Main TL Research Articles

Study on the effects of preparation processes on OSL and TL properties of NaMgF3:Dy,Eu

OSL fading with storage time after irradiation remains a major obstacle in the development of ideal OSL materials. Dy and Eu co-doped NaMgF3 are attractive candidates for various rare earth doped matrix materials. In this study, NaMgF3:Dy,Eu was synthesized by a solid-state reaction, and the effects of heating temperature, duration, atmosphere, and cooling rate on XRD, TL and OSL properties were studied. A simple, safe, efficient, and time-saving solid-state reaction was identified as a potential method for the preparation of NaMgF3:Dy,Eu, which could be optimally prepared by heating at 750 °C for 2 h under nitrogen atmosphere (2 l/min) followed by rapid cooling. The results show that NaMgF3:Dy,Eu has a more stable OSL response and an excellent TL glow curve, with only a 0.4% decrease in the OSL signal read after 1 d of dose irradiation compared to that immediately after irradiation, and a high main TL peak at ∼320 °C. It has been indicated the OSL signal in this material seems to be strongly related to the main TL peak. The material has a considerable OSL sensitivity and decay rate than the Luxel Detector. NaMgF3:Dy,Eu will have a promising future in the field of OSL dosimetry due to its near tissue equivalence, low OSL fading without preheating, fast OSL decay rate, and predictable and easily reusable dose elimination.

Synthesis, characterization and thermoluminescence properties of MgB4O7 phosphor co-doped with Tm and Dy

The luminescent and dosimetric properties of the MgB4O7 phosphor co-doped with Tm and Dy ions (MgB4O7:Tm,Dy) obtained by the solution combustion technique were investigated. With the prepared material, sintered dosimeters in pellet form were made. The MgB4O7 dosimeters doped with Tm and Dy with 0.25 and 0.10 mol% respectively and sintered at 1223 K for 3 h showed a sensitivity almost 11 times greater than the sensitivity of the TLD-100 commercial dosimeter. The TL response as a function of the gamma dose showed linearity up to 50 Gy followed by a supralinearity region and, above 500 Gy, the saturation region of the electron traps is reached. The fading of the main TL peak was negligible in the first five days after irradiation reaching 13% after 60 days and the lower detection limit was 43 μGy. The kinetic parameters were determined using the deconvolution method revealing general and second order kinetics. The morphology, crystallography and photoluminescence of the prepared phosphor samples are also reported.

Flow synthesized LiBaF3 nanocubes as a promising optically stimulated luminescence phosphor

Integrating dosimeters are used in fields like personal dosimetry and radiotherapy quality assurance. Nanoparticles of LiBaF3 have been synthesized using a low-cost, high-throughput flow-synthesis setup and are found to be crystallographically phase-pure. Their radioluminescence (RL) emission shows three peaks corresponding to core-valence-band luminescence, self-trapped-exciton luminescence, and possibly impurity-related violet emission. Optically- and thermally stimulated luminescence (OSL and TL, respectively) overlap spectrally and show only the low-energy violet band, indicating a common luminescence pathway. The rapidly read-out OSL signal is linear in dose up to ∼1 kGy. The main TL glow peak, found around 120∘C, is depleted by optical stimulation, and similarly the OSL signal disappears following a TL readout. The thermal trap depth is found by the peak position method to be ∼1 eV. The high OSL light yield and reasonable fading of the nanoparticles qualifies them as an excellent candidate for OSL dosimetry.

Optically stimulated luminescence of K2SO4:Ce and its relationship with TL glow-curves

K2SO4:Ce was investigated with respect to its OSL and TL properties. Due to the doping with Ce3+ ions, the material shows strong emission in the range of 300–400 nm with a maximum of approx. 330 nm. The spectrum of OSL stimulation is wide and enables stimulation with visible light and infrared. When comparing the 550 nm and 900 nm stimulation, differences in the initial intensity, decay rate and total counts can be seen. The higher total counts are obtained for 550 nm green light, with the initial intensity being higher for 900 nm infrared. The OSL signal, for both stimulations, is sensitive to preheat, however, this relationship is different in both cases. The study of the mutual correlation of the TL and OSL signal showed that only a part of the peaks in the TL curve are bleached by optical stimulation. The result indicates that there are both optically active and non-optically active traps in the material. The OSL-TL correlation study involves the deconvolution of the TL curves and the estimation of the bleaching of two main TL peaks and one minor peak. At least three traps are optically active but are emptied to varying degrees by different stimulations.

Thermoluminescence dosimetry properties of calcium and dysprosium activated zinc gallate nanocrystals

The ZnGa2O4:Ca and ZnGa2O4:Dy nanocrystals are synthesized by sol-gel method and their thermoluminescence and dosimetric characteristics have been investigated. The main TL glow peaks of ZnGa2O4:Ca and ZnGa2O4:Dy are observed at about 180 °C and 200 °C, respectively. The molar ratio of both dopants (Ca and Dy) was varied from 1 mol% to 9 mol%. It was found that the optimum concentration of both dopants is about 2 mol%, where the sensitivity of ZnGa2O4:Dy nano particles is 1.5 times higher than ZnGa2O4:Ca samples. Moreover, the linearity dose response of dosimetric peak follows a good linearity up to 5 kGy in both activated nanocrystals. The results of presented nanophosphors suggest the good candidates towards dosimetric applications.

NaLi\(_{2}\)PO\(_{4}\): 0.5 mole% Eu\(^{3+}\) Phosphor Used for Carbon Dosimetry

New NaLi\({}_{2}\)PO\({}_{4}\), phosphor doped with 0.5 mole% Eu\({}^{3}\)\({}^{+}\) prepared by solid state method were used for carbon dosimetry. XRD of the material matched with the data available in the literature (JCPDS file #80-2110) and confirmed formation of the material in its orthorhombic structure. The TL of the carbon beam irradiated sample recorded on Harshaw TLD-3500 reader. The samples are irradiated for different fluencies from the range of \(5\times 10^{9}\) to \(1\times 10^{13}\) ions cm\({}^{-2}\). TL glow curve consist of single main TL peak around 457 K surrounded by kinks at 408, 504 and 542 K. TL glow curve of the carbon irradiated sample has same shape as that of gamma irradiated one. With increasing dose the intensity is increases. The phosphor is much more sensitive than the standard available standard phosphor. It is about 6.5 and 41.3 times more sensitive than the TLD-100 and TLD-700H. For these range of fluences phosphor show sub-linearity. Efficiency of the for phosphor for C\({}^{6+}\) with respect to gamma radiation is calculated and is around 0.50754 for the fluence of \(5\times 10^{09}\) ions cm\({}^{-2 }\).

Recombination pathways in a BeO yielding two main dosimetric TL peaks

Apart from the commercially used Thermalox, BeOR is a new type of Beryllium Oxide fabricated by a different company in Turkey. As it is shown by other groups, this dosimeter yields two overlapping main dosimetric TL peaks in the temperature region of 100–300 °C and one peak at 350 °C. The aim of the present study is the calculation of the activation energies of these two peaks with the use of specific protocols, including the Fractional Glow Technique (FGT), an Isothermal Decay signal (PID) and the Peak Shape Methods (PSM). Also, these experimental procedures were conducted in two different readers, namely the Harshaw and the Risø reader, for better repeatability and in order to minimize the error of the calculations. Moreover, another goal is to correlate the activation energy values with the recombination pathways that are present in the BeOR and its corresponding peaks. Specifically, both peaks have activation energies around 1–1.3 eV in most cases, although there are some kinds of indications for a difference in the pathways, as the high-temperature region TL main peak seems to follow the localized recombination via tunneling, in contrast with the low-temperature region TL main peak which sticks to the delocalized model with the passing via the conduction band.

A Co‐Precipitated α‐Alumina (Al2O3) used as a TL‐Micro Dosimeter

AbstractThis study describes the preparation method of alumina (Al2O3) as a type of thermoluminescence dosimeter (TLD) to monitor gamma photons (γ‐rays) in abroad band of radioactive doses (0.5 : 2000 Gy). Alumina is selected in this study because it has a relatively low cost TL material and can be easily prepared. Aluminum oxide (Al2O3) was chemically prepared using two different methods which are the Sol‐Gel and Co‐precipitation methods. For each method, the produced alumina (Al2O3) was divided into 4 groups which was thermally treated at (400, 600, 800, 1100 °C) respectively for 6 hours for each group. The crystalline features, morphology and sample composition of the prepared samples were chemically characterized by X‐ray diffraction (XRD), Scanning Electron Microscopy (SEM) and Energy Dispersive X‐ray (EDX). Al2O3 prepared by the Co‐precipitation method which was treated at 1100 °C (P4) was found to exhibit the highest gamma ray response compared to other samples. The deconvolution analysis showed that the main TL glow curve consisted of (5) overlapped peaks corresponding to number of traps. The linearity of the gamma response for this sample appeared in doses ranging from 1 Gy up to 200 Gy. The minimum detectable dose that can be detected by precipitated‐alumina sample (P1) was calculated mathematically to be 3.653 mGy. The fading was found to be 45.6 % after being stored for 45 days at room temperature and approximately 65 % after 90 days. This sample was reproducible according to the repeated TL results for the same sample for 5 times as their values were very close from one other with standard deviation (±σ) 0.96 %. Henceforth, Co‐precipitated α‐alumina can be used as a TL‐Micro dosimeter.

Fractional Curve in Adult Spinal Deformity: Is it a Driver of or a Compensation for Coronal Malalignment?

This was a retrospective review of the multicenter adult spine deformity database. The objective of this study was to investigate the role of the fractional curve (FC) on global coronal malalignment. Despite being very common, the role of the coronal FC as either a driver or compensation for global coronal malalignment is not well documented. Patients with the following characteristics were extracted from a prospective multicenter database: lumbar/thoracolumbar (TL) major coronal curve >15 degrees, apex at T11-L3, lower end vertebra at L3 or L4, above 45 years old, and FC >5 degrees. In addition to the classic radiographic parameters, baseline analysis included Cobb angle, pelvic obliquity (PO), fractional ratio (fractional Cobb/main Cobb), the sum of PO and FC, as well as the coronal Qiu classification. Curves distribution (TL vs. FC) were compared across the 3 Qui types, and the role of the FC was investigated. A total of 404 patients (63 y old, 83.3% female) were included: 43 patients were classified as type B, 120 as type C, and 241 were coronally balanced (type A). Compared with the balanced patients, type C patients had similar major TL Cobb angles but significantly larger fractional Cobb angles (17.5 vs. 22.3 degrees, P<0.001). By opposition, type B patients had significantly larger major TL Cobb angles (49 vs. 41 degrees, P=0.001) but smaller fractional Cobb angles (P<0.001). PO>5 degrees in the same direction as FC was more common in type B patients (20%) than in type C patients (7.5%), which suggests the preferential role of pelvic compensation. Our findings challenge the idea that FC is only a compensatory curve below a main lumbar or TL curve. In type B patients, FC acts as a compensation mechanism but fails to maintain coronal alignment despite the presence of PO. In type C patients, however, the lumbosacral FC acts as a primary driver of coronal malalignment. Level III.

Thermally and optically stimulated luminescence properties of BeO dosimeter with double TL peak in the main dosimetric region

Beryllium oxide (BeO), which has a widely known single main TL peak over the main dosimetric region, is an important luminescent material widely used in personal, medical, and environmental dosimetry fields. The thermal and optically stimulated luminescence properties (TL and OSL) of the BeO dosimeter, supplied by a private company in Turkey (BeOR) that yields a double peak in the main dosimetric region (100–300 °C; heating rate = 2 °C/s) were studied. The corresponding properties were compared to the commercially prevalent Thermalox 995 BeO (BeOT). Multiple characterization techniques including x-ray diffraction analysis (XRD), energy dispersive x-ray spectroscopy (EDX), scanning electron microscope (SEM) image and electron spin resonance (ESR) were used to detect possible differences in TL and OSL signals. It was hypothesized that the calcination and or sintering process applied during the manufacturing process might lead to a double peak in the main dosimetric region of BeOR TL signals. Moreover, dosimetric properties of this dosimeter such as reproducibility, dose-response, minimum detectable dose (MDD), thermal quenching, bleaching, and thermal stability in combination with annealing properties were comprehensively investigated. An analysis of the results shows that BeOR has lower detection limits in TL than BeOT. In contrast, BeOT exhibited lower detection limits in the OSL signal than BeOR. Although both dosimeters have dissimilarities in several aspects, both are appropriate for dosimetric research on health physics applications. Therefore, selecting the appropriate BeO dosimeter could be an important factor to consider when assessing accurate doses in studies. With this outline in mind and by investigating using different characterization methods, the available luminescence knowledge base of BeO dosimeters was expanded.

Study of thermoluminescence of green quartz pellets for low dose dosimetry

Green quartz is usually studied for low dose TL dosimetry of gamma and X radiation. The aim of the present work is the dosimetric characterization of natural green quartz in the dose range of 0.47 mGy up to 1000 mGy of gamma and X radiation. Green quartz pellets were produced by cold pressing green quartz powder. The pellets are very sensitive to gamma and X radiation with main prominent TL peak at 230 °C. The TL sensitivity of MTS-N (LiF:Mg,Ti) and green quartz pellets were also compared. The dose response curve presented linear behavior in the dose range studied. The glow curve was deconvoluted. Kinetic parameters such as trap depth, kinetic order (b) and frequency factor (s) are determined. The TL photon energy dependence was also evaluated.

Gamma Ray Dosimetric Properties of Tb- and Dy-doped Ba0.88Sr0.12SO4 Phosphor

The chemical co-precipitation method was used to prepare Ba0.88Sr0.12SO4:Dy1.5mol%,Tb1mol% nanocrystalline powder. Ba0.88Sr0.12SO4:Dy1.5mol%,Tb1mol% pellets were fabricated in order to measure gamma ray irradiation. A main TL glow peak around 207 °C, a small peak at 157 °C and a good linear response for doses in the range of 0.01–5 kGy were observed. The TLE spectra of the pellets were recorded at 207 °C. The results of energy response showed that these pellets are energy dependent. The pellets showed fading about 18% during 4 weeks of storage time. The effect of different heating rates on the TL glow peaks of prepared pellets which were recorded after a gamma exposure of 5 kGy was investigated. The intensity of TL glow curves was decreased by an increase in heating rate from 2 °C/s up to 6 °C/s. The dosimetric results showed that the Ba0.88Sr0.12SO4:Dy1.5mol%,Tb1mol% pellets could be useful for monitoring gamma radiation for accidental dose assessment.

Luminescence properties of natural dead sea salt pellet dosimetry upon thermal stimulation

In the event of a radiological accident or attack, immediate need arises for reliable estimation of dose to the population from an affected environment. This would contribute to proper medical treatment and any need for isolation of affected areas. As such, it is important to improve dosimetry assessment through use of locally available materials, the latter acting as accident/prospective dosimeters. Present investigation has examined the TL properties of natural salt collected in Jordan, from the Dead Sea, and exposed using 60Co gamma radiation. Entrance doses ranging from 2 to 10 Gy have been delivered, providing desirable luminescence features. Natural Dead Sea NaCl are produced in cylindrical pellet form, achieved with 0.1 and 0.3 cm thickness sized from the salt grains obtained by a compression force of 5.0 ± 0.1 tonnes. With these NaCl pellets, linear dose response has been achieved, producing strong TL yield for a 0.1 cm thick layer, exceeding that of 0.3 cm thickness by a factor of 3. The shape of the glow curves was found to be independent of delivered dose, the main TL dosimetric peak remaining within the range 180 °C to 280 °C and 300 °C to 400 °C for the 0.1- and 0.3 cm NaCl pellets respectively. Computerised glow curve deconvolution was carried out, comprising of ten peaks, with associated activation energies and frequency factors. TL response per unit mass of NaCl pellets for both thicknesses were found to be energy dependent, predominating in yield at 60 keV. Over a period of 35 days the 0.3 cm NaCl pellet showed the least effect of fading, with loss of TL signals of 56% compared to an 81% loss for the 0.1 cm pellet. It is also noted that the combination of low activation energy and high frequency factors for the electrons to escape a trap for the 0.1 cm NaCl pellet samples subjected to 2 Gy gamma irradiation resulted in a highly substantial loss of TL signal over the first 7 days in comparison to the 0.3 cm NaCl pellet. Both samples thicknesses were unable to produce reproducible TL responses for the second and greater use. It has also been found that in addition to particle size, moisture and pre-irradiation annealing influence the TL properties. The excellent TL properties achieved by 0.1 cm NaCl pellets indicate their potential use as an accident/prospective dosimeter.

Investigation of dosimetric properties of newly-developed Li2B4O7:Ag+,La3+ using thermoluminescence (TL) technique

The aim of this study was to investigate the dosimetric properties of newly developed Li2B4O7 doped with Ag+ and La3+ using TL technique. In this study, the concentrations of Ag1%wt and La0.1-3%wt dopants were introduced in Li2B4O7 by Solution Combustion Synthesis (SCS) method. The most TL sensitivity of the synthesized phosphors was recorded at 1%wt for each concentration of Ag+ and La3+. The structural characterizations were investigated using X-ray Diffraction (XRD), Scanning Electron Microscope (SEM). Besides, X-ray Luminescence (XL) spectrum was studied. The main dosimetric TL Peak of the Li2B4O7:Ag1%,La1% exhibited a simple TL Peak located at 220 °C with a heating rate of 2 oCs−1. Some dosimetric properties of this TL Peak, such as dose-response, reusability, fading in dark, were investigated under beta radiation. The TL signal of the phosphor exhibited a linear ranging from 0.1 to 50 Gy. The good reusability, by 4% standard deviation, was in the experiment cycle of 10. Fading was studied up to 4 weeks. The kinetic parameters using whole Glow curve, Initial rise (IR), Fraction Glow Curve (FGT) and CGCD were obtained and discussed.

Highly efficient removal of thallium(I) from wastewater via hypochlorite catalytic oxidation coupled with adsorption by hydrochar coated nickel ferrite composite

In this study, tannery wastewater was used as carbon source to hydrothermally synthesize magnetic carbon-coated nickel ferrite composite (NiFe2O4@C), which was employed as a catalyst for thallium (Tl) oxidation by hypochlorite and simultaneously as an adsorbent for Tl removal from wastewater. Compared with NiFe2O4@C adsorption or hypochlorite oxidation alone, the combination of NiFe2O4@C and hypochlorite substantially enhanced the rate and efficiency of Tl(I) removal. In addition, this process was highly effective for Tl(I) removal over a wide pH range (6–12). The maximum Tl(I) removal capacity was 1699 mg/g at pH 10, which is the highest one reported so far. Electron spin resonance spectra suggested the formation of hypochlorite-based free radicals induced by the NiFe2O4@C composite, which enhanced the Tl(I) oxidation and removal. Oxidation-induced surface precipitation and surface complexation were found to be the main Tl(I) removal mechanisms. Consecutive cyclic regeneration tests implied robust regeneration and reuse performance of the composite. Moreover, it was effective for Tl(I) removal from real industrial wastewater. Therefore, the hypochlorite catalytic oxidation coupled with adsorption by the magnetic NiFe2O4@C composite is a promising technique for Tl(I) removal from wastewater. This hybrid process also has great potential for the removal of other pollutants.

Particle size effect on TL/OSL response of NaMgF3:Tb phosphor

NaMgF3 is a nearly tissue equivalent material with low Zeff = 10.4 and a well-known phosphor for its high sensitivity concerning luminescence. The type of preparation route followed greatly affects the luminescence efficiency of a material. Grinding of NaMgF3:Tb phosphor for a long time induces several lattice defects in the phosphor. In this work, effect of particle size on TL/OSL response of NaMgF3:Tb irradiated by 60Co source of gamma radiations with a dose of 15 Gy has been investigated. NaMgF3:Tb samples has been synthesized by solid state reaction method using different grinding times i.e. 1 h and 5 h. XRD technique confirms its formation and crystallite size is calculated. TL studies show that sample synthesized by 5 h grinding is almost 2 times more intense than the sample obtained by 1 h grinding. Also, a clear enhancement is seen in the shoulder peak of sample grinded for 5 h. This could be due to increase in occupancy of trapped charge carriers in the trap levels. However, the position of main TL glow peak remains same in both the samples. Associated TL kinetic parameters such as order of kinetics, activation energy, frequency factor and trap density have been calculated by deconvoluting the TL glow peaks to understand the TL phenomenon. Continuous-wave optically stimulated luminescence (CW-OSL) decay curves have been obtained under blue LED stimulation for 40 s. Analyzing the CW-OSL decay curves reveal that grinding time significantly affects the OSL intensity of the phosphor as well. The decay constant and photoionization cross-section is determined for the faster and slower components of the total OSL intensity. It could be concluded that the time of grinding taken during preparation of the material has a major role in affecting the concentration of trap levels formed inside the forbidden gap of the phosphor.

On the orange-red persistent luminescence of ScPO4:Eu3+

ScPO4:0.1%Eu3+ sintered materials were found to generate orange-red persistent emission following exposure to X-rays. A set of thermoluminescence techniques and isothermal decay measurements were used to study the mechanisms of the carriers’ trapping and detrapping processes. The two main TL peaks at around 90 °C (363 K) and 160 °C (433 K) were found to result from so-called continuous distribution of trap depths. Room temperature fading proved that the persistent luminescence was connected with the strong TL peak at ∼90 °C (363 K). The persistent emission kinetics was characterized by a linear dependence of I−1(t). This was consistent with the continuous distribution of trap energies observed in the material. The main persistent emission components were located around 590, 620, and 720 nm. The most significant contribution was from the first and the third of them, resulting from the 5D0→7F1 and 5D0→7F4 transitions, respectively.

Optically stimulated luminescence of α-Al2O3:C by the vertical gradient freezing (VGF) method

A highly sensitive α-Al2O3:C crystal was directly grown by the vertical gradient freezing (VGF) method, which combines the advantages of the crystal growth in the highly reducing atmosphere in the presence of graphite and the crystal directly grown by the using Al2O3 and graphite powder as raw materials. The main OSL characteristics of the detectors as grown were investigated. The OSL signal originates from the main TL peak, the responsible electron trap can be emptied basically by OSL readout. The mean OSL sensitivity per unit mass of the VGF α-Al2O3:C is 1.6 times higher than that of the TLD-500K. The OSL detection thresholds of the VGF α-Al2O3:C and the TLD-500K are 0.21 μGy and 0.51 μGy respectively. The OSL signals for the two kinds of detectors are reproducible within a coefficient of variation of less than 2.5% over ten re-use cycles without systematic decrease. The VGF α-Al2O3:C detectors shown an excellent linear response within the dose range from 1 μGy to 15 Gy. The dose can be independently re-analysed multiple times. The VGF α-Al2O3:C can be used to measure the very low dose in environmental monitoring and personnel dosimetry.

Step annealing and fading studies on EPR signals of Durango apatite for various grain size fractions at the edge of the nano-scale; comparison with the corresponding luminescence results

Durango apatite is a material that exhibits very strong athermal fading (AF) of luminescence signal. In this study, the EPR signals of natural Durango apatite in various different grain dimensions (ball milled for various durations up to 48 h and microscale grain size) were studied. The obtained EPR signal at room temperature yielded three different components with g values 2.0534 (hole center), 2.0398 (hole center) and 1.9920 (electron center). These components were observed for the reference grain size fraction of 100–180 μm; however, prolonged ball milling erases the two hole centers. The behaviour of all obtained components was investigated by step annealing processes (a) between room temperature and 400 °C in steps of 25 °C for 5 min and (b) between 400 °C and 1100 °C, in steps of 100 °C for 1 h. The EPR component with g value 1.9918 was almost totally removed until 1100 °C, while those with g values 2.0534, 2.0398 were erased after annealing at 500 °C and 400 °C respectively. The fading of EPR components was investigated for each ball milling (BM) and microscale grain size independently, at different storage times between 0 and 1000 min. Based on the results of fading and step annealing studies, the EPR component with g value 2.0398 could be directly correlated to the main dosimetric TL trap, while the component with g value 1.9920 appears to be responsible for TA – OSL signal for microscale grain size apatite, corresponding thus to a very deep trap. The behaviour of remnant EPR signal versus storage time could be successfully described by equations based on quantum mechanical tunnelling mechanism.

Synthetic polycrystals of CaSiO3 un-doped and Cd, B, Dy, Eu-doped for gamma and neutron detection

The undoped and B, Cd, Dy, Eu doped synthetic CaSiO3 polycrystals were produced in the laboratory. They are very sensitive γ-ray detectors with main prominent TL peak occurring at about 270 °C, this peak was obtained using 4 °C/s heating rate. The TL behavior changes very little by doping with B, Cd and Dy while Eu doping brings changes. These minerals can be used also for neutron dosimetry. Thermal neutrons react with Ca, Si and O through (n, γ) process and γ emitted in this reaction added to γ-rays of the reactor that produces thermal neutrons and are responsible for induction of thermoluminiscence. The TL response of CaSiO3 is linear for dose < 10 Gy and then has a supralinear behavior up to about 7 kGy and saturating beyond.