to establish absorbed dose standards for use in radiation therapy. However, a conversion process is necessary to convert from dose to graphite to dose to water, which is the quantity of clinical interest. In order to more directly measure the dose to water, considerable effort has been devoted in the last fifteen years to the development of water calorimetry. This article reviews these developments and summarizes the present status of water calorimetry. Absorbed dose standards based on water calorimetry and with a relative standard uncertainty of 0.5–1% now seem achievable.

Contents 1 2

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Introduction Large, unsealed, water calorimeters 2.1 Basic principles 2.2 Domen’s calorimeter 2.3 Calorimeters based on the Domen design The heat defect of aqueous systems 3.1 The radiation chemistry of water 3.2 Relative measurements 3.3 Absolute measurements The second generation of water calorimeters 4.1 The Yale calorimeter 4.2 The NRC calorimeter 4.3 The NIST calorimeter 4.4 The Ghent calorimeter Technical considerations 5.1 Convection 5.2 Temperature sensors 5.3 Water quality 5.4 Excess heat Discussion

Page 1 3 3 5 6 8 8 11 12 16 16 18 19 21 21 21 24 24 25 26

1. Introduction The quantity absorbed dose is used to specify the amount of energy deposited in a material by ionizing radiation. It is defined as the energy absorbed per unit mass and is assigned c 1996 Canadian Federal Government

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the SI unit gray (Gy) where 1 Gy = 1 J kg−1 . The absorbed dose depends on both the radiation field and on the material with which the radiation interacts. Knowledge of the absorbed dose is required for a wide range of applications involving ionizing radiation, but the most demanding in terms of accuracy is radiation therapy. In this case, the material of interest is tissue and the goal of treatment planning is to predict accurately the absorbed dose received by all irradiated tissues. In general, the standard uncertainty† on the dose delivered to the treatment volume should be less than 5% and in some cases less than 3% (Brahme 1984). As a first step in determining the dose to tissue, the absorbed dose to water is determined for some well defined reference geometry. Water is chosen because its radiation absorption characteristics are similar to those of tissue, and because the spatial distribution of absorbed dose can be measured easily using a movable probe. The standard uncertainty on the absorbed dose under reference conditions should be sufficiently small that it does not contribute significantly to the overall uncertainty, so a goal of 0.5–1% is desirable. Primary absorbed dose to water standards are not yet widely available, so usually dosimeters are calibrated in terms of absorbed dose to water using some indirect approach. The most common technique is to have an ionization chamber calibrated in terms of air kerma for 60 Co γ -rays, and then calculate (using some well defined protocol, such as that of the AAPM (1983) or the IAEA (1987)) the absorbed dose to water calibration factor for the ionization chamber. Unfortunately, the uncertainty in this approach may be as large as 4%, which is a significant contribution to the overall uncertainty in the treatment planning process. As a result, several standards laboratories are devoting considerable effort to the development of absorbed dose to water standards (Rogers 1992). Calorimetry is recognized as the best approach for establishing absorbed dose standards. The basic assumption is that all (or a known fraction) of the absorbed radiation energy appears as heat, so that the measurement of absorbed dose reduces to a measurement of a temperature change. If the absorbed dose to water is to be established, ideally the calorimetric measurements should be made using water. However, most calorimeters developed for the purposes of radiation dosimetry have been constructed from graphite because of the perceived difficulties of working with a liquid system. Graphite has been chosen because its radiation absorption characteristics are similar to those of water, and thermally isolated segments can be machined and configured so as to permit the measurement of absorbed dose to graphite. Given the dose to graphite, the dose to water is obtained using a conversion process which usually is based on ionization chamber measurements. Several standards laboratories, including the National Research Council (NRC), now offer absorbed dose to water calibration services which are based on graphite calorimetry (see, for example, Pruitt et al 1981, Burns 1994). Unfortunately, the conversion from dose to graphite to dose to water introduces additional uncertainty, so there has been an ongoing interest in developing improved absorbed dose to water standards. The main technical difficulty which seemed to rule out the use of water calorimetry to establish directly the absorbed dose to water was the problem of constructing a thermally isolated segment in which to measure the temperature change. Any wall which might be used to hold a small mass of water (of the order of 1 g) would significantly perturb the measurement. Domen (1980) provided a new perspective on the problem when he showed that the thermal properties of water were such that, under the right conditions, there was no need to thermally isolate a small volume. He was able to construct and operate a large † The standard uncertainty refers to the uncertainty estimated as one standard deviation (ISO 1992). Unless noted otherwise, all uncertainty estimates correspond to the standard uncertainty.

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water calorimeter which was capable of yielding the absorbed dose at a point in water. Since then, there has been a large effort devoted to water calorimetry and absorbed dose standards based on water calorimetry now seem achievable. There have been major review articles by Laughlin and Genna (1966) and Domen (1987) which discuss all aspects of calorimetry as it relates to radiation dosimetry. As well, Gunn (1976) has produced an extensive summary and bibliography of work related to calorimetric applications and instrumentation. This review article is more restrictive in its coverage and focuses only on water calorimetry and its use in determining the absorbed dose to water. Section 2 describes the main characteristics of Domen’s first water calorimeter and reviews the work of others who constructed similar calorimeters. One of the main difficulties in calorimetry is establishing the heat defect, that is, the fraction of the absorbed energy which does not appear as heat. For water, the heat defect may depend on dissolved gases or other impurities, so considerable effort has been devoted to establishing the heat defect of various aqueous systems. This work is reviewed in section 3. Using knowledge of the radiation chemistry of water, calorimeters can be constructed which utilize the conditions necessary to maintain an aqueous system with a well defined heat defect. Several such calorimeters have been built and tested, and this work is reviewed in section 4. One of the major technical considerations in designing a large water calorimeter is the control of heat transfer by convection. The effect of convective flow on the performance of water calorimeters is discussed in section 5, as well as the various techniques which have been proposed to eliminate convection. Section 5 also reviews other technical issues which must be addressed in building a water calorimeter. The final section summarizes the present status of water calorimetry. 2. Large, unsealed, water calorimeters 2.1. Basic principles Measurement of the temperature rise of irradiated water has a long history in radiation physics and dosimetry. For example, Davison et al (1953) measured the output of a high intensity 60 Co source using a small water calorimeter. Later, Pettersson (1967) used a water calorimeter to determine the response of ferrous sulphate dosimeter solution to 60 Co γ -rays and 33 MeV electrons (for a brief review of this work, see Ross et al 1989). Many of the earliest measurements of absorbed dose using water calorimetry are referenced by Busulini et al (1968). They used a small water calorimeter to determine the energy deposited by 60 Co γ -rays, and compared their calorimetric results with ferrous sulphate dosimetry. A more recent application was made by Lovell and Shen (1976) who measured the temperature rise of water irradiated by high energy electrons as a means of determining the electron energy. However, it was Domen (1980) at the National Institute of Standards and Technology (NIST) in the United States who first considered the possibility of using a large water calorimeter to measure directly the absorbed dose at a point. A calorimetric determination of the dose at a point requires that a thermally isolated element has been arranged so that no significant heat transfer occurs during the irradiation. If 1T is the measured temperature rise in this element, then the absorbed dose to the material, Dm , is given by Dm = cm 1T /(1 − kH D )

(1)

where cm is the specific heat of the calorimetric material and kH D is the heat defect. The

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heat defect, which can be positive or negative, is given by kH D = (Ea − Eh )/Ea

(2)

where Ea is the energy absorbed by the irradiated material and Eh is the energy which appears as heat. The effect of conductive heat transfer on the measured temperature change can be estimated using the general equation for heat transport which is given by (AIP 1989) ∂T /∂t = α∇ 2 T

(3)

where T is the temperature and t is the time. The thermal diffusivity, α, is equal to κ/ρc where κ is the thermal conductivity, ρ is the density and c has the same meaning as in equation (1). When a large phantom is irradiated by a broad beam of x-rays the main temperature gradient (away from the field boundaries) is along the central axis, so equation (3) can be simplified to ∂T /∂t = α∂ 2 T /∂z 2

(4)

where the distance z lies along the central axis of the x-ray beam, and increases with depth in the phantom. Beyond the maximum of the depth–dose curve, the variation of the dose with depth, D(z), can be represented approximately by (Johns and Cunningham 1978) D(z) = D0 e−µ(z−z0 )

(5)

where D0 is the dose at depth z0 and µ for 60 Co γ -rays is approximately 0.05 cm−1 . If we assume that the absorbed dose is delivered in a very short time, the initial temperature gradient also will be given by equation (5), so that initially ∂ 2 T /∂z 2 = µ2 T .

(6)

Using equations (4) and (6) we can estimate how quickly the initial temperature distribution will deviate from the dose distribution. The result is 1t ≈ (1/αµ2 )(1T /T )

(7)

where 1t is the time required for the temperature to change by a small amount, 1T . If our objective is to measure the absorbed dose with a relative standard uncertainty smaller than 0.5%, then we require 1T /T 6 0.005. For graphite, α = 0.80 cm2 s−1 while for water α = 1.41 × 10−3 cm2 s−1 (AIP 1989), so equation (7) predicts values for 1t of 2.5 s and 1400 s for graphite and water respectively. For dose rates typical of those used for radiation therapy, 2.5 s is not enough time to complete an irradiation and measure the associated temperature rise, hence the necessity of thermally isolating the absorbing element in a graphite calorimeter. On the other hand, because the thermal diffusivity of water is so small, this simple estimate indicates that the temperature profile in water may be stable on a time scale long compared to that required to perform an irradiation and measure the associated temperature rise. However, conduction is not the only mechanism for transporting heat in a liquid medium. Consider a mass of water in which a temperature gradient exists such that the temperature increases as the depth increases. Above 4 ◦ C the density of water decreases as the temperature increases, so a small volume of water at depth will be less dense than the liquid above. As a result, there will be a buoyant force acting on this volume element and, if a number of conditions are satisfied, convective flow may be established in the water. The general problem of heat transfer by convection is quite complicated (Burmeister 1983, Velarde and Normand 1980). However, if a large water calorimeter is irradiated by a beam directed vertically downward, apart from the build-up region, the temperature will in

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fact decrease with increasing depth. So, at depths well beyond the peak of the depth–dose distribution, the liquid will be stable with respect to convection. On the basis of these ideas, Domen proceeded to construct a water calorimeter in which no effort would be made to thermally isolate the volume element in which the dose was to be measured. 2.2. Domen’s calorimeter The essential features of Domen’s calorimeter are shown in figure 1. The calorimeter consisted of a 30 cm cube of once-distilled water. During irradiation, the water was assumed to be motionless. Although the water was thermally isolated from the environment, it was not sealed against the exchange of gases with the atmosphere. The water temperature at a depth of 5 cm was measured using two thermistors sandwiched between thin polyethylene films. The calorimeter was irradiated with a 60 Co γ -ray beam directed vertically downward.

Figure 1. Main features of Domen’s first absorbed dose to water calorimeter. The large mass of motionless water was thermally isolated from the environment. The thermistors were fixed in position and protected from the water by polyethylene film. The large electrodes at opposite sides of the container were used to control temperature drifts (Domen 1982. Reproduced with permission of the NIST Journal of Research).

The measuring thermistors were connected in opposite arms of a Wheatstone bridge (this technique doubles the sensitivity obtained with a single thermistor) and the output of the bridge was monitored using a sensitive voltmeter. Figure 2 shows the response of the calorimeter to a series of 60 Co irradiations at a dose rate of 18 mGy s−1 . The large spikes are caused by manual rebalancing of the bridge during the irradiation. By calibrating the thermistors, the measured resistance changes can be converted to temperature changes, and equation (1) used to calculate the absorbed dose. The sample standard deviation (based on up to 45 runs similar to those shown in figure 2) was typically 0.6%. Although Domen’s calorimeter could measure with good precision the temperature changes caused by irradiating water with 60 Co γ -rays, the results demonstrated two worrisome features. Firstly, the measured temperature change depended on the electrical power being dissipated in the thermistors. When the power was increased from about 10 µW to over 200 µW, the measured temperature change (for the same absorbed dose)

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Figure 2. Chart recorder output for three typical calorimeter runs. The dose rate was 18 mGy s−1 and each irradiation lasted 3 min. The spikes are due to manual rebalancing of the bridge during the run (Domen 1982. Reproduced with permission of the NIST Journal of Research).

decreased by about 3.7%. The reason for this effect was not understood, but Domen argued that the result at zero power was most likely correct, and corrected all his measurements by extrapolating the measured response to what would be expected at zero power. Secondly, the absorbed dose to water calculated using equation (1) but with kH D = 0 was about 3.5% higher than the absorbed dose to water obtained using graphite calorimetry. Domen was well aware of the possibility that irradiating the water would give rise to chemical reactions which could lead to a nonzero heat defect. He investigated the response of the calorimeter to a wide range of additives, some of which had a dramatic effect on the response. However, no source of the exothermic reactions in once-distilled, air-saturated water was identified. 2.3. Calorimeters based on the Domen design With the apparent success of Domen’s calorimeter, several groups constructed calorimeters using the same basic design and attempted to use them to carry out dosimetric measurements. Mendez de Marles (1981) used a calorimeter similar to Domen’s to measure the absorbed dose due to 60 Co γ -rays, 6, 18 and 25 MV x-rays and 13, 17 and 20 MeV electron beams. She used doubly distilled water which was bubbled with nitrogen gas. During irradiation, a constant flow of nitrogen was maintained over the surface of the water, although no difference in response was noted when the flow was stopped. The heat defect was assumed to be zero. She compared the absorbed dose determined calorimetrically to that obtained using ionization chambers. The ionization chamber dosimetry was based on the Nordic Protocol (NACP 1980) and the work of Loevinger (1981). Mendez de Marles found that, for either photons or electrons, the ratio of the absorbed dose to water determined calorimetrically to that determined ionometrically was independent of beam quality. However, the ratio averaged over all electron beam qualities was 1% less than unity for electron beams, while for photon beams it was 3.8% greater than unity. No uncertainty estimates were provided for these results, although some information was provided on the uncertainties for each beam quality. We estimate that the uncertainty on the ratio averaged over beam quality was somewhat greater than 1%.

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Kubo (1983) also constructed a large water calorimeter using Domen’s design principles, and used it to measure the absorbed dose to water for 60 Co γ -rays, 10 and 25 MV x-rays and 16.6 and 22.3 MeV electrons. He used demineralized, air-saturated water and assumed the heat defect was zero. He also determined the absorbed dose for the same fields by using ionization chambers and applying the formalism of Loevinger (1981). Kubo reported that for photon beams the dose measured by calorimetry was from 2 to 4% higher than the dose obtained using ionization chambers, while for electron beams it was 3.5% higher. The estimated uncertainty on the calorimetric measurements was 1%. Since both Kubo and Mendez de Marles used similar formalisms for calculating the dose from ionization chamber measurements, systematic errors in their ionometric results should be the same. Therefore, their results for photon beams are consistent, but the difference of 4.5% in the electron beam results lies outside the estimated uncertainties. Mattsson (1984, 1988) constructed and operated a calorimeter based on Domen’s design, but because of the problem of determining the heat defect, he did not use it for absolute dosimetry. Instead, he compared the response of his calorimeter when filled with oncedistilled, air-saturated water to the dose determined using liquid ionization chambers which had been calibrated at NIST using 60 Co γ -rays. The apparent absorbed dose to water measured with his calorimeter was 3.3% larger than expected, in good agreement with the value of 3.5% which Domen observed. Mattsson assumed that this correction (presumably due to a chemical heat defect) would be independent of beam quality thus allowing him to compare Fricke dosimetry, ionization chamber dosimetry and water calorimetry for various photon and electron beams. Generally, he found that the different methods agreed to within 1% for high energy photon and electron beams. However, for orthovoltage x-rays (100 and 200 kV) the calorimetric dose was a further 2–4% higher than that determined using ionization chamber dosimetry based on ICRU Report 24 (ICRU 1976). Barnett (1986) found that his version of the Domen calorimeter also gave values for the absorbed dose to water due to photons and electrons which were a few per cent larger than expected on the basis of ionization chamber dosimetry. However, he noted that the response of his calorimeter sometimes decreased (by as much as 5%) with accumulated dose, reaching a steady state after 100 Gy. A group in Edinburgh (Galloway et al 1986, Williams et al 1987, Kehoe and Galloway 1988) used a calorimeter based on Domen’s design for neutron dosimetry. In tests with photon and electron beams, their calorimeter gave absorbed doses which were a few per cent larger than expected, in agreement with others. However, they found that the absorbed dose to water due to neutrons determined calorimetrically was a few per cent smaller than the corresponding ionization chamber results. By and large, Domen’s original observations were confirmed by those who built calorimeters based on his design. The possibility of measuring the temperature rise at a point in a large water phantom irradiated from above was clearly demonstrated. However, most measurements supported Domen’s observation that there was a problem in converting the measured temperature rise to absorbed dose to water. Generally, the absorbed dose determined calorimetrically was a few per cent larger than expected on the basis of conventional dosimetric techniques. The differences were well outside the estimated uncertainties and pointed to some systematic problem with water calorimetry. Equation (1) shows that both the specific heat, cm , and the heat defect, kH D , must be known accurately if absorbed dose calorimetry is to succeed. For graphite calorimetry, cg is normally determined by injecting a known amount of electrical energy into the calorimeter core, or absorber. This approach cannot be used with water calorimetry since there is no thermally isolated absorbing element, so cw is obtained from independent measurements.

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The most extensive measurements of cw were by Osborne et al (1939). They do not give detailed uncertainty estimates, but their values of cw are given to five significant figures. They also present a comparison of their data to the results of several measurements, and the maximum discrepancy in the results is less than 0.1% near room temperature. Therefore, uncertainty in the specific heat of water has a negligible effect in calculating the absorbed dose. In general, the heat defect, kH D , is less well known and more difficult to determine that the specific heat. McDonald and Goodman (1982) state that there appears to be no mechanism that could give rise to a heat defect in gold or platinum. Using ion beams, they compared the response of aluminium to gold and platinum, and concluded that the heat defect of aluminium is also zero with an uncertainty of 1.5%. Using low energy x-rays, Sabel et al (1973) compared the response of graphite to that of lead, which was assumed to have no heat defect. They found that the heat defect of graphite was consistent with zero (with an uncertainty of 0.6%) and because no mechanism has been identified which could give rise to energy storage in graphite, all absorbed dose calorimetry based on graphite assumes the heat defect is zero. Because of the possibility of radiation-induced chemical reactions, the situation is considerably more complicated for water, and the most likely cause of the discrepancies observed with water calorimeters is inadequate knowledge of the heat defect. Considerable effort has been devoted to the study of the heat defect in aqueous systems, and this work will be reviewed in the next section. 3. The heat defect of aqueous systems Equation (2) gives the formal definition of the heat defect. When less energy appears as heat than was deposited by the ionizing radiation, endothermic processes are at work and the heat defect is positive. Conversely, if more heat energy is generated than was absorbed from the radiation field, exothermic processes are present and the heat defect is negative. In general, there are several mechanisms that can give rise to a heat defect. In a transparent liquid such as water these include radiation-induced optical emission, acoustic energy generated by energetic charged particles and radiation-induced chemical reactions. Estimates (Ross et al 1989) indicate that chemical reactions are likely to be the only significant source of a heat defect in water. 3.1. The radiation chemistry of water When an energetic charged particle passes through matter, it produces ionized and excited atoms and molecules. For ionizing events, the ejected electron often has sufficient energy to give rise to additional ionization and excitation. The result is small clusters of ionized and excited species. Since the amount of energy deposited in each cluster can vary widely, they are often characterized in terms of the energy deposited (Mozumder and Magee 1966). The clusters are referred to as spurs, blobs or short tracks if the energy per cluster is from 6 to 100 eV, 100 to 500 eV or 500 to 5000 eV, respectively. For low-linear-energy-transfer (LET) radiation, about 70% of the energy is deposited in spurs and for simplicity we will refer to all the clusters of reactive species as spurs. In water, the primary spur products are highly reactive, but some may escape from the region of the spur before reacting. Others may undergo reactions within the spur to give rise to stable products which diffuse throughout the liquid. The spur reactions are localized and not affected by low concentrations of reactive solutes in the water, although they do depend on the LET of the ionizing radiation. After about 0.1 µs the spur species behave as if they were homogeneously distributed throughout

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the water and react with scavengers which are present at millimolar (mM) concentrations. Therefore, for a given LET, each species which escapes from the spur can be assigned a yield, G, which is independent of the composition of the dilute aqueous solution. For water, the species which escape from the spurs have been identified and their Gvalues measured for a wide range of LET. Figure 3 shows how the G-values of the eight spur products change with LET. As the LET increases, adjacent spurs begin to overlap, so that reactions within the spurs become more important. The result is that fewer of the highly reactive species, such as e− aq and OH, escape from the region of the spur before reacting. Six of the smooth curves in figure 3 are based on a compilation of experimental data by Elliot (1994). Elliot did not include OH− or H+ in his compilation, so for these species we use the results of Anderson et al (1985) for low LET. For higher LET, we assume that + G(OH− ) increases by an amount equal to 50% of the decrease in G(e− aq ) and that G(H ) − − is given by the sum of G(OH ) and G(eaq ).

Figure 3. G-values of various spur products as a function of the track-averaged LET. The smooth curves summarize the trends in the measured data. Except for H+ and OH− , the data were taken from a compilation by Elliot (1994). See the text for a description of the curves for H+ and OH− .

The chemical reactions induced in water by ionizing radiation have been extensively studied and their rate constants measured. The characteristics of these reactions are

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independent of the LET of the radiation, so any dependence of the radiation chemistry on LET enters only through the G-values. Boyd et al (1980) compiled a list of the reactions and their associated rate constants as well as the G-values for low-LET radiation. They used these data as input to a computer program (Carver et al 1979) which solved the relevant coupled differential equations and gave the product concentrations as a function of time. They used this model to study several aqueous systems for which there existed experimental data. Although their work was not oriented to studying the chemical heat defect of water, it served as a benchmark of their model for the radiolysis of water. In response to Domen’s measurements, Fletcher (1982) used the model of Boyd et al to calculate the heat defect for various aqueous systems irradiated by low-LET radiation. Although there are about 15 species which participate in the radiolysis of water, most of these are short lived and are present only when the radiation field is present or for a short time afterward. For systems containing only water and hydrogen and oxygen gases there are only six stable species. They are O2 , H2 , H2 O, H2 O2 , OH− and H3 O+ and their heats of formation are known (Wagman et al 1982). Fletcher calculated the change in stable products for specified radiation conditions and then used the heats of formation to calculate the energy consumed or liberated by the chemical reactions. He generated graphs of the endothermicity or exothermicity of several aqueous systems for various dose rates and a wide range of accumulated dose. His results apply to sealed aqueous systems in which there is no gas volume in contact with the liquid. At NRC, we (Ross et al 1984, Klassen and Ross 1991) extended the work of Fletcher to additional aqueous systems and accounted for the effects of a gas volume in contact with the liquid. We also incorporated the more recent data on the reaction rate constants into the model. The complete data set is given by Klassen and Ross (1991) and the main results of the work are summarized in section 3.2. More recently, Elliott (1994) has provided an up-to-date set of 47 reactions, their rate constants at 25 ◦ C and the G-values of the spur products over a wide range of temperature. For the most part, water calorimetry has been applied to the measurement of absorbed dose in high-energy x-ray and electron beams, for which the LET is low. However, there have been some efforts to apply water calorimetry to neutron beams (Galloway et al 1986, Williams et al 1987), proton beams (Schulz et al 1992) and low-energy x-ray beams (Seuntjens et al 1993a) which are characterized by higher values of LET. Therefore, there has been some motivation for estimating how increasing LET affects the heat defect of various aqueous systems (Klassen and Ross 1988, Seuntjens et al 1993a). The data in figure 3 can be used to estimate the G-values for a given LET, and these values can be used with the standard reaction set to calculate the heat defect. Klassen and Ross (1988) used this approach to calculate the heat defect of air-saturated water irradiated by neutrons with an LET of about 30 eV nm−1 in order to simulate the measurements of Galloway et al (1986) and Williams et al (1987). They found that, for an accumulated dose of 20 Gy, the system was endothermic by 2.9%. Galloway et al and Williams et al did not measure the heat defect in a neutron beam, but compared the dose determined calorimetrically to that obtained using ionization chambers. Because of uncertainties in the ionization chamber dosimetry, no definitive conclusions could be drawn, but the results were consistent with a heat defect of 2–4%, in rough agreement with the calculated value. The same approach was used by Seuntjens et al (1993a) to estimate the heat defect induced by low-energy x-rays. Using data similar to that of figure 3 they calculated the heat defect for water equilibrated with a 50:50 mixture of hydrogen and oxygen. They found no significant change in the heat defect as the LET was increased from 0.2 to 2 eV nm−1 .

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3.2. Relative measurements For the measurements reported by Domen (1982), air-saturated water showed a heat defect of about −3.5%. Furthermore, he saw no difference if the water was first bubbled with either oxygen or nitrogen. For the dose rate used by Domen, Fletcher showed that the heat defect of pure water should be zero beyond about 20 Gy while for oxygenated water it should be about +2% for doses from about 20 to 200 Gy. These calculations indicated that Domen should have seen a difference of approximately 2% between his oxygen-saturated and nitrogen-saturated systems (nitrogen does not participate in the radiolysis). Furthermore, the calculations gave a positive heat defect of 2% for oxygen- (or air-) saturated water, indicating that the calorimetric response would be expected to be low by 2%. In other words, if the calculated heat defect were incorporated into Domen’s measurements, the discrepancy between the calorimeter and ionization chamber measurements would be about 5.5%. A possible source of the discrepancy between the calorimetric measurements and the model predictions can be suggested by considering an example. If oxygen-saturated water is irradiated for 90 s at a dose rate of 0.4 Gy s−1 , the model predicts the following change in the stable products: 1.4µM O2 + 5.4µM H2 O ⇒ 1.3µM H2 + 4.1µM H2 O2 . −1

(8)

This conversion consumes 0.76 J kg of energy, or about 2% of the absorbed dose. A concentration of 1 µM corresponds to only approximately 20 molecules/109 water molecules. Therefore, small concentrations of stable products can represent a significant heat defect. This observation also suggests that small concentrations of reactive impurities might lead to a large (and unpredictable) heat defect. Domen (1982), and most who followed his design, used singly distilled water in their calorimeters. However, the water was in contact with large areas of various materials, including plastics, as well as being exposed to the atmosphere. This meant that impurities could enter the water after it was placed in the calorimeter. As well, the large volume of water made it difficult to achieve a complete exchange of gases by bubbling. In order to more easily compare the calculated heat defect based on the radiolysis of water with calorimetry, Ross et al (1984) constructed a small, sealed calorimeter. Because the volume of water was small and the calorimeter sealed from the atmosphere, it was relatively easy to saturate the water with various gas mixtures. Ross et al compared the relative response per unit absorbed dose of their calorimeter for three aqueous systems. These systems were prepared by bubbling highly purified water with either N2 gas, O2 gas or a 50:50 mixture of H2 and O2 gases. They found that the measured response of the N2 and O2 systems relative to the response of the H2 –O2 system agreed with the calculated relative response to better than 0.5%. This result is to be contrasted with Domen’s results, which showed no difference in the response of water bubbled with N2 or O2 gases. Ross et al speculated that the heat defect of the large calorimeters was dominated by impurities, although no specific impurity was identified. The work of Ross et al was extended by Klassen and Ross (1991) to a wider range of aqueous systems. Using 20 MV x-rays, they measured the response per unit absorbed dose of six aqueous systems relative to the response of the 50:50 H2 –O2 system. By accepting the calculated heat defect of −2.4% for the H2 –O2 system, the authors could obtain a measured heat defect for the other six systems. The measured heat defects were compared with the calculated values, as shown in figure 4. The largest discrepancy between any measured and calculated heat defect was 0.8%. However, Klassen and Ross divided the systems into two classes based on whether or not

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Figure 4. Comparison of the measured and calculated heat defect for six aqueous systems. The measured results are relative to the response of water saturated with a 50:50 mixture of H2 and O2 , to which the calculated heat defect of −2.4% is assigned. The measured results are indicated by symbols, where the different symbols serve to identify different measuring thermistors. The error bars represent the statistical standard uncertainty while the calculated results are shown by the horizontal lines.

a scavenger for the OH radical was present. In addition to the H2 –O2 reference system, three other aqueous solutions contained an OH scavenger. These were the formate, CO and H2 systems, and they showed the best agreement between the measured and calculated heat defect. Systems in which the OH radical is not scavenged seem to be very sensitive to impurities. On the basis of these results, Klassen and Ross concluded that the H2 and H2 –O2 systems are best suited for absorbed dose calorimetry. The H2 system has the added attraction that after a small dose a steady state is reached in which there is no longer any net change in the stable products, and thus the heat defect is zero. However, small concentrations of O2 will affect the response, and considerable care is required to reduce the O2 concentration to suitably low levels. 3.3. Absolute measurements Fleming and Glass (1969) established a technique to measure the heat defect of tissueequivalent (A-150) plastic using 2 MeV protons. They constructed an absorbing element which consisted of discs of aluminium and plastic, each thick enough to fully stop the proton beam. The discs were in good thermal contact with each other and thermally isolated from

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Figure 5. Section through the measuring system of Selbach et al (1992). The principal components are identified by numbers as follows: 1, x-ray beam; 2, calorimeter casing; 3, vacuum container; 4, water-filled absorber, 30 mm in diameter and 15 mm long; 5, mu-metal disc which can be moved through the water using magnets; 6, permanent magnets; 7, assembly for changing the location of the mu-metal disc; 8, plastic foils; 9, beryllium window; 10, vacuum container. (Reproduced with the permission of the Bureau International des Poids et Mesures.)

the environment so that the temperature of the assembly could be measured. The assembly could be rotated so that the proton beam could be stopped in either the aluminium or the plastic. Since the assembly consisted of two separate absorbers, but with a common heat capacity, if the same total energy was delivered by the proton beam to either the aluminium or the plastic, any difference in the temperature rise must be due to a difference in the heat defect of the two materials. Fleming and Glass assumed that the heat defect of aluminium was zero and thereby measured the heat defect of A-150 plastic with a standard uncertainty of about 0.2%. They found that the heat defect of A-150 decreased from 4.2% to 3.7% as the accumulated dose increased from 0.1 to 1 MGy. Schulz and Venkataramanan (1988) proposed using the same technique to measure the heat defect of water. They constructed a composite absorber of water and copper, with the water confined behind a thin Mylar window. They assumed that the heat defect of copper is zero. Although preliminary measurements were carried out in a 1 MeV proton beam, no results have been published. Selbach et al (1992) applied the same technique as Fleming and Glass to the measurement of the heat defect of water, but used low-energy (17–30 kV) x-rays rather than protons as the radiation source. As mentioned in subsection 3.1 the radiation chemistry of water, and therefore the heat defect, is dependent on the LET of the radiation. Most of the current interest in water calorimetry is for high-energy photon and electron beams which have low LET. Low-energy x-rays better simulate low LET than do protons. (Sabel et al (1972, 1973) also used the total absorption of low-energy x-rays to measure the heat defect of graphite and several plastics, although their experimental technique was quite different from that of Selbach et al.) Figure 5 shows the experimental arrangement used by Selbach et al (1992). The water-

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filled absorber was 30 mm in diameter and 15 mm long. A mu-metal disc 1 mm thick was immersed in the water and its position along the axis of the radiation field could be varied by using magnets. The disc was thick enough to be almost totally absorbing, and measurements were made with the disc either completely forward or completely back. The assembly was similar to that of Fleming and Glass in that it consisted of separate absorbers (mu-metal or water) but with a common heat capacity. The reference material used by Selbach et al was mu-metal, an alloy consisting of 75% Ni, 18% Fe, 5% Cu and 2% Cr by weight, and they assumed that its heat defect is zero. Assuming no heat loss corrections and total absorption of the x-ray beam, equation (2) w can be used to show that the heat defect of water, kH D , is given by w kH D = 1 − (1Tw /1Tµm )

(9)

where 1Tw and 1Tµm are the measured temperature changes of the composite absorber. They are both measured for the same incident x-ray fluence, but 1Tw is the result when water intercepts the beam, while 1Tµm is obtained when the mu-metal is in the upstream position. Selbach et al noted that the thermal response of the absorber was quite different depending on whether the mu-metal was at the front or the back. Because the specific heat of mu-metal is considerably less than that of water, the temperature of the front face of the composite absorber will rise higher during the irradiation when the mu-metal is at the entrance face. They carried out detailed calculations to account for the different heat loss depending on which material was at the front of the absorber. The correction was obtained as a factor (kw ) which multiplied the ratio of temperature changes in equation (9), and varied from 0.998 to 1.004 as the x-ray energy increased from 17 to 30 kV. Two additional corrections having to do with the absorption of the x-rays by the composite absorber had to be considered by Selbach et al. The first had to do with the fact that for the same incident fluence the amount of radiation energy absorbed depended on whether the mu-metal was in the forward (upstream) or rear position. Selbach et al carried out Monte Carlo calculations to determine the fraction of the incident energy which was lost from the absorber. The effect on the heat defect could be expressed in terms of a factor kabs , which is the ratio of the energy absorbed with the metal disc in the forward position to that when it is at the back. The ratio varied from 1.006 to 1.017 as the x-ray energy increased from 17 to 30 kV. The second correction had to do with the fact that the x-ray beam was not totally absorbed in either the water or the mu-metal. This meant that the two positions of the disc do not cleanly measure Ea and Eh as defined in equation (2). To account for this effect, Selbach et al calculated the fraction of the energy which was absorbed by the water for both positions of the disc. These fractions were denoted by awf and awr depending on whether the disc was in the front or rear, respectively. As the x-ray energy increased from 17 to 30 kV, awf decreased from 0.053 to 0.025 and awr decreased from 0.81 to 0.70. Using energy conservation and the various correction factors, the heat defect can be expressed as w kH D = [1 − kabs kw (1Tw /1Tµm )]/[awr − awf kabs kw (1Tw /1Tµm )].

(10)

Since the denominator in equation (10) is approximately awr and the other factors are all w near unity, any change in kabs or kw gives rise to approximately the same change in kH D . On w is approximately zero, the result is independent of the denominator the other hand, if kH D in equation (10) and therefore insensitive to uncertainties in awr and awf . Selbach et al w assign an overall uncertainty to kH D of 0.006. They report measurements of the heat defect of only one aqueous system. Water, which was distilled several times, was degassed under

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vacuum and placed in the absorber. It was pre-irradiated to 50 Gy. The estimated absorbed dose for each irradiation was about 10 Gy at a dose rate of approximately 0.04 Gy s−1 and over 50 irradiations were carried out. For the four x-ray energies, the measured heat defect was zero within the uncertainty of 0.006. We used the model described in subsection 3.1 to calculate the heat defect for pure water and a dose rate of 0.04 Gy s−1 . After 50 Gy, the calculated heat defect for a 10 Gy irradiation was less than 0.1%, in good agreement with the measurements. Roos et al (1992) have described a technique for measuring the heat defect of water which is based on the total absorption of low-energy (1–5 MeV) electrons. A similar approach was used by Feist (1982) to calibrate the Fricke chemical dosimetry system. The method makes uses of the fact that if the incident electron energy is known and the number of electrons measured, then the energy delivered to the target is known, assuming the beam is totally absorbed. Roos et al compared the temperature rise induced in water by the electron beam with the temperature rise caused by a known amount of electrical energy. Any difference (after making any necessary corrections) must be due to the heat defect of the water used.

Figure 6. Apparatus of Roos et al (1992) for measuring the heat defect of water using the total absorption of electrons. The components identified by numbers are: 1, electron beam from the 5 MeV microtron; 2, toroidal monitor for measuring the charge; 3, temperature-stabilized container; 4, vacuum container; 5, absorber vessel filled with water; 6, beam entrance window (23 µm of Mylar); 7, thermistors; 8, heating resistor; 9, magnetically coupled stirrer; 10, 11, annular detectors to monitor electron loss. (Reproduced with the permission of the Bureau International des Poids et Mesures.)

The essential features of their apparatus are shown in figure 6. The electron beam energy was determined with an uncertainty of 0.2% using a magnetic spectrometer. The charge delivered to the absorber was measured with an uncertainty of 0.3% using a toroidal monitor. The beam entered the water through a Mylar window 23 µm thick. The water was stirred during both irradiation and electrical heating in order to minimize the effects of temperature gradients. The temperature rise was measured for both modes of heating, and

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the temperature rise per unit input energy calculated. The heat defect was then obtained from w kH D = 1 − (1Tr /1Te )

(11)

where 1Tr and 1Te are the temperature changes per unit energy for radiation and electrical heating, respectively. Roos et al had to correct for the fact that not all of the energy carried by the electron beam was absorbed in the water. Some electrons backscatter and do not enter the water, and some generate bremsstrahlung radiation which escapes from the water. Roos et al used Monte Carlo calculations to determine the energy loss, and for 5 MeV electrons found it to be 1.7% of the incident energy. For what they described as high-purity, pre-irradiated water, they obtained a heat defect which was zero within their estimated uncertainty of 0.004. In a later publication Krauss and Roos (1993) described measurements in which they used multiply distilled water which was not explicitly stated as being saturated with any gas. They found that the heat defect started out at about −3.5% (i.e., the system was exothermic) and slowly increased, becoming zero after about 5 kGy. Assuming the water was initially air-saturated and then sealed in the calorimeter, this result is not consistent with model predictions. Air-saturated water is expected to behave like oxygen-saturated water, which is endothermic at low doses (i.e., positive heat defect) and reaches a steady state at a dose of about 16 kGy. Krauss and Roos state that for these measurements no great care was taken regarding impurities in the absorber vessel, and the results suggest that the response (at least for doses less than 5 kGy) was dominated by impurities. 4. The second generation of water calorimeters The initial work using large water calorimeters gave values for the absorbed dose to water which were larger than expected on the basis of other dosimetric techniques. Furthermore, if the value of the heat defect for air-saturated water which was predicted by the standard model for the radiolysis of water was applied to the calorimetric measurements, the discrepancy was even larger. However, detailed studies of the heat defect of aqueous systems showed that when water quality was carefully controlled, results were generally consistent with the model predictions. This work also demonstrated that impurities could have a major impact on the heat defect, and although specific impurities were not identified, empirical indications were that they generally give rise to exothermic processes. These results suggested that, if water calorimetry was to be successful, water quality would have to be carefully controlled. 4.1. The Yale calorimeter One of the first efforts to construct a calorimeter in which water quality was carefully controlled was made by Schulz et al (1987). Figure 7 shows a cross section of their calorimeter in which the water was held in a sealed glass cylinder. The water was purified using a commercial ion exchange system. The thermistors for measuring the temperature rise were embedded in glass capillary tubes so that the only non-glass material in contact with the water was Teflon associated with the valves used for sealing the vessel. Schulz et al bubbled the water with either nitrogen or oxygen gas before filling and sealing the calorimeter. In order to reduce or eliminate the possibility of convection currents they operated the calorimeter at 4 ◦ C (see subsection 5.1). The calorimeter response was measured

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for both aqueous solutions using 4 MV x-rays and converted to absorbed dose to water, assuming a heat defect of zero.

Figure 7. Cross section of the water calorimeter of Schulz et al (1987). The absorbing element or core is a 10 cm × 10 cm right cylinder made of Pyrex glass. High purity water is bubbled with a suitable gas before being sealed in the core. The circulating water is maintained at 4 ◦ C to eliminate convection. (Reproduced with the permission of the American Institute of Physics.)

In order to compare the calorimeter response to ionization chamber measurements, Schulz et al constructed a second glass core, this one containing an opening in which an ionization chamber could be inserted. Ionization chamber measurements were carried out under the same irradiation conditions as the calorimetry, and converted to absorbed dose to water using the formalism of the AAPM (1983) dosimetry protocol and electron stopping power ratios calculated by Andreo and Brahme (1986). For oxygen-saturated water, the ratio of the absorbed dose based on calorimetry to that obtained using an ionization chamber was about 1.02 at low doses, but decreased with accumulated dose and became constant at 0.991 after about 60 Gy. For nitrogen-saturated water the initial response of the calorimeter depended on how long the water had been left in the calorimeter. For the first irradiation after 1 week or more of storage, the ratio was as much as 3% greater than the mean value. If these spikes in the response were ignored, the mean value of the ratio was about 1.006, or 1.5% higher than obtained for oxygen. Because this difference was consistent with the model predictions and since the calorimeter and ionization chamber measurements were in reasonable agreement, Schulz et al suggested that nitrogen-saturated water (for which the heat defect is predicted to be zero) is a good candidate for water calorimetry. In a later publication Schulz et al (1991) extended their measurements using nitrogensaturated water to additional beam qualities from 60 Co γ -rays to 25 MV x-rays. Ionization chamber dosimetry was again based on the AAPM dosimetry protocol, although the corrected version (Rogers and Ross 1988) was used. They saw no trend in the ratio of

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calorimeter to ionization chamber measurements with beam quality and report a mean value for the ratio of 1.001 (±0.001). The stated uncertainty includes only statistical uncertainties thus ignoring the systematic uncertainties in the ionization chamber dosimetry which are up to 3 or 4% (IAEA 1987). 4.2. The NRC calorimeter Another calorimeter in which water quality was carefully controlled was developed by Ross et al (1984, 1989) and is shown in figure 8. The water was purified by passing it through a particulate filter, an ion exchange column, a 5 nm filter and an ozonizer. Finally, the water was doubly distilled and stored in quartz containers. Approximately 100 ml of water was held in a thin-walled glass vessel which was thermally isolated from the environment. The water was stirred, and the temperature rise measured using thermistors. Facilities were provided for bubbling the water with various gases and for sealing the vessel from the atmosphere. Because the water was stirred, the calorimeter measured the energy change averaged over the 100 ml of water. Although the calorimeter was originally developed for measuring the relative response of various aqueous systems, Ross et al (1989) showed that it could be adapted to measure D w , the absorbed dose averaged over the volume of the liquid. If the measured temperature change was 1T , then w D w = [cw 1T /(1 − kH D )]kF M

(12)

which is similar to equation (1), except for the factor kF M which accounts for the effect of the glass (‘foreign mass’) in contact with the water. Measurements were carried out using water saturated with a 50:50 mixture of H2 and O2 gases, for which the heat defect was calculated to be −2.1%. This value is slightly different from the value of −2.4% reported in subsection 3.2, which is based on more recent calculations (Klassen and Ross 1991). The foreign mass correction, kF M , arises because the specific heat of glass is only about one fifth that of water, and thus most of the heat due to radiation energy deposited in the glass is transferred to the water. Since the water is stirred, the excess heat from the glass affects directly the measured temperature rise and amounts to about 3% of the energy deposited in the water. Ross et al showed that kF M should vary linearly with the mass of the glass and determined kF M by repeating the calorimeter measurements with different amounts of glass in contact with the water and extrapolating the response per unit dose to zero mass. Once D w was established, the calorimeter was used to determine the calibration factor for Fricke dosimeter solution by replacing the water in the calorimeter with the same amount of Fricke solution. For high-energy photons and electrons, the Fricke system is approximately water equivalent, so the average absorbed dose to the Fricke solution can be related to the average absorbed dose to water using a correction factor which is close to unity. For 20 MV x-rays, the value obtained for the Fricke calibration factor, G, was 3.505 (±0.021) cm2 J−1 at 25 ◦ C (Klassen et al 1991). This value is 0.2% lower than, but agrees within the estimated uncertainty with, the value recommended by Svensson and Brahme (1979). Once the Fricke system was calibrated in terms of dose to water it was used to establish the dose at a point in a large water phantom. The absorbed dose to water based on this technique has recently been compared with the absorbed dose standard of the German national standards laboratory (Shortt et al 1993) and the difference was found to be less than 0.5%.

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Figure 8. Cross sectional view of the calorimeter of Ross et al (1984, 1989). The water occupies a cylindrical volume about 5 cm in diameter and 5 cm high. The key elements are: A, channels for temperature-regulated water (the flow of water through these channels establishes a temperature-stabilized shroud which almost completely surrounds the sensitive volume of the calorimeter); B, outlet tube for gas flow; C, glass filling and bubbling tube; D, thin-walled (0.040 g cm−2 glass (Pyrex) calorimeter vessel; E, one of two thermistors; F, glass stirring paddle; G, Styrofoam insulation.

4.3. The NIST calorimeter More recently, Domen (1994) has shown that his original calorimeter design can be modified so that water quality is carefully controlled. Figure 9 shows the revised calorimeter in which the water in the vicinity of the measuring thermistors is enclosed in a clean glass vessel. The water is prepared using a filter, deionizer and organic absorber. The rest of the water in the calorimeter does not need to be of high quality, since any heat defect in it will not affect the temperature measurement in the vicinity of the thermistors. The diameter of the glass vessel is about 33 mm, and its length is such that it holds 90 cm3 of water. The thickness of the glass wall is about 0.3 mm. The diameter of the vessel is a compromise based on two considerations. If the diameter were too small, excess heat generated in the glass by the radiation field would affect the measured temperature rise. On the other hand, if the diameter were too large, the vessel would not serve as a convective barrier. For the

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diameter chosen, Domen showed that the effect of excess heat should be less than 0.1% 60 s after a 60 s irradiation. Furthermore, he estimated that the glass should act as an effective convective barrier, permitting measurements to be made in a horizontally directed electron beam.

Figure 9. Main features of Domen’s sealed water calorimeter (Domen 1994). As in his original design (figure 1), the main body of the calorimeter consists of a large mass of motionless water thermally isolated from the environment. The measuring thermistors are located in a sealed glass vessel in which the water quality is carefully controlled. With this design, the heat defect of the water at the point of measurement is known, and the vessel also acts as a convective barrier potentially permitting measurements in horizontally directed radiation fields. (Reproduced with the permission of the NIST Journal of Research.)

The glass vessel was removed from the calorimeter for filling with high-purity water and for bubbling with an appropriate gas mixture. The vessel was then sealed and placed in the calorimeter assembly. Domen reported measurements for water saturated with nitrogen and hydrogen gases, as well as a mixture of hydrogen and oxygen gases. All the irradiations were performed using 60 Co γ -rays directed vertically downward. Domen concluded that the most reliable results were obtained with the hydrogen system, for which he took the heat defect to be zero, with an estimated standard uncertainty of 0.3%. The overall uncertainty for the absorbed dose to water based on the hydrogen system was 0.4%. The absorbed dose based on the nitrogen system (also assumed to have zero heat defect) agreed within about 0.1% with the hydrogen system, but showed significant exothermic effects after filling. The H2 –O2 system showed large, variable, changes in response with accumulated dose, at least partly due to the fact that the relative amounts of H2 and O2 were not carefully controlled during the initial filling of the vessel. The absorbed dose to water obtained using the H2 and N2 systems agreed to better than 0.5% with the absorbed dose based on other techniques, notably graphite calorimetry. This result is to be contrasted with the discrepancy of 3.5% reported by Domen (1982) for his large, unsealed calorimeter.

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4.4. The Ghent calorimeter Seuntjens et al (1993a) used a water calorimeter based on Domen’s revised design to measure the absorbed dose due to medium-energy x-rays (100 kV–250 kV). Their sealed core was 15 cm in length, 4 cm in diameter and was constructed from Lucite (PMMA) with a wall thickness of 0.5 mm. The core was filled with water which had been distilled several times and bubbled with argon. For this aqueous system the heat defect is expected to be positive for small absorbed doses, but to decrease to zero by about 100 Gy. Instead, Seuntjens et al observed initial exothermic effects when the vessel was first filled, and after the water had been left in it for several days. However, the response decreased with accumulated dose and became constant after a dose of a few kilogray. By comparing the steady state calorimeter response in a 60 Co beam with the absorbed dose to water based on ionization chamber dosimetry, they assigned a heat defect of −1.5 (±1.4)% to the aqueous system. They used this value of the heat defect to determine the absorbed dose to water for the x-ray measurements. In a subsequent paper Seuntjens et al (1993b) reported the results of using their calorimeter to measure the absorbed dose to water in high-energy x-ray beams. They compared the response per unit dose of the calorimeter using three different aqueous systems for which the heat defect could be calculated. The three systems were argonsaturated water (equivalent to pure water), oxygen-saturated water and oxygen-saturated water containing 1 mM of sodium formate. They found that the response of the O2 – formate system was independent of accumulated dose, while the response of the oxygensaturated system decreased by about 5% over the first 150 Gy before becoming constant. Seuntjens et al also reported that pure water showed initial exothermic effects, although not as pronounced as for O2 -saturated water. They compared the relative response of the calorimeter (once steady state had been reached) with the model predictions for the three aqueous systems. Using the O2 –formate system as a reference, the measured response of pure water and O2 -saturated water differed by 0.3% and 0.7% respectively from the calculations. The estimated standard uncertainty on the results was 0.5%. Seuntjens et al speculate that the dependence of the response of O2 -saturated water (and, to a lesser extent, pure water) on accumulated dose is due to impurities which enter the water from the Lucite walls of their sealed core. In this respect, their design differs from that of Domen who used a glass core. 5. Technical considerations 5.1. Convection Next to the heat defect, the effect of convection on the performance of water calorimetry has generated the most concern. Section 2 briefly reviewed the mechanism that gives rise to convection, and it was pointed out that for measurements beyond the depth of maximum dose, for radiation beams directed vertically downward, convection should not be a problem. Indeed, Domen’s measurements with his first water calorimeter, as well as measurements by others using a similar design, seemed to confirm this. However, the situation is more complicated for beams directed horizontally, and Schulz and Weinhous (1985) reported evidence for convection currents in a calorimeter which was irradiated with horizontal beams of 25 MV x-rays or 19 MeV electrons. Their calorimeter contained measuring thermistors which were located 12 mm and 50 mm from a polystyrene plate. The plate was at right angles to the beam direction so that for horizontal irradiations the plate was vertical. The effects Schulz and Weinhous saw were large and implied a sudden rapid cooling of the

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thermistor nearest the polystyrene plate. In a series of notes and papers (Domen 1986, 1988a, b) Domen clarified the mechanism leading to the effects observed by Schulz and Weinhous. When the horizontally directed radiation beam enters the calorimeter, the entrance wall rises to a higher temperature than the water because of its lower specific heat. As a result, upward convective flow parallel to the vertical wall is established, and Domen estimated that the width of the velocity stream was about 18 mm and the maximum velocity was about 0.4 mm s−1 . For a broad radiation field, fluid motion with these characteristics should not lead to sudden changes in the water temperature near the measuring thermistor. Instead, Domen concluded that the effect observed by Schulz and Weinhous was due to the effect that the flow had on the equilibrium temperature gradient which exists near the thermistor. Because of the electrical energy being dissipated in the thermistor, its temperature rises above the ambient water temperature by about 2 mK µW−1 , or about 160 mK for a power of 80 µW, as used by Schulz and Weinhous. On the other hand, the temperature rise due to irradiation is only a few millikelvin, so Domen concluded that the convective flow was disturbing the temperature distribution in the immediate vicinity of the thermistor, thus leading to large changes in response. In order to put his speculations on firmer ground, Domen (1988b) constructed an apparatus which allowed him to measure the effect of varying flow rates on thermistor response. He showed that flow over the thermistor caused it to cool, and that he could express the effect in terms of an apparent negative dose rate. He presented data for a wide range of thermistor power levels and fluid velocities. In a related note (Domen 1988a) he applied his results to a reanalysis of the data of Schulz and Weinhous. By interpreting the sudden changes in response that they observed in terms of a negative dose rate, he estimated that the upward convective velocity was about 3.3 mm min−1 for the x-ray beam and about 5.8 mm min−1 for the electron beam. These velocities are in reasonable agreement with the expected convective velocities near a heated, vertical plate. Domen pointed out that the effect of the convective flow on the thermistor response can be greatly reduced by operating at low thermistor powers (a few microwatts rather than tens of microwatts). Roos (1988) also observed cooling effects similar to those of Schulz and Weinhous when using a horizontal 60 Co beam. In his calorimeter, 0.5 mm diameter thermistors dissipating 15 µW were sandwiched between polyethylene films as in figure 1. Note that the films were oriented vertically when the calorimeter was irradiated by a horizontally directed beam. In an extension of this work, Domen et al (1991) saw no convective effects with 0.25 mm diameter thermistors, even for power levels up to 100 µW. They speculate that the smaller-diameter thermistor does not sense the upward convective velocity profile, which (for laminar flow) must be zero at the surface of the film. Seuntjens (1991) studied the effect of convection which is initiated by the electrical energy dissipated in the thermistor. By assuming that the only mechanism of heat loss from the thermistor to the water was by conduction, he was able to predict how the thermistor resistance should change with power. For large powers, the measured thermistor resistance was larger than the predicted value, suggesting additional cooling due to convection. Seuntjens used Domen’s data (Domen 1988b) to estimate the convective velocity, and concluded that convection may be present for thermistor power levels as small as 5 µW. This result is in disagreement with the measurements of Domen (1988b) which showed no evidence for thermistor-induced convection for power levels below about 50 µW. This discrepancy may be explained by Seuntjens’ observation that his results are less reliable for low thermistor powers because they require an accurate separation of the small convective heat loss component from the much larger conductive component.

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Figure 10. Volume expansion coefficient of water as a function of temperature (CRC 1981).

Domen’s work on convection clearly demonstrated that the onset of convective flow in the water can have dramatic effects on the thermistor response. However, the effect of convective heat transfer on the temperature profile within the water has not been studied as thoroughly. For a liquid sandwiched between two horizontal plates which are held at constant temperature, convection sets in when the Rayleigh number exceeds 1700. The Rayleigh number depends on several properties of the fluid (Burmeister 1983) and it is proportional to 1T x 3 , where 1T is the temperature difference between the plates, and x is their separation. It has been assumed (see, e.g., Domen 1987) that the same threshold for convection applies to imaginary horizontal surfaces within a large calorimeter. At this point, there are no measurements which directly explore the characteristics of convection set in motion by a radiation field in a large water calorimeter. Seuntjens (1991) considered the possibility of convection near the beam penumbra in a large water calorimeter irradiated by a horizontal x-ray beam. For the geometry appropriate to his calorimeter, he estimated the time for the onset of convection to be about 60 min, much longer than any irradiation time. Furthermore, his measurements showed no indication of any effects due to convection in the beam penumbra. Rather than trying to control the effects of convection in large water calorimeters, Schulz and Weinhous (1985) proposed a technique to eliminate convection. The driving force for convection is buoyancy, and it arises because the density of water at room temperature decreases as the temperature increases. Figure 10 shows how the volume expansion coefficient of water changes as a function of temperature. At room temperature the density of water decreases by about 0.02% per degree rise in temperature. However, at 4 ◦ C the expansion coefficient passes through zero so that small changes in temperature lead to no change in density, and therefore there is no buoyant force to drive convection. Schulz and Weinhous successfully operated their calorimeter at 4 ◦ C and demonstrated that the convective effects they observed at room temperature were not present. Schulz et al (1987, 1991) went on to perform detailed absorbed dose measurements using a water

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calorimeter operated at 4 ◦ C. The same approach has also been adopted by a group at the Physikalisch-Technische Bundesanstalt (PTB) (Roos 1988, Krauss and Roos 1993). Figure 10 can be used to estimate how closely the calorimeter temperature must be held to 4 ◦ C. In the range of 3–5 ◦ C, the expansion coefficient is less than one-tenth of its value at room temperature, indicating that an operating temperature anywhere within 1 ◦ C of 4 ◦ C should greatly suppress convection. Schulz et al (1987) state that their temperature regulator maintained 4 ◦ C within 0.1 ◦ C, thereby restricting the expansion coefficient to approximately one hundredth of its room-temperature value. Another approach which has been proposed recently (Rosser 1994) and which eliminates convection is to construct an ice calorimeter. Rosser demonstrated that it is technically possible to operate such a calorimeter although she observed significant instabilities in the post-irradiation temperature drift. Although this form of ‘water’ calorimeter eliminates convection, the heat defect may prove difficult to determine since the radiation chemistry of ice near 0 ◦ C is not as well studied as that of water. 5.2. Temperature sensors The basic measurement in water calorimetry is a temperature change. Pettersson (1967) used the volumetric expansion of water to measure the temperature rise due to irradiation, but all subsequent work has used thermistors. With all measurements based on the same type of temperature sensor, there is the possibility of some systematic effect being overlooked. A water calorimeter based on some other form of temperature sensor would help to eliminate this possibility. Thermistors are formed from semiconductor materials for which the resistance is a strong function of temperature. Typically, the temperature coefficient is about 4% K−1 , with the resistance decreasing as the temperature increases. Another important characteristic of thermistors is that they are available in small sizes, thus minimizing the perturbation introduced by the temperature sensor. Spherical bead thermistors with a diameter of only 0.25 mm have been used in several water calorimeters (see, e.g., Domen 1994). Because thermistors were also used in earlier work with other forms of calorimetry, the same bridge and sensing techniques developed for these systems can also be applied to water calorimetry. Typically, the thermistor resistance is monitored using a bridge circuit. Both DC (see, e.g., Domen 1994) and AC (see, e.g., Seuntjens et al 1993a) bridges have been used successfully. One complication in using thermistors in a water calorimeter arises from the fact that water is a conducting liquid, so care must be taken to electrically isolate the thermistor from the water, while at the same time maintaining good thermal contact. In Domen’s original calorimeter, the thermistors were isolated from the water by polyethylene sheets. However, in most later designs the thermistors were mounted in thin-walled capillary tubes. Another complication is due to the large specific heat of water (approximately five times that of graphite) which means that the measuring circuits must be about five times more sensitive in a water calorimeter than in a graphite calorimeter. 5.3. Water quality It is now clear that the control of water quality is crucial for water calorimetry. The early calorimeters tended to give values for the absorbed dose to water which were too high by a few per cent, probably because of impurities in the water. Because small quantities of additives can have a significant impact on the heat defect, great care is required in the

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preparation and handling of the water which is in contact with the temperature-sensing element. There is no simple test which can be used to decide whether the water quality is satisfactory. However, the calorimeter measurements themselves can be used as a guide. If the change in response with accumulated dose is consistent with the model predictions for the aqueous system being used, it is a good indication that the heat defect is not being dominated by impurities. Furthermore, if the relative response of two or more aqueous systems is consistent with the model predictions, it is likely that water quality is adequate. 5.4. Excess heat The specific heat of most materials is significantly less than water. This means that most of the radiation energy deposited in any material in contact with the water in a water calorimeter will be transferred as heat to the water. If the foreign material is near the point of measurement, it may have a significant impact on the measured temperature rise. In the NRC calorimeter (Ross et al 1984, 1989), because the water was stirred, the excess heat from the glass in contact with the water was quickly transferred to the water. For the thinnest glass vessel the extra heat amounted to about 3% of the absorbed energy. Ross et al measured the effect of the glass on the calorimeter response by changing the amount of glass in contact with the water and extrapolating to zero mass. The effect is more difficult to account for in large water calorimeters since the transfer of heat leads to thermal gradients which change slowly with time. Domen (1994) identified three sources of excess heat in his sealed water calorimeter and used numerical techniques to estimate their effect on the measured temperature change. Firstly, most of the calorimeter was filled with once-distilled water. Domen estimated that this water showed an exothermicity of 3.5% compared to the high-purity water in the sealed core. This meant that heat energy was transferred from the water outside the core to the water inside. For a vessel 30 mm in diameter, this extra heat contributed less than 0.05% to the measured temperature rise 60 s after a 60 s irradiation. Secondly, the excess heat from the glass wall of the core can affect the measured temperature rise. Domen calculated the effect for various configurations, but for a 30 mm diameter vessel the excess heat would led to a 0.3% error in the measured temperature 60 s after a 60 s irradiation. Finally, excess heat from the thermistor probes themselves can also affect the measured temperature rise. Domen estimated that this effect was negligible because of the small mass of the probes used in his calorimeter design. The thermistor probes used by Schulz et al (1987, 1991) were of similar construction to those used by Domen (1994) but considerably larger in diameter (0.7 mm versus 0.4 mm). Domen (1994) pointed out that excess heat from the thermistor probes will lead to a sharp drop in the temperature a few seconds after the end of the irradiation. Furthermore, he showed that the effect of the excess heat can extend for several tens of seconds after the end of the irradiation. Domen did not see any post-irradiation effects with his low-mass probes, but Schulz et al (1987) observed about a 2% drop in the first few seconds after an irradiation of 120 s. Although Schulz et al ignore the initial drop when analysing their runs, they do not estimate what the effect of the slower component might be. The calorimeter of Seuntjens et al (1993a, b) was of similar design to that of Domen. However, they used their calorimeter in medium-energy x-ray beams for which the absorbed dose rate was rather low. In order to obtain adequate precision, they needed 300 s irradiations. In this case, they calculated that the excess heat from the vessel wall can contribute up to 3% to the measured temperature rise 300 s after the end of the irradiation. The calculated contribution of the excess heat was subtracted from the measured temperature

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change as a function of time before analysing each calorimeter run. For their measurements using 10 and 25 MV x-ray beams (Seuntjens et al 1993b), the effect of the excess heat was not as large because the irradiation times were shorter (60 or 90 s). Nevertheless, failure to account for excess heat would lead to errors of 1–2%. Seuntjens et al tested the accuracy of the calculated correction by using different post-irradiation intervals to extrapolate to mid-run. They found that the error introduced by using the calculated correction was within experimental uncertainties if the end of the extrapolation interval was not more than about 2 min after the end of the irradiation run. 6. Discussion Radiation therapy requires accurate knowledge of the absorbed dose to water. This need for accurate dosimetry has been the primary motivation for the development of water calorimetry. The complexity of calorimetry in general, and especially water calorimetry, makes it unlikely that calorimetry will become a routine dosimetric tool in the clinical environment. However, calorimetry is the best way of establishing the absorbed dose absolutely, and graphite calorimetry already forms the basis for several national standards for the absorbed dose to water (Pruitt et al 1981, Burns 1994). The expectation is that water calorimetry will reduce some of the uncertainties associated with graphite calorimetry, especially for high-energy x-ray and electron beams. For absorbed dose calorimetry to be successful, the heat defect must be known. Depending on the material from which the calorimeter is constructed and the LET of the radiation, there are several mechanisms which can contribute to the heat defect. Measurements and calculations indicate that the heat defect of graphite should be zero for low-LET radiation, and this has contributed to its wide use for absorbed dose calorimetry. The situation is more complicated for water, for which any heat defect is expected to be due to radiation-induced chemical reactions. The radiation chemistry of water has been studied extensively, so that model calculations of the heat defect of various aqueous systems can be carried out. A variety of measurements have demonstrated that, for several systems, the calculated heat defect is in reasonable agreement with the measured results. However, the measurements have also shown that the heat defect can be strongly influenced by impurities, and that considerable care must be taken in preparing the water for use in the calorimeter. Nevertheless, several different calorimeter designs using various aqueous systems have now demonstrated results which are consistent, to 1% or better, with the absorbed dose to water obtained by more conventional techniques. A second major problem with any form of calorimetry is that of heat transfer to and from the point of measurement. Because the thermal diffusivity of water is small, heat transfer by conduction is not a problem for most irradiation conditions. However, convection is a more serious concern, and various techniques have been used or proposed to reduce or eliminate the effects of convective flow. Each has its advantages and disadvantages. Ross et al (1989) avoided the effects of convection altogether by using a small calorimeter in which the water was stirred. However, their calorimeter does not give the dose at a point, thus requiring a transfer medium (Fricke solution) to establish the dose at a point in a large water phantom. Domen (1994) used a sealed glass vessel within a larger phantom to maintain water quality and to act as a convective barrier. Additional measurements are needed in different irradiation geometries to determine whether or not additional barriers may be needed. Schulz and Weinhous (1985), Schulz et al (1987, 1991) greatly increased the threshold for the onset of convection by operating their calorimeter at 4 ◦ C where the volume expansion coefficient of water is zero. This technique increases the technical

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complexity of the calorimeter, and requires that model calculations of the heat defect be performed for the appropriate aqueous system at 4 ◦ C. Although no primary standards are based as yet on water calorimetry, a number of interesting results have been obtained. Schulz et al (1987, 1991) compared the results obtained with their calorimeter to the absorbed dose to water obtained using ionization chamber dosimetry based on the formalism of the AAPM (1983) TG-21 dosimetry protocol. For four x-ray beams from 4 to 25 MV, they report a ratio of calorimeter to ionization chamber dose of 1.001(±0.001). The stated uncertainty included only statistical uncertainties, and neglected systematic uncertainties on the ionization chamber dosimetry, which could amount to a few per cent. Measurements which were a more definitive test of the calorimeter response were reported by Domen (1994) who compared the response of his water calorimeter to 60 Co γ -rays to the absorbed dose measured using other types of calorimeter, including a graphite calorimeter. The results obtained using hydrogensaturated water agreed to within 0.1% with the absorbed dose to water based on graphite calorimetry, well within the estimated uncertainty of 0.4%. Shortt et al (1993) compared the absorbed dose to water for 20 MV x-rays based on the NRC water calorimeter with the high-energy absorbed dose standard at the PTB. Ionization chamber calibration factors between the two laboratories were found to agree within 0.4%, well within the estimated uncertainties. Seuntjens et al (1993a) used a water calorimeter to measure the absorbed dose due to medium-energy x-ray beams. The calorimeter measurements were used to derive correction factors for use with ionization chamber dosimetry. The correction factors derived calorimetrically were in good agreement with those based on an independent determination, although the overall uncertainties approached 2%. The last fifteen years have seen major advances in our understanding of water calorimetry. It is now practical to construct a standard for the absorbed dose to water which is based on water calorimetry. For a carefully designed calorimeter used with a dose rate typical of that for radiation therapy, the relative standard uncertainty on the absorbed dose should be less than 1%. Various calorimeter designs have been proposed, so comparisons of the absorbed dose to water based on the various techniques, including results derived from graphite calorimetry, should help to eliminate systematic errors and lead to a robust set of international absorbed dose standards. References AAPM 1983 A protocol for the determination of absorbed dose from high-energy photon and electron beams Med. Phys. 10 741–71 AIP 1989 A Physicist’s Desk Reference: The Second Edition of Physics Vade Mecum ed H L Anderson (New York: American Institute of Physics) pp 37–9 Anderson R F, Vojnovic B and Michael B D 1985 The radiation–chemical yields of H3 O+ and OH− as determined by nanosecond conductimetric measurements Radiat. Phys. Chem. 26 301–3 Andreo P and Brahme A 1986 Stopping power data for high-energy photon beams Phys. Med. Biol. 31 839–58 Barnett R B 1986 Water calorimetry for radiation dosimetry PhD Thesis University of Calgary Boyd A W, Carver M B and Dixon R S 1980 Computed and experimental product concentrations in the radiolysis of water Radiat. Phys. Chem. 15 177–85 Brahme A 1984 Dosimetric precision requirements in radiation therapy Acta Radiol. Oncol. 23 379–91 Burmeister L C 1983 Convective Heat Transfer (New York: Wiley) Burns J E 1994 Absorbed-dose calibrations in high-energy photon beams at the National Physical Laboratory: conversion procedure Phys. Med. Biol. 39 1555–75 Busulini L, Cescon P, Lora S and Palma G 1968 Dosim´etrie des rayons γ de Co-60 par une simple m´ethode calorim´etrique Int. J. Appl. Radiat. Isotopes 19 657–62 Carver M B, Hanley D V and Chaplin K R 1979 MAKSIMA-CHEMIST: A program for mass action kinetics simulation by automatic chemical equation manipulation and integration using stiff techniques AECL, Chalk River Nuclear Laboratories AECL-6413

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CRC 1981 CRC Handbook of Chemistry and Physics ed R C Weast and M J Astle (Boca Raton, FL: Chemical Rubber Company) p F-5 Davison S, Goldblith S A, Proctor B E, Karel M, Kan B and Bates C J 1953 Dosimetry of a kilocurie cobalt-60 source Nucleonics 11 22–6 Domen S R 1980 Absorbed dose water calorimeter Med. Phys. 7 157–9 ——1982 An absorbed dose water calorimeter: theory, design, and performance J. Res. NBS 87 211–35 ——1986 Comments on ‘Convection currents in a water calorimeter’ Phys. Med. Biol. 31 1166–68 ——1987 Advances in calorimetry for radiation dosimetry The Dosimetry of Ionizing Radiation vol II, ed K R Kase, B E Bjarngard and F H Attix (Orlando, FL: Academic) pp 245–320 ——1988a Further comments on convection currents in a water calorimeter Phys. Med. Biol. 33 1083–6 ——1988b Convective velocity effects on a thermistor in water J. Res. NBS 93 603–12 ——1994 A sealed water calorimeter for measuring absorbed dose J. Res. Natl Inst. Stand. Tech. 99 121–41 Domen S R, Krauss A and Roos M 1991 The problem of convection in the water absorbed dose calorimeter Thermochim. Acta 187 225–33 Elliot A J 1994 Rate constants and G-values for the simulation of the radiolysis of light water over 0–300 ◦ C range AECL, Chalk River Nuclear Laboratories AECL-11073 Feist H 1982 Determination of the absorbed dose to water for high-energy photons and electrons by total absorption of electrons in ferrous sulphate solution Phys. Med. Biol. 27 1437–47 Fleming D M and Glass W A 1969 Endothermic processes in tissue-equivalent plastic Radiat. Res. 37 316–22 Fletcher J W 1982 Radiation chemistry of water at low dose rates—emphasis on the energy balance: a computer study AECL, Chalk River Nuclear Laboratories AECL-7834 Galloway G, Greening J R and Williams J R 1986 A water calorimeter for neutron dosimetry Phys. Med. Biol. 31 397–406 Gunn S R 1976 Radiometric calorimetry: a review Nucl. Instrum. Methods 135 251–65 IAEA 1987 Absorbed dose determination in photon and electron beams IAEA Technical Report 277 (Vienna: IAEA) ICRU 1976 Determination of absorbed dose in a patient irradiated by beams of x or gamma rays in radiotherapy procedures ICRU Report 24 (Washington, DC: ICRU) ISO 1992 Guide to the expression of uncertainty in measurement ISO Report ISO/TAG 4/WG 3 (Geneva: ISO) Johns H E and Cunningham J R 1978 The Physics of Radiology (Springfield, IL: Thomas) p 329 Kehoe T M and Galloway G 1988 Water calorimetry in Edinburgh Proc. NRC Workshop on Water Calorimetry NRC-29637, ed C K Ross and N V Klassen (Ottawa: NRC) pp 31–7 Klassen N V and Ross C K 1988 The radiation chemistry of water at high LET Proc. NRC Workshop on Water Calorimetry NRC-29637, ed C K Ross and N V Klassen (Ottawa: NRC) pp 95–7 ——1991 Absorbed dose calorimetry using various aqueous solutions Radiat. Phys. Chem. 38 95–104 Klassen N V, Shortt K R and Ross C K 1991 Calibration of Fricke dosimetry by water calorimetry Proc. 7th Tihany Symp. on Radiation Chemistry (Balatonszeplak, 1990) (Budapest: Hungarian Chemistry Society) pp 543–7 Krauss A and Roos M 1993 The heat defect in the water absorbed dose calorimeter Thermochim. Acta 229 125–32 Kubo H 1983 Absorbed dose determination with a water calorimeter in comparison with an ionization chamber Phys. Med. Biol. 28 1391–9 Laughlin J S and Genna S 1966 Calorimetry Radiation Dosimetry vol II, ed F H Attix and W C Roesch (New York: Academic) pp 389–441 Loevinger R 1981 A formalism for calculation of absorbed dose to a medium from photon and electron beams Med. Phys. 8 1–12 Lovell S and Shen H 1976 A flow calorimetric method of determining electron beam energy Phys. Med. Biol. 21 198–208 Mattsson O 1984 Application of the water calorimeter, Fricke dosimeter and ionization chamber in clinical dosimetry PhD Thesis University of Goteburg ——1988 Water calorimetry at Radiation Physics Department Goteburg Proc. NRC Workshop on Water Calorimetry NRC-29637, ed C K Ross and N V Klassen (Ottawa: NRC) pp 17–24 McDonald J C and Goodman L J 1982 Measurements of the thermal defect for A-150 plastic Phys. Med. Biol. 27 229–33 Mendez de Marles A E 1981 Comparison of measurements of absorbed dose to water using a water calorimeter and ionization chambers for clinical radiotherapy photon and electron beams PhD Thesis University of Texas Mozumder A and Magee J L 1966 Model of tracks of ionizing radiations for radical reaction mechanisms Radiat. Res. 20 203–14 NACP 1980 Procedures in external radiation therapy dosimetry with electron and photon beams with maximum energies between 1 and 50 MeV Acta Radiol. Oncol. 19 55–79

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Osborne N S, Stimson H F and Ginnings D C 1939 Measurements of heat capacity and heat of vaporization of water in the range 0 to 100 ◦ C J. Res. NBS 23 197–259 Pettersson C 1967 Calorimetric determination of the G-value of the ferrous sulfate dosimeter with high-energy electrons and Co-60 gamma-rays Ark. Fys. 34 385–400 Pruitt J S, Domen S R and Loevinger R 1981 The graphite calorimeter as a standard of absorbed dose for cobalt-60 gamma radiation J. Res. NBS 86 495–502 Rogers D W O 1992 New dosimetry standards Advances in Radiation Oncology Physics (Medical Physics Monograph 19) ed J Purdy (New York: AAPM) pp 90–110 Rogers D W O and Ross C K 1988 The role of humidity and other correction factors in the AAPM TG-21 Dosimetry Protocol Med. Phys. 15 40–8 Roos M 1988 The current status of water absorbed dose calorimetry in the PTB Proc. NRC Workshop on Water Calorimetry NRC-29637, ed C K Ross and N V Klassen (Ottawa: NRC) pp 77–83 Roos M, Grosswendt B and Hohlfeld K 1992 An experimental method for determining the heat defect of water using total absorption of high energy electrons Metrologia 29 59–65 Ross C K, Klassen N V, Shortt K R and Smith G D 1989 A direct comparison of water calorimetry and Fricke dosimetry Phys. Med. Biol. 34 23–42 Ross, C K, Klassen N V and Smith G D 1984 The effects of various dissolved gases on the heat defect of water Med. Phys. 11 653–8 Rosser K E 1994 An ice calorimeter for photon dosimetry Phys. Med. Biol. 39 293–8 Sabel M, Schmidt Th and Pauly H 1972 Heat defect of low energy x-rays absorbed in tissue-equivalent plastic Health Phys. 23 744–6 ——1973 Heat defect of low energy x-rays absorbed in carbon and various plastics Health Phys. 25 519–21 Schulz R J, Huq M S, Venkataramanan N and Motakabbir K A 1991 A comparison of ionization-chamber and water-calorimeter dosimetry for high-energy x-rays Med. Phys. 18 1229–33 Schulz R J and Venkataramanan N 1988 Measurement of the thermal defect of water exposed to protons in the range 0.9–40 MeV Proc. NRC Workshop on Water Calorimetry NRC-29637 ed C K Ross and N V Klassen (Ottawa: NRC) pp 115–19 Schulz R J, Verhey L J, Huq M S and Venkataramanan N 1992 Water calorimeter dosimetry for 160 MeV protons Phys. Med. Biol. 37 947–53 Schulz R J and Weinhous M S 1985 Convection currents in a water calorimeter Phys. Med. Biol. 30 1093–9 Schulz R J, Wuu C S and Weinhous M S 1987 The direct determination of dose-to-water using a water calorimeter Med. Phys. 14 790–6 Selbach H-J, Hohlfeld K and Kramer H M 1992 An experimental method for measuring the heat defect of water using total absorption of soft x-rays Metrologia 29 341–7 Seuntjens J 1991 Comparative study of ion chamber dosimetry and water calorimetry in medium energy x-ray beams PhD Thesis University of Gent Seuntjens J, Thierens H and Schneider U (1993a) Correction factors for a cylindrical ionization chamber used in medium-energy x-ray beams Phys. Med. Biol. 38 805–32 Seuntjens J, Van der Plaetsen A, Van Laere K and Thierens H (1993b) Study of the relative heat defect and correction factors of a water calorimetric determination of absorbed dose to water in high-energy photon beams Proc. Symp. on Measurement Assurance in Dosimetry IAEA-SM-330/6 (Vienna: IAEA) pp 45–59 Shortt K R, Ross C K, Schneider M, Hohlfeld K, Roos M and Perroche A-M 1993 A comparison of absorbed dose standards for high-energy x-rays Phys. Med. Biol. 38 1937–55 Svensson H and Brahme A 1979 Ferrous sulfate dosimetry for electrons. A re-evaluation Acta Radiol. Oncol. 18 326–36 Velarde M G and Normand C 1980 Convection Sci. Am. 243 93–108 Wagman D D, Evans W H, Parker V B, Schumm R H, Halow I, Bailey, M, Churney K L and Nutall R L 1982 The NBS tables of chemical thermodynamic properties J. Phys. Chem. Ref. Data 11 (Supplement 2) Williams J R, Galloway G and Greening J R 1987 Dosimetry with a water calorimeter in a p(62)+Be neutron beam Phys. Med. Biol. 32 403–6